THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING KINETICS OF THE PHASE TRANSFORMATION OF CALCIUM SULFATE IN AQUEOUS AND BRINE SOLUTIONS David R. Johnson A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan Department of Chemical and Metallurgical Engineering 1967 October, 1967 IP-790

ACKNOWLEDGEMENTS It is a pleasure for the author to express his appreciation to the following individuals and organizations for their contributions to this research: The late Dr. Kenneth F. Gordon who initially proposed the kinetic study. Professor Wilbur C. Bigelow, chairman of the doctoral committee, for his assistance, encouragement, and guidance. The other members of the doctoral committee, Professors Lawrence O. Brockway, Giuseppe Parravano, Robert D. Pehlke, and J. Louis York, for their interest, suggestions, and patience. My brother and sister for their assistance in transcribing part of the data. Messrs. Murry Player and Bernard Schorle, fellow graduate students, for their suggestions, criticisms, and assistance. The Industry Program of the College of Engineering for their excellent work in the preparation of this dissertation. The Office of Saline Water of the United States Department of the Interior for their financial support. iii

TABLE OF CONTENTS Page ACKNOWLEDGEMENTS iii LIST OF TABLES............................................ vi LIST OF FIGURES............................................... ix LIST OF APPENDICES.....................................x..vi NOMENCLATURE............................................xviii ABSTRACT................................... CHAPTER I INTRODUCTION........................................ 1 II REVIEW OF THE LITERATURE.............................. 5 A. Time-Temperature-Transformation Studies...........5 B. Crystallographic Studies.......................... 10 C. Summary....................................... 15 III KINETIC THEORY FOR TRANSFORMATIONS IN SOLIDS....... 17 IV STUDIES OF TIME- TEMPERATURE- TRANSFORMATION RELATIONSHIPS......................................... 25 A. Experimental Procedures......................... 25 B. Experimental Results.......................... 45 1. Dehydration of Dihydrate to Hemihydrate....... 45 a. Effect of Temperature.................... 46 b. Effect of Concentration................. 55 c. Effect of Initial Particle Size......... 60 2. Dehydration of Hemihydrate to Anhydrite.......63 3. Comparison of Results........................65 V DIHYDRATE TO HEMIHYDRATE TRANSFORMATION MECHANISM........................................72 A. Experimental Procedures........................... 72 B. Experimental Results............................. 74 C. Derivation of Kinetic Equations................... 90 iv

TABLE OF CONTENTS (CONT'D) Page 1. Model of the Transformation Mechanism............ 91 2. Formulation of Equations........................ 92 a. Rate of Nucleation........................... 93 b. Volume Transformed per Nucleus............... 95 Co Total Volume of Hemihydrate Transformed...... 96 d. Correction for Impingement..................98 e. Fraction Reacted Equations...................105 3. Evaluation of Kinetic Constants..................108 a. Method......................................109 b. Numerical Values.............................115 c. Variations with Temperature and Concentration...............................126 4. Test of the Theoretical Equations...............140 VI DISCUSSION..................... A. Dihydrate-Hemihydrate Transformation.........1.......159 1. Effect of Temperature............................159 2. Effect of Water Activity.........................160 3. Effect of Initial Particle Size................1 B. Hemihydrate-Anhydrite Transformation.................162 C. Reaction Model.......................................163 1o Basic Assumptions...............................164 2, Rate Controlling Process.........................165 3. Theoretical Equations...........................166 ao Limitations...............................167 b. Range of Applicability.......................175 D. Applicability of Results.............................175 E. Areas of Possible Future Research....................178 VII SUMMARY................................................. 179 APPENDICES..................................................... 183 REFERENCES...................................................... 320 v

LIST OF TABLES Table Page I Corrected Experimental Data from Run 62.................... 31 II Values of a and da/dt Calculated for Experimental Run 62 on the Transformation of Calcium Sulfate Dihydrate to Hemihydrate at 245~F in Water........................... 42 III Values of Average Linear Growth Rates of Hemihydrate Crystals Within Dihydrate Crystals Immersed in Water....... 88 IV Values of Z and E Corresponding to Figure 37............... 90 V Values of Kinetic Constants.,............................ 124 VI Values of Z and E Corresponding to Figures 51, 52, and 53.. 131 VII Values of Z and E of Equation (85) for the Least Squares Lines Shown in Figure 58.................,,....,.. 139 VIII Values of Z and E Corresponding to Figure 59.....:......... 143 A-1 X-ray Data by Newman and Wells.......................,.... 189 A-2 Experimental Results of Budnikoff....................... 190 B-l Vapor Pressure Data for Ethanol.................. 192 B-2 Data Obtained Calibrating Thermocouples................... 195 C-l Calibration for Capillary Used in the Dilatometric Experiments.......................... 195 G-l Time-Temperature-Transformation Results for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate Showing the Effect of the Concentration of the Solution in which the Solids Were Immersed on the Transformation...,,,,,,....... 210 G-2 Time-Temperature-Transformation Results for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate Where the Solids Were Immersed in Aqueous Solutions at Temperatures below 270~0F......................................... 211 G-3 Time-Temperature-Transformation Results for the Dehydration of Calcium Sulfate Hemihydrate to Anhydrite Where the Solids Were Immersed in Aqueous Solutions................. 212 vi

LIST OF TABLES (CONT'D) Table Page G-4 Time-Temperature-Transformation Results for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate Where the Solids Were Immersed in Aqueous Solutions at Temperatures above 275~F........o........o.. o................. 213 G-5 Time-Temperature-Transformation Results for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate Showing the Effect of the Initial Dihydrate Crystal Fragment Size on the Reaction Where the Solids Were Immersed in Watero,,o. o o o o.......... 0,, a..o...a a 0 o.... 214 H-l Composition of Normal Synthetic Sea Water..,,......o...... 215 I-1 Crystal Classification Information................. 217 J-1 Results of Studies on the X-ray Powder Diffraction Patterns,, o o o. 0... o.... o.....0.e.O o 221 J-2 Comparison of X-ray Diffraction Data from Calcium Sulfate Dihydrate (Selenite) with Data Reported for CaS04'2H20 on ASTM Card Number 6-0046 and 6-0047.,...... 222 J-3 Comparison of X-ray Diffraction Data from Calcium Sulfate Hemihydrate Formed from Dihydrate in Water with the Data Reported for CaS04ol/2 H20 on ASTM Card Number 2-0675.................................. 223 J-4 Comparison of X-ray Diffraction Data from Calcium Sulfate Anhydrite Formed from Hemihydrate in Water with the Data Reported for Calcium Sulfate, CaS04, Anhydrite on ASTM Card Number 6-0226..,............... 224 J-5 Comparison of X-ray Diffraction Data from CO P. Sodium Chloride with Data Reported for NaCl on ASTM Card Number 5-0628, o o o.......o....o.......................... 225 K-1 Coefficients of Equation (K-l)........................... 227 K-2 Coefficients of Equation (K-2)........................... 227 K-3 Vapor Pressure Ratios................................ 228 L-1 Values of the Physical Constants for Calcium Sulfate.,... 231 L-2 Height and Volume Values................................. 231 vii

LIST OF TABLES (CONTID) Table Page M-1 Data from Microscopic Studies, o.............. o,....... 233 M-2 Computer Program Used to Calculate Linear Rates of Growth from Microscopic Data........................ 240 P-1 Thickness of Crystal Fragments................ o...... 250 P-2 Lengths and Widths of Crystal Fragments..............,.6 251 R-l Computer Program for Three-Dimensional Model........... 258 S-1 Dimensions of Hemihydrate Subcrystals................ o 263 S-2 Number of Nuclei per Dihydrate Particle.................. 263 viii

LIST OF FIGURES Figure Page 1 Solubilities of the Solid Phases in the Calcium SulfateWater System.............................. 2 2 The Relationships between the Crystallographic Axes a and b and Optical Axes a and 7 for Gypsum Viewed Perpendicular to Its (010) Cleavage Plane. 13 3 Construction of Dilatometer.............................. 26 4 Schematic Drawing of Constant Temperature Bath and Pressurized Glass Tube for Containing the Dilatometer.... 28 5 Vernier for Reading Position of Meniscus................ 30 6 Values of Height of Liquid Meniscus in Dilatometer Capillary Versus Time for Run 62 for the Transformation.of Calcium Sulfate Dihydrate to Hemihydrate in Water at 245~F....................... 32 7 Values of Temperature Versus Time for Dilatometric Run Number 62 on the Transformation of Calcium-Sulfate Dihydrate to Hemihydrate in Water at 245 ~F....... 33 8 Total Change in Meniscus Height Due to Reaction Versus Temperature for Runs in Water........................... 37 9 Total Change in Meniscus Height Due to Reaction Versus Temperature for Runs in 3.5% Sodium Chloride Solutions.. 37 10 Total Change in Meniscus Height Due to Reaction Versus Temperature for Runs in Synthetic Sea Water............. 37 11 Total Change in Meniscus Height Due to Reaction Versus Sodium Chloride Solution Concentration................ 40 12 Total Change in Meniscus Height Due to Reaction Versus Synthetic Sea Water Concentration...................... 40 13 Fraction of Calcium Sulfate Dihydrate Transformed to Calcium Sulfate Hemihydrate in Water at 245~F During Run 62......................................... 43 ix

LIST OF FIGURES (CONT'D) Figure Page 14 Variation of the Reaction Rate with Time for Run 62 for the Transformation of Calcium Sulfate Dihydrate to Hemihydrate in Water at 245~F......................... 44 15 Time-Temperature-Transformation Curves for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Watero......oo......................o............ 47 16 Time-Temperature-Transformation Curves for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in 3.5% Sodium Chloride Solution......................... 48 17 Time-Temperature-Transformation Curves for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Synthetic Sea Water............................. 49 18 Time-Temperature-Transformation Curves for 50% Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Water, 3.5% Sodium Chloride Solution, and Synthetic Sea Water o....................................... 50 19 Estimated Time-Temperature-Transformation Curves for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Water at High Temperatures.................... 52 20 Estimated Time-Temperature-Transformation Curves for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in 3.5% Sodium Chloride Solution at High Temperatures,....... o..,,. o................... 53 21 Estimated Time-Temperature-Transformation Curves for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Synthetic Sea Water at High Temperatures...... 54 22 The Effect of the Concentration of Sodium Chloride Solutions on the Transformation Time for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate at 240~F....................................... 56 23 The Effect of Concentration of Synthetic Sea Water on the Transformation Time for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate at 240~F................ 57 24 The Effect of the Activity of Water in Solution on the Transformation Time for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate at 240~F.............. 58 x

LIST OF FIGURES (CONT'D) Figure Page 25 The Effect of Dihydrate Crystal Fragment Size as a Function of Screen Opening on the Transformation Time for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Water at 250~F for Washed Samples...................................... 62 26 The Effect of Dihydrate Crystal Fragment Size as a Function of Screen Opening on the Maximum Rate of Reaction Observed During the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Water at 250~F for Washed Samples...................... 6..,o * o 6.. 64 27 Time-Temperature-Transformation Curves for the Dehydration of Calcium Sulfate Hemihydrate to Anhydrite in Water.......6.............................. 66 28 Time-Temperature-Transformation Curves for the Dehydration of Calcium Sulfate Hemihydrate to Anhydrite in 3.5% Sodium Chloride Solution........................ 67 29 Time-Temperature-Transformation Curves for the Dehydration of Calcium Sulfate Hemihydrate to Anhydrite in Synthetic Sea Water................................... 68 30 Time-Temperature-50% Transformation Curves for the Dehydration of Calcium Sulfate Hemihydrate to Anhydrite in Water, in 3.5% Sodium Chloride Solutions, and in Synthetic Sea Water..................,...... 69 31 Summary of the Time-Temperature-Transformation Results for 50% Dehydration................................... 70 32 Reaction Cell Used for Microscopic Observations......... 73 33 Sequence of Micrographs (85X) Showing the Transformation of a Single Crystal of Calcium Sulfate Dihydrate to Hemihydrate in Water........................ 75 34 Micrographs (480X) Showing the Cross Sections of Hemihydrate Needles in Large Crystals of Calcium Sulfate Dihydrate............................................... 81 35 Parameters Used in Describing the Orientation and Growth of Hemihydrate Needles in the Parent Dihydrate Crystal... 86 36 Hemihydrate Needles Observed in the Solution Near a Large Calcium Sulfate Dihydrate Crystal................ 87 xi

LIST OF FIGURES (CONT'D) Figure Page 37 Arrhenius Plot for the Linear Growth Rates UA, UB, and UC for the Transformation of Calcium Sulfate Dihydrate to Hemihydrate in Water........................ 89 38 Schematic Representation of the Relationships Between the FunctionsdN/dx, va(x,t)i, and Va(t).................. 97 39 The Relationships Between the Different Stages of the Impingement Process, the Geometry of a Growing Hemihydrate Needle, and the Transformed Hemihydrate Subcrystal,.o....o........................................ 99 40 Schematic Representation of the Relationships Between the Functions dN/dy, vc(yt)i, Vc(t), Va(t), and V(t)... 102 41 Types of Rate Curves Exhibited by Most Experimental Runs....... o o..... o........................................ 111 42 Graphical Solution for Equation (79)................... 114 43 Fit of the Theoretical Curve to the Experimental Data for Run 10 for the Dehydration of Calcuim Sulfate Dihydrate to Hemihydrate in Water at 258~F.............. 116 44 Fit of the Theoretical Curve to the Experimental Data for Run 20 for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Water at 251~F................ 117 45 Fit of the Theoretical Curve to the Experimental Data for Run 30 for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Water at 250~F................ 118 46 Fit of the Theoretical Curve to the Experimental Data for Run 40 for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in a 14% Sodium Chloride Solution at 237~Fo, o..o....o...........oe...... o................. 119 47 Fit of the Theoretical Curve to the Experimental Data for Run 50 for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Normal Synthetic Sea Water at 240~F o o o a o a a o.... o........................... e e o........... e 120 48 Fit of the Theoretical Curve to the Experimental Data for Run 60 for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Normal Synthetic Sea Water. at 247~F....,..e......................................... 121 xii

LIST OF FIGURES (CONT D) Figure Page 49 Fit of the Theoretical Curve to the Experimental Data for Run 62 for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Water at 245~F,.............a 122 50 Fit of the Theoretical Curve to the Experimental Data for Run 64 for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Water at 265~F........, oo.. 123 51 Arrhenius Plot of the Kinetic Constants K, Ug/a, UB/b, UA/a, and UA/b for the Transformation of Calcium Sulfate Dihydrate to Hemihydrate in Water........................ 128 52 Arrhenius Plot of the Kinetic Constants K, UB/a, UB/b, UA/a, and UA/b for the Transformation of Calcium Sulfate Dihydrate to Hemihydrate in 3.5% Sodium Chloride Soluti on d1.................................................. 129 53 Arrhenius Plot of the Kinetic Constants K, UB/a, UB/b, UA/a and UA/b for the Transformation of Calcium Sulfate Dihydrate to Hemihydrate in Normal Synthetic Sea Water..o..................... o.......o 130 54 Extrapolation of Values of Nucleation Rate Constant K to the Constant Temperature of 239,6~F for Sodium Chloride Solutions..e, o e a................... 133 55 Extrapolation of Values of Nucleation Rate Constant K to the Constant Temperature of 239,60F for Synthetic Sea Water Containing 12,93, and 4 Times the Salts of Normal Synthetic Sea Water,.......... 134 56 Plot of Smoothed Data from Figures 54 and 55 Showing the Effect of Dissolved Solids on the Nucleation Rate Constant Ko,,o., o o o,,,, 135 57 Plot of Smoothed Data from Figures54 and 55 Showing the Effect of the Activity of the Water (P/P~) in the Solution Surrounding the Reaction Mixture on the Nucleation Rate Constant K. a., o.,,,............a 136 58 Least Squares Lines Correlating the Variations of the Kinetic Constants with both Temperature and Water Activity, o oo.... o........ a.a6.............. o.. o 138 59 Least Squares Lines Based on the Arrhenius Equation Fitted to Time-Temperature-5% Transformation Data,...,.. 142 xiii

LIST OF FIGURES (CONT'D) Figure Page 60 Comparison of TTT Curves Calculated from the Theoretical Equations with Experimentally Measured TTT Data for the Dihydrate-Hemihydrate Transformation in Water.......... e 144 61 Comparison of TTT Curves Calculated from the Theoretical Equations with Experimentally Measured TTT Data for the Dihydrate-Hemihydrate Transformation in 3.5% Sodium Chloride Solution....................................... 145 62 Comparison of TTT Curves Calculated from the Theoretical Equations with Experimentally Measured TTT Data for the Dihydrate-Hemihydrate Transformation in Normal Synthetic Sea Water................................................ 146 63 Initial Portion of the Potentiometric Chart for Run 42 Showing the Irratic Thermocouple Behavior at the Beginning of the Experiment................................ 148 64 Comparison of TTT Curves Calculated form the Theoretical Equations with Experimentally Measured TTT Data for the Dihydrate-Hemihydrate Transformation in Water Using the Values for Run 42.......o.....1..................... 149 65 Least Squares Lines Based on the General Correlation Fitted to Time-Temperature-5% Transformation Data........ 152 66 Comparison of TTT Curves Calculated from the Theoretical Equations with Experimentally Measured TTT Data for the Dihydrate-Hemihydrate Transformation in 355% Sodium Chloride Solutions Using the Generalized Correlation for 1/T5%................................... 153 67 Comparison of TTT Curves Calculated from the Theoretical Equations with Experimentally Measured TTT Data for the Dihydrate-Hemihydrate Transformation in Normal Synthetic Sea Water Using the Generalized Correlation for 1/T5.......................................... 154 68 Comparison of TTT Curves Calculated from the Theoretical Equations with Experimentally Measured TTT Data for the Dihydrate-Hemihydrate Transformation in 7%, 14%, and 21% Sodium Chloride Solutions................. 155 69 Comparison of TTT Curves Calculated from the Theoretical Equations with Experimentally Measured TTT Data for the Dihydrate-Hemihydrate Transformation in Synthetic Sea Water Containing 2,3, and 4 Times the Salts of Normal Synthetic Sea Water........................... 156 xiv

LIST OF FIGURES (CONTDD) Figure Page 70 Fit of the Theoretical Curve, Calculated Using the Three-Dimensional Model, to the Experimental Data for Run 6 for the Dehydration of a Single Crystal of Calcium Sulfate Dihydrate to Hemihydrate in Water at 261F. e o o a a o................................ a e 170 71 Variation in the Reaction Rate as a Function of Time for Run 33 on the Transformation of Calcium Sulfate Dihydrate to Hemihydrate in Water at 250~F Using Extremely Fine Dihydrate Particles....................... 172 72 Variation in the Reaction Rate as a Function of Time for Run 16 on the Transformation of Calcium Sulfate Dihydrate to Hemihydrate in Water at 2600F Using Extremely Fine Dihydrate Particles................ 173 73 Relationship Between Values of the b Dimension of the Hemihydrate Subcrystals as a Function of Temperature and the Average Particle Size for Runs 16 and 33...............o..o...............O 174 A-1 Relationships Between the Different Unit Cells Reported in the Literature for Gypsum Viewed Perpendicular to the (010) Cleavage Plane................................ 185 A-2 Time-Temperature-Transformation Relationships for the Phase Transformation of y-CaS04 to 3-CaS04 Determined by Newman and Wells Using X-ray Methods................ 186 A-3 Variation in the Reaction Rate as Function of Time Observed by Budnikoff for the Transformation of Calcium Sulfate Dihydrate (Coated with Sodium Chloride) to Hemihydrate in Air at 107~C....,.............. 187 A-4 Variation in the Reaction Rate as a Function of Time Observed by Budnikoff for the Transformation of Valcium Sulfate Dihydrate to Hemihydrate in Air at 107~C.,.. 188 J-1 X-ray Powder Diffraction Pattern for Calcium Sulfate Dihydrate. a0eooa.. oe.........a.................O 220 J-2 X-ray Powder Diffraction Pattern for Calcium Sulfate Hemihydrat e ooa e a;aa a.. o.....o.e......doc.o.e.a...o.e.e 220 J-3 X-ray Powder Diffraction Pattern for Calcium Sulfate Anhydrite.... o o.............................. o......... 220 J-4 X-ray Powder Diffraction Pattern for Co P. Sodium Chloride...ee0, o....o 6.. o........... 220 xv

LIST OF APPENDICES Appendix Page A Results in the Literature................................ 184 B Thermocouple Calibrations................................. 191 C Calibration of Dilatometer Capillary..................... 194 D Computer Program Used to Make Temperature and Height Corrections for the Capillary Used in the Dilatometric Experiment s.............................................. 196 E Computer Programs Used to Calculate Normalized Data from Corrected Time-Temperature-Transformation Data for the Dihydrate-Hemihydrate and the HemihydrateAnhydrite Transformations................................. 197 F Summary of Experimental Conditions........................ 207 G Summary of All the Time-Temperature-Transformations Relationships.......................................... 209 H Composition of Synthetic Sea Water....................... 215 I Classification of Initial Particle Sizes................ 216 J Phase Identification Using X-Ray Powder Diffraction Patterns.............................. 218 K Vapor Pressure Ratios for Sodium Chloride Solutions.......226 L Volume Changes in the Calcium Sulfate-Water System........ 229 M Results from Microscopic Observations................... 232 N Computer Program Used to Calculate Fraction Reacted and Rate of Reaction Values as Function of Time Using the Model................................................ 242 0 Computer Program Used to Calculate T-T-T Data from Theoretical Equations..................................... 244 P Measurements of Dihydrate Crystal Dimensions.............. 248 Q Derivations of the Chemical Reaction and' the Diffusion Equations................................................ 252 xvi

LIST OF APPETDICES (CONT'D) Appendix Page R Three-Dimensional Model o................. o. O......... 255 S Dimensions of the Hemihydrate Subcrystals as Functions of Temperature..................o........................o.. 261 T Normalized Data o....o.................................. 264 U Observed Experimental Data o.. o.o...........O.... 0.o 295 xvii

NOMENCLATURE A Distance in the A direction defined in Figure 35, cm A' Cross-sectional area of capillary, cm2 a Activity a Thickness of hemihydrate needle, cm a' Thickness of dihydrate particle, cm B Distance in the B Direction defined in Figure 35, cm b Width of hemihydrate needle, cm b' Width of dihydrate particle, cm bo Constant defined by Equation (K-l) bl Constant defined by Equation (K-l) C Distance in the C direction defined in Figure 35, cm c Length of hemihydrate needle, cm c' Length of dihydrate particle, cm D Average crystal diameter, cm D Amount of dihydrate reacted, moles Do Initial amount of dihydrate, moles Di Constants used in Equations (62) to (69) where i = 1, 2,.., 12 D' Constant defined by Equation (Q-ll) D" Constant defined by Equation (Q-10) D"' Constant defined by Equation (Q-9) d Distance, cm E Activation energy, Kcal/gm mole f Fugacity, mm Hg xviii

f/p Fugacity coefficient AG Total free energy change, ergs AG* Free energy change for critical nucleus, ergs AG# Free energy of activation, Kcal/gm mole AG Free energy change per molecule, ergs/molecule AH# Enthalpy of activation, Kcal/gm mole h Height of liquid meniscus, cm J Constant defined by Equation (57) K Nucleation rate constant, minl K1 Constant defined by Equation (Q-4) K2 Constant defined by Equation (Q-4) k General kinetic rate constant, min1 m Number of molecules per nucleus m* Number of molecules per critical nucleus Am Change in number of moles, gm moles N Number of nuclei No Total number of nuclei No/p Number of nuclei per dihydrate particle Nf Number of crystal fragments per sample P Pressure, mm Hg P~ Pressure of pure component, mm Hg P/PO Vapor pressure ratio ~R Gas constant, 1.987 Kcal/gm mole/~K Ri General term for any of the kinetic constants: K, UB/a, U/b, UA/a, or UA/b, min-1 Rio General term for any of the kinetic constants for the reaction in water xix

r Radius, cm S Slope, min-1 S# Entropy of activation, Kcal/gm mole/~K SS Sign of the Slope, defined by Equation (79) T Temperature, ~K or ~F t Time of observation, min U Linear growth velocity, cm/min UA Linear growth velocity in the A direction, cm/min UB Linear growth velocity in the B direction, cm/min UC Linear growth velocity in the C direction, cm/min UO Linear growth velocity for reaction in water, cm/min U/d General kinetic growth constant, min1 UA/a Kinetic growth constant, min-1 UA/b Kinetic growth constant, min1 U/a Kinetic growth constant, minlUB/b Kinetic growth constant, min-1 UC/c Kinetic growth constant, min-1 u Impingement time, min V Volume, cc Vf Volume of one dihydrate crystal, cc AV Volume change, cc AV1 Volume change for dihydrate-hemihydrate reaction, cc AV2 Volume change for hemihydrate-anhydrite reaction, cc V Molar volume, cc/gm mole v Volume of a hemihydrate needle, cc vm Volume per molecule, cc/molecule xx

W Constant w Impingement time, min WD Weight of dihydrate, gm X Weight fraction x Nucleation time, min x Distance, cm Y Chlorinity, gm C1 per 1000 gm solution y Impingement time, min Z Pre-exponential factor, min' z Impingement time, min Greek Letters a Fraction reacted a 3Number of successive events occuring in the formation of a nucleus y Strain energy per unit area, ergs/cm2 81 First impingement time, b/2UB, min 92 Second impingement time, (b/2)/(UB - UA/S3), min "3 Third impingement time, a/2UA, min ~c C direction impingement time, c/UC, min v Frequency of lattice vibration, cycles/min p Density, gm/cc pT Density at temperature T, gm/cc p Molar density, moles/cc a Shape factor, cm2 Tc5 Time for 5% transformation, min (T5%)o Time for 5% transformation in water, min xxi

Subscripts A Anhydrite D Dihydrate H Hemihydrate W Water a First part of reaction c Second part of reaction c Corrected t, h, or T values e Third part of reaction g Fourth part of reaction o observed r reaction t temperature tot total xxii

ABSTRACT Although evaporative processes presently provide the most economical means of recovering potable water from sea water, they are limited by calcium sulfate scale which forms on the heat transfer surfaces. This scale forms by the nucleation and growth of calcium sulfate dihydrate or hemihydrate from solution, usually followed by the dehydration of these phases to the hemihydrate or anhydrite phase. In order to understand this scaling process so that it can either be controlled or eliminated, the fundamental nature of both the formation and transformation processes must be known. In this connection, an investigation has been made of the phase transformation of calcium sulfate dihydrate to hemihydrate and anhydrite at temperatures encountered in desalinization processes. This investigation was divided into two major parts: (1) studies of the time-temperature-transformation (TTT) relationships of the dihydrate-hemihydrate and the hemihydrate-anhydrite transformations and (2) a study of the kinetic mechanism of the dihydrate-hemihydrate transformation. The TTT relationships for the dihydrate-hemihydrate and the hemihydrate-anhydrite transformationswere obtained from dilatomnetric measurements of the net volume change accompanying the transformation of 0.7 gram samples in water, in sodium chloride solutions containing from 0.5% to 21o NaCl, and in synthetic sea water, over the temperature range from 230~ to 350~F. Initial dihydrate particle sizes ranged from one large crystal to a very fine powder. The different phases occurring were indentified by their X-ray powder diffraction patterns. A total of 63 experimental runs were made. xxiii

The dihydrate-hemihydrate transformation was found to be affected by three major variables: temperature, water activity, and initial dihydrate particle size. Both nucleation time and reaction time decreased with increasing temperature and decreasing water activity, indicating that both the nucleation and growth processes were accelerated by these changes. A minimum nucleation time was observed for particles about 0.01 inches long. The hemihydrate-anhydrite transformation was affected in a similar manner by changes in temperature and water activity. Initial particle sizes were not varied in this study. In the study of the transformation mechanism, the geometric details of the dihydrate-hemihydrate transformation were observed microscopically in a special cell designed to duplicate the conditions used in the dilatometer. Based on these observations, a simplified physical model was developed for the nucleation, growth, and impingement of hemihydrate needles with each other and the boundaries of the parent dihydrate crystals. Kinetic equations were derived for this model, and their kinetic rate constants were determined by fitting the equations to the rate data calculated from the dilatometric measurements. Empirical equations were derived for the variation of the kinetic constants with temperature and water activity. Using these empirical equations and the theoretical equations, time-temperature-transformation curves were calculated which compared favorably with the experimentally measured TTT values. This agreement helped to establish the validity of the theoretical equations and provided a means for interpolating and extrapolating the data obtained in this research. xxiv

Io INTRODUCTION Although the formation of thermally insulating scale on boiler and heat exchanger surfaces has been a serious engineering problem for many years, it has recently become more serious with the growth of progress to recover potable water from the oceans and brackish inland water supplies. At present, scale formation is a major factor limiting the efficiency and increasing the cost of production of potable water by evaporative processes. While all salts dissolved in the feed water to an evaporator are potential scale formers if the evaporation is carried beyond the limit of their solubilities, calcium sulfate is particularly bothersome because of its inverted solubility characteristics. As shown in Figure 1, two of the three solid crystalline modifications of calcium sulfate occurring in aqueous solutions, CaSO4 (anhydrite) and CaSO2t 1/2H20 (hemihydate), exhibit this phenomenon over their entire range of solubilities, while CaSO2p2H2O (dihydrate) exhibits the normal behaviour of increasing solubility for temperatures below 100~F, and then exhibits inverted or decreasing solubility above 100~Fo This decrease in solubility with an increase in temperature permits scale formation to occur on the heat transfer surface where a thin film of feed water can quickly become supersaturated causing scale to form,often before an appreciable amount of desalinated water is produced, In general, this phenomenon of scale formation involves the nucleation of calcium sulfate, either within the solution itself (homogeneous nucleation) or on some other phase, for example, the heating surface of the evaporators (heterogeneous nucleation), followed by growth of one or more of the three principal phases of calcium sulfate which are -1

-22.8 2.4 z 0o 0 2.0 0 o U.6- I-J 0.8 0 0.4 50 100 150 200 250 300 350 400 32 TEMPERATURE, OF Figure 1. Solubilities of the Solid Phases in the Calcium Sulfate - Water System (Reference 69).

-5stable in aqueous solutions, Since both calcium sulfate hemihydrate and dihydrate are metastable over the range of conditions commonly encountered in evaporators, scale formation may subsequently involve the transformation of the dihydrate to the hemihydrate, or the hemihydrate to the anhydrite. The development of effective means of controlling calcium sulfate scale formation must ultimately involve the development of means of controlling these nucleation, growth, and transformation processes based on an understanding of the fundamental mechanisms involved, The purpose of this investigation was to study the fundamental mechanism and the kinetics of the direct transformation of solid calcium sulfate dihydrate, CaS0402H20O to solid calcium sulfate hemihydrate, CaS041l/2H O, in water, in aqueous sodium chloride solutions, and in synthetic sea water concentrates at various temperatures. The net reaction for this transformation is represented by the following equation: CaS04 2H20(S) CaS04j1/2H20(S) + 3/2H20(L) (1) This reaction was chosen because the formation of calcium sulfate scale on heat exchanger surfaces necessarily causes an increase in temperature, due to its insulating properties, resulting in favorable temperature conditions for the above dehydration reaction to occur. Because the transformation reaction probably also starts at the heat exchanger surface where the temperature is highest, an understanding of the changes involved might provide a key for effective control or the removal of calcium sulfate scale. The research on the dehydration of calcium sulfate dihydrate to hemihydrate was divided into two major parts: (1) studies of the

-4time-temperature-transformation (TT9) relationships based entirely on observations of the volume change accompanying the reaction, and (2) the studies of the kinetic mechanism, using primarily microscopic observations. The use of optical grade selenite, CaS04'2H20, for these observations rather than actual calcium sulfate scale, increased the utility of these studies by allowing the transformation occurring within the solid crystals to be photographed showing details of the transformation which otherwise could not have been obtained, Combining these visual details with TTT data made it possible to develop kinetic equations for the dehydration process which have both scientific and engineering applications.

II. REVIEW OF THE LITERATURE Five solid phases have been identified in the calcium sulfatewater system: the dihydrate, CaS04~2H20; the hemihydrate, CaS4' 1/2H20; soluble anhydrite, y-CaSO4; natural anhydrite, 3-CaS04; and a high temperature form of anhydrite, C-CaS04. The transformations between these phases were observed by differential thermal analysis showing that the dihydrate to hemihydrate transformation occurs near 130~C, (6 4'7379) that the hemihydrate to y-CaSO4 transformation occurs near 170~C,(6'48.73'79) and that the P-CaS04 transformation occurs near 1230~C.(3638,60,62) The transformation between y-CaSO4 and B-CaS04, requiring considerably less energy, was not detected by differential thermal analysis but was observed in x-ray diffraction studieso(63'73) X-ray powder diffraction patterns(82) have been reported for all but the a high temperature phase which is extremely unstable below 1230~C. These patterns are sufficiently distinctive to permit ready identification of the calcium sulfate phases, although the patterns for hemihydrate and y-CaS04 are almost identical, making it difficult to distinguish them from each other unless: (1) care is taken to eliminate the possibility of hydration to hemihydrate, (2) the exposures are standardized, and (3) an x-ray camera capable of giving highly accurate d values is used,(73,99) Ao Time-Temperature-Transformation Studies'. In the CaSO4 - water system, the hydrates can be dehydrated with the formation of either gaseous or liquid water depending on whether the reactants are heated in contact with air or are immersed in an aqueous -5

-6solution. Three phase transformations have been detected when the solid phases were heated in contact with air, but only two were found when they were submerged in an aqueous solution, resulting in five different phase reactions describing the dehydration of calcium sulfateo Examination of the time-temperature-transformation information available in the literature on the reactions occurring in air indicates that the vapor pressure of the water in the air has a marked effect in determining which dehydration reaction occurs. When samples of dihydrate were heated in a stream of air dried over phosphoric acid they dehydrated directly to soluble anhydrite (y-CaSO4) without any indication of the formation of hemihydrate appearing in the TTT data.(ll' 19'0) When samples were heated in a furnace where there was a minimum movement of the air around the sample, the dihydrate began to transform to hemihydrate which, in turn, began to transform to y-CaSO4 before the dihydrate was completely transformed to hemihydrate(1) When samples of dihydrate were deliberately heated in a stream of moist air, only the transformation of the dihydrate to the hemihydrate was observed( 2' 3954 8o) probably due to termination of the observations before the second reaction had initiated, Other observations(55'98,99) yielding isobaric dehydration curves for the transformation of the dihydrate to hemihydrate, and the hemihydrate to 7-CaSO4 (soluble anhydrite) showed that the reactions were reversible under these conditions and occurred in a sequential manner with the dihydrate transforming completely to the hemihydrate which in turn transformed to y-CaSO4, Since the vapor pressure of the water was not reported, except for the isobaric experiments, it was impossible to quantitatively describe its effect on the reaction. It can be pointed out, however, that the rate of dehydration of the hemihydrate to anhydrite becomes

-7faster than the dehydration of the dihydrate to hemihydrate for some vapor pressures of water, causing the latter reaction to become the rate controlling step for the conversion of dihydrate to anhydrite. Examination of the time-temperature-transformation studies available in the literature for the dehydration of the dihydrate while submerged in aqueous solutions indicated that the salts dissolved in the aqueous media had a marked effect on the reactions and on their mechanism. The detailed studies of Taperova and associates899 ) showed that the concentration of phosphoric acid in the solution in which the phases were submerged determined what reaction would occur at a particular temperature. Using radioactive isotope techniques, Ketelaar and Heijmann(51) concluded that whenever one of the phase reactions observed by Taperova occurred, either by hydration or dehydration, it occurred through the solution, as indicated by a decrease in the radioactivity of the phosphoric acid solutions. Ostroff(66) followed the dehydration of calcium sulfate dihydrate immersed in an aqueous solution containing sodium and magnesium chlorides at 90.5~C. Even.though the free energy relationships indicated that the dihydrate should transform directly to anhydrite, he observed that the hemihydrate first formed completely, and then it transformed to natural anhydrite (P-CaS04). From this he concluded that the anhydrite could form from the dihydrate only when the conditions for the transformation of the dihydrate to the hemihydrate also existed. Droste and Grim(24) followed the continuous change of calcium sulfate dihydrate to hemihydrate in an atmosphere of saturated steam

-8by observing the change in intensity of x-rays diffracted from the (020) planes of dihydrate and hemihydrate crystals using an autoclave combined with conventional x-ray diffraction equipment. Their results showed that the transformation occurred by a solid-solid transformation, and provided no indication of any intermediate step or liquid phase occurring during the transformation. The hydration of hemihydrate to dihydrate was studied in much detail by observing the setting of Plaster of Paris(l81l97l172l100) which involves the crystallization of the dihydrate from a supersaturated solution.(20) Mechanistic studies on the hydration of anhydrite to dihydrate were also made showing that the initial particle size of the anhydrite(29) and the solution phase containing the reacting solids(16) affected the rate of reaction considerably. Isolated values of the transition temperature for the dihydratehemihydrate and dihydrate-anhydrite equilibria were determined from the intersections of the respective solubility curves and by the direct observation of the effect of temperature on the overall rates of reaction.' Using the intersection of solubility curves, for example, Partridge(69, 70,75) found the temperature for the gypsum-anhydrite transition to be 37~C, and the gypsum-hemihydrate transition to be 98~C (41) in water; Hill(4 found the temperature for the gypsum-anhydrite transition to be 420~C in water by extrapolating solubility data obtained in potassium sulfate solutions; and Posnjak(89) found the temperature of the gypsum-anhydrite transformation to be 30~C in sea water concentrated 4.8 times. Southard( obtained values of 100~C41~C for the transition temperature between gypsum and hemihydrate in water, by

-9measuring the volume change of selenite partially reacted to hemihydrate in a dilatometer, and by plotting the square root of the absolute value of the rate of volume change versus temperature, retaining the sign associated with the rate. He also determined the transition temperature of the same transformation to be 95~C~1lC in an ethanol-water solution in which the activity of the water was 0.94 (at 950C). Using free energy relationships and measured thermodynamic properties, Kelley and Southard(50) developed the following equation giving the transition temperature for the dihydrate-hemihydrate equililibrium as a function of the activity of the water in the solution: RT ln a3/2 = -856,0 - 50.99 T Log1o T + 0.0185 T2 + 126.41 T (2) (94) On the other hand, Toriumi and Hara calculated the temperatures for the dihydrate-hemihydrate and for the dihydrate-anhydrite transitions from the intersection of the solubility curves measured in sea water concentrated to various degrees, and correlated the values of the reciprocal of the equilibrium temperature with the logarithm of the vapor pressure ratio P/POo The correlating equations are: loglo(P/Po) = - 537.20/T + 1.4476 (3) for the dihydrate to hemihydrate transformation, and log1(P/po) = - 373.64/T + 1.2010 (4) for the dihydrate to anhydrite transformation, where P is the vapor pressure of the sea water, P~ is the vapor pressure of pure water at the same temperature, and T is the equilibrium temperature in degrees Kelvin.

-10MacDonald(57) examined the thermodynamic data existing in the literature on the equilibrium between calcium sulfate dihydrate and anhydrite and derived thermodynamic relationships for the effect of lithostatic pressure on the transforming solids and of hydrostatic pressure on the solution phases in pure water and saturated sodium chloride solutions, Using the available data measured at 40~C, he was able to determine that the relationship between the pressure of the system and the equilibrium temperature was approximately linear. When the system was only under a hydrostatic load, he calculated the slopes of the pressure versus temperature lines as 84.4 bars per degree centigrade for dilute calcium sulfate solutions and as 90.8 for saturated sodium chloride solutions. When the solid in the system was under a lithostatic pressure approximately 2,4 time the applied hydrostatic pressure, he calculated the slope of the pressure versus temperature lines as -39,45 for dilute calcium sulfate solutions and as -48.3 for saturated sodium chloride solutions. B. Crystallographic Studies Crystal structures have been reported in the literature for four phases of calcium sulfate: the dihydrate (selenite or gypsum) the hemihydrate (bassanite), soluble anhydrite (y-CaSO4), and natural anhydrite (P-CaS04). In addition, Kelley(50) has reported thermodynamic data which suggest the possibility of the existence of modifications of these phases although no confirming crystallographic data have been reported. Studies of the crystal structure of calcium sulfate dihydrate by Onorato(64), Wooster(l03), Gossner(21) Bragg(9) De Jong and Wooste~~~~rag, DeJn

-11Bouman(22), and Strunz(84) have resulted in six different unit cells appearing in the literature, with each author choosing the b axis perpendicular to the planes of easiest cleavage, but six different sets of a and c axes. The relationships between these six different unit cells for calcium sulfate dihydrate are shown in Figure A -l of Appendix A where the lattice is viewed perpendicular to the (010) cleavage planes.(10,22,23) The centers of the sulfate radicals and the calcium ions are represented by the intersection of the lines while the different unit cells are shown by heavy outlining. According to De Jong and Bouman, calcium sulfate dihydrate has a monoclinic unit cell containing four molecules of CaS04o2H20 with: a = 5.68, b = 15.18, c = 6.29 A, and P = 113~50'. The locations of the individual atoms in the structure have been given by Wooster(i03), Strunz (84) and Wyckoff, (104,10506) while investigations using proton magnetic resonance (67).infrared spectroscopy^(2) and neutron diffraction(40) have accurately located the positions of the hydrogen atoms and have provided information on the nature of the bonding between the sulfate radicals and the water molecules. When calcium sulfate dihydrate is viewed perpendicular to the (010) cleavage planes, the crystal transmits polarized light in four different directions which are 90 degrees apart, representing the a and y optical axis of the crystal,(l3) These axes are rotated 37~28' to the c axis of the morphological cell(27 78) which also is the c axis of the unit cell of De Jong and Bouman. These optical axes can be used, in conjunction with the predominant cleavage planes, to determine the orientation of the unit cells in the crystal fragments. Cleavage(68) occurs most

-12easily between (010) planes yielding thin polished foliae, between (100) planes forming cleaved surfaces with conchoidial fractures (convex elevations and concave depressions), and between (011) planes resulting in a fibrous fracture plane parallel to (001) planes. The relationships of the cleavage planes to the crystallographic and optical axes are shown in Figure 2. The crystal structure of calcium sulfate hemihydrate formed in solution has been studied by Onorato,(l5) Gallitelli,(31) Caspari,(l4,15) and Fl5rke.(30) The monoclinic structure proposed by Gallitelli was described by Florke using a hexagonal unit cell having: a = 6.83, c = 5.25 and containing three molecules. Florke also studied the structure of y-CaS04 formed by dehydrating hemihydrate in air. He proposed a hexagonal structure similar to that of the hemihydrate except that the water molecules were missingO The dimensions of this hexagonal unit cell are: a = 6,99, c = 6.34 A. It contains three molecules, and the locations of the atoms in the structure were also given by Florke. The crystal structure of anhydrite was studied by Wasastjerna (Reference 9,21) and Dickson and Binks(23) who determined the cell to be orthorhombic with a=-6.19, b = 6.94, and c = 6.94 a and containing four CaS04 molecules. More recently Swanson, Fuyat, and Ugrinic(86) measured the following lattice constants: a = 6.238, b = 6.991, and c = 6.996 X which were redesignated by Deer(21): a = 6.991, b = 6.996, and c = 6.238 A. The locations of the individual atoms in the structure were reported by Wyckoff(104,105) The four phases resulting from the successive decomposition of calcium sulfate dihydrate to anhydrite are related by the preferential

-13a 52.5~ 76.50 13. 5~' 1130501' Figure 2. The Relationships Between the Crystallographic Axes a and c and the Optical Axes C and y for Gypsum Viewed Perpendicular to Its (010) Cleavage Plane.

-14orientation of the forming crystals within the original crystal structure. Examination of these different structures shows that they are all related by a chain-like feature comprised of calcium and sulfate ions approximately 3.1 A apart which is preserved in each structure during the decomposition along their c axes.(L'2l'30'77) The a axes of the hemihydrate crystals tend to be randomly oriented with respect to the original dihydrate structure(77) whereas the a axes of the anhydrite, which formed from single crystals of hemihydrate, tend to form parallel to one of the a axes Of the hemihydrate.(30) The phase transformation of y-CaSO4 to P-CaS04 in air was studied by Posnjak() and Newman and Wells'6) who identified the phases by x-ray diffraction patterns. The 5-CaS04 phase was first detected as a minor component in the 7-CaS04 which formed when samples of dihydrate were heated at 200~C for 670 hours. Samples heated above 450~C were subsequently found to be entirely composed of P-CaSO4 which was also observed during the manufacture of Plaster of Paris.(0ll) The addition of liquid water to the samples during heating resulted in the formation of -C.aS04 at 170~C after the comparatively short time of one and onehalf hours, indicating that y-CaSO4 is not stable in aqueous solutions. The results of these investigations are summarized in Table A-1 and Figure A-2 of Appendix A. Grahmann(36)observed the high temperature form of calcium sulfate, a-CaS04, while studying binary phase equilibria. Masuda(60) also observed this transformation and reported a transition temperature of 1231~C. Gruver(38) observed this same transformation at 1230~C, and another at

-151350~C involving the melting of an eutectic compound between calcium sulfate and calcium oxide.(62) The change in crystal structure at 1230~C is probably associated with a rotation of some of the sulfate ions, changing the structure from a low temperature barite (orthorhomibic) structure to a high temperature (cubic) structure resembling that of sodium c(hloride. This phenomenon has been observed in other compounds (i.e. CsC104, KBF4, KC104, NHi4BF4, NHC104, RbCl04, and T1C104) containing radicals of BF a and C10l which have been shown by Magignac(76) to behave anal o(u,:;sly to SO. C. Summary Investigations of the dehydration reactions in air led to the postulate that gypsum (CaS04.2H20) first dehydrated to hemihydrate (CaS04'1/2H20) which was further dehydrated to "solible' anhydrite" (y-CaSO4) which gradually transforms to natural anhydrite (B-CaSO) when heated above 170~C. Further heating of natural anhydrite results in another phase change to a high temperature form a-CaS04. Investigations of the dehydration reactions occurring when the reactants were immersed in aqueous solutions showed that gypsum dehydrates to hemihydrate which in turn dehydrates to natural anhydrite without any indication of the formation of y-CaSO4. Studies of the reverse of this process show that the hemihydrate and natural anhydrite readily rehydrate through the solution phase to the dihydrate(20) although much longer times are required for crystals of anhydrite. Investigations of the equilibrium conditions existing between the three stable phases in solution, primarily using solubility experiments, have established the transition temperature for the dihydrate-hemihydrate and the dihydrate-anhydrite equilibria in aqueous solutions by the intersection of the respective solubility

-16curves. Determinations of the solubilities in sea water concentrates have shown.that the respective solubilities change differently with increased concentrations of sea salts, resulting in a lowering of the equilibrium temperatures with increasing salt concentration. Rates of dehydration of the hydrated phases of calcium sulfate were reported in a few cases for the reactions occurring in salt and phosphoric acid solutions. The information presented from the literature describes the general characteristics and properties of the calcium sulfate-water system that are needed to understand the physical and chemical changes occurring during the dehydration of calcium sulfate dihydrate. The only measurements of individual rates of dehydration applicable to accurate kinetic analysis are those of Budnikoff for the dehydration of dihydrate to hemihydrate in moist airo His experimental values are reproduced in Table A-2 of Appendix A. The remaining TTT measurements mentioned in the review were not observed at equal time intervals and, consequently, could not be analyzed without first smoothing the data. Some detailed kinetic studies on related solidsolid-vapor and solid-solid-liquid reactions were found, however, containing adequate theoretical treatments for their particular reactions. The following section of this dissertation presents some of these fundamental kinetic concepts which are applicable to the calcium sulfate -water system.

IIIo KINETIC THEORY FOR TRANSFORMATIONS IN SOLIDS Determinat.ion of the reaction mechanism of solid-solid-gas or solid-solid-liquid reactions requires information on: (1) the rate of nucleation of the second phase within the first, (2) the shape of the forming nuclei and their growth geometry throughout the entire reaction, and (3) the pattern of any interferences occurring between the growing nuclei and the edges of the crystal or neighboring nuclei. In the literature, four different laws were used to describe nucleation rates: the exponential law, dN/dx = KNO exp (-Kx); the linear law dN/dx = KNo; the power law, dN/dx = Dpx-l; and the law of instantaneous nucleation, N = No; where dN/dx is the rate of nucleation, K is the nucleation rate constant, x is time, No is the total number of nuclei, D is a constant, and 3 is the number of successive events occurring in the formation of a nucleus. The shapes of growing nuclei were successfully determined using microscopic observation revealing such shapes as: hexagons, rhombohedrons, (32,33) squares, circles, and four pointed stars. As these reactions progressed, the growing nuclei were observed to overlap making it necessary to modify the rate equation describing their growth to account for this interference. Both generalized and specific theories describing the combined effects of nucleation and a growth have been postulated in the literature attempting to adequately describe this complicated phenomenon. A generalized method for developing a simple mathematical equation describing the overall kinetics of the transformations in solids which occur by nucleation and growth processes was described by Erofeev,(20,26'27'28) Mample,(58'59) and Avrami!3,4$5) However,this generalized approach does not appear suitable for the present investigation, -17

-18because it cannot easily incorporate information on the shape and growth patterns of the forming nuclei with information on the overall rate of nucleation and, therefore, is not particularly useful in developing and testing models of reaction mechanisms. Instead, kinetic equations have been developed specifically for this study, based on the experimentally observed characteristics of the nucleation and growth process. Previously successful studies, using this individualized approach, have served as encouraging guides in the present work: i.e. studies of the dehydration of calcium carbonate hexahydrate (CaCO36H20) in solutions;(8'47'93) of copper sulfate pentahydrate (CuS04o5H20) in air;(46) and of potassium hydrogen oxalate hemihydrate (KHC204 1/2H20) in air.(45) From the most general, theoretical point of view, the decomposition of salt hydrates consists of the nucleation of a lower hydrate on, or within, the crystal of a higher hydrate, followed by the growth of the lower hydrate until the original crystal is completely transformed. When a nucleus of the lower hydrate first forms and starts to grow within the crystal lattice of the higher hydrate, the region of the parent lattice surrounding the growing nucleus is deformed due to the difference in molecular volume of the lower hydrate crystal forming and the original crystal. This deformation results in strain energy which must be considered in the determination of the minimum size for a stable nucleus. If the size of a particular nucleus is greater than the critical size determined by free energy requirements, the nucleus will grow; however, if it is less than the critical size, it will disappear. The free energy change(33) associated with the formation of a nucleus within the lattice of a parent crystal is given by the following

-19equation: AG mAG + cry (5) where: AG is the total free energy change, m is the number of molecules in the nucleus, A G is the bulk free energy change per molecule, a is the shape factor, i.e. the external area of phase formed (this term is equal to 4rxr2 for the simple case of a spherical nucleus)> and y is the strain energy per unit interfacial area. Upon substituting the values of the shape factor for a spherical nucleus into Equation (5), the result is: AG = mG + y4cr2 (6) The r2 term can be replaced by an equivalent term which is a function of m. If v is designated as the volume per molecule of product, then the number of molecules in a spherical nucleus is equal to the ratio of the volume of the nucleus (4/3)7r3 to the volume per molecule vm, i.e, m = 4tr3/3vm. Solving this expression for r2 and substituting it into Equation (6), yields: AG = Am + y(36rv2)1/3m2/3 (7) Incorporating the fact that AG must be negative if the reaction is to occur spontaneously, the above equation becomes: AG = -,lm + ( 36V2m1/3m2/3, (8) AG = - y(36~cvm, (8)

-20which is of the form: A G = - bm + am2/3 (9) The strain energy y, can be positive, negative, or zero depending on the particular structures involved. If y is positive, AG = 0 for m = 0 and for m = (a/b)3, and has a maximum value for m = m* = (2a/3b)3 = (2 /3'G )336 vm,determined from the conditions that the slope is zero at a maximum, i.e, = 0. The value of the free energy for m = m* dm m=m* is: A G* = 4a3/27b2 = m* IZAG /2. If the strain energy y is zero or negative, the equation for A G is zero for m = 0 and negative for all positive values of m, indicating that under these conditions a maximum size for a critical nucleus does not exist, provided Equation (10) takes into consideration all the applicable energy terms; therefore, the reaction occurs spontaneously after the first molecule decomposes. In general nucleation occurs when local energy fluctuations provide the activation energy necessary to initiate the reaction at the potential nucleation site in the parent crystal. Assuming that the decomposition of a single molecule results ultimately in a stable nucleus, the probability of such a unimolecular reaction (33,35) is given by: K = vexp(- A G/RT) (10) were: K is the nucleation rate constant,, v is the frequency of lattice vibration, A G 0 is the free energy of activation, R is the gas constant, and

-21T is the absolute temperature. Substituting the thermodynamic equation: AG# = AH# -T AS (11) into Equation (15), gives: K = v exp(A S/R) exp(- AH#/RT) (12) which has the general form of the Arrhenius equation: K = Z exp(- E /RT), (13) The nucleation rate constant K can be determined in some instances by observing the change in the number of nuclei with time(102) but in most cases it is determined indirectly by fitting the observed kinetic data to equations describing the combined effects of nucleation and growth. Microscopic observations made on growing nuclei suggest that in most cases they grow at constant linear rates once they become visible(33) allowing the volume transformed per nucleus v(t,x) to be calculated as a function of time of nucleation x and the specific time of observation x = t. The total volume transformed V(t) at any particular time x = t is the integral of the product of the rate of nucleation dN/dx (i.e. the number of nuclei forming per minute) and the volume transformed per nucleus va(xt) V(t) = x= -dN va(xt)dx. (14) x =0 d V('~x'

-22This equation satisfactorily describes the total volume transformed as a function of time until two nuclei grow into each another; thereafter, the equation as shown predicts more growth than actually occurs because actual growth no longer occurs in the direction of the interferenceo The interference of two nuclei therefore alters their individual growth patterns, previously described by va(x,t), and requires a correction term vb(y,t) to be applied at the time of the interference y = 01. This gives the following equation for the volume transformed per nucleus: v2(x,t) = va(x,t) + vb(yt) (15) The first term describes the unrestricted growth of a nucleus while the second term describes the effect of the interference on the unrestricted growth after one nucleus intersects another nucleus or the edge of the parent crystal. After the first interference occurs, the remaining nuclei begin to intersect one another with the same rate of occurrence as they nucleated, ie. nuclei which formed early in the reaction have a higher probability of intersecting neighboring nuclei or the sides of the parent crystal than nuclei which nucleated later simply because they have been in existence longer. Since the original rate of nucleation was described by dN(x)/dx, the rate of interference, or distribution of interference times, is given by the same function only starting at time 91: i.e., by dN(y-G1)/dy. Upon incorporating these terms into Equation (14), the equation describing the total volume transformed as a function of time becomes: V(t) = x=t dN(x)/dx va(x,t)dx + y=t dN(y-G1)/dy vb(y,t)dy x=O y=G1 (16)

-23The first integral represents the total volume that would be transformed by unrestricted growth while the second integral represents the interference volume correction which must be applied to the first integral so that the entire equation gives the correct value for the actual total volume transformed. For example, Bradley, Colvin, and Hume(8) successfully used this method to describe the complete dehydration of calcium carbonate hexahydrate, CaC03.6H20, which proceeds in a simple manner when flat crystals are used, Nucleation of these crystals was observed to occur almost entirely on the two opposite flat surfaces, so that as the transformation proceeded these two faces grew toward each other until they met at the center of the crystal. The rate of nucleation was found to follow the exponential law, dN/dx = KNo exp(-Kx), and the rate of growth for each individual nucleus was given by va(x,t) = 2AU(t-x), where A is the area of the growing crystal face and U is the linear rate of growth of the transforming interface, and t-x is the time of growth, i.e. the difference in time between observation x = t and nucleation x. After the two opposite growing faces of one crystal met each other at the center of the crystal, the contribution of the growth of that particular crystal to the total transformation process was ended. The following equation which contains the interference correction term vb(y,t) = - 2AU(t-y), was used to describe the volume transformed as a function of time: V(t) = x=tx KNo exp(-Kx)2A(t-x)dx - N exp(K(y-1))2A(t-y) dy x=O y=Gl (17) The growth of nuclei which have more complicated shapes can be restricted from growing in several directions by interference with

-24neighboring nuclei or the sides of the parent crystals. In a case like this, the equation describing the unrestricted growth must be corrected each time a growing nucleus meets opposition, requiring two, three, or more correction terms depending on the geometry of the system. As will be shown later in this dissertation, the transformation of calcium sulfate dihydrate to hemihydrate exhibits three different impingements, and the volume of the hemihydrate formed as a function of time for this process is: x=t y=t V(t) = t dN(x)/dx va(x,t)dx + = dN(y-gl)/dy vc(y,t)dy x=O y=01 (18) z=t w=t + f dN(z-92)/dz ve(z,t)dz + f dN(w-09)/dw vg(w,t)dw. z=92 w=93 The particular analytical expressions for V(t), va(x,t), Vc(yt), ve(z,t) and vg(w,t) and for G1, 02, and 93 were derived from microscopic observations of the shapes and rates of growth of the hemihydrate phase within single crystals of the dihydrate phase. These observations, and the calculations based on them, are presented in Chapter V following the description of the work on the time-temperature-transformation characteristics of the reaction.

IVy' STUDIES OF TIME-TEMPERATUREE-RANSFORMATION RELATIONSHIPS These studies involve measurements of the overall rates of dehydration (1) of calcium sulfate dihydrate to hemihydrate and (2) of calcium sulfate hemihydrate to anhydrite, in water, in sodium chloride solutions, and in synthetic sea water concentrates. The reactions were followed by observing the change in the total volume of the system as a function of time in a glass dilatometer using special equipment which permitted automatic, simultaneous recording of the temperature and the height of the liquid meniscus in the dilatometer capillary at equal time intervals. The results of these studies are presented as timetemperature-transformation (TTT) curves showing the general effects of solution concentration, temperature, and initial particle size on the rates of the reactions. A. Experimental Procedures The essential features of the special glass dilatometer used in these experiments are shown in Figure 3. The reaction mixture was contained in the reaction bulb of the dilatometer which was a Pyrex glass tube about two inches long and 3/8 inch in diameter. The temperature of the reaction mixture was measured by means of a copper-constantan thermocouple made from 30 gauge wires which were sealed through a glass plug that fitted into the ground glass joint at the bottom of the reaction bulb. Changes in the volume of the reaction mixture were detected by measuring the changes in height of the liquid in a calibrated capillary tube which was connected to the reaction bulb by a second ground glass joint. These measurements were made relative to a metal scale which was firmly attached to the capillary, -25

PRESSURE SEAL ASSEMBLY NUT -TEFLON 0-RING PLUG CONTAINING THERMOCOUPLE SEAL CAPILLARY LIQUID MENISCUS ^^^^y^^~~ 3-iJONT 50 CM METAL SCALE — JOINT SINGLE CRYSTAL SAMPLE "^^^i^N^-T JOINT REACTION BULB ---- PLUG WITH THERMOCOUPLE Figure 3. Construction of Dilatometer (Approximately Actual Size).

-27In preparing the dilatometer for use, the reaction mixture was loaded into the reaction bulb by first distributing a measured weight of crystals of calcium sulfate dihydrate around the thermocouple, and then injecting the solution into the bottom of the reaction bulb with a hypodermic syringe. Particular care was taken to displace all the entrained air between the crystals. Finally, a small volume of solution, determined by experience, was added to the capillary to adjust the initial location of the meniscus, a thin layer of silicone grease was applied to the ground glass joints, and the capillary, the reaction bulb, and the thermocouple plug were wired firmly together. During use, the dilatometer was enclosed in a heavy-walled glass tube inside the insulated constant-temperature bath shown schematically in Figure 4. The desired reaction temperature was achieved by circulating the heated air inside the bath rapidly past the tube containing the dilatometer. The temperature of the air was maintained constant to —+ 0.5~F by a sensitive bimetallic thermo-regulator. Nitrogen gas was introduced into the glass tube containing the dilatometer to prevent the solutions in the dilatometer from boiling. A constant pressure was obtained by a pressure regulating valve which maintained a constant minimum pressure and a back pressure regulating valve which maintained a maximum pressure by venting any excess pressure caused by the expansion of dilatometer and its contents. These two valves were set to operate within 2 psig of each,other. During an experimental run, the temperature indicated by the thermocouple within the reaction bulb was recorded at 5-second intervals by a recording potentiometer. The height of the liquid meniscus in the capillary tube was recorded simultaneously with every twelfth temperature reading (i.e. at one minute intervals) by photographing the position of the

PRESSUR _}THERMOCOUPLE PRESSURE LEADS GAUGE TO TOESSUR REGULATINGPORT FOR INSERTATION PRESSURE REGULAT.ING OFDILATOETER SYSTEM BIMETALIC THERMOREGU AT R GLASS TUBE CONTAINING DILATOMETER BAFFLE AIR HEATER AIR CIRCULATING FAN Figure 4. Schematic Drawing of Constant Temperature Bath and Pressurized Glass Tube for Containing the Dilatometer.

-29 liquid meniscus against the metal scale, using a 16 mm movie camera whose shutter was operated, one frame at a time, by a solenoid actuated by a clock used in conjunction with the printing mechanism of the recording potentiometer. The height of the liquid meniscus was obtained by projecting the photographic image, frame by frame, on a screen and reading the position of the meniscus between the millimeter reference marks using a vernier scale of the type shown in Figure 5 which allowed interpolation of the data to + 0.02 mmo The values of temperature were read to + 0.2~F directly from the potentiometerer's chart using a 15X magnifying glass, and the corresponding values of time were determined from the chart speed of one-third inch per minute. The values of the observed time to temperature To, and height of the liquid meniscus ho determined by the above procedures are listed in Appendix U for all the experimental runs. These observed data values were then punched on IBM cards and corrected on the IBM 7090 electronic digital computer using the thermocouple calibration given in Appendix B, the capillary calibration given in Appendix Cy and the computer program given in Appendix D, giving values of corrected data: tc, Tc and hc where tc = to. A typical set of corrected values obtained from the observed data by this procedure for experimental run 62 is listed in Table I. These data were plotted in Figure 6 and 7 to show the general characteristics of the changes in the height of the meniscus and temperature during a typical reaction. In order to obtain hrP the height due to the reaction alone, from the corrected values of hc, it was necessary to determine the height ht caused by the rapid thermal volume expansion which occurred when the dilatometer and its contents at room temperature were inserted into the

-30IMAGE OF CAPILLARY, MENISCUS, AND SCALE STATIONARY SCREEN.- REFERENCE LINE SHOWN COINCIDENT WITH SCALE..___/ DIVISION SCREEN VERNIER SCALE Figure 5. Vernier for Reading Position of Meniscus (Approximately One-Half Size).

-31TABLE I CORRECTED EXPERIMENTAL DATA FROM RUN 62 Time Temp. Height Time Temp. Height Time Temp. Height min ~F cm min ~F cm min ~F cm.0 72.6.000oo 165.0 244.8 32.597 330.0 244.9 38.374 5.0 199.6 24.084 170.0 244.8 32.824 335.0 244.9 38.415 10.0 231.6 28.470 175.0 244.7 33.055 340.0 244.9 38.442 15.0 240.7 29.811 180.0 244.7 33.287 345.0 244.8 38.469 20.0 243.7 30.195 185.0 244.7 33.512 350.0 244.9 38.501 25.0 244.7 30.308 190.0 244.6 33.740 355.0 244.8 38.525 30.0 245.1 30.348 195.0 244.6 33.965 360.0 244.9 38.541 35.0 245.0 30.363 200.0 244.6 34.206 365.0 244.8 38.558 40.0 245.1 30.367 205.0 244.6 34.441 370.0 244.9 38.572 45.0 245.0 30.371 210.0 244.6 34.682 375.0 244.9 38.586 50.0 245.1 30.371 215.0 244.6 34.927 380.0 245.0 38.601 55.0 245.0 30.377 220.0 244.6 35.164 385.0 244.9 38.605 60.0 245.1 30.386 225.0 244.6 35.407 390.0 245.0 38.616 65.0 245.0 30.395 230.0 244.6 35.641 394.0 244.9 38.623 70.0 245.1 30.408 235.0 244.6 35.880 400.0 245.0 38.624 75.0 245.0 30.424 240.0 244.6 36.119 405.0 244.9 38.634 80.0 245.1 30.445 245.0 244.6 36.331 410.0 244.9 38.638 r85.0 245.0 30.469 250.0 244.6 36.544 415.0 244.9 38.645 90.0 245.1 30.512 255.0 244.6 36.735 420.0 244.9 38.648 95.0 245.0 30.554 260.0 244.6 36.916 425.0 244.9 38.653 100.0 245.1 30.611 265.0 244.7 37.070 430.0 245.0 38.660 105.0 245.0 30.681 270.0 244.7 37.234 435.0 244.9 38.660 110.0 245.0 30.764 275.0 244.7 37.389 440.0 245.0 38.664 115.0 245.0 30.863 280.0 244.7 37.537 445.0 244.9 38.664 120.0 245.0 30.978 285.0 244.7 37.676 450.0 244.9 38.672 125.0 245.0 31.102 290.0 244.7 37.792 455.0 244.9 38.674 130.0 244.9 31.241 295.0 244.7 37.898 460.0 244.9 38.676 135.0 244.9 31.396 300.0 244.7 38.000 465.0 244.9 38.676 140.0 244.9 31.563 305.0 244.7 38.082 470.0 244.9 38.679 145.0 244.8 31.744 310.0 244.8 38.164 475.0 245.0 38.680 150.0 244.8 31.940 315.0 244.8 38.222 480.0 244.9 38.679 155.0 244.8 32.152 320.0 244.8 38.272 160.0 244.8 32.369 325.0 244.8 38.332

40... * * C' - 0 0~ z 00 J.-, _.. L 30 U Z-ZONE I 0j 30 O -"',,'2ZONE 2. C ZONE 3 28 1LIl l_ — lll\l _ l _ l _ l _ l 0 100 200 400 600 800 TIME, MINUTES Figure 6. Values of Height of Liquid Meniscus in Dilatometer Capillary Versus Time for Run 62 for the Transformation of Calcium Sulfate Dihydrate to Hemihb.Trate in Water at 245~F. to Hemib~irnrate in Water at 245~F.

248 1 245 0 0000~ 00000000000 0 0 00000 0 000000 240 1~- { ZONE I j, jZONE 2 ZONE 3 236- I I I I I I I I 0 100 200 300 400 500 TIME, MINUTES Figure 7. Values of Temperature Versus Time for Dilatometric Run 62 for the Transformation of Calcium Sulfate Dihydrate to Hemihydrate in Water at 245~F.

-34hot constant temperature bath at the beginning of an experimental run. This rapid expansion caused the height of the liquid column in the capillary to increase rapidly at first and then to approach asymptotically the value corresponding to the volume of the reaction mixture of crystals and solution at the bath temperature (Figure 6, Zone 1). The meniscus height then remained at this value until the dehydration reaction started (Figure 6, Zone 2), whereupon it again increased as the volume of the reaction mixture increased (Figure 6, Zone 3), finally reaching another steady state value at the end of the reaction. The temperature of the reaction mixture inside the dilatometer followed a similar cycle, increasing asymptotically to the temperature of the bath (Figure 7, Zone 1), remaining constant until the dehydration reaction started (Figure 7, Zone 2), then decreasing slightly due to the absorption of heat from the reaction mixture by the endothermic reaction, and finally coming back to the bath temperature when the reaction was completed (Figure 7, Zone 3). The change in height of the meniscus due to thermal effects ht was calculated from an equation of the form: ht = A + B(Tc - Tc.) + C(Tc - Tc)2 (19) which is a power series relationship between the volume and the temperature of a liquid and solid system. In this equation, A, B, and C are constants determined for each run, Tc is the corrected temperature at the time of the measurement, and Tc is the initial corrected temperature at the start i of the run (usually room temperature). The values of the constants were obtained, by the method of least squares from the data taken before the

-35 - reaction began, (ioe. during the period of Zone 1, Figure 6, before the change due to the reaction was detectable) when ht was assumed equal to hc. These values were substituted in Equation (19) and the values of ht corresponding to the value of the temperature Tc were calculated for the remainder of the experimental runo Finally, the values due to the reaction were obtained as follows: hr = hc - ht and Tr =Tc, and tr = tc - tc where tc* is the time when the reaction began. The accuracy of the method used in obtaining the values of ht was evaluated using time-temperature-height values obtained from two experiments when the dilatometer was charged with water alone. Equation (19) was fitted to the height and temperature values for the first 25 minutes of each experiment obtaining values of the coefficients A, B, and C, by the method of least squares with each fit having a standard error estimate of less than 0.04 cm. Using these coefficients, values of height were calculated by Equation (19) and compared with of the corresponding experimental values for the remaining 95 minutes of each experiment. The calculated values corresponding to approximately 1% of the total height of reaction. This close agreement between the calculated and experimental values indicated that the method was more than satisfactory for determining the height change due to thermal expansion of the contents of the dilatometer during an experimental run. The method of calculating hr was also evaluated by comparing values of the total height of reaction hr with the corresponding theortot retical height values calculated from the physical properties of the individual phases to see if the experimental data behaved correctly with respect to changes in temperature and solution concentration. The

-36theoretical values of h were calculated from published and experimentaltot ly measured densities of calcium sulfate dihydrate and hemihydrate measured at room temperature using the stoichiometric relationships as shown in Appendix L. The temperature dependence of values of h was assumed tot to be that of the water in the system alone since the densities of the solid phases as a function of temperature were not readily available and are small. The values of the total height of reaction h resulting tot from the experiments using water, 3.5% sodium chloride solutions, and normal synthetic sea water are listed in Appendix F and shown in Figures 8, 9 and 10, with the calculated least squares line drawn through the points. The dashed line also shown on each figure represents the temperature dependence of the theoretical values of h corresponding to tot the complete dehydration of calcium sulfate dihydrate to hemihydrate in waterO Examination of each figure shows (1) that the points lie very close to the least squaresline, (2) that the slopes of all the lines are very similar, and (3) that the actual values lie near, but below, the theoretical curve for all the data. The standard deviation of the values of h. from the least squares line shown in each figure is 0.057 cm, tot 0033 cm, and 0.081 cm, respectively, indicated good precision and reproducibility of the values. Likewise, the similarity in the values of slopesof 0.024 cm/~F, 0.014 cm/OF, and 0,019/OF, to each other, and to the theoretically determined slope of 0.020 cm/OF, show that the experimental values exhibit the necessary temperature dependence. The small differences between the experimental values and the theoretical line are easily accounted for by examining the calculation

-3710., 8 7 - 230 240 250 260 270 TEMPERATURE, OF Figure 8. Total Change in Meniscus Height Due to Reaction Versus Temperature for Runs in Water. 2 ___I0 0 L. -C 7 230 240 250 260 270 TEMPERATURE, OF Figure 9. Total Change in Meniscus Height Due to Reaction Versus Temperature for Runs in 3.5% Sodium Chloride Solutions. 10 46 M- ml I.. t.) 230 240 250 260 270 TEMPERATURE, ~F Figure 10. Total Change in Meniscus Height Due to Reaction Versus Temperature for Runs in Normal Synthetic Sea Water.

-38used to determine the line. The total volume change is the difference between the combined volumes of the hemihydrate and product water formed during the reaction and the original volume of the dihydrate before the reaction. Since the observed volume change is the small difference of three relatively large numbers, a relatively small error in one of the individual values would result in a large error in the final value. Such an error could result from the fact that the densities are not known to enough significant places or because the change in densities with temperature was not used. A calculated change of 1% in the values of one of the volumes used in the calculations resulted in a 10% change in the calculated value of the total height of reaction, and could easily account for the difference between the data and the theoretical line. Another very small portion of the difference can also be accounted for by considering the compressibility of the liquid in the system. Calculations showed that a value of 0,08 cm would be reasonable for the amount of liquid used at the temperature and pressure of the system. This amounts to 10% of the total discrepancy of 0.80 cm., Two other hypothetical causes of the discrepancy, which were easily eliminated, are: (1) that the reaction did not go to completion and (2) that liquid was lost from the dilatometer by evaporation. The reactions were shown to have gone to completion by observing the height of the liquid meniscus as a function of time until the second reaction occurred, ie. the transformation of calcium sulfate hemihydrate to anhydrite. Such observations showed that the height remained constant after the first reaction and stopped.until the second reaction had begun, indicating that the first reaction had gone to completion. The fact that

-39very little water was lost from the dilatometer by evaporation can be seen by examining the data given in Figure 8. Each run was made with the dilatometer pressurized at approximately 90 psig. Since the vapor pressure of the solution doubled over the temperature range investigated (i.e. 25.4 psia at 240~F to 41.8 psia at 270~F) under conditions of constant total pressure, the rate of evaporation through the capillary would probably be increased by both the pressure and the temperature effects. On the other hand, the 240~F run lasted approximately 30 hours while the 270~F run lasted only one and one-half hourso This twenty fold increase in the length of time should mask any change in rate of evaporation due to the 30~F increase in temperature and doubling of vapor pressure. Consequently, the run at 240~F should show a greater water loss than the higher temperature runs, resulting in an increased slope of the observed data. Since this was not observed, the loss of water by evaporation was assumed to be negligible. Another characteristic of the total height of reaction hrt tot indicating the consistency between the theoretical and experimental data values, is shown in Figures 11 and 12 where values of hr are plotted tot versus the percent dissolved solids in the solutions surrounding the reaction mixture for reactions run at approximately one constant temperature. The values of hrtot decrease with increasing dissolved solids as predicted by the partial molal volume relationships for sodium chloride solutions, where small additions of pure water to any sodium chloride solution result in a final volume which is less than the sum of the two original uncombined volumeso This relationship is also shown in Figure 12 for synthetic sea water concentrates which should behave similarly since their constituent also is sodium chlorideo

0 9t 8 0 5 10 15 20 24 PERCENT DISSOLVED SOLIDS Figure 11. Total Change in Meniscus Height Due to Reaction Versus Sodium Chloride Solution Concentration..10 9 0 7L.. 8 5 0 15 20 24 0 5 10 15 20 24 PERCENT DISSOLVED SOLIDS Figure 12. Total Change in Meniscus Height Due to Reaction Versus Synthetic Sea Water Concentration.

-41Since each value of hr is directly proportional to the volume change during the reaction, which is proportional to the amount of calcium sulfate dihydrate reacted, hr is proportional to the number of moles of dihydrate reacted or the number of moles of hemihydrate formed. A more convenient way of expressing the amount reacted for further analysis is obtained by normalizing the experimental results by dividing the number of moles of calcium sulfate dihydrate reacted D by the initial number of moles Do, giving the fraction reacted, a = D/Do. In terms of the experimental data, D corresponds to height of reaction hr, and Do to the total height of reaction hr after the reaction has gone to completion, or tot a = hr/ hr. Differentiation of these expressions gives the relationtot ship between the different forms of the reaction rate; d (1/Do)_ = (1/htot (20) dt dt ( (20) Since the experimental results consist of discrete values measured at uniform time intervals, it was necessary to use numerical methods to obtain values of the reaction rate da/dt from the normalized data. This was accomplished by the following second order numerical differential approximation: du Z~ i c~a'n+l - atn1 (21) da) A a n+l tnl 0 -(t) = /At = tn+l - tn-21 The computer program given in Appendix E was used to calculate the normalized data a(t), da/dt,, T, and t from the corrected data hc, tc, and Tc after first calculating values of ht, hr, tr and Tr. Values of a, da/dt, and t, calculated for experimental run number 62 are listed in Table II and plotted as functions of time in Figure 13 and 14 to show the general characteristics of the normalized data obtained by these procedures. The remaining normalized data is given in Appendix To

-42TABLE II VALUES OF a AND da/dt CALCULATED FOR EXPERIMENTAL RUN 62 ON THE TRANSFORMATION OF CALCIUM SULFATE DIHYDRATE TO HEMIHYDRATE AT 2450F IN WATER Time, da m-1 Time, da -1 Min dt min Min dtmn 0..00000.00000 215..81023.00365 5..00180.00012 220..82991.00383 10.. 0019.00022 225..84852.00364 15..00396.00026 230..86628.00344 20..00384.00035 235..88297.00306 25..00744.00044 240..89689.00266 30..00828.00054 245..90961.00250 35..01284.00080 250..92186.00221 40..01632.00102 255..93170.00180 45..02304.00119 260..-93986.00151 50..02820.00152 265..94683.00130 55..03829.00200 270..95283.00132 60..04825.00218 275..96003.00106 65..06013.00257 280..96339.00100 70..07394.00287 285..96999.00082 75..08882.00332 290..97155.ooo65 80..10719.00370 295..97647.00071 85..12579.00387 300..97863.00067 90..14584.00435 305..98320.00048 95..16924.00469 310..98344.00040 100..19277.0049o 315..98716.00037 105..21822.00515 320..98716.00017 110..24426.00534 325..98884.00018 115..27163.00546 330..98896.00023 120..29888.00567 335..99112.00018 125..32829.00573 340..99076.00022 130..35614.00549 345..99328.00010 135..38314.00561 350..99172.00013 140..41219.00561 355..99460.00034 145..43920.00559 360..99508.00013 150..46813.00571 365..99592.00012 155..49634.00571 370..99628.00010 160..52527.00583 375..99688 -.00002 165..55467.00579 380..99604.00008 170..58312.00576 385..99772.00005 175..61229.00573 390..99652.00005 180..64039.00568 395..99820.00026 185..66907.00574 400..99916.00012 190..66775.00541 405..99940.00005 195..72320.00510 410..99964.00002 200..74877.00485 415..99964.00004 205. ~77170.00447 420. 1.00000.00000 210..79342.00385

1.0 0@ *.**.................. -000 ~~~~~1.0 one~~~~~. 0.5 s 0 ~~~~0 *~~~~~~~~~~~ 0 100 200 300 400 w 0 < r.Z -, 0 0 0......'I' I I I I i I I 0 100 200 300 400 500 TIME, MINUTES Figure 13. Fraction of Calcium Sulfate Dihydrate Transformed to Calcium Sulfate Hemihydrate in Water at 245~F During Run 62.

.006 *...I.005 z.004 z 00.003 0.002 * LL 0 I. IJ I.001 *0 0o 0 00 0.. 0.000 1 1 1'1 1 1 ***... t. I -— lI 0 100 200 300 400 500 TIME, MINUTES Figure 14. Variation of the Reaction Rate with Time for Run 62 for the Transformation of Calcium Sulfate Dihydrate in Water at 245'F.

-45B. Experimental Results After all the data were transformed to the normalized form using the IBM 7090 computer, the values of time, temperature, and fraction transformed were read directly from the computer print out. For each experimental run, the temperature of the reaction and the time corresponding to 5%, 25%, 50%, 75%, and 95% transformation were punched on IBM cards to facilitate grouping of the data according to the parameters studied, as shown in Appendix G, to enumerate the effects of (1) temperature, (2) brine solution concentration, and (3) initial particle size. The results pertaining to the dehydration of calcium sulfate dihydrate to hemihydrate are presented first, followed by the results pertaining to the dehydration of hemihydrate to anhydrite. 1. Dehydration of Dihydrate to Hemihydrate The chemical equation representing the dehydration of solid calciums sulfate dihydrate (selenite) to solid calcium sulfate hemihydrate when the sol.ids are immersed in an aqueous solutions is: CaS04 2o20(S) solution CaS041/2 H0(S) + 3/2H20(L). (22) The TTT relationships for this reaction were studied over a range of temperatures from 230~F to 300~F in distilled water, and in solutions containing 0.0,'0.5%, 1.0%, 3.5%, 7.0%, 14.0%, and 21.0% sodium chloride, and, 1.0, 2.0, 3.0,and 4.0 times the salt concentration in normal synthetic sea water according to the composition given in Appendix H. The dihydrate crystal particles used as starting materials were separated between 11 different screens having hole sizes shown in Appendix I. Particles obtained between screens having 0.0082 and 0.0069 inch openings

-46were used for most of the experiments, with other particle sizes being used only in a series of experiments conducted to determine the effect of initial crystal particle size on the reaction. The phases occurring during the experiments were identified by their x-ray diffraction patterns as described in Appendix J. a. Effect of Temperature. The effect of temperature over the range from 250~F to 265oF on the dehydration of calcium sulfate dihydrate to hemihydrate when the solids were in solutions of constant composition is shown by the time-temperature-transformation curves of Figures 15, 16, and 17, for solutions of water, 3.5% sodium chloride, and normal synthetic sea water, respectively. In all three cases, the TTT curves have the same general configuration consisting of five almost equally spaced and parallel curves exhibiting decreasing slope with increasing temperature, The times for a given percent transformation of calcium sulfate dihydrate to hemihydrate, when the solids were immersed in 3.5% sodium chloride solutions and in normal synthetic sea water solutions, are almost identical except that values of the times for the sea water experiments are slightly longer. Even though the values of time for a given percent transformation in water were measured over a slightly higher temperature range, they still exhibit the same general relationship with respect to time as do the values measured for the reaction in 355% sodium chloride solutions and in normal synthetic sea water over the lower temperature range. The 50%-transformation curves from Figures 15, 16, and 17, were redrawn in Figure 18 showing primarily the effect of temperature on the TTT curves for the dehydration of calcium sulfate dihydrate to hemihydrate and, secondarily the effect of the solute concentration on the

-4710' 10 TRANSFORMAT ION' 0 95,oE 75 %o 10 - 0 50% _ LJ) 095% - A 25% o/o v 5% 220 I I I I I I I I 2 220 230 240 250 260 270 TEMPERATURE, OF Figure 15. Time-Temperature-Transformation Curves for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Water.

-4810 TRANSFORMATION O 95% E 75% 10o3- 50 o% A 25% v 5% cn 10 10220 230 240 250 260 270 TEMPERATURE, OF Figure 16. Time-Temperature-Transformation Curves for the Dehydration of Calcium Sulfate Dihydrate to Hemihdtrate in 3.5% Sodium Chloride Solution.

-4910 103ss- 75 % _ I 50% _: QA 25% 10- 220 230 240 250 260 270 TEMPERATURE, ~F Figure 17. Time-Temperature-Transformation Curves for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Synthetic Sea Water.

-50104 w I — - 102 10 — O WATER SOLUTION O SYNTHETIC SEA WATER 3.50/ SODIUM CHLORIDE SOLUTION I I I I I I I I I! 220 230 240 250 260 270 TEMPERATURE, ~F Figure 18. Time-Temperature-Transformation Curves for 50%0 Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Water, in 3.5%o Sodium Chloride Solution, and in Synthetic Sea Water.

-51reaction. For solutions of constant composition, the time for 50%transformation decreases with increasing temperature, and for solutions of variable concentration, the time decreases at constant temperature as the concentration of dissolved solids increases. Since the overall rate of reaction is inversely proportional to the time of reaction, the overall rate of reaction increases with both increasing temperature for constant solution concentration and with increasing concentration of dissolved solids for the reaction occurring at a constant temperature. Further observations were made on the dehydration of calcium sulfate dihydrate to hemihydrate over the temperature range 265~F to 300~F using the temperature response observed in the dilatometer rather than the volume change. The primary reaction under consideration at the time of these observations was the dehydration of calcium sulfate hemihydrate to anhydrite at temperature above 325~F, with the hemihydrate being formed in the dilatometer by the dehydration of the dihydrate. The first reaction occurred almost immediately and was completed long before the dilatometer and its contents reached the steady state temperature of the bath where the second reaction later occurred. The high rate of reaction encountered, as indicated by the temperature response for the dehydration of the dihydrate to the hemihydrate, as well as the transient temperature conditions, made it difficult to determine precisely the beginning and the ending of this reaction, except by graphical means, resulting in data with a high degree of scatter. The results of these observations are shown in Figure 19, 20, and 21, for the reaction when the solids were immersed in water, in 3.5% sodium chloride solutions and in synthetic sea water, respectively. All the curves exhibit the same negative slopes as the previous data except the 5% curve for the reaction in 3.5% sodium chloride solutions

15 1 1 1 I II I I 95% TRANSFORMATION 10 z S - 5% TRANSFORMATION 5 1 5 - -i iu 270 280 290 300 TEMPERATURE, OF Figure 19. Estimated Time-Temperature-Transformation Curves for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Water at High Temperatures.

15 I, - I,' I u, 10 w i - tz c o -^- ^^ y5 % TRANSFORMATION Z __ r':'l ~ 950~/0 TRANSFORMATION 270 280 290 300 TEMPERATURE, ~F Figure 20. Estimated Time-Temperature-Transformation Curves for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in 3.5% Sodium Chloride Solution at High Temperature.

15 n 1 95% TRANSFORMATION Z _. z 5 - 5% TRANSFORMATION tures. tures.

-55which exhibits a positive slope, and is probably in error due to the experimental uncertainties enumerated in the preceding paragraph, Analysis of these curves'shows that the overall rate of reaction continues to increase with increasing temperature for the reaction in solutions of constant concentration, and with increasing concentration of dissolved solids for conditions of constant temperature, bo Effect of Concentration, The dehydration of calcium sulfate dihydrate to hemihydrate was observed at 240~F when the solids were immersed in aqueous solutions of sodium chloride and in synthetic sea water concentrates ranging in concentration from water (actually dilute calcium sulfate solutions) to':solutions containing up to 21% dissolved solidso The effect of the solution concentration is shown in Figure 22 for aqueous sodium chloride solutions, and in Figure 23 for synthetic sea water concentrates, The three curves shown in Figure 22 for sodium chloride solutions, all have the same general shape. Each curve starts from the time value corresponding to the reaction occurring in water and decreases with increasing solution concentration, exhibiting a continuously decreasing negative slope. Likewise, the three curves for the synthetic sea water concentrates shown in Figure 23 exhibit the same general characteristics as those shown in Figure 22 after they were extrapolated to the value for pure water, The data for the reaction in synthetic sea water concentrates and sodium chloride solutions fall on the same curves as shown in Figure 24 when the activities of the water in the solution surrounding the reacting solids were used rather than the weight percent dissolved solidse The individual data points for the sodium chloride solutions tend to lie

-56500 ['' 1 1 I I I I 1 TRANSFORMATION 0 95% O 50% P\I o 5 % 100 50 I- 0 I0 0 5 10 15 20 25 WEIGHT PERCENT SODIUM CHLORIDE Figure 22. The Effect of the Concentration of Sodium Chloride Solutions on the Transformation Time for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate at 240~F.

-57500 I II TRANSFORMATION 0 95% X o50% 0 5% \\ \\l 100o \ w I —:\ \ 7|'I o5 10 0 5 10 15 20 25 WEIGHT PERCENT DISSOLVED SOLIDS Figure 23. The Effect of Concentration of Synthetic Sea Water on the Transformation Time for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate at 240~F.

-58 104 _O II I I XI I O SODIUM CHLORIDE SOLUTION D SYNTHETIC SEA WATER c () w 10 950% TRANSFORMATION -50% i TRANSFORMATION' - \ * i 2 -r* 5.5, TRANSFORMATION 10 -L -I- I-l -I- I -I- I —\ I I 1.0 0.9 0.8 WATER ACTIVITY Figure 24. The Effect of the Activity of the Water in Solution on the Transformation Times for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate at 240~F.

-59slightly above the curves, and those for the synthetic sea water tend to lie slightly below. These small trends could be due to the normally expected scatter in the data or to some secondary effect, such as the presence of additional ions in the synthetic sea water, or to slight inaccuracies in the calculated activities for the water in either or both of the solutions. Examination of the free energy relationships for the transformation of calcium sulfate dihydrate to hemihydrate shows that only the activity of the product water should be affected by changes in the solution surrounding the solids since the activity of a pure solid is unity. Thus, besides temperature, the activity of the water in solution is a major variable for this reaction, as well as other dehydration reactions, possibly even for phase equilibria between hydrates and aqueous solutions. The activity of the water in the solutions discussed above was calculated from the following relationships: a = f/fo (f/p)p/(f/p)opo = P/Po (23) where a is activity, f is fugacity, (f/p) is fugacity coefficient, and P is the vapor pressure of the solution. The variables represent the properties of the various brine solutions while the superscripted variables represent the properties of pure water. Values of the ratio P/Po for sodium chloride solutions were calculated from vapor pressure data given in the International Critical Tables.(97) The data were correlated by the method shown in Appendix K yielding the following relationships based on the method introduced by Cox:(43) P/P~ = 1 - 0.643 X for < X < 0.10 (24)

-6o - P/P~ = 0.962 - 2.93 X2 for 0.10 < X < 0.25 (25) where X is the weight fraction of dissolved solids. A similar relationship was available in the book "The Oceans"(85) for sea water with the vapor pressure ratio expressed in terms of chlorinity, where Y = the grams of chlorine (Cl-) per 1000 grams of solution: P/P~ 1 1 0.00096 Y. (26) The effect of concentration on the overall rate of reaction can be obtained from the TTT curves shown in Figures 22, 23, and 24 by using the fact that, the overall rate of reaction is inversely proportional to the total time of reaction, estimated by the time difference between the 5% and the 95% transformation curves. In both cases, the rate of reaction increases with increasing solution concentration or decreasing activity of the water in the solution. The increase occurs very quickly for small additions of sea water salts or sodium chloride to very dilute aqueous solutions and less quickly for concentrated solutions approaching saturation. The effect of concentration on the time required for initiation of the reaction can also be seen by using the 5% transformation curves as a first order estimate of the initiation time. In both types of solutions, the time for initiation decreases very quickly for small additions of solute when the solutions are dilute, but much less spectacularly as the solution concentration approaches saturation. c. Effect of Initial Particle Size. The effect of initial particle size on the dehydration of calcium sulfate dihydrate to hemihydrate while the solids were immersed in water was studied under conditions

-61of approximately constant temperature by varying the size of the dihydrate crystallites comprising the original sample. Crystal fragments were obtained between screens having; 0,0, 0.0021, 0,0029, 0.0035, 0o0041, 0,0058, 0o0069, 0.0082, 0o0116, 0o0138, and 0,0164 inch openings. As shown in Figure 25, a minimum time for the reaction occurred, for each curve of constant transformation for samples collected between screens having 0.0116 and 0,0082 inch openings indicating a maximum overall rate of reaction for initial particles of this size range. This effect of initial particle size on the reaction indicates the possibility that two independent processes are occurring, one limiting the rate at the beginning of the transformation and the other at the end. As shown in the next chapter, the reaction occurs by nucleation of hemihydrate on the surface of the crystal with subsequent growth of the hemihydrate phase through the parent dihydrate crystal. When the reacting particles are large, the rate of nucleation is low due to the small surface area available for nucleation and the transformation results primarily by a large amount of growth of a few nuclei, On the other hand, when the reacting particles are small, the rate of nucleation is high due to the large surface area, but the transformation results primarily by a small amount of growth of a large number of nuclei. Thus, at one end of the spectrum, the rate of nucleation is controlling and at the other end growth rate is controlling, with a maximum rate existing some place in between. Consequently, the time for a given amount of reaction, which is inversely proportional to the rate of reaction, exhibits a minimum when plotted as a function of particle size as shown in Figure 25.

-62300 rT | I | 1 1 1 1| TRANSFORMATION 95% - 50% 0 5% 250 D 200 s 150 100 — 0. 50 50 O 0, I I I I I I I 0.0050.0100.0150.0200 AVERAGE SCREEN OPENING, INCHES Figure 25. The Effect of Dihydrate Crystal Fragment Size as a Function of Screen Opening on the Transformation Time for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Water at 250~F for Washed Samples.

-63 Assuming that the overall rate of reaction is directly proportional to the maximum rate of reaction, then the values of the maximum rate of reaction should be inversely proportional to the total time for the reaction and should exhibit a maximum when plotted as a function of initial particle size. This characteristic is shown clearly in Figure 26 where the values of the smoothed maximum rate of reaction are plotted versus initial particle size, indicating a good degree of consistency between the different forms of the data obtained in these studies. 2. Transformation of Hemihydrate to Anhydrite The chemical equation representing the dehydration of calcium sulfate hemihydrate to calcium sulfate anhydrite when the solids are immersed in aqueous solutions is: CaSO0 l/2H20(S) solution, CaSO(S) + 1/2H 0(L) (27) To study the TTT characteristics of this reaction, calcium sulfate hemihydrate was formed in the dilatometer reaction bulb at the beginning of each experimental run from a sample of dihydrate crystals separated between screens having 0.0116 and 0.0082 inch openings. Experimental runs were made at temperatures of about 325~, 340~, and 347~F in water, in 3.5% sodium chloride solution, and in synthetic sea water. The dilatometric procedures used for these runs were identical to those previously described except greater care was required in estimating the amount of solution to be added to the dilatometer to keep the meniscus within the length of the capillary during the entire experiment. This was necessary because three volume increases occurred: that due to the thermal expansion of the dilatometer's contents, that due to the dehydration of the

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-65dihydrate to the hemihydrate, and that due to the dehydration of the hemihydrate to the anhydrite. The effect of temperature on the dehydration of calcium sulfate hemihydrate to anhydrite is shown in Figures 27, 28, and 29, for the reaction where the solids were immersed in water, in 3.5% sodium chloride solutions, and in synthetic sea water, respectively. Over the temperature range covered by these experiments, the TTT curves for water, sea water, and sodium chloride solutions are straight lines with negative slopes, except for the 5% transformation curve for water which has a positive slope, and is probably in error. Analysis of the shapes of the curves and their relative orientation shows that the overall rate of reaction for the dehydration of calcium sulfate hemihydrate to anhydrite increases with increasing temperature. Conversely, the time for reaction decreases with increasing temperature. The reaction is also accelerated by increasing the concentration of the solute in the solution containing the reaction mixture. The time required for a given fraction transformation at a given temperature is considerably longer in water than in normal synthetic sea water where it is only slightly longer than in the 3.5% sodium chloride solutions, as shown in Figure 30 where the 50% transformation curves for these three cases are presented together. 3. Comparison of Results The relationship between the time-temperature-transformation results for the dehydration of calcium sulfate dhydrate e to hemihydrate, and hemihydrate to anhydrite is shown graphically in Figure 31 where the 50% transformation curves are plotted for each reaction where the solids

-66-,3 10 C/) zr to0- TRANSFORMATION t0 E]T 95% / 0 5 % tF~ ~o 50/% 345 550 330335 340 TEMPERATURE, OF Te2e7. TemperstureTrnsformation Curves for the Figure 27 hydrtion of Calcium Sulfate emirte to Anhydrite in Water.

-67TRANSFORMATION o 95% o 50% 0 5% 102 13250 350 340 345 350 325 330 350 340 345 350 TEMPERATURE, OF Figure 28. Time-Temperature-Transformation Curves for the Dehydration of Calcium Sulfate Hemihydrate to Anhydrite in 3.5% Sodium Chloride Solutions.

-68TRANSFORMATION E 95% 0 50% o 5% 103 LL) 102 0 I I I I I I 325 330 335 340 345 350 TEMPERATURE, OF Figure 29. Time-Temperature-Transformation Curves for the Dehydration of Calcium Sulfate Hemihydrate to Anhydrite in Synthetic Sea Water.

-69 104 w - UJ - t- _ Id lo' 0 WATER E SYNTHETIC SEA WATER O 3.5% SODIUM CHLORIDE SOLUTION I, 1 l I I I I I.1 I II I I.i 10 325 330 335 340 345 350 TEMPERATURE,OF Figure 30. Time-Temperature- 50% Transformation Curves for the Dehydration of Calcium Sulfate Hemihydrate to Anhydrite in Water, in 3.5% Sodium Chloride Solution, and in Synthetic Sea Water.

1000 -0 1000 DIHYDRATE TO HEMIHYDRATE c) Z. HEMIHYDRATE TO ANHYDRITE I00 too 0 WATER SYNTHETIC SEA WATER | 3.5% SODIUM CHLORIDE SOLUTION 10 200 250 300 350 TEMPERATURE, ~F Figure 31. Summary of Time-Temperature-Transformation Results for 500 Dehydration.

-71were immersed in water, in 355% sodium chloride solutions, and in synthetic sea water. The 50% transformation curves for each reaction occupy the same relative positions to each other with respect to time: the reaction in water requiring considerably more time than the reaction in synthetic sea water whichin turn, requires slightly more time than reaction in 355% sodium chloride solution. The relative positions of the two sets of curves show that when the two reactions occur consecutively as under the conditions used here: the dehydration of the dihydrate to hemihydrate goes to completion before the dehydration of the hemihydrate to anhydrite starts,

V. DIHYDRATE TO HEMIHYDRATE TRANSFORMATION MECHANISM While the time-temperature-transformation data describe the overall kinetics of the transformation processes, they do not fulfill the traditional objective of a kinetic investigation which is the derivation of an appropriate rate equation based on the mechanism of the reaction being studied. For this purpose information on the nature of the transformation mechanism is needed. It was found that this could be obtained for the dehydration of dihydrate to hemihydrate from microscopic observations of dihydrate crystals during the transformation process. Ao Experimental Procedures These microscopic observations were carried out in a special cell designed to duplicate as nearly as possible the conditions of temperature and pressure used in the dilatometric experiments while permitting observation of the transforming crystals with an optical microscope. As shown in Figure 32, this reaction cell was formed by a neoprene rubber 0-ring and two optically flat quartz disks which were clamped. together by a set of brass spacers and flanges designed to support the cell on the stage of an inverted column optical metallograph and to conduct heat from an electric heater to the cell. The temperature of the reaction mixture inside the cell was recorded at 5-second intervals using the same recording potentiometer used in the dilatometric studies and a copperconstantan thermocouple made from 30 gauge wires inserted through the 0-ring. The crystals were photographed simultaneously with the recording of the temperature at either one or five minute intervals, depending on the rate of transformation, using the synchronizing system previously described -72

HEATER - CRYSTAL -T\ / - THERMOCOUPLE SUPPORT FLANGE L- ____ O-RING | \STAGE MICROSCOPE FLANGE OBJECTIVE OBJE —CV uQUARTZ WINDOWS I I Figure 32. Reaction Cell Used for Microscopic Observations of Phase Transformation.

-74and a 35 mm through-the-lens reflex camera attached to the ocular tube of the metallograph. Polarized light was used to achieve maximum contrast and best delineation of the phases. Magnification was determined by means of a standard B & L metric stage micrometer slide, Temperatures were read directly from the chart of the recording potentiometer, using a 15X magnifying glass to facilitate interpolation, while the time intervals between photographs were determined from the known chart speed of onethird inch per minute, B. Experimental Results The general characteristics of the mechanism involved in the transformation of calcium sulfate dihydrate to hemihydrate were observed and photographed using thin rhombic crystals (approximately 1 x 1 x 0,05 mm in size) of optical grade selenite (CaSOi';2H20) which were similar to those used in the dilatometric experiments. A number of such crystals were sealed in the appropriate liquid medium in the reaction stage and heated quickly into the temperature range from 2500F to 275~F and photographed at appropriate time intervals. Because of their plate-like shapes they generally laid flat on the bottom of the chamber and could therefore be viewed only in a direction perpendicular to the (010) cleavage planes. Figure 33 consists of a series of micrographs showing the transformation of two crystals. In these micrographs the larger crystal is oriented with its (001) cleavage planes parallel to the vertical edges of the micrographs, and its (100) cleavage planes slightly skew to the top and bottom edges. During the first 10 to 20 minutes, -while the temperature of the reaction mixture increased rapidly, considerable material apparently

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-77(j) Time 36 min 269O0~F, (i) Time 34 min~ 268.4~F. WIN, (k) Time 8 min. 269 8~F. (I) Time 40 min 270 F Figure 55 (CONT D)

-78(m) Time 45. min, 271 8~F0 (n) Time 50 min, 272.2~F. (o) Time 55 min~ 272~8~F (p) Time 60 minx 275}2~F~ Figure 55 (COITrn) ~i~~~~~~~:~P ---------

-79deposited from solution onto existing crystals, as evidenced by the marked growth of the smaller crystal, by the disappearance of the randomly oriented scratches and abrasions initially present on the surface of the larger crystal, and by subsequent development of striations parallel to the (100) cleavage planes of the larger crystal. The first hemihydrate nucleus developed in the upper central portion of the larger crystal after about 25 minutes and can be seen in micrograph 335c Additional nuclei developed shortly thereafter at various locations throughout the larger crystal. These nuclei all appeared initially as thin black lines parallel to the (100) planes which grew very rapidly in length, usually penetrating a major portion of the distance through the crystal before developing appreciable widtho They then slowly increased in width, appearing as white bands having sharp black outlines, and ultimately grew into one another, consuming the entire dihydrate crystalo After the transformation was substantially complete, the aggregate of hemihydrate crystals began to break into fragments. Evidence that the solution is involved to some extent in the transformation process was provided by the dissolution of the smaller crystal during the last 15 minuteso This crystal did not transform to hemihydrate but remained as dihydrate and apparently dissolved once the concentration of ions in solution began to decrease toward the concentration for equilibrium with the less soluble hemihydrateo The growth of some of the hemihydrate needles beyond the boundaries of the parent dihydrate crystal indicates the process of the precipitation of calcium and sulfate ions from the solution onto the hemihydrate phaseo

-80The numerous tiny black flecks which appeared after about 20 minutes and increased in size and number throughout the remainder of the reaction are believed to be small hemihydrate crystals which nucleated either in the solution or from it onto the surface of the glass cover plate of the reactor, These processes involving transfer and precipitation of calcium and sulfate ions in solution appeared to constitute only a small fraction of the total transformation process, however, and it was concluded that the principal transformation mechanism consisted of the nucleation and growth, of plate-like or needle-like hemihydrate crystals within the dihydrate crystals, The cross-sectional shapes of hemihydrate needles were examined by observing the transformation process in large (about 1 x.3 x.3 cm) dihydrate cyrstals which had been cut and polished to produce a surface perpendicular to the axial direction of the hemihydrate needles (i.e. perpendicular to both the (100) and (010) planes of the dihydrate crystals), The initial cutting of this surface was done with a fine jewelers' saw using water as a lubricant. The crystals were then embedded in a 50-50 mixture of carnauba wax and rosin, the cut surface was carefully polished down to Linde-B grade alumina on metallographic wheels, after which the wax was removed by immersion in boiling water. The crystals were then placed in the microscope reaction stage with the polished surface resting on the bottom quartz plate, and the nucleation and growth of the hemihydrate needles was observed and photographed as described above. Typical micrographs are reproduced in Figure 34. As shown, most of the needles observed had cross sections which were elongated hexagons whose widths ranged from two to three times their thickness, and whose long edges were parallel to the (010) cleavage planes of the parent dihydrate crystals.

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-82(c) Micrograph 13 O0 (d) Micrograph 120 5 Figure 34 (COTMD)

-83 F~~~~~~;:: ~~~~-::::-;ue: ~%002 ~!:.diD Sk-:-:is\ f <\0 te~'~~~~~~~::~c $*: X',I a~~:-:~| " E^ i | | M g| 0! r!X~~n "n~~- ~ ~ W D~~'~::S ~ D s-.jf.0 g i n~~~~~~~~~~~~~~ ( A) Mu eroFgraph e 22 Figure 34 (C()IZ:D )

-84(g) Micrograph 4. 02 I~~~~~~~~~~I'gow<~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~g- ~ ~ ~ ~ ~ ~ ~ ~: ii11 (h).cogap 102 Fgr4 I\ID Jim~~~~~,

-85In some cases the hexagonal shape was not fully developed; however, this was attributed to localized effects, particularly at the polished surface, and it was concluded that in general the hemihydrate phase consists of long needles with elongated hexagonal cross sections. The needles' axes appeared to run parallel to the direction defined by the intersection of the (100) and (010) cleavage planes of the dihydrate crystals and the long, cross-sectional direction was parallel to the (010) planes as shown schematically in Figure 35, This needle-like shape is consistent with the crystal sturcture of the hemihydrate phase and with the shapes of the hemihydrate crystals shown in Figure 36 which were observed in the solution near one of the large dihydrate crystals. In addition, the large crystal in Figure 34f appears to have developed a cross-sectional substructure of hexagonal units. It was also noted that a number of hemihydrate needles usually appeared side by side, with somewhat irregular spacings but apparently on the same (010) cleavage plane, even in the large dihydrate crystal. This appeared to be due to inherent imperfections or incipient cleavage of the particular planes, and would be expected to be more pronounced in the smaller dihydrate crystals used in the dilatometric experiments. To provide a basis for subsequently developing a kinetic equation, the rates at which the hemihydrate needles grew in thickness UA width UB, and length UC, corresponding respectively to the rates of growth in the A, B, and C directions of Figure 35, were determined as a function of temperature from measurements of the dimensions of the growing needles in the sequential micrographs. The calculated values of 215 individual measurements are given in Appendix M and the average values are summarized in Table III and Figure 37. These results show that the

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-88TABLE III VALUES OF AVERAGE LINEAR GROWTH RATES OF HEMIHYDRATE CRYSTALS WITHIN DIHYDRATE CRYSTALS IMMERSED IN WATER Average Micro. Direction Average Rate Reciprocal of No. Measured Temp. ~F cm/min Avg. Temp. ~K3. A 253.61.00002.0025235 3. A 253.61.00001.0025235 4. A 253.60.00001.0025235 12. A 278.94.0001.0024369 12. A 278.94.0001.0024369 13. A 279.71.00009.0024344 3. B 253.61.000031.0025235 3. B 253.61.000036.0025235 8. B 261.44.oooo00061.0024961 9. B 271,02.00017.0024634 10. B 273.59.00025.0024547 11. B 274.70.00034.0024510 12. B 278.94.00041.0024369 12. B 278.94.00025.0024369 13. B 279.71.00039.0024344 14. C 255.82.00376.0025157 6. C 258.42.00392.0025066 7. C 260.87.00494.0024980 8. C 261.52.00508.0024958 9. c 271.02.00612.0024634 10. c 273.59.00743.0024547 11. C 274.55.00693.0024515

-8910 L L -r w ^4 U 10_.00243.00245.00250.00253 TEMPERATURE', KK' I I I I I I I 280 270 260 250 TEMPERATURE, OF Figure 37. Arrhenius Plot for the Linear Growth Rates UA UB, and UC for the Transformation of Calcium Sulfate Dihydrate to Hemihydrate in Water.

-90rate of growth in width UB was from 2 to 3 times greater than the rate of growth in thickness UA, while the rate of growth in length Up was from 20 to 120 times greater than UB, depending on the temperature. Plots of the logarithms of the rates versus the reciprocal of the absolute temperature gave reasonably good straight lines as shown in Figure 37, indicating that the temperature dependence of the growth rates could be described by equations of the form in U = In Z - E/RT or U= Zexp(-E/RT), in which the constants Z and E have approximately the values shown in Table IV. TABLE IV VALUES OF Z AND E CORRESPONDING TO FIGURE 37 Rate, cm/min Z, cm/min E, Kcal/gm mole UA 3.97 x 1020 46.2 A UB 1.17 x 1026 55.4 UC 1.65 x 108 19.3 By analogy, the Z's may be interpreted as pre-exponential factors and the E's as activation energies in classical Arrhenius equations for the respective growth processes. C. Derivation of the Kinetic Equations From these results it is possible to develop a model of the transformation mechanism which can be used as the basis for formulating the desired kinetic equations. To facilitate the mathematical analysis, it is convenient to highly idealize the model.

-91lo Model of the Transformation Mechanism In the model adopted, the transformation process is considered to start with the formation of hemihydrate nuclei on the (001) cleavage planes of the dihydrate crystals. Based on the micrographs of Figure 33, and the relative values of UA, UB, and UC, the nuclei are considered to propagate almost instantaneously through the entire lengths of the tiny dihydrate crystals along (010) cleavage planes before they attain appreciable thickness, so that negligible material is transformed by the time the growth in the C direction is completed. Instead, virtually all of the dihydrate phase is transformed by subsequent slower growth of the nuclei in the A and B directions, during which they develop as needles having elongated hexagonal cross sections with interfacial angles of 120~, as indicated in Figure 35. Since a large number of nuclei develop in each dihydrate crystal, this cross-sectional growth must terminate when they encounter one another or the edges of the dihydrate crystals. Because of the apparent tendency for numerous nuclei to form on the same (010) plane, and because UB is several times greater than UA, it is considered that these encounters occur first in the B direction. When the material surrounding the needles at the time of initial encounter is subsequently transformedeach needle will, in effect, have produced a hemihydrate subcrystal of rectangular cross section. Thus, a fully transformed dihydrate crystal is considered to consist of numerous hemihydrate subcrystals having average dimensions a, b, and c measured parallel to their A, B, and C axes, as indicated in Figure 35. The value of c will equal the average length of the hemihydrate crystals. The values of a and b will depend on the relative rates of nucleation and growth, and will therefore probably vary with temperature. Because the dihydrate crystals are

-92considered to have idealized shapes with plane external faces, the volume of the average subcrystal will be simply V = abc. 2. Formulation of Equations As indicated in the theoretical discussion, the total volume of hemihydrate formed can be expressed as a function of time by an equation of the form: x = t V(t) = dN/dx v(x,t)dx (28) x =0 where dN/dx is the nucleation rate and v(x,t) is the volume of an individual hemihydrate needle. Since it is necessary to deal simultaneously with the nucleation process and a multi-stage growth process, several time variables are utilized. Times referring explicitly to the nucleation process are designated by the variable x which is assigned the value of zero at the instant the first nucleus forms. The overall time of reaction, or the "time of observation", is designated by the variable t which is defined such that t = 0 when x = 0. The period of growth for a particular needle at any instant of observation will thus be equal to (t-x), the difference between the time of reaction at that instant and the time at which the needle nucleated, so that v(x,t) will in general be an explicit function of (t-x). Likewise,periods for the various stages of the growth process delineated by the impingement phenomenon are expressed as (t-y), (t-z), and (t-w), where y, z, and w are time variables each assigned to a different growth stage and each being equal to zero when t = 0. Dividing Equation (28) by Vtot the total volume of hemidydrate formed upon completion of the reaction, gives the fraction transformed a = V(t)/Vtot which corresponds to the dilatometric data. Differentiation

-93with respect to time then gives the desired kinetic equation for the rate of transformation da/dt. It is therefore now necessary to proceed to formulate expressions for these various functions, based on the theoretical model just described. a. Rate of Nucleation. The experimental observations indicated that nucleation occurs predominately on the (001) cleavage planes which form two of the edges of each dihydrate crystal in the polycrystalline sample. Initially the rate of nucleation will be proportional to No the total number of available nucleation sites, which will be proportional to the total area of such surfaces in the sample. After nucleation has started and N nuclei have formed, the rate will be proportional to (No-N) the number of nucleation sites still available at a given time x, or: dN/dx = K(No - N) (29) where K is the nucleation rate constant. The rate of nucleation, expressed as an explicit function of time is obtained by separating the variables: N=N =x dN/(No-N) - K dx (30) J N=O J x=O and integrating to obtain: N=N x=x - [ln(No-N)] = K[x] (31) N=O x=0 or ln(No - N)/N = -Kx (32) Writing this in exponential form gives: (No - N)/No = exp(-Kx) (33)

-94which yields: N- NO[l-exp(-Kx)]. (34) Differentiation of this equation with respect to time gives the following desired expression relating nucleation rate and time: dN/dx = NoK exp(-Kx). (35) The validity of this equation can be examined by comparing it with Equation (29) which defines dN/dx, as the difference of two integer variables, N and No. Equation (35) which is continuous with respect to time, can be considered a valid approximation to Equation (34), if, and only if, the value of No is large, so that the time between successive values of N (i.e. N and N+l) is small for most values of N. An analytic expression for the time between N and N+l can be obtained by solving Equation (32) for x(N) and for x(N+l), and subtracting to obtain the corresponding difference in time: Ax = x(N+l)-x(N) = (l/K)ln [(No-N)/(No-N-l)]. (36) This shows that the change in time corresponding to a unit change in N depends on K, No, and N. Assuming that a time increment of one minute or less would provide a sufficiently accurate approximation of the discontinuous function by the continuous one, and choosing K = 0.01 min, a value less than any reported to date, then the solution of Equation (36) is No-N = 101. Thus, for a sample containing less than 101 hemihydrate needles, the time between successive increments of N would be greater than the one minute chosen as the maximum acceptable time difference. For samplescontaining more than 101 needles, the

-95equation would be valid [(No-10l)/No] 100% of the time. In these studies there was considerably more than one nucleus per original crystal, and there were approximately 211,000 initial crystals per sample as calculated in Appendix P; therefore, the above equation should be acceptable more than 99 percent of the time, which is more than sufficient. b. Volume Transformed per Nucleus. Calculation of the volume transformed per nucleus, based on the assumed model, is considerably simplified by the instantaneous propagation of the nuclei in the C direction, since only the rates of growth in the A and B directions then need be considered the overall rate determining growth factors. Further simplification is achieved by choosing a symmetrical cross section for the growing hemihydrate needles and an idealized shape for the parent dihydrate crystals. Thus,the volume of a hemihydrate needle is equal simply to its length c multiplied by its cross-sectional area. This cross-sectional area is equal to 2A(2B) - 2A2/J, where A and B are the dimensions of the needle in their respective axial directions, as defined in Figure 355 giving va = 4 ABc - 2A2c/J3. This can be made time dependent by substituting UA(t-x) for A, and UB(t-x) for B, givingva(x,t) = (2 UAUB - U/3)2c(t-x)2. (37) The subscript "a" is affixed to this equation to call explicit attention to the fact that it accurately represents the volume of a growing needle only during the initial stages of growth prior to the time when impingement occurs. Thereafter, the expression for the volume transformed must be corrected. This can be done by considering growth in time to

-96continue according to Equation (37) and subtracting from va(x t) the amount by which this continuously expanding hypothetical volume of the needle in question interpenetrates other needles. c, Total Volume of Hemihydrate Transformed. Before making this correction for impingement, however, it is convenient to combine Equations (35) and (37), as indicated by Equation (28), to obtain a basic equation for the total volume of hemihydrate formed, as follows: x=t Va (t ) WaK exp(-Kx)(t-x)2dx (38) x=O where Wa = 2Noc(2UAUB - UA/35). This can be evaluated by two successive integrations by parts, using the standard relationship fudv = uv - fvdu For the first integration u = (t-x)2, du = -2(t-x)dx, v = -(1/K) exp(-Kx), and dv = exp(-Kx)dx, giving: Judv = -(l/K)(t-x)2 exp(-Kx) - (2/K) f(t-x) exp(-Kx)dx The integral in this equation can be evaluated by choosing u = (t-x) du = -dx, v = -(1/K) exp(-Kx), and dv = exp(-Kx)dx, giving as the final solution: Vl(t) = Va(t) = Wa[2/K2 - 2t/K + t2 - (2/K2) exp(-Kt)]. (39) The physical significance of Equation (39) and its relationship to Equations (35) and (37) is illustrated schematically in Figure 38. Each curve ki represents the growth curve described by Equation (37) for a particular nucleus which formed at time xi and grew to a volume

-97t / a0 3 FzoI / D k x0x2 x3 x4 X1 t TIME Figure 38. Schematic Representation of the Relationships Between the Functions dN/dx, va(xt)i, and Va(t') i Va(t) ~

-98v. at the time of observation t. The variation in density of the Xi along the time axis represents the variation in nucleation rate with time, as given by Equation (35). The result of the integration is the sum of the v.'s which is equal to Va(t) for any value of t 1 d. Correction for Impingement. As indicated above, Equations (37) and (39) do not include the necessary correction for impingement of the growing needles as they increase in size and number and ultimately consume the entire parent dihydrate crystal. This correction is relatively simple to accomplish using the concept of the average transformed subcrystal, since it amounts only to calculating the amount by which the growth volume described by Equation (39) extends beyond the volume of a coaxial average transformed subcrystal. These calculations can conveniently be carried out in three stages, corresponding to the stages of growth of the extended needle volume shown in Figures 39c, e, and g, where the cross section of a growing hexagonal needle is shown schematically in relation to the cross section of the average transformed subcrystal it will ultimately produce as its net contribution to the transformation. Equation (39) will represent the actual volume of a growing needle only during the time when B < b/2 and (t-x) < 01, corresponding to Figure 39. According to the transformation model, impingement is considered most likely to occur first in the direction of the B axis when (t-x) = Q1 = b/2UB and B = b/2, as indicated in Figure 39b. Thereafter it is necessary to subtract twice the volume corresponding to the triangle LMN of Figure 39c from va(x,t). The area of triangle

L IL,L PtU PK)PUBP H B- A 0- K -' K J (t-x)< < xk (a~) (c),< (t-x) <, 3L (-X)>'L (e) (g) L I M( b/2 (t-x),= =b/2UB (t-x) = UB-UA// -) 2 (b) (-x) =8 a/2UA (d) Figure 39. The Relationships Between the Different Stages of the Impingement Process, the Geometry of a Growing Hemihydrate Needle, and the Transformed Hemihydrate Subcrystal.

-100LMN is equal to (LP)(MN)/2 (LP)2(LP)cot()0~)/2 = (B-b/2)2 43, and the corresponding volume is v = 2c 43 (B-b/2)2 In order to make this equation time dependent, both B and b/2 must be expressed as functions of timeo B represents the hypothetical total distance the needle would have grown in the B direction if impingement had not occurred, and as before is equal to UB(t-x). The term b/2 represents the actual distance of growth in the B direction up to the instant of impingement, and therefore can be expressed as b/2 = UB(y-x), where y is a new time variable referring explicitly to the initiation of the impingement and interpenetration process, i.e. y = 0 when t = 0 With these substitutions, the time dependent equation: Vc(y,t) = 2c f3 UB(t-y) (40) is obtained as the correction per hemihydrate needle, The correction Vc(t) to be applied for the total volume of hemihydrate formed can be calculated by incorporating this expression into an equation of the form: /y=t Vc(t) = \ dN/dy vc(yt)dy (41) where dN/dy is the rate of impingement. Since the model uses idealized hemihydrate needles transforming idealized subcrystals, the rate of impingement is equal to the rate of nucleation, except that the impingement starts @1 minutes later than the nucleation. Thus, dN/dy = KNoexp[-K(y-Gl)]. Substituting into Equation (41) gives: V(t) =texp[-K( (ty dy VC(t) = WC-K \ exp[-K(y-91) I(t-y)2dy (42) }y=9-1

-1012 where Wc = 2 cNoUB \3 o Integration by parts and evaluation, taking the lower limit of integration as 01 = b/2UB, yields: Vc(t) = We {2/K2 - 2(t-01)/K + (t- 1)2 - (2/K2)exp(-K(t-Gl))} for t > (43) The physical significance of this equation and its relationship to the functions vc(y,t), dN/dy, and Va(t) are shown schematically in Figure 40. Each curve 1. represents the volume correction to be added to a particular nucleus which formed at xi, experienced impingement at yi, and was observed at time t. The variations in densities of the yi along the time axis represent the variations in impingement rate with time. The result of the integration is the calculated sum of the vc(xt)i which is equal to Vc(t) for any particular time t The time of impingement for the needles which formed at time zero representsthe limiting case where y = 91 o The corrected volume incorporating this first correction is: V2(t) Va(t) - Vc(t) for t Q1 ~ (44) To facilitate mathematical operations, it was convenient to calculate Vc(t) for all (t-x) > Q1. As shown in Figure 39, however, once (t-x) becomes greater than O2, the triangle LMN becomes greater than that part of the cross-sectional area of the extended needle which is outside the average transformed volume by an amount corresponding to four times the volume associated with the triangle MQR, and the continued use of Equation (44) results in an over correction, It is therefore

-102^ / 10(!t) / l / (X=Vo(t)V()-Vc(t) Vx I - VC(Xlt^ FE L _____yo Yz3Y4 YN v C(xt)n -VC/t) TIME Figure 40. Schematic Representation of the Relationships Between the Functions dN/dy, Vc(yt)i, Vc(t), Va(t) and V(t).

-103convenient to correct for this condition by adding to Equation (44) a term Ve(t) based on the volume given by 4c times the area of triangle MQR The area of triangle MQR is equal to (MQ)(QR)/2 = (MQ)2tan(30~)/2 = (MQ)2 \3/6 = (J3/6) [f3 B-A-b v3/2], and the corresponding correction volume per needle is ve = 2c J3 (B-A/\3 - b/2) The time dependent form of ve is obtained by substituting UB(t-x) for B and UA(t-x) for A, giving ve = 2c f3 [(UB - UA/N3)(t-x) - b/2]2. Since b/2 is a specific value of B-A/l3, it corresponds to (UB - UA/\3)(t-x) when t equals z, which is the time when the impingement process changed for the hemihydrate needle which nucleated at time x o The time dependent equation for the volume per needle now becomes: ve(z,t) = 2c J3 (UB - UA//3)2 (t-z)2 (45) The corresponding expression for the total correction is: z=t Ve(t) = dN/dz ve(z,t)dz o (46) Tz=2 The rate of initiation of this change in the impingement process dN/dz will have the same form as the rate of nucleation but will start 02 minutes later in time for each needle, It can therefore be expressed mathematically as dN/dz = KNo exp[-K(z-02)] o Substituting the values of dN/dz and the ve(z,t) into Equation (46) gives: z=t Ve(t) = WeoK exp [-K(z-92)] (t-z)2 dz (47) 2z=92

-104where We = 2c No(UB - UA/\3)2 Integration by parts yields: Ve(t) = We {2/K2 - 2(t-2)/K + (t-2)2 (48) - (2/K2) exp [-K(t-92)]} where G2 = (b/2)/(UB - UA/3) Adding this to Equation (44) gives: V3(t) = Va(t) - Vc(t) + Ve(t) for t > 92 (49) as the revised expression for the corrected volume. Impingement occurs in the A direction when (t-x) = Q3 = a/2UA and A = a/2, as indicated in Figure 39f. Thereafter, the total volume of hemihydrate calculated by Equation (49) will be too large by the amount corresponding to twice the volume associated with rectangle HKTQ of Figure 39g& and it is necessary to subtract this from Equation (49) to obtain the final corrected volume, The area of rectangle HKTQ is (QH)(HK) = (A-a/2)(b), and the corresponding volume is vg = be (A-a/2) o This equation can be made time dependent by substituting UA(t-x) for A and UA(w-x) for a/2, where w is the impingement time in the A direction, i.e., w = 0 when t = 0 o With these substitutions, the time dependent equation for the corrected volume per needle is: vg(w,t) = 2bc UA(t-w), (50) and the correction for this impingement Vg(t), to be applied to the total volume of hemihydrate, can be calculated by: (w=t Vg(t) = dN/dw vg(w,t)dw (51) w=G5

-105where dN/dw is the rate of impingement. Again, because of the ideality of the model, this rate of impingement is equal to the rate of nucleation except that this stage of impingement starts 93 = a/2UA minutes later than the initial nucleation, giving dN/dw = KNo exp [-K(w-93)] o Substituting the values of vg(w,t) and dN/dw into Equation (51) gives w=t Vg(t) = WgK exp [-K(w-93)] (t-w)dw (52) J w=93 where Wg = 2bcNoUA o This equation can be integrated by parts using u = t-w, du = -dw, v = -(1/K) exp [-K(w-93)], and dv = exp [-K(w-53)] dw, giving: Vg(t) = Wg {(t-3) + (1/K) [exp [-K(t-93)] -1]} (53) where O3 = a/2UA. Subtracting this from Equation (49) gives the final expression for the total volume of hemihydrate formed: v4(t) = Va(t) - Vc(t) + Ve(t) - Vg(t) for t > 93 o (54) These corrected values Vl(t), V2(t), V3(t), and V4(t), for the total volume of hemihydrate formed during the various stages of the reactioncan be related directly to the net volume change observed in the dilatometer, and thereby used as a basis for developing theoretical equations for the fraction reacted a and the rate of reaction da/dt e, Fraction Reacted Equations. The net volume change AVr measured in the dilatometer for reaction at constant temperature is the sum of the volume changes of the dihydrate AVD, hemihydrate AVH, and the product water AVW: AVr = AVD + AVH + AVw (55)

-lo6These individual volume changes are proportional to the respective changes in the number of moles Am and the molar volumes V for each species: i.ee, AVD = mDVD v'H = AmHVH 9 and AVW =: ZNVW From the stoichiometry of this reaction given by Equation (22), AmD = -AmiH and ArnW = /2 AmH o Upon substituting these into Equation (55), the equation for the net volume change becomes: AVr = Am(VH + 3/2 VW - VD) - (56) The change in the number of moles of hemihydrate can now be represented by AmH = AVHpH, the product of the volume change and the molar density (p = moles/cc), giving: AVr = H[PH(VH + 3/2 Vw - vD)] (57) = AVH J where J is a constant. Dividing this equation by the total net volume change upon completion of the reaction AVrtot, noting that AVrtot =JAVHtot, gives: \ AV AVH a(t) r= -v _ AVH (58) tArtot AVHtot where a(t) is the fraction reacted expressed as a function of time, Since AVH starts from zero and increase as the reaction progresses, AVH = VH - 0, and Equation (58) can be rewritten as: (t) = AVr _ VH (59) AVrtot VHtot

-107where VH is the value at any particular stage of the reaction. The calculated volume of hemihydrate VH formed at any time t will be given by Vl(t), V2(t), V3(t) and V4(t) for the respective stages of the reaction, and the total volume at completion of the reaction is VHtot = abc No, therefore, the above equation can be written: Avr Vi(t) Oi(t) = (t (60) AVrtot abc No where i = 1, 2, 3, 4 correspond to the four stages of the reaction. The volume changes detected in the dilatometer capillary are proportional to the height changes, since AVr = A'Ahr and Vrtot = A'hrtot 9 where AT is the cross-sectional area of the capillary, therefore, the final form of the equation for oai(t) is: Ahr V-(t) i~(t) = /Ahrtot abc NO (6) Using this relationship, and the equations derived above for the Vi(t), the following four theoretical equations describing the fraction of hemihydrate formed as a function of time are obtained: al(t) = D1 + D2t + D3t2 + D4 exp(-Kt) for 0 < t < 01, (62) a2(t) = D5 + D6t + D7t2 + D8 exp(-Kt) for 91 < t <_ 2, (63) a3(t) = D9 + Dlot + Dll exp(-Kt) for G2 < t < 93, and (64) a4(t) = 1 + D12 exp(-Kt) for t > 03. (65)

-108Differentiation of these four equations with respect to time gives four differential equations for the rate of reaction: dOl/dt = D2 2 D3t - KD4 exp(-Kt) for 0 < t < 91, (66) do2/dt D6 + 2D7t - KD8 exp(-Kt) for G1 < t < G2, (67) da3/dt Do - KDl1 exp(-Kt) for QG2 < t < e3 3 and (68) do4/dt = -D12 exp(-Kt) for t > 93. (69) The constants appearing in the eight equations above are: D1 = (4/K2)[2(UA/a)(UB/b)-(1/N[3)(UA/a)(UA/b) ] D2 = -KD1 D3 = (K2/2)D1 D4 = -D1 D5 = D - (4 3/K2)(UB/b) - (2 43/K)(UB/a) - (3/2)(b/a) D6 = D2 + (2 J3)(UB/a) + (4 $3/K)(UB/a)(UB/b) D7 = D - (2/ 43)(UB/a)(UB/b) D8 D4 + (4 $3/K2)(UB/a)(UB/b) exp(KGL) D9 =-(2/K)(UA/a) DlO= 2(UA/a) Dll= D1[exp(KG2)-L] + (4 $3/K2)(UB/a)(UB/b) [exp(Ki1) - exp(KG2)] D12= D11 - (2/K)(UA/a) exp(KG5) 3. Evaluation of Kinetic Constants Equations (62-69) are the desired kinetic equations expressing the fraction transformed and the rate of transformation as functions of time. As written, these equations involve the twelve constants D1...Dioo.D12; however, these D' s are functions only of the four

-109kinetic growth constants (UA/a), (UB/b), (UA/b), and (UB/a), so the kinetic equations are actually functions only of these four growth constants, the nucleation rate constant K, and time to. To complete the derivation of the kinetic equations, it is now necessary to evaluate these kinetic constants. a. Method. In many previous studies of the kinetics of transformationsin solids, the coefficients Di of the theoretical equations have been relatively simple functions of the kinetic rate constants, so that it has been possible to evaluate the rate constants from values of the coefficients Di obtained by fitting the equations to the experimental data. This procedure could not be used in the present case, however, because of inaccuracies introduced by the complex mathematical manipulations which were involved as a result of the relatively complex nature of the rate equations themselves, and because the coefficients Di are not simple functions of the desired kinetic constants. Instead, values of 91, 02, and 93 were determined by fitting the rate equations to the experimental data and the four growth constants were calculated using the following relationships, derived from the expressions given for the limits of integration for Equations (42), (47), and (53): UA/a = 1/293, (70) UB/b = 1/291, (71) UA/b = %3(1/291) -4 3(1/292), and (72) UB/a = (UA/a)(UB/b)/(UA/b) ~ (75) On the basis of the model used in deriving the theoretical equations, curves of da/dt versus time would be expected to show recognizable changes in slope at times equal approximately to W1 and W3 corresponding to the start of the initial and final stages of the impingement

-110process, with possibly some distinctive change at an intermediate time corresponding approximately to @2. Rate curves were plotted for each of the 54 experimental runs, and the majority was found to have shapes of Type I shown in Figure 41(a) where the rate increasesrapidly at first, goes through a maximum, decreases to a point of abrupt change in slope, and then decreases exponentially to zero. The curves for seven of the experimental runs (numbered 6, 16, 21, 40, 41, 45, and 52) had shapes of Type II shown in Figure 41(b) where the maximum value coincided with the abrupt change in slope preceding the final exponential decay. Run 33, which involved extreme experimental conditions, had a shape different from either of these types and will be discussed separatel, later. In each case, the time corresponding to the point of inflection following the initial rapid growth was tal.en as the initial estimate of 91, while the time corresponding to the point of discontinuity in slope preceding the final exponential decay was taken as the initial estimate of 9, as shown in Figure 41. Calculation of values of the nucleation rate constant K was based on the equation: da/dt = K(1 - a) for t. 9 (74) obtained by combining Equations (65) and (69). This equation indicates that a plot of da/dt versus (1 - X), for values measured as the reaction nears completion, should be a straight line which passes through the origin having a slope equal to K o A least squares fit of this equation to the data taken toward the end of each experimental run should therefore provide a reliable determination of the value of K, independent of the other rate constants. In making this least squares fit,

4z z o 0 0T 0 4/ i i 4 i wJ I I w I \ /i IL I \1 FI1 /\ h- i \ a I <1 /V < 0 /i I i H I i i I I I H= Q 1 Q2^^ ^ ^ ~5 1 1 I i 4 IZ 02 83 B2 82 83 TIME,t TIME, t (a) Type I (b) Type II Figure 4i. Types of Rate Curves Exhibited by Most Experimental Runs.

-112however, Equation (74) was modified as follows: da/dt = K a + K(1-a) (75) so that the least squares line was not required to go through the origin which would be somewhat arbitrarily defined by the last available experimental data point. This was considered desirable because there was no way of being sure that the reaction had been allowed to go until it was 100% complete in all experimental runs. Furthermore, the use of this more general equation would eliminate the effects of any undetermined systematic errors in the experimental measurements that might have tended to bias the experimental values slightly in one direction or another. The values of K and Za calculated in this manner for the various experimental runs are listed in Table V. The fact that the AY values are small in all cases indicates that all experimental runs were carried substantially to completion and that the data are substantially free from bias. This considerably enhances the confidence which can be placed in the previous calculations based on these data, Estimation of values for 02 was considerably more difficult than estimation of values of 91, 3, and K, primarily because there was no distinctive feature in either type of experimental rate curve that could be reliably associated with O2 o Estimations of 02 based only on visual inspection of the experimental rate curves often produced curves of the wrong type when used in Equations (66) to (69) to calculate a theoretical curve for comparison with the experimental data, Since the two types of rate curves differ fundamentally in the sign of their slope in the region of 02, an analysis of the factors governing the slope at 02

-113was undertaken to attempt to develop some procedure to assist in estimating 92. Differentiating Equation (68) gives the desired slope as: d2a0/dt2 = D11 K2 exp(-Kt). (76) The coefficient Dll can be expressed in terms of 91, 92, and $3 as follows: Dll = (2/9012)[exp(KG2)-1] (77) -(1/l92)(l-,1/92) [exp(KG2)-1 +( 1/193) [/( 1-Go/o2) ][exp(KG1)-exp(KG2)]. Substituting this into Equation (76) and setting it equal to G2 yields: d2O/dt2 - (K2/9192)(SS) (78) where SS is the following collection of terms in KS1 and KS2 which determines the "Sign of the Slope" of the theoretical curve at: SS = (1 + KGj/KG2)[exp(K2 )-l] (79) + [exp(KG1) - exp(KG2)]/(1 - K91/KG2). Values of SS were calculated for different combinations of KG1 and Kg2, and the particular combinations for which SS = 0 were determined by graphical interpolation. As shown in Figure 42, these combinations define a line which separates a zone containing combinations of values which give curves of positive slope from a zone containing combinations which gives curves of negative slope. Furthermore, for constant 91 and 93 the values of the slope increase as the values of G2 depart from the value at the line of zero slope. Combinations for which G2 < G1 define a third zone which has no physical meaning in the present problem. Thus,

4 - \ ZONE OF NEGATIVE SLOPE 3 ZONE OF POSITIVE SLOPE \ O2.H ~~~~0 ~~0.5 1.0 1.5 KS, Figure 42. Graphical Solution for Equation (79).

-115once values of K, 01, and 03 were estimated, it was possible to determine from Figure 42 the range of values of 02 which would give a slope of the correct sign. It was then necessary to select, more or less by guess, a value in this range for use in the initial estimation of 92. The values of 01, 02 and 03 estimated in this manner for each experimental curve were then substituted into Equations (70) to (73) to give values for the kinetic growth constants which, together with the calculated value of the nucleation rate constant K, were used in Equations (66) and (69) to obtain calculated values for the rate of reaction as a function of time. These calculated rate values were then plotted and compared with plots of the corresponding experimental values for each experimental run and the values of 01, G2, and 03 were adjusted by trial and error until the smooth calculated rate curves fel approximately along the center of the slightly scatonered distribution of plotted experimental values. These calculations were carried out on an IBM 7090 computer using the program given in Appendix N, b. Numerical Values. This procedure was generally successful in providing an acceptable fit of the theoretical equations to the experimental data with a reasonable expenditure of time and effort (except in the case of experimental runs 6 and 33 which will be considered in detail later). Typical examples of the fit of the theoretical curves to the experimental data are shown in Figures 43 through 50, while the final values of 01, 02, and 03 chosen for all runs, together with the values of the four growth rate constants (UB/a)X, (UB/b), (UA/a), and (UA/b) calculated from them, are listed in Table V.

.05 [:: r.o4.0^ A 0~~~~~~~~~~6 "o -ozr t lo a,~~~~8 w[ / e, 8, _____ ^ ^r-Tlt^ MINUTES O~~~~~~ \0 O2e - 0r -— \eMn.-a ^ toe tto tie periental Data for Run 1O for ie ~igure 4 ehya'ration of calcium lf

.015 * * S.010 z.005 0 0 50 100 * ISO 200 TIME, MINUTES Figure 44. Fit of the Theoretical Curve to the Experimental Data for Run 20 for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Water at 2510F.

~~~~~~~~~~~~~.014 rid g III ~ *.010-:* 7''' ~ 0-, /' We'.0,00- 0 *~00ee O0 50 100 150 * 200.005 0 TIME, MINUTES Figure 45. Fit of the Theoretical Curve to the Experimental Data for Run 30 for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Water at 250 ~F.

.07.06 ee, *.04 -.02~.01- l e' I 2 3 0 ~0 10 20 30 * * 40 50 TIME, MINUTES Figure 46. Fit of the Theoretical Curve to the Experimental Data for Run 40 for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in a 14% Sodium Chloride Solution at 237~F.

.03 *.02 /.02 ~_'^1 ^ ^ _ 83 0 10 20 30 40 50 60 70 80 90 100 TIME, MINUTES Figure 47. Fit of the Theoretical Curve to the Experimental Data for Run 50 for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Normal Synthetic Sea Water at 240~F.

-121-.07 I,.06.05 *.04 - z 0O*I0 V.03 -.02 - \.01 - 0, 2z a 0 10 20 30 40 50 TIME, MINUTES Figure 48. Fit of the Theoretical Curve to the Experimental Data for Run 60 for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Normal Synthetic Sea Water at 247~F.

.010 z 4N.005 *0 -cr~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~r 81 a, a8 0~~~~~~~~~~~~~~~~ 0 100 200 300 400 TIME, MINUTES Figure 49. Fit of the Theoretical Curve to the Experimental Data for Run 62 for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Water at 2450F.

.10 I I 7" I ~ Z %%.05 Ho j 10 O 20 30 TIME, MINUTES Figure 50. Fit of the Theoretical Curve to the Experimental Data for Run 64 for the Dehydration of Calcium Sulfate Dihydrate to Hemihydrate in Water at 2650F.

TABLE V VALUES OF KINETIC CONSTANTS Run Temp. Temp.1 1 02 35 K UB/a UB/b UA/a UA/b No. ~F ~K-1 ZAL Min Min Min Min-1 Min-1 Min-1 Min-1 Min-1 P/Po 6 261.01.0024976.03045 —.- —. - —.-.02489. —-.-. 1.000 7 258.oo.0025080.00734 19.0o 26.o 34.o.09213.03045.02632.01563.01351 1.000 8 257.98.0025081.02233 18.o 26.0 34.0.o8164.02759.02778.01471.01480 1.000 9 258.96.0025047.01578 17.0 24.0 35.0.1247.02828.02941.01429.01486 1.000 10 257.84.0025086.01867 18.0 25.0 35.0.1181.02946.02778.01429.01347 1.000 11 258.90.0025049.01248 10.0 12.0 31.0.1222.05587.05000.01613.01443 1.000 12 259.41.0025031.00579 17.0 23.0 34.0.1786.03255.02941.01471.01329 1.000 13 259.79.0025018.00626 17.0 24.0 30.0.1888.03299.02941.01667.01486 1.000 14 260.20.0025004.02746 10.0 25.0 29.0.1271.01659.05000.01724.05196 1.000 15 258.73.0025055.00071 12.0 31.0 36.0.1815.01308.04167.01389.04423 1.000 16 260.13.0025006.00356 5.0 6.o 38.0.1542.04558.1000.01316.02887 1.000 19 251.07.0025325.00991 35.0 90.0 102.0.05555333.00463.01429.00490.01512 1.000 20 250.53.0025344.00115 55.0 80.0 102.0.06573.00906.00906.00490.00492 1.000 21 251.03.0025326.00425 20.0 23.0 89.0.06675.02487.02500.00562.00565 1.000 22 250.54.0025344.00627 45.0 6o.o 90.0.05531.01283.01111.00556.00481 1.000 23 250.53.00255344.01459 55.0 80.0 95.0.04875.00972.00909.00526.00492 1.000 24 250.22.0025355.00541 65.0 90.0 105.0.04420.00990.00769.00476.00370 1.000 25 250.534.0025351.00392 40.o 55.0 95.0.03794.01111.01250.00526.00590 1.000 26 250.34.0025351 -.00029 60.0 85.0 125.0.04207.00785.oo833.00440.00425 1.000 27 250.71.0025338.00872 6o.o 80.0 105.0.03923.01100.oo833.00476.00361 1.000 28 249.83.0025369.00910 65.0 90.0 120.0.03238.oo866.00769.00417.00370 1.000 29 249.99.0025364.00952 45.0 95.0 110.0.03131.00499.01111.00455.01013 1.000! 30 249.96.0025365.01267 6o.o 90.0 110.0.04144.00787.00833.00455.0048 1.000481 31 250.53.0025344.00706 55.0 75.0 100.0.05424.01083.0 0909.00500.00420 1.000 32 250.73.0025337.01325 85.0 130.0 140.0.02840.00596.00588.00357.00353 1.000 33 250.40.0025349.02498 --.-.02498. - - -.. ---- -- 1.000oo 34 250.11.0025359.02185 50.0 o 80. 97.0.04312 oo794.01000.00515.oo6o 1.000 35 249.27.0025389.01135 80.0 105.0 133.0.o4611.00912.00625.00376.00258 1.000 36 247.03.0025470.00459 9.0 11.0 19.0.1700.08356.05556.02632.01750 0.978 37 237.34.0025824.02565 3.5 4.5 9.5.3633.1367.1429.05263.05499 0.831 38 240.01.0025725.00627 23.0 30.0 47.0.07015.02632.02174.01064.00879 0.978 39 239.04.0025761 -.00145 15.0 28.0 34.0.1812.01829.03333.01471.02681 0.956 40 236.83.0025843.00955 7.0 9.0 18.0.1861.07217.07143.02778.02749 0.903 41 230.29.0026088.01289 11.0 13.0 18.0.1324.1042.04546.02778.01211 0.831 42 240.55.0025705 -.00744 275.0 375.0 450.0.00399.00241.00182.001 11.00ooo84 1.000 43 240.27.0025716.01262 70.0 95.0 125.0.02616.00878.00714.00400.00326 0.994 44 240.67.0025701.02264 110.0 180.O 230.0.01586.00323.00455.00217.00306 0.997 45 239.01.0025762.01299 20.0 25.0 50.0.05540.02887.02500.01000.oo866 0.982 47 239.49.0025744.00193 11.0 15.0 22.0.2223.04921.04546.02273.02100 0.945 48 238.86.0025768.00982 9.0 13.0 17.0.2062.05519.05556.02941.02961 0.926 49 240.04.0025724.02361 11.0 15.0 24.0.1155.04511.o4546.02083.02100 0.963 50 241.01.0025689.01379 17.0 23.0 36.o.08124.03074.02941.01389.01329 0.982 51 235.03.0025910.01375 42.0 55.0 95.0.03408.01286.01191.00526.00487 0.982 52 235.15.0025905.01586 45.0 6o.o 80.0.02975.01443.01111.00625.oo481 0.978 53 230.93.0026064.01543 8o.0 110.0 140.0.01786.00756.00625.00357.00295 0.978 54 230,88.0026065.00969 100.o 130.0 240.0.01640.00521.00550.00208.00200 0.982 55 243.74.0025589.00435 15.0 20.0 27.5.1213.04199.03333.01818.01443 0.978 58 255.40.0025172.00098 30.0 40.0 55.0.08280.02100.01667.00909.00722 1.000 59 249.08.0025396.00384 70.0 90.0 105.0.05892.01237.00714.00476.00275 1.000 60 247.01.0025470 -.oo40 11.0 15.0 22.0.1938.04921.04546.02273.02100 0.982 61 243.35.0025603.00395 16.0 22.0 34.0.1026.03113.03125.01471.01476 o.982 62 244.73.0025553 -.00018 90.0 190.0 210.0.02654.00261.00556.00238.005o 6 1.000 63 260.44.0024995.00234 17.0 21.0 30.0.1727.05052.02941.01667.00970 1.000 64 265.20.0024831.00001 10.0 13.0 17.0.2417.07358.05000.02941.01999 1.000

-125In general the fit of the theoretical curves to the experimental data is good for values of t < 91 and t > 93 where the shapes of the theoretical curves are primarily dependent on the values of K, 91, and 93 which can be determined relatively easily and reliably. It the interval between t = 91 and t = 93 the fit is usually less satisfactory. Here the shapes of many of the experimental curves are not well defined, probably because this is the interval where the reaction rate is maximum so that all experimental measurements are more subject to random variations, In addition, both the numerical differentiation technique used in calculating the experimental rates and the numerical procedure used to calculate the shrinkage of volume of the system due to endothermic cooling, are least reliable in this region. The greatest possible cause of this discrepency is the fact that the theoretical curves were calculated assuming that the reaction occurred at a constant temperature, where in reality, the reaction temperature changed continuously with the rate of reaction because of the absorption of the endothermic heat of reaction by the solids. Thus, each reaction started and ended approximately at the temperature of the thermostat, but decreased to some minimum value as the reaction rate reached its maximum value. Since the calculated average temperature of the reaction lies between the temperature of the thermostat and the minimum observed temperature and since the theoretical curves were calculated on the basis of the average temperature and not on the basis of the changing temperature profile, the calculat-ed rate curves should be necessarily slightly higher than the experimental data in the region where the rate of reaction is maximum and slightly lower than the experimental data near the beginning and end of each reaction.

-126This not only made it extremely difficult to establish when a satisfactory fit of the theoretical curve to the experimental data had been achieved, but also contributed to the uncertainty in the determination of the values of 92 which basically determined the shape of the theoretical curve in this interval. The extent to which the basic problems relating to measurements and corrections of the experimental data determined the ultimate outcome is perhaps indicated by the comparison of Figure 45 and 46. Figure 45 shows the results for run number 30 where very good agreement between the experimental and theoretical curves was achieved, In this case? the reaction was carried out under conditions for which the reaction rates were relatively slow and all the above problems would be at a minimum. Figure 46, on the other hand, shows the results for run number 40 which was carried out under conditions for which the reaction rates were high and the problems in the data handling were more serious. Here the fit of the theoretical curve to the experimental data is rather poor in the interval between t = 91 and t = 93 c, Variations with Temperature and Concentration. From both the theoretical and the practical standpoints it would now be desirable to develop equations giving the kinetic constants as functions of temperature and solution concentration, since these equations would complete the theoretical description of the transformation and since they would be useful in extending the kinetic data somewhat beyond the limits of the measured values. Characteristically, kinetic rate constants vary exponentially with temperature according to the classical Arrhenius equation: k = Z exp(-E/RT) (80)

-127where Z is the pre-exponential factor, which may be related to the entropy change as noted in connection with Equation (13), and E is the experimental activation energy. Written in logarithms this equation becomes: in k = in Z - E/RT. (81) Since In k and 1/T are variable, the above equation is the equation for a straight line with a slope of -E/R and intercept in Z Figures 51, 52, and 55 show the least squares lines based on Equation (81) fitted to the calculated values for K, UB/a, UB/b, UA/a, and UA/b for the reaction occurring in water, in 3.5% sodium chloride solutions, and in normal synthetic sea water. The corresponding values of Z and E for K, UB/a, UB/b, UA/a, and UA/b are listed in Table VI. Except for the data for Run 42, the agreement between the least squares lines and the experimental data is sufficiently good to justify the use of the Arrhenius type equation for representing the temperature dependence of these rate constants over the temperature range involved. When the data from Run 42 were included, the dashed-least squares line shown in Figure 51 was obtained. This line does not fit any of the data particularly well. When the data from Run 42 were omitted, however, the solid line was obtained which shows excellent agreement with all the data points except the omitted one from Run 42. On this basis it was concluded that the data for Run 42 are not consistent with data from the other runs in water. Other calculations, given later, provide an even stronger basis for this point of view; consequently, data for Run 42 were omitted from these and all subsequent theoretical calculations,

-1281.O' O 1 ^xFo I1~ I i ~I- ~ s.01 w <RUN 42~ 001.00247.00250.00255 A TEMPERATURE, 0K'1 270 260 250 240 TEMPERATURE,OF Figure 51. Arrhenius Plot of the Kinetic Constants K, UB/a, UB/b, UA/a, and UA/b for the Transformation of Calcium Sulfaie Dihydrate to Hemihydrate in Water.

-1291. I ue/o U /b 0.1 I-. /UA'.01.00252.00255.00260 250 240 230 TEMPERATURE, O TEMAPERATURE,~F Figure 52. Arrhenius Plot of the Kinetic Constants K, U/a, UB/b, UA/a, and UA/b for the Transformation of Calcium Sulfate Dihydrate to Hemihydrate in 3.5% Sodium Chloride Solutions.

-1301.0 1I/ 0.1. —UA/b z 00 -I-, I I I i-. 0.01.000252.00255.00260 TEMPERATURE-',K-' I I I I 250 240 230 TEMPERATURE, ~F Figure 53. Arrhenius Plot of the Kinetic Constants K, U/a, Ug/b, UA/a, and UA/b for the Transformation of Calcium Sulfate Dihydrate to Hemihydrate in Normal Synthetic Sea Water.

-131TABLE VI VALUES OF Z AND E CORRESPONDING TO FIGURES 51, 52 AND 53. Pre-Exponential Activation Energy Rate Constant Factor Z, min1- E, Kcal/gm mole Reaction Occurring in Water K 8.21 x 1032 61.7 UB/a 7.96 x 10l1 79.2 UB/b 6.70 x 1033 64.7 UA/a 6.86 x 1035 68.4 UA/b 1.17 x 1029 56.7 Reaction Occurring in 3.5% Sodium Chloride Solutions K 7.93 x 1042 78.4 UB/a 2.51 x 1042 78.2 UB/b 1.00 x 1039 72.3 UA/a 3.35 x 1035 66.7 UA/b 1.37 x lo32 60.8 Reaction Occurring in Synthetic Sea Water K 1.07 x 1044 80.4 UB/a 1.14 x 1039 72.4 UB/b 5.02 x 1037 70.0 UA/a 1.41 x 1042 78.5 UA/b 1.68 x 1042 78.7

-132An equation for the variation of the nucleation rate constant K with the concentration of salts added to the reaction solution was derived from the results of 20 experimental runs using starting solutions which contained from 0.5% to 21% sodium chloride and 1, 2, 3, and 4 times the concentrations of salts for normal sea water. These experimental runs were all carried out at the same nominal temperature of 240~F; however, the actual temperatures of the runs were not all the same because the cooling of the reaction mixture due to the endothermic nature of the reaction caused the reaction temperature to vary slightly both with the rate of reaction and with the solute concentration. Therefore, values corresponding to a constant temperature of 239.60F were estimated for the more concentrated solutions from plots of the logarithm of K versus 1/T, by extrapolating the experimental values for the high concentrations to the constant temperature of 239.6~F using lines having the same slopes as the line for the 3.5% sodium chloride data and for the normal synthetic sea water as shown in Figures 54 and 55, respectively. As shown in Figure 56, two straight lines are obtained when these values of K are plotted against the weight fraction of dissolved solids for these two types of solutions, In seeking a more general relationship, it has been found that the data for both types of solutions fall on a common straight line when K is plotted versus 1-P/P~ as shown in Figure 57. Here P/Po is the ratio of the vapor pressure of water in the solution to that of pure water at the same temperature and is approximately equal to the activity of the water in the solution. The equation describing this relationship has the general form: K = Ko + S(1-P/P~), (82)

-133210/0 14% 70/0 |*-l' 1 z 0 3.5% z.0% o-3 L.0.0/0 3l/.00252.00255.00260 I TEMPERATURE"', OK' Figure 54. Extrapolation of Values of Nucleation Rate Constant K to the Constant Temperature of 239.6 ~F for Sodium Chloride Solutions.

-1341.0 j 3X I- - ^SIX -n IX z 0 ~~(K~ TEPRTR N'' 0 10.00252.00255.00260 TEMPERATURE', 0K' Figure 55. Extrapolation of Values of Nucleation Rate Constant K to the Constant-Temperature of 239.6~F for Synthetic Sea Water Containing 1, 2, 3, and 4 Times the Salts of Normal Synthetic Sea Water.

-1350:7'C'' I I I I I,1I O SODIUM CHLORIDE SOLUTION O SYNTHETIC SEA WATER O 0.6 z - 2 0.4 0 0.3.1 0.2 W 0 - 0 0 WEIGHT FRACTION DISSOLVED SOLIDS Figure 56. Plot of Smoothed Data from Figures 54 and 55 Showing the Effect of Dissolved Solids on the Nucleation Rate Constant K.

-1360.7 O SODIUM CHLORIDE SOLUTION D SYNTHETIC SEA WATER 0.6 0.5 z.C) 0.4 z 0 LLI I0.3- z 0 0W lC -0 ~0.2 0 0.1 0.0 0.1 0.2 Figure 57. Plot of Smoothed Data from Figures 54 and 55 Showing the Effect of the Activity of the Water (.P/PO) in the Solution Surroundingthe Reaction Mixture on the Nucleation Rate Constant K.

-137where K is the nucleation rate constant, S is the slope of the line, and Ko is the intercept having the value of the nucleation rate constant in water when 1-P/P~ is zero. Since 1-P/Po is a dimensionless quantity, the term S should be similar in characteristics to K and K, and should also vary exponentially with temperature according to the Arrhenius equation. It should therefore be permissible to write: S = (K-Ko)/(1-P/Po) = Z exp(-E /RT), or (83) in (K-Ko)/(1-P/P~) = in Z -E /RT. (84) These equations relate mathematically the nucleation rate constant K to both the temperature and the activity of the: water in the solution. By analogy, it was assumed that equations of the form: (Ri-Rio)/(l-P/Po)= Z exp(-E/RT), (85) and in (Ri -Ri )/(1-P/P~o)= InZ -:E/RT (86) might be used to represent the variations of all the rate constants with temperature and the activity of the water in the solutions, where R = K, UB/, UB/b, UA/a, and UA/b. Figure 58 shows that the experimental data exhibit satisfactory agreement with the least squares lines derived from these equations when the logarithm of (Ri-Rio)/(l-P/P~) is plotted versus 1/T. The values of Z and E for the least squares line of Figure 58 are listed in Table VII.

-138_I', I I l 10,0, R-UUA/o Ri=UAU/ 003.0025.00260.00263 TEMPERATURE', OK~I l~ I I,~ ll~ I 250 240 230 TEMPERATURE, ~F Figure 58. Least Squares Lines Correlating the Variations of the Kinetic Constants with both Temperature and Water Activity.

-139TABLE VII VALUES OF Z AND E OF EQATION (85) FOR THE LEAST SQUARES LINES SHOWN IN FIGURE 58. Parameter, min-1 Z, min-1 E, Kcal/gm mole K-K 7.85 x 1045 80.8 /a)(UB/a) B/a)o x 4 1.01 x o10 60o.5 (1-P/Po) (UB/b) -(UB/b) 5.73 x 1037 67.2 (1-P/P0) (UA/a)-(UA/a)o 8. 3 — -.67 x 10 8 69.2 (1-P/Po) (UA/b)-(UA/b)o 2.08 x 143 77.8 (1-P/PO)

-14o4, Test of the Theoretical Equations Having completed the derivations of the theoretical equations, it now becomes desirable to test their validity. For thi-; purpose it would be preferable to compare values of (X or da/dt calculated from the theoretical equations with experimentally measur.e.i vaLues not used in the evaluation of the c(-'ntants of the theoretical equations. Unfortunately, unused experimental data of this kind are not available, and to obtain such data would be beyond the scope of this study. Therefore, the adopted test consists of comparing theoretically calculated TTT curves with the experimentally determined TTT values reported in the previous chapter. This is perhaps the best test that can be devised with the available databecause the experimental TTT values were obtained from the basic dilatometric data with a minimum of calculation and mathematicaL manipulationwhile the theoretical TTT curves were based on equations whose constants were calculated from da/dt values obtained by numerical differentiation of the basic data. Since these calculations could introduce considerable random variations, and other uncertainties, the experimental TTT values may be considered sufficiently independent of the calculated ones to serve as a basis for a test of the equations, In order to compare the experimental TTT values with the TTT values calculated from the theoretical equations, a common time base must be established for the two sets of data since the time values for the experimental data were measured from the time the experimental run was started, whereas the time values for the theoretical equations were measured from the time the first nucleus appeared. The difference between these times is the induction time or nucleation time for the

-141transformation. and addition of this value to the theoretically calculated time values will accomplish the desired time base correction. Ideally, values for the nucleation time could be determined from experimental TTT values for zero percent transformation. In practice, however, the zero percent TTT values are very difficult to evaluate, and more accurate results can be obtained using the 5 percent TTT values, The time base adjustment was therefore achieved by adding to the theoretically calculated transformation time values the difference between the 5 percent transformation time and those calculated theoretically. In order to make this correction effectively, a mathematical expression for the variation of the 5 percent transformation time 75% with temperature was needed, For this purpose the following equation was used: l/Tr5 = Z exp(-E/RT). (87) Least squares lines based on this equation agree very satisfactorily with the experimental data as shown in Figure 59, The values of the constants Z and E for these lines are listed in Table VIII. The final TTT curves calculated from the theoretical rate equations, using the computer program given in Appendix 0, are shown in Figures 60, 61, and 62 together with the experimentally determined TTT data points from Figures 15, 16, and 17 and estimates of the 5% and 95% TTT points at 270~F obtained by extrapolation of the curves of Figures 19, 20, and 21, Except for the case of Run 42 shown in Figure 60, the agreement between the theoretically calculated TTT curves and the experimental TTT data is excellent over the temperature range 230~ to 250~F where the experimental values are considered to be reasonably accurate. In addition, the agreement of the theoretical curves with

0.1z.01 t - ~ WATER 0 3.5% SODIUM CHLORIDE SOLUTION < RUN 42 - ri Q SYNTHETIC SEA WATER.001, I,, I I,.00247.00250.00255.00260.00263 TEMPERATURE-' OKi I I I, I, I I 270 260 250 240 230 TEMPERATURE, OF Figure 59. Least Squares Lines Based on the Arrhenius Equation Fitted to Time-Temperature-5% Transformation Data.

-143TABLE VIII VALUES OF Z AND E CORRESPONDING TO FIGURE 59 Solution Z, min-1 E, Kcal/gm mole Water 5,92 x 1023 46.2 3.5o NaCi Solution 3.21 x 1019 37.4 Synthetic Sea Water 4.42 x 1031 59. -~~~~~~~~5.

~~~~-10444o II TRANSFORMATION \\~ O ~0 95% E\ 75% <> 50% A 25% I I 10 -V LJ Oi 10 I0,, L l l i l l l! l 1220 230 240 250 260 270 TEMPERATURE, OF Figure 60. Comparison of TTT Curves Calculated from the Theoretical Equations with Experimentally Measured TTT Data for the Dihydrate-Hemihydrate Transformation in Water.

-145104 104to —-— |-i -|- I | —--' II -- - TRANSFORMATION 0 95% -E 75% _> 50% \ 25% V 5% 10$3 Cf) w I3 L, I, I I I, r 7 220 230 240 250 260 270 TEMPERATURE, OF Figure 61. Comparison of TTT Curves Calculated from the Theoretical Equations with Experimentally Measured TTT Data for the Dihydrate-Hemihydrate Transformation in 3.5% Sodium Chloride Solution.

-146104 TRANSFORMATION 0 95% o 75% _ 50% A 25% V 5% I 0 010 220 230 240 250 260 270 TEMPERATURE, OF Figure 62. Comparison of TTT Curves Calculated from the Theoretical Equations with Experimentally Measured TTT Data for the Dihydrate-Hemihydrate Transformation in Normal Synthetic Sea Water.

-147the extrapolated experimental estimates at 270~F is quite acceptable, considering the large uncertainty- associated with the experimental estimates at these temperatures, The disagreement between the points for Run 42 and the theoretical curves is sufficient to cast doubt on the validity of the data from this run, and it is instructive to consider the basis for this in some detail because of the additional insight it provides concerning the role of various factors in the theoretical calculations. When the experimental TTT curves of Figure 15, 16, and 17 were first prepared, the rather sharp bend introduced by the points for Run 42 was noted and questioned but not considered particularly unusual because of the complex character of the system involved and because "C" or "S" shaped TTT curves are frequently encountered for solid transformations. The original experimental data were re-examined and the calculation of the TTT values was re-checked but no obvious mistakes were found, Some difficulty had been encountered with the thermocouple during the early part of the run, as indicated by the discontinuity in the potentiometer chart record which is reproduced in Figure 63; however, this difficulty had supposedly been taken care of, and the temperature values were subsequently assumed to be accurate. When Equation (87) was applied to the 5 percent transformation data for the reaction in water including the data from Run 42, the dashed least squares line shown in Figure 59 was obtained (with Z = 4.25 x 1028min-1 and E = 55.1 Kcal/gm mole). Using this as the basis for the time correction, the theoretically calculated TTT curves shown in Figure 64 were obtained. The agreement between these curves and the experimental TTT data points was so much poorer than that for the

-148-..;;': -;'_: i9 0 ~~~~12~~ ~~~~~~ 1,'I 23~.,.; i. j j,.. - ~.:'.'"' i'~......!...............~,' Z3 9.0 0 j.':.:;., i'g6,1Bt i "H M4E.'.f!t 75 100 125 150 231s 200 225 2 8.7 27.1 i0 2'j;3.S I-;; i': I; 2 3 Z. 9:!.: ~.', i: i' 2 3' -i.::; j i - i; j i ij |j - 2 3 86. 0 75 100 0 125 150 17 200 S25 I 2o' t 275 8,..: I * i i i: -:. I V I! 1' I I:;o' j:'';;: |i i',,! ~:,.........,............ l:. 4: /*. I j;' g. I 0 4O R EE ~l 0 75 100:'125 150' 175 2001 25;20. 275 5. 2 4 /'.., /") i Asl-' —, \^ 7 ff n ^ *,':'**; i nSOR^8KA~f\E^\E<T i.; *; j;, I ji!. J... i ^l~.'n- S ~ J. tEE \; "7,: i4 I 5 I H..0 125 1i 1 2 2 T*'ii~~~ MA^ I-, ~ N: i i,'.''::$. t 1 0 M -' i j h iM: r, * I, ~:'' "'' " Figure 63. Initial Portion of the Potentiometric Chart for Run 42 Showing the Irratic Thermocouple Behavior at the Beginning of the Experiment

-149104 TRANSFORMATION 0 95% 0 75% \\\\ V 75% cS 50% A 25% 103 ta) 107 1-1 It n O(n 1 K 111 7 220 230 240 250 260 270 TEMPERATURE, OF Figure 64. Comparison of TTT Curves Calculated from the Theoretical Equations with Experimentally Measured TTT Data for the Dihydrate-Hemihydrate Transformation in Water Using the Values for Run 42.

-150curves of Figures 61 and 62 that it was decided to disregard the data from Run 42 in these calculations, whereupon the curves shown in Figure 60 were obtained. The reason for the apparent discrepancy between the data from Run 42 and the data from the other runs in water is not clear. It seems most likely that the trouble with the thermocouple was not fully eliminated and that the recorded temperature values are about 5~F too high. It is possible, however, that the reaction mechanism was different, since the reaction rates were the lowest encountered in the entire investigation due to the combined effects of the low reaction temperature and high activity value for water in the liquid of the reaction mixture (i.e. dilute calcium sulfate solution). Unfortunately, it has not been possible to repeat this run because the dilatometer has been dismantled for modification for use in another study. In any event, discarding the data from Run 42 seems justified from the practical point of view since it brings the theoretical curves into better agreement with the experimental data at the higher temperature which are of greatest importance in the operation of evaporators and heat exchangers. Thus, the theoretical curves are made potentially more useful for purposes of extrapolation. Comparison of the TTT curves in Figure 60 with those in Figure 64 showsthe relative contributions of the various factors to the theoretical curves. In particular, it is evident that Equation (87), which relates temperature to the nucleation time for the transformation, establishes the time base for the theoretical curves and determines both the magnitude of the time values and the "slopes" of the curves.

-151Equations (62) to (65), which relate to the transformation mechanism, determine the spacing of the curves for different percent transformation relative to one another. The use of Equations (62) to (65) has been restricted so far to calculation of TTT curves for the transformation of calcium sulfate dihydrate to hemihydrate in water, in 3.5% sodium chloride solutions, and in normal synthetic sea water. Ideally, it would be desirable to develop a means for making similar calculations for solutions of other compositions and concentrations. To do this, however, it is necessary to have an equation similar in function to Equation (87) but which gives the variation of T5% with both temperature and solution composition. Only the following equation, selected by analogy with Equation (85), has been tried for this purpose to date: [(1/T56)-(1/T5%)]/[1-P/P~] = Z exp(-E/RT). (88) The least squares line, based on this equation and calculated using all the 1/T5% values available for sodium chloride solutions and synthetic sea water concentrates and calculated (1/T5%)o values for water, is shown in Figure 65 together with the points which indicate the individual calculated values for the variables of the equation. The values of the constants Z and E for this line are 4.40 x 1026 min- and 475 Kcal/gm mole, respectively. The agreement between the point values and the line is not considered especially good because of the considerable deviation of many of the points from the line, but particularly because points calculated from runs in the sodium chloride solutions and in the synhetic synthetic sea water concentrates appear to define separate least squares lines (shown dashed in Figure 65) rather than to be

-152I'- I I I I I I 0 3.5% SODIUM CHLORIDE SOLUTION * SYNTHETIC SEA WATER 10 0 TEMPERATURE', OK' Figure 65. Least Squares Lines Based on the General Correlation Fitted to Time-Temperature-5% Transformation Data. Fitted to Time-Temperature-5% Transformation Data.

-153104 10, _ I I I I I TRANSFORMATION 0 95% 13 75% _ 50% A 25% V 5% CU) w to'.1' i <7').i I l I i_ I __ I I 220 230 240 250 260 270 TEMPERATURE, ~F Figure 66. Comparison of TTT Curves Calculated from the Theoretical Equations with Experimentally Measured TTT Data for the Dihydrate-Hemihydrate Transformation in 3.55 Sodium Chloride Solutions Using Generalized Correlation for l/T'%.

-154104 -- TRANSFORMATION 0 95% - 75% 0 50% A 25% 100 Lr) I-. 10 I.. ~ ~ P L, I. I ) 220 230 240 250 260 270 TEMPERATURE, ~F Figure 67. Comparison of TTT Curves Calculated from the Theoretical Equations with Experimentally Measured TTT Data for the Dihydrate-Hemihydrate Transformation in Normal Synthetic Sea Water Using Generalized Correlation for 1/TX5.

cIJ i-,jr~~~~~ ~TIME, MINUTES (D _5. 0" " coI 1- 1 1 11 1 11 I I I I I lII II,l I I I11 1 I 11111 I HH-tmQ _0 ~~~~~0 Om N~ ~~~~~~~~~~~~0 N H t I. C' o D H. 0 0 P,: F. - (D!.' o 0) (D H -0 F-J ~ - 0 F.e.. I-..' m7' o H o. p.,M~,,1'-" i (DH ~~~~ 0 ~~~~~~~~'1 0~~~~0'a~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~'a- C D 0. ~ o -eP Ir Nn"4~O) (D 5N CA H~ c U) 0 P,~oo o~.-.-3!-E f,,~ ~ ~ —- ~- c+ ('D ~~~~~~~0 0 0 F.... N D

-156-,o-, o0'' o95. ~IOr'~ "^3'' 104 10 1 222420 26 1 0I 102 TEMPERASTURE,0F Figure 69. Comparison of TTT Curves Calculated from the Theoretical Equations with Experimentally Measured TTT Data for the Dihydrate-Hemihydrate Transformation in Synthetic Sea Water Containing 2, 3, and - Times the Salts of Normal Synthetic Sea Water. 2 25% Synthetic Sea Water.

-157distributed randomly around the least squares line obtained using the pooled data (shown solid in Figure 65). TTT curves for the transformation in 3.5% sodium chloride solutions and in normal synthetic sea water, calculated from Equations (62) to (65), using T5V values calculated from Equation (88) to establish the time base, are shown in Figures 66 and 67 together with the experimentally derived TTT values from Figuresl6 and 17 and the estimated 5% and 95% TTT values at 270~F obtained from Figures 20 and 21. Although the agreement of these theoretically calculated TTT curves with the experimental results is not as good as before over the temperature range from 230~ to 250~F,.it is nonetheless acceptable, considering the overall complexity of the undertaking. On the other hand, the agreement between the extrapolated theoretical curves and the two extrapolated data points at 270~F is nearly as good as before. This suggests that the theoretical TTT curves in Figures 66 and 67 may be useful for estimating TTT values at higher temperatures for applications where high accuracy is not required, On this basis, the procedure was also applied to 7.0%, 14.0% and 21.0% sodium chloride solutions and to synthetic sea water concentrates of 2, 3, and 4 times that of normal synthetic sea water, Only limited experimental data are available for these solutions; however, the agreement between the theoretically calculated curves and the data points is generally good, as shown in Figures 68 and 690 The theoretical curves were calculated over the temperature range from 220~ to 260~F, even though data were not available to test them over this entire range, providing "order of magnitude" values in a form readily available for comparison with future measurements.

VI. DISCUSSION The dehydration of calcium sulfate dihydrate to hemihydrate occurs in aqueous and brine solutions by nucleation of hemihydrate needles on the surface of the dihydraate crystals followed by the growth of these needles through the dihydrate phase, Impingement between adjacent nuclei or between nuclei and the sides of the parent dihydrate crystal eventually terminates the reaction. Because the dihydrate phase is transformed by many hemihydrate needles, the rate of reaction measured dilatometrically represents the sum of the growth rates of all these needles. Consequently, changes in either their growth rates or growth patterns may change the total rate of the reaction, A practical meaning was added to these observations by postulating a model which describes the total rate of reaction as the sum of these individual growth rates, making it possible to understand the characteristics of the reaction from both microscopic and macroscopic points of view, The special technique for synchronizing the recording of time, temperature, and liquid height in the capillary provided data suitable for numerical differentiation, resulting in rate values exhibiting a minimum of scatter and clearly indicating the detailed changes in the rate of reaction with time, Fitting the theoretical equations describing the postulated mechanism to this differentiated data yielded values for the kinetic constants contained in these equations for different conditions of temperature, solution composition, and initial dihydrate crystal size. From these observations, empirical equations were developed describing the effects of temperature and water activity on these kinetic constants, -158

-159making it possible to calculate the values of the kinetic constants for the desired reaction conditions. Using these empirical correlations and the theoretical equations, TTT curves were calculated which passed through the experimental data points as accurately as those drawn by visual inspection, indicating the highly acceptable accuracy of these calculations, Comparison of the theoretical TTT values for 270~F with extrapolated experimental values obtained at higher temperatures showed good agreement indicating that extrapolation up to 270~F is reasonable, A. Dihydrate-Hemihydrate Transformation Changes in the;characteristics: of the dihydrate-hemihydrate transformation can be described in terms of three major variables: temperature, activity of the water in the solution surrounding the reacting solids, and the initial dihydrate particle size. Because of the close agreement between the theoretical curves and the experimental data, changes in the characteristics can be described in terms of either of these equally well, In the following discussion, the values used in the numerical examples were obtained from the theoretical curves. 1, Effect of Temperature The overall rate of reaction increases rapidly with rising temperature because both the nucleation and growth processes increase with increasing temperature. The acceleration of the nucleation process over the temperature range 230~ to 270~F is shown by the marked decrease in induction time for the reaction, estimated by the 5% transformation curves, For the reaction in water the induction time decreases from 400

to 15 minutes, in 3o5% sodium chloride solutions it decreases from 66 to 6 minutes, and in synthetic sea water it decreases from 150 to 2 minutes. Acceleration of the nucleation process is also shown by the rapid increase in the values of the nucleation rate constant with increasing temperature0 Small changes in temperature result in large changes in the values of the nucleation rate constant because the slopes of the correlating lines are very steep as indicated by the high activation energies of 62, 78, and 80 Kcal/gm mole for the reaction in water, in 3.5% sodium chloride solutions, and in synthetic sea water, respectively, The growth processes were also greatly accelerated by relatively small increases in temperature as shown by the changes in reaction time, estimated by the time difference between the 5% and the 95% transformation curves, Over the same temperature range (230~ to 270~F) for the reaction in water, the reaction time decreases from 1200 to 10 minutes, in 3.5% sodium chloride solutions it decreases from 224 to 1 minute, and in normal synthetic sea water it decreases from 250 to 1 minute. Correspondingly, the kinetic growth constants also increase with increasing temperature very rapidly as indicated by the high experimental values obtained for their activation energies, i.e. between 56 and 80 Kcal/gm mole. 2, Effect of Water Activity The overall rate of reaction also increases with decreasing activity of the water in the solution surrounding the solids, Both the nucleation and growth processes are accelerated by small changes in the water activity which was obtained by using different sodium chloride solutions and synthetic sea water concentrates at 240~F. The acceleration of the nucleation process is shown by the decrease in induction time from

-16l170 to 6 minutes for a change in activity from 1.0 to 0,83, i.e. from water to 21% sodium chloride solution., For this same change in activity, the nucleation rate constant increases by a factor of almost 40 from a value of 0.017 to a value of 0.62. Likewise, the growth processes were also accelerated by relatively small changes in water activity, as indicated by the decrease in the reaction time from 350 to 10 minutes for the same activity change from 1.0 to 0.83. The kinetic growth constants also increase from relatively small values to relatively large ones for this change in activity. Thus, the overall rate of reaction increases because of the increase in the rates of nucleation and growth resulting from the decrease in water activity. 3o Effect of Initial Particle Size For changes in initial dihydrate particle size, the overall rate of reaction does not appreciably change except when very large or very small particles are used, then the entire reaction mechanism also changes. This change in mechanism was observed experimentally in a large single crystal and in a fine powder sample. Each case is discussed in detail later. However, between these two extremes, the slight changes in the overall rate of reaction are due primarily to changes in the nucleation process, since all the kinetic growth constants remain approximately constant and independent of the initial dihydrate particle size. The induction times measured at 250~F seemingly go through a minimum value with changing particle size. They decrease from values near 120 minutes to a value near 60 minutes at the minimum as the particle sizes change from of 0.018 and 0.002 inches to the values at the

-162minimum of 0.01 inches. On the other hand, the nucleation rate constant goes through a maximum for approximately this same particle size, increasing from values near 0.025 to a value near 0..05 at the maximum. Thus, the nucleation parameters change by a factor of two for these changes in particle size, while the growth parameters remain essentially constant, resulting in very little change in the overall rate of reaction. B. Hemihydrate-Anhydrite Transformation Although the characteristics of the dihydrate-hemihydrate transformation were studied in considerable detail, the hemihydrate-anhydrite reaction was examined only to confirm the stepwise transformation of calcium sulfate dihydrate to hemihydrate to anhydrite, in water, in 3.5% sodium chloride solutions, and in normal synthetic sea water. This reaction was observed only at three different temperatures for the three different solutions resulting in nine sets of data values. The effects of temperature and water activity on the hemihydrate-anhydrite transformation were estimated from the TTT curves drawn through these data values. The increase in the overall rate of reaction observed for the hemihydrate-anhydrite reaction probably results from increases in both the nucleation and growth processes with rising temperature. The increase in the nucleation process is indicated by the decrease in the induction time. In water, the induction time decreases from 510 to 475 minutes, while in 3.5% sodium chloride solutions and in normal synthetic sea water, it decreases from 185 to.100 minutes over the temperature range 325~ to 350~F. Based on the observed relationships between the behavior of the induction time and nucleation rate constant for the dihydratehemihydrate reaction, one can assume that the nucleation rate constant increases with temperature for this reaction. Judging from the rate of

-163change of the induction time with temperature, one can also assume that the rate of nucleation is less sensitive to temperature changes for this reaction than for the first reaction. The growth rates, likewise, are assumed to increase with increasing temperature because the reaction time decreases with increasing temperature. For example, in water, the reaction time decreases from 1000 to 500 minutes, while in the two brine solutions, it decreases from 245 to 145 minutes. The overall rate of reaction also increases with decreasing activity of water, again probably because of increases in both the nucleation and growth processes. These increases are indicated by the decreases in induction time from 490 to 190 minutes, and the decrease in the reaction time from 1100 to 250 minutes, for a decrease in activity form 1.0 to 0.98. From these time changes, it seems that the hemihydrate-anhydrite reaction is more sensitive to changes in activity of water than the dihydrate-hemihydrate reaction, but this can only be confirmed after a model has been successfully postulated and the functional relationships between the water activity and the rate constants have been established. C. Reaction Model The postulated reaction model for the dihydrate-hemihydrate transformation has been shown to describe adequately both the rate and TTT data over a fairly wide range of temperature and water activity. Certain aspects of the model which were presented earlier in the dissertation, but not discussed fully, are treated here along with some new aspects. In particular, the nature of the assumptions and possible refinements are examined along with a brief discussion on the rate controlling step of the mechanism. The correlations of the kinetic

constants are examined showing their limitations and their range of applicability. 1o Basic Assumptions The model for the reaction mechanism was highly idealized in order to obtain theoretical equations which describe the nucleation and growth phenomenon encountered in the dehydration of calcium sulfate dihydrateo The basic assumptions are: (1) that all the dihydrate crystals used in each sample have the same size and shape, (2) that nucleation of the hemihydrate phase occurs on the (001) cleavage planes of the dihydrate crystals with uniform spacing, (3) that all the hemihydrate needles grow with the same velocities UA, UB, and UC in their respective directions, and (4) that impingement occurs simultaneously at the opposite sides of the transformed hemihydrate subcrystals. Starting with these assumptions, equations were developed which describe the experimental rate data reasonably well and the TTT data remarkably wello Based on this good agreement between the values calculated using the model and the experimental data, any modification of these assumptions, in an attempt to improve the model, can only be considered secondary refinements. One such possible refinement would be to bring the configuration of the initial dihydrate particles into closer agreement with the assumption of uniform particle sizes by growing uniform crystals from solution. This change would probably decrease the scatter in the experimental data to some extent. Another possible refinement would be to assume a more complicated impingement process to characterize the transformation mechanism. This change could result in the addition

-165of several adjustable parameters which could improve the fit of the experimental data between ~1 and 3. 2. Rate Controlling Process When a reaction is composed of more than one process, it is valuable to know which process is the rate controlling one. In the dihydrate-hemihydrate reaction where both nucleation and growth processes occur, the rate controlling step was found to be the growth process where the hemihydrate interface moves through the dihydrate crystal, since the nucleation process is relatively quickly terminated, The movement of this interface can itself be limited by two processes occurring at the interface: the chemical reaction resulting in the formation of the hemihydrate phase containing an excess of water, and the diffusion of this excess water from this transition zone to the bulk solution. The chemical reaction step was found to be the rate controlling one by the elimination of the possibility that diffusion was controlling. This was accomplished by observing the rates of interfacial movements recorded in Appendix M. Since these rates are approximately constant and independent of the length of the Lemihydrate needles, the diffusion process was eliminated because it predicts a decrease in rate with an increase in length of the hemihydrate needle. It is still valuable, however, to compare the theoretical equations derived in Appendix Q for the chemical reaction: (U/d) - (U/d) i_ /o73//2 = Z exp(-E/RT) (89) (U/d) - (U/d) exp(E/RT) ( (u/d) ---- ( = exp(-E/RT) (90) 1-P/P~ x

-166with empirically derived Equation (85): (U/d) - (U/d)o (u/d) - d- = Z exp(-E/RT) 1 - p/po The chemical reaction equation indicates that the P/P~ term should be raised to the 3/2 power, and the diffusion equation indicates that a distance parameter x is needed. The interesting fact here is that the equation for the chemical reaction is the same as Equation (85) since the term 1-P/P0 is proportional to l-(P/P)3/2 as long as P/PO > 0o6, Consequently, it can not be said whether Equation (89) or (85) best describes the relationship between the water activity and the kinetic constants over the complete range of water activity, 0.0 to 1.0 o Since all the data available are for values of P/PO > 0.8, the validity of the chemical reaction equation can neither be proven conclusively nor disproven until additional data becomes available. Obviously once this happens, the true relationship can be determined. Until this occurs, however, the empirical correlation given by Equation (85) will be used to describe the relationship between temperature and water activity for the kinetic constants. 3o Theoretical Equations The theoretical equations were previously shown to describe the experimental rate data over the temperature range 2300 to 270~F and over the water activity range of 1.0 to 0.83 for one set of particles separated between screens having 0.0082 and 0.0069 inch openings. The equations were also applied to experimental results obtained using 10 different initial particle sizes separated between 11 screens

-167bracketed by screens having 0.0164 and 0.0021 inch openings. Whenever these equations are used to extrapolate the data beyond this limited range of experimental conditions, caution should be exercised. a. Limitations. Six limitations must be considered whenever the equations describing the dihydrate-hemihydrate reaction mechanism are used: (1) the range of water activity, (2) the initial dihydrate particle size, (3) the accuracy of the l/T j correlation, (4) the mechanism change for large particles, (5) the mechanism change for small particles, and (6) the mechanism change caused by temperature changes. (1) From the discussion on the rate controlling step, it is obvious that the theoretical equations can only be safely extrapolated to values of activity near 0.6, because beyond this point the form of the correlating equation is questionable. Since the limits of solubility of sodium chloride solutions and synthetic sea water concentrates occur for an activity near 0.7, this particular problem should not restrict the applicability of this equation to aqueous and brine solutions normally encountered in desalinization processes. However, this limitation will become important whenever the reaction occurs in aqueous solutions capable of having extremely low water activities, i.e. concentrated ethanolwater solutions. (2) Another limitation on the application of these equations results from the fact that the effects of initial dihydrate particle size were never incorporated into the equations giving the nucleation rate constant and the induction times as functions of temperature and water activity. These equations are all based on measurements made using only one initial dihydrate particle size close to the size which gives a

-168maximum nucleation rate constant and a minimum induction time. Consequently, the results from this study exhibit almost the shortest possible induction times and the highest possible nucleation rates. Applying these results to processes where the dihydrate crystals may have different sizes under different experimental conditions may result in conservative estimates with respect to nucleation times, since the actual reactions would probably exhibit induction times greater than those calculated from these correlations. (3) Another limitation also exists on the correlation of induction timeso The correlation of 1/T 5 with temperature and water activity was not considered as satisfactory as the other correlations because the data for sodium chloride solutions and synthetic sea water fell around two separate lines instead of around the one least squares line for all the data pooled together as shown in Figure 65. This correlation can be improved by the addition of another parameter which should bring the data into one straight line. One such parameter might be the supersaturation of the bulk solution with respect to the nucleating, hemihydrate phase, but this possibility could not be checked since the concentration of calcium sulfate was not known for all the solutions used, (4) One of the more important factors limiting the range of applicability of the model is the assumption that the hemihydrate phase grows almost instantaneously through the dihydrate crystal in the C direction and that the remaining growth is two-dimensional, allowing the transformation to be described by a two-dimensional, mathematical model, This assumption is valid as long as the time for growth in the C direction is small and considerably less than 01 o The time for growth

-169depends upon both the final hemihydrate crystal dimension c and on the rate of growth of the hemihydrate needle UC, and it is defined as: 9c = c/UC ~ Whenever this assumption is no longer valid, growth can not be described by a two-dimensional model but must be described by a three-dimensional model. For such a case, the growth in the C direction must also be treated as a function of time, Such a treatment results in four possible, three-dimensional models, one applicable for each of the following conditions: Gc < 91, 91 < Oc < 2 9 92 K -c G< 3' and Oc 903. Experimental evidence of this change in mechanismwhere growth in the C direction is no longer instantaneous,is shown by the results of run 6 which represent the conditions where Oc 03 The theoretical equations for this special case were derived as shown in Appendix R and used to calculate the theoretical rate curve based on four impingement times: Q, 92 0 @3' and Gc. Figure 70 shows the experimental data points obtained for this run along with the smooth rate curve calculated using the three-dimensional model. The agreement is considered fairly good as a first estimate, since only a few estimates of the four impingement times were made. For the first 50 minutes of this reaction, the data values were probably masked by the thermal volume expansion because the reaction probably nucleated faster than usual because of the sawing technique used in shaping the initial crystal. Nevertheless, the overall agreement is considered satisfactory. (5) Another important factor limiting the model is the assumption that all the initial dihydrate particles are parallelepipeds having the same size and shape. The inherent cleavage properties of the dihydrate crystals allow this assumption to remain valid for all but the smallest

I I I I I I I I'''' I I I I'.010 * 00 0 ~0 -~~~~ * TEMPERATURE, 0F O0 50 100 150 200 250 TEMPERATURE. ~F Figure 70. Fit of the Theoretical Curve, Calculated Using the Three-Dimensional Model, to the Experimental Data for Run 6 for the Dehydration of a single crystal of Calcium Sulfate Dihydrate to Hemihydrate in Water at 261~F.

-171particles, where crushing and grinding eventually results in particles having the shapes of polyhedrons or spheres with rough surfaces. As the particles become smaller and more nearly spherical in shape, the impingement process probably changes because of the increasing percentage of impingement between the hemihydrate needles and the spherical surface. This is accompanied, of course, by a decrease in the amount of impingement between adjacent nuclei because the number of nuclei per particle decreases as the particle size decreases. When this happens, the shape of the reaction rate-versus-time curves changes to the shape of one exhibiting a minimum between two maxima as shown in Figures 71 and 72 for runs 33 and 16, respectively. (6) Changes in temperature for a constant initial particle size can also cause this same effect to occur. In this case, as the temperature decreases, the number of hemihydrate needles per particle also decreases resulting in more impingement between nuclei and the curved surface of the dihydrate particle, and less impingement between adjacent nuclei. Thus, the transformation mechanism can be changed by either grinding the particles small enough and reacting at one temperature, or by lowering the temperature while holding the particle size constant. The conditions under which this phenomenon occurs are shown graphically in Figure 73 where the average particle diameters (estimated by the average screen size openings D) are plotted along with the values of the b dimension of the transformed hemihydrate subcrystal calculated in Appendix S. As the value of b approaches that of the average crystal diameter D, the change in reaction mechanism becomes more apparent as shown by the change in shape between runs 33 and 16, where the depth of

.0 0 6 I I - 1 I I | - 1 - |\.005.004 * -'00 ^r L:-003~ O0 0 0.. *..0 I.001- * * Joe.0 ~ @0 0 ~~~ ~ *Z 0 100 200 300 400 500 TIME, MINUTES Figure 71. Variation in the Reaction Rate as a Function of Time for Run 3355 on the Transformation of Calcium Sulfate Dihydrate to Hemihydrate in Water at 2500F Using Extremely Fine Dihydrate Particles.

.05.04.03 * * * X I **.01 0* ~ x2".02* *oC ~ * *! l I., — * —— t. l l 0 10 20 30 40 50 60 * 70 80 TIME, MINUTES Figure 72. Variation in the Reaction Rate as a Function of Time for Run 16 on the Transformation of Calcium Sulfate Dihydrate to Hemihydrate in Water at 2600F Using Extremely Fine Dihydrate Particles.

.0045 I I I.0040 0.0035 lr) ( _ \. _ w Z \.0025 RUN 33 > AVERAGE PARTICLE S:I SIZE FOR RUNS 16 03- 8 33: 0.0027 CM LLJ \ RUN 16.0020.0015- 220 230 240 250 260 270 TEMPERATURE, OF Figure 73. Relationship Between Values ofthe b Dimension of the Hemihydrate Subcrystals as a Function of Temperature and the Average Particle Size for Runs 16 and 33.

-175the minimum increases with decreasing temperature. For a reaction at still lower temperatures, this change should become even more apparent. This was confirmed by the characteristic shapes of the rate curves observed by Budnikoff(l2) for the dehydration in air at 225~F of samples of powdered selenite, shown in Figures A-3 and A-4 of Appendix A. b. Range of Applicability. The theoretical equations derived from the postulated reaction mechanism should be applicable over the temperature range 2300 to 270~F, and over the water activity range 0.6 to 1.0, provided the initial particles meet the following conditions: First, the particles must be small enough so that the time of growth in the C direction is almost instantaneous: i.e., 0 ~ c/Uc Q< 1 Second, the crystal must be large enough so that each particle is approximately a parallelepiped transformed by several hernihydrate needles: i.e., b <D. D. Applicability of Results The aim of most engineering research is to obtain numerical results which can be applied to industrial processes. Before the TTT results obtained in this study can be applied directly to the calcium sulfate scale problem, some means of classifying the crystal size and shapes in industrial dihydrate scale must be obtained. Some estimate must also be obtained of the effects of impurities entrained in the scale on the rate of reaction and on the impingement process. Since the proposed model accurately describes the rate of transformation in irregularly shaped dihydrate crystal fragments, it is believed that the model will also be able to describe the transformation in actual calcium sulfate scale.

-176The time-temperature-transformation results reported in this dissertation should be especially useful in the design and evaluation of certain phases of many desalinization processes. Information previously available for this purpose, on the calcium sulfate-water system, consists primarily of the values of transition temperatures which only indicate if the phase transformation can occur or not, whereas the TTT relationships presented here show not only whether or not the reaction will occur, but also the extent to which it will occur for different combinationsof time and temperature. In particular, the TTT relationships should be useful in the evaluation of phase equilibrium and solubility data previously reported on the calcium sulfate-water system. When the data of different investigators were plotted on a single figure, there was so much scatter that it was difficult to determine the exact solubility curves(81). One possible explanation for this is that the time required to reach equilibrium exceeded the induction time for a phase change. Once such a phase change was initiated, the concentration of the dissolved solids in the solution would change due to the transport phenomenon in which the more stable phase would dissolve and the less stable phase would precipitate resulting in a concentration gradient existing in the solution. Samples taken under such conditions would, undoubtedly, have a concentration between the two solubility values depending upon the relative rates of solution and dissolution. It is in fact possible that the time required to reach equilibrium could be -longer than the time necessary for the initiation of the transformation, whereupon the true values of the solubility could not be measured.

-177The TTT relationships should also be useful in the evaluation of desalinization processes using seeding techniques to prevent scale formation. In general, such processes involve the addition of small, solid, seed crystals to the feed water of evaporators in hopes that the scale will form on the seeds in preference to the heat transfer surface. In the past, successful operation of pilot plants using seeding techniques did not always result in successful designs of full size plants using the same techniques. This might have been caused by the transformation of the seed crystals due to longer exposure or higher temperatures in the larger evaporators compared to the pilot size units in which the processes were originally developed. Furthermore, these TTT relationships may also be useful in developing descaling processes especially where the scale which forms can be dehydrated to another phase under the prevailing operating conditions. When such conditions are encountered, a knowledge of the physical and chemical properties of each phase will determine which phase would be easier to remove*. Using this information along with the TTT relationships, the necessary operating conditions can be determined to optimize the descaling operation. For example, in the calcium sulfate - water system, the hemihydrate phase might be easier to chemically attack since the dehydration of the dihydrate to the hemihydrate results in the formation of hemihydrate crystals fragmented by small cracks. Thus, it might be possible to chemically attack the hemihydrate scale formed from dihydrate scale by first allowing the heat transfer surface to become dry, vaporizing the water in these cracks and crevasses,and then to apply some cold

-178chemical which will be pulled into the cracks by the condensing vapor, thereby increasing the surface area and facilitating the chemical removal of the scale. E. Areas of Possible Future Research During the writing of this dissertation, several areas for possible future research became apparent. These are enumerated below for reference as seven possible future studies: (1) Studies on the dihydrate-hemihydrate transformation in aqueous solutions over the range of water activity, 0.0 to 0.8. (2) Studies on the dihydrate-hemihydrate transformation in air over the range of water activity, 0.0 to 1.0, along with a comparison with the results of the first study. (3) Studies on the effects of changing the length of dihydrate crystals on the four possible, three-dimensional, reaction models. (4) Studies on the effects of extremely small particle sizes on the dihydrate-hemihydrate transformation. (5) Studies on the velocities of the dihydrate-hemihydrate interface for the reaction in air and in aqueous solutions over.the range of water activity, 0.0 to 1.0. (6) Studies on the heterogeneous nucleation of calcium sulface hemihydrate on, or within, crystals of dihydrate from solutions supersaturated with respect to calcium sulfate hemihydrate. (7) Studies on the hemihydrate-anhydrite transformation in air and in aqueous and brine solutions to determine the effects of temperature, water activity, and initial particle size and configuration on the reaction mechanism.

VII. SUMMARY Presently, evaporative processes are the most feasible means of recovering potable water from sea water, but these processes are limited by calcium sulfate scale which forms on the heat transfer surfaces. This scale forms by the nucleation and growth of calcium sulfate dihydrate, hemihydrate, or anhydrite from solution, usually followed by the dehydration to the anhydrite phase whenever possible. In order to understand this scaling process, so that it can be either controlled or eliminated, both the fundamental steps of its formation and transformation must be known. The purpose of this investigation was primarily to study the dihydratehemihydrate transformation in detail as one part of the whole problem. This research was divided into two major studies: (1) the studies of the time-temperature-transformation (TTT) relationships of the dihydratehemihydrate and the hemihydrate-anhydrite transformations and (2) studies of the kinetic mechanism of the dihydrate-hemihydrate transformation. In the TTT studies, the reactions were followed dilatometrically by observing the change in total volume of the system, as a function of time, in a special glass dilatometer while simultaneously recording the temperature and height of the liquid meniscus in the dilatometer capillary at equal time intervals. In the mechanism studies, the dihydrate-hemihydrate transformation was observed microscopically in a special cell designed to duplicate the conditions encountered in the dilatometer. The dihydrate-hemihydrate transformation was observed in 0.0%, 0.5%, 1.0%, 3.5%, 7.0%, 14.0%, and 21.0% sodium chloride solutions and in -179

-180solutions containing 1.0, 2.0, 3.0, and 4.0 times the salt concentration of normal synthetic sea water over a temperature range 230~ to 270~F. All the experiments were made using dihydrate crystal fragments separated between screens having 0.0082 and 0.0069 inch openingsexcept for those used to study the effect of changing the initial particle size. The particles used in these experiments ranged from one large crystal to a fine powder. The hemihydrate-anhydrite transformation was observed in water, in 3.5% sodium chloride solutions, and in normal synthetic sea water over a temperature range 325~ to 3500F using dihydrate particles separated between screens having 0.0116 and 0.0082 inch openings, which were first reacted to hemihydrate in the dilatometer, then to anhydrite. The phases occurring in all the experiments under different steady state conditions were verified from their x-ray powder diffraction patterns. The TTT curves obtained show that both the induction times and the reaction times for both reactions decrease with increasing temperature or decreasing water activity, indicating that the overall rate of reaction increases from both of these changes. Changes in the initial dihydrate particle size were shown to affect only the induction time and the nucleation rate constant for the dihydrate-hemihydrate transformation, resulting in a minimum induction time and a maximum nucleation rate constant being observed for particles of about 0.01 inches in length. The studies on the transformation mechanism, describing the microscopic observations, the measurements, and the calculations, resulted in a solid state reaction mechanism for the dihydrate-hemihydrate transformation in aqueous solutions.

-181The transformation was observed by photographing the growing hemihydrate phase within single crystals of optical grade selenite at equal time intervals while simultaneously recording the temperature of the system on a recording potentiometer. The micrographs obtained show the configuration and orientation of the forming hemihydrate phase to the known cleavage planes of selenite, and measurements on the micrographs gave values of the rates of transformation in three different directions within the dihydrate crystals as functions of temperature. Based on these observations, a mathematical model was derived which describes the nucleation, growth, and impingement of growing hemihydrate needles with each other and the boundaries of the parent dihydrate crystals during the transformation process. Using this model, the values of the kinetic constants appearing in the equations describing the rate of reaction were obtained by fitting the smooth curves generated using these equations to the experimental rate values using a trial-and-error procedure. The dependence of these rate constants on temperature was successfully described using the Arrhenius equation, and their dependence on both temperature and water activity was described using Equation (85): (Ri - Rio)/(l - p/pO) = Z exp (-E/RT) Using this correlation and the equations describing the reaction mechanism, time-temperature-transformation curves were calculated which compared favorably with the experimentally measured TTT values, establishing

-182the validity of the model, and providing a means of interpolating and extrapolating the data obtained in this research. The time-temperature-transformation results obtained in this investigation should be useful in evaluating phase equilibrium and solubility data presented in the literature on the calcium sulfate - water system in terms of possible transformations, and in the evaluation of processes using calcium sulfate seed crystals for preferential nucleation sitesvby providing information on the stability and transformation characteristics of these crystals in aqueous or brine solutions.

APPENDICES -183

APPENDIX A RESULTS IN THE LITERATURE Some of the important results encountered in the literature are presented briefly in this appendix. The relationship between the six different unit cells of gypsum reported are shown in Figure A-l. This diagram was extremely valuable in understanding the crystallographic data when the authors were discussing the same phenomenon using different unit cell designations. (63) The results of the investigations of Newman and Wells on the transformation of y-CaSO4 to P-CaSO4 are presented in Figure A-2 and Table A-1 showing the time-temperature-transformation zone for this reaction. Their results show the extreme instability of y-CaSO4 in the presence of water and, consequently, also show that the transformation of dihydrate to hemihydrate in aqueous solutions is followed by the dehydration of the hemihydrate to natural anhydrite without the formation of "soluble anhydrite". The experimental data of Budnikoff(12) on the dehydration of gypsum flakes in air are presented in detail in Table A-2, Since his experimental observations were reported at equal time intervals, they were analyzed using the methods described in this text. The data were converted into the dimensionless a form by dividing the percent transformation by the total theoretical percent transformation, i.e. 15.69. The rate of reaction da/dt was obtained using Equation (26). The rate data are shown plotted in Figures A-3 and A-4. -184

-185a O8 NORATO L for GysTER d STRUNZ r t t CleavBRAGGee Hwie and Zussman (21) ) GOSSNER DEJONG a\ MORPHOLOGICAL BOUMAN CELL 6.29/=c / a=5.68 A Figure A-1. Relationships Between the Different Unit Cells Reported in the Literature for Gypsum Viewed Perpendicular to the (010) Cleavage Plane (After Deer, Howie, and Zussman (21)).

-1865,000 1,000 \ \ NATURAL ANHYDRITE, _~\ \ -CoSO4 V) 100 0 I \ zr P W |- "SOLUBLE ANHYDRITE, \ 0 F- -caso4 \ \' 10 0 100 200 300 40 500 TEMPERATURE, ~C Figure A-2. Time-Temperature-Transformation Relationships for the Phase Transformation of C - CaS04 to ( - CaSO0 Determined by Newman and Wells Using X-ray Methods.

.O0O 1i I I I I l I I I I I I i I i.010 T o 0 cr' 005 0g~~~~ - P Os\0~~~~~ 0 0 50 100 150 200 250 300 TIME, MINUTES Figure A-3. Variation in the Reaction Rate as a Function of Time Observed by Budnikoff for the Transformation of Calcium Sulfate Dihydrate (Coated with Sodium Chloride) to Hemihydrate in Air at 107~C.

.01 I I A i II.01050 T~~~ z. 0 0: f\.~~ -o w F -.005 z or0 w 0 50 100 150 200 250 300 TIME, MINUTES Figure A-4. Variation in the Reaction Rate as a Function of Time Observed by Budnikoff for the Transformation of Calcium Sulfate Dihydrate to Hemihydrate in Air at 107~C.

-189TABLE A-1 X-RAY DATA BY NEWMAN AND WELLS Temp., Time Phase ~C Hours Identified 110 3,670 SA 150 170 SA 624 SA 2,080 SA 200 3 SA 145 SA 670 SA & NA 300 2 SA 19 SA & NA 48 SA & NA 115 NA 400 1/2 SA & NA 425 1 SA & NA 114 NA 450 1 NA 500 1/2 NA 625 1 NA 114 NA 900 1 NA 114 NA 1,100 4 NA 1,225 2 NA Reaction in Presence of Liquid Water 170 1 1/2 NA 210 44 NA SA = "Soluble Anhydrite", y - CaS04 NA = "Natural Anhydrite", F - CaS04

-190 - TABLE A-2 EXPERIMENTAL RESULTS OF BUDNIKOFF The Dehydration in air at 107~C of: Gypsum and 5% NaC1 Gypsum Time, Percent da/dt, Percent dac/dt min Wt Losmin Wt. Loss a min 0 0.00.0000.0000 0.00.0000.0000 10 0.20.0127.0009 0.58.0369.0050 20 030.o0191.0006 1.60.1019.0070 30 0.40 00254.0013 2.78.1771.0091 40 0.72.0458.0031 4.48.2855.0082 50 1o40.0892.0053 5.38.3428.0079 60 2.40.1529.0066 6.96.4435.0080 70 3.50.2230.0057 7.90.5035.0064 80 4.20.2676.0057 8.98.5723.0071 90 5.30.3377.0051 10.14.6462.0068 100 5.82.3709.0049 11.14.7100.0058 110 6.86.4372.0037 11.98.7635.0049 120 7.0.4461.0017 12.68.8081.0041 130 7.40 o4716.0041 13.28.8463.0035 140 8.30o 5289.0047 13.78.8782.0026 150 8.90o 5672 o0044 14.12.8999.0016 160 9-70.6182.0041 14.30.9114.0017 170 10.20.6500.0035 14.68.9356.0015 180 10o80.6883.0031 14.78.9420.0012 190 11.20.7138.0035 15.06.9498 o0008 200 11o90.7584.0031 15.o4.9685 210 12,20 07775.0025 220 12o70 08094.0019 230 12.80 o 8158.0009 240 13o00.8285.0019 250 13o4o0 8540.0015 260 13.50.8604.0012 270 13080.8795.0012 280 13o90o 8856.0001oo 290 13.84.8820.0000 300 13.90 08859.0008 310 14o10o 8986.0015 320 14.40.9177.0009 330 14.40.9177.0003 340 14.50.9241. —--

APPENDIX B THERMOCOUPLE CALIBRATIONS The copper-constantan thermocouples used in the dilatometric and microscopic experiments were calibrated by inserting the four inches of available thermocouple wire with the glass plug attached into the vapor of gently refluxing pure ethanol, and pure water, and into solidifying sodium sulfate decahydrate (Na2S04 10H20), and the values of the temperature indicated by the thermocouples were automatically printed on the chart paper of the recording potentiometer used in the experiments. The values of the reference temperatures were determined from the published reference values using the standard barometric corrections for water.(42) A barometric correction for ethanol based on the following equation was obtained by fitting the vapor pressure data given in Table B-1(42,97) using the method of least squares: Tact = 78.26 + 0.03396(P-760) - 0.00001846(P-760)2 (B-l) Here, Tact is the boiling point in degrees centigrade corresponding to the barometric pressure P in millimeters of mercury. Linear calibration equations for the three thermocouples used were obtained from the values of the recorded and reference temperatures given in Table B-2 by the method of least squares. The equation for thermocouple No. 1, which was used in dilatometric experiments number 5 through 55, was: Tact = - 1.520 + 1.010 Trec (B-2) -191

-192The equation for thermocouple No. 2, which was used in dilatometric experiments 56 through 76, was: Tact = - 1.380 + 1.009 Trec and the equation for thermocouple No. 3, which was used in the microscopic experiments, was: Tact - 3.11 + 1.015 T act rec where Tact is the reference temperature (Tact was set equal to the given reference temperature when determining the coefficients appearing in these equations) and T r is the recorded temperature. qrec When the data given in Table B-2 was correlated it had a standard error estimate of 0.34~F, 0.18~F, and 0.20~F, respectively. The absolute accuracy of the recording potentiometer was reported as + 0.030 my, corresponding to a probable error of + 1.4~F at 50~F and of + 1.0~F at 350~F. Therefore the thermocouple calibration was well within the accuracy of the instruments. TABLE B-l VAPOR PRESSURE DATA FOR ETHANOL(24,97) Temperature Pressure ~C mm of Hg 70.00 542.5 77.26 750.0 78.26 760.0 79.26 770.0 80o00 812.6 85.00 986.3

-193TABLE B-2 DATA OBTAINED CALIBRATING THERMOCOUPLES Reference Recorded Reference Recorded Reference Recorded Temp., ~F Temp.,~F Temp., OF Temp.,~F Temp. OF Temp., F Data for Thermocouple No. 1. 90.29 90.10 171.88 171.10 210.66 209.50 90.29 90.20 171.51 171.25 210.65 209.50 90.29 90.40 171.20 171.10 210.80 209.90 90.29 90.60 171.19 171.45 210.83 210.00 90.29 91.10 171.15 171.45 210.84 210.30 90.29 90.70 171.39 171.40 210.55 209.50 90.29 90.95 171.48 171.55 210.53 210.00 90.29 90.60 171.64 171.55 210.18 209.60 90.29 91.35 171.69 171.80 210.17 210.15 90,29 91.00 171.73 171.80 210.14 209.70 90.29 91.00 172.07 172.00 210.41 209.90 90.29 91o00 171.63 171.45 210.49 210.00 90.29 91.00 171.61 171.00 210.67 209.95 90.29 91.00 171.65 171.20 210.73 210o00 90.29 91.00 171.66 171.55 210.76 210.10 90.29 90.95 171.67 171,70 211.13 210.15 90.29 90.50 171.68 171.40 210,75 209.95 90.29 90 50 171.72 171.90 210,64 209 45 90.29 90.90 171.71 171.70 210.70 209.70 90.29 90.80 Data for Thermocouple No. 2. 90.29 90o80 171.15 171.10 211.09 210.60 90.29 91.00 171.43 171.20 210.30 209.70 90.29 90.90 171.42 171.60 210.11 209.40 90.29 90.60 171.56 171.75 210.42 209.90 90.29 90.70 171.53 171.60 210.63 210,00 171.45 171,30 210.59 210.00 210.51 209.95 Data for Thermocouple No. 3. 9029 9190 17131 171.90 210.38 210.10 90.29 91.95 171.22 171.95 210,32 210.00 90o29 91.95 171.12 171.95 210.20 210.10

APPENDIX C CALIBRATION OF DILATOMETER CAPILLARY The capillary tube, with attached metal scale used in the dilatometric experiments, was calibrated by injecting equal volumes of deionized water into the capillary using a micrometer syringe (calibrated by weighing mercury displacements to give 0.1975+0.0003 ml/1000 scale divisions). The height after each injection was read against the metal scale with a precision cathetometer under conditions of constant temperature and atmospheric pressure. During the calibration 70 equal volume increments of 0.001975 ml each were infected into the capillary giving a total observed height change of 45.515 cm corresponding to 0.650 cm per increment, and an average crosssectional area of 0.0030375 cm2, calculated by dividing the total volume added by the total height change observed. The difference between the values read from the metal scale attached to the capillary and the reference values calculated by successive additions of the value 0.650 cm to the first scale reading of 0.110 cm was calculated for each value of the observed height as the correction at that point. The corrections needed for the intermediate points were determined by a linear interpolation between the measured values using the computer program given in Appendix D and the calibration corrections shown in Table C-lo -194

-195TABLE C-1 CALIBRATION FOR CAPILLARY USED IN THE DILATOMETRIC EXPERIMENTS. Height, Correction, Height, Correction, cm cm cm cm 0.110 0.000 23.518 -0.347 0.735 0.025 24.168 -0.377 1,440 -0.030 24.818 -0.392 2.105 -0o044 25.468 -0o397 2.770 -0.059 26.119 -0.371 3.435 -0.074 26.769 -0,356 4.095 -0oo84 27.805 -0.386 4.775 -0.114 28.455 -0.386 5.430 -0.118 29.090 -0.371 6.085 -0.123 29.710 -0.340 7.400 -0.133 30.340 -0.320 8.090 -0.138 31.000 -0.330 8,725 -0.177 31.645 -0.325 6.745 -0.162 32.280 -0,310 9.400 -0.187 32.885 -0.264 10.055 -0.192 33.505 -0.234 10.700 -0.187 34.175 -0.254 11 385 -0.221 34.820 -0.249 12.035 -0.221 35.465 -0.243 12.680 -0.216 36.085 -0.213 13.330 -0.216 36.705 -0.183 13.985 -0.221 37.390 -0.218 14.66o -0.245 38.025 -0.203 15.315 -0.250 38.665 -0.192 15.965 -0.250 39.270 -0o147 16.160 -0.245 39.885 -0 112 17.270 -0.254 40.555 -0.123 17.940 -0.274 41.210 -0.137 18061o -0.294 41.850 -0.126 19.270 -0.304 42,450 -0.076 19.915 -0.299 43 060 -0.036 20.570 -0,303 43.725 -0.051 21.255 -0.338 44.370 -o0.45 21.915 -0.348 45.020 -0.045 22.570 -0.353 45.625 -0.000 23.210 -0.345

APPENDIX D COMPUTER PROGRAM USEI TO MAKE TEMPERATURE AND HEIGHT CORRECTIONS FOR THE CAPILLARY USED IN THE DILATOMETRIC EXPERIMENTS DIMENSION C(100), L(100), H(600), T(600) INTEGER NF,K,J,I,START,NUMBER,CO,C1,C2,C3,C4,C5, IE,B,A,FACTOR,D READ FORMAT CONST, N READ FORMAT LENGTH, L(O)...L(N) READ FORMAT CORR, C(O-)*..C(N) PRINT COMMENT $1$ THROUGH THREE, FOR K=O,1,K.G.N THREE PRINT RESULTS L(K), C(K) BEGIN READ FORMAT RUNNO, NUMBER READ FORMAT PR, D READ FORMAT CONTRL,CO,C1,C2,C3,C4,C5 READ FORMAT CON,F,E,B,A READ FORMAT HEIGHT, H(O)...H(F) READ FORMAT TEMP, T(O)...T(F) START=1 THROUGH FOUR, FOR J=O,1,J.G.F THROUGH FIVE, FOR K=START,1,K.G.N FIVE WHENEVER H(J).GE.L(K-1).AND. H(J).L.L(K), 1TRANSFER TO CAL CAL H(J)=H(J)+(H(J)-L(K-1))/(L(K)-L(K-1))* 1(C(K)-C(K-1) )+C(K- ) FUUR START=K WHENEVER K G. 1, START=K-1 THROUGH SIX, FOR I=O,1O,I.G.F SIX PUNCH FORMAT HCARD, H(I), H(I+1), H(I+2), H(I+3), 1H(I+4), H(I+5), H(I+6), H(I+7), H(I+8), H(I+9) WHENEVER NUMBER.G. 55, TRANSFER TO GO THROUGH SEVEN, FOR J=O,1,J.G.F SEVEN T ( J ) =-15246773+1.0103362*T(J) TRANSFER TO NINE GO THROUGH EIGHT, FOR J=O,1,J.G.F EIGHT T( J)=-1.3804684+1.0089389*T(J) NINE THROUGH TEN, FOR I=O,10,I.G.F TEN PUNCH FORMAT TCARD, T(I), T(I+l), T(I+2), T(I+3), 1T(I+4), T(I+5), T(I+6), T(I+7), T(I+8), T(I+9) TRANSFER TO BEGIN VECTOR VALUES CONST=$ I5*$ VECTOR VALUES CORR=$7F10.3*$ VECTOR VALUES LENGTH=$7F10.3*$ VECTOR VALUES RUNNO=$I5*$ VECTOR VALUES PR=$I5*$ VECTOR VALUES CONTRL=$6I5*$ VECTOR VALUES CON=$3I5,F5.2*$ VECTOR VALUES HEIGHT=$1()F7.3*$ VECTOR VALUES TEMP=$10F7.1*$ VECTOR VALUES HCARD=$10F7.3*$ VECTOR VALUES TCARD=$10F7. 1*$ END OF PROGRAM -196

APPENDIX E COMPUTER PROGRAMS USED TO CALCULATE NORMALIZED DATA FROH CORRECTED TIME-TEMPERATURE-HEIGHT DATA FR THE:DIHYDRATEHEMIHYDRATE AND THE HEMIHYDRATE-ANHYL)RITE TRANSFORMATIONS R R PROGRAM FOR THE DIHYDRATE-HEMIHYDRATE TRANS. R DIMENSION V(60000) (600), Z(600), X(600), Y(600), 1ALPHAA(600), ZCAL(600), ALPHA(600), TIvflE1(600), T 1IME2(600), RATE(600), XX(600), D(600), DLI(vi(600), 1S(60), TIME(600), USED(600), VHT(600), VEST(600), 1DELV(600), SS(60), ERROR(600), lUELT(600), THT(60() 1), PERCDV(600), SSS(60), CHECK(600), VRXN(600), T 1WT(600), WEIGHT(600), OBSNO(600), I)RATE(600), DD( 1 600), VDELT(600), BETA(600), bLTAA(600), DBETA(6 100) INTEGER B, F, I, J, K, L, N, START, STOP, LIMIT, 1CONSI, CONSJ, TMX, TMAX, TFINAL, USED, C, E, M, ICONTRL, A, NP1, ITER, I TMAX, STARTP, STOPP, TLI N, 1LINT, TAPU, TBDU, LIM, G, H, P, TT CCO, CC1, CC2 1, CC3, 4 CC4, CC5 NORXN STATEMENT LABEL S, SS, SSS R BEGIN READ FORMAT RUNNO, NUMBER READ FORMAT PH, P READ FORMAT CNTRL,CCO,CC1,CC2,CC3,CC4,CC5 READ FORMAT CONST,F,A,BDELTAT READ FORMAT VOLUME, V(O)...V(F) READ FORMAT TEMiP, T(O)...T(F) EXECUTE FTRAP. THROUGH ITO, FOR J=0,l, J.G. F OBSNO( J ) =J+1. TIME1(J )=J*DELTAT TIME2(J)=TIME1 ( J )*TIME1(J) ITO TIME(J)=J*DELTAT C=O LIMIT=14 TEMPMX=O THROUGH IT6, FOR I=0,1,I.G.F/2 WHENEVER T(I) oG. TEMPMX TEMPMX=T (I) C=I IT6 END OF CONDITIONAL LIM=30./DELTAT WHENEVER LIM.G. (F-1)/2, LIM=(F-1)/2 THROUGH ITl, FOR J=B,1,J.G.LIM+LIM ITi VEST(J)=V(J+1)-V(J) VMIN=.ABS. ( VEST ( L IM)) -l17

-198G=L I M THROUGH IT4, FOR J=B,1,J.G.LIM WHENEVER.ABS. ( VEST(J)).L. VMIN V II I\=VEST( J ) G=J IT4 END OF CONDITIONAL L=3 S(3) CONTINUE CONT RL =2 THROUGH IT5, FOR J=B,1,J.G.LIM+LIM ARG=VEST ( J) WHENEVER ARG.LE. 0., ARG=1. Z( J) =ELOG. (ARG) X( J )=TIME J) Y(J)=1. IT5 ZCAL(J)=Z(J) START=B STOP=G-5 STARTP=B STOPP=LIM+L IM WHENEVER CONTRL.E. I, TRANSFER TO CALC PRINT FORMAT TITLE, NUMBER PRINT FORMAT NAME3 TRANSFER TO CALC S(4) CONTINUE H=LIM THROUGH IT8, FOR J=A,1,J.G.LIM+LIM WHENEVER Z(J)oG.ZCAL(J)+.25,AND. Z(J+1).G.ZCAL(J+1 )+.25 H=J TRANSFER TO IT9 IT8 END OF CONDITIONAL IT9 CONTINUE PRINT RESULTS C, G, H WHENEVER H.L. 25.AND. H.G. 20 H=H+(25-H) OR WHENEVER H.LE. 20 H=H+5 END OF CONDITIONAL PRINT RESULTS H WHENEVER H.L. C, C=H PRINT RESULTS C SUMX=O. SUMX2=0. SUMX3=0. SUMX4=0. SUMY=O. SUMXY=0. SUMX2Y=O. N=O NORXN=C-5 WHENEVER CCO.E. 10, NORXN=CC1 THROUGH SQUIGL, FOR J=B,1,J.G. NORXN X(J)=T(J)-T(O)

-199XX(J)=X(J)*X(J) Y(J )=V( J) SUMX=SUMX+X ( J) SUMY=SUMY+Y ( J) SUMXY=SUMXY+X( J )*Y(J) SUMX2=SUMX2+XX ( J) SUMX3=SUMX3+XX(J)*X(J) SUMX2Y=SUMX2Y+XX( J )*Y(J) SUMX4=SUMX4+XX(J)*XX(J) SQUIGL N=N+1 A1=N A2=SUMX A3=SUMX2 B1=SUMX B2=SUMX2 B3=SUMX3 C1=SUMX2 C2=SUMX3 C3=SUMX4 D1l=SUMY D2=SUMXY D3=SUMX2Y R2=A2/A1 R3=A3/A1 E2=B2-B *R2 F2=C2-C1*R2 G2 =2-D 1*R2 E3=B3-B1*R3 F3=C3-C1*R3 G3=D3-D1*R3 Z1=(G2-G3*E2/E3)/( F2-F3*E2/E3) ZBAR=Z1 Yl=(G2-F2*Z1 )/E2 Y2=(G3-F3*Z )/E3 YBAR=(YI+Y2)/2. X=( D1-B1*Y1-C1*Z 1 )/A1 X2=( D2-B2*Yl-C2*Z ) /A2 X3=( D3-B3*Y1-C3*Zl1 )/A3 X4=( D1-B1*Y2-C*Z )/A1 X5=( D2-B2*Y2-C2*Z 1 )/A2 X6=( D3-B3*Y2-C3*Z1)/A3 XBAR=( X1+X2+X3+X4+X5+X6)/6. PRINT FORMAT TITLE, NUMBER PRINT RESULTS Z1 PRINT RESULTS ZBAR PRINT RESULTS Yl, Y2 PRINT RESULTS YBAR PR INT RESULTS Xl, X2, X3 PRINT RESULTS X4, X5, X6 PRINT RESULTS XBAR N=O SUMDD=O. THROUGH IT10, FOR J=B,1,J.G. NORXN TFUNCT=T(J )-T(0)

-200Z(J)=XBAR+YBARe*TFUNCT+ZBAR*TFUNCT *TFUNCT D(J)=V(J)-Z(J) SUMDD=SUMDD+D(J) D(J) PERCDV(J)=(V(J)-Z(J))/V(J)*100. IT10 N=N+1 STDERE=SORT.(SUMDD/N) PRINT FORMAT TITLE? NUMBER PRINT FORMAT NAME1 THROUGH IT12, FOR J=B,1,J.G. NORXN IT12 PRINT FORMAT ABLE, V(J), Z(J), D(J), PERCDV(J) PRINT RESULTS STDERE THROUGH IT13, FOR J=B-1,-1,J.L.O TFUNCT=T ( J)-T (0) IT13 V(J)=XBAR+YBAR*TFUNCT+ZBAR*TFUNCT*TFUNCT THROUGH N11, FOR I=O,1,I.G.F TFUNCT=T( I )-T(0) VHT( I) =XBAR+YBARI*TFUNCT+ZBAR*TFUNCT*TFUNCT VRXN( I)=V( I )-VHT( I) N11 CONTINUE MXDELV=O. THROUGH S8A, FOR I=C,,tI.G. F WHENEVER VRXN(I).G. MXDELV MXDELV=VRXN(I) E=I S8A END OF CONDITIONAL THROUGH N2, FOR I=O,1, I.G. F ALPHAA(I)=VRXN(I)/VRXN(E) N2 CONTINUE THROUGH N3, FOR I=F,-1,VRXN(I).LE. 0.00099999999 N3 CONTINUE CONSI=I I=0 THROUGH N4, FOR J=0,1, I.G. F I=CONSI+J N4 ALPHA(J)=ALPHAA(I) ALPHA(J-1)=1. ALPHA(J)=1. ALPHA(O)=0 I=O THROUGH NI5, FOR J=l,1, I.G. F I=CONSI+J N5 RATE(J)=(ALPHA(J+1)-ALPHA(J-1))/(2i*ELTAT) RATE(0)=ALPHA(1)/(2*DELTAT) I=0 THROUGH N5A, FOR J=ltl,I.G.F I=CONSI+J N5A DRATE(J)=(RATE(J+i)-RATE(J-1))/(2.'DELTAT) DRATE(O)=RATE(1)/(2.*DELTAT) RATE(J-1 )=0. RATE(J)=O. TIME1(0)=O TIME2 (0) =0 I =0 THROUGH S8, FOR J=1,1,I.G.F-1

-201I=CiNS I +J WEIGHT(J)=(ALPHA(J+1)-ALPHA(J-1))/2. TWT(J)=T(I)*WEIGHT(J) S8 CONTINUE WEIGHT(O)=ALPHA( 1)/2. WEIGHT(F)=(ALPHA(F)-ALPHA(F-1))/2. TWT (0) =T ( CONSI )"WE IGHT ( 0 ) TWT( F )=T(CONSI+F )*WEIGHT( F) SUM A=0 SUMT=O THROUGH ITll, FOR J=i,1, ALPHA(J).G. 0.999995 I=CONSI+J SUJMT=SUMT+WE I GH ( J ) T (I) SUMA=SUMA+WE I GHT ( J) IT11 CUNTINUE WEIGHT(J)=(ALPHA(J)-ALPHA(J-1))/2. TWT( J)=T (CONS I+J ) WEIGHT ( J) TRXNAV=(SUMT+WEIGHT(0)*T(CONSI)+WEIGHT(J)* 1T(CONSI+J))/(SUIvIA+WEIGHT(O)+WEIGHT(J)) PRINT FORMAT TITLE, NUMBER PRINT FORMAT NAME2 I=O THROUGH IT3, FOR J=0,1, I.G. E I=CONSI+J PRINT FORMAT ANSB, OBSNO(J), TIME(J), ALPHA(J), 1RATE(J), DRATE(J), T(I), NUMBER IT3 CONTINUE PRINT RESULTS TRXNAV PRINT FORMAT TITLE, NUMBER PRINT FORMAT NAME8 THROUGH IT2, FOR I=0,1, I.G. F IT2 PRINT FORMAT ANSO, TIME(I), T(I), V(I), VHT(I), VRXN( I), ALPHAA(I) WHENEVER P.NE. 1, TRANSFER TO BEGIN I=0 THROUGH IT7, FOR J=O,l,I.G.E I=CONS I+J PUNCH FORMAT CARD, OBSNO(J), TIME(J), ALPHA(J), 1RATE(J), T(I), NUMBER IT7 CONTINUE TRANSFER TO BEGIN CALC CONTINUE THROUGH ONE, FOR J=0,1, J.G. F USED(J)=8 ONE D(J)=0 DLIM(O)=0 SUMZ=O THROUGH ONEA, FOR J=START,1, J.G. STOP ONEA SUMZ=SUMZ+.ABS.(Z(J)) DLIM( 1 )=SUMZ DIF=1. THROUGH TWO, FOR K=l,l, DIF.L..00001 N=0 SUMXX=O

-202SUMXY=O SUMYY=O SUMXZ=O SUMYZ = THROUGH THREE, FOR J=START,1, J.G. STOP USED( J )=O WHENEVER D(J).LE. DLIM(K) USED(J)=1 N=N+1 SUMXX=SUMXX+X(J)*X(J) SUMXY=SUMXY+X ( J )Y ( J) SUMYY=SUMYY+Y(J )Y(J) SUMXZ=SUMXZ+X(J)*Z ( J) SUMYZ=SUMYZ+Y ( J )*Z( J) THREE END OF CONDITIONAL BCONST=(SUMXZ*SUMXY-SUMYZ*SUMXX)/(SUMXY*SUMXY1SUMYY*SUMXX) SUMDD=O THROUGH FOUR, FOR J=O,1,J.G.STOPP ZCAL ( J ) =ACONSTX ( J ) +BCONST*Y(J) D(J)=.ABS.(ZCAL(J)-Z(J)) DD(J )=Z ( J )-ZCAL(J) WHENEVER USED(J).E. 1 SUMDD=SUMDD+D( J )*D(J) FOUR END OF CONDITUONAL THROUGH FOURA, FOR J=STARTP,1, J,G. STOPP FOURA PERCDV(J)=(Z(J)-ZCAL(J))/ZCAL(J)*100. STDERE=SORT. (SUMDD/N) DLIM( K+1 ) =2*STDERE DIF=.ABS.(DLIM(K+1)-DLIM(K)) WHENEVER CONTRL.G. 0 DIF=O TWO END OF CONDITIONAL WHENEVER CONTRL.E. 1, TRANSFER TO SS(L) THROUGH FIVE, FOR J=STARTP,1, J.G. STOPP FIVE PRINT FORMAT ANS, TIME(J), Z(J), ZCAL(J), X(J), 1Y(J), DD(J), USED(J) VECTOR VALUES ANS=$1H,F10.2,5F20.5, 9*$ PRINT RESULTS START PRINT RESULTS S1 JP PRINT RESULTS AC )NST PRINT RESULTS i'U NST PRINT RESULTS STDERE PRINT RESULTS DLIM(K) PRINT RESULTS DIF R WHENEVER L.L. LIMIT L=L+1 TRANSFEF TO S(L) END OF.JNDITIONAL TRANSFER TO BEGIN R VECTJR VALUES RUNNO=$I5*$ VECTOR VALUES PH=$I5*$

-203VECTOR VALUES CNTRL=$6I5 $ VECTOR VALUES CONST=$3I5,F5.2:$ VECTOR VALUES VOLUIME=$1OF7.5':$ VECTOR VALUES TEMP=$10F7.2. $ VECTOR VALUES TITLE=$1H1,S4,23HEXPERIMENTAL RUN 1\ 1UMBERSi17H...... I 5'$ VECTOR VALUES ANSB=$1H,FO0.O,F10.2,3F10.5, F10.2, 1S55,15'$ VECTOR VALUES ANSO=$1H,2F10.2,3F10.3, F10.5'$ VECTOR VALUES ABLE=$1H,4F20.3'$ VECTOR VALUES CARD=$F1O.O0F10.2,2F10.5,F10.2,S5 I 15, $ R VECTOR VALUES NAME1=$1H,S14,6HHEIGHTS1O, lOHCAL 1HEIGHTS5,15HDEV FROiMV HEIGHTS9,11HPERCENT DEV':'$ VECTOR VALUES NAME3=$1H,S6,4HTIMES1O 10HELOG(DE 1LV),S16,4HZCALS16,4HTIMES18,2HY=,S12,8HDEV ZCAL, S4, 5HUSED=.'$ VECTOR VALUES NAME2=$1H,S4,6HOBS NOS6,4HTIME,S5 t, 5HALPHA, S6,4HRATE, S55HDRATES6,4HTEMP, S4,6HNUrMB 1ER: $ VECTOR VALUES NAME8=$1H,S6,4HTI ME, S6,4HTEMPS7 3 1HVOL,S7,3HVHT, S6,4HVRXN, S4,6HALPHAAg*$ R END OF PROGRAM

-204R R PROGRAM FOR THE HEMIHYDRATE-ANHYDRITE TRANS. R DIMENSION H(500), T('500), TIME(500), ALPHAA(500), 1RATE(500), TIMEA(500), OBSNO(500), ALPHA(500), 1PERCTD(500), X(500), Y(500), Z(500), 1(500) INTEGER J, START, STOP, ZERO, END, F BEGIN READ FORMAT RUNNO, NUMBER READ FORMAT CONST, F, DELTAT, TRANSL, START, STOP READ FORMAT HVAR, H(O)...H(F) READ FORMAT TVAR, T(0)...T(F) THROUGH FIVE, FOR J=O,1,J.G.F TIME( J )=(DELTAT'J+TRANSL)/100. X(J)=(T(J)-T(O) )/100. FIVE Y( J )=X( J ) X ( J) TIME(O)=0. N=O. SUM W = 0. SUM iX= 0 SUMv Y = 0. SU MF Z= 0. SUMWX=O. SUMWY=0. SUMW Z = 0. SUMXX=0. SUMXY=0. StUMXZ=0, SUIVMYY=O0 SUMY.Z=O. SUMtiZZ=0. THROUGH SIX, FOR J=START,1,J.G.STOP SUMW=SUMW+H( J) SUMX=SUX+X ( J ) SUM VY=SJMY+Y ( J ) SUMZ=SUMZ+T IME ( J) SUMWX=SUMWX+H ( J ) X ( J ) SUIMWY=SUMWY+H ( J ) *Y (J ) SUMWZ=SUMIWZ+H( J ) *T IME J) SUMXX=SUMXX+X ( J ) X ( J) SUMXY=SUMXY+X (J) *Y J ) SUMXZ=SUMXZ+X ( J )*TIME (J) SUMYY=SUMYY+Y( J )*Y ( J) SUMYZ=SUMYZ+Y( J )*TIME(J) SUMZZ=SUMZZ+T IME ( J )TIME( J) S I X N=lN+1. A1=N SUMXZ-SUMX*SUMZ B1=SUMX'-SUMXZ-SUMXX-SUMZ C 1=SUMY* SUMXZ-SUMXY*SUMZ D1=SUMWSUMXZ-SUMWX*SUMZ

-205A2 = N: SU MY Z - S UMY: S UM Z B 2= S U MX S UMY Z - S UMX Y *S M Z C 2 =S U MY S U M Y Z - S U Mi Y Y S U M Z D2 =SUMW:S U MY Z-SUMWY*SU M Z A 3= N S U M Z Z - S U M Z S SU M Z B3=SUMX^. SUMZZ-SUMvlXZ" SUMZ C 3 = S U vM X SUMl Z Z - SUM X Z 7: S Uj I Z C 3=SUMY SU M ZZ-UMY SUMYZ SMZ D3=S UMW SUMZZ-SUM WZ SUMIIZ E 1=A 1C 2-A2'-C 1 F 1= B 1 C 2- B 2 C1 G1=D1 C 2-D2*C1 E2=A 1 -C3-A3 C 1 F2=B 1*C3-83 C 1 G2=D 1 C 3-D 3'C 1 AA=( G1'F2-G2F 1)/ ( E1F2-E2*F1) BB=( G1-AA:-E1 )/F1 CC=(D1-AA Al1-BB"B1 )/C1 DD=( SUMW-AA N-BB'SUMX-CC SUJMY )/SUMZ THROUGH SEVEN, FOR J=O, 1,J.G.F Z (J)=AA+BB", X(J)+CCY( J )+DD*TIME(J) D( J )=H(J)-Z(J) SEVEN PERCTD(J)=(D(J)/Z(J ) )100. S U.i =O. N=O THROUGH EIGHT, FO'R J=START,1,J.G.STOP N' =:N+ 1. EIGHT S JMDD= S UivlUMDD+D ( J ) D ( J ) STDERE=SORT. (SUMDD/N) PRINT FORMAT TITLE, NUMBER PRINT FORMAT NAME THROUGH FOURTN, FOR J=START,1,J.G.STOP FOURTN PRINT FORMAT ANS, H(J), Z(J), D(J), PERCTD(J) PRINT RESULTS STDERE PRINT RESULTS AA, BB, CC, DD PRINT RESULTS A1, B1, C1. Dl PRINT RESULTS A2, 82, C2, D2 PRINT RESULTS A3, B3, C3, 03 PRINT RESULTS El, Fl, G1 PRINT RESULTS E2, F2, G2 PRINT RESULTS START PRINT RESULTS STOP THROUGH NINE, FOR J=F,-1,J.LE. START NINE WHENEVER D(J).LE. 0., TRANSFER TO TEN TEN ZERO=J MAX=(). THROUGH ELEVEN, FOR J=ZERO,1,J.G.F WHENEVER D(J).G. MAX MAX=D(J) END=J ELEVEN END OF CONDITIONAL THROUGH TWELVE, FOR J=O,1,J.G.F TIME( J )=DELTAT*J+TRANSL ALPHAA ( J ) =D( J )/MAX TWELVE ALPHA(J)=ALPHAA(J)

-206TIME( )= O0 ALPHA(ZERO)=O. ALPHA( END+ )=1. ALPHA(ZERO-1 )=0. SUMAT=O. SUMA=O. THROUGH THIRTN, FOR J=ZERO,1,J.G.END TIMEA( J )= ( J-ZERO)'DELTAT OBSNO( J )=(J-ZERO) 1.+l. RATE(J)=(ALPHA(J+l)-ALPHA(J-1))/(2.'DELTAT) SUMA=SUJMA+RATE( J ) "IELTAT SUMAT=SUIAT+RATE ( J ) T ( J )'DEL TAT THIRTN CONTINUE TRXNAV=SUMAT/SUMA PRINT FORMAT TITLE, NUMBER PRINT FORMAT NAiME1 THROUGH FIFTN, FOR J=ZERO,1lJ.G.END FIFTN PRINT FORMAT ANSil OBSNO(J), TIMEA(J), ALPHA(J), 1RATE(J), T(J), NUMBER PRINT RESULTS TRXNAV PRINT FORMAT TITLE, NIUMIBER PRINT FORMAT NAME2 THROUGH SIXTIN FOR J=O 1,J.G.F SIXTN PRINT FORMAT ANS2, TIME(J), T(J), H(J), Z(J), 1D(J), ALPHAA(J) THROUGH SEVNTN, FOR J=ZERO,1 J.G.END SEVNTN PUNCH FORMAT CARD, OBSNO(J), TIMEA(J), ALPHA(J), 1RATE(J), T(J), NUMBER TRANSFER TO BEGIN VECTOR VALUES RUNNO=$I'5$ VECTOR VALUES CONST=$I5,F5.2,F5.1,2 I 5$ VECTOR VALUES HVAR=$10F7.3^:'$ VECTOR VALUES TVAR=$10F7.1*$ VECTOR VALUES TITLE=$1H1,17HEXPERI MENTAL RUN, 1 14HNUMBER.......,I 5//*$ VECTOR VALUES NAME=$1H,S14,6HHEIGHT,S10, 4HCAL, 16HHEIGHTS5,15HDEV FROM HEIGHT,S9, 8HPERCENT, 13HDEV// $ VECTOR VALUES AiNS=$1H,4 F20.3' $ VECTOR VALUES NAME1=$1H,S4,6HOBS NO,S6,4HTIME, 1S5,5HALPHAS6,4HRATE TS6, 4HTEMP, S4,6HNL)UMBER:'$ 14HRATE, S 6, 4HTEMP, S4,6HNVUMBER-*$ VECTOR VALUES ANS1=$1H,E10.O,F10.1 2F10.5,F10.1, 1I 10* $ VECTOR VALUES NAME2=$1H,S6,4HTIME,S6,4HTEMvIPS4, 16HEIGHT, 16HHEIGHTS6,4HHCALTS6,4HHRXNS4,6HALPHAA//*$ VECTOR VALUES ANS2=$1H,2F10.1,3F10.3,F10.5*$ VECTOR VALUES CARD=$F10.O,F F10.1,2F105F10.1, I10: $ END OF PROGRAM

APPENDIX F SUMMARY OF EXPERIMENTAL CONDITIONS ** RUN SOLID CRYSTAL SOLUTION PRESS TEMP HEIGHT NO. WT.,GM DIA.,IN CON. PSIG OF CM DEHYDRATION OF CALCIUM SULFATE DIHYDRATE TO HEMIHYDRATE 1-5 PRELIMINARY RUNS NOT ANALYZED 6 1.010 SING.CRYST. DIW 59.0 261.3 12.789 7.630.0195-.0138 DIW 95.* 259.8 7.735 8.770.0138-.0116 DIW 95.* 259.4 9.095 9.720.0116-.0082 DIW 95,* 260.3 7.902 10.705.0082-.0069 DIW 95.* 259.3 8.079 11.700.0069-.0058 DIW 95.* 261.0 7.736 12.700.0058-.0041 DIW 94.0 261.2 7.87 13.700.0041-.0035 DIW 93.* 261.3 5.897 14.700.0035-.0029 DIW 93.* 261.7 6.954 15.700.0029-.0021 DIW 92.0 260.4 7.894 16.700 00021-.0000 DIW 90.0 261.4 7.702 17 PHOTOGRAPHIC HEIGHT READINGS INCOMPLETE 18 PHOTOGRAPHIC HEIGHT READINGS INCOMPLETE 19.700.0041-.0035 DIW 90.0 251.1 8.575 20.700.0058-.0041 DIW 87.* 250.9 8.528 21.700.0035-.0029 DIW 87.* 251.3 8.414 22.700.0069-.0058 DIW 87.* 250.9 8.360 23.700 *0082-.0069 DIW 87.* 251.0 8.393 24.700.0116-.0082 DIW 87.* 250.4 8.479 25.700.0116-.0082 DIW 87.* 251.0 8.506 26.700.0058-.0041 DIW 87.* 250.9 8.279 27.700.0138-.0116 DIW 87.* 251.0 8.405 28.700.0164-.0138 DIW 87.0 250.3 8.384 29.700.0041-.0035 DIW 87.* 249.8 8.037 30.700.0082-.0069 DIW 87.0 250.4 8.337 31.700.0069-.0058 DIW 97.0 251.0 8.440 32.700.0029-.0021 DIW 97.* 250.5 8.243 33.700.0021-.0000 DIW 97.5 250.3 8.222 34 700.0082-.0069 DIW 87.3 250.3 8.434 35.700.0082-.0069 DIW 86.0 249.7 8.368 36.700.0082-.0069 3.5% NaC1 86.* 249.9 8.148 37.700.0082-.0069 21.0% NaCl 86.0 245.0 6.729 38.700.0082-.0069 3.5% NaCl 86.* 240.8 8.060 39.700.0082-.0069 7.0% NaC1 85.0 241.5 7.778 40.700.0082-.0069 14.0% NaCl 85.* 241.1 7.417 41.700.0082-.0069 21.0% NaC1 85.* 236.0 6.948 42.700.0082-.0069 DIW 85.* 240.9 8.102 43.700.0082-.0069 1.0o NaC1 85.* 239.9 8.220 -207

-208RUN SOLID CRYSTAL SOLUTION PRESS TEMP HEIGHT NO. WT.,GM DIA.,IN CON. PSIG OF CM 44.700.0082-.0069 0.5% NaCi 85.* 240.5 8.238 45.700.0082-.0069 1X SSW 85.0 239.4 8.139 46 PHOTOGRAPHIC DATA NOT READABLE 47.700.0082-.0069 3X SSW 89.* 242.0 7.943 48.700.0082-.0069 4X SSW 88.* 242.5 7.794 49.700.0082-.0069 2X SSW 87.0 242.1 7.923 50.700.0082-.0069 1X SSW 87.0 242.0 8.083 51.700.0082-.0069 IX SSW 86.* 235.3 8.134 52.700.0082-.0069 3.5% NaCl 85.0 235.7 7.997 53.700.0082-.0069 3.5% NaC1 85.0 230.9 7.888 54.700.0082-.0069 1X SSW 85.0 231.0 7.867 55.700.0082-.0069 3.5% NaCl 85.0 246.1 8.162 56 CHECK RUN ON THERMAL VOLUME EXPANSION CORRELATION 57 CHECK RUN ON THERMAL VOLUME EXPANSION CORRELATION 58.700.0082-.0069 DIW 90.0 256.9 8.566 59.700.0082-.0069 DIW 90.0 249.6 8.426 60.700.0082-.0069 1X SSW 89.0 249.4 8.261 61.700.0082-.0069 IX SSW 87.5* 245.0 8.244 62.700.0082-.0069 DIW 86.0 244.9 8.331 63.700.0082-.0069 DIW 87.0 262.8 8.723 64.700.0082-.0069 DIW 89.0 269.3 8.823 DEHYDRATION OF CALCIUM SULFATE HEMIHYDRATE TO ANHYDRITE 65.700.0116-.0082 DIW 155.0 TERMINATED 66.700.0116-.0082 DIW 205.0 325.5 3.044 67.700.0116-.0082 3.5% NaCL 200.* TERMINATED 68.700.0116-.0082 1X SSW 200.* 326.2 3.279 69.700.0116-.0082 3.5% NaC1 200.* 326.1 3,416 70.700.0116-.0082 3.5% NaC1 200 3385. 3.434 71.700.0116-.0082 1X SSW 200.0 338.8 3.412 72A.700.0116-.0082 DIW 200.* TERMINATED 72.700.0116-.0082 DIW 200.* 3 9.1 3.453 73A.700.0116-.0082 3.5% NaC1 200.* TERMINATED 73.700.0116-.0082 3.5% NaCl 200.* 347.9 3.658 74A.700.0116-.0082 IX SSW 200.* TERMINATED 74B.700.0116-.0082 1X SSW 200.4* TERMINATED 75.700.0116-.0082 1X SSW 171.0 347.6 3.617 76.700.0116-.0082 DIW 200.* 346.8 3.379 * PRESSURE VALUES DETERMINED BY INTERPOLATION. * CONCENTRATION FOR SODIUM CHLORIDE SOLUTIONS ARE IN WEIGHT PERCENT. CONCENTRATIONS FOR SYNTiHETIC SEA WATER CONCENTRATES ARE EXPRESSED AS A CONCENTRATION FACTOR WHICH IS THE RATIO OF THE WEIGHT PERCENT DIISSOLVED SOLIDS IN SOLUTION TO THE WEIGHT PERCENT —DISSOLVED SOLIDS IN NORMAL SYNTHETIC SEA WATER.

APPENDIX G SUMMARY OF ALL THE TIME-TEMPERATURE-TRANSFORMATION RELATIONSHIPS All the time-temperature-transformation relationships determined during the dilatometric studies are summarized in five different tables in this appendix. Tables G-l through G-4 contain the results for the dehydration of calcium sulfate dihydrate to hemihydrate and Table G-5 contains the results for the dehydration of calcium sulfate hemihydrate to anhydriteo Tables G-1, G-2, and G-5 show the results for the reactions where the solids were immersed in water, 3.5% sodium chloride solutions, and in synthetic sea water. Table G-3 shows the effect of changing solution concentration on the relationships, and Table G-4 shows the effect of changes in initial particle size on the relationships for the dehydration of calcium sulfate dihydrate to hemihydrate. -209

-210TABLE G-1 TIMiE-TEMPERATURE-TRANSFORMAT ION RESULTS FOR THE DEHYDRATION OF CALCIUM SULFATE DIHYDRATE TO HEMIHYDRATE SHOWING THE EFFECT OF THE CONCENTRATION OF THE SOLUTION IN WHICH THE SOLII)S WERE IMMERSED ON THE TRANSFORMATION RUN TEivMP. SOLUTION TIME IN MIN FOR PERCENT REACTED NO. OF CON. 5 25 50 75 95 RESULTS FOR SODIUM CHLORIDE SOLUTIONS 42 240.6 0.0 310 450 570 720 1280 44 240.7 0.5 119 174 224 278 354 43 240.3 1.0 70 98 123 155 206 38 240.0 3.5 35 46 57 69 90 39 239.0 7.0 24 31 37 45 57 40 236.8 14.0 15 19 23 28 36 41 23.04 21.0 12 16 21 27 39 37 237.3 21.0 9 11 14 16 20 RESULTS FOR SYNTHETIC SEA WATER CONCENTRATES 42 240.6 0.0 310 450 570 720 1280 50 241.0 1.0 39 49 57 67 84 49 240.0 2.0 28 34 40 47 57 47 239.5 3.0 21 26 31 36 44 48 238.9 4.0 16 20 24 28 35 * WEIGHT PERCENT DISSI.LVED SOLIDS::* CONCENTRATION FACTOR = (WEIGHT PERCENT DISSOLVED SOLIDS / WEIGHT PERCENT DISSOLVED SOLIDS IN NORMAL SYNTHETIC SEA WATER)

-211TABLE G-2 TIME-TEMPERATURE-TRANSFORMATION RESULTS FOR THE DEHYDRATION OF CALCIUM SULFATE DIHYDRATE TO HEMIHYDRATE WHERE THE SOLIDS WERE IMMERSED IN AQUEOUS SOLUTIONS AT TEMPERATURES BELOW 2700F * RUN TEMP. A-TIME TIME IN MIN FOR PERCENT REACTED NO. OF MIN 5 25 50 75 95 RESULTS FOR WATER 64 265.2 1 22 26 30 34 40 63 260.4 1 30 37 42 49 59 58 255.4 1 41 55 66 77 95 23 250.5 1 66 91 111 130 158 34 250.1 1 76 100 119 139 168 30 250.0 1 95 124 146 169 202 35 249.3 1 83 112 136 162 194 59 249.1 1 63 87 107 127 155 62 244.7 5 110 160 205 250 320 42 240.6 10 310 450 570 720 1280 23-59 249.8 AVE. VALUES 77 103 124 145 175 RESULTS FOR 3.5 PERCENT SODIUM CHLORIDE SOLUTIONS 36 247.0 1 22 27 32 37 46 55 243.7 22 28 34 42 53 38 240.0 1 35 46 57 69 90 52 235.1 1 45 64 83 107 149 53 230.9 1 63 97 133 175 249 RESULTS FOR NORMAL SYNTHETIC SEA WATER 60 247.0 1 25 30 35 40 49 61 243.3 1 33 42 49 58 72 50 241.0 1 39 49 57 67 84 45 239.0 1 56 70 83 99 124 51 235.0 1 78 101 123 148 187 54 230.9 1 147 197 251 310 398 * TIME INTERVAL BETWEEN DATA POINTS

-212TABLE G-3 TI ME-TEMPERATURE-TRAN\ISF)RivMATIOtN RESULTS FOR THE DEHYDRATION CALCIUM SULFATE HEM IHYDRATE TO ANHYDRITE WHERE THE SOLIDS WlERE I!MMLERSED I N A,)UEOLUS SO)LUT I ONS RUN TEMP. A-T IM E TIME IN 1\ IN FOR PERCENT REACTED NO). OF MIN\ 5 25 50 75 95 RESULTLS FOR WATER 66 325.8 10 474 774 1034 1264 1504 72 339.0 10 574 894 1054 1184 1334 76 346.8 10 510 680 790 880 1000 RESULTS FOR 3.5 PERCENT SODIUMI CHLO-RIDE SOLUTIONS 69 326.0 5 175 250 310 360 400 70 338.5 5 125 175 215 250 280 73 347,8 5 95 135 165 195 220 RESULTS FOR Ni!ORMAL SYNTHETIC SEA WATER 68 326.3 5 195 275 350 415 460 71 338.8 5 135 180 225 265 295 75 347,7 5 100 145 195 240 265' TIME INTERVAL BETWEEN DATA POINTS

-213TABLE G-4 TIIME-TEMPERATURE-TRANSFORMATION RESULTS FOR THE DEHY)DRAT'IC)'O OF CALCIUM SULFATE DIHYIDRATE TO HEMIHYDRATE WlHERE THE SCOLIDS WERE IvMMERSED IN A(OUEOUS SOLUTIONS AT TEMiPERATU.RES ABOVE 2750F RUN TEMP. A-T IME TIME IN vMIN FOR PERCENT REACTEL) NO. OF MIN 5 25 50 75 95 RESULTS FOR WATER 65 282.5 0.1 7.5 -.- -.- -.- 12.5 66 289.6 0.1 6.0 -.- -.- -.- 10. 72A 297.1 0.1 6.2 -.- -.- -.- 8. 72 297.8 0.1 6.0 -.- -.- 9.0 76 298.7 0.1 5.7 -- -.- -.- 8.0 RESULTS FOR 3.5 PERCENT SODIUM CHLORIDE SOLUTIONS 67 275.8 0.1 3.3 -.- -.- -.- 8.( 69 279.3 0.1 4.1 -.- -.- -.- 8.9 70 286.7.1 4.8 -.- -.- -.- 7.8 73A 282.9 0.1 4.3 -.- -.- -- 6.8 73 283.5 0.1 4.7 -.- -. - - 6.6 RESULTS FOR NORMAL SYNTHETIC SEA WATER 68 282.5 0.1 5.2 -.- -.- -.- 8.9 71 285.6. 0.1 5.2 -.- -.- -.- 7.6 74A 289.0 0.1 4.4 -.- - -.- 6.4 74B 288.4 0.1 4.8 -.- -.- -.- 69 75 287.4 0.1 4.8 -.- -- -.- 6.9 TIME INTERVAL BETWEEN READINGS

-214TABLE G-5 TIME-TEMPERATURE TRANSFORMATION RESULTS FOR THE DEHYDRATION OFCALCIUM SULFATE DIHYDRATE TO HEMIHYDRATE SHOWING THE EFFECT OF THE INITIAL DIHYDRATE CRYSTAL FRAGMENT SIZE ON THE REACTION WHERE THE SOLIDS WERE IMMERSED IN WATER RUN TEMP. SCREEN TIME IN MIN FOR PERCENT REACTED NO. OF OPENING, IN 5 25 50 75 95 UNWASHED CRYSTALS RUN AT APPROXIMATELY 260oF 6 261.0 SING. CRY. 33 58 88 123 171 7 258.0.0195.-0138 28 36 43 52 67 8 258.0.0138.-0116 23 31 39 49 63 9 259.0.0116.-0082 31 39 46 54 66 10 257.8._0082.-0069 29 37 44 52 63 11 258.9.0069.-0058 32 39 47 54 65 12 259.4 -,0058.-0041 35 42 48 55 64 13 259.8.0041.-0035 32 40 45 51 59 14 260 2.0035.-0029 29 36 42 49 58 15 258.7.0029.-0021 34 41 49 57 67 16 260.1,0021.-0000 33 42 52 61 72 UNWASHED CRYSTALS RUN AT APPROXIMATELY 250OF 24 250.2.0116.-0082 61 90 112 133 167 23 250.5.0082.-0069 66 91 111 130 158 22 250.5,0069.-0058 60 84 103 123 149 20 250.5.0058.-0041 65 90 109 129 156 19 251.1,0041.-0035 71 92 114 136 165 21 251.0.0035.-0029 61 80 103 124 150 WASHED CRYSTALS RUN AT APPROXIMATELY 250OF 28 249.8.0164.-0138 89 121 145 173 217 27 250,7.0138.-0116 76 101 122 147 184 25 250.3.0116.-0082 44 66 87 111 150 30 250.0.0082.-0069 95 124 146 169 202 34 250.1.0082.-0069 76 100 119 139 168 35 249.3.0082.-0069 83 112 136 162 194 31 250.5.0069.-0058 85 110 130 151 180 26 250.3.0058.-0041 83 111 137 164 205 29 250.0.0041.-0035 82 109 134 161 205 32 250.7.0029.-0021 114 147 175 204 251 33 250.4.0021.-0000 205 292 398 470 529

APPENDIX H COMPOSITION OF SYNTHETIC SEA WATER The composition of the normal synthetic sea water used during these studie.s was given by Lyman and Fleming(56) in 1940 and is quoted below in Table H-l from the "Oceans" p. 185. It contains all the major inorganic salts of real sea water and has a chlorinity of 19%. The three synthetic sea water concentrates used during these studies contained dissolved solids of 2, 3, and 4 times that given below for normal synthetic sea water. TABLE H-l COMPOSITION OF NORMAL SYNTHETIC SEA WATER Compound Mass, grams NaCl 23.476 MgCl2 4.981 Na2S04 3.981 CaC12 1.102 KC1 0. 664 NaHC03 0.192 KBr 0.096 H3B03 0.026 SrC12 0.024 NaF 0.003 H20 965.519 Total Weight 1000.000 -215

APPENDIX I CLASSIFICATION OF INITIAL PARTICLE SIZES The solid samples of optical grade selenite used in the dilatometric experiments were composed of small rhombic crystal fragments obtained by crushing and grinding larger crystals with a mortar and pestle, then classifying the product into different size distributions using 11 Tyler Standard Screens, shaken mechanically for two minutes. The pertinent screen data are shown in Table I-l. A portion of each dry sample classified was washed several times in deionized water to remove all the adhering powder from the crystal fragments by forming a suspension of the fine particles and separating them from the bulk crystal fragments by decanting the liquid. This washing procedure was continued until the supernatant liquid was clear. The slurry of usable crystal fragments was dried over night at 100~F, cooled, and stored for use in the dilatometric experiments. -216

-217TABLE I-1 CRYSTAL CLASSIFICATION INFORMATION Tyler Standard Screen Data Average Opening, Opening, Limited Screen Opening, Mesh mm Inches Openings, Inches Inches 32.495.0195.0195-.0164.0180 35.417.0164.0164-.0138.0151 42.351.0138.0138-.0116.0127 48.295.O116 60.246.0097.0116-.0082.0099 65.208.0082.0082-.0069.0076 80.175.0069.oo69-.oo58.oo64 100.147.0058 115.124.0049.0058-.0041.0050 150.104.0041.0041-.0035.0038 170.088.0035.0035-.0029.0032 200.074.0029 250.062.0024.0029-.0021.0025 270.053.0021.0021-.0000.0011

APPENDIX J PHASE INDENTIFICATION USING X-RAY POWDER. DIFFRACTION PATTERNS The dihydrate, hemihydrate, and anhydrite phases occurring in the dilatometer under the different steady state conditions encountered during the experimental runs were identified using powder x-ray diffraction patterns. Samples were removed from the dilatometer before either of the two reactions studied became detectable and after each one had gone to completion. The samples were dried in air over night at 100~F, cooled in a desiccator, and a small portion was finely ground, mixed with "Duco" cement, and formed into small cylinders for use in the x-ray camera. Exposures were made in a 114.7 mm diameter Straumanis powder camera using Cu(K;) radiation for 8 hours at 40 KV and 15 MA with a piece of thin nickel foil placed over the film to reduce the background, The phases identified by these x-ray powder diffraction patterns corresponded to those predicted by the chemical equations describing each reaction, confirming the hypothesis that calcium sulfate hemihydrate dehydrates to calcium sulfate hemihydrate which in turn dehydrates to calcuim sulfate anhydrite in that particular sequential manner under nonequilibrium conditions encountered when the solids were immersed and heated in water, 3.5% sodium chloride solutions, and in synthetic sea water. The detailed results of this study are summarized in Table J-l. From the four of the x-ray powder diffraction patterns shown in Figures J-l1 J-2, J-3, and J-4, values of the interplaner distances d were measured for calcium sulfate dihydrate, hemihydrate, and anhydrite, and for sodium chloride, and compared with the published reference values -218

-219in Tables J-2, J-35 J-4 and J-5, respectively. The remaining x-ray powder diffraction patterns were identified by physically superimposing one film upon the other since the patterns are unmistakeably different. Comparison of the x-ray powder diffraction patterns from each of the three different phases revealed that none of the strongest lines occurring in any one of the phases occurred in either of the other phases, indicating that the reactions were observed at steady state conditions either before or after the reactions had occurred,

Figure J-1 X-ray Powder Diffraction Pattern for Calcium Sulfate Dihydrate. Figure J-2 X-ray Powder Diffraction Pattern for Calcium Sulfate Hemihydrate. Figure J-3. X-ray Powder Diffraction Pattern for Calcium Sulfate Anhydrite. Figure J-4e X-ray Powder Diffraction Pattern for C. P. Sodium Chloride.

TABLE J-1 RESULTS OF STUDIES OF THE X-RAY POWDER DIFFRACTION PATTERNS Removal of X-ray samples from dilatometer in relationship to Phase the reactions detected by a Identified volume increase as shown below: by X-ray X-ray Run Starting Temp., Dihydrate to Hemihydrate to Diffraction No. No. Material Solution ~F Hemihydrate Anhydrite Patterns 1 All Selenite Water ----- Before Before Dihydrate 1A* All Selenite Water ----- Before Before Dihydrate 2 28 Selenite Water 250.3 After Before Hemihydrate 2A* 28 Selenite Water 250.3 After Before Hemihydrate 3 65 Selenite Water 4310. After After Anhydrite 4 66 Selenite Water 325.5 After After Anhydrite 5* -- NaCl --- ----- ----- ---— NaC1! 6* 72 Selenite Water 339.1 After After Anhydrite 7 72A Selenite Water 337. After Before Hemihydrate 8 76 Selenite Water 346.8 ~ After After Anhydrite 9 36 Selenite 3-1/2% NaCl 349.9 After Before Hemihydrate 10 73 Selenite 3-1/2% NaCl 347.9 After After Anhydrite 11 73A Selenite 3-1/2% NaC1 346. After Before Hemihydrate 12 60 Selenite Sea Water 249.4 After Before Hemihydrate 13 -- Selenite Air - -250. After ------ Hemihydrate 14 74A Selenite Sea Water > 350. After Before Hemihydrate 15 74B Selenite Sea Water nu 346. After After Anhydrite * Measured values of interplaner distances d are shown for these samples.

-222TABLE j-2 COMPARISON OF X-RAY DIFFRACTION DATA FROM CALCIUM SULFATE DIHYDRATE (SELENITE) WITH DATA REPORTED FOR CaS04,2H20 ON ASTM CARD NUMBER 6-0046 AND 6-0047(82). CaSO4o2H20 Sample of Starting Material, Selenite d(A) I/I1 d(A) I/I1 7.56 100 7o63 Vs 4.27 51 4.27 VS 3~79 21 3.80 M 3.163 3 3.149 VW 3.059 57 3.056 VS 2.867 27 2.861 S 2.786 5 2.697 28 2.670 s 2.591 4 2.530 1 2.495 6 2.450 4 2.400 4 2.216 6 2.211 M 2.139 1 2.080 10 2.078 M 2.073 8 1.990 4 1.953 2 1.898 16 1.895 M 1.879 10 1.877 M 1.864 4 1.843 1 1,812 10 1.809 w 1.796 4 1.778 10 1o 784 W 1.711 1 1.684 1 1,664 4 1.645 2 etc. VS = very strong W = weak S = strong VW = very weak M = medium

-223TABLE J-3 COMPARISON OF X-RAY DIFFRACTION DATA FROM CALCIUM SULFATE HEMIHYDRATE FORMED FROM DIHYDRATE IN WATER WITH THE DATA REPORTED FOR CaSO4.1/2H20 ON ASTM CARD NUMBER 2-0675.(82) Standard Sample Formed in CaSO4dl/2H20 Dilatometric Run d(A) I/Il d(A) I/Il 5.98 90 6.020 S 4.35 20 4.333 VW 3.45 80 3.480 S 2.98 100 2.997 VS 2.78 100 2.812 S 2.69 30 2.713 VW 2.33 40 2.343 vw 2.26 20 2.263 VW 2.20 20 2.12 80 2.136 M 1.99 30 1.89 6o 1.908 w 1.84 90 1.846 s 1.72 40 1.729 w 1.69 80 1.692 M 1.65 60 1.662 M 1.60 20 1.53 30 1.47 40 1.44 30 VS = very strong S = strong M = medium W = weak VW = very weak

TABLE J-l RESULTS OF STUDIES OF THE X-RAY POWDER DIFFRACTION PATTERNS Removal of X-ray samples from dilatometer in relationship to Phase the reactions detected by a Identified volume increase as shown below: by X-ray X-ray Run Starting Temp., Dihydrate to Hemihydrate to Diffraction No. No. Material Solution ~F Hemihydrate Anhydrite Patterns 1 All Selenite Water ----- Before Before Dihydrate 1A* All Selenite Water ----- Before Before Dihydrate 2 28 Selenite Water 250.3 After Before Hemihydrate 2A* 28 Selenite Water 250.3 After Before Hemihydrate 3 65 Selenite Water 4310. After After Anhydrite 4 66 Selenite Water 325.5 After After Anhydrite 5* -- NaC1 — l- - ----- NaC1 H 6* 72 Selenite Water 339.1 After After Anhydrite 7 72A Selenite Water 4337. After Before Hemihydrate 8 76 Selenite Water 346.8 After After Anhydrite 9 36 Selenite 3-1/2% NaCl 349.9 After Before Hemihydrate 10 73 Selenite 3-1/2% NaCl 347.9 After After Anhydrite 11 73A Selenite 3-1/2% NaCl,346. After Before Hemihydrate 12 60 Selenite Sea Water 249.4 After Before Hemihydrate 13 -- Selenite Air r 250. After ----— Hemihydrate 14 74A Selenite Sea Water >350. After Before Hemihydrate 15 74B Selenite Sea Water 4 346. After After Anhydrite * Measured values of interplaner distances d are shown for these samples,

-222TABLE J-2 COMPARISON OF X-RAY DIFFRACTION DATA FROM CALCIUM SULFATE DIHYDRATE (SELENITE) WITH DATA REPORTED FOR CaSO42H20 ON ASTM CARD NUMBER 6-0046 AND 6-0047(82). CaSO4 2H20 Sample of Starting Material, Selenite d(A) I/I1 d(A) I/I1 7.56 100 7.63 VS 4.27 51 4.27 VS 3.79 21 3.80 M 3.163 3 3.149 VW 3.059 57 3.056 VS 2.867 27 2.861 S 2.786 5 2.697 28 2.670 S 2.591 4 2.530 1 2.495 6 2.450 4 2.400 4 2.216 6 2.211 M 2.139 1 2.080 10 2.078 M 2.073 8 1.990 4 1.953 2 1.898 16 1.895 M 1.879 10 1.877 M 10864 4 1.843 1 1o812 10 1.809 w 1.796 4 1.778 10 1.784 w 1.711 1 1.684 1 1,664 4 1.645 2 etc. VS = very strong W = weak S = strong VW = very weak M = medium

-223TABLE J-3 COMPARISON OF X-RAY DIFFRACTION DATA FROM CALCIUM SULFATE HEMIHYDRATE D ORED FROM DIHYDRATE IN WATER WITH THE DATA REPORTED FOR CaSO4.1/2H20 ON ASTM CARD NUMBER 2-0675. (C2) Standard Sample Formed in CaSO4 1/2H20 Dilatometric Run d(A) I/Il d(A) I/Il 5.98 90 6.020 s 4.35 20 4.333 vw 3.45 80 3.480 S 2,98 100 2.997 VS 2078 100 2.812 S 2.69 30 2.713 VW 2.33 40 2.343 VW 2.26 20 2.263 VW 2.20 20 2.12 80 2,136 M 1.99 30 1.89 60 1.908 w 1.84 90 1.846 s 1.72 40 1.729 w 1.69 80 1.692 M 1.65 60 1.662 M 1.6o 20 1.53 30 1.47 40 1.44 30 VS = very strong S = strong M = medium W = weak VW = very weak

-224TABLE J-4 COMPARISON OF X-RAY DIFFRACTION DATA FROM CALCIUM SULFATE ANHYDRITE FORMED FROM HEMIHYDRATE IN WATER WITH THE DATA REPORTED FOR CALCIUM SULFATE, CaS04 ANHYDRITE ON ASTM CARD NUMBER 6-0226. (82) Standard Sample Formed During CaS04 Dilatometric Run d(A) I/I1 d(A) I/I, 3087 6 3.88 vw 3.498 100 3.502 VS 30118 3 2.849 33 2.840 M 2.797 4 2.473 8 2.469 W 2.328 22 2.330 M 2.208 20 2.192 M 2,183 8 2.086 9 2.076 W 1.993 6 1.990 vw 1.938 4 1.932 VW 1.869 15 1.865 M 1.852 4 1.749 11 1 747 M 1.748 10 1.648 14 1.645 M 1.594 3 1.591 VW 1.564 5 1.561 VW 1.525 4 1.521 VW 1.515 1 1.490 5 1.488 W 1.424 33 1.423 W 1.418 1 1.398 3 1.396 W 1.396 2 1.365 1 1.319 4 1.318 W 1.296 2 1.277 5 1.275 W VS = very strong W = weak S = strong VW = very weak M = medium

-225TABLE J-5 COMPARISON OF X-RAY DIFFRACTION DATA FROM C.Po SODIUM CHLORIDE WITH DATA REPORTED FOR NaCl ON ASTM CARD NUMBER 5-0628. (82) Standard C.P. NaCl Sodium Chloride (A)d(A) I/I d() I/I 3.258 13 3.25 M 3.10 M 2.821 100 2.80 VS 2.20 M 1.994 55 1.98 VS 1,80 VW 1.701 2 1.69 W 1.628 15 1.62 S 1.410 6 1.405 M 1.390 VVW 1.294 1 1.290 W 1.261 11 1.256 S 1,1515 7 1.148 S 1.0855 1 1.082 VW 0.9969 2 1.040 VVW 0.9533 1 0.952 W 0.9401 3 0.938 M 0.8917 4 0.890 M 0o8601 1 0.860 vvw 0.8503 3 0.850 M 0.848 M 0,834 vvw 0.8141 2 0.814 W 0.812 W VS = Very Strong W = Weak S = Strong VW = Very Weak M = Medium VVW = Very Very Weak

APPENDIX K VAPOR PRESSURE RATIOS FOR SODIUM CHLORIDE SOLUTIONS Values of the vapor pressure ratio P/P~, i'.e. the ratio of the vapor pressure of sodium chloride solutions P to the vapor pressure of pure water P~ at identical temperatures, were calculated from the vapor pressure data given in the International Critical Tables(49 97) (17) using the method introduced by Cox(17) The linear relationship between the logarithm of the vapor pressure of pure water for the same temperature was determined by the method of least squares using Equation K-l yielding the coefficients shown in Table K-l for different values of the weight fraction of sodium chloride X in the solution: in P = In bo(X) + bl in P~ (K-l) where bo and bl are constants. The value of b1 was found almost equal to unity and consequently the data were correlated again forcing bl=l resulting in the following relationship. in (P/P~) = In bo(X) or P/P~ = bo(X) o (K-2) The values of bo(X) obtained using this squation for solutions having different values of X are shown in Table K-2. Values of the function bo(X) for values of X different from those shown in Table K-2 were calculated using the following interpolation formulas determined by a least squares fit of the data~ bo(X) = 1.000 - o.643x for 0.0 <X < 0,10 (K-3) bo(X) = 0o962 - 293X2 for OolO < X < 0.25 (K-4) Thus, the vapor pressure ratios for all sodium chloride solutions car be determined as a function of the amount of dissolved solid up to 25% solution. -226

-227TABLE K-1 COEFFICIENTS OF EQUATION (K-l) X In bo (X) bl.000.000000 1.000000.025 -.013438.999613.050 -.035468 1.oo000607.075 -.041760.998586.100 -. 064684.999357.125 -.086805.999633.150 -.112222 1.000094.175 -.138777 1.000135.200 -.184505 1.002890.225 -.221218 1.003168.250 -.273199 1.005370 TABLE K-2 COEFFICIENTS OF EQUATION (K-2) X In bo (X) bo (X).000.000000 1.000000.025 -.015208.984907.050 -.032694.967835.075 -.048219.952925.100 -.067612.934623.125 -.088484.915318.150 -.111794.89423.175 -.138161.87096.200 -.171302.84257.225 -.206747.81323.250 -.248668.77984

-228The vapor pressure ratios calculated using Equations (K-3) and (K-4) for the six different sodium chloride solutions used in these studies are shown in Table K-3o For comparison, the vapor pressure ratios calculated by Equation (26) for synthetic sea water concentrates are also shown in this table. TABLE K-3 VAPOR PRESSURE RATIOS Sodium Chloride Solutions Vapor Weight Pressure Fraction, Ratio X p/po.005 0.997.010 0.994 035 0.978.070 0.956. 14 0 o903.210 o0831 Synthetic Sea Water Concentrates Vapor Pressure Chlorinity, Ratio Y p/po 19 0.982 38 0,963 57 0~945 76 0,926

APPENDIX L VOLUME CHANGES IN THE CALCIUM SULFATE - WATER SYSTEM The two dehydration reactions observed in the calcium sulfate - water system can be represented by the following equationso CaSO4o2H20(S) A CaS04 1/2 H20(S) + 3/2 H20(L) (L-1) CaS04O1/2 H20(S) AV2 CaS04(S) + 1/2 H20(L) o (L-2) Assuming that the densities of the solids remain constant with changes in temperature, the total volume change occurring with each reaction was calculated using the physical constants listed in Table L-l and the following equations: AV1 = VH + V3/2W - VD (L-3) V2 = VA + V1/2W - VH (L-4) where VD, VH, VA, and Vxw represent the volume of the dihydrate, hemihydrate, anhydrite, and water phases, respectively. For a Oo7 gram sample of dihydrate, the volumes at 4~C are: VD = 0.3017, VH = 0.2130 VA = 0.1870, V3/2W = 0,1100, Vl/2W = 0.03679 AV1 = 0.0213, and AV2 ~ 0.0107 cc. When the volume changes are desired as a function of temperature, only the volume of water must be calculated as a function of temperature using: V(T)3/2W = 01100 P40/PT (L-5) V(T)l/2w = 0o0567 P4o/PT o (L-6) -229

-230The results of the calculations using these equations are summarized in Table L-2 where the changes in the values are listed as a function of temperature. The theoretical height changes which should be observed in the dilatometer capillary for each reaction are also listed in the last two columns of this table. These values were calculated by dividing the volume change for each reaction by the average cross-sectional area of the capillary, 0.0030375 cm2.

-231TABLE L-l VALUES OF THE PHYSICAL CONSTANTS FOR CALCIUM SULFATE Compound CaS04 2H20 CaS04'1/2 H20 CaSO4 H20 Molecular Weight 172.18 145.15 136.15 18.02 Density 2.32 2,75 2.96 1.000 gm/cc (2.9) 4~C Values found in Reference 7, 19, 42, and 61. TABLE L-2 HEIGHT AND VOLUME VALUES Water Temp., Density, V3/2Ws Vl/2W, AVl, AV29, hl, Ah2, 0F gm/cc cc cc cc cc cm cm 39.2 1.0000 0. 0.1100 0367 0.0213 0.0107 7.01 3.52 212.0 0.9584 0.1148 0.0383 0.0261 0.0123 8.59 4.05 230,0 0.9510 0.1157 0.0385 0.0270 0.0126 8.89 4.15 248.0 0.9434 0.1166 0.0389 0.0279 0.0129 9.19 4.25 266.0 0.9352 0.1176 0.0392 0.0289 0.0132 9.51 4.35 284.0 0.9264 0.1187 0.0396 0.0300 0.0136 9.88 4.48

APPENDIX M RESULTS FROM MICROSCOPIC OBSERVATIONS The dimensions of the growing hemihydrate needles were measured in three different directions on micrographs made from the 35 mm negatives taken during the microscopic observations. Using the known magnifications along with the measured lengths, the rates of growth were calculated using the computer program given in Table M-2. Table M-1 contains the dimensions measured and the temperature of the reaction listed according to micrograph number. Values of average temperature, rate, and reciprocal absolute temperature calculated from adjacent micrographs are shown along with the average values of temperature, rate, and reciprocal absolute temperature for each series of measurements. Micrographs numbered 6 and 14 represent 197X magnifications and the remaining ones 477.5X. -232

-233TABLE M-1 DATA FROM MICROSCOPIC STUDIES MICRO. LENGTH TEMP. AVE.TEIP. RATE TEMP. NO. CM F OF CM / l I N OKDETERMINATION OF LINEAR GRO)WTH VELOCITY, UA 1.01 3.55 251.20 251.45 0000314.0025320 1.02 3.70 251.71 251.86.0000209.0025302 1.03 3.80 252.01 252.37.0000147.0025291 1.04 3.87 252.72 252.82.0000141.0025266 1.05 3.94 252.93 253.08 0000377.0025259 1.06 4.12 253.23 253.38.0000168.0025248 1.07 4.20 253.53 253.64.0000209.0025237 1.08 4.30 253.74 253.84.0000209.0025230 1.09 4.40 253.94 254.09.0000105.0025223 1.10 4.45 254.25 254.19.0000209.0025212 1.1 4.55 254.14 254.14.0000209.0025216 1.12 4.65 254.14 254.14.0000168.0025216 1.13 4.73 254.14 254.09.0000147.0025216 1.14 4.80 254.04 254.04.0000209.0025220 1.15 4.90 254.04 254.04.0000209.0025220 1.16 5.00 254.04 253.99.0000209.0025220 1.17 5.1-0 253.94 253.94.0000314.0025223 1.18 5.25 253.94 253.84.0000419.0025223 1.19 5.45 253.74 253.74.0000733.0025230 1.20 5.80 253.74 253.64.0000419 0025230 1.21 6.00 253.53 253.53.0000628.0025237 1.22 6.30 253.53.....AVERAGE VALUES..... 253.52.0000274.0025238 DETERMINATION OF LINEAR GROWTH VELOCITY, UA 2.01 2.90 255.36 256.02.0000524.0025173 2.02 3.15 256.68 256.78.0000524.0025127 2.03 3.40 256.88 257.04.0000796.0025119 2.04 3.78 257.19 257.39.0000565.0025109 2.05 4.05 257.60 256.63.0000733.0025095 2.06 4.40 255.67 254.30.0000524.0025162 2.07 4.65 252.93 252.93.0000524.0025259 2.08 4.90 252.93 253.33.0000628.0025259 2.09 5.20 253.74 254.30.0000628.0025230 2.10 5.50 254.85 255.16.0000419.0025191 2.11 5.70 255.46 255.36.0000984.0025169 2.12 6.17 255.26 255.06.0000796.0025177 2.13 6.55 254.85 254.50.0000524.0025191 2.14 6.80 254.14 253.89.0000628.0025216 2.15 7.10 253.64.....AVERAGE VALUES..... 255.19.0000628.0025179

-254TABLE M-l (CONT'D) MICRO. LENGTH TEMP. AVE.TEMP. RATE TEMP-I. NO. CM OF'oF Civ/M IN OK - DETERMINATION OF LINEAR GROWTH VELOCITY, UA 3.01 1.75 253.84 253.64.0000105.0025227 3.02 1.80 253.43 253.43.0000105.0025241 3.03 1.85 253.43 253.53.0000105.0025241 3.04 1.90 253.64 253.69.0000314.0025234 3.05 2.05 253,74 253.74.0000314.0025230 3.06 2.20 253.74.....AVERAGE VALUES..... 253.61.0000188.0025235 DETERMINATION OF LINEAR GROWTH VELOCITY, UA 3.01 2.30 253.84 253.64.0000105.0025227 3.02 2.35 253.43 253.43.0000209.0025241 3.03 2.45 253.43 253.53.0000105.0025241 3.04 2.50 253.64 253.69.0000105.0025234 3.05 2.55 253.74 253.74.0000105.0025230 3.06 2.60 253.74.....AVERAGE VALUES...., 253.61.0000126.0025235 DETERMINATION OF LINEAR GROWTH VELOCITY, UB 3.01 6.25 253.84 253.64.0000314.0025227 3.02 6.40 253.43 253.43.0000209.0025241 3.03 6.50 253.43 253.53.0000209.0025241 3.04 6.60 253.64 253.69.0000314.0025234 3.05 6.75 253.74 253.74.0000524.0025230 3.06 7.00 253.74.....AVERAGE VALUES..... 253.61.0000314.0025235 DETERMINATION OF LINEAR GROWTH VELOCITY, UB 3.01 4.75 253.84 253.64.0000314.0025227 3.02 4.90 253.43 253.43.0000419.0025241 3.03 5.10 253.43 253.53.0000209.0025241 3.04 5.20 253.64 253.69.0000419.0025234 3.05 5.40 253.74 253.74.0000419.0025230 3.06 5.60 253.74..,..AVERAGE VALUES..... 253.61.0000356.0025235 DETERMINATION OF LINEAR GROWTH VELOCITY, UA 4.01 2.55 253.43 253.43.0000105.0025241 4.02 2.60 253.43 253.53.0000105.0025241 4.03 2.65 253.64 253.69.0000105.0025234 4.04 2.70 253.74 253.74.0000105.0025230 4.05 2.75 253.74.....AVERAGE VALUES..... 253.60.0000105.0025235

-255TABLE M-1 (CONT'D) MICRO. LENGTH TEIMP. AVE.T EMP. RATE TEMP";I NO. C l OF OF C VM/MI N OK-1 DETERMINATION OF LINEAR GROWTH VELOCITY, Uc 6.01 9.05 258.00 257.95.0053299.0025080 6.02 11.15 257.90 257.90.0038071.0025084 6.03 12.65 257.90 258.15.0032995.0025084 6.04 13.95 258.41 258.46.0040609.0025066 6.05 15.55 258.51 258.61.0031726.0025063 6.06 16.80 258.71 258.81.0035533.0025056 6.07 18.20 258.92 259.02.0041878.0025049 6.08 19.85 259.12.....AVERAGE VALUES..... 258.42.0039159.0025066 DETERMINATION O)F LINEAR GROWTH VELOCITY, Uc 7.01 12.60 260.03 260.29.0047120.0025010 7.02 14.85 26().54 260.64.0042932.0024992 7.03 16.90 260. 74 260.79.0043979.0024985 7.04 19.00 260.84 260.84.0062827.0024981 7.05 22.00 260.84 260.95.0050262.0024981 7.06 24.40 261.05 261.15.0069110.0024974 7.07 27.70 261.25 261.45.0029319.0024967 7.08 29.10 261.66.....AVERAGE VALUES..... 260.87.0049364.0024980 DETERMINATION OF LINEAR GROWTH VELOCITY, UC 8.01 5.90 261.86 261.81.0056545.0024946 8.02 8.60 261.76 261.76.0050262.0024950 8.03 11.00 261.76 261.76.0047120,0024950 8.04 13.25 261.76 261.66.0047120,0024950 8.05 15.50 261.56 261.45,0053403.0024957 8.06 18.05 261,35 261.25.0052356.0024964 8.07 20.55 261.15 261.15.0050262.0024971 8.08 22.95 261.15 261.35.0049215.0024971 8.09 25.30 261.56.....AVERAGE VALUES..... 261.52.0050785.0024958 DETERMINATION OF LINEAR GROWTH VELOCITY, UB 8.01 1.75 261.76 261.76.0000524.0024950 8.02 1.80 261.76 261.66.0000524.0024950 8.03 1.85 261.56 261.45.0000314.0024957 8.04 1.88 261.35 261.25.0000733.0024964 8.05 1.95 261.15 261.15.0000733.0024971 8.06 2.02 261.15 261.35.0000838.0024971 8.07 2.10 261.56.....AVERAGE VALUES..... 261.44.0000611.0024961

-256TABLE M-1 (CONT'D) MICRO. LENGTH TEMP. AVE.TEMP. RATE TEMP.' NO. CM OF OF CM/MIN OK' DETERMINATION OF LINEAR GROWTH VELOCITY, UC 9.01 6.90 269.58 269.78.0062199.0024682 9.02 9.87 269.98 270.13.0059267.0024669 9.03 12.70 270.29 270.59.0058639.0024658 9.04 15.50 270.90 271.00.0064293.0024638 9.05 18.57 271.10 271.50.0065550.0024631 9.06 21.70 271.91 271.96.0062408.0024604 9.07 24.68 272.01 272.16.0056126.0024600 9.08 27.36 272.32.....AVERAGE VALUES..... 271.02.0061212 0024634 DETERMINATION OF LINEAR GROWTH VELOCITY, UB 9.01 1.95 269.58 269.78.0001047.0024682 9.02 2.05 269.98 270.13.0002304.0024669 9.03 2.27 270.29 270.59.0001361.0024658 9.04 2.40 270.90 271.00.0002094.0024638 9.05 2.60 271.10 271.50.0002094.0024631 9.06 2.80 271.91 271.96.0001571 0024604 9.07 2.95 272.01 272.16.0001571.0024600 9.08 3.10 272.32.....AVERAGE VALUES..... 271.02.0001720.0024634 DETERMINATION OF LINEAR GROWTH VELOCITY, UC 10.01 7.77 272.62 272.87.0071204.0024580 10.02 11.17 273.13 273.08.0070995.0024563 10.03 14.56 273.03 273.43.0071623.0024566 10.04 17.98 273.84 273.94.0075602.0024539 10.05 21.59 274.04 274.09.0077906.0024532 10.06 25.31 274.14 274.14.0078325.0024529 10.07 29.05 274.14.....AVERAGE VALUES..... 273.59.0074276.0024547 DETERMINATION OF LINEAR GROWTH VELOCITY, UB 10.01 2.95 272.62 272.87.0003141.0024580 10.02 3.25 273.13 273.08.0002618.0024563 10.03 3.50 273.03 273.43.0002932.0024566 10.04 3.78 273.84 273.94.0002827.0024539 10.05 4.05 274.04 274.09.0001152.0024532 10.06 4.16 274.14 274.14.0002513.0024529 10.07 4,40 274.14.....AVERAGE VALUES..... 273.59.0002531.0024547

-237TABLE M-1 (CONT'D) MICRO. LENGTH TEMP. AVE.TEMP. RATE TEMP-' NO. CM OF OF CM/MIN OK-' DETERMINATION OF LINEAR GROWTH VELOCITY, UC 11.01 11.76 274.55 274.45.0062827.0024515 11.02 14.76 274.35 274.65.0075812.0024522 11.03 18.38 274.96.....AVERAGE VALUES..... 274.55.0069319.0024515 DETERMINATION OF LINEAR GROWTH VELOCITY, UB 11.01 4.25 274.55 274.45.0002618.0024515 11.02 4.50 274.35 274.65.0003141.0024522 11.03 4.80 274.96 275.01.0004398.0024502 11.04 5.22 275.06.....AVERAGE VALUES..... 274.70.0003386.0024510 DETERMINATION OF LINEAR GROWTH VELOCITYt UA 12.01 1.72 277.60 277.54.0000419.0024414 12.02 1.76 277.49 277.54.0000628.0024417 12.03 1.82 277.60 277.85.0000838.0024414 12.04 1.90 278.10 278.15.0002094.0024397 12.05 2.10 278.20 278.61.0000838.0024394 12.06 2.18 279.02 279.07.0001047.0024367 12.07 2.28 279.12 279.27.0002304.0024364 12.08 2.50 279.42 279.47.0002618.0024354 12.09 2.75 279.52 279.88.0001571.0024350 12.10 2.90 280.24 280.34.00016,75.0024327 12.11 3.06 280.44 280.64.0002304.0024320 12.12 3.28 280.84.....AVERAGE VALUES..... 278.94.0001485.0024369 DETERMINATION OF LINEAR GROWTH VELOCITY, UB 12.01 3.22 277.60 277.54.0001885.0024414 12.02 3.40 277.49 277.54.0004607.0024417 12.03 3.84 277.60 277.85.0003770.0024414 12.04 4.20 278.10 278.15.0002723.0024397 12.05 4.46 278.20 278.61.0003351.0024394 12.06 4,78 279.02 279.07.0004398.0024367 12.07 5.20 279.12 279.27.0005236.0024364 12.08 5.70 279.42 279.47.0003770.0024354 12.09 6.06 279.52 279.88.0004607.0024350 12.10 6.50 280.24 280.34.0005026.0024327 12.11 6.98 280.44 280.64.0005445.0024320 12.12 7.50 280.84.....AVERAGE VALUES..... 278.94.0004074.0024369

-238TABLE M-1 (CONT'D) MICRO. LENGTH TEMP. AVE.TEMP. RATE TEMP.' NO. C Ivi F OF CM/MIN OK-1 DETERMINATION OF LINEAR GROWTH VELOCITY, UA 12.01 1.05 277.60 277.54.0000524;.0024414 12.02 1.10 277.49 277.54.0001047.0024417 12.03 1.20 277.60 277.85.0001047.0024414 12.04 1.30 278.10 278.15.0001047.0024397 12.05 1.40 278.20 278.61.0000209.0024394 12.06 1.42 279.02 279.07.0001361.0024367 12.07 1.55 279.12 279.27.0000733.0024364 12.08 1.62 279.42 279.47.0001675.0024354 12.09 1.78 279.52 279.88.0001466.0024350 12.10 1.92 280.24 280.34.0001885.0024327 12.11 2.10 280.44 280.64.0002094 0024320 12.12 2.30 280.84.....AVERAGE VALUES..... 278.94.0001190.0024369 DETERMINATION OF LINEAR GROWTH VELOCITY, UB 12.01 1.40 277.60 277.54.0000838.0024414 12.02 1.48 277.49 277.54.0001257.0024417 12.03 1.60 277.60 277.85.0001152.0024414 12.04 1.71 278.10 278.15 *0001466.0024397 12.05 1.85 278.20 278.61.0002094.0024394 12.06 2.05 279.02 279.07.0001780.0024367 12.07 2.22 279.12 279.27.0002408.0024364 12.08 2.45 279.42 279.47.0003665.0024354 12.09 2.80 279.52 279.88.0004188.0024350 12.10 3.20 280.24 280.34.0003141.0024327 12.11 3.50 280.44 280.64 *0005236.0024320 12.12 4.00 280.84.....AVERAGE VALUES..... 278.94.0002475.0024369 DETERMINATION OF LINEAR GROWTH VELOCITY, UA 13.01 2.27 280.13 280.13.0000628.0024330 13.02 2.33 280.13 279.98.0000733.0024330 13.03 2.40 279.83 279.83.0000942.0024340 13.04 2.49 279.83 279.63.0000942.0024340 13.05 2.58 279.42 279.42.0000628.0024354 13.06 2.64 279.42 279.27.0001675.0024354 13.07 2.80 279.12.....AVERAGE VALUES..... 279.71.0000925.0024344

-239TABLE M-1 (CONT'D) MICRO. LENGTH TEMP. AVE.TEMP. RATE TEMvL P NO. CM OF ~F CM/MIN I K DETERMINATION OF LINEAR GROWTH VELOCITY, UB 13.01 7.22 280.13 280.13.0003979.0024330 13.02 7.60 280.13 279.98.0003665.0024330 13.03 7.95 279.83 279.83.0004607.0024340 13.04 8.39 279.83 279.63.0003560.0024340 13.05 8.73 279.42 279.42.0004712.0024354 13.06 9.18 279.42 279.27.0002618.0024354 13.07 9,43 279.12...AVERAGE VALUES..... 279.71.0003857.0024344 DETERMINATION OF LINEAR GROWTH VELOCITY, UC 14.01 13.55 256.07 256.07.0039086.0025148 14.02 14.32 256.07 256.07,0046193.0025148 14.03 15.23 256.07 255.97.0044670.0025148 14.04 16.11 255.87 255.87.0047716.0025155 14.05 17.05 255.87 255.87.0038071.0025155 14.06 17.80 255.87 255.87.0035533.0025155 14.07 18.50 255.87 255.82.0036548.0025155 14.08 19.22 255.77 255.72.0038071.0025159 14.09 19.97 255.67 255.72.0028426.0025162 14.10 20.53 255.77 255.77.0031472.0025159 14.11 21.15 255.77 255.77.0030457.0025159 14.12 21.75 255.77 255.77.0035533.0025159 14.13 22.45 255.77 255.72.0032995.0025159 14.14 23 10 255.67 255.72.0040609.0025162 14.15 23.90 255.77 255.77.0043655.0025159 14.16 24.76 255.77 255.77.0042640.0025159 14.17 25.60 255.77 255.72.0026904.0025159 14.18 26.13 255.67.....AVERAGE VALUES..... 255.82.0037563.0025157

-240TABLE M-2 COMPUTER PROGRAM USED TO CALCULATE LINEAR RATES OF GROWTH FROM MICROSCOPIC DATA DIMENSION TAG(10), T(40), TAVE(40), L(40), 1RATE(40), RT(40) INTEGER I, J, F, S BEGIN READ FORMAT CONST, RUN, F, S, DELTAT, MAG READ FORMAT LABLE, TAG(1)...TAG(S) READ FORMAT TEMP, T(1)*..T(F) THROUGH ONE, FOR J=1,1,J.G.F T( J )=-3.1140346+1.0152246*T( J) ONE RT(J)=1.8/(T(J)+459.69) SUMT=O. N=O. THROUGH TWO, FOR J=1,ltJ.G.F-l TAVE(J)=(T(J+1)+T(J))/2. SUMT=SUMT+TAVE ( J) TWO N=N+1. AVTEMP=SUMT/N RECPTK=1.8/( AVTEMP+459.69) THROUGH THREE, FOR I=ti,I.IG.S READ FORMAT LENGTH, L(1)...L(F) SUMR=O. N=0. THROUGH FOUR, FOR J=I1,,J.G.F-1 RATE(J)=TAG(I)"'(L(J+1)-L(J))/DELTAT/MAG SUMR=SUMR+RATE( J) FOUR N=N+1. AVRATE=SUMR/N LNAVR=ELOG.(AVRATE) PRINT FORMAT NAME THROUGH FIVE, FOR J=1,1,J.G.F K=O.O1*J PRINT FORMAT ANS, RUN, K, L(J), T(J), TAVE(J), 1RATE(J), RT(J) FIVE CONTINUE PRINT RESULTS AVTEMP, AVRATE PRINT RESULTS RECPTK, LNAVR THROUGH SIX, FOR J=1,1,J.G.F K=O.01 *J SIX PUNCH FORMAT CARDI, RUN, K, L(J), T(J), TAVE(J), 1RATE(J), RT(J) PUNCH FORMAT CARD2, AVTEMP, AVRATE, RECPTK THREE CONTINUE TRANSFER TO BEGIN VECTOR VALUES CONST=$F5.2,2I5,2F5.1*$ VECTOR VALUES LABLE=$10F5.0*$ VECTOR VALUES TEMP=$10F7.1*$ VECTOR VALUES LENGTH=$10F7.2*$ VECTOR VALUES NAME=$1H1,S2,7HRUN NO.,S3,6HLENGHT, 1S6,4HTEMP,S2,8HAVE TEMP,S9,4HRATE,S3, 8HREC TEMP, 12H K*$

-241TABLE M-2 (CONT'D) VECTOR VALUES ANS=$1HO,F6.0,F3.2,F9.2,2F10.2, 12 F 13. 7 $ VECTOR VALUES CARD1=$F2.0,F3.2,F9.2,2Fl0.2, 12F13.7*7 $ VECTOR VALUES CARD2=$S24,F10.2,2F13.7" $ END OF PROGRAM

APPEND IX N COMPUTER PROGRAM USED TO CALCULATE FRACTION REACTED AND RATE OF REACTION VALUES AS FUNCTIONS OF TIME USING THE MODEL R RW=UADA, X=UBUB, Y=UADB, Z=UBDA R INTEGER T1, T2, T3, J, END DIMENSION ALPHA(1000), RATE(1000), TIME(1000) BEGIN READ FORMAT DATA, N, K, E, F, G, CONTRL, DELTAT ROOT3=SQRT. ( 3.) W=1./(2.*G) X=1./(2.*E) Y=(X-1./(2.F) )*ROOT3 Z=W*X/Y WW=1./W XX=1./X YY=1./Y ZZ=1./Z A=4.*W*X-2 /ROOT3*W*Y B=-2.*ROOT3*X*Z C=2.*ROOT3* (Z*X-2./ROOT3*X*W+1 /3.00*W*Y) D=-2. *W T1=1. / ( 2*X )/DELTAT T2=1./(2.*X-2./ROOT3*Y)/DELTAT T3=1. / (2.*W)/DELTAT TFIl=./ (2.*X) TF2=1,/(2.*X-2./RR TF2=1./ (2 *X-2./ROOT3*Y) TF3=1./ (2.*W) END=10./K+T3 PRINT COMMENT $1$ PRINT RESULTS N, TF1, TF2, TF3 PRINT RESULTS END, T1, T2, T3 PRINT RESULTS A, B, C, D PRINT RESULTS W, X, Y, Z PRINT RESULTS WW, XX, YY, ZZ WHENEVER TF1.G. TF2.OR. TF1.G. TF3.OR. 1TF2.G. TF3 TRANSFER TO BEGIN END OF CONDITIONAL THROUGH ONE, FOR J=O,5,J.G.T1 T=J*DELTAT TIME(J)=T ARG1=T*T-2./K*(T+I./K*(EXP.(-K*T)-l.) ) DARG1=2.*T-2./K*(1.-EXP. (-K*T)) RATE( J)=A*DARG1 ONE ALPHA (J)=A*ARG1 THROUGH TWO, FOR J=T1+1,1,J.G. T2 T=J*DELTAT TIME(J)=T ARG1=T*T-2./K*( T+1./K* (EXP. (-K*T)- 1. ) ) DARG1=2.*T-2./K*( 1.-EXP. (-K*T)) -242

-245T=J DELT AT-TF1 ARG2=T*T-2./K* (T+1./K*(EXP. (-K*T)-l.)) DARG2=2';*T-2./K*( 1.-RXP. (-K*T) ) RATE( J ) =A*DARG+B*DARG2 TWO ALPHA(J)=A*ARG1+B*ARG2 THROUGH THREE, FOR J=T2+1,i,J.G. T3 T=J*DELTAT TIME(J)=T ARGI=T*T-2./K*(T+1./K*(EXP.(-K*T)-1.)) DARG1=2.*T-2./K( 1 -EXP. (-K*T) ) T=J*DELTAT-TF ARG2=T*T-2./K* (T+1./K*(EXP.(-K*T)-1.)) DARG2=2.*T-2./K* ( 1 -RXP. (-K*T)) T=J*DELTAT-TF2 ARG3=T*T-2./K*(T+1./K*(EXP.(-K*T)-!1.)) DARG3=2.*T-2./K*( 1.-EXP.(-K*T)) RATE( J )=ADARG1+B*DARG2+C*DARG3 TWO ALPHA( J)=A*AARG +BARG2+C*ARG3 THROUGH FOUR, FOR J=T3+1,5,JG. END.OR. IALPHA(J-10).G. 0.99999 T=J*DELTAT TIME(J)=T ARG1=T*T-2./K*( T+1./K*(EXP.(-KK*T)-1.)) DARG1=2.*T-2./K*( 1.-EXP. (-K*T) ) T=J*DELTAT-TF DARG2=2.*T-2./K*(.-RXP.(-K*T)) ARG2=T*T-2./K*( T+1./K*(EXP. (-K*T)-1.)) T=J*DELTAT-TF2 ARG3=T*T-2./K*( T+1./K*(EXP.(-K*T)-.) ) DARG3=2.*T-2./K*(.-EXP. (-K*T) ) T=J*DELTAT-TF3 ARG4=T+(EXP. (-K*T)-1 )/K DARG4=1.-EXP. (-K*T) RATE ( J ) =A*DARG1+B*DARG2+C*DARG3+D*DARG4 FOUR ALPHA(J)=A*ARG1+B*ARG2+C*ARG3+D*ARG4 PRINT FORMAT NAME THROUGH FIVE, FOR J=0,5,J.G. TI PRINT FORMAT ANS, J, ALPHA(J), RATE(J), TIME(J) THROUGH SIX, FOR J=Tl+1,1,J.G. T3 SIX PRINT FORMAT ANS, J, ALPHA(J), RATE(J), TIME(J) THROUGH SEVEN, FOR J=T3+1,5,J.G. END.OR. lALPHA(J-10).G. 0.99999 SEVEN PRINT FORMAT ANS, J, ALPHA(J), RATE(J), TIME(J) TRANSFER TO BEGIN VECTOR VALUES DATA=$F2.0,F11.5/S10,3F10.0/1, 1F9.2*$ VECTOR VALUES NAME=$1HO,S7,2HNO,S5,5HALPHA,S6, 14HRATE*$ VECTOR VALUES ANS=$1H,U9,2F10.o5,F10.1*$ END OF PROGRAM

APPENDIX 0 COMPUTER PROGRAM USED TO CALCULATE T-T-T DATA FROM THEORETICAL EOUATIONS INTEGER T 1,2 T2, 3, J END, T4, I,H,N, M DIMENSION ALPHA(3000), RATE(3000),TIME(3000) 1, CHECK(O1), RLTIME(3000) BEGIN PRINT COMMENT $1$ READ AND PRINT DATA ROOT3=SQRT. (3.) CHECK (0) =0.05 CHECK( 1)=0.25 CHECK(2)=0.50 CHECK( 3 )=0.75 CHECK(4)=0.95 DELTAT=10. THROUGH LOOP, FOR H=O,1, H.G. 10 TEMP=220.+5.*H TK=(TEMP-32 ) /.8+273.16 RECTK=1./TK WHENEVER N.E. 1 THATA=1./(EXP.(65.919412-27714.276/TK)) TRANSFER TO GO END OF CONDITIONAL WHENEVER N.E. 2 THATA=1./(EXP. (44.914749-18815.948/TK) ) TRANSFER TO GO END OF CONDITIONAL WHENEVER N.E. 3 THATA=1./(EXP. (72 867142-29835.423/TK)) TRANSFER TO GO END OF CONDITIONAL WHENEVER N.E. 4 THATA=1./(EXP.(54.737652-23270.542/TK)) TRANSFER TO GO END OF CONDITIONAL THATA=1./(EXP.(54.737652-23270.542/TK)+(1.-ACT) 1EXP.(61.349550-23884.856/TK)) GO K=EXP.(75*837088-31093.767/TK)+(1.-ACT)* 1EXP.( 105.67753-40687.348/TK) UBDB=EXP. ( 77883003-32579. 302/TK)+(1.-ACT)* 1EXP. (86.941237-33827.652/TK) UADA=EXP. (81.935544-34415.472/TK) + (1.-ACT )* 1EXP. (88.798765-34844.749/TK) ARG=EXP. (89.521356-37331. 503/TK )+(1.-ACT)* 1EXP. (85.559312-33397.799/TJ) UADB=(UBDB-ARG)*SQRT. (3. ) UBDA=UBDB*UADA/UADB W=UADA X=UBDB Y=UADB Z=UBDA -244

-245WW=1./W XX=1./X YY=1./Y ZZ=1./Z A=4.*W*X-2./ROOT3*W*Y B=-2.*ROOT3*X*Z C=2.*ROT(Z*X./RT3(XOOT3*X*W+1. /3. OO0*W*Y ) D=-2.*W Tl=1./(2.*X)/DELTAT T2=1./ ( 2.*X-2./ROOT3*Y)/DELTAT T3=1./(2.*W)/DELTAT TF1=1./(2.*X) TF2=1./(2.*X-2./ROOT3*Y) TF3=1./( 2 oW) END=2998 PRINT RESULTS TEMP, TK, RECTK PRINT RESULTS THATA, K, ARG PRINT RESULTS UBDA, UBDB, UADA, UADB PRINT FORMAT NAME =O0 THROUGH ONE, FOR J=O,1,J.G.T1 T=J*DELTAT TIME( J )=T ARG1=T*T-2./K*(T+1./K* (EXP.(-K*T)-i.)) DARG1=2.*T-2./K*(.-EXP. (-K*T)) RATE(J)=A*DARG1 ALPHA (J) =A*ARG1 WHENEVER I.E. 0.AND. ALPHA(J).GE. CHECK(I) M=J ARG1=ALPHA(M)-0.05 ARG2=0.05-ALPHA(M-1) WHENEVER ARG1.G. ARG2, M=M-1 END OF CONDITIONAL WHENEVER ALPHA(J).GE. CHECK(I) RLTIME(J)=TIME( J )+THATA-TIME(M) RLTIME(J-1)=TIME(J-1)+THATA-TIME(M) PRINT FORMAT ANS, I, J, TIME(J), ALPHA(J), 1RATE(J), RLTIME(J) PRINT FORMAT ANS, I, J-1, TIME(J-1), ALPHA(J-1), 1RATE(J-I), RLTIME(J-1) I=I+l ONE END OF CONDITIONAL THROUGH TWO, FOR J=T1+l1,,J.G. T2 T=J*DELTAT TIME(J)=T ARG1=T*T-2./K*(T+./K*(EXP.(-K*T)-1.) ) DARG1=2. *T-2./K* ( 1.-EXP. (-K*T)) T=J*DELTAT-TF ARG2=T*T-2./K*(T+1./K*(EXP. (-K*T)-.)) DARG2=2.*T-2./K*( 1.-EXP.(-K*T)) RATE ( J )=ADARG1+B*DARG2 ALPHA(J ) =A*ARG1+B*ARG2 WHENEVER ALPHA(J).GE. CHECK(I) RLTIME ( J ) =TIME ( J ) +THATA-T I ME(M)

-246RLTIME(J-1)=TIME(J-1)+THATA-TIME(M) PRINT FORMAT ANS, I, Jt TIME(J), ALPHA(J), 1RATE(J), RLTIME(J) PRINT FORMAT ANS, I, J-1, TIME(J-l), ALPHA(J-1), 1RATE(J-1), RLTIME (J-1) I=I+1 TWO END OF CONDITIONAL THROUGH THREE, FOR J=T2+1,1,J.G. T3 T= JDELTA T TIME(J)=T ARG1=T*T-2./K*(T+1./K*(EXP. (-K*T)-1.)) DARG1=2.*T-2./K*(1.-EXP.(-K*T)) T=J -DELTAT-TF1 ARG2=T*T-2./K*(T+1./K* (EXP.(-K*T)-1.)) DARG2=2.",T-2./K*(1.-EXP.(-K*T)) T=J*DELTAT-TF2 ARG3=T*T-2./K*(( T+./K*( EXP. (-K*T)-1.) ) DARG3=2.*T-2./K*( 1 -EXP. (-KT)) RATE( J ) =A*DARG1+B*DARG2+C*DARG3 ALPHA( J ) =AARG1+B'-ARG2+C*ARG3 WHENEVER ALPHA(J).GE. CHECK(I) RLTIME(J)=TIME(J)+THATA-TIME(M) RLTIME ( J-1 )=TIME( J-1 ) +THATA-TIME ( M) PRINT FORMAT ANS, I, J, TIME(J), ALPHA(J), 1RATE(J), RLTIME(J) PRINT FORMAT ANS, I, J-l, TIME(J-1), ALPHA(J-1), 1RATE(J-1), RLTIME(J-1) 1=1+1 THREE END OF CONDITIONAL THROUGH FOUR, FOR J=T3+1,1,,JG. END T=J*DELTAT TIME(J)=T ARG1=T*T-2./K*(T+1./K*(EXP.(-K*T)-1.)) DARG1=2.*T-2./K*(1.-EXP (-K*T)) T=J*DELTAT-TF1 DARG2=2.*T-2./K*(1.-EXP.(-K*T)) ARG2=T*T-2./K*(T+1./K*(EXP.(-K*T)-1.)) T=J*DELTAT-TF2 ARG3=T*T-2./K*(T+1./K*(EXP.(-K*T)-1.)) DARG3=2.*T-2./K*(1.-EXP.(-K*T)) T=J*DELTAT-TF3 ARG4=T+(EXP.(-K*T)-1.)/K DARG4=1.-EXP. (-KT) RATE(J)=A*DARG1+B'*DARG2+C*DARG3+D*DARG4 ALPHA(J)=A*ARG1+B*ARG2+C*ARG3+D*.ARG4 WHENEVER ALPHA(J).GE. CHECK(I) RLTIME(J)=TIM E(J)+THATA-TIME(M) RLTIME ( J-1 ) =TIME(J-1 )+THATA-TI ME(M) PRINT FORMAT ANS, I, J, TIME(J), ALPHA(J), 1RATE(J), RLTIME(J) PRINT FORMAT ANS, I, J-1, TIME(J-1), ALPHA(J-1), 1RATE(J-1), RLTIME(J-I) I=I+1 WHENEVER I.GE. 5, TRANSFER TO OUT

-247FOUR END OF CONDITIONAL OUT CONTINUE WHENEVER RATE(T2),GE. O.(0)005, ELTAT=5. WHENEVER RATE(T2).GE. 0.001, DELTAT=1. WHENEVER RATE(T2).'GE. 0.010, DELTAT=0.1 WHENEVER RATE(T2).GE. 0.100, DELTAT=O.01 LOOP CONTINUE TRANSFER TO BEGIN VECTOR VALUES NANE=$1HO,S8,1HIS9 1HJ,S6, 4HTI MVE, 1S5,5HALPHA, S6,4HRATE, S4,6HRLT I iMEv $ VECTOR VALUJES ANS=$1H tI9,I,F10.1,2F10.5,F10.1 E$ END OF PROGRAM

APPENDIX P MEASUREMENTS OF DIHYDRATE CRYSTAL DIMENSIONS The average configuration and dimensions of the dihydrate crystal fragments used in the dilatometric experiments were measured from micrographs made at known magnifications on crystal fragments separated between screens having 0.0069 and 0.0082 inch openings. The fragments were thin, flat plates resulting from cleavagebetween (010) cleavage planes having outlines of a parallelogram with interior angles of 66~ and 114~. The outlines of most of the crystals approached the shape of perfect parallelograms exhibiting small chips and protrusions along their edges when examined microscopically. Micrographs were made showing the thickness as well as the length and width of the crystal fragments allowing the measurements of their dimensions to be made directly from the micrographs. Two clear plastic scales glued together at 114~ were used in measuring the lengths of the edges of the crystal fragments shown in one set of micrographs while the thicknesses were measured on another set of micrographs. The values obtained by these measurements are shown in Tables P-1 and P-2, resulting in crystal fragments having an average thickness of a' = 4.1 x 10-3 cm, and average parallelogram edges of c' = 1.50 x 102 and b' = 2.54 x 102 cm. Examination of ten crystal fragments using polarized light showed that the optical axes were inclined approximately 37 1/2~ to the shortest sides of seven of the ten crystals fragments examined indicating that the shortest sides of the crystals were probably formed by (100) cleavage planes and that the longest sides were probably formed by (001) cleavage planes. Combining this information with the measurements on -248

-249the average crystal sizes just given, the shortest length of c' = lo50 x 10-2 cm most probably corresponds to the average length of the (100) cleavage planes and the longest length of b' = 2.54 x 10-2 cm to the average length of the (001) cleavage plane length. The average number of dihydrate crystal fragments in a 0.7 gram sample was calculated by dividing the total volume of dihydrate by the volume of one of these crystal fragments. The volume of an average crystal fragment is: Vf = a'b'c' sin(66010T) = 1.43 x 10-6 cm using the values of a', b', and c' just calculated. Division of the total volume of dihydrate VD, where VD = WD/PD = 0.7 x 2.32 = 0.213 cm, by Vf gives the number of crystal fragments per sample, Nf = VD/Vf = 211,000.

-250TABLE P-1 THICKNESS OF CRYSTAL FRAGMENTS Micro. Thickness Micro. Thickness No. cm at 480X No. cm at 480X 16.01 2.0 16.23 1,1 16.02 1.6 16.24 2.0 16.03 1.4 16.25 1.3 16.04 1.7 16.26 1.3 16.05 1.9 16.27 1.3 16.0.66 16.28 1.4 16.07 2.0 16.29 1.2 16.08 1.5 163.0 1.4 16.09 1.4 163.1 0.7 16.10 3.4 16.32 0.8 16.11 4.0 16.33 2.4 16.12 0.9 16.34 1.3 16.13 2.8 16.35 1.9 16.14 1.6 16.36 0.9 16.14 2,3 16.37 2.1 16.15 2.2 16.38 1.9 16.16 2.2 16.39 1.1 16.17 2.9 16.18 1.9 15.30 1.7 16.19 2.4 15.31 3.0 16.20 2.1 15.32 4.7 16.21 2.5 15.33 1.9 16.22 2.7 Sum of Thicknesses 86.4 cm @ 480X Average Thickness 1.96 cm @ 480X Actual Average Thickness 4.1 x 10-3 cm

-251TABLE P-2 LENGTHS AND WIDTHS OF CRYSTAL FRAGMENTS Longest Shortest Micro. Dimension Dimension No. cm @ 305X cm @ 305X 15.01 5.8 5.1 15.02 6.0 3.9 15.03 8.2 5.4 15.04 8.1 4.8 15.05 8.6 4.5 15.06 6.0 5.2 15.07 6.8 4.9 15.08 6.3 5.4 15.08 4.1 3.5 15.09 6.3 5.4 15.10 7.0 4.2 15.10 7.5 4.5 15.11 8.6 4.4 15.12 6.6 4.1 15.13 6.5 4.1 15.14 6.2 3.1 1-5.14 7.7 4.6 15.15 8.0 4.5 15.16 7.1 3.0 15.17 7.6 4.1 15.18 7.1 2.9 15.19 9.4 5.9 15.20 9.5 4.4 15.21 7.5 5.0 15.22 9.1 6.6 15.23 9.2 3.3 15.24 7.4 5.2 15.25 5.5 2.8 15.26 7.5 7.5 15.27 7.8 4.5 15.28 10.6 5.2 15.29 15.0 5.5 15.30 14.0 3.5 15.31 5.4 4.3 Sum of Lengths 263.2 cm @ 305X 155.3 cm @ 305X Average Length 7.74 cm @ 305X 4.57 cm @ 305X Actual Length 2.54 x 10-2 cm 1.50 x 10-2 cm

APPENDIX Q DERIVATIONS OF THE CHEMICAL REACTION AND THE DIFFUSION EQUATIONS The movement of the dihydrate-hemihydrate interface is caused by two processes occurring at the interface: the chemical reaction resulting in the formation of the hemihydrate phase containing an excess of water, i.e,: CaS04~2H20 - CaS04 1/2 H20 + 3/2 H20, (Q-l) and the diffusion of the excess water from the interface to the bulk solution. The chemical reaction occurring at the interface can be described mathematically by: dmH/dt = K1' aD - K2' aH a3/2 (Q-2) where mH is the mass of hemihydrate formed, K1' and K2' are reaction rate constants, and aD, aH, and aW are the activities of the dihydrate, hemihydrate, and water phases, respectively. Since the activity of a pure solid is unity, Equation (Q-2) reduces to: dmH/dt = K1' - K2' aW/2 (Q-3) For a constant cross-sectional area, the rate of mass transformation is proportional to the velocity of the moving interface: U = K - K2 a/2 (Q-4) -252

-253and using pure water for the bulk solution results in: Uo = K1 - K2 (Q-5) Subtracting Equation (Q-5) from Equation (Q-4) yields: U - Uo = K2 (1 - aw5/2) (Q-6) where K2 traditionally is assumed to have an Arrhenius temperature dependence resulting in: U - 2o/ = Z'exp(-E/RT) (Q7) which can be made similar to Equation (85) by division of both sides by some arbitrary constant d and substituting P/P~ for aW (U/d) - (u/d)( 1 - (p/pO3/2 = Z exp(-E/RT) (Q-8) 1 - (p/po)3/-/ The diffusion of water through the hemihydrate crystal can likewise be described by: DT dmW = - (a# - a) dt (Q-9) where mW is the mass of water flowing, (a# - a) is the difference in activities between the interface and the bulk solution, x is the length of the diffusion path, D"' is a constant, and t is time. Since the mass of hemihydrate formed is proportional to the mass of water removed, Equation (Q-9) is equivalent to:

-254dm D (a# - a) at (Q-10) H x and for a constant cross-sectional area, where the change in mass is proportional to the distance the interface moves, this equation becomes: dx = D' (a# - a) dt (Q-ll) x or: U =dx/dt D (a# - a) o (Q-12) For constant values of x, the difference in velocities of two interfaces resulting from the use of two different bulk solutions can be represented by the following equation: U - U = (a - a) (Q-13) where Uo and ao = 1 represent the values obtained for pure water and U and a = P/Po represent the values in any salt solution. Since the coefficient D' usually exhibits an Arrhenius temperature dependence, the above equation takes on a form similar to that of Equation (85) after division by an arbritrary length d (U - = x/) exp(-E/RT). (Q-14) (1 - P/PO)

APPENDIX R THREE-DIMENSIONAL MODEL The equations for the three-dimensional model were derived directly from the two-dimensional model using the following substitution for c: c = Uc(t-x), assuming that the growth in the C direction terminated after @ minutes by impingement with another needle and that the cross sectionsof the hemihydrate needles are approximately uniform over their entire length. Thus, each needle eventually transforms a volume equal to abc o After the first impingement, the term (t - x) must be expressed as functions of the variables being used: y, z, and w. This is easily accomplished by noting that 91 is the value of the time difference between nucleation at time x and impingement at the time y: Q1 = Y - x, or (t - x) = (t - y) + 91 for 1l < Y < 92. Similarly, (t - x) = (t - z) + Q for 92 < z < Q93 and (t - x) = (t - w) + @3 for 3 < w < @c After impingement occurs in the C direction, a new term must be added for the final correction. The volume transformed by one hemihydrate needle growing in three-dimensions is: va(xt) = 2(2UAUB-U2/A3) UC (t-x)3 (R-l) The total volume transformed by many such needles is: x = t Va(t) = dN/dx v (x,t)dx (R-2) x = 0 where dN/dx = K No exp(-K x). When t = @1 = b/2UB, the first impingement occurs requiring the subtraction of the following volume: Vc(x,y,t) = 2 ~3 UB UC (t-y)2 (t-x). (R-5) -255

-256Since the term (t-x) is equal to (t-y) + 91 for values of 91 < y < 2 2 the correction volume for the first impingement becomes: vc(yt) = 2 3B Uc u [(t-y)3 + Gl(t-y) (-4) and, consequently, the total volume correction for the first impingement is: VT(t) dN/dy vc(y t)dy (R-5) c C J y = 91 where dN/dy = K No exp[-K(y-91)]. After t = 92 = b/[2(UB-UA/3)], the second impingement occurs requiring a volume addition term. This addition for a single hemihydrate needle is: ve(z,t) = 2 /3 (UB - UA/3)2Uc [(t-z) + 2(t-z)2] (R-6) corresponding to a total volume correction of: z = t V(t) = dN/dz ve(z,t)dz (R-7) z = 2 where dN/dz = K No exp[-K(z-92)]. After t = 93 = a/2UA, the correction for impingement for a single needle is: vg(w,t) = 2 b UAUC[(t + (t-w)2 + (t-w (R-8) corresponding to a total volume correction: rw = t V'(t) = dN/dw g(w,t)dw (R-9) g Jw = 3 where dN/dw = K No exp[-K(w-3)]. After t = Oc = c/UC, the final correction for impingement of a single needle is: vi(ut) = a b UC(t-u) (R-10)

-257corresponding to a total volume correction: fu = t Vi(t) dN/du vi(u,t)du (R-ll) u = ~c where dN/du = K No exp[-K(u-Gc)]. Thus, the total volume for t > Qc can be expressed as: V'(t) = V'(t) - V'(t) + V'(t) - V'(t) - V'(t). (R-12) a c e g i Division of the above equation by the total volume of hemihydrate formed abcNo gives the fraction reacted as a function of time: o(t) = V'(t)/abcNo (R-13) and differentiation of this equation gives the equation for the rate of reaction: da/dt = (l/abcNO) d[V'(t)/dt. (R-14) Values of da/dt were calculated on the IBM 7090 computer using the program shown in Table R-l. The program uses Equations (R-13) and (R-14) directly without calculating explicitly the coefficients of the time terms.

-258TABLE R-1 COMPUTER PROGRAM FOR THREE-DIMENSIONAL MODEL R R W=UADA, X=UBDB, Y=UADB, Z=UBDA, U=UCDC R INTEGER T1, T2, T3, J, END, T4 DIMENSION ALPHA(1000), RATE'(1000),TIME(1000) BEGIN READ FORMAT DATAN,K,E,F,G,H,CONTRL,DELTAT ROOT3=SQRT. (3.) W=1./(2.*G) X=1./(2.*EE) Y=(X-1./(2.*F ) )*ROOT3 Z=W*X/Y U=1./H WW=I./W XX=1. /X YY=1./Y ZZ=1./Z UU=1./U A=4.*W*X-2./ROOT3*W*Y B=-2.*ROOT3*X*Z C=2.*ROOT3* (Z*X-2./ROOT3*X*W+1./3.00*W*Y ) D=-2.*W A=A*U B = B *U C=C*U D=D*U DD=-U T1=l./(2.*X)/DELTAT/5. T2=1./(2.*X-2./ROOT3*Y)/DELTAT/5. T3=1./(2.*W)/DELTAT/5. T4=1./U/DELTAT/5. TF1=i./ (2.*X) TF2=1./( 2.*X-2./ROOT3*Y) TF3=1./(2.*W) TF4=1./U END=(10./K+T3)/5. PRINT COMMENT $1$ PRINT RESULTS N, TF1, TF2, TF3 PRINT RESULTS TF4 PRINT RESULTS END, T1, T2, T3 PRINT RESULTS T4 PRINT RESULTS A, B, C, D PRINT RESULTS DD PRINT RESULTS W, X, Y, Z PRINT RESULTS U PRINT RESULTS WW, XX, YY, ZZ PRINT RESULTS UU THROUGH ONE, FOR J=O,1,J.G. Ti T=5. *J*DELTAT TIME(J)=T

-259TABLE R-1 (CONT'D) ARG1=T*'T*T-3./K. * (T'.T-2./K "*(T-1 /K* ( 1.-EXP.(-K*T)))) DARGl=3B.T.T-*./KT(2.T-2./K'(1.-EXP. (-K*T))) RATE (J)=A*DARG1 ONE ALPHA(J)=A*ARG1 THROUGH TWO, FOR J=Ti+l,1,J.G. T2 T=5.*J*DELTAT TIME(J)=T ARG1=T*T*T-3./K(T.T-2. /K*(T-1./K*(1.-EXP. (-KT)))) DARG1=3.*T*T-3./K.'(2.*T-2./K( 1.-EXP. (-K*T))) T=5.*J*DELTAT-TF1 ARG2=T*T*T-3./K*( *T-2./KT2 (T-1./K*(.-EXP. (-K*T ) ) ) ) DARG2=3.*T*T-3./K*(2.*T-2./K*(1.-EXP.(-K*T))) ARG3=Te'T-2./K*(T-I./K*(1.-EXP.(-K*T))) DARG3=24*T-2./K*(1.-EXP.(-K*T)) RATE( J ) =A*DOARG1+B' ( DARG2+TF 1*DARG3) TWO ALPHA(J)=A*ARGI+B*(ARG2+TF1*ARG3) THROUGH THREE, FOR J=T2+,1,,J.G. T3 T=5.*J*DELTAT TIME(J)=T ARG1=T*T*T /K(T-3./K*(TT2/K*(T-./K*(l.-EXP.(-K*T)))) DARGl=3.*T*T-3./K (2.*T-2./K* (1.-EXP.(-KT))) T=5.J*DELTAT-TF 1 ARG2=T*T*T-3./K*(T*T-2./K*(T-1./K*(1.-EXP.(-K*T)))) DARG2=3.-*TT'T-3./K,(2.*T-2o/K"'(1.-EXP.(-K*T))) ARG3=T*T-2./K*(T-1./K *(1.-EXP.(-K*T))) DARG3=2.*T-2./K* (1.-EXP.(-K*T)) T=5.*J*DELTAT-TF2 ARG4=T*:T*T-3./K*(T*T-2./K*(T-1./K*(l.-EXP.(-K*T)))) DARG4=3.*'TT-3./K'- (2.*T-2./K*(1.-EXP.(-K*T))) ARG5=T*T-2./K*(T-1./K*(1.-EXP.(-K*T))) DARG5=2.*T-2./K (1.-EXP. (-K*T)) RATE(J)=A*DARG1+B* (DARG2+TF 1*DARG3)+C* (DARG4+TF2* 1DAR G5 ) THREE ALPHA(J)=A*ARG1+B*( ARG2+TF1*ARG3)+C*(ARG4+TF2*ARG5) THROUGH FOUR, FOR J=T3+1,1, J.G. T4 T=5.*J*DELTAT TIME(J)=T ARG1=T*T*T 3./K*(T*T-2./K(T*(T-1./K*(l.-EXP.(-K*T)))) DARG1=3.*T*T-3.//K*(2.*T-2./K*(1.-EXP.(-K*T))) T=5.*J*DELTAT-TF 1 ARG2=T3*T*T-3./K*(T*T-2./K*T (T-./K':(1.-EXP.(-K*T)))) DA R G2=3. T T-33/K(2.,T-2./K.( l.-EXP. (-KTP) ) ) ARG3=T*T-2./K*(T-1./K*(1.-EXP.(-K*,T))) DARG3=2. *T-2./K ( 1.-EXP, (-K*T)) T=5.*J*DELTAT-TF2 ARG4=T*T*T-3./K*( T*T-2./K*(T-1./K( 1.-EXP. (-KT)) ) ) DARG4=3.*T*T-3./K*( 2. *T-2./K* ( 1.-EXP. (-K*T) )) ARG5=T*T-2./K*(T-1./K*(1.-EXP.(-K*T) )) DARG5=2.*T-2./K*( 1.-EXP. (-K*T) ) T=5.*J*DELTAT-TF3 ARG6=T*T-2./K* ( T-./K* (.-EXP. (-K*T) ) )

-260TABLE R-1 (CONIT'D) DARG6=2, T( — 2.-/ K.- (. - EX P.( -KT ) ) ARG(7=T- 1./K:( 1.-EXP. (-K",T)) ARG7= 1.-EXP. (-KT ) RATE ( J ) =A, I:)ARG1+B' ( DARG2+-TF1'DARG3 )+C ( D)ARG4+TF2,' 1DARG(5) 1+D' ( DARG 6+TF3, *DARG7 ) FOUR ALPHA( A( J ) = + ARG2+TFi; ARG3)+C' (ARG4+TF2',.ARG5) 1+ D ('- (A R G 6+TF3: A R G7) THROUGH SIX, FOR J=T4+11,,J.G. END.OR. 1ALPHA(J-1().G. 0.99999 T= 5-J. -JD ELTAT TIiME(J)=T ARG1=T'T T-3./K' -. (T -2/K ( T T - /K ( 1 -EXP. (-K *T ) ) ) ) DARG 1 =3. T: T-3. / K ( 2. T-2. / K* ( 1. -EXP. ( -K T ) ) ) T =5 J D E L TA T- T F 1 ARG2=T'-T,:'-3./K 3 (TT- 2. /K': (T-1. /K* (1.-EXP. (-K*T)))) DARG2=3.*1- T-3. /K:: ( 2.T-2, /K* (.-EXP. ( -K*T ) ) ) ARG3=T"T-2./K*( T-./K"(1,.-EXP. (-KT))) DARG3=2.-:t-2./K".( 1.-EXP. (-K*T ) ) T=5.. J-.DELTAT-TF2 ARG4=T T':*T-3./K.,- ( T,T-2./K T (-i. /K-,- 1 -EXP. (-K*T ) ))) DARG4=3. T:1 —3. / K. ( 2. T-2. /K ( 1 -EXP. (-K T ) ) ) ARG5=T-/T-2./K' ( T-1./K* (1.-EXP.(-K*T))) DARG5=2.:T-2./K".(1.-EXP.(-KT)) T = 5..: J * DE L T A - T F 3 ARG6=T5T-2./K (T-1./K (1.-EXP.(-KTT)) ) DARG6=2.*T-2./K ( 1.-EXP. (-K*T ) ) ARG7=T-1./K*( 1.-EXP, (-K':T) ) DARG7= 1.-EXP. (-K*T) T=5, J*DELTAT-TF4 ARG8=T-1./K' ( i.-EXP. (-K*'T)) DARG8= 1.-EXP. (-K, T) RATE ( J ) =A Dl)ARG(;+B> ( DARG2+TF 1ODARG3 ) +C* ( DARG4+TF2 * 1DARG5 ) 1+D ( DARG6+TF3D)ARG7 ) +DD*DARG8 SIX ALPHA(J)=A*ARG1+B- ( ARG2+TF1*ARG3 )+C* (ARG4+TF2*ARG5) 1+D* ( ARG6+TF3^ARG7) +DD*ARG8 PRINT FORMAT NAME THROUGH FIVE, FUR J=O,1,J.G. END.OR. ALPHA(J-1O) 1.G. 0.99999 FIVE PRINT FORMAT ANS, JALPHA(J),RATE(J),TIME(J) TRANSFER TO BEGIN VECTOR VALUES DATA=$F2.0,F11.5/S10,4F10.0/I1,F9.2*$ VECTOR VALUES NAME=$1HO, S7,2HNO,S5,5HALPHA, S 6,4HRATE*$ VECTOR VALUES ANS=$1H,I9,2F10.5,F10.1*$ END OF PROGRAM

APPENDIX S DIMENSIONS OF THE HEMIHYDRATE SUBCRYSTALS AS FUNCTIONS OF TEMPERATURE The dimensions of the hemihydrate needles were calculated as functions of temperature from the values of the kinetic growth constants UB/a, UB/b, UA/a, and UA/b using the values of UA and U measured directly in large single crystals of dihydrate. Since the B temperature dependencesfor these six terms are known, the temperature dependence for a and b can be calculated directly from these relationships by dividing the equations describing the temperature dependence of UA and UB by the equations describing the temperature dependence for the kinetic growth constants. This results in four equations, two describing the temperature dependence of a, and two describing the temperature dependence of b, all having the form of the Arrhenius equation. Averaging the coefficients of the two equations for a, and the two equations for b yields: a = 3.89 x 10-16 exp(ll,571/T) (S-1) b = 7.82 x 10-9 exp( 4,993/T) (S-2) where T is the absolute temperature in degrees Kelvin. Values calculated using these equations are given in Table S-l. It should be pointed out that the temperature dependence for a and b probably is the result of the temperature dependence of the nucleation phenomenon which determines the density of the nuclei on the surface of the crystal and, consequently, determines the values of a and b. As the reaction temperature increases, the total number of nucleation sites also increases due to the increase in molecular -261

-262vibrations and the size of the hemihydrate subcrystals decreases accordingly, since the surface area remains constant. The number of nuclei per initial dihydrate particle can be calculated from the values of a and b previously calculated using the following relationship: VH = a b c No/p Nf where a, b, and, are the average dimensions of the hemihydrate subcrystal, VH is the final volume of hemihydrate formed, Nf is the number of dihydrate particles per sample, and No/p is the number of nuclei per dihydrate particle. For the 0.7 gram samples used in these experiments, VH = 0.2130 cc, c = 0.015 cm, and Nf = 211,000 particle/sample (See Appendices L and P), and the equation for No/p is: No/p = 2.21 x 1019 exp(-16,564/T) (S-4) where T is the absolute temperature in degrees Kelvin. Values of No/p calculated at several temperatures are shown in Table S-2o

-263TABLE S-1 DIMENSIONS OF HEMIHYDRATE SUBCRYSTALS Temp., a, b, OF cm cm 220 0.00786 0.00423 230 0.00504 0.00357 240 0.00328 0.00296 250 0.00215 0.00247 260 0.00143 0.00207 270 0.00o96 0.00175 TABLE S-2 NUMBER OF NUCLEI PER DIHYDRATE PARTICLE No/p, Temp., Nuclei per ~F Particle 220 1.98 230 3.74 240 6.93 250 12.7 260 22.7 270 70.1

APPENDIX T NORMALIZED DATA NORMALIZED DATA FROM RUIN 6 NORMALIZED DATA FROM RUN 6 (CONT'D) INORMALIZED DATA FROM RUN 6 (CIINT'I)] TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. T IE ALPHA RATE TEMP. MIN MI N-' OF I I MI N' OF I M f I N-' OF.00.00000.00018 260.20 50.00.37077.0009 261.00 100.00.74571.00579 261.00 1.00.00037.00229 260.40 51.00.37906.00848 261.00 101.00.75173.00622 261.00 2.00.00459.00278 260.40 52.00.38774.00868 261.00 102.00.75815.00606 261.00 3.00.00592.00293 260.70 53.00.39642.00845 261.00 103.00(.76385.00590 261.00 4.00.01045.00477 260.80 54.00.40463.00829 261.00 104.00.76995.00555 261.00 5.00.01545.00477 260.90) 55.00.41299.00813 261.00 105.00.77496.00575 261.00 6.00.01999.00539 261.00 56.00.42089.00825 261.00 106.00.78145.00610 261.00 7.00.02624.00641 261.00 57.00.42949.00856 261.00 107.00.78716.00555 261.00 8.00.03281.00657 261.00 58.00.43802.00833 261.00 108.00.79255.00575 261.00 9.00.03938.00661 261.00 59.00'.44615.00805 261.00 109.00.79865.00571 261.00 10.00.04603.00704 261.00 60.00.45413.00790 261.00 110.(00.90397.00461 261.00 11.00.05346.00755 261.00 61.10.46194.00778 261.00 111.00.80788.00575 261.00 12.00.06112.00762 261.00 62.00.46969.00778 261.00 112.00.81546.00622 261.00 13.00.06H70.00770 261.00) 63.00.47751.00798 261.00 113.00.82031.00512 261.00 14.00.07652.00801 261.00 64.00.48564.00798 261.00 114.00.82571.00504 261.00 15.00.08473.00801 261.00 65.00.49346.00782 261.00 115.00.83040.00504 261.00 16.00.09255.00805 261.00 66.00.50128.00813 261.00 116.00.83579.00485 261.00 17.00.10084.00829 261.00 67.00.50972.00809 261.00 117.00.84009.00426 261.00 18.00.10913.00805 261.00 68.00.51746.00751 261.00 118.00.84432.0(0516 261.00 19.00.11695.00805 261.00 69.00.52474.00770 261.00 119.00.85042.00504 261.00 20.00.12524.00829 261.00 70.00.53287.00809 261.00 120.00.85440.00438 261.00 21.00.13353.00829 261.00 71.00.54092.00790 261.00 121.00.85917.00465 261.00 22.00.14182.00841 261.00 72.00.54866.00755 261.00 122.00.86371.00450 261.00 23.00.15034.00841 261.00 73.00.55601.00735 261.00 123.00.86817.00528 261.00 24.00.15863.00809 261.00 74.00.56336.00755 261.00 124.00.87427.00407 261.00 25.00.16653.00801 261.00 75.00.57110.00774 261.00 125.00.87630.00348 261.00 26.00.17466.00790 261.00 76.00.57885.00833 261.00 126.00.88123.00450 261.00 27.00.18232.00809 261.00 77.00.58776.00778 261.00 127.00.88529.00446 261.00 28.00.19084.00848 261.00 78.00.59441.00719 261.00 128.00.89014.00426 261.00 29.00.19929.00801 261.00 79.00.60215.00786 261.00 129.00.89381.00387 261.00 30.00.20687.00833 261.00 80.00.61012.00755 261.00 130.00.89788.00387 261.00 31.00.21594.00833 261.00 81.00.61724.00731 261.00 131.00.90156.00368 261.00 32.00.22353.00798 261.00 82.()0.62475.00755 261.00 132.00.90523.00325 261.00 33.00.23190.00833 261.00 83.00.63233.00735 261.00 133.00.90805(.0(0364 261.00 34.00.24018.00833 261.00 84.00.63945.00755 261.00 134.00.91250.00352 261.00 35.00.24855.00817 261.00 85.00.64742.00735 261.00 135.00.91508.00297 261.00 36.00.25653.00798 261.00 86.00.65415.00704 261.00 136.00.91845.00328 261.00 37.00.26450.00798 261.00 87.10.66150.00)719 261.00 137.00.92165.00258 261.00 38.00.27248.00833 261.00 88.00.66854.00700 261.01 138.OU.92361.00238 261.10 39.00.28116.00813 261.00 89.00.67549.00700 261.00 139.00.92642.00321 261.10 40.00.28874.00778 261.00 90.0(1.682>3.00700 261.00 140.00.93002.00282 261.10 41.00.29672.00801 261.00 91.00.68949.00661 261.00 141.00.93205.00282 261.10 42.00.30477.00829 261.00 92.00.69575.00680 261.00 142.00.93565.00235 261.10 43.00.31330.00829 261.00 93.00.70310.00649 261.00 143.00.93674.00180 261.20 44.00.32135.00790) 261.00 94.00.70873.00583 261.00 144.00.93924.00223 261.10 45.00.32909.00829 261.00 95.00.71475.00672 261.00 145.00O.94120.,00258 261.20 46.00.33793.00864 261.00 96.00.72218.0()672 261.00 146.00.94441.00258 261.111 47.00.34637.00817 261.00 97.00.72820.0()598 261.00 147.100.94636.00262 261.20 48.00.35427.00825 261.00 98.00.73414.00(598 261.00 148.00.94964.00238 261.10 49.00.36287.00825 261.00 99.00.74016.0(10579 261.001) 149.00.95113.00)219 261.20 NORMALIZED DATA FROM RUN 6 (CONT'D) NORMIALIZEDI DATA FROM R5N16 7 NURMALIZE1) D(ATA FRIIM RUN 7 (CONT'D) T I NiE ALPHA RATE TEMP. TI E ALPHA RATE TEMP. T I ME ALPHA RATE T EM P. IN- I 11- OF I i, M I OF -I I'. I N 1 OF 150.00,.95402.00184 261.1(0.(00 0000 00184 25920.0 4 29.2(..97461.00324 259.30 151.00.95480.00199 261.20 1.00.0036.(0057H 259.30 51.00.97721.00291 259.40 152.00.958(11.00246 261.10 2.00.01157.00847 259.30 52.00.98044.00291 259. 40 153.00.95973.00203 261.20 3.00.02062.01092 259.30 53.00.98302.00284 259.40 154.00.96208.00149 261.10 4.00.03342.01280 259.30 54.00.98613.00194 259.40 155. 0.96270.00145. 261.20 5.00.04622.01635 259.30 55.00.98691.00123 259.50 156.00.96497.00168 261.20 6.00.06611.02048 259.20 56.00.98859.00065 259.50 157.00. 96606,.00149 261.20 7.00.08718.02068 259.1(0 57.0U.98822.00046 259.60 158.00.96794.00168 261.20 8.10.10747.02281 259.10 58.00.98951 -.00018 259.60 159.00.96943.00149 261.20 9.(0.13280.02681 259.00 59.00.98785.00104 259.80 160 0,9791.00113 261.20 10.100.16109.02893 256.80 60.1(1.99159.00162 259.70 161.(0.97169.()0152 261.20 11.00.1967.03312 258.6() 61.00.99108.00129 259.80 162.00.97396.00188 261,.20 12.00.22733.03410 258.20 62.00.99417.00123 259.70 163.(0.97545.00149 261.20 13.00.22886.132650 258 1(0 63.00.993b4.00091 259.80 164.00.97693.00109 261.20 14.00.29233.103353 258.00 64.,00.99598.00245 259.70 165.00.97764.00149 261.20 15.00.32593.03328 257.90 65.00.99843.00162 259.60 166.00.97991.00168 261,.20 16.00.3589.()3502 257.90 66.00.99921 -.00018 259.70 167.00.9810(.00113 261.20 17.01).39597.03849 257.70 67.00.99806 -.00058 259.80 168.00.98217.00094 261.20 18.00.43589.03791 257.50 68.00.99806.00032 259.80 169.00,98288.00(109 261.20 19.(00.47179.013572 257.30 69.00.99871.00032 259.80 170.00.98436.00113 261.20 20.00.50733.03399 257.20 70.00.99871.00065 259.80 171.00.98514.00113 261.20 21.00.53978.03161 257.20 71.00 1.00000 -.00115 259.80 172.00.98663.00168 261.20 22.00.57055.02961 257.20 173.00.98851.00113 261.20 23.00.59899.12844 257.20 174.00.98890.00094 261.20 24.00.62743.02780 257.20 175.00.99038.00109 261.20 25.00.65458.02715 257.20 176.00.99109.00074 261.20 26.(0.68173.0)2683 257.20 177.00,99187.00078 261.20 27.00.70824.02566 257.20 178.00.99265.00031 261.20 28.00.73306.02431 257.20 179.00.99249.00090 261.30 29.00.75685.02289 257.20 180.00.99445.00074 261.20 30.00.77884.11891 257.30 181.00.99398.00059 261.30 31.00.79467.1)1775 257.60 182.00.99562.00016 261.20 32.00).81434.01915 257.70 183.00.99429.00()31 261.40 33.00.83297.01631 257.801) 184.00.99625.00094 261.30) 34.00.84696.01463 258.00 185.00.99617.00055 261.40 35.00.86223.01539 258.10 186.10.99734.00035 261.30 36.00.87775.01545 258.10 187.00.99687.00039 261.40 37.00.89313.01467 258.10 188.00.99812.00039 261.30 38.00.90710.01087 258.10 189.00.99765.00027 261.40 39.00.91488.00868 258.3)0 190.00.99867.00027 261.30 40,00.92446.00797 258.4) 191.00.99820.00027 261.40 41.00.93083.00694 258.60 192,001).99922,)00027 261.30 42.0()0.93834.00847 258.70) 1.93.00.99875.00)039 261.40 43.00.94778.00(731 258.70 194.00 1.001)00.00039 261.30 44.00.95296.00)345 258.80 45.00(.95468.0104013 259.10 46.00.96101.001601 259.10 47.00.96670(.00478 259.10( 48.00.97058.00202 259.10 49.00(.97073.00202 259.30 -264

-265NORMALIZED DATA FROM RUN 8 NORMALIZED DATA FROM RUN 8 (CONT'D) NORMALIZED DATA FROM RUN 9 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN'' oF MIN MIN' OF MIN' OF.00.00000.00027 257.30 50.00.97299.00276 258.60.00.00000.00008 260.10 1.00.00055.00426 257.90 51.00.97385.00364 259.00 1.00.00015.00113 260.20 2.00.00852.00740 258.10 52.00.98026.00394 258.90 2.00.00225.00182 260.30 3.00.01535.00857 258.40 53,00.98174.00250 259.10 3.00.00379.00097 260.50 4.00.02566.01DO3 258.50 54.00.98526.00346 259.10 4.00.00419.00457 260.70 5.00.03681.01315 258.70 55.00.98866.00224 259.10 5.00.01292.00810 260.70 6.00.05195.01630 258.80 56.00.98973.00167 259.20 6.00.02039.00873 260.70 7.00.06940.0189.0 258.90 57.00.99201.00231 259.30 7.00.03039.01211 260.70 8.00.08974.02150 258.90 58.00.99435.00046 259.20 8.00.04462.01304 260.60 9.00.11239.02315 258.90 59.00.99293.00114 259.50 9.00.05646.01559 260.70 i0.00.13603.02474 258.90 60.00.99662.00115 259.30 10.00.07580.01913 260.50 11.00.16187.03083 258.90 61.00.99524.00115 259.50 11.00.09471.02223 260.40 12.00.19769.03175 258.30 62.00.99893 -.00009 259.30 12.00..12025.02321 260.20 13.00.22536.03043 258.40 63.00.99506.00053 259.70 13.00.14113.02293 260.20 14.00.25855.03166 258.10 64.00 1.00000.00026 259.40 14.00.16611.02794 260.10 15.00.28868.03097 258.10 15.00.19702.03379 259.80 T6.00.32048.03086 258.00 16.00.23370.03264 259.30 17.00.35039.03150 258.00 17.00.26230.03061 259.30 18.00.38349.02994 257.60 18,.00.29492.03162 259.10 19.00.41027.02951 257.80 19.00.32554.03358 259.10 20.00.44251.03053 257,70. 20.00.36208.03421 258.90 21.00.47132.02966 257.70 21.00.39397.03640 258.90 22.00.560183.02981 257.50 22.00.43489.03621 258.50 23.00.53094.02881 257.60 23.00.46640.03518 258.50 24.00.55945.02815 257.50 24.00.50524.03505 258.20 25.00.58724.02842 257.60 25.00.53650.03063 258.20 26.00.61629.02844 257.50 26.00.56649.03025 258.20 27.00.64411.02723 257.50 27.00.59699.03082 258.20 285.00.67075.02540 257.40 28.00.62813.02923 258.20 29.00.69491.02437 257.50 29.00.65546.02936 258.20 30.00.71949.02206 257.30 30.00.68685.02949 258.20 31.00.73903.02044 257.40 31.00.71444.02702 258.20 32.00.76036.01983 257.40 32.00.74089.02658 258.20 33.00.77870.01974 257.50 33.00.76759.02620 258.20 34.00.79984.01942 257.40 34.00.79328.02506 258.20 35.00.81754.01776 257.40 35.00.81770.02310 258.20 36.00.83535.01535 257.40 36.00.83947.02042 258.20 37.00.84824.01537 257.70 37.00.85854.01991 258.30 38.00.86608.01427 257.60 38..00.87930.01896 258.30 39.00.87677.01205 257.90 39.00.89647.01563 258.40 40.00.890i9.01212 257.90 40.00.91056.01200 258.60 41.00.90101.01108 258.10 41.00.92047.01139 258.80 42.00.91234.01198 258.10 42.00.93334.01076 258.90 43.00,92498.01155 258.10 43.00.94198.01040 259.10 44.00.93543.00860 258.10 44.00.95413.01088 259.10 45.00.94219.00739 258.30 45.00.96375.00884 259.10 46.00.95021.00679 258.30 46.00.97181.00658 259.20 47.00.95576.00624 258.50 47.00.97690.00565 259.40 48.00.96269.00629 258.50 48.00.98310.00423 259.40 49.00.96834.00515 258.70 49.00.98537.00339 259.70 NORMALIZED DATA FROM RUN 9 (CONT'D) NORMALIZED DATA FROM RUN 10 NORMALIZED DATA FROM RUN 10 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MINI' MIN MIN' OF MIN MI N-' OF 50.00.98987.00186 259.80.00.00000.00157 258.10 50.00.98725.00099 259.00 51.00.98909.00098 260.10 1.00.00314.00009 258.10 51.00.99207.00254 259.00 52.00.99183.00257 260.20 2.00.00018.00044 258.40 52.00.99232.00192 259.10 53.00.99423.00225 260.20 3.00.00401.00192 258.40 53.00.99591.00142 259.10 54.00.99633.00140 260.30 4.00.00402.00254 258.80 54.00.99517.00192 259.30 55.00.99704.00184 260.40 5.00.00910.00297 258.80 55.00.99975 -.00043 259.20 56.00 1.00000.00099 260.30 6.00.00997.00508 259.10 56.00.99431.00012 259.50 7.00.01925.01133 259.10 57.00 1.00000 -.00099 259.30 8.00.03262.01368 259.10 9.00.04661.01498 259.10 10.00.06258.01696 259.10 11.00.08053.01888 259.10 12.00.10033.02525 259.10 13.00.13103.02556 259.00 14.00,15145.02562 258.90 15.00.18227.02977 258.70 16.00.21099.03119 258.60 17.00.24465.03243 258.30 18.00.27584.03280 258.20 19.00.31025.03280 258.00 20.00.34144.03262 258.00 21.00.37548.03299 257.90 22.00.40742.03694 257.90 23.00.44937.03818 257.50 24.00.48378.03676 257.50 25.00.52289.03534 257.20 26.00.55446.03311 257.30 27.00.58912.03218 257.20 28.00.61883.03175 2.57.30 29.00.65262.03453 257.10 30.00.68789.02736 257.10 31.00.70733.02426 257.10 32.00.73642.02785 257.10 33.00.76303.02624 257.10 34.00.78890.02525 257.10 35.00.81354.02364 257.10 36.00.83619.01634 257.10 37.00.84621.01907 257.10 38.00.87432.02754 257.30 39.00.90130.01993 257.10 40.00.91418.01609 257.30 41.00.93349.00985 257.30 42.00.93387.00787 257.90 43.00.94922.01232 257.80 44.00.95851.01052 258.00 45.00.97027.01182 258.00 46.00.98216.00836 258.20 47,00.98698 -.00030 258.10 48,00.98155.00155 258.70 49.00.99009.00285 258.60

-266NORMALIZED DATA FROM RUN 11 NORMALIZED DATA FROM RUN 11 (CONT'D) NORMALIZED DATA FROM RUN 12 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF MIN MIN' OF lIN MIN'' OF.00.00000.00313 260.70 50.00.99921.00026 260.70.00.00000.00016 261.20 1.00.00626.00895 260.70 51.00.99805.00013 260.80 1.00.00033.00461 261.20 2.00.01789.01286 260.70 52.00.99947.00013 260.80 2.00.00922.00978 261.20 3.00.03199.01654 260.70 53.00.99832 -.00019 260.90 3.00.01989..01226 261.20 4.00.05098.01906 260.50 54.00.99909.00020 260.90 4.00.03373.01546 261.20 5.00.07010.02210 260.40 55.00.99871.00013 261.00 5.00.05082.01769 261.10 6.00.09517.02430 260.20 56.00.99935,00065 261.00 6.00.06911.02061 261.10 7.00.11870.02669 260.20 57.00 1.00000.00032 261.00 7.00.09203.02385 261.00 8.00.14855.02985 260.00 8.00.11680.02959 261.00 9.00.17839.03339 259.80 9.00.15122.03410 260.60 10.00.21532.03333 259.30 10.00.18501.03448 260.40 11.00.24505.03179 259.30 11.00.22018.03476 260.20 12.00.27890.03147 259.10 12.00.25454.03606 260.10 13.00.30799.03147 259.10 13.00.29231.03723 259.80 14.00.34184.03192 258.90 14.00.32900.03660 259.60 15.00.37183.03565 258.90 15.00.36551.04059 259.50 16.00.41314.03656 258.40 16.00.41019.04180. 259.10 17.00.44495.03258 258.50 17.00.44910.03870 259.00 18.00.47829.03412 258.40 18.00.48759.04031 259.00 19.00.51319.03489 258.30 19.00.52973.04038 258.80 20.00.54808.03406 258.20 20.00.56834.03959 258.80 21.00.58130..03412 258.20 21.00.60891.04091 258.70 22.00.61632.03270 258.10 22.00.65016.03977 258.50 23.00.64670.03148 258.10 23.00.68844.03442. 258.40 24.00.67928.03096 258.10 24.00.719(0.03283 258.50 25.00.70862.02883 258.10 25.00.75411.03317 258.40 26.00.73693.02754 258.10 26.00.78535.03004 258.40 27.00.76369.02547 258.10 27.00.81418.02779 258.40 28.00.78787.02501 258.10 28.00.84093.02618 258.50 29.00.81372.02527 258.10 29.00.86653.02389 258.60 30.00.83841.02282 258.10 30.00.88871.01961 258.70 31.00.85935.02037 258.10 31.00.90575.01783 258.90 32.00.87916.01857 258.30 32.00.92436.01754 259.00 33.00.89649.01489 258.40 33.00.94082.01544 259.10 34.00.90894.01237 258.70 34.00.95524.01341 259.20 35.00.92124.01320 258.90 35.00.96764.00935 259.30 36.00.93535.01313 259.00 36.00.97394.00703 259.60 37.00.94751.01139 259.10 37.00.98170.00538 259.80 38.00.95812.00868 259.20 38.00.98470.00394 260.10 39.00.96486.00623 259.40 39.00.98959.00521 a60.20 40.00.97057.00436 259.70 40.00.99512.00419 2A0.30 41.00.97357.00409 260.00 41.00.99798.00076 260.40 42.00.97875.00582 260.10 42.00.99664 -.00063 260.70 43.00.98522.00537 260.20 43.00.99671.00070 260.80 44.00.98949.00240 260.20 44.00.99804.00032 260.90 45,.00.99002.00362 260.40 45.00.99734.00035 261.00 46.00.99673.00259 260.30 46.00.99874.00035 261.00 47.00.99519.00149 260.50 47.00.99803 -.00064 261.10 48.00.99971.00117 260.40 48.00.99746.00003 261.20 49.00.99752 -.00025 260(1.60 49.00.99809.00064 261.20 NORMALIZED DATA FROM RUN 12 (CONT'D) NORMALIZED DATA FROM RUN 13 NORMALIZED DATA FROM RUN 14 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN' OF MIN MIN-' Of MIN MIN-' OF 50.00.99873.00032 261.20.00.00000.00123 261.10.00.00000.00129 261.20 51.00.99873.00032 261.20 1.00,.00246.00250 261.10 1.00.00257.00278 261.20 52.00.99936.00032 261.20 2.00.00499.00567 261.20 2.00.00555.00587 261.30 53,00.99936.00032 261.20 3.00.01381.00967 26.1.20 3.00.01432.00947 261.30 54.00 1.00000.00032 261.20 4.00.02432.01136 261.20 4.00.02449.01170 261.40 5.00.03653.01306 261.20 5.00.03772.01610 261.40 6.00.05044.01399 261.20 6.00.05670.02020 261.40 7.00.06451.01560 261.20 7.00.07813.02360 261.40 8.00.08164.01899 261.20 8.00.10391.02794 261.30 9,00.10249.02520 261.20 9.00.13400.02921 261.20 10.00.13203.03047 261.00 10.00.16233.03081 261.20 11.00.16344.03276 260.70 11.00.19563.03303 261.00 12.00.19755.03352 260.40 12.00.22839.03684 260.70 13.00.23047.03282 260.20 13.00.26930.03912 260.50 14.00.26320.03596 260.20 14.00.30662.03665 260.30 15.00.30238.04436 260.00 15,00.34260.03489 260.20 16.00.35192.04851 259.60 16.00.37639.03663 260.20 17.00.39941.04638 259.30 17.00.4L586.03757 260.00 18.00.44469.04545 259.20 18.00.45152.04128 260.00 19.00.49030.04511 259.10 19.00.49842.04293 259.50 20.00.53490.04460 259.10 20.00.53739.03818 259.50 21.00.57950.04544 259.10 21.00.57478.03710 259.50 22.00.62579.04417 259.10 22.00.61159.03755 259.50 23.00.66784.04205 259.10 23.00.64987.03647 259.40 24.00.70989.04087 259.10 24.00.68452.03453 259.40 25.00.74957.03739 259.10 25.00.71892.03374 259.30 26.00.78467.03595 259.10 26.00.75199.03163 259.30 27.00.82147.03425 259.10 27.00.78219.02822 259.30 28.00.85318.02857 259.10 28.00.80844.02488 259.50 29.00.87861.02365 259.30 29.00.83196.02411 259.70 30.00.90048.02017 259.50 30.00.85666.02303 259.80 31.00.91895.01609 259.70 31.00.87801.01992 260.00 32.00.93266.01397 260.00 32.00.89649.01988 260.20 33.00.94689.01295 260.20 33.00.91777.01889 260.20 34.00.95857.00998 260.40 34.00.93427.01731 260.30 35.00.96686.00735 260.60 35.00.95239.00892 260.30 36.00.97328.00515 260.80 36.00.95212.00555 261.00 37.00.97715.00456 261.00 37.00.96348.01062 261.00 38.00.98240.00584 261.10 38.00.97337.00873 261.10 39.00.98884.00406 261.10 39.00.98095.00681 261.20 40.00.99052.00271 261.20 40.00.98698.00645 261.20 41.00.99425.00348 261.20 41.00.99385.00384 261.30 42.00.99747.00109 261.20 42.00.96467.00226 261.40 43.00.99644.00033 261.30 43.00.99836.00226 261.50 44.00.99813.00178 261.30 44.00.99918.00082 261.60 45.00 1.00000.00025 261.30 45.00 1.00000 -.00107 261.70

-267NORMALIZED DATA FROM RUM 15 NORMALIZED DATA FROM RUN 15 (CONT'D) NORMALIZED DATA FROM RUN 16 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. T IMRE ALPHA RATE TEMP. MIN MI N-' OF MIN M I N-' OF MIN ii I N - OF.00.00000.00259 260.00 50.00.99477.00036 260.20.00.00000.00121 261.20 1.00.00518.00593 260.00 51.00.99604.00063 260.20 1.00.00242.00445 261.20 2.00.01185.00891 260.10 52.00.99604.00032 260.20 2.00.00891.00773 261.20 3.00.02300.01292 260.10 53.00.996E7 -.00040 260.20 3.00.01787.01078 261.20 4.00.03769.01533 260.10 54.00.99523.00032 260.30 4.00.03046.01350 261.20 5.00.05365.01786 260.10 55.00.99731 -.00015 260.20 5.00.04487.01623 261.20 6.00.07341.02061 260.10 56.00.99493.00036 260.40 6.00.06292.01915 261.20 7.00.09487.02244 260.00 57.00.99802.00095 260.30 7.00.08318.02142 261.20 8.00.11830.02419 260.00 58.00.99683 -.00028 260.40 8.00.10577.02414 261.20 9.00.14326.02552 260.00 59.00 *.99747.00004 260.40 9.00.13146.02382 261.10 10.00.16935.03252 260.00 60.00.99691.00063 260.50 10.00.15340.02478 261.10 11.00.20830.03476 259.30 61.00.99873.00154 260.40 11.00.18102.02601 260.90 12.00.23887.03051 259.20 62.00 1.00000.00063 260.40 12.00.20543.02672 260.90 13.00.26931.03146 259.10 13.00.23445.02485 260.60 14.00.30178.03158 259.00 14.00.25513.02492 260.80 15.00.33248.03139 258.90 15.00.28428.02626 260.50 16.00.36457.03603 258.80 16.00.30765.02497 260.50 17.00.40455.03500 258.30 17.00.33422.02471 260.30 18.00.43457.03143 258.30 18.00.35708.02414 260.30 19.00.46742.03285 258.20 19.00.38250.02388 260.20 20.00.50026.03264 258.10 20.00.40483.02388 260.20 21.00.53269.03249 258.10 21.00.43026.02388 260.10 22.00.56525.03293 258.10 22.00.45259.02658 260.10 23.00.59856.03300 258.10 23.00.48341.02563 259.80 24.00.63124.03346 258.10 24.00.50385.02710 260.00 25.00.66548.03300 258.00 25.00.53760.02755 259.50 26.00.69724.03186 258.10 26.00.55895.02577 259.70 27.00.72920.02983 258.00 27.00.58915.02738 259.50 28.00.75690.02926 258.10 28.00.61372.02904 259.60 29.00.78772.02825 258.00 29.00.64723.02937 259.20 30.00.81339.02584 258.10 30.00.67245.02746 259.30 31.00.83940.02362 258.00 31.00.70215.02733 259.20 32.00.86064.02392 258.10 32.00.72711.02720 259.30 33.00.88724.02134 258.10 33.00.75655.02681 259.20 34.00.90333.01638 258.10 34.00.78073.02616 259.30 35.00.92001.01548 258.20 35.00.80888.02486 259.20 36.00.93429.01280 258.30 36.00.83046.02254 259.30 37.00.94561.00912 258.50 37.00.85396.02183 259.30 38.00.95254.00851 258.90 38.00.87412.01976 259.40 39.00.96263.00914 259.00 39.00.89349.01430 259.50 40.00.97082.00821 259.10 40.00.90271.01299 260.00 41.00.97905.00817 259.10 41.00.91946.01514 260.00 42.00.98716.00477 259.10 42.00.93299.01262 260.10 43.00.98859.00019 259.30 43.00.94470.01106 260.20 44.00.98753.00078.259.70 44.00.95511.01014 260.30 45.00.99015.00107 259.80 45.00.96498.00762 260.30 46.00.98967.00044 260.00 46.00.97035.00575 260.50 47.00.99102.00071 260.10 47.00.97647.00419 260.60 48.00.99110.00215 260.20 48.00.97872.00321 260.80 49.00.99533.00184 260.10 49.00.98290.00263 260.90 NORMALIZED DATA FROM RUN 16 (CONT'D) NORMALIZED DATA FROM RUN 19 NORMALIZED DATA FROM RUN 19 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF MIN MIN-' OF MIN MIN-' Of 50.00.98398.00146 261.10.00.00000.00106 251.70 50.00.42056.01214 251.00 51.00.98581.00274 261.20 1.00.00211.00093 251.60 51.00.43364.01178 250.90 52.00.98945.00305 261.20 2.00.00186.00187 251.70 52.00.44411.01172 251.00 53.00.99191.00150 261.20 3.00.00585.00268 25,1.60 53.00.45708.01266 250.90 54.00.99245.00150 261.30 4.00.00722.00297 251.70 54.00.46944.01189 250.90 55.00.99492.00188 261.30 5.00.01179.00292 251.60 55.00.48087.01160 250.90 56.00.99622.00097 261.30 6.00.01305.00409 251.70 56.00.49265.01184 250.90 57.00.99687.00130 261.30 7.00.01998.00350 251.50 57.00.50454.01166 250.90 58.00.99881.00156 261.30 8.00.02005.00385 251.70 58.00.51597.01172 250.90 59.00.99998.00020 261.30 9.00.02768.00431 251.50 59.00.52798.01113 250.90 60.00.99922 -.00032 261.40 10.00..02868.00466 251.70 60.00.53822.01166 251.00 61.00.99935.00006 261.40 11.00.03701.00548 251.50 61.00.55130.01189 250.90 62.00.99935.00013 261.40 12.00.03964.00571 251.70 62.00.56201.01224 251.00 63.00.99961 -.00064 261.40 13.00.04844.00571 251.50 63.00.57579.01201 250.90 64.00.99807.00019 261.50 14.00.05107.00713 251.70 64.00.58603.01178 251.00 _65,00 1.00000.00032 261.40 15.00.06269.00753 251.40 65.00.59935.01178 250.90 16.00.06614.00711 251.60 66.00.60959.01172 251.00 17.00.07691.00764 251.40 67.00.62279.01214 250.90 18.00.08141.00793 251.60 68.00.63387.01160 250.90 19.00.09277.00722 251.40 69.00.64600.01143 250.90 20.00.09585.00845 251.70 70.00.65673.01185 250.90 21.00.10968.00940 251.40 71.00.66969.01137 250.80 22.00.11465.00969 251.60 72.00.67947.01125 250.90 23.00.12906.00987 251.30 73.00.69220.01079 250.80 24.00.13438.00981 251.50 74.00.70104.01132 250.90 25.00.14868.01062 251.20 75.00.71484.01038 250.70 26.00.15563.00908 251.40 76.00.72180.00926 250.90 27.00.16685.01086 251.30 77.00.73336.01009 250.80 28.00.17734.01044 251.30 78.00.74197.00926 250.90 29.00.18772.01050 251.30 79.00.75188.00980 250.90 30.00.19833.01032 251.30 80.00.76156.00986 250.90 31.00.20836.01073 251.30 81.00.77161.00933 250.80 32.00.21979.01273 251.30 82.00.78022.00968 250.90 33.00.23383.01144 251.10 83.00.79097.00939 250.80 34.00.24267.01050 251.20 84.00.79900.00815 250.90 35.00.25482.01067 251.10 85.00.80728.00869 250.90 36.00.26401.01079 251.20 86.00.81637.00957 250.90 37.00.27640.01167 251.10 87.00.82642.00822 250.80 38.00.28736.01114 251.10 88.00.83282.00845 250.90 39.00.29867.01037 251.10 89.00.84333.00787 250.80 40.00.30809.01096 251.20 90.00.84856.00817 250.90 41.00.32059.01138 251.10 91.00.85968.00775 250.70 42.00.33086.0101.5 251.10 92.00.86407.00717 250.90 43.00.34088.01061 251.10 93.00.87402.00688 250.70 44.00.35208.01185 251.10 94.00.87783.00617 250.90 45.00.36458.01090 251.00 95.00.88636.00671 250.80 46.00.37389.01079 251.10 96.00.89124.00530 250.90 47.00.38615.01085 251.00 97.00.89695.00606 250.90 48.00.39558.01160 251.10 98.00.90337.00524 250.90 49.00.40936.01249 251.00 99.00.90743.00495 251.00

-268NORMALIZ'ED DATA FROM RUN 19 (CONT'D) NORMALIZED DATA FROM RUN 20 NORMALIZED DATA FROM RUN 20 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF MIN MIN'' OF MIN MIN-' OF 100.00.91326.00660 251.00.00.00000.00102 250.90 50.00.34048.01237 250.60 101.00.92063.00531 250.90 1.00.00204.00202 250.90 51.00.35611.01249 250.40 102.00.92387.00419 251.00 2.00.00403.00147 250.90 52.00.36546.01307 250.60 103.00.92900.00501 251.00 3.00.00497.00182 250.90 53.00.38225.01313 250.40 104.00.93390.00426 251.00 4.00.00767.00235 250.90 54.00.39172.01290 250.60 105.00.93752.00420 251.00 5.00.00966.00199 250.90 55.00.40805.01201 250.40 106.00.94230.00461 251.00 6.00.01165.00217 250.90 56.00.41575.01284 250.70 107.00.94673.00367 251.00 7.00.01400.00229 250.90 57.00.43373.01337 250.40 108.00.94964.00379 251.00 8.00.01623.00252 250.90 58.00.44248.01378 250.70 109.00.95431.00325 251.00 9.00;01904...00293 250.90 59.00.46128.01661 250.40 110.00.95615.00267 251.10 10.00.02209.00287 250.90 60.00.47571.01490 250.40 111.00.95965.00332 251.10 11.00.02479.00281 250.90 61.00.49108.01366 250.30 112.00.96280.00292 251.10 12.00.02772.00311 250.90 62.00.50303.01490 250.40 113.00.96548.00268 251.10 13.00.03100.00257 250.90 63.00.52088.01449 250.20 114.00.96816.00297 251.10 14.00.03286.00375 251.00 64.00.53200.01319 250.30 115.00.97143.00251 251.10 15.00.03850.00464 250.90 65.00.54726.01295 250.20 116.00.97318.00204 251.10 16.00.04214.00381 250.90 66.00.55790.01366 250.40 117.00.97551.00110 251.10 17.00.04613.00440 250.90 67.00.57446.01396 250.20 118.00.97537.00233 251.20 18.00.05093.00469 250.90 68.00.58582.01461 250.30 119.00.98018.00304 251.10 19.00.05551.00398 250.90 69.00.60369.01255 250.00 120.00.98146.66140 251.10 20.00.05889.00439 251.00 70.00.61092.01184 250.30 121.00.98297.00140 251.10 21.00.06428.00569 251.00 71.00.62737.01184 250.00 122.00.98426.00122 251.10 22.00.07026.00569 251.00 72.00.63460.01214 250.30 123.00.98542.00057 251.10 23.00.07566.00598 251.00 73.00.65164.01173 250.00 124.00.98540.00034 251.20 24.00.08222.00722 251.00 74.00.65805.01173 250.30 125.00.98610.00117 251.20 25.00.09010.00651 250.90 75.00.67509.01184 250.00 126.00.98773.00199 251.20 26.00.09524.00698 251.00 76.00.68174.00995 250.30 127.00.99009.00176 251.10 27.00.10405.00739 250.90 77.00.69500.01084 250.20 128.00.99125.00105 251.10 28.00.11001.00679 251.00 78.00.70342.01167 250.40 129.00.99219.00111 251.10 29.00.11764.00780 251.00 79.00.71834.01161 250.20 130.00.99347.00087 251.10 30.00.12561.00898 251.00 80.00.72663.01137 250.40 131.00.99394.00064 251.10 31.00.13559.00833 250.90 81.00.74108.01090 250.20 132.00.99475.00047 251.10 32.00.14226.00874 251.00 82.00.74844.01079 250.40 133.00.99487.00023 251.10 33.00.15306.00968 250.90 83.00.76266.01085 250.20 134.00.99522.00064 251.10 34.00.16162.00920 250.90 84.00.77014.01232 250.40 135.00.99615.00064 251.10 35.00.17147.00950 250.90 85.00.78731.01026 250.00 136.00.99650.00052 251.10 36.00.18062.00967 250.90 86.00.79066.00819 250.40 137.00.99720.00070 251.10 37.00.19082.01008 250.90 87.00.80370.00985 250.20 138.00.99790.00023 251.10 38.00.20079.00991 250.90 88.00.81035.01133 250.40 139.00.99767.00035 251.10 39.00.21064.01003 250.90 89.00.82635.01027 250.00 140.00.99860.00047 251.10 40.00.22084.01032 250.90 90.00.83089.00767 250.30 141.00.99860.00000 251.10 41.00.23127.01067 250.90 91.00.84169.00791 250.20 142.00.99860.00023 251.10 42.00.24218.01167 250.90 92.00.84670.00856 250.40 143.00.99907.00058 251.10 43.00.25462.01090 250.80 93.00.85881.00856 250.20 144.00.99977.00047 251.10 44.00.26399.01090 250.90 94.00.86382.00821 250.40 145.00 1.00000 -.00065 251.10 45.00.27643.01155 250.80 95.00.87522.00762 250.20 46.00.28709.01296 250.90 96.00.87907.00745 250.40 47.00.30236.01190 250.70 97.00.89012.00674 250.20 48.00.31089.01450 250.90 98.00.89254.00627 250.50 49.00.33137.01480 250.40 99.00.90265.00657 250.30 NORMALIZED DATA FROM RON 20 (CONT'D) NORMALIZED DATA FROM RUN 20 (CONT'D) NORMALIZED DATA FROM RUN 21 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN' OF MIN MIN" OF MIN MIN' OP 100.00,.90567.00610 250.50 150.00.99635.00012 251.00.00.00000.00097 251.20 101.00,.91484.00604 250.30 151.00.99836.00012 250.90 1.00.00194.00234 2.51.20 102.00.91775.00586 250.50 152.00.99658.00023 251.00 2.00.00468.00273 251.20 02Q._00O 9.26571,00510 250.30 153.00.99883.00047 250.90 3.00 0Q741.00297 251.20 104.00.92795.00534 250.50 154.00.99752.00023 251.00 4.00.01062.00345 251.20 105.00.93724.00580 250.30 155.00.99930.00012 250.90 5.00.01430.00404 251.20 106.00.93956.00516 250.50 156.00.99776.00000 251.00 6.00.01870.00475 251.20 107,00.94756.00357 250.30 157.00.99930.00000 250.90 7.00.02381.00541 251.20 108.00.94669.00322 250.60 158.00.99776 -.00012 251.00 8.00.02952.00582 251.20.LQ9_.00.953_99..00369 250,40 159.00.99906 -.00012 250.90 9.00.03546.00618 251.20 110.00.95408.00287 250.60 i60.00.99752 -.00083 251.00 10.00.04188.00689 251.20 111.00.95972.00287 250.50 161.00.99740.00000 251.00 11.00.04925.00743 251.20 112.00.95981.00340 250.70 162.00.99752.00012 251.00 12.00.05674.00784 251.20 113.00.96652.00311 250.50 163.00.99764.00029 251.00 13.00.06494.00856 251.20 114.00.96603.00317 250.70 164.00.99811.00100 251.00 14.00.07385.01003 251.20 115.00.97286.00281 250.50 165.00.99965.00089 250.90 15.00.08499.01039 251.10 116.00.97165.00235 250.70 166.00.99988.00012 250.90 16.00.09462.00951 251.10 117.00.97755.00128 250.50 167.00.99988.00006 250.90 17.00.10401.00975 251.10 118.00.97422.00099 250.80 168.00 1.00000.00006 250.90 18.00.11411.01034 251.10 119.00.97953.00116 250.60 19.00.12469.01082 251.10 120.00.97655.00105 250.90 20.00.13574.01105 251.10 121.00.98162.00170 250.70 21,00.14680.01105 251.10 122.00.97995.00081 250.90 22.00.15785.01111 251.10 123.00.98325.00058 250.80 23.00.16902.01111 251.10 124.00.98111.00017 251.00 24.00.18008.01105 251.10 125.00.98358.00070 250.90 25.00.19113.01105 251.10 126.00.98251.00123 251.00 26.00.20218.01105 251.10 12700,.98605.00147 250.90 27.00.21324.01141 251.10 128.00.98544.00088 251.00 28.00.22500.01123 251.10 129.00.98781.00106 250.90 29.00.23570.01105 251.10 130.00.98756.00023 251.00 30.00.24711.01199 251.10 131.00.98826.00059 251.00 31.00.25968.01199 251.00 132.00.98873.00047 251.00 32.00.27109.01117 251.00 133.00.98920.00024 251.00.33.00..28203.01105 251.00 134.00.98824.00153 251.10 34.00.29320.01070 251.00 135.00.99226.00159 250.90 35.00.30342.01076 251.00 136.00.99142,.00064 251.00 36.00.31471.01099 251.00 137.00.99355.00035 250.90 37.00.32541.01082 251.00 138.00.99213,00047 251.00 38.00.33634.01111 251.00 139.00.99449.00064 250.90 39.00,34763.01064 251.00 140.00.99342.00059 251.00 40.00.35762.01040 251.00 141.00.99566.00035 250.90 41.00.36843.01018 251.00 142.00.99412.00012 251.00 42.00.37797.01111 251.10 143.00.99590.00023 250.90 43.00.39066.01105 251.00 144.00.99459.00023 251.00 44.00.40008.01135 251.10 145.00.99637.Q0059 250.90 45_00,413365.01165 251.00 146.00.99576.00070 251.00 46.00.42337.01141 251.10 147.00.99777.00023 250.90 47.00.43618.01241 251.00 148.00.99623.00018 251.00 48.00.44819.01159 251.00 149.00.99812.00006 250.90 49.00.45936.01147 251.00

-269NORMALIZED DATA FROM RUN 21 (CONT'D) NORMALIZED DATA FROM RUN 21 (CONT'D) NORMALIZED DATA FROM RUN 22 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF MIN MIN-i oF MIN' MIN-' Of 50.00.47112.01177 251.00 100.00.94955.00428 251.10.00.00000.00088 251.10 51.00.48289.01147 251.00 101.00.95359.00368 251.10 1.00.00176.00166 251.10 52.00.49406.01165 251.00 102.00.95692.00279 251.10 2.00.00332.00221 251.10 53.00.50619.01101 251.00 103.00.95917.00327 251.10 3.00.00619.00269 251.10 54.00.51608.01183 251.10 104.00.96345.00392 251.10 4.00.00870.00395 251.10 55.00.52984.01206 251.00 105.00.96702.00291 251.10 5.00.01408.00371 251.10 56.00.54021.01171 251.10 1.06.00.96928.00232 251.10 6.00.01611.00209 251.10 57.00.55325.01211 251.00 107.00.97165.00285 251.10 7.00.01827.00329 251.10 58.00.56443.01141 251.00 108.00.9.7498.00250.251.10 8.00.02269.00433 251.10 59.00.57607.01117 251.00 109.00.97665.00190 251.10 9.00.02692.00233 251.00 60.00.58677.01223 251.00 110.00.97879.00144 251.10 10.00.02736.00183 251.10 61.00.60053.01246 250.90 111.00.97953.00178 251.20 11.00.03059.00329 251.10 62.00.61170.01129 250.90 112.00.98235.00236 251.10 12.00.03394.00305 251.10 63.00.62311.01129 250.90 113.00.98425.00190 251.10 13.00.03669.00305 251.10 64.00.63428.01177 250.90 114.00.98615.00085 251.10 14.00.04004.00365 251.10 65.00.64664.01194 250.90 115.00.98595.00143 251.20 15.00.04398.00407 251.10 66b,00 65817.01177 250.90 116.00.98901.00143 251.10 16.00.04817.00413 251.10 67.00.67018.01159 250.90 117.00.98880.00101 251.20 17.00.05224.00407 251.10 68.00.68135.01123 250.90 118.00.99103.00171 251.10 18.00.05630.00431 251.10 69.00.69264.01:165 250.90 119.00.99222.00089 251.10 19.00.06085.00490 251.10 70.00.70465.01153 250.90 120.00.99281.00065 251.10 20.00.06611.00532 251.10 71.00.71570.01111. 250.90 121.00.99352.00083 251.10 21.00.07149.00532 251.10 72.00.72687.01147 250.90 122.00.99447.00053 251.10 22.00.07676.00586 251.10 73.00.73864.01141 250.90 123.00.99459.00018 251.10 23.00.08322.00628 251.10 74.00.74969.01006 250.90 124.00.99483.00107 251.10 24.00.08932.00640 251.10 75.00.75875.01082 251.00 125.00.99673.00131 251.10 25.00.09601.00676 251.10 76.00.77132.01058 250.90 126.00.99745 -.00028 251.10 26.00.10283.00652 251.10 77.00.77991.00946 251.00 127.00.99617 -.00016 251.20 27.00.10905.00712 251.10 78.00.79025.01016 251.00 128.00.99712.00071 251.20 28.00.11707.00881 251.10 79.00.80024.01092 251.00 129.00.99759.00042 251.20 29.00.12668.00929 251.00 80.00.81209.01022 250.90 130.00.99795 -.00022 251.20 30.00.13565.00849 251.00 81.00.82068.00911 251.00 131.00.99715.00077 251.30 31.00.14366.00849 251.00 82.00.83031.00945 251.00 132.00.99950.00042 251.20 32.00.15263.00885 251.00 83.00.83958.00979 251.00 133.00.99798 -.00076 251.30 33.00.16137.00909 251.00 84.00.84989.00885 250.90 134.00.99798 -.00070 251.30 34.00.17082.00987 251.00 85.00.85729.00862 251.00 135.00.99658.00018 251.40 35.00.18110.01029 251.00 86.00.86712.00790 250.90 136.00.99834.00012 251.30 36.00.19139.01082 251.00 87.00.87309.00814 251.00 137.00.99682.00030 251.40 37.00.20275.01035 251.00 88.00.88340.00761 250.90 138.00.99893.00030 251.30 38.00.21208.01136 251.00 89.00.88831.00643 251.00 139.00.99741.00030 251.40 39.00.22548.01226 251.00 90.00.89627.00755 251.00 140.00.99952.00024 251.30 40.00.23660.01154 251.00 91.00.90340.00672 251.00 141.00.99789.00018 251.40 41.00.24856.01226 251.00 92.00.90970.00542 251.00 142.00.99988.00024.251.30 42.00.26112.01342 251.00 93.00.91425.00600 251.10 143.00.99836.00006 251.40 43.00.27540.01324 250.90 94.00.92171.00600 251.00 144.00 1.00000.00000 251.30 44.00.28760.0r208 250.90 95.00.92625.00576 251.10 45.00.29956.01336 250.90 96.00.93323.00481 251.00 46.00.31432.01378 250.80 97.00.93588.00475 251.10 47.00.32711.01286 250.80 98.00.94274.00458 251.00 48.00.34003.01446 250.80 99.00.94503.00340 251.10 49.00.35603.01410 250.60 NORMALIZED DATA FROM RUN 22 (CONT'D) NORMALIZED DATA FROM RUN 22 (CONT'D) NORMALIZED DATA FROM RUN 22 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN'- oF MIN MIN'l OF MIN MIN-' OF 50.00.36823.01348 250.60 100.00.92123.00752 250.20 150.00.99685.00006 251.00 51.00.38298.01422 250.50 101.00.93064.00728 250.00 151.00.99856.00048 250.90 52.00.39666.01244 250.40 102.00.93579.00407 250.00 152.00.99780.00042 251.00 53.00.40786.01078 250.50 103.00.93878.00478 250.00 153.00. -9994...00012 250.90 54.00.41822.01250 250.60 104.00.94536.00355 250.00 154.00.99804.00030 251.00 55.00.43286.01366 250.50 105.00.94587.00179 250.20 155.00 1.00000 -.00050 250.90 56.00.44554.01390 250.50 106.00.94894.00399 250.30 57.00.46065.01390 250.40 107.00.95385.00153 250.30 58.00.47333.01402 250.40 108.00.95201.00209 250.40 59.00.48868.01396 250.30 109.00.95803.00419 250.30 60.00.50124.01286 250.30 110.00.96038.00341 250.40 61.00.51440.01328 250.30 111.00.96485.00299 250.30 62.00.52779.01316 250.30 112.00.96636.00353 250.40 63.00.54071.01298 250.30 113.00.97191.00305 250.30 64.00.55375.01407 250.30 114.00.97246.00221 250.40 65.00.56886.01310 250.20 115.00.97633.00233 250.30 66.00.57994.01304 250.30 116.00.97713.00159 250.40 67.00.59494.01310 250.20 117.00.97952 -.00006 250.40 68.00.60614.01298 250.30 118.00.97700.00085 250.70 69.00.62089.01310 250.20 119.00.98123.00129 250.60 70.00.63233.01481 250.30 120.00.97959 -.00004 250.80 7150o.65052.01316 250.00 121.00.98114.00167 250.80 72.00.65865.01138 250.30 122.00.98294.00155 250.80 73.00.67328.01256 250.20 123.00.98425.00046 250.80 74.00.68377.01244 250.30 124.00.98385.00126 250.90 75.00.69816.01220 250.20 125.00.98677.00114 250.80 76.00.70817.01244 250.30 126.00.98613.00161 250.90 77.00.72304.01214 250.20 127.00.99000.00167 250.80 78.00.73245.01142 250.30 128.00.98947.00084 250.90 79.00.74588.01118 250.20 129.00.99167.00042 250.80 80.00.75481.01176 250.30 130.00.99031 -.00038 250.90 81.00.76941.01073 250.00 131.00.99091.00084 250.90 82.00.77627.00815 250.20 132.00.99199.00102 250.90 83.00.78571.00883 250.20 133.00.99294.00072 250.90 84.00.79393.01176 250.30 134.00.99342.00042 250.90 85.00.80924.00939 250.00 135.00.99378.00036 250.90 86.00.81271.00843 250.30 136.00.99414.00140 250.90 87.00.82610.01113 250.00 137.00.99657.00072 250.80 88.00.83496.00927 250.00 138.00.99557 -.00032 250.90 89_,QO,84464.00726 250.00 139.00.99593.00078 250.90 90.00.84947.00843 250.20 140.00.99713.00066 250.90 91.00.86151.00746 250.00 141.00.99725.00036 250.90 92.00.86438.00600 250.30 142.00.99785.00006 250.90 93.00.87351.00863 250.20 143.00.99737 -.00110 250.90 94.00.88164.00760 250.20 144.00.99565.00036 251.00 95.QQ0.88870.00638 250.20 145.00.99809.00018 250.90 96.00.89440.00718 250.30 146.00.99601.00036 251.00 97.00.90305.00738 250.20 147.00.99880.00128 250.90 98.00.90915.00628 250.20 148.00.99856 -.00018 250.90 99.00.91561.00604 250.20 149.00.99845 -.00086 250.90

-270N(RMALIZFI) DATA FROM KRU? 73 NIORALIZA!) UATA FROMi RUN 23 (CONT'D) NORMALIZED DATA FROM RUN 23 (CONT'D) TI lE ALPHA RKA T TEFP., T I -E ALPHA RATE TEMP. TIME ALPHA RATE TEMP. M I MN I OF Mu 11I N" OF 11 MIN- OF.00.00(00.00064 250.90 50.00.306315.01299 250.50 100.00).91137.00566 250.40 1..00.00127.00183 250.90 1l.00.3'778.01281 250.50 101.00.91709.00578 250.40 2.00.00365.00238 250.90 52.00.38876.0122] 250.50 102.00.92292.00459 250.40 3.00.00604.00226 250.90 53.(0.40020.0)1287 250.60 103.00.92626.00483 250.50 4.00.)OO18.(00328 250.90 54.00.41450.0)1370 250. 50 104.00.93258.00536 250.40 5.00,012D9.002H6 250.80 55.00.42761.01311 250.50 105.00.93698.00465 250.40 6.00.01390.(00208 250.90 56.)00.44071.01263 250. 50 106.00.94187.00494 250.40 7.0().016756.00274 25)0.90) 57.,00.45287.01358 250.60 107.00.94687.00447 250.40 H8.().01938.00298 250.90 58.00.46788.01)340 250. 50 108. (.95081.00393 250.40 9.100.02272.00328 750.90 59.00.47967.01245 250.60 109.00).95474.00411 250.40 10.00.02594.00429 250.90 60.00.49278.01317 250.60 110.00.95903.00304 250.40 11.0).03130.00346 250.80 61.00U.0601.01436 250.60 111.00.96081.00268 250.50 12.00.03285.00340 250.90 62.00),52150.01442 250.50 112.00.96439.00250 250. 50 13.00.03809.00399 250.P80 63.00.53484.01340 250.50 113.00.96581.00125 250.60 14.00.04083.00310 250.90 64.00.54831.01400 250.50 114.00.96688.00125 250.70 15.00.04428.00381 250.90 65.00,56285.01448 250.40 115.00.96831.0()232 250.80 16.00.04846 6.00423. 250.9) 66.00).57727.01305 250.30 116.00.97153.00196 250.80 17.00.05274.00453 250.90 67.,)0.58894.01227 250.40 117.00.97224.00155 250.90 18.00.05751.00441 250.90 68.00.60181.01352 250.40 118.00.97462.00238 250.90 19.(0.06156.00447 250.90 69.00.61599.01424 250.30 119.00.97701,.00232 250.90 20.00.06645.00542 250.90 70.00.63029.01358 250.30 120.)0.97927.00191 250.90 21.00.07240.00596 250.90 71.0).64316.01281 250.30 121.00.98082.00191 250.90 22.00,.07836.00590 25(0.90 72.00.65591.01257 250.30 122.00.98308.00220 250.90 23.00.08420.00560 250.90 73.00.66830.01269 250.30 123.00.98523.00179 250.90 24.,0.08956.00620 250.90 74.)0.68128.01263 250.30) 124.00.98666.00036 250.90 25.00.09659.00691 250.90 75.00.69356.01215 250.30 125.00.98594.00042 251.00 26.00.10338.00810 250.90 76.00.70559,.01186 250.30 126.00.98749.00155 251.00 27.00.11280.00804 250.80 77.00.71727.01168 250.30 127.00.98904.00227 251.00 28.00.11947.00625 250.80 78.00.72895,.01144 250.30 128.00.99202.00155 250.90 29.00.12531.00786 250,90 79.00.74015.01078 250.30 129.00.99214.00053 251.00 30.00.13520.00828 250.80 80.00.75051.01174 250.30 130.00.99309.00095 251.00 31.00.14187.00756 250.90 81.00.76362.01066 250.20 131.00.99404.00083 251.00 32.00.15033.00906 250.90 82.00.77184.00798 250.30 132.00.99476.00066 251.00 33.00.15998.01001 250.90 83.00.77958.00929 250.40 133.00.99535.00161 251.00 34.00.17035.01114 250.80 84.00.79043.00935 250.30 134.00.99798.00089 250.90 35.00.18227.01019 250.70 85.lO.79829.00941 250.40 135.00.99714 -.00012 251.00 36.00.19073,.01037 250.80 86.00.80925.00971 250.30 136.00.99774.00054 251.00 37.00.20300.01108 250.60 87.00.81771.00858 250.30 137.00.99821.00048 251.00 38.00.21289.01054 250.70 88.00.82641.00757 250.30 138.00.99869.00042 251.00 39.00.22409.01204. 250.70 89.(10.83284.00804 250.40 139.00.99905.00036 251.00 40.00.23696.01341 250.60 90.00.84250.00834 250.30 140.00.99940 -.00042 251.00 41.00.25090.01245 250.50 91.00.84953.00804 250.40 141.00.99821.00018 251.10 42.00.26187.01162 250,.50 92.00.85858.00745 250.30 142.00.99976.00078 251.00 43.00.27414.01233 250.50 93.00.86442.00763 250.40 143.00.99976.00000 251.00 44.00.28653.01227 250.50 94.00.87383.00834 250.30 144.00.99976 -.00078 251.00 45.00.29868.01215 250.50 95.)00.88110.00679 250.30 145.00.99821.'00012 251.10 46.00.31084.01275 250.50 96.10.88742,.00590 250.30 146.00 1.00000.00090 251.00 47.00.32418.01305 250.50 97.00.89290.00667 250.40 48.00.33693.01281 250.50 98.00.90076.00643 250.30 49.00.34980.01311 250.50 99.00.90577.00530 250.40 NORMALIZED DATA FROM RUN 24 NORMALIZED DATA FROM RUN 24 (CONT'D) NORMALIZED DATA FROM RUN 24 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN M I N-I OF INMIN MIN-' OP MIN MIN'~ OF.00.00000.00307 250.80 50.00.31052.01138 250.40 100.00.85193.00573 250.00 1.00.00615.00297 250.60 51.00.32360.01250 250.30 101.00.85878.00666 250.00 2.00.00593.00307 250.80 52.00.33552.01208 250.30 102.00.86526.00649 250.00 3.00,.01228.00324 250.60 53.00.34777.01144 250.20 103.00.87175.00637 250.00 4.00.01242.00336 250.80 54.00.35840.01320 250.30 104.00.87800.00619 250.00 5.00.01900.00230 250.60 55.00,.37416.01120 250.00 105.00.88413.00578 250.00 6.00.01703.00389 250.90 56.00.38080.01150 250.30 106.00.88956.00548 250.00 7.00.02677.00523 250.50 57.00.39716.01208 250.00 107.00.89510.00543 250.00 8.00.02749.00295 250.60 58.00.40497.01150 250.20 108.00,.90041.00519 250.00 9.00.03267.00236 250.50 59.00,.42016.01203 250.00 109.00.90548.00525 250.00 10.00.03222.00336 250.70 60.00.42903.01232 250.20 110.00.91090.00489 250.00 11.00.03939.00318 250.50 61.00.44481.01215 250.00 111.00.91527.00436 250.00 12.00.03859.00295 250.70 62.00.45333.01209 250.20 112.00.91963.00454 250.00 13.00.04529.00313 250.50 63.00.46898.01238 250.00 113.00.92435.00436 250.00 14.00.04484,.00336 250.70 64.00.47809.01221 250.20 114.00.92836.00401 250.00 15.00,.05201.00360 250.50 65.00,49340.01209 250.00 115.00.93237.00401 250.00 16.00.05203.00260 250.70 66.00.50227.01232 250.20 116.00.93638,.00377 250.00 17.00.05721.00354 250.60 67.00.51805.01156 250.00 117.00.93992.00336 250.00 18.00.05911.00459 250.70 68.00.52540.01244 250.30 118.00.94310.00324 250.00 19.00.06640.00483 250.50 69.00.54293.01350 250.00 119.00.94640,.00301 250.00 20.00.06877.00442 250.60 70.00.55239.01256 250.20 120.00.94912.00137 250.00 21.00.07525.00249 250.50 71.00.56805.01244 250.00 121.00.94914.00125 250.20 22.00.07375.00442 250.80 72.00.57728.01221 250.20 122.00.95162.00178 250.20 23.00.08409.00589 250.50 73.00.59247.01384 250.00 123.00.95269,.00231 250.30 24.00.08553.00507 250.70 74.00.60497.01221 250.00 124.00.95623.00289 250.30 25.00.09424.00531 250.50 75.00.61688.01185 250.00 125.00.95847.00160 250.30 26.00.09614.00537 250.70 76.00.62867.01197 250.00 126.00.95943,.00259 250.40 27.00,.10497.00654 250.50 77.00.64082.01138 250.00 127.00.96366.00254 250.30 28.00.10922.00596 250.60 78.00.65144.01126 250.00 128.00.96450.00230 250.40 29.00.11688.00561 250.50 79.00.66335.01179 250.00 129.00.96826.00183 250.30 30.00.12044.00514 250.70 80.00.67503.01126 250.00 130.00.96816.00189 250.40 31.00.12716,.00578 250,70 81.00.68588.01103 250.00 131.00.97204.00183 250.30 32.00.13201.00690 250.80 82.00.69708.01161 250.00 132.00.97181.00200 250.40 33.00.14096.00801 250.70 83.00.70910.01056 249.90 133.00.97605.00300 250.30 34.00.14804.00831 250.70 84.00.71819.00968 250.00 134.00.97782.00159 250.30 35.00.15758.00761 250.60 85.00.72845.00985 250.00 135.00.97923.00147 250.30 36.00.16325.00890 250.70 86.00.73789.00932 250.00 136.00.98076,.00130 250.30 37.00.17538.00879 250.50 87.00.74709.00932 250.00 137.00.98183,.00136 250.30 38.00.18082.00879 250.70 88.00.75652.00926 250.00 138.00.98348.00130 250.30 39.00.19295.01096 250.50 89.00.76560.00867 250.00 139.00.98442.00094 250.30 40.00.20274.01161 250.50 90.00.77386.00849 250.00 140.00.98536.00118 250.30 41.00.21616.01084 250.30 91.00,.78259,.00867 250).00 141.00.98678.00094 250.30 42.00.22443.00991 250.40 92.00.79120.00907 250.00 142.00.98725 -.00005 250.30 43.00.23598.00979 250.30 93.00.80073.00872 249.90 143.00.98667.00001 250.40 44.00.24401.01044 250.40 94.00.80864.00826 249.90 144.00.98726.00083 250.40 45.00.25685.01050 250.30 95.00.81725.00837 249.90 145.00.98832.00088 250,40 46.00.26500.01067 250.40 96.00.82538.00755 249.90 146.10.98903.00088 250.40 47.00.27820.01120 250.30 97.00.83234.00725 249.90 147.00.99009.00083 250.40 48.00.28741.01132 250.40 98.00.83989.00749 249.90 148.00.99068.00059 250.40 49,00.30084.01156 250.30 99.00.84732.00602 249.90 149.00.99127,00059 250.40

-271NORMALIZED DATA FROM RUN 24 (CONT'D) Nk!l'`AL7.t-) A.iATA FROIJ", Rl,.I>, 25 NIIRMALIZED DATA FRUM RON 25 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEIP. T I A L PHA ATE TEMP. MIN MIN' PIE lNN-' Oo F I'l M I NF- OF 150.00.99186.00053 250.40.00.()(00.00007 250.90 00. O0.42385.01446 249.80 151.00.99233.00065 250.40 1.00.00014.00048 250.90 1. )00).43290.01146 250.00 152.00.99316.00077 250.40 2.00.0096.00194 251.00 52.00.4467H.01234 249.90 153.00.99387.00065 250.40 3.00.()0402.002B8 251.00 53.00.45759.01193 250.00 154.00.99446.00053 250.40 4.00.0067?.00217 251.00 54.()0.47064.01170 249.90 155.00.99493.00053 250.40 5.().00836.00217 251.10 05.00.48099.01193 250.00 156.00.99552.00029 250.40 6.00(.01107,00359 251.10 56.00.49451.01193 249.90 157.00.99552 -.00052 250.40 7.00.01554.00417 251.10 57.00.50485.01228 250.00 158.00.99447 -.00035 250.50 8.00.01942.00417 251.10 58.(0.51908.01117 249.80 159.00.99482 -.00035 250.50 9.00.0238R.00464 251.10 59.00.52719.01152 250.00 160.00.99377.00029 250.60 10.00.02870).00494 251.10 60.00.54212.01140 249.80 161.00.99541.00029 250.50 11.00.03376.00523 251.10 61.00.54999.01134 250.00 162.00.99436 -.00035 250.60 12.)O.03917.00553 251.1( 62.00.56481.01117 249.80 163.00.99472.00035 250.60 13.00.04481.00582 251.10 63.00.57233.01076 250.00 164.00.99507.00106 250.60 14.00.05080).00600 251.10 64.00.58632.01052 249.80 165.00.99683 -.00006 250.50 15.00.05680.00688 251.10 65.00.59337.01035 250.00 166.00.99495.00018 250.60 16.00.06456.00782 251.00 66.00.60701.01005 249.80 167.00.99718.00006 250.50. 17.00.07244.00741 251.00 67.00.61348.00988 250.00 168.00.99507 -.00006 250.60 18.00.07938.0()717 250.90 68.00.62676.00993 249.80 169.00.99706.00012 250.50 19.00.08679.00729 250.90 69.00.63335.01023 250.00 170.00.99531.00006 250.60 20.1(0.09396.00770 250.90 70.00.64722.01005 249.80 171.00.99718.00000 25.5.0 21.00.10219.00917 250.90 71.00.65345.00976 250.00 172.00.99531 -.00082 250.60 22.00.11230.00829 250.80 72.00.66673.00982 249.80 173.00.99554.00018 250.60 23.00.11876.00858 250.90 73.00.67308.00958 250.00 174.00.99566 -.00006 250.61 24.00.12946.00970 250.80 74.00.68590.00917 249.80 175.00.99542 -.00006 250.60 25.00.13816.00911 250.110 75.00.69142.00935 250.00 176.00.99554.00029 250.60 26.00.14769.00935 250.80 76.00.70459.00935 249.80 177.00.99601.00024 250.60 27.00.15686,01205 250.80 77.00.71011.00893 250.00 178.00.99601.00018 250.60 28.00.17179.01111 250.50 78.00.72246.00982 249.80 179.00.99637.00012 250.60 29.00.17908.01017 250.60 79.00.72975.00870 249.90 180.00.99625.00076 250.60 30.00.19213.00993 250.40 80.00.73986.00764 249.80 181.00.99789.00012 250.50 31.00.19895.01052 250.60 81.00.74503.00846 250.00 182.00.99648.00018 250.60 32.00.21318.0(1988 250.30 82.00.75678.00852 249.80 183.00.99824.00094 250.50 33.00.21870.01023 250.60 83.00.76208.00805 250.00 184.00.99836.00088 250.50 34.00.23363.01017 250.30 84.00.77289.00605 249.80 185.00 1,00050.00000 250.40 35.00.23904.00.982 250.60 85.00.77418.00611 250.20 36.00.25327.01170 250.40 86.00.78512.00770 250.00 37.00.26243.01123 250.50 87.00.78958.00747 250.20 38.00.27572.01170 250.30 88.00.80005.00747 250.00 39.00.28583.01152 250.40 89.00.80451.00752 250.20 40.00.29876.01140 250.30 90.00.81510.00670 250.00 41.00.30864.01234 250.40 91.00.81792.00564 250.30 42.00.32345.01258 250.20 92.00.82638.00694 250.20 43.00.33380.01181 250.30 93.00.83179.00617 250.30 44.00.34708.01040 250.20 94.00.83872.00517 250,.30 45.00.35460.01317 250.40 95.00.84213.00570 250.50 46.00.37342.01199 250.00 96.00.85013.00605 250.40 47.00.37859.01170 250.40 97.00.85424.00705 250.50 48.00.39681.01270 250.00 98.00.86423.00576 250.30 49.00.40398.01352 250.30 99.00.86576.00594 250,60 NORMALIZED DATA FROM RUN 25 (CONT'O) NORMALIZED DATA FROM RUIJ 25 (C)ONT'D) NORMALIZED DATA FROM RUN 25 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN OF MIN MIN-' OF MIN MIN-' OF 100.00.87611.00529 250.30 150,.0.98659.00071 251.10 200.00.99894 -.00088 251.00 101.00.87634.00382 250.60 151.00.98730.00059 251.10 201.00.99717.00000 251.10 102.00.88375.00335 250.50 152.00.98777.00065 251.10 202.00.998594.00018 251.00 103.00.88303,00464 250.80 153.00.98859.00059 251.10 203.00.99753.00029 251.10 104.00.89303.00494 250.50 154.00.98895.00041 251.10 204.00.99953.00018 251.00 105.00.89291.00494 250.80 155.00.98942.00153 251.10 2q5.00.99788.00000 251.10 106.00.90291.00559 250.50 156.00.99201.00053 251.00 206.00.99953.00006 251.00 107.00.90408.00441 250.70 157.00.99047 -.00053 251.10 207.00.99800.00006 251.10 108.00..91173.00270 250.50 158.00.99094 -.00047 251.10 208.00.99965.00000 251.00 109.00.90948.00353 250.90 159.00.98953.00053 251.20 209.00.99800.00006 251.10 110.00.91878.00388 250.60 160.00.99200.00135 251.10 210.00.99976.00094 251.00 111.00.91724.00359 250.90 161.00.99224.00029 251.10 211.00.99988.00012 251.00 112.00.92595.00394 250.60 162.00.99259.00041 251.10 212.00 1.00000 -.00006 251.00 113.00.92512.00211 250.90 163.00.99306.00024 251.10 114.00.93018.00347 250.80 164.00.99306.00024 251.10 115.00.93205.00429 250.90 165.00.99353.00035 251.10 116.00.93876.00300 250.70 166.00.99377.00018 251.10 117.00.93805.00276 250.90 167.00.99388.00018 251.10 118.00.94429.00317 250.70 168.00.99412.0001,2 251.10 119.00.94440.00312 250.90 169.00.99412.00012 251.10 120.00.95052.00288 250.70 170.00.99435.00018 251.10 121,00.95016.00182 250,90 171.00,.99447.00006 251.10 122.00.95416.00212'250.80 172.00.99447.00006 251.10 123.00.95439.00117 250.90 173.00.99459.00012 251.10 124.00.95651.00223 250.90 174.00.99471.00041 251.10 125.00.95886,00212 250.90 175.00.99541.00041 251.10 126.00.96074.00141 250.90 176.00.99553.00018 251.10 127.00.96167.00212 251.00 177.00.99576.00018 251.10 128.00.96497.00159 250.90 178.00.99588.00012 251.10 129.00.96485.00165 251.00 179.00.99600.00082 251.10 130.00.96826.00170 250.90 180.00.99753.00000 251.00 131.00.96826.00165 251.00 181.00.99600 -.00071 251.10 132.00.97155.00141 250.90 182.00.99612.00006 251.10 133.00.97108.00153 251.00 183.00,99612.00000 251.10 134.00.97461.00141 250.90 184.00.99612.00006 251.10 135.00.97390.00129 251.00 185.00.99623.00006 251.10 136.00.97720.00135 250.90 186.00.99623.00012 251.10 137.00.97661.00123 251.00 187.00.99647.00106 251.10 138.00.97967.00141 250.90 188.00.99835.00029 251.00 139.00.97943.00029 251.00 189.00.99706.00006 251.10 140.00.98025.00035 251.00 190.00.99847 -.00012 251.00 141.00.98013.00118 251.10 191.00.99682.00018 251.10 142.00.98260.00082 251.00 192.00.99882.00018 251.00 143.00.98177.00094 251.10 193.00.99717.00006 251.10 144.00.98448.00076 251.00 194.00.99894.00006 251.00 145.00.98330 -.00035 251.10 195.00.99729.00006 251.10 146.00.98377,00082 251.10 196.00.99906.0000 251.00 147,00.98495.00076 251.10 1 97.00.99729 -.00012 251.10 148,00.98530.00047 251.10 198.00,99882.00082 251.00 149.00.98589.00065 251.10 199.00.99894.00006 251.00

-272NORMALIZED DATA FROM RUN 26 NORMALIZED DATA FROM RON 26 (CONT'D) NORMALIZED DATA FROM RUN 26 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF I N MIN-I OF MIN MIN-' Of.00.00000.00044 251.00 50.00.28425.00906 250.40 100.00.76076.00803 250.20 1.00.00088.00053 250.80 51.00.29506.00936 250.30 101.00.77235.00809 250.00 2.00.00106.00181 250.90 52.00.30297.00960 250.40 102.00.77695.00803 250.20 3.00.00450.00082 250.80 53.00.31426.00948 250.30 103.00.78842.00680 250.00 4.00.00269.00251 251.00 54.00.32193.01048 250.40 104.00.79054.00580 250.30 5.00.00951.00368 250.70 55.00.33522.00954 250.20 105.00.80002.00767 250.20 6.00.01006.00311 250.80 56.00.34102.00873 250.40 106.00.80588.00743 250.30 7.00.01573.00223 250.60 57.00.35267.00984 250.30 107.00.81488.00731 250.20 8.00.01453.00248 250.80 58.00.36071.00984 250.40 108.00.82050.00713 250.30 9.00.02068.00260 250.60 59.00;37236.00990 250.30 109.00.82913.00676 250.20 10.00.01972.00190 250.80 60.00.38052.01015 250.40 110.00.83403.00845 250.30 11.00.02449.00220 250.70 61.00.39265.01081 250.30 111.00.84603.00728 250.00 12.00.02413.00396 250.90 62.00.40214.01096 250.40 112.00.84858.00441 250.20 13.00.03240.00314 250.60 63.00.41458.01042 250.20 113.00.85486.00616 250.20 14.00.03041.00356 250.90 64.00.42297.00939 250.30 114.00.86090.00785 250.20 15.00.03953.00486 250.60 65.00.43336.00909 250.30 115.00.87055.00592 250.00 16.00.04013.00323 250.80 66.00.44115.00966 250.40 116.00.87274.00550 250.20 17.00.04599.00347 250.70 67.00.45269.01003 250.30 117.00.88155.00480 250.00 18.00.04708.00462 250.90 68.00.46121.01009 250.40 118.00.88234.00351 250.30 19.00.05523.00510 250.60 69.00.47286.00997 250.30 119.00.88856.00495 250.20 20.00.05729.00556 250.80 70.00.48114,01003 250.40 120.00.89225.00507 250.30 21.00.06634.00519 250.60 71.00.49291.00997 250.30 121.00.89871.00477 250.20 22.00.06767.00601 250.80 72.00.50107.01084 250.40 122.00.90179.00326 250.30 23.00.07836.00625 250.50 73.00.51459.01003 250.20 123.00.90523.00266 250.40 24.00.08017.00574 250.70 74.00.52112.01159 250.40 124.00.90711.00393 250.50 25.00.08984.00604 250.50 75.00.53778.01322 250.00 125.00.91309.00305 250.40 26.00.09225.00604 250.70 76.00.54756.01042 250.00 126.00.91321.00263 250.60 27.00.10191.00628 250.50 77.00.55861.00930 249.90 127.00.91834.00362 250.50 28.00.10482.00640 250.70 78.00.56616.00942 250.00 128.00.92046.00362 250.60 29.00.11472.00565 250.50 79.00.57745.00966 249.90 129.00.92559.00320 250.50 30.00.11611.00652 250.80 80.00.58549.00954 250.00 130.00.92686.00332 250.60 31.00.12776.00752 250.50 81.00.59654.00912 249.90 131.00.93223.00332 250.50 32.00.13115.00689 250.70 82.00.60373.00936 250.00 132.00.93350.00190 250.60 33.00.14153.00713 250.50 83.00.61526.00997 249.90 133.00.93604.00172 250.60 34.00.14540.00713 250.70 84.00.62366.00930 250.00 134.00.93695.00353 250.70 35.00.15579.00803 250.50 85.00.63386.00888 249.90 135.00.94310.00341 250.50 36.00.16147.00785 250.70 86.00.64141.00855 250.00 136.00.94377.00172 250.60 37.00.17149.00676 250.50 87.00.65096.00761 250.00 137.00.94655.00166 250.60 38.00.17500.00770 250.70 88.00.65664.00906 250.20 138.00,94709.00036 250.70 39.00.18689.00867 250.40 89.00.66908.00906 250.00 139.00.94727.00112 250.80 40.00.19233.00882 250.60 90.00.67476.00930 250.20 140.00.94933.00242 250.80 41.00.20452.00852 250.40 91.00.68768.00918 250.00 141.00.95211.00223 250.80 42.00.20936.00933 250.60 92.00.69312.00888 250.20 142.00.95380.00263 250.80 43.00.22318.00951 250.30 93.00.70543.00906 250.00 143.00.95736.00269 250.70 44.00.22838.00864 250.50 94.00.71124.00894 250.20 144.00.95917.00163 250.70 45.00.24046.00876 250.30 95.00.72331.00839 250.00 145.00.96062.00245 250.70 46.00.24590.00993 250.50 96.00.72803.00827 250.20 146.00.96406.00245 250.60 47.00.26033.00993 250.20 97.00.73986.00821 250.00 147.00.96551.00145 250.60 48.00.26577.00831 250.40 98.00.74446.00821 250.20 148.00.96696.00115 250.60 49.00.27694.00924 250.30 99.00.75629.00815 250.00 149.00.96781.00103 250.60 NORMALIZED DATA FROM RUN 26 (CONT'D) NORMALIZED DATA FROM RUN 26 (CONT'D) NORMALIZED DATA FROM RUN 27 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF MIN MIN-a OF MIN MIN-I OF 150.00.96902.00238 250.60 200.00.99469.00042 250.90.00.00000.00144 251.30 151.00.97258.00245 250.50 201.00.99493 -.00057 250.90 1.00.00288.00133 251.20 152.00.97391.00103 250.50 202.00.99354.00024 251.00 2.00.00266.00161 251.30 153.00.97463.00015 250.50 203.00.99541.00118 250.90 3.00.00609.00178 251.20 154.00.97421.00039 250.60 204.00.99589.00024 250.90 4.00.00623.00202 251.30 155.00.97542.00103 250.60 205.00.99589.00006 250.90 5.00.01014.00202 251.20 156.00.97626.00097 250.60 206.00.99601 -.00006 250.90 6.00.01028.00202 251.30 157.00.97735.00079 250.60 207.00.99577 -.00006 250.90 7.00.01419.00226 251.20 158.00.97783.00054 250.60 208.00.99589.00012 250.90 8.00.01480.00238 251.30 159.00.97844.00103 250.60 209.00.99601 -.00063 250.90 9.00.01894.00262 251.20 160.00.97989.00066 250.60 210.00.99462.00042 251.00 10.00.02003.00268 251.30 161.00.97977 -.00075 250.60 211.00.99686.00136 250.90 11.00.02430.00291 251.20 162.00.97838.00027 250.70 212.00.99734.00012 250.90 12.00.02586.00263 251.30 163.00.98031.00226 250.70 213.00.99710 -.00076 250.90 13.00.02955.00369 251.30 164.00.98291.00091 250.60 214.00.99583.00030 251.00 14.00.03324.00357 251.30 165.00.98212.00079 250.70 215.00.99770.00018 250.90 15.00.03669.00387 251.30 166.00.98448.00148 250.60 216.00.99619.00024 251.00 16.00.04097.00422 251.30 167.00.98508.00060 250.60 217.00.99819.00124 250.90 17.00.04514.00434 251.30 168.00.98568.00048 250.60 218.00.99867.00030 250.90 18.00.04966.00564 251.30 169.00.98605 -.00021 250.60 219.00.99879.00012 250.90 19.00.05642.00482 251.20 170.00.98526.00066 250.70 220.00.99891.00012 250.90 20.00.05930.00576 251.30 171.00.98738.00160 250.60 221.00.99903.00018 250.90 21.00.06794.00694 251.10 172.00.98846.00066 250.60 222.00.99928.00012 250.90 22.00.07318.00547 251.10 173.00.98870.00036 250.60 223.00.99928.00018 250.90 23.00.07889.00595 251.10 174.00.98919 -.00033 250.60 224.00.99964.00018 250.90 24.00.08508.00743 251.10 175.00.98804.00054 250.70 225.00.99964.00018 250.90 25.00.09374.00660 251.00 176.00.99027 -.00039 250.60 226.00 1.00000 -.00051 250.90 26.00.09828.00631 251.10 177.00.98726 -.00027 250.80 27.00.10636.00672 251.00 178.00.98973.00242 250.70 28.00.11173.00744 251.10 179.00.99209.00054 250.60 29.00.12123.00661 251.00 180.00.99082 -.00057 250.70 30.00.12495.00732 251.20 181.00.99094.00030 250.70 31.00.13586.00850 251.00 182.00.99142.00118 250.70 32.00.14195.00756 251.10 183.00.99329.00124 250.60 33.00.15097.00785 251.00 184.00.99390.00054 250.60 34.00.15765.00857 251.10 185.00.99438.00048 250.60 35.00.16811.00951 251.00 186.00.99486.00042 250.60 36.00.17667.00957 251.00 187.00.99523.00036 250.60 37.00.18724.00916 250.90 188.00.99559.00042 250.60 38.00.19499.00910 251.00 189.00.99607.00036 250.60 39.00.20545.00934 250.90 190.00.99631.00024 250.60 40.00.21367.00970 251.00 191.00.99656.00024 250.60 41.00.22484.01052 250.90 192.00.99680 -.00063 250.60 42.00.23471.01011 250.90 193.00.99529 -.00151 250.70 43.00.24506.01059 250.90 194.00.99378 -.00145 250.80 44.00.25589.01141 250.90 195.00.99239 -.00133 250.90 45.00.26789.01023 250.80 196.00.99112.00060 251.00 46.00.27636.01135 250.90 197,00.99360.00136 250.9047.00.29059.01101 250.70 198.00.99384.00024 250.90 48.00.29837.01089 250.90 199.00.99408.00042 250.90 49.00.31237.01035 250.70

-273NORMALIZED DATA FROM RUN 27 (CONT'D) NORMALIZED DATA FROM RUN 27 (CONT'D) NORMALIZED DATA FROM RUN 27 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN'' OF MIN. MIN'' OF MIN MIN-' OF 50.00.31907.01142 250.90 100.00.83559.00702 250.50 150.00.98751.00077 251.00 51.00.33521.01202 250.70 101.00.84390.00666 250.40 151.00.98999.00089 250.90 52.00.34310.01078 250.90 102.00.84892.00666 250.50 152.00.98929.00077 251.00 53.00.35677.01166 250.80 103.00.85722.00542 250.40 153.00.99153.00166 250.90 54.00.36642.01437 250.90 104.00.85976.00513 250.60 154.00.99260.00077 250.90 55.00.38550.01378 250.50 105.00.86748.00607 250.50 155.00.99308 -.00035 250.90 56.00.39399.01308 250.70 106.00.87190.00660 250.60 156.00.99191.00065 251.00 57.00.41165.01320 250.40 107.00,88068.00572 250.50 157.00.99439.00166 250.90 58.00.42038.01225 250.60 108.00.88334.00547 250.70 158.00.99522.00089 250.90 59.00.43616.01225 250.40 109.00.89163.00488 250.50 159.00.99617 -.00041 250.90 60.00.44489.01214 250.60 110.00.89310.00406 250.70 160.00.99441 -.00059 251.00 61.00 46043.01302 250.40 111.00.89974.00476 250.60 161.00.99500 -.00035 251.00 62.00.47092.01202 250.50 112.00.90262.00564 250.70 162.00.99371 -.00059 251.10 63.00.48447.01196 250.40 113.00.91102.00558 250.50 163.00.99383.00018 251.10 64.00.49484.01190 250.50 114.00.91378.00340 250.60 164.00.99407.00042 251.10 65.00.50826.01084 250.40 115.00.91783.00216 250.60 165.00.99466.00030 251.10 66.00.51651.01266 250.60 116.00.91810.00293 250.80 166.00.99466.00000 251.10 67.00.53358.01201 250.30 117.00.92368.00369 250.70 167.00.99466.00018 251.10 68.00.54053.00983 250.50 118.00.92548.00293 250.80 168.00.99502.00118 251.10 69.00.55323.00971 250.40 119.00.92953.00369 250.80 169.00.99703.00042 251.00 70.00.55994.01053 250.60 120.00.93286.00327 250.80 170.00.99585.00030 251.10 71.00.57429.01053 250.40 121.00.93607.00327 250.80 171.00.99762.00036 251.00 72.00.5810.01041 250.60 122.00.93940.00309 250.80 172.00.99657.00042 251.10 73.00.59511.01029 250.40 123.00.94226.00209 250.80 173.00.99845.00000 251.00 74.00.60158.01011 250.60 124.00.94359.00315 250.90 174.00.99657 -.00070 251.10 75.00.61534.01035 250.40 125.00.94856.00297 250.80 175.00.99704.00030 251.10 76.00.62228.01023 250.60 126.00.94953.00162 250.90 176.00.99716.00012 251.10 77.00.63581.01105 250.40 127.00.95179.00244 250.90 177.00.99728.00024 251.10 78.00.64439.01041 250.50 128.00.95441.00338 250.90 178.00.99764.00018 251.10 79.00.65663.01029 250.40 129.00.95856.00244 250.8( 179.00.99764.00006 251.10 8O.00.66498.00988 250.50 130.00.95929.00150 250.90 180.00.99776.00100 251.10 81.00.67638.00940. 25Q.40 131.00.96155.00202 250.90 181.00.99964.00012 251.00 82.00.68377.00964 250.50 132.00.96334.00184 250.90 182.00.99800.00018 251.10 83.00.69565.00988 250.40.133.00.96524.00120 250.90 183.00 1.00000.00012 251.00 84.00.70353.00940.250.50 134.00.96573.00120 251.00 85.00.71445.00822 250.40 135.00.96764.00190 251.00 86.00.71997.00892 250.60 136.00.96954.00178 251.00 87.00.73230.00786 250.40 137.00.97121.00173 251.00 88.10.73569.00869 250.70 138.00.97299.00243 251.00 89.00.74967.00845 250.40 139.00.97607.00155 250.90 90.00.75259.00845 250.70 140,00.97609.00072 251.00 91.00.76656.00951 250.40 141.00.97751.00213 251.00 92.00.77160.00839 250.60 142.00.98035.00213 250.90 93.00.78334.00827 250.40 143.00.98178.00049 250.90 94.00.78814.00815 250.60 144.00.98132.00043 251.00 95.00.79964.00885 250.40 145.00.98263.00119 251.00 96.00.80585.00785 250.50 146.00.98370.00101 251.00 97.00.81534.00844 250.40 147.00.98465.00113 251.00 98.00.82272.00726 250.40 148.00.98596.00189 251.00 99.00.82986.00644.250.40 149.00.98844.00077 250.90 NORMALIZED DATA FROM RUN 28. NORMALIZED DATA FROM RUN.28 (CONT'D) NORMALIZED DATA FROM RUN 28 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN' oF MIN. MIN'1 OF MIN MIN-' OF.00.00000.00059 250.40 50.00.17191.00763 250.30 100.00.64865.00889 249.50 1.00.00118,00020 250.20 51.00.18474.00757 250.00 101.00.65909,00853 249.40 2.00.00040.00101 250.30 52.00.18706.00751 250.30 102.00.66571.00865 249.50 3.00.00321.00101 250.20 53.00.19977.00775 250.00 103.00.67638.00883 249,.40 4.00.00243.00107 250.30 54.00.20257.00862 250.30 104.00.68336.00871 249.50 5.00.00536.00125 250.20 55.00.21701.01083 249.90 105.00.69380.00877 249.40 6.00.00494.00107 250.30 56.00.22422.0001( 250.00 106.00.70089.00784 249.50 7.00.00750.00113 250.20 57.00.21720 -.00014 250.90 107.00.70948.00859 249.50 8.00.00720.00310 250.30 58.00.22394.00865 251.00 108.00.71807.00933 249.50 9.00.01371.00039 250.00 59.00.23450.01744 250.90 109.00.72815.00787 249.40 10.00.00797 -.00030 250.40 60.00.25881.01848 250.00 110.00.73381.00799 249.50 11.00.01311.00167 250.20 61.00.27146.00993 249.80 111.00.74413.00817 249.40 12.00.01131..00167 250.40 62.00.27867.00993 249.90 112.00.75015.00704 249.50 13.00.01645.00185 250.20 63.00.29132.00942 249.70 113.00.75820.00844 249.40 14.00.01501.00098 250.40 64.00.29752,00966 249.90 114.00.76703.00799 249.40 15.00.01841.00029 250.30 65.00.31064.01065 249.70 115.00.77418.00710 249.40 16.00.01560.00128 250.60 66.00.31881.01071 249.80 116.00.78122.00734 249.40 17.00.02097.00221 250.40 67.00.33205.01071 249.60 117.00.78885.00617 249.40 18.00.02001.00274 250.60 68.00.34022.00990 249.70 118.00.79356.00626 249.50 19.00.02646.00256 250.40 69.00.35185.00903 249.60 119.00.80138.00650 249.40 20.00.02514.00227 250.60 70.00.35829.00990 249.80 120.00.80656.00587 249.50 21.00.03099.00245 250.40 71.00.37165.00996 249.60 121.00.81312.00644 249.50 22.(0.03003.00268 250.60 72.00.37820.00990 249.80 122.00.81945.00626 249.50 23.00.03636.00379 250.40 73.00.39145.01106 249.60 123.00.82565.00608 249.50 24.00.03761.00298 250.50 74.00.40033.01008 249.70 124.00.83161.00572 249.50 25.00.04232.00316 250.40 75.00.41160.01002 249.60 125.00.83710.00432 249.50 26.00.04393.00322 250.50 76.00.42037.01088 249.70 126.00.84026.00537 249.60 27.00.04876.00340 250.40 77.00.43337.00960 249.50 127.00.84783.00635 249.50 28.00.05073.00433 250.50 78.00.43957.00966 249.70 128.00.85296.00531 249.50 29.00.05741,00370 250.30 79.00.45269.00960 249.50 129.00.85845.00489 249.50 30.00.05812.00388 250,50 80.0(.45877.00948 249.70 130.00.86274.00459 249.50 31.00.06517.00295 250.30 81.00.47166.00948 249.50 131.00.86763.00414 249.50 32.00.06402.00307 250.60 82.00.47774.00984 249.70 132.00.87103.00408 249.60 33.00.07131.00423 250.40 83.00.49134.00930 249.50 133.00.87580.00477 249.60 34.0).07249.00459 250.60 84.00.49634.00906 249.70 134.00.88057.00459 249.60 35.00.08049.00447 250.40 85.00.50946.00984 249.50 135.00.88498.00355 249.60 36.00.08143.00540 250.60 86.00.51602.00868 249.70 136.00.88767.00244 249.70 37.(0.09129.00483 250.30 87.00..52682.00948 249.60 137.00.88987.00325 249.80 38.00.09109.00507 250.60 88.00.53499.01070 249.70 138.00.89416.00411 249.80 39.00.10143.00606 250.30 89.00.54823.00954 249.50 139.00.89810.00411 249.80 40.00.10321.00572 250.50 90.00.55407.00930 249.70 140.00.90239.00406 249.80 41.00.11288.00671 250.30 91.00.56683.00838 249.50 141.00.90621.00203 249.80 42.00.11663.00689 250.40 92.00.57082.00930 249.80 142.00.90644.00307 250.00 43.00.12665.00707 250.20 93.00.58544.01023 249.50 143.00.91235.00468 249.90 44.(0.13077.00811 250.30 94.00.59128.01011 249.70 144.00.91581.00340 249.90 45.00.14288.00656 250.00 95,00.60566,00900 249.40 145,00,91915..00253 249.90 46.00.14389.00644 250.30 96.00.60929.0)0912 249.70 146.00.92088.00310 250.00 47.00.15576.00668 250.00 97.00.62390.00975 249.40 147.00.92535.00286 249.90 48.00(1.15724.00686 250.30 98.00.62879.00871 249.60 148,()0.92660.00310 250.00 49.00.16948.00734 250.00 99.00.64132.00993 249.40 149.00.93155.00340 249.90

-274NORMALIZED DATA FRO)M RUN 28 (CO)NT'I) Nl)RiALIZED DATA (-R91 RUN 28 (CONT'I)) NORMALIZED DATA FRUM RUN 29 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN Ml I N -1 OFMIIN O F M IN MIN-' O 150.00.93340.00322 250.00 200.00.99385.00030 250.40.00.00000.00162 250.60 151.00.93799.00274 249.90 201.00.99433 -.00039 250.40 1.00.00324.00044 250.50 152.00.93888.00256 250.00 202.00.99307.00054 250.50 2.00.00088.00124 250.70 153.00.94312.00274 249.90 203.(0.99540.00122 250.40 3.00.00573.00156 250.50 154.00.94437.00280 250.00 204.00.99552.00030 250.40 4.00.00399.00093 250.70 155.00.94873.00262 249.90 205.00.99600.00036 250.40 5.00.00760.00193 250.60 156.00.94962.00128 250.00 206.00.99624.00000 250.40 6.00.00785.00199 250.70 157.00.95129.00030 250.00 207.00.99600.00006 250.40 7.00.01158.00187 250.60 158.00.95021.00047 250.20 208.00.99636,.00036 250.40 8.00.01158.00205 250.70 159.00.95224.00122 250.20 209.00.99672.00024 250.40 9.00.01569.00305 250.60 160.00.95265.00209 250.30 210.00.99684.0)000 250).40 10.00.01768.00286 250.60 161.00.95641.00260 250.20 211.00.99672 -.00087 250.40 11.00.02141.00168 250.50 162.00.95784.00191 250.20 212.00.99510.00012 250.50 12.00.02104.0()280 250.70 163.00.96023.00221 250.20 213.00.99695.00012 250.40 13.00.02701.00261 250.50 164.00.96226.00185 250.20 214.00.99534.00024 250.50 14.00.02626.00193 250.70 165.00.96392.00092 250.20 215.00.99743.00111 250.40 15.00).03087.00311 250.60 166.00.96410.00(161 250.3.0 216.00.99755.00006 250.40 16.00.03249.00305 250.70 167.00.96715.00236 250.20 217.00.99755.00006 250.40) 17.00.03696.00299 250.60 168.00.96881,.00155 250.20 218.1)0.99767.00006 250.40 18.00.03846.00367 250.70 169.00.97025.00155 250.20 219.00.99767.00006 250.40 19.00.04430.00305 250.60 170.00.97192.00161 250.20 220.00.99779.00105 250.40 20.00.04456.00473 250.80 171.00.97347.00328 250.20 221.00.99976.00111 250.30 21.00.09376.00404 250.50 172.00.97848.00161 250.)0 222.00 1.00000.00006 250.30 22.00.05264.00330 250.80 173.00.97669 -.00024 250.20 23.00.06036.00547 250.60 174.00.97800.00137 250.20 24.00.06359.00566 250.70 175.00.97943.00316 250.20 25.00.07168.00417 250.50 176.00.98433.00125 250.00 26.00.07193.00523 250.80 177.00.98193 -.00066 250.2) 27.00.08213.00535 250.50 178.00.98301.()0101 250.20 28.00.08263.00634 250.80 179.00.98396.00101 250.20 29.00.09482.00666 250.40 180.00.98504.00083 250.20 30.00,.09594.00610 250.70 181.00.98563.00078 250.20 31.00.10701.00591 250.40 182.00.98659.00101 250.20 32.00.10776.00715 250.70 183.00,.98766.00107 250.20 33.00.12132.00746 250.30 184.00,.98873.00101 250.20 34.00.12269.00691 250.60 185.00.98969.00072 250.20 35.00.13513,.00896 250.30 186.00.99016 -.00021 250.20 36.00.14061.00728 250.40 187.00.98927 -.00015 250.30 37.00.14969.00740 250.30 188.00.98986.00054 250.30 38.00.15541.00715 250.40 189.00.99034 -.00027 250.30 39.00.16400.00722 250.30 190.00.98932 -.00021 250.40 40.00.16985.00809 250.40 191.00.98992.00048 250.40 41.00.18017.00827 250.30 192.00.99028.00054 250.40 42.00.18640).00815 250.40 193.00.99099 -.00021 250.40 43.00.19647.00852 250.30 194.00.98985.01)0060 250.50 44.00.20344.00964 250.40 195.00.99218.00060 250.40 45.00.21576.00977 250.20 196.00.99105.00060 250.50 46.00.22298.01082 250.30 197.00.99338.00030 250.40 47.00.23740.01182 250.00 198.00.99164.00018 250.50 48.00.24661.01039 250.00 199.00.99373.00111 250.40 49.00.25818.00977 249.90 NORMALIZED DATA FROM RUN'29 (CONTID) NORMALIZED DATA FROM RUN 29 (CONT'D) NORMALIZED DATA FROM RUN 29 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-i OF MIN MIN-' OF MIN MIN' OF 50.00,.26614.01076 250.00 100.00.74854.00902 249.90 150.00.95919.00087 250.00 51.00,.27970.00977 249.80 101.00.75501.00666 249.80 151.00.96044.00162 250.00 52.00.28568.00902 250.00 102.00.76185.00715 249.80 152.00.96243,.00255 250.00 53.00.29774.01014 249.90 103.00),76931.00728 249.80 153.00.96554.00162 249.90 54.00.30596.00989 250.00 104.00,.77641.00715 249,80 154.00.96566.00174 250.00 55.00.31753.00977 249.90 105.00.78362.00585 249.80 155.00.96902.00156 249.90 56.00.32549.00977 250.00 106.00.78811.00635 249.90 156.00.96878.00069 250.00 57.00.33706.01008 249.90 107.00.79632.00647 249.80 157.00.97039.00174 250.00 58.00.34565.01039 250.00 108.00.80105.00610 249.90 158.00.97226.00168 250.00 59.00.35784.01020 249.90 109.00.80851.00579 249.80 159.00.97375.00131 250.00 60.00,.36606,.01002 250.00 110.00.81262,.00579 249.90 160.00.9748-7.00112 250.00 61.00.37787.00989 249.90 111.00.82008.00572 249.80 161.00.97599.00112 250.00 62.00.38584.01002 250.00 112.00,.82407.00572 249.90 162.00.97711.00112 250.00 63.00,.39791.00989 249.90 113.00.83153.00547 249.80 163.00.97823.00093 250.00 64.00.40562.00952 250.00 114.00.83501.00523 249.90 164.00.97898.00118 250.00 65.00.41694.00964 249.90 115.00.84198.00473 249.80 165.00.98060,.00112 250.00 66.00.42491.01113 250.00 116.00.84447,.00498 250.00 166.00.98122,.00075 250.00 67.00.43921.01144 249.70 117.00.85193.00516 249.80 167.00,.98209.00075 250.00 68.00.44780.01101 249.80 118.00.85480.00479 249.90 168.00.98271.00081 250.00 69.00.46123.01008 249.60 119.00.86151.00485 249.80 169.00.98371.00106 250.00 70.00,46796.00915 249.80 120.00.86450.00491 249.90 170.00.98483,.00087 250.00 71.00.47952.00983 249.70 121.00.87134.00585 249.80 171.00.98545.00068 250.00 72.00.48762.00983 249.80 122.00.87620.00448 249.80 172.00.98619.00062 250.00 73.00.49918.01020 249.70 123.00.88030.00417 249.80 173.00.98669.00068 250.00 74,00,.50802.01027 249.80 124.00.88453.00435 249.80 174.00.98756.00075 250.00 75.00.51971.01002 249.70 125.00.88901.00442 249.80 175.00.98819.00050 250.00 76.00.52805.00971 249.80 126.00.89337.00404 249.80 176.00,.98856 -.00143 250.00 77.00.53912.00977 249.70 127.00.89710.00286 249.80 177.00.98533.00044 250.20 78.00,.54759.01014 249.80 128.00.89909.00392 249.90 178.00,98943.00230 250.00 79.00.55941.00958 249.70 129.)0.90494.00473 249.80 179.00,98993,.00037 250.00 80.00.56675.00958 249.80 130.00.90855.00355 249.80 180.00,99018 -.00137 250.00 81.00.57857.00983 249.70 131.00.91203.00361 249.80 181.00.98720,.00025 250.20 82.00.58641.00964 249.80 132.0O.91576.00355 249.80 182.00.99067.00025 250.00 83.00.59785.01057 249.70 133.00.91912.00342 249.80 183.00.98769 -.00143 250.20 84.00,.60756.01008 249.70 134.00.92261.00336 249.80 184.00.98782.00025 250.20 85.00.61801.00921 249.60 135.00.92584.00305 249.80 185.00.98819.00031 250.20 86.00,.62597.00828 249.70 136.00.92870.00386 249.80 186.00.98844.00019 250.20 87.00.63456.00840 249.70 137.00.93355.00305 249.70 187.00.98856.00037 250.20 88.00.64277.00952 249.80 138.00.93480.00299 249.80 188.00.98919.00031 250.20 89.00.65360.00927 249,.70 139.00.93953.00292 249.70 189.00.98919.00193 250.20 90.00.66131.00908 249.80 140.00.94065.00174 249.80 190.00.99304.00193 250.00 91.00.67176.00883 249.70 141.00.94301.0(249 249.80 191.00,.99304.00012 250.00 92.00,.67898.00896 249.80 142.00.94563.00255 249.80 192.00.99329,.00000 250.00 93.00.68968.00871 249.70 143.00.94811.00205 249.80 193.00.99304.00006 250.00 94.00.69640.00784 249.80 144.00.94973.00187 249.80 194.00,.99341.00031 250.00 95.00.70536,00784 249.70 145.00.951H5.010243 249.80 195.00.99366.00012 250.00 96.00.71208.00834 249.90 146.00.95458.00230 249.80 196.00.99366.00006 250.00 97.00.72203.00790 249.80 147.00.95645.00112 249.80 197.00.99378.00019 250.00 98.00.72788.00747 249.90 148.)0.95683.00112 249,90 198.00.99403,00025 250.00 99.00,73696.01033 249.80 149.00.95869.))11 249.90 199.)00.99428.00037 250.00

-275NORMALIZED DATA FROM RUN 29 (CONT'D) NORMALIZED DATA FROM RUN 30 NORMALIZED DATA FROM RUN 30 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF MIN MIN't OF MIN MIN-' OF 200.00.99478.00031 250.00 00.00000.00113 250.70 50.00.25063.01020 250.20 201.00.99490.00006 250.00 1.00.00225.00185 250.60 51.00.26459.01190 250.00 202.00.99490.00006 250.00 2.00.00369.00126 250.60 52.00.27443.01050 250.00 203.00.99503.00012 250.00 3.00.00477.00132 250.60 53.00.28558.01091 250.00 204.00.99515.00019 250.00 4.00.00633.00244 250.60 54.00.29626.01138 250.00 205.00.99540..00025 250.00 5.00.00965.00144 250.50 55.00.30833.01162 249.90 206.00.99565.00019 250.00 6.00.00921.00050 250.60 56.00.31949.01103 249.90 207.00.99578.00006 250.00 7.00.01065.00174 250.60 57.00.33040.01121 249.90 208.00.99578.00106 250.00 8.00.01269.00192 250.60 58.00.34192.01103 249.90 209.00.99789.00106 249.90 9.00.01449.00186 250.60 59.00.35247.01085 249.90 210.00.99789.00093 249.90 10.00.01641.00292 250.60 60.00.36363.01215 249.90 211.00.99975.00019 249.80 11.00.02033.00298 250.50 61.00.37678.01221 249.80 212.00.99826.00012 249.90 12.00.02237.00210 250.50 62.00.38806.01109 249.80 213.00 1.00000.00000 249.80 13.00.02453.00234 250.50 63.00.39897.01080 249.80 14.00.02705.00246 250.50 64.00.40965.01173 249.80 15.00.02945.00276 250.50 65.00.42244.01109 249.70 16.00.03256.00312 250.50 66.00.43184.01004 249.80 17.00.03568.00288 250.50 67.00.44251.01085 249.80 18.00.03832.00282 250.50 68.00.45355.01109 249.80 19.00.04132.00418 250.50 69.00.46470.01027 249.80 20.00.04668.00418 250.40 70.00.47409.01157 249.90 21.00.04968.00266 250.40 71.00.48785.01251 249.80 22.00.05199.00390 250.50 72.00.49912.01163 249.80 23.00.05748.00508 250.40 73.00.51112.01187 249.80 24.00.06215.00432 250.40 74.00.52287.01145 249.80 25.00.06611.00450 250.40 75.00.53403.01063 249.80 26.00.07115.00568 250.40 76.00.54414.01097 249.90 27.00.07747.00492 250.30 77.00.55598.01198 249.80 28.00.08098.00416 250.40 78.00.56809.01169 249.80 29.00.08578.00540 250.40 79.00.57937.01045 249.80 30.00.09178.00564 250.40 80.00.58900.01209 249.90 31.00.09706.00570 250.40 81.00.60356.01215 249.70 32.00.10317.00600 250.40 82.00.61331.01069 249.80 33.00.10905.00606 250.40 83.00.62495.01121 249.80 34.00.11529.00642 250.40 84.00.63574.01103 249.80 35.00.12189.00760 250.40 85.00.64702.01115 249.80 36.00.13049.00672 250.30 86.00.65805.01209 249.80 37.00.13532.00620 250.40 87.00.67121.01068 249.70 38.00.14288.00832 250.40 88.00.67940.00962 249.80 39.00.15196.00850 250.30 89.00.69044.01056 249.80 40.00.15987.00780 250.30 90.00.70051.01014 249.80 41.00.16755.00874 250.30 91.00.71071.01002 249.80 42.00.17735.00904 250.20 92.00.72054.00972 249.80 43.00.18562.01022 250.20 93.00.73014.00920 249.80 44.00.19778.00864 250.00 94.00.73893.01014 249.90 45.00.20289.00864 250.20 95.00.75041.00972 249.80 46.00.21505.01064 250.00 96.00.75836.00942 249.90 47.00.22417.00954 250.00 97.00.76924.00946 249.80 48.00.23412.01002 250.00 98.00.77728.00828 249.80 49.00.24420.00825 250.00 99.00.78579.00840 249.80 NORMALIZED DATA FROM RUN 30 (CONT'D) NORMALIZED DATA FROM RUN 30 (CONT'D) NORMALIZED DATA FROM RUN 31 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF MIN MIN-' OF MIN MIN' OF 100.00.79407.00792 249.80 150.00.98753.00090 250.40.00.00000.00022 251.00 101.00.80162.00868 249.80 151.00.99025.00102 250.30 1.00.00044.00093 251.00 102.00.81142.00910 249.70 152.00.98956.00096 250.40 2.00.00186.00160 251.00 103.00.81982.00762 249.70 153.00.9217.00078 250..30 3.00.00364.00154 251.00 104.00.82665.00708 249.70 154.00.99112.00054 250.40 4.00.00494.00172 251.00 105.00.83397.00656 249.70 155.00.99325 -.00034 250.30 5.00.00707.00136 251.00 106.00.83977.00614 249.80 156.00.99044 -.00016 250.50 6.00.00767.00160 251.00 107.00.84624.00666 249.80 157.00.99292.00060 250.40 7.00.01027.00219 251.00 108.00.85308.00654 249.80 158.00.99164.00036 250.50 8.00.01205.00190 251.00 109.00.85932.00654 249.80 159.00.99364 -.00040 250.40 9.00.01407.00122 251.00 110.00.86615.00630 249.80 160.00.99084.00066 250.60 10.00.01449.00152 251.10 111.00.87191.00618 249.80 161.00.99496.00142 250.40 11.00.01710.00261 251.10 112.00.87851.00694 249.80 162.00.99368.00048 250.50 12.00.01971.00261 251.10 113.00.88579.00564 249.70 163.00.99592 -.00046 250.40 13.00.02231.00278 251.10 114.00.88978.00582 249.80 164.00.99276.00030 250.60 14.00.02528.00284 251.10 115.00.89742.00570 249.70 165.00.99652.00030 250.40 15.00.02800.00235 251.10 116.00.90118.00446 249.80 166.00.99336.00036 250.60 16.00.02997.00247 251.20 117.00.90634.00480 249.80 167.00.99724.00024 250.40 17.00.03293.00405 251.20 118.00.91077.00586 249.80 168.00.99384.00030 250.60 18.00.03807.00379 251.10 119.00.91805.00480 249.70 169.00.99784.00118 250.40 19.00.04052.00421 251.20 120.00.92037.00374 249.80 170.00.99620.00012 250.50 20.00.04649.00530 251.10 121.00.92553.00468 249.80 171.00.99808.00106 250.40 21,00.05111.00379 251.10 122.00.92972.00402 249.80 172.00.99832.00018 250.40 22.00.05407.00474 251.10 123.00.93356.00320 249.80 173.00.99844 -.00070 250.40 23.00.06059.00648 251.10 124.00.93612.00320 249.90 174.00.99692.10030 250.50 24.00.06703.00589 251.00 125.00.93996.00266 249.90 175.00.99904 -.00046 250.40 25.00.07236.00551 251.00 126.00.94144.00384 250.00 176.00.99599.00048 250.60 26.00.07805.00587 251.00 127.00.94764.00454 249.90 177.00 1.00000.00118 250.40 27.00.08409.00598 251.00 128.00.95051.00324 249.90 28.00.09002.00622 251.00 129.00.95411.00324 249.90 29.00.09653.00658 251.00 130.00.95699.00318 249.90 30.00.10317.00687 251.00 151.00.96047.00200 249.90 31.00.11028.00711 251.00 132.00.96099.00258 250.00 32.00.11739.00741 251.00 133.00.96563.00340 249.90 33.00.12509.00782 251.00 134.00.96779.00366 249.90 34.00.13303.00800 251.00 135.00.97294.00290 249.93 35.00.14108.00835 251.00 136.00.97358.00216 250.00 36.00.14973.00877 251.00 137.00.97726.00198 249.90 37.00.15862.00871 251.00 138.00.97754.00204 250.00 38.00.16715.00912 251.00 139.00.98134.00192 249.90 39.00.17687.01027 251.00 140.00.98138.00198.250.00 40.00.18769.01009 250.90 141.00.98530.00186 249.90 41.00.19705.00954 250.90 142.00.98510.00044 250.00 42.00.20677.00978 250.90 1.43.00.98618.00120 250.00 43.00.21660.01001 250.90 144.00.98750.00150 250.00 44.00.22679.01025 250.90 145.00.98917.00132 250.00 45.00.23710.01049 250.90 146.00.99013 -.00080 20.900 46.00.24777.01043 250.90 147.00.98757 -.00150 250.20 47.00.25796.01049 250.90 148.00.98713.00044 250.30 48.00.26874.01243 250.90 149.00.98845.00020 250.30 49.00.28281.01334 250.70

-276NORMALIZED DATA FROM RUN 31 (CONT'D) NORMALIZED DATA FROM RU8 31 (CONT'D) NORMALIZED DATA FRO'M RUN 31 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF PIN MIN- OF MIN MIN-' OF 50.00.29541.01187 250.60 100.00(.86890.00571 250.00 150.00.99810.00018 251.00 51.00.30655.01120 250.60 101.00.87226.00541 250.20 151.00.99652.00018 251.10 52.00.31781.01070 250.60 102.00.87972.00887 250.20 152.00.99846.00103 251.00 53.00.32795.01126 250.70 103.00.89000.00632 250.00 153.00.99858 -.00061 251.00 54.00.34032.01229 250.60 104.00.89236.00438 250.(30 154.00.99723 -.00032 251.10 55.00.35252.01203 250.60 105.oU.89876.00555 250.30 155.00.99794.00133 251.10 56.00.36437.01185 250.60 1U6.00.90346.00549 250.40 156.00.99988.00103 251.00 57.00.37622.01276 250.60 107.00.90974.00616 250.40 157.00 1.00000 -.00056 251.00 58.00.38989.01306 250.50 1(8.00.91578.00496 250.40 59.00.40233.01335 250.50 109.10.91963.00575 250.50 60.00.41659.01420 250.40 110.00.92727.00600 250.40 61.00.43073.01341 250.30 111.00.93166.00474 250.40 62.00.44341.01274 250.30 112.00.93675.00492 250.40 63.00.45621.01268 250.30 113.00.94149.00468 250.40 64.00.46877.01256 250.30 114.00.94611.00359 250.40 65.00.48133.01268 250.30 115.00.94868.00245 250.50 66.00.49412.01286 250.30 116.00.95100.00233 250.60 67.00.50704.01280 250.30 117.00.95333.00306 250.70 68.00.51972.01292 250.30 118.00.95712.00276 250.70 69.00.53287.01333 250.30 119.0.95885.00247 250.80 70.00.54638.01333 250.30 120.00.96205.00235 250.80 71.00.55953.01315 250.30 121.10.96355.00193 250.90 72.00.57268.01268 250.30 122.00.96592.00255 250.90 73.00.58489.01244 250.30 123.00.96865.00284 250.90 74.00.59756.01274 250.30 124.00.97161.00243 250.90 75.00.61036.01341 250.30 125.00.97350.00213 250.90 76.00.62438.01244 250.20 126.00.97587.00190 250.90 77.00.63524.01153 250.30 127.00.97729.00154 250.90 78.00.64745.01167 250.30 128.00.97895.00166 250.90 79.00.65858.01155 250.30 129.00.98061.00178 250.90 80.00.67055.01143 250.30 130.00.98251.00160 250.90 81.00.68145.01193 250.30 131.00.98381.00142 250.90 82.00.69441.01126 250.20 132.00.98535.00087 250.90 83.00.70396.00993 250.30 133.00.98554.00098 251.00 84.00.71427.01110 250.30 134.00.98732.00130 251.00 85.00.72616.01128 250.20 135.00.98815.00089 251.00 86.00.73683.01049 250.20 136.00.98910.00101 251.00 87.00.74714.01025 250.20 137.00.99017.00101 251.00 88.00.75733.01195 250.20 138.00.99111.00089 251.00 89.00.77103.01189 250.00 139.00.99194.00083 251.00 90.00.78111.00813 250.00 140.00.99277 -.00008 251.00 91.00.78730.00790 250.20 141.00.99178 -.00014 251.10 92.00.79690.01082 250.20 142.00.99249.00065 251.10 93.00.80895.00889 250.00 143.00.99308.00071 251.10 94.00.81467.00918 250.20 144.00.99391.00059 251.10 95.00.82732.00901 250.00 145.00.99427.00036 251.10 96.00.83268.00871 250.20 146.00.99462.00065 251.10 97.00.84473.01017 250.00 147.00.99557.00053 251.10 98.00.85303.00806 250.00 148.00.99569.00030 251.10 99.00.86085.00794 250.00 149.00.99616.00121 251.10 NORMALIZED DATA FROM RUN 32 NORMALIZED DATA FROM RUN 32 (CONT'D) NORMALIZED DATA FROM RUN 32 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF MIN MIN-' OF MIN MIN-f OF.00.00000.00178 251.10 50.00.25890.00795 250.90 100.00.70446.00789 250.40 1.00.00357.00281 251.00 51.00.26678.00801 250.90 101.00.71247.00801 250.40 2.00.00563.00200 251.00 52.00.27491.00902 250.90 102.00.72047.00728 250.40 3.00.00757.00200 251.00 53.00.28483.00825 250.80 103.00.72702.00734 250.40 4.00.00963.00212 251.00 54.00.29141.00837 250.90 104.00.73515.00776 250.40 5.00.01181.00255 251.00 55.00.30157.00933 250.80 105.00.74255.00716 250.40 6.00.01473.00291 251.00 56.00.31007.00873 250.80 106.00.74947.00673 250.40 7.00.01764.00273 251.00 57.00.31904.00849 250.80 107.00.75602.00578 250.40 8.00.02019.00279 251.00 58.00.32705.00933 250.80 108.00.76102.00643 250.50 9.00.02322.00315 251.00 59.00.33770.00957 250.70 109.00.76888.00685 250.40 10.00.02649.00411 251.00 60.00.34619.00867 250.70 110.00.77473.00644 250.50 11.00.03144.00417 250.90 61.00.35505.00892 250.70 111.00.78176.00565 250.50 12.00.03484.00334 250.90 62.00.36402.00904 250.70 112.00.78604.00637 250.60 13.00.03811.00274 250.90 63.00.37312.00922 250.70 113.00.79450.00649 250.50 14.00.04032.00292 251.00 64.00.38246.01036 250.70 114.00.79902.00643 250.60 15.00.04396.00388 251.00 65.00.39384.01036 250.60 115.00.80736.00631 250.50 16.00.04809.00419 251.00 66.00.40318.00940 250.60 116.00.81163.00678 250.60 17.00.05233.00443 251.00 67.00.41264.00946 250.60 117.00.82092.00576 250.40 18.00.05694.00437 251.00 68.00.42211.00850 250.60 118.00.82316.00487 250.60 19.00.06107.00461 251.00 69.00.42965.00881 250.70 119.00.83065.00546 250.50 20.00.06616.00581 251.00 70.00.43972.00899 250.70 120.00.83407.00540 250.60 21.00.07269.00569 250.90 71.00.44763.00934 250.80 121.00.84145.00546 250.50 22.00.07754.00479 250.90 72.00.45840.00922 250.70 122.00.84499.00474 250.60 23.00.08227.00426 250.90 73.00.46607.00863 250.80 123.00.85094.00456 250.60 24.00.08606.00546 251.00 74.00.47565.01018 250.80 124.00.85412.00402 250.70 25.00.09319.00528 250.90 75.00.48643.00904 250.70 125.00.85897.00396 250.70 26.00.09661.00564 251.00 76.00.49373.00850 250.80 126.00.86203.00396 250.80 27.00.10447.00594 250.90 77.00.50343.00977 250.80 127.00.86688.00383 250.80 28.00.10850.00594 251.00 78.00.51326.00958 250.80 128.00.86970.00359 250.90 29.00.11636.00588 250.90 79.00.52260.01000 250.80 129.00.87406.00431 250.90 30.00.12027.00613 251.00 80.00.53325.00951 250.70 130.00.87831.00437 250.90 31.00.12861.00564 250.90 81.00.54162.00843 250.70 131.00.88280.00431 250.90 32.00.13155.00564 251.00 82.00.55011.00939 250.70 132.00.88692.00406 250.90 33.00.13989.00708 250.90 83.00.56040.00957 250.60 133.00.89092.00400 250.90 34.00.14572.00619 250.90 84.00.56925.00957 250.60 134.00.89493.00472 250.90 35.00.15227.00649 250.90 85.00.57954.00951 250.50 135.00.90036.00454 250.80 36.00.15870.00637 250.90 86.00.58827.00831 250.50 136.00.90400.00286 250.80 37.00.16500.00655 250.90 87.00.59616.00819 250.50 137.00.90609.00280 250.90 38.00.17180.00679 250.90 88.00.60465.00957 250.50 138.00.90961.00328 250.90 39.00.17859.00685 250.90 89.00.61530.00945 250.40 139.00.91264.00309 250.90 40.00.18551.00679 250.90 90.00.62355.00735 250.40 140.00.91579.00309 250.90 41.00.19218.00643 250.90 91.00.63000.00747 250.50 141.00.91883.00297 250.90 42.00.19837.00698 250.90 92.00.63850.00849 250.50 142.00.92174.00279 250.90 43.00.20613.00746 250.90 93.00.64699.00837 250.50 143.00.92441.00291 250.90 44.00.21329..00728 250.90 94.00.65524.00915 250.50 144.00.92756.00291 25090 45.00.22069.00728 250.90 95.00.66528.00890 250.40 145.00.93023.00243 250.90 46.00.22784.00752 250.90 96.00.67304.00795 250.40 146.00.93241.00249 250.90 47.00.23573.00770 250.90 97.00.68117.00705 250.40 147.00.93520.00285 250.90 48.00.24325.00758 250.90 9800 68714.00776 250.50 148.00.93811.0021 25090 49.00.25089.00782 250.90 99.00.69670.00866 250.40 149.00.93957.00200 250.90

-277NORMALIZED.DATA FROM RUN 32 (CONT'D) NORMALIZED DATA FROM RUN 32 (CONT'D) NORMALIZED DATA FROM RUN 33 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIMIN-' OF 150.00.94212.00237 250.90 200.00.99207.00042 250.80.00.00000.00013 250.60 151.00.94430.00230 250.90 201.00.99268 -.00053 250.80 2.00.00051.00016 250.50 152.00.94673.00296 250.90 202.00.99101.00012 250.90 4.00.00063.00015 250.50 153.00.95022.00(260 250.80 203.00.99292.00006 250.80 6.00.00111.00015 250.50 154.00.95192.00194 250.80 204.00.99113.00090 250.90 8.00.00124.00030 250.50 155.00.95410.00194 250.80 205.00.99472.00012 250..70 10.0'.00233.00093 250.50 156.00.95580.00176 250.80 206.00.99137.00024 250.90 12.00.00496.00102 250.40 157.00.95762.00182 250.80 207.00.99520.00114 250.70 14.00.00642.00061 250.40 158.00.95944.00164 250.80 208.00.99365.00024 250.80 16.00.00739.00070 250.40 159.00.96090.00176 250.80 209.00.99569 -.00078 250.70 18.00.00922.00085 250.40 160.00.96296.00349 250.80 210.00.99210.00000 250.90 20.00.01080.00067 250.40 161.00.96788.00146 250.60 211.00.99569.00090 250.70 22.00.01189.00088 250.40 162.00.96587.00062 250.80 212.00.99389.00000 250.80 24.00.01432.00103 250.40 163.00.96912.00133 250.70 213.00.99569.00096 250.70 26.00.01603.00103 250.40 164.00.96854.00127 250.80 214.00.99581.00006 250.70 28.00.01846.00106 250.40 165.00.97167.00307 250.70 215.00.99581 -.00084 250.70 30.00.02028.00116 250.40 166.00.97467.00115 250.60 216.00.99413.00012 250.80 32.00.02308.00131 250.40 167.00.97397.00013 250.70 217.00.99605.00108 250.70 34.00.02551.00131 250.40 i68.00.97494.00211 250.70 218.00.99629.00198 250.70 36.00.02831.00146 250.40 169.00.97819.00109 250.60 219.00 1.00000.00185 250.50 38.00.03135.00146 250.40 170.00.97713.00001 250.70 40.00.03415.00152 250.40 171.00.97822.00026 250.70 42.00.03743.00176 250.40 172.00.97764.00205 250.80 44.00.04120.00176 250.40 173.00.98232.00091 250.60 46.00.04449.00173 250.40 174.00.97946.00001 250.80 48.00.04813.00185 250.40 175.00.98234.00187 250.70 50.00.05190.00198 250.40 176.00.98319.00079 250.70 52.00.05604.00204 250.40 177.00.98392 -.00017 250.70 54.00.06005.00213 250.40 178.00.98285.00055 250.80 56.00.06455.00225 250.40 179.00.98501.00138 250.70 58.00.06905.00219 250.40 180.00.98562.00061 250.70 60.00.07331.00237 250.40 181.00.98622.00085 250.70 62.00.07854.00252 250.40 182.00.98732.00055 250.70 64.00.08340.00258 250.40 183.00.98732.00030 250.70 66.00.08888.00274 250.40 184.00.98792.00061 250.70 68.00.09435.00261 250.40 185.00.98853 -.00047 250.70 70.00.09934.00246 250.40 186.00.98698.00036 250.80 72.00.10420.00243 250.40 187.00.98926.00049 250.70 74.00.10907.00249 250.40 188.00.98795.00042 250.80 76.00.11417.00240 250.40 189.00.99011.00055 250.70 78.00.11867.00274 250.40 190.00.98904.00049 250.80 80.00.12512.00286 250.40 191.00.99108 -.00059 250.70 82.00.13011.00249 250.40 192.00.98785.00030 250.90 84.00.13509.00243 250.40 193.00.99168.00114 250.70 86.00.13984.00237 250.40 194.00.99013.00036 250.80 88.00.14458.00249 250.40 195.00.99241.00042 250-.70 90.00.14981.00249 250.40 196.00.99098.00042 250.80 92.00.15455.00231 250.40 197.00.99326 -.00053 250.70 94.00.15905.00249 250.40 198.00.98991 -.00072 250.90 96.00.16452.00240 250.40 199.00.99183.00108 250.80 98.00.16866.00231 250.40 NORMALIZED DATA FROM RUN'33 (CONT'D) NORMALIZED DATA FROM RUN 33 (CONT'D) NORMALIZED DATA FROM RUN 33 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN' OF MIN MIN-' OF MIN MIN-' OF 100.00.17377.00249 250.40 200.00.39674.00225 250.50 300.00.69359.00395 250.20 102.00.17863.00219 250.40 202.00.40149.00246 250.50 302.00.70211.00401 250.20 104.00.18252.00216 250.40 204.00.40659.00246 250.50 304.00.70965.00392 250.20 106.00.18727.00219 250.40 206.00.41134.00246 250..50 306.00.71780.00410 250.20 108.00.19128.00168 250.40 208.00.41644.00252 250.50 308.00.72607.00410 250.20 110.00.19400.00174 250.50 210.00.42143.00234 250.50 310.00.73421.00423 250.20 112.00.19826.00213 250.50 212.00.42581.00225 250.50 312.00.74297.00441 250.20 114.00.20252.00213 250.50 214.00.43043.00240 250.50 314.00.75185.00438 250.20 116.00.20677.00225 250.50 216.00.43542.00243 250.50 316.00.76048.00438 250.20 118.00.21152.00216 250.50 218.00.44016.00240 250.50 318.00.76936.00468 250.20 120.00.21541.00189 250.50 220.00.44502.00237 250.50 320.00.77921.00486 250.20 122.00.21906.00198 250.50 222.00.44965.00240 250.50 322.00.78882.00462 250.20 124.00.22331.00216 250.50 224.00.45463.00243 250.50 324.00.79770.00444 250.20 126.00.22769.00231 250.50 226.00.45938.00243 250.50 326.00.80658.00450 250.20 128.00.23256.00225 250.50 228.00.46436.00271 250.50 328.00.81570.00447 250.20 130.00.23669.00204 250.50 230.00.47020.00277 250.50 330.00.82446.00432 250.20 132.00.24070.00219 250.50 232.00.47543.00261 250.50 332.00.83297.00407 250.20 134.00..24545.00237 250.50 23.4.00.48066.00268 250.50 334.00.84075.00401 250.20 136.00.25019.00225 250.50 236.00.48613.00271 250.50 336.00.84902.00398 250.20 138.00.25445.00222 250.50 238.00.49148.00280'250.50 338.00.85669.00374 250.20 140.00.25907.00222 250.50 240.00.49732.00280 250.50 340.00.86398.00374 250.20 142.00.26333.00216 250.50 242.00.50267.00265 250.50 342.00.87164.00339 250.20 144.00.26770.00231 250.50 244.00.50790.00280 250.50 344.00.87753.00305 250.30 146.00.27257.00243 250.50 246.00.51386 00274 250.50 346.00.88385.00331 250.30 148.00.27743.00216 250.50 248.00.51885.00265 250.50 348.00.89079.00337 250.30 150.00.28120.00219 250.50 250.00.52444.00289 250.50 350.00.89735.00313 250.30 152.00.28619.00237 250.50 252.00.53040.00268 250.50 352.00.90331.00292 250.30 154.00.29069.00234 250.50 254.00.53514.00261 250.50 354.00.90903.00283 250.30 156.00.29555.00210 250.50 256.00.54086.00307 250.50 356.00.91462.00268 250.30 158.00.29908.00225 250.50 258.00.54743.00316 250.50 358.00.91973.00249 250.30 160.00.30455.00243 250.50 260.00.55351.00289 250.50 360.00.92460.00234 250.30 162.00.30881.00216 250.50 262.00.55898.00286 250.50 362.00.92910.00204 250.30 164.00.31319.00222 250.50 264.00.56494.00307 250.50 364.00.93274.00210 250.30 166.00.31769.00225 250.50 266.00.57127..00316 250.50 366.00.93749.00213 250.30 168.00.32219.00210 250.50 268.00.57759.00313 250.50 368.00.94126.00192 250.30 170.00.32608.00243 250.50 270.00.58379.00313 250.50 37(.00.94515.00182 250.30 172.00.33192.00237 250.50 272.00.59012.00313 250.50 372.00.94856.00170 250.30 174.00.33557.00219 250.50 274.00.59632.00319 250.50 374.00.95196.00170 250.30 176.00.34068.00231 250.50 276.00.60289.00337 250.50 376.00.95537.00158 250.30 178.00.34481.00222 250.50 278.00.60982.00325 250.50 378.00.95828.00140 250.30 180.00.34955.00234 250.50 280.00.61590.00337 250.50 380.00.96096.00131 250.30 182.00.35418.00225 250.50 282.00.62332.00347 250.50 382.00.96351.00131 250.30 184.00.35855.00243 250.50 284.00.62976.00337 250.50 384.00.96619.00149 250.30 186.00.36390.00261 250.50 286.00.63682.00368 250.50 386.00.96947.00134 250.30 188.00.36901.00243 250.50 288.00.64448.00365 250.50 388.00.97154.00119 250.30 190.00.37363.00243 250.50 290.100.65141.00362 250.50 39.00.97422.00128 250.30 192.00.37874.00237 250.50 292.00.65895.00415 250.50 392.00.97665.00125 250.30 194.00.38312.00231 250.50 294.00.66803.00463 250.40 394.00.97920.00116 250.30 196.00.38799.00234 250.50 296.00.67747.00457 250.30 396.00.98127.00103 250.30 198.00.39249.00219 250.50 298.00.68630.00403 250.20 398.00.98334.00091 250.30

-278NORMALIZED DATA FROM RUN 33 (CONT'ID) NORMALIZED DATA FROM RUN 34 NORMALIZED DATA FROM RUN 34 (CONTID) TIME ALPHA RATE T MP. TI, E ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MI 141N -i O I MIN' - F MIN MIN-' OF 400.00.98492.00088 250.30.00.00000.00099 250.60 50.00.38508.01304 250.00 402.0).98687.00076 250.30 1.0.00198.00164 250.60 51.00.39813.01269 250.00 404.00.98796.00055 250.30 2.00.00328.00178 250.60 52.00.41046.01357 250.00 406.00.98905.00061 250.30 3.00.00553.00225 250.60 53.00.42526.01339 249.90 408.00.99039.00067 250.30 4.00.00779.00213 250.60 54.00.43723.01239 249.90 410.00.99173.00052 250.30 5.00.00980.00207 250.60 55.00.45004.01280 249.90 412.00.99246.00052 250.30 6.00.01193.00219 250.60 56.00.46284.01251 249.90 414.00.99380.00046 250.30 7.00.01419.0(302 250.60 57.00.47506.01292 249.90 416.00.99428.00033 250.30 8.(0.01798H.00332 250.60 58.00.48869.01328 249.90 418.00.99514.0004 3 250.30 9.00;02083.00296 250.60 59.00.50161.01304 249.90 420.00.99599.00033 250.30 10.00.02391.00332 250.60 60.00.61478.01304 249.90 422.00.99647.00033 250.30 11.00.02747.00350 250.60 61.00. 770.01286 249.90 424.00.99732.00024 250.30 12.00.03091.00368 250.60 62.00.54050.01280 249.90 426.00.99745.00006 250.30 13.00.03482.00427 250.60 63.00.55331.01316 249.90 428.00.99757.00015 250.30 14.00.03944.00456 250.6) 64.00.56682.01322 249.90 430.00.99805.00021 250.30 15.00.04395.00451 250.60 65.00.57975.01251 249.90 432.00.99842.00015 250.30 16.00.04845.00474 250.60 66.00.59184.01239 249.90 434.00.99866.00009 250.30 17,00.05343.00534 250.60 67.00.60453.01263 249.90 436.00.99878.00006 250.30 18.00.05912.00557 250.60 68.00.61710.01215 249.90 438.00.99891.00003 250.30 19.10.06458.00557 250.60 69.00.62883.01227 249.90 440.00.99891.00003 250.30 20.00.07027.00611 250.60 70.00.64164.01275 249.90 442.00.99903.00000 250.30 21.00.07679.00640 250.60 71.00.65432.01251 249.90 444.00.99891.00000 250.30 22.00.08307.00658 250.60 72.00.66666.01186 249.90 446.00.99903.00003 250.30 23.00.08995.00664 250.60 73.00.67804.01162 249.90 448.00.99903.00003 250.30 24.00.09635.00676 250.60 74.00.68989.01168 249.90 450.00.99915.00009 250.30 25.00.10347.00771 250.60 75.00.70139.01180 249.90 452.00.99939.00009 250.30 26.00.11177.00824 250.60 76.00.71349.01144 249.90 454.00.99951.00009 250.30 27.00.11995.00830 250.60 77.00.72428.01061 249.90 456.00.99976.00012 250.30 28.00.12836.00830 250.60 78.00.73471.01073 249.90 458.00 1.00000.00006 250.30 29.00.13654.00854 250.60 79.00.74574.01079 249.90 30.00.14544.00889 250.60 80.00.75629.01049 249.90 31.00.15433.00919 250.60 81.00.76672.01008 249.90 32.00.16381.00949 250.60 82.00.77644.00978 249.90 33.00.17330.00984 250.60 83.00.78629.00966 249.90 34.00.18350.01172 250.60 84.00.79577.00943 249.90 35.00.19675.01214 250.40 85.00.80514.00889 249.90 36.00.20777.01103 250.40 86.00.81356.00848 249.90 37.00.21880.01097 250.40 87.00.82209.00848 249.90 38.00.22971.01097 250.40 88.00.83051.00830 249.90 39.00.24073.01126 250.40 89.00.83869.00806 249.90 40.00.25224.01180 250.40 90.00.84663.00771 249.90 41.00.26433.01197 250.40 91.00.85410.00747 249.90 42.00.27619.01321 250.40 92.00.86157.00723 249.90 43.00.29075.01339 250.30 93.00.86857.00717 249.90 44.00.30297.01503 250.30 94.00.87592.00682 249.90 45.00.32082.01533 250.00 95.00.88220.00646 249.90 46.00.33363.01286 250.00 96.00.88884.00676 249.90 47.00.34655.01298 250.00 97.00.89572.00622 249.90 48.00.35959.01275 250.00 98.00.90129.00581 249.90 49.00.37204.01275 250.00 99.00.90734.00599 249.90 NORMALIZED DATA FROM RUN 34 (CONTID) NORMALIZED DATA FROM RUN 35 NORMALIZED DATA FROM RUN 35 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN' OF MIN MIN' OF MIN MIN-' OF 100.00.91327.00563 249.90.00.00000i.00204 249.90 50.00.29616.00956 249.50 101.00.91860.00516 249.90 1.00.00407.00281 249.80 51.00.30548.00962 249.50 102.00.92358.00498 249.90 2.00.00562.00167 249.80 52.00.31540.00986 249.50 103.00.92856.00486 249.90 3.00.00742.00203 249.80 53.00.32520.01050 249.50 104.00.93330.00486 249.90 4.00.00969.00227 249.80 54.00.33639.01104 249.40 105.00.93828.00462 249.90 5.00.01196.00239 249.80 55.00.34727.00998 249.40 106.00.94255.00415 249.90 6.00.01447.00251 249.80 56.00.35635.00968 249.40 107.00.94658.00409 249.90 7.00.01698.00281 249.80 57.00.36663.01062 249.40 108.00.95073.00409 249.90 8.00.02008.00293 249.80 58.00.37759.01092 249.30 109.00.95476.00385 249.90 9.00.02283.00293 249.80 59.00.38846.01070 249.30 110.00.95844.00373 249.90 10.00.02594.00323 249.80. 60.00.39898.01076 249.30 111.00.96223.00226 249.90 11.00.02929.00353 249.80 61.00.40997.01076 249.30 112.00.96296.00196 250.00 12.00.03299.00364 249.80 62.00.42049.01076 249.30 113.00.96616.00320 250.00 13.00.03658.00376 249.80 63.00.43148.01070 249.30 114.00.96936.00285 250.00 14.00.04052.00406 249.80 64.00.44188.01082 249.30 115.00.97185.00261 250.00 15.00.04470.00424 249.80 65.00.45311.01187 249.30 116.00.97458.00261 250.00 16.00.04901.00436 249.80 66.00.46563.01127 249.20 117.00.97707.00231 250.00 17.00.05343.00448 249.80 67.00.47566.01052 249.20 118.00.97920.00196 250.00 18.00.05797.00478 249.80 68.00.48666.01076 249.20 119.00.98098.00184 250.00 19.00.06299.00514 249.80 69.00.49717.01110 249.20 120.00.98288.00184 250.00 20.00.06825.00520 249.80 70.00.50885.01127 249.10 121.00.98466.00202 250.00 21.00.07338.00590 249.80 71.00.51972.01034 249.10 122.00.98691.00178 250.00 22.00.08004.00590 249.70 72.00.52952.01098 249.10 123.00.98822.00160 250.00 23.00.08518.00532 249.70 73.00.54168.01145 249.00 124.00.99011.00172 250.00 24.00.09068.00580 249.70 74.00.55243.01010 249.00 125.00.99165.00130 250.00 25.00.09677.00615 249.70 75.00.56187.00968 249.00 126.00.99272.00136 250.00 26.00.10299.00615 249.70 76.00.57179.00980 249.00 127.00.99438 -.00152 250.00 27.00.10908.00703 249.70 77.00.58147.00980 249.00 128.00.98968 -.00170 250.30 28.00.11705.00727 249.60 78.00.59139.00962 249.00 129.00.99099.00095 250.30 29.00.12363.00687 249.60 79.00.60071.00968 249.00 130.00.99158.00089 250.30 30.00.13080.00711 249.60 80.10.61075.00974 249.00 131.00.99277.00101 250.30 31.00.13785.00681 249.60 81.00.62019.00974 249.00 132.00.99360.00089 250.30 32.00.14442.00769 249.60) 82.00.63023.00962 249.00 133.00.99455.00059 250.30 33.00.15323.00811 249.50 83.00.63943.00980 249.00 134.00.99478.00059 250.30 34.00.16064.00735 249.50 84.00.64983.00998 249.00 135.00.99573.00083 250.30 35.00.16793.00735 249.50 85.00.65939.00956 249.00 136.00.99644.00077 250.30 36.00.17534.00759 249.50 86.00.66895.00938 249.00 137.00.99727.00053 250.30 37.00.18310.00771 249.50 87.00.67815.00932 249.00 138.00.99751.00053 250.30 38.00.19075.00771 249.50 88.00.68759.00908 249.00 139.00.99834.00041 250.30 39.00.19852.00813 249.50 89.00.69632.00926 249.00 140.00.99834.00024 250.30 40.10.20700.00825 249.50 90.00.70612.00956 249.00 141.00.99881.00071 250.30 41.00.21501.00819 249.50 91.00.71544.00932 249.00 142.00.99976.00059 250.30 42.00.22338.00843 249.50 92.00.72476.00932 249.00.143.00 1.00000 -.00064 250.30 43.00.23186.00860 249.50 93.00.73408.00902 249.00 44.00.24059.00890 249.50 94.00.74280.00878 249.00 45.00.24967.00890 249,50 95.00.7b165.00878 249.00 46.00.25839.00920) 249.50 96.0.7.6037.00866 249.00 47.00.26807.00920 249.50 97.00).76h98.00854 249.00 48.00.27680 00914 249.50 9H.00.7/746.00848 249.00 49.00.28636.0096 249.50 99.00.78595.00860 249.00

-279NORMALIZED DATA FROM RUN 35 (CONT'D) NORMALIZED DATA FROM RUN 35 (CONT'D) NORMALIZED DATA FROM RUN 36 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-i OF MIN MIN'' OF mIN MIN - OF 100.00.79467.00843 249.00 150.00.99356.00026 249.40.00.00000.00081 247.00 101.00.80280.00771 249.00 151.00.99288.00020 249.50 1.00.00162.00172 247.30 102.00.81009.00777 249.00 152.00.99395.00060 249.50 2.00.00345.00643 247.90 103.00.81833.00795 249.00 153.00.99407.00042 249.50 3.00.01449.01091 248.00 104.00.82598.00723 249.00 154.00.99479.00084 249.50 4.00.02528.01546 248.30 105.00.83279.00711 249.00 155.00.99575.00090 249.50 5.00.04541.02191 248.30 106.00.84020.00759 249.00 156.00.99658.00008 249.50 6.00.06909.02608 248.30 107.00.84797.00723 249.00 157.00.99590.00014 249.60 7.00.09757.03253 248.30 108.00.85466.00675 249.00 158.00.99686.00060 249.60 8.00.13414.04162 248.20 109.00.86147.00669 249.00 159.00.99710.00030 249.60 9.00.18080.04775 247.80 110.00.86805.00645 249.00 160.00.99745 -.00052 249.60 10.00.22965.05401 247.60 111.00.87438.00609 249.00 161.00.99606 -.00022 249.70 11.00.28882.05523 247.00 112.00.88024.00609 249.00 162.00.99701.00066 249.70 12.00.34012.05455 247.00 113.00.88657.00609 249.00 163.00.99737.00042 249.70 13.00.39792.05584 246.70 114.00.89243.00586 249.00 164.00.99785.00036 249.70 14.00.45180.05412 246.60 115.00.89828.00538 249.00 165.00.99809.00030 249.70 15.00.50617.05081 246.30 116.00.90318.00532 249.00 166.00.99845.00042 249.70 16.00.55342.04780 246.30 117.00.90892.00544 249.00 167.00.99892.00042 249.70 17.00.60177.04682 246.20 118.00.91406.00496 249.00 168.00.99928.00018 249.70 18.00.64706.04424 246.20 119.00.91884.00472 249.00 169.00.99928.00030 249.70 19.00.69026.04234 246.20 120.00.92350.00448 249.00 170.00.99988.00030 249.70 20.00.73174.04044 246.20 121.00.92780.00454 249.00 171.00.99988.00006 249.70 21.00.77114.03700 246.20 122.00.93258.00448 249.00 172.00 1.00000.00006 249.70 22.00.80575.03400 246.30 123.00.93676.00406 249.00 23.00.83913.02866 246.30 124.00.94071.00400 249.00 24.00.86307.02301 246.70 125.00.94477.00370 249.00 25.00.88516.02154 246.90 126.00.94812.00293 249.00 26.00.90615.01902 247.00 127.00.95063.00265 249.00 27.00.92321.01319 247.20 128.00.95341.00301 249.10 28.00.93253.01227 247.70 129.00.95664.00305 249.10 29.00.94774.01276 247.80 130.00.95951.00299 249.10 30.00.95804.00950 248.00 131.00.96261.00293 249.10 31.00.96675.00735 248.20 132.00.96536.00217 249.10 32.00.97275.00656 248.50 133.00.96695.00187 249.20 33.00.97986.00471 248.60 134.00.96910.00257 249.20 34.00.98217.00416 248.90 135.00.97209.00251 249.20 35.00.98819.00503 248.90 136.00.97412.00215 249.20 36.00.99223.00331 249.00 137.00.97639.00221 249.20 37.00.99480.00239 249.10 138.00.97855.00109 249.20 38.00.99700.00196 249.20 139.00.97858.00127 249.30 39.00.99871.00042 249.30 140.00.98109.00203 249.30 40.00.99783 -.00050 249.50 141.00.98265.00131 249.30 41.00.99770 -.00001 249.60 142.00.98372.00143 249.30 42.00.99781 -.00007 249.70 143.00.98551.00173 249.30 43.00.99756 -.00044 249.80 144.00.98719.00091 249.30 44.00.99693.00006 249.90 145.00.98734.00068 249.40 45.00.99767.00068 249.90 146.00.98854.00114 249.40 46.00.99828.00055 249.90 147.00.98961.00125 249.40 47.00.99877.00049 249.90 148.00.99105.00137 249.40 48.00.99926.00037 249.90 149.00.99236.00125 249.40 49.00.99951.00025 249.90 50.00.99975.00025 249.90 51.00 1.00000 -.00080 249.90 NORMALIZED DATA FROM RUN 37 NORMALIZED DATA FROM RUN 38 NORMALIZED DATA FROM RUN 38 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF MIN MIN-' OF MIN MIN-' OF.00.00000.00797 228.00.00.00000.00016 240.80 50.00.85779.01061 239.80.50.00797.01775 230.10 1.00.00033.00252 240.80 51.00.86834.00984 239.80 1.00.01775.03254 232.10 2.00.00504,.00376 240.80 52.00.87747.00922 239.90 1.50.04051.06244 233.50 3.00.00785.00457 240.90 53.00.88678.00943 239.90 2.00.08018.08128 234.20 4.00.01418.00639 240.90 54.00.89633.00906 239.90 2.50.12179.09324 235.00 5.00.02063.00689 240.90 55.00.90489.00761 239.90 3.00.17342.10474 235.40 6.00.02795.00806 240.90 56.00.91155.00641 240.00 3.50.22653.11139 235.80 7.00.03676.00912 240.90 57.00.91770.00711 240.10 4.00.28481.11937 236.00 8.00.04619.01042 240.90 58.00.92577.00726 240.10 4.50.34590.11451 236.10 9.00.05760.01185 240.90 59.00.93222.00658 240.10 5.00.39932.10814 236.60 10.00.06989.01290 240.90 60.00.93892.00556 240.10 5.50.45404.10854 236.90 11.00.08341.01510 240.90 61.00.94334.00442 240.20 6.00.50786.10720 237.10 12.00.10009.01754 240.80 62.00.94776.00291 240.30 6.50.56124.10438 237.40 13.00.11850.01823 240.70 63.00.94915.00355 240.50 7.00.61224.10036 237.70 14.00.13654.01984 240.60 64.00.95486.00509 240.50 7.50.66160.09369 238.00 15.00.15818.02247 240.50 65.00.95933.00351 240.50 8.00.70593.09159 238.50 16.00.18147.02348 240.30 66.00.96188.00262 240.60 8.50.75319.08742 238.70 17.00.20514.02327 240.10 67.00.96456.00289 240.70 9.00.79334.07820 239.10 18.00.22802.02248 240.00 68.00.96767.00329 240.70 9.50.83140.06928 239.40 19.00.25010.02304 240.00 69.00.97114.00347 240.70 10.00.86262.05605 239.90 20.00.27410.02409 239.90 70.00.97461.00246 240.70 10.50.88745.04861 240.50 21.00.29829.02370 239.90 71.00.97605.00165 240.80 11.00.91123.04473 241.00 22.00.32149.02453 239.90 72.00.97791.00217 240.80 11.50.93218.03892 241.50 23.00.34735.02478 239.80 73.00.98040.00217 240.80 12.00.95015.03058 242.00 24.00.37105.02357 239.80 74.00.98226.00174 240.80 12.50.96275.02491 242.60 25.00.39450.02345 239.80 75.00.98387.00199 240.80 13.00.97506.01999 243.10 26.00.41795.02333 239.80 76.00.98623.00066 240.80 13.50.98274.01403 243.70 27.00.44115.02264 239.80 77.00.98519.00041 240.90 14.00.98909.01090 244.20 28.00.46323.02329 239.80 78.00.98705.00161.240.90 14.50.99364.01091 244.70 29.00.48772.02291 239.70 79.00.98841.00124 240.90 15.00 1.00000.00509 245.00 30.00.50906.02217'239.70 80.00.98953.00099 240.90 31.00.53206.02236 239.60 81.00.99040.00099 240.90 32.00.55377.02103 239.60 82.00.99151.00093 240.90 33.00.57412.02091 239.60 83.00.99226.00112 240,90 34.00.59559.02078 239.60 84.00.99375.00074 240.90 35.00.61569.02016 239.60 85.00.99375.00037 240.90 36.00.63591.02010 239.60 86.00.99449.00081 240.90 37.00.65589.01917 239.60 87.00.99536.00031 240.90 38.00.67425.01867 239.60 88.00.99511.00031 240.90 39.00.69323.01867 239.60 89.00.99598.00043 240.90 40.00.71160.01836 239.60 90.00.99598.00031 240.90 41.00.72996.01805 239.60 91.00.99660.00043 240.90 42.00.74770.01642 239.60 92.00.99685.00019 240.90 43.00.76279.01518 239.70 93.00.99697.00025 240.90 44.00.77806.01551 239.70 94.00.99734.00012 240.90 45.00.79381.01520 239.70 95.00.99722.00012 240.90 46.00.80845.01458 239.70 96.00.99759.00114 240.90 47.00.82297.01319 239.70 97.00.99950.00089 240.80 48.00.83484.01207 239.80 98,00.99938.00019 240.80 49.00.84712.01148 239.80 99.00 99988.00025 240.80 100.00.99988.00000 240.80 101.00.99988.00006 240,80 102.00 1.00000 -.00031 240.80

-280NORMALIZED DATA FROM RUN 39 NORMALIZED DATA FROM RUN 39 (CONT'D) NORMALIZED DATA FROM RUN 40 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN~- OF MIN MIN-' OF MIN MIN-' OF.00.00000.00052 238.70 50.00.99216.00052 240.80.00.00000.00451 232.70 1.00.00104.00355 239.10 51.00.99293.00052 240.90.50.00451.00646 233.30 2.00.00710.00574 239.30 52.00.99319.00096 241.00 1.00.00646.00465 234.20 3.00.01251.00657 239.60 53.00.99486.00154 241.00 1.50.00916.00959 235.00 4.00.02024.01010 239.80 54.00.99627.00122 241.00 2.00.01606.01864 235.60 5.00.03271.01466 239.90 55.00.99730.00090 241.00 2.50.02779.02720 235.90 6.00.04956.01787 239.90 56.00.99807.00096 241.00 3.00.04326.03263 236.10 7.00.06846.02096 239.90 57.00.99923.00006 241.00 3.50.06043.03299 236.20 8.00.09147.02424 239.90 58.00.99820 -.00019 241.10 4.00.07625.03915 236.60 9.00.11693.02629 239.90 59.00.99884.00013 241.10 4.50.09958.04881 236.60 10.00.14406.03072 239.90 60.00.99846.00019 241.10 5.00.12506.04953 236.60 11.00.17837.03323 239.60 61.00.99923.00058 241.10 5.50.14911.04890 236.70 12.00.21052.03471 239.60 62.00.99962.00032 241.10 6.00.17396.05353 236.80 13.00.24779.03830 239.40 63.00.99987.00013 241.10 6.50.20263.05775 236.70 14.00.28712.03939 239.10 64.00.99987 -.00064 241.10 7.00.23171.05739 236.60 15.00.32657.03805 238.90 65.00.99859 -.00058 241.20 7.50.26003.05569 236.60 16.00.36322.03786 238-.90 66.00.99872.00045 241.20 8.00.28740.05501 236.60 17.00.40230.03953 238.80 67.00.99949 -.00045 241.20 8.50.31504.05690 236.60 18.00.44228.03934 238.70 68.00.99782 -.00090 241.30 9.00.34430.05852 236.60 19.00.48097.03940 238.60 69.00.99769.00019 241.30 9.50.37356.05865 236.60 20.00.52107.03921 238.50 70.00.99820.00039 241.30 10.00.40295.05906 236.60 21.00.55938.03696 238.40 71.00.99846 -.00071 241.30 10.50.43261.05946 236.60 22.00.59500.03504 238.40 72.00.99679 -.00064 241.40 11.00.46241.05973 236.60 23.00.62945.03253 238.40 73.00.99717 -.00064 241.40 11.50.49234.05960 236.60 24.00.66005.03009 238.40 74.00.99550 -.00109 241.50 12.00.52201.05879 236.60 25.00.68963.02893 238.40 75.00.99499 -.00006 241.50 12.50.55113.05798 236.60 26.00.71791.02829 238.40 76.00.99537.00026 241.50 13.00.57998.05676 236.60 27.00.74620.02636 238.40 77.00.99550.00006 241.50 13.50.60789.05488 236.60 28.00.77064.02463 238.50 78.00.99550 -.00026 241.50 14.00.63486.05285 236.60 29.00.79545.02366 238.50 79.00.99499 -.00006 241.50 14.50.66075.05151 236.60 30.00.81796.02142 238.60 HO.10.99537.00019 241.50 15.00.68637.04840 236.60 31.00.83828.01891 238.70 81.00.99537.00051 241.50 15.50.70915.04625 236.60 32.00.85579.01852 238.90 82.00.99640.00064 241.50 16.00.73261.04517 236.60 33.00.87533.01807 238.90 83.00.99666.00026 241.50 16.50.75432.04355 236.60 34.00.89192.01576 239.00 84.00.99691.00039 241.50 17.00.77616.04076 236.60 35.00.90684.01332 239.10 85.00.99743.00077 241.50 17.50.79509.03546 236.70 36.00.91856.01184 239.30 86.00.99846.00045 241.50 18.00.81163.03501 236.90 37.00.93052.01215 239.40 87.00.99833 -.00013 241.50 18.50.83010.03312 236.90 38.00.94286.01003 239.40 88.00.99820 -.00006 241.50 19.00.84475.02741 237.10 39.00.95059.00740 239.60 89.00.99820.00026 241.50 19.50.85751.02583 237.30 40.00.95767.00695 239.80 90.00.99871.00064 241.50 20.00.87058.02844 237.60 41.00.96449.00637 239.90 91.00.99949.00051 241.50 20.50.88595.02980 237.60 42.00.97041.00553 240.00 92.00.99974.00000 241.50 21.00.90038.02476 237.60 43.00.97555.00450 240.10 93.00.99949.00006 241.50 21.50.91071.01985 237.80 44.00.97941.00489 240.20 94.00.99987.00013 241.50 22.00.92023.02062 238.00 45.00.98533.00258 240.20 95.00.99974 -.00006 241.50 22.50.93133.01769 238.10 46.00.98457.00078 240.50 96.00.99974 -.00006 241.50 23.00.93792.01409 238.40 47.00.98688.00199 240.60 97.00.99961.00013 241.50 23.50.94542.01233 238.60 48.00.98856.00251 240.70 98.00 1.00000 -.00058 241.50 24.00.95026.01229 238.90 49.00.99190.00180 240.70 24.50.95771.01554 239.00 NORMALIZED DATA FROM RtjN 40 (CONT'D) NORMALIZED DATA FROM RUN 41 NORMALIZED DATA FROM RUN 41 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN_' OF MIN MIN'' OF MIN MIN'' OF 25.00.96580.01221 239.00.00.00000.00076 156.10 25.00.75328.03187 232.00 25.50.96992.00666 239.20.50.00076.00441 165.60 25.50.76858.02913 232.10 26.00.97247.00689 239.50 1.00.00441.00144 173.70 26.00.78241.02857 232.30 26.50.97682.01028 239.60 1.50.00220 -.00177 181.20 26.50.79716.02907 232.40 27.00.98275.00762 239.60 2.00.00264.00163 187.40 27.00.81148.02444 232.50 27.50.98444.00298 239.80 2.50.00384.00542 193.00 27.50.82159.02326 232.80 28.00.98573.00520 240.00 3.00.00806.00448 197.80 28.00.83474.02538 232.80 28.50.98964.00597 240.00 3.50.00832.00676 202.30 28.50.84697.02306 232.90 29.00.99170.00317 240.10 4.00.01483.00403 205.80 29.00.85780.02110 233.00 29.50.99281 -.00013 240.20 4.50.01235.00039 209.40 29.50.86807.01970 233.10 30.00.99157.00118 240.50 5.00.01522.00612 212.30 30.00.87750.01844 233.20 30.50.99400.00445 240.50 5.50.01847 -.00053 214.70 30.50.88651.01598 233.30 31.00.99602 -.00097 240.50 6.00.01468 -.00554 217.30 31.00.89348.01254 233.50 31.50.99302 -.00097 240.80 6.50.01293.00364 219.50 31.50.89906.01360 233.70 32.00.99504.00324 240.80 7.00.01833.00141 221.00 32.00.90709.01438 233.80 32.50.99626.00324 240.80 7.50.01433.00088 222.90 32.50.91344.01340 233.90 33.00.99828.00098 240.80 8.00.01921.00504 224.10 33.00.92049.01215 234.00 33.50.99724 -.00168 240.90 8.50.01937.01161 225.60 33.50.92559.01103 234.10 34.00.99660.00084 241.00 9.00.03081.01355 226.20 34.00.93152.00885 234.20 34.50.99808.00216 241.00 9.50.03292.01873 227.50 34.50.93443.00801 234.40 35.00.99875 -.00037 241.00 10.00.04954.03197 227.90 35.00.93953.00879 234.50 35.50.99771 -.00037 241.10 10.50.06489.03814 228.50 35.50.94322.00669 234.60 36.00.99838.00148 241.10 11.00.08768.04374 228.70 36.00.94622.00585 234.70 36.50.99919.00081 241.10 11.50.10863.04829 229.10 36.50.94907.00571 234.80 37.00.99919.00081 241.10 12.00.13597.05306 229.20 37.00.95193.00459 234.90 37.50 1.00000 -.00078 241.10 12.50.16169.05426 229.40 37.50.95366.00551 235.00 13.00.19022.05306 229.40 38.00.95744.00481 235.00 13.50.21475.05116 229.70 38.50.95848.00355 235.10 14.00.24139.05461 229.80 39.00.96099.00235 235.10 14.50.26936.05447 229.80 39.50.96083.00397 235.30 15.00.29586.05356 229.90 40.00.96497.00448 235.20 15.50.32292.05454 230.00 40.50.96530.00350 235.30 16.00.35040.05426 230.10 41.00.96846.00392 235.20 16.50.37717.05328 230.20 41.50.96922.00081 235.30 17.00.40367.04870 230.30 42.00.96928 -.00193 235.40 17.50.42588.04920 230.70 42.50.96729 -.00003 235.60 18.00.45287.05265 230.70 43.00.96925 -.00101 235.60 18.50.47853.05399 230.80 43.50.96629 -.00156 235.80 19.00.50687.05209 230.70 44.00.96769.00062 235.80 19.50.53063.04922 230.90 44.50.96690.00006 235.90 20.00.55608.04930 230.90 45.00.96774.00020 235.90 20.50.57992.04734 231.00 45.50.96710 -.00171 236.00 21.00.60342.04594 231.00 46.00.96604 -.00022 236.10 21.50.62586.04376 231.10 46.50.96688.00274 236.10 22.00.64719.03857 231.20 47.00.96878.00070 236.00 22.50.66443.03549 231.50 47.50.96758 -.00050 236.10 23.00.68268.03691 231.60 48.00.96828.00028 236.10 23.50.70134.03487 231.70 48.50.96786.00056 236.10 24.00.71755.03537 231.90 49.00.96884.00112 236.10 24.50.73671.03573 231.90 49.50.96898.00042 236.10

-281NORMALIZED DATA FROM RUN 41 (CONT'D) NORMALIZED DATA FROLM RUrN 42 lURti',LLIZED DATA FRO;"i RUN 42 (CONT'D) TIME ALPHA RATE TEMP. T IE ALPHA RATE TMP.' ImE ALPHA RATE TEAMP. MI\ MIN~1 OF IMU HIN ION I' A P I N MI N r' 0 - 50.00.96926.00056 236.10.00 00.000(.0D110 240.(80 500.00.62146.001827 240.30 50.50.96954.00028 236.10 10.00.00110.000086 240.70 510.00.64010.001777 240.30 51.00.96954.00000 236.10 20.00.00 172.000058 240.70 20.00 (0.65701.001551 240.30 51.50.96954.00014 236.10 30.00.00226.000051 240.HO 530.00.67113.001539 240.50 52.00.96968.00042 236.10 40.00.00275 -.000022 240.80 540.00.68779.001568 240.50 52.50.96996.00056 236.10 50.00.00182.000016 240.90 550.00.70248.001421 240.50 53.00.97024.00000 236.10 60.00.00306.000111 240.90 560.00.71621.001353 240.60 53.50.96996.00000 236.10 70,00.00404.000182 240.90 570.00.72954.001352 240.60 54.00.97024.00014 236.10 80.00.1) 00670.10()256 240.80 580.00.74324.001309 240.60 54.50.97010.00162 236.10 90.00.00917.000235 240.80 590.00.75571.001185 240.60 55.00.97186.00042 236.00 100.00.01139.000240 24(0.80 600.00.76694.001035 240.60 55.50.97051 -.00162 236.10 R110.00.01398.00027H 240.80 610.00.77641.001181 240.50 56.00.97024.02949 236.10 120.00.01695.000346 2410.80 620.00.79056.001220 240.30 56.50 1.00000.00162 234.10 130.00.02090.000395 240.80 630.00.80081.000987 240.30 140.00.02485.000420 240.80 640.00.81031.000870 240.30 150.00.02929.000549 240.80 650.00.81821.000771 240.30 160.00.03583.000679 240.80 660.00.82574.000728 240.30 170.()0.04287.000740 240.80 670.00.83278.000558 240.30 180.00.05064.000740 240.80 680.00.83689.000514 240.50 190.00.0576h.000852 241.00 690.00.84306.000617 240.50 200.00.06767.001].067 241.00 700.00.84923.000352 240.50 210.00.07903.001173 241.00 710.00.85010.000291 240.80 220.00.9113.001253 241.00 720.00.85504.000445 240.80 230.)0.10409.001333 241.00 730.00.85899.000497 240.80 240.00.11779.001462 241.00 7401.00.86498.000575 240.70 250.()0.13334.001506 240.80 750.00.87050.000461 240.60 260.00.14791.0()01555 2410.80 760.00.87420.000405 240.60 270.0. 16445.001653 240.80 770.00.87861.000400 240.50 280.00.1098.0(01653 2410.80 780.00.88219.000334 240.50 290.)0.19752.001741 24().80 790.00.88528.000339 240.50 300.00.21579.001864 240.80 800.()0.88898.000466 240.50 310.00.23480.001925 240.80 810.00.89461.000423 240.30 320.00.25430.001901 240.80 820.00.89745.000272 240.30 330.00.27282.001966 240.80 830.00.90005.000107 240.30 340.00.29363.1)02028 240.70 840.00.89959.000053 240.50 350.00.31338.002045 240.70 850.00.90111.000169 240.60 36(0.00.334D3.002179 240.50 860.)0.90296.000150 240.60 370.00.35695.002108 240.30 870.00.90411.000157 240.70 380.00.37670.002036 240.30 880.00.90609.000197 240.70 390.00.39768.002141 240.20 890.00.90806.000257 240.70 400.00.41952.002123 240.20 900.001).91123.000245 240.60 410.00,().44014.002055 240.20 910.00.91296.000173 240.60 420.00.46062.002080 240.20 920.00.91469.000144 240.60 430.00.48173.002105 240.20 930.00.91584.000156 240.70 440.00.40271.002062 240.20 940.00.91781.000166 240.70 450.00.52296.002024 240.20 950.00.91917.000179 240.70 460.00.5432(.002011 240.20 960.00.92139.000238 240.70 470.00.56319.002036 240.20 970.00.92394.000226 240.60 480.00.58393.002018 240.20 980.00.92592.000167 240.60 490.00.60356.001877 240.20 990.00.92728.000093 240.60 NJRIALI ZEi) DATA FROM RoN 42 (COl\T'(')) I(')1RMALIZED DATA FROUM RUN 42 (COlT'D) NORMALIZED DATA FROM RUN 43 TIME ALPHA RATE TEi P. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN I - OF I I N - F i I N MIN-' OF 1000.00.92777.1)0058 240.60 1500.00.99649.000003 241.00.00.00000.00066 240.70 1010.00.92843.000119 240.70 1510.00.99723.000049 241.00 1.00.00132.00145 240.70 1020.00.93016.000142 240.70 1520.00.99747.000031 241.00 2.00.00290.00170 240.70 1030.00.93127.000135 240.70 1530.00.99784.000031 241.00 3.00.00473.0015.8 240.70 1040.00.93287.000179 240.70 1540.00.99-809.000077 241.00 4.00.00607.00176 240.70 1050.00.93485.000130 240.70 1550.00.99938.000096 240.90 5.00.00826.00219 240.70 1060.00.93546.000070 240.70 1560.00 1.001)00.000031 240.90 6.00 (.01045.00255 240.70 1070.00.93625.000095 240.80 7.00.01337.00336 240.70 1080.00.93736.000186 240.80 8.(10.01716.00312 240.60 1090.00.93996.000204 240.80 9.()0.01960.00336 240.60 1100.00.94144.000117 240.80 10.00.02388.00385 240.50 1110.00.94230.000124 240.80 11.00.02729.00347 240.50 1120.00.94391.000244 240.80 12.00.03082.00341 240.50 1130.00.94719.000257 240.70 13.00.03410.00353 240.50 1140.00.94904.000161 240.70 14.00.03787.00371 240.50 1150.00.95040.000192 240.70 15.00.04152.00401 240.50 1160.00.95287.000222 240.70 16.00.04590.00408 240.50 1170.00.95484.000107 240.70 17.00.04968.00414 240.50 1180.00.95501.000061 240.80 18.00.05418.00462 240.50 1190.00.95606.000127 240.90 19.00.05892.00493 240.50 1200.00.95754.000089 240.90 20.00.06403.00523 240.50 1210.00.95785.000083 241.00 21.00.06938.00493 240.50 1220.00.95921.000155 241.00 22.00.07389.00511 240.50 1230.00.96094.100155 241.00 23.00.07960.00578 240.50 1240.00.96230.000185 241.00 24.00.08544.00572 240.50 1250.00.96464.000203 241.00 25.00.09104.00627 240.50 1260.00.96637.000179 241.00 26.00.09797.00675 240.50 1270.00.96822.000172 241.00 27.00.10454.00651 240.50 1280.00.96982.000155 241.00 28.00.11099.00657 240.50 1290.00.97131.000173 241.00 29.00.11768.00657 240.50 1300.00.97328.000216 241.00 30.00().12413.00687 240.50 1310.00.97563.000210 241.00 31.00.13143.00712 240.50 1320.00.97748.000197 241.00 32*00.13837.00724 240.50 1330.00.97958.000172 241.00 33.00.14591.00724 240.50 1340.00.98093.000130 241.00 34.00.15284.00742 240.50 1350.00.98217.000118 241.00 35.00.16075.00773 240.50 1360.00.98328.000142 241.00 36.00).16829.00797 240.50 1370.00.98501.000161 241.00 37.00.17669.00827 240.50 1380.00.98649.000135 241.00 38.00.18484.00815 240.50 139(.00.98772.000130 241.00 39.10.19299.00827 240.50 1400,00.98908.000124 241.00 40.00.20139.00839 240.50 1410.00.99019.000087 241.00 41.00.20978.01049 240.50 1420.00.99081.000055 241.00 42.00.22237.01055 240.30 1430.00.99130.000074 241.0( 43.00.23088.((900 240.30 1440.00.99229.000142 241.00 44.100).24037.00931 240.30 1450.00.99414.000124 241.00) 45.()0.24950(.01017 240.30 1460.00.99476.000)133 241.00 46.00.26()71.01035 240.20) 1470.00(.99679.000((107 24(.90 47.00.27020.0()925 240.20 1480.00.99691.000018 240(1.90 48.001.27921.0()0943 240.20 1490.00.99716 -.000021 240.90( 49,00.28906.(00992 240.20

-282NORMALIZEI) DATA FROM RUN 43 (C.ONT'I)) NORMALIZ 1) DATA FRU, kRiU 43 (C +. [j \i\T)' OmRiALIZED DATA FROM RUN 43 (CONT'D) TIME ALPHA RATE T EMP. TIME ALPHA RATE TFP. TI, ALPHA RATE TEMP. MIN MHI N OF MIN HI rN - 0F HI \ | ~IN- 1 OF 50.00.29904.00998 240.20 100.00.73565.00700 240.30 150.00.94420.00182 240.20 51.00.30901.00979 240.20 101.00.74210.00681 240.30 151.00.94615.00195 240.20 52.00.31862.00973 240.20 102.00.74928.00712 240.30 152.00.9481.).00164 240.20 53.00.32848.01010 240.20 103.00.75633.00750 240.30 153.00.94944.00146 240.20 54.00.33882.01034 240.20 104.00.76427.00737 240.20 154.00.95102.00176 240.20 55.00.34916.01004 240.20 105.00.77108.0(0639 240..20 155.00.95296.00263 240.20 56.00.35889.00979 240.20 106.00.77704.0(0627 240.20 156.00.95627.00239 240.10 57.00.36875.010)34 240.20 107.00.78361.00602 240.20 157.00 95773.00152 240.10 58.00.37958.01046 240.20 1(8.0O.78909.00566 240.20 158.00(.95932..00140 240.10 59.00.38967.1109( 240.20 109.00.'79493.00578 240.20 159.00.96053.00152 240.10 60.00.40138.01072 240.10 110.00.80064.00584 240.20 160.00.96236.00146 240.10 61.00.41111.01022 240.10 111.00.80661.00602 240.20 161.10.96345 00122 240.10 62.00.42182.01071 240.10 112.00.81269.00572 240.20 162.00.96479.00116 240.10 63.00.43252.01022 240.10 113.00.81804.00541 240.20 163.00.96576.00109 240.10 64.00.44226.00992 240.10 114.00.82352.00523 240.20 164.00.96698.00134 240.10 65.00.45236.00992 240.10 115.00.82850.00505 240.20 165.00.96844.00103 240.10 66.00.46209.00992 240.10 116.(00.83361.00462 240.20 166.00.96905.00079 240.10 67.00.47219.01004 240.10 117.00.83775.00468 240.20 167.00.97002.00122 240.10 68.00.48216.00973 240.10 118.00.84298.00487 240.20 168.00.97148.00109 240.10 69.00.49165.00949 240. 10 119.00.84748.00487 240.20 169.00.97221.00085 240.10 70.00.50114.00961 240.10 120.00.85272.00511 240.20 1(oP.00.97319.00091 240.10 71.00.51087.00937 240.10 121.00.85770.00487 240.20 171.00.97404.00091 240.10 72.00.51988.00802 240.10 122.00.86245.00450 240.20 172.00.97501.00091 240.10 73.00.52691.00783 240.20 123.00.86671.00462 240.20 173.00.97586.(00091 240.10 74.00.53555.00833 240.20 124.00.87169.00444 240.20 174.00.97683.00085 240.10 75.00.54358.00839 240.20 125.00.87559.00359 240.20 175.00.97756.00079 240.10 76.00.55234.00852 240.2(0 126,00.87887.00347 240.20 176.00.97842.00079 240.10 77.00.56061.00858 240.20 127.00.88252.00389 240.20 177.00.97915.00067 240.10 78.00.56949.00882 240.20 128.00.88666.00395 240.20 178.00.97975.00073 240.10 79.00.57825.00765 240.20 129.00.89043.00377 240.20 179.00.98061.00055 240.10 80.00.58479.00759 240.30 130.0O.89420.00365 240.20 180.(0O.98085.00061 240.10 81.00.59343.00809 240.30 131.00.89773.00359 240.20 181.00.98182.00061 240.10 82.00.60097.00803 240.30 132.00.90138.00316 240.20 182.00.98207.00049 240.10 83.00.60949.00821 240.30 133.0(0.90406.00292 240.20 183.00.98280.00061 240.10 84.00.61740.00827 240.30 134.00.90722.00304 240.20 184.00.98328.00055 240.10 85.00.62604.00858 240.30 135.00.91014.00274 240.20 185.00.98389.00049 240.10 86.00.63455.00797 240.30 136.00.91269.00268 240.20 186.00.98426.00067 240.10 87.00.64197.00742 240.30 137.00.91549.00262 240.20 187.00.98523.00067 240.10 88.00.64939.00791 240.30 138.00.91793.00249 240.20 188.00.98559.00061 240.10 89.00.65779.00766 240.30 139.00.92048.00255 240.20 189.00.98645.00264 240.10 90.00.66472.00736 240.30 140.00.92304.00219 240.20 190.00.99088.00221 239.90 91.00.67251.00754 240.30 141.00.92486,00225 240.20 191.00.99088.00030 239.90 92.00.67981.00748 240.30 142.00.92754.00243 240.20 192.00.99148.00030 239.90 93.00.68747.00773 240.30 143.00.92973.00225 240.20 193.00.99148.00024 239.90 94.00.69526.00724 240.30 144.00.93204.00207 240.20 194.00.99197.00024 239.90 95.00.70195.00675 240.30 145.00.93386.00225 240.20 195.00.99197.00043 239.90 96.00.70876.00681 240.30 146.00.93654.00225 240.20 196.00.99282.00043 239.90 97.00.71558.00620 24(0.30 147.00.93836.00195 240.20 197.00.99282.00049 239.90 98.00.72117.00627 240.30 148.00.94043.00207 240.20 198.00.99380.00055 239.90 99.00.72811.00724 240.30 149.00.94250.00189 240.20 199.00.99392.00018 239.90 NORMALIZED DATA FROM RUN 43 (CONT'D) NORMALIZED) DATA FROM RUN 44 NORMALIZED DATA FROM RUN 44 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIM iE ALPHA RATE TEMP. IM N IN' OF MIN MIN- OF MII OMIN' OF 200.00.99416.00012 239.90.00.00000.00034 240.90 100.00.42495.00549 240.90 201.00.99416.00000 239.90 2.00.00137.00147 240.90 102.00.43724.00574 240.80 202.00.99416.00018 239.90 4.00.00589.00232 240.90 104.00.44793.00518 240.80 203.00.99453.00024 239.90 6.00.01067.00251 240.90 106.00.45798.00531 240.80 204.00.99465.00024 239.90 8.00.01594.00264 240.90 108.10.46916.00540 240.80 205.00.99501.00036 239.90 10.00.02122.00267 240.90 110.00.47959.00521 240.80 206.00.99538.00024 239.90 12.00.02662.00280 240.90 112.00.49002.00518 240.80 207.00.99550.00(018 239.90 14.00.03240.00295 240.90 114.00.50032.00525 240.80 208.00.99574.00030 239.90 16.00.03844.00298 240.90 116.00.51100.00521 240.80 209.00.99611.00036 239.90 18.00.04434.00295 240.90 118.00.52118.00512 240.80 210.00.99647.00030 239.90 20.00.05025.00324 240.90 120.00.53148.00521 240.80 211.00.99672.00043 239.90 22.00.05728.00352 240.90 122.00.54204.00525 240.80 212.00.99732.00024 239.90 24.00.06432.00358 240.90 124.00.55247.00562 240.80 213.00.99720.00006 239. 90 26.00.07161.00368 240.90 126.00.56452.00527 240.70 214.00.99745.00024 239.90 28.00.07902.00364 240.90 12R.00.57356.00487 240.70 215.00.99769.00030 239.90 30.00.08618.00377 240.90 130.00.58399.00512 240.70 216.00.99805.00000 239.90 32.00.09410.00390 240.90 132.00.59404.00499 240.70 217.00.99769 -.00006 239.90 34.00.10177..00383 240.90 134.00.60397.00543 240.70 218.00.99793.00018 239.90 36.00.10943.00402 240.90 136.00.61577.00546 240.60 219.00.99805.00030 239.90 38.00.11785.00424 240.90 138.00.62582.00527 240.60 220.00.99854.00024 239.90 40.00.12639.00440 240.90 140.00.63686.00505 240.50 221.00.99854.00018 239.90 42.00.13544.00446 240.90 142.00.64603.00481 240.50 222.00.99891.00043 239.90 44.00.14424.00462 240.90 144.00.65609.00477 240.50 223.00.99939.00036 239.90 6.00.15391.00481 240.90 146.00.66513.00421 240.50 224.00.99963.00012 239.90 48.00.16346.00477 240.90 148.00.67294.00428 240.60 225.00.99963.00012 239.90 50.00.17301.00490 240.90 150.00.68224.00462 240.60 226.00.99988 -.00006 239.90 52.00.18306.00487 240.90 152.00.69141.00446 240.60 227.00.99951 -.00012 239.90 54.00.19249.00481 240.90 154.00.70008.00408 240.60 228.00.99963.00006 239.90 56.00.20229.00490 240.90 156.00.70775.00)399 240.60 229.00.99963.00018 239.90 58.00.21209.00499 240.90 158.00.71604.00443 240.60 230.00 1.00000 -.00068 239.90 60.00.22227.00506 240.90 160.00.72545.00443 240.50 62.00.23232.00493 240.90 162.00.73374.00390 240.50 64.00.24199.00499 240.90 164.00.74103.00368 240.50 66.00.25230.00515 240.90 166.00.74844.00374 240.50 68.(J0.26260.00515 240.90 168.(00.75598.00371 240.50 70.00.27291.00528 240.90 170.00.76327.00358 24(0.50 72.00.28371.00518 240.90 1.72.00.77031.00346 240.50 74.00.29364.00506 240.90 174.00.77709.00333 240.50 76.00.30394.00490 240.90 176.00.78362.00352 240.50 78.10.31324.00487 240.90 178.00.79116.00372 240.50 80.00.32342.00506 240.90 180.(0.79770.00411 240.50 82.00.33347.00493 24(0.90 1821. 0.80729.00454 240.730 84.00.34315.00493 240.901 144.00.1587.00367 240.20 86.00.35320.00493 240.90 186.1(10 2.222).00311 240.20 88.00.36287.00506 240.90 158.00.2H31.00)314 240.20 90.00.37343.00515 240.90 19(.1(1.3484.00295 240.20 92.00.38348.00512 240.90 192.00,oA().5 00298 240.20 94.00.39391.00518 240.90 194.0).4678.00305 240.20 96.00.40421.00534 240.90 196.00.oh244.11)1251) 240.2(1 98.00.41527.00518 240.90 198.00.5796.00276 240.20

-2835NORMALIZED DATA FROM RUN 44 (CUOIT'D) NORI.)mALIZED DATA) FROM RUN 44 (COoNT'I)) \ORMALIZ tED DAA PFRM RUN 45 TIME ALPHA RATE TE P. T I iE ALPHA RATE TE P. T I IE ALPHA RATE T EMP. MIN mil l- O - I \mI N-A IOF IM I HMI N -1 OF 200.00.86349.00261 240.20 300.00.99669.00038 240.20.00.00000.00056 240.10 202.00.86839.00270 240.20 302.00.99731.00022 240.20 1.00.00111.00185 240.10 204.00.87430.00286 240.20 304.00.99757.00013 240.20 2.00.00369.00360 240.10 206.00.87983.00258 240.20 306.00.99782 -.0()025 240.20 3.00.00831.00384 240.00 208.00.88H460.00242 240.20 30.00.99658 -.00025 240.30 4.00.01138.00283 240.00 210.00.88950.00239 240.20 310.00.99683.00022 240.30 5. )0.01396.00477 240.00 212.00.89415.00242 240.20 312.00.99746 -.00059 240.30 6.00.02092.00587 239.90 214.00I.89918.00232 240.2(0 314.00.99447 -.00078 240.50 7. (0.02571.00408 239.90 216.00.90345.01)210 240.20 316.00.99435.00006 240.50 8. O.02908.00525 240.00 218.00.90760.00201 240.20 318.00;99472.00()31 240.51O 9.0).03620.00670 240.00 220.00.91149.00217 240.20 320.00.99560.00035 240.50 10.03.04247.00765 240.00 222.00.91627.00210 240.20 322.00.99610.00013 240.50 11.00.05151.00876 239.90 224.E00.91991.00192 240.20 324.00.99610.00025 240.50 12.)0.105999.00897 239.90 226.00.92393.00)182 240.20 326.00.99711.00031 240.50 13.00.06945.00977 239.90 228.00.92720.00176 240.20 328.00.99736.00013 240.50 14.00.07952.01069 239.90 230.00.93097. 00179 240.20 330.00.99761.00013 240.50 15.00.09082.01124 239.90 232.00.93436.00166 240.20 332.00.99786.00019 240.50 16.10.10201.01275 239.90 234.00.93763.00160 240.20 334.00.99837.00035 240.50 17.00.11633.01327 239.80 236.00.94077.()0154 240.20 336.00.99925.00025 240.50 18.00.12854.01626 239.90 238.00.94379.00154 240.20 338.00.99937.00013 240.50 19.00.14886.01771 239.50 240.00.94693.()0151 240.20 340.)0.99975.00009 240.50 20.00.16397.01798 239.50 242.00.94982.00148 240.20 342.00.99975.00006 240.50 21.00.18482.01705 239.20 244.00.95283.00141 240.20 344.00.99789.00018 240.20 22.00.19807.01742 239.40 246.00.95547.00135 240.20 346.00.99813.00012 240.20 23.00.21966.01838 239.10 248.00.95824.00148 240.20 348.00.99838 -.00024 240.20 24.1)0.23482.01828 239.20 250.0().96138.00123 240.20 350.00.99718 -.00024 240.30 25.00.25622.02038 239.00 252.00.96314.0107 240.20 352.00.99742.00018 240.30 26.00.27558.01896 238.90 254.00.96565.100113 240.20 354.00.99791 -.00060 240.30 27.00.29413.01812 238.90 25 6.)00.97466.00094 240.20 356.0)0.99(502 -.00075 24(1.50 28.00.31182.01782 238.90 258.00.96942.00091 240.20 358.00.99490.00006 240.50 29.00.32976.01788 238.90 260.00.97130.00094 240.20 360.00.99527.00027 240.50 30.00.34757.01902 238.90 262.00.97319.00094 240.20 362.00.99399.00030 240.50 31.00.36779.01831 238.80 264.00 1.95(`)7.00094 240.20 364.00.99648.00012 240.50 32.00.38419.01831 238.90 266.00.97696.00091 240.20 366.00.99648.00024 240.50 33.00.40441.01874 238.80 2 68.00.97872.00091 24(). 20 368.00.99745.00027 240).50 34.00.42166.01898 238.90 270.00.98060).00079 240.20 370.()0.99757.00009 240.50 35.00.44237.01843 238.80 272.00.98186.00063 240).20 372.00.99782.00012 240.50 36.00.45852.01914 238.90 274.00.98311.00069 240.20 374.00.99806.)00018 240.50 37.00.48065.01957 238.70 27 6.00.95462.00()1079 240).20) 3746.)00.99854.00030 240. 50 38.00.49766.01979 238.80 278.100.9 8626.00069 240.20 378. 0(0 99927.00021 240.50 39.1)0.52022.01775 238.50 280.0().98739.00063 240.20 380.00).99939.00012 240.50 40.()0.53317.01735 238.80 282.00.98877.00044 240.20 382.00.99976.00009 240.50 41.00.55493.01939 238.60 284.00.9 915.0)1044 240.20 384.00.99979.01)006 240.50) 42.003.57194.01831 238.70 286.00.99()3.00053 240.20 386.00 1.00)00 -.00042 240.50 43.()0.59154.01757 238.60 288.00).99128.00038 240.20 44.00.60708.01816 238.70 290.1)00.99204.00041 240.20 45.00.62785.01600 238.50 292.00.99292.00057 240.20 46.00.63907.01628 238.80 294. ()00.99430.00050 240.20 47.00.66041.01597 238.50 296.00.99493.(0)1)38 240.20 48.00.67102.01286 238.80 298.00.99581.00044 240).2)0 49.00.68613.01736 238.80 NORMALIZED 0AT0A FROM W)1(8 45 (CONTT'D) NORMALIZED DATA 0FROM RU 45 (LUST'0) )3ORmALIZED DATA 8ROM RUN8 47 TI IE ALPHA RATE TEMIP. T I E ALPHA RATE T EMP. T IE ALPHA RATE TEMP. I N I IN- oF M I N M I N - OF I 1\1 MI N-' o 50.00.70575.01626 238.50 100.00.99349.00098 239.40.00.00000.00024 238.20 51.00.71865.01136 238.50 101.00.99602.00169 239.30 1.00.00047.00041 238.90 52.00.72846.01136 238.70 102.00.99688.00080 239.30 2.00).00082.00566 239.70 53.00.74136.01241 238.7)) 103.00.99761 -.00022 239.30 3.00.01180.01017 239.90 54.00.75328.01210 238.70 104.00.99644.00037 239.40 4.00.02115.01158 240.30 55.00.76557.01133 238.70 105.00.99835.00120 239.30 5.00.03497.01861 240.60 56.00.77594.01192 238.80 106.00.99884 -.00028 239.30 6.00.05838.02433 240.60 57.00.78940.01232 238.70 107.00.99779 -.00040 239.40 7.00.08363.02752 240.70 58.00.80058.01106 238.70 108.00.99803.00025 239.40 8.00.11341.03439 240.80 59.00.81152.01010 238.70 109.00.99828.00037 239.40 9.00.15242.041?5 240.60 60.00.82079.00973 238.80 110.00.99877.00043 239.40 10.00.19591.04831 240.50 61.00.83099.00912 238.80 111.00.99914 -.00053 239.40 11.00.24905.05218 240.00 62.00.83903.00977 238.90 112.00.99772.00018 239.50 12.00.30026.05416 239.80 63.00.85052.01029 238.80 113.00.99951.00114 239.40 13.00.35737.05761 239.40 64.00.85961.00897 238.80 114.00 1.00000.00025 239.40 14.00.41548.05552 239.00 65.00.86846.00777 238.80 15.0 o.40840.05158 238.90 66.00.87515.00780 238.90 16.00.5 863.04903 238.90 67.00.88406.00768 238.80 17.00. 56647.04721 238.90 68.00.89051.00697 238.90 18.00.61305.04726 238.90 69.00.89800.00694 238.90 19.00.66099.04581 238.70 70.00.90439.00663 238.90 20.00.70467.04205 238.70 71.00.91127.00651 238.90 21.00.74508.04003 238.70 72.00.91741.00608 238.90 22.00.78473.03718 238.70 73.00.92343.00577 238.90 23.00.81943.03378 238.80 74.00.92896.00571 238.90 24.00.85229.03063 238.80 75.00.93486.00522 238.90 25.00.88069.02714 238.90 76.00.93941.00479 238.90 26.00.90657.02277 239.00 77.00.94444.00396 238.90 27.00.92624.01556 239.20 78.00.94732.00359 239.00 28.00.93769.01298 239.70 79.00.95162.00448 239.00 29.00.95219.01221 239.90 80.00.95629.00405 239.00 30.00.96210.00825 240.20 81.00.95973.00338 239.00 31.00.96869.00551 240.60 82.00.96305.00350 239.00 32.00.97312.00694 241.00 83.00.96674.00267 239.00 33.00.98257.00778 241.00 84.00.96839.00236 239.10 34.00.98868.00313 241.10 85.00.97146.00224 239.10 35.00.98883.00241 241.50 86.00.97286.00187 239.20 36.00.99349.00199 241.50 87.00.97520.00095 239.20 37.00.99281 -.00033 241.80 88.00.97476.00162 239.30 38.00.99282.00126 242.00 89.00.97845.00199 239.30 39.)0.99534.00161 242.00 90.00.97874.00107 239.40 40.00.99604.00233 242.10 91.00.98059.00268 239.40 41.0)0 1.00000.00091 242.00 92.00.98410'.00280 239.30 93.00.98619.00178 239.30 94.00.98766.00147 239.30 95.00.98914.00218 239.30 96.00.99203.00154 239.20 97.00.99221.100058 239.30 98.00.99319.00092 239. 30. 99.00.99405.00015 239.30

-284NORMALIZED DATA FROM RUN 48 NORMALIZED DATA FROM RUN 48 CUNT'OD) NORMALIZED DATA FROM RUN 49 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN O MI MIN I oF MIN MIN-I OF.00.00000.00833 237.80 25.00.98642.00452 241.30.00.00000.00229 241.90.50.00833.00911 238.00 25.50.98781.00155 241.50 1.00.00457.00503 241.90 1.00.00911.00904 238.70 26.00.98796.00201 241.80 2.00.01006.00748 242.00 1.50.01737.01682 239.00 26.50.98981.00544 241.90 3.00.01953.01054 242.00 2.00.02593.02537 239.40 27.00.99340.00429 241.90 4.00.03114.01313 242.00 2.50.04274.03605 239.40 27.50.99410.00164 242.00 5.00.04578.01647 242.00 3.00.06198.03977 239.40 28.00.99505.00262 242.10 6.00.06408.02237 242.00 3,50.08251.04278 239.40 28.50.99672.00121 242.10 7.00.09053.02774 241.70 4.00.10476.04753 239.50 29.00.99625 -.00074 242.20 8.00.11956.03304 241.50 4.50.13004.05235 239.50 29.50,99597 -.00087 242.40 9.00.15660.03610 241.00 5.00.15711.05633 239.50 30.00.99538.00069 242.50 10.00.19175.03878 240.90 5.50.18636.05979 239.50 30.50.99666.00205 242.50 11.00.23416.04203 240.50 6.00.21690.06307 239.50 31.00.99743.00167 242.50 12.00.27581.04423 240.30 6.50.24943.06597 239.40 31.50.99833.00115 242.50 13.00.32263.04332 239.90 7.00.28287.06860 239.30 32.00.99859.00167 242.50 14.00.36244.04300 239.80 7.50.31804.06996 239.10 32.50 1.00000.00018 242.50 15.00.40863.04322 239.40 8.00.35282.06906 238.90 16.00.44889.04149 239.40 8.50.38710.06732 238.70 17.00.49161.04162 239.30 9.00.42014.06384 238.60 18.00.53212.04250 239.30 9.50.45094.06171 238.60 19.00.57661.04256 239.00 10.00.48186.06539 238.60 20.00.61725.04080 239.00 10.50.51633.06668 238.30 21.)0.65820.03947 238.90 11.00.54853.06332 238.30 22.00.69619.03616 238.90 11.50.57965.06063 238.20 23.00.73052.03212 238.90 12.00.60916.06211 238.20 24.00.76044.02935 239.10 12.50.64176.06173 238.00 25.00.78921.02566 239.10 13.00.67089.05722 238.00 26.00.81175.02335 239.40 13.50.69899.05479 238.00 27.00.83592.02159 239.50 14.00.72568.05196 238.00 28.00.85492.02080 239.80 14.50.75095.04927 238.00 29.00.87751.02007 239.80 15.00.77494.04573 238.00 30.00.89506.01805 240.00 15.50.79668.04053 238.10 31.00.91361.01411 240.00 16.00.81547.03868 238.20 32.00.92327.01143 240.50 16.50.83536.03553 238.20 33.00.93646.01111 240.60 17.00.85100.03064 238.40 34.00.94549.01044 240.90 17.50.86600.02774 238.60 35.00.95735.00966 240.90 18.00.87874.02929 238.90 36.00.96480.00760 241.10 18.50.89529.03098 238.90 37.00.97256.00640 241.20 19.00.90972.02467 239.00 38.00.97761.00612 241.40 19.50.91997.01778 239.20 39.00.98480.00296 241.40 20.00.92750.01863 239.60 40.00.98353.00246 241.80 20.50.93859.02115 239.70 41.00.98972.00347 241.80 21.00.94866.01736 239.80 42.00.99047.00214 242.00 21.50.95595.00962 240.00 43.00.99401.00341 242.00 22.00.95828.01079 240.50 44.00.99729.00278 242.00 22.50.96674.01332 240.50 45.00.99956.00136 242.00 23.00.97160.00907 240.70 46.00 1.00000.00006 242.10 23.50.97581.00889 240.90 24.00.98048.00747 241.00 24.50.98329.00593 241.20 NORMALIZED DATA FROM RUN 50 NORMALIZED DATA FROM RUN 50 ICONT'D) NORMALIZED DATA FROM RUN 51 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF M'IN MIN' oF MIN MIN'' OF.00.00000.00123 241.90 50.00.93942.00618 241.20.00.00000.00017 235.90 1.00.00246.00370 241.90 51.00.94374.00504 2 1.40 1.00.00034.00085 235.90 2.00.00741.00520 241.90 52.00.94949.00603 2-41.50 2.00.00170.00123 235.90 3.00.01285.00588 241.90 53.00.95580.00600 241.50 3.00.00280.00154 235.90 4.00.01916.00724 241.90 54.00.96149.00312 241.50 4.00.00477.00203 235.90 5.00.02732.00792 241.90 55.00.96203,00355 241.80 5.00.00686.00184 235.90 6.00.03499.01002 241.90 56.00.96859.00380 241.80 6.00.00846.00209 235.90 7.00.04736.01188 241.90 57.00.96963.00263 241.90 7.00.01104.00252 235.90 8.00.05875.01330 241.90 58.00.97384.00390 241.90 8.00.01350.00270 235.90 9.00.07396.01553 241.90 59.00.97743.00256 241.90 9.00.01645.00264 235.90 10.00.08980.01602 241.90 60.00.97897.00232 242.00 10.00.01879.00277 235.90 11.00.10600.02011 241.90 61.00.98206.00272 242.00 11.00.02198.00320 235.90 12.00.13001.02277 241.70 62.00.98441.00254 242.00 12.00.02518.00332 235.90 13.00.15154.02332 241.70 63.00.98713.00229 242.00 13.00.02862.00350 235.90 14.00.17666.02803 241.50 64.00.98899.00173 242.00 14.00.03219.00393 235.90 15.00.20760.02973 241.10 65.00.99060.00173 242.00 15.00.03649.00436 235.90 16.00.23612.02787 241.00 66.00.99245.00186 242.00 16.00.04092.00461 235.90 17.00.26334.02765 241.00 67.00.99431.00167 242.00 17.00.04571.00467 235.90 18.00.29142.02839 241.00 68.00.99579.00111 242.00 18.00.05026.00510 235.90 19.00.32012.02985 241.00 69.00.99654.00111 242.00 19.00.05591.00547 235.90 20.00.35111.02917 240.90 70.00.99802.00148 242.00 20.00.06120.00638 235.90 21.00.37845.02849 240.90 71.00.99951.00099 242.00 21.00.06866.00765 235.80 22.00.40808.02811 240.80 72.00 1.00000 -.00087 242.00 22.00.07650.00783 235.70 23.00.43468.02780 240.80 23.00.08433.00748 235.60 24.00.46369.02873 240.70 24.00.09146.00785 235.60 25.00.49215.02821 240.70 25.00.10003.00810 235.50 26.00.52011.02830 240.70 26.00.10765.00756 235.50 27.00.54875.02852 240.60 27.00.11515.00775 235.50 28.00.57714.02719 240.50 28.00.12314.00908 235.50 29.00.60312.02616 240.50 29.00.13331.00939 235.40 30.00.62947.02604 240.50 30.00.14192.00818 235.40 31.00.65520.02499 240.50 31.00.14966.00861 235.40 32.00.67945.02412 240.50 32.00.15913.00922 235.40 33.00.70345.02301 240.50 33.00.16810.00928 235.40 34.00.72547.02177 240.50 34.00.17769.00977 235.40 35.00.74700.02091 240.50 35.00.18765.00990 235.40 36.00.76728.01961 240.50 36.00.19748.01062 235.40 37.00.78621.01738 240.50 37.00.20888.01098 235.30 38.00.80205.01617 240.50 38.00.21945.01129 235.30 39.00.81856.01599 240.60 39.00.23147.01111 235.20 40.00.83403.01413 240.60 40.00.24167.01051 235.20 41.00.84683.01311 240.70 41.00.25249.01082 235.20 42.00.86025.01274 240.80 42.00.26331.01160 235.20 43.00.87231.01234 240.90 43.00.27569.01238 235.10 44.00.88493.01206 240.90 44.00.28807.01244 235.00 45.00.89643.01055 240.90 45.00.30057.01172 234.90 46.00.90602.00884 241.00 46.00.31151.01094 234.90 47.00.91412.00888 241.10 47.00.32245.01125 234.90 48.00.92377.00863 241.10 48.00.33401.01100 234.90 49.00.93137.00782 241.20 49.00.34446.01100 234.90

-285NORMALIZED DATA FROM RUN 51 (CONT'D) NORMALIZED DATA FROM RUN 51 (CONT'D) NORMALIZED DATA FROM RUN 51 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF MIN MIN-' OF MIN MIN-' OF 50.00.35602.01106 234.90 100.00.83360.00627 234.80 150.00.98705.00104 235.20 51.00.36659.01094 234.90 101.00.83963.00609 234.80 151.00.98792.00080 235.20 52.00.37790.01113 234.90 102.00.84577.00602 234.80 152.00.98865.00080 235.20 53.00.38884.01119 234.90 103.00.85167.00578 234.80 153.00.98951.00098 235.20 54.00.40027.01125 234.90 104.00.85733.00559 234.80 154.00.99062.00033 235.20 55.00.41134.01119 234.90 105.00.86286.00547 234.80 155.00.99016.00020 235.30 56.00.42265.01106 234.90 106.00.86827.00529 234.80 156.00.99103.00068 235.30 57.00.43347.01131 234.90 107.00.87343.00516 234.80 157.00.99152.00049 235.30 58.00.44527.01131 234.90 108.00.87860.00516 234.80 158.00.99201.00031 235.30 59.00.45609.01094 234.90 109.00.88'376.00486 234.80 159.00.99213.00037 235.30 60.00.46715.01113 234.90 110.00.88831.00486 234.80 160.00.99275.00068 235.30 61.00.47834.01106 234.90 111.00.89347.00424 234.80 161.00.99348.00049 235.30 62.00.48928.01191 234.90 112.00.89679.00443 234.80 162.00.99373.00025 235.30 63.00.50216.01197 234.80 113.00.90232.00498 234.80 163.00.99398.00043 235.30 64.00.51322.01113 234.80 114.00.90675.00418 234.80 164.00.99459.00049 235.30 65.00.52441.01076 234.80 115.00.91068.00381 234.80 165.00.99496.00043 235.30 66.00.53473.01051 234.80 116.00.91437.00393 234.80 166.00.99545.00043 235.30 67.00.54543.01057 234.80 117.00.91855.00430 234.80 167.00.99582.00037 235.30 68.00.55588.01063 234.80 118.00.92298.00400 234.80 168.00.99619.00012 235.30 69.00.56670.01070 234.80 119.00.92654.00357 234.80 169.00.99607.00049 235.30 70.00.57727.01076 234.80 120.00.93011.00350 234.80 170.00.99717 -.00584 235.30 71,00.58821.01094 234.80 121.00.93355.00326 234.80 171.00.98439.00006 235.30 72.00.59915.01082 234.80 122.00.93663.00235 234.80 172.00.99730.00658 235.30 73.00.60985.01076 234.80 123.00.93826.00235 234.90 173.00.99754.00037 235.30 74.00.62067.01057 234.80 124.00.94133.00307 234.90 174.00.99803.00031 235.30 75.00.63100.01027 234.80 125.00.94441.00295 234.90 175.00.99816.00025 235.30 76.00.64120.01033 234.80 126.00.94723,.00283 234.90 176.00.99852.00006 235.30 77.00.65165.01002 234.80 127.00.95006.00270 234.90 177.00.99828 -.00645 235.30 78.00.66124,.00971 234.80 128.00.95264.00258 234.90 178.00.98562 -.00621 235.30 79.00.67107.00990 234.80 129.00.95523.00270 234.90 179.00.98586.00658 235.30 80.00.68103.00947 234.80 130.00.95805.00246 234.90 180.00.99877.00670 235.30 81.00.69001.00910 234.80 131.00.96014.00234 234.90 181.00.99926.00025 235.30 82.00.69923.00940 234.80 132.00.96273.00227 234.90 182.00.99926.00031 235.30 83.00.70882.00922 234.80 133.00.96469.00215 234.90 183.00.99988.00037 235.30 84.00.71767.00867 234.80 134.00.96703.00221 234.90 184.00 1.00000 -.00072 235.30 85.00.72615.00848 234.'80 135.00.96912.00191 234.90 86.00.73463.00811 234.80 136.00.97084.00197 234.90 87.00.74238,.00781 234.80 137.00.97305.00197 234.90 88.00,75025.00762 234.80 138.00.97477.00119 234.90 89,00.75762,.00842 234.80 139.00,.97543.00100 235.00 90.00.76709.00781 234.80 140.00,.97678.00148 235.00 91.00.77324.00652 234.80 141.00.97838.00166 235.00 92.00.78012.00701 234.80 142.00.98010.00076 235.00 93.00.78725.00688 234.80 143.00.97989.00069 235.10 94.00.79389.00676 234.80 144.00.98149.00117 235.10 95.00.80078.00664 234.80 145.00.98222,.00111 235.10 96.00.80717.00664 234.80 146.00.98370.00063 235.10 97.00,.81405,.00670 234.80 147.00.98349,.00045 235.20 98.00.82057.00652 234.80 148.00,.98460.00117 235.20 99.00.82709.00652 234.80 149.00,.98583.00123 235.20 NORMALIZED DATA FROM'RUN 52 NORMALIZED DATA FROM RUN 52 (CONT'D) NORMALIZED DATA FROM RUN 52 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF MIN MIN-' OF MIN MIN' OF.00.00000.00045 235.80 50.00.51307.01219 234.90 100.00.90721.00388 234.90 1.00.00091.00189 235.80 51.00.52470.01219 234.90 101.00.91109.00406 234.90 2.00.00378.00313 235.80 52.00.53746,.01238 234.90 102.00.91534.00306 234.90 3.00.00716.00369 235.80 53.00.54946.01194 234.90 103.00.91721.00288 235.00 4.00.01116,.00406 235.80 54.00.56134.01188 234.90 104.00.92109.00356 235.00 5.00.01529.00356 235.80 55.00.57322.01150 234.90 105.00.92434.00331 235.00 6.00.01829.00456 235.80 56.00.58435.01144 234.90 106.00.92772.00175 235.00 7.00,.02441.00569 235.80 57.00,.59610.01132 234.90 107.00.92785.00188 235.20 8.00,.02967.00550 235.80 58.00.60698.01082 234.90 108.00.93147.00350 235.20 9.00,.03542,.00569 235.80 59.00,.61773.01069 234.90 109.00.93485.00325 235.20 10.00.04104.00625 235.80 60.00.62836.01063 234.90 110.00.93798.00300 235.20 11.00.04792.00706 235.80 61.00.63899.01069 234.90 111.00.94085.00200 235.20 12.00,.05517.00725 235.80 62.00.64975.01032 234.90 112.00.94198.00188 235.30 13.00.06243.00757 235.80 63.00,.65962.00957 234.90 113.00.94460.00269 235.30 14.00.07030.00838 235.80 64.00.66888.00925 234.90 114.00.94735.00256 235.30 15.00.07918.00875 235.80 65.00.67813.00950 234.90 115.00.94973.00244 235.30 16.00,.08781,.00907 235.80 66.00.68788.00932 234.90 116.00.95223.00244 235.30 17.00,.09731.00969 235.80 67.00.69676,.00882 234.90 117.00.95461.00238 235.30 18.00.10719.01000 235.80 68.00,.70551.00882 234.90 118.00.95698.00206 235.30 19.00,.11732.01207 235.80 69.00.71439.00857 234.90 119.00.95873.00200 235.30 20.00.13133.01232 235.60 70.00.72265.00832 234.90 120.00.96098.00213 235.30 21.00.14195.01263 235.60 71.00.73102.00838 234.90 121.00.96299.00194 235.30 22.00.15658.01288 235.40 72.00,.73940.00832 234.90 122.00.96486.00181 235.30 23.00.16771.01144 235.40 73.00.74765,.00813 234.90 123.00.96661.00175 235.30 24.00.17947.01163 235.40 74.00,.75566.00813 234.90 124.00.96836.00181 235.30 25.00,.19097.01175 235.40 75.00,.76391.00800 234.90 125.00.97024.00100 235.30 26.00,20297,.01200 235.40 76.00.77166.00750 234.90 126.00.97036.00100 235.40 27.00.21498.01175 235.40 77.00.77891.00732 234.90 127.00.97224.00150 235.40 28,00.22648,.01232 235.40 78.00.78629.00719 234.90 128.00.97336.00131 235.40 29.00.23961.01275 235.40 79.00.79329.00694 234.90 129.00.97487.00156 235.40 30.00.25199.01300 235.40 80.00.80017,.00725 234.90 130.00.97649.00150 235.40 31.00.26562.01363 235.30 81.00.80780.00656 234.90 131.00.97787.00131 235.40 32.00.27925.01388 235.20 82.00.81330.00594 234.90 132.00.97912.00138 235.40 33.00.29338.01344 235.10 83.00.81968.00625 234.90 133.00.98062.00125 235.40 34.00.30613.01244 235.10 84.00.82581.00663 234.90 134.00.98162.00088 235.40 35.00,31826.01250 235.10 85.00.83293.00631 234.90 135.00.98237.00094 235.40 36,00.33114.01282 235,10 86.00,83844.00569 234.90 136,00,98349.00113 235.40 37.00.34389.01369 235.10 87.00.84431.00575 234.90 137,00,98462.00106 235.40 38,00,35852.01369 235.00 88.00.84994.00569 234,90 138.00.98562 -,00075 235,40 39,00.37128.01313 235.00 89.00,85569.00569 234.90 139.00.98312 -.00062 235.60 40,00.38478.01375 235.00 90.00,86132.00531 234,90 140.00.98437.00119 235.60 41,00.39878.01338 234.90 91.00.86632.00475 234.90 141.00.98550.00081 235.60 42.00.41154.01294 234.90 92,00.87082.00469 234,90 142.00.98600.00044 235.60 43.00.42467.01275 234.90 93,00,87570.00481 234.90 143.00.98637.00063 235.60 44.00.43705.0,1263 234,90 94.00.88045.00463 234.90 144.00.98725.00081 235.60 45.00.44993,01275 234.90 95.00.88495.00481 234,90 145.00,98800.00075 235.60 46.00,46256,01275 234.90 96.00.89008,00494 234.90 146.00.98875.00063 235.60 47.00.47544.01257 234.90 97.00.89483.00456 234.90 147.00.98925.00044 235.60 48.00.48769.01244 234.90 98.00.89921.00425 234.90 148.00.98962,00056 235.60 49.00.50032,01269 234.90 99.00.90333.00400 234.90 149,00.99037.00056 235.60

-286NORMALIZED DATA FROM RUN 52 (CONT'D) NORMALIZED ATA FROM RUN 53'NORMALIZED DATA FROM RUN 53 (CUNT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. M I N MIN' OF MIN IIN OF MIN M I N O 150.00.99075.00056 235.60.00.00000.00011 230.90 50.00.18684.00647 231.00 151.00.99150 -.00006 235.60 1.00.00021.00061 230.90 51.00.19318.00672 231.00 152.00.99062.00013 235.70 2.00.00123.00076 230.90 52.00.20028.00742 231.00 153,00.9,9.175.00069 235.70 3.00.00173.00076 230.90 53.00.20802.00735 231.00 154.00.99200.00006 235.70 4.00.00275.00127 230.90 54.00.21499.00666 231.00 155.00.99187.D0025 235.70 5.00.00427.00120 230.90 55.00.22133.00697 231.00 156.00.99250.00056 235.70 6.00.00516.00032 230.90 56.00.22893.00729 231.00 157.00.99300.00031 235.70 7.00.00491.00051 231.00 57.00.23591.00735 231.00 158.00.99312.00025 235.70 58.00.00618.00139 231.00 58.00.24364.00754 231.00.159.00,99350.00050 235.70 9.00.00770.00165 231.00 59.00.25099.00754 231.00 160.00.99412..00038 235.70 10.00.00948.00158 231.00 60.00.25873.00735 231.00 161.00.99425.00031 235.70 11.00.01087.00152 231.00 61.00.26570.00704 231.00 162.00.99475.00063 235.70 12.00.01252.00190 231.00 62.00.27280.00697 231.00 163.00.99550.00025 235.70 13.00.01468.00222 231.00 63.00.27965.00716 231.00 164.00.99525.00025 235.70 14.00.01696.00241 231.00 64.00.28713.00748 231.00 165.00.99600.00088 235.70 15.00.01949.00222 231.00 65.00.29461.00723 231.00 166.00.99700.00019 235.70 16.00.02140.00216 231.00 66.00.30155.00735 231.00 167.00.99637 -.00006 235.70 17.00.02380.00273 231.00 67.00.30931.00754 231.00 168.00.99687.00050 235.70 18.00.02685.00273 231.00 68.00.31667.00735 231.00 169.00.99737.00031 235.70 19.00.02926.00216 231.00 69.00.32402.00735 231.00 170.00..99750.00006 235.70 20.00.03116.00317 231.00 70.00.33137.00704 231.00 171.00.99750.00013 235.70 21.00.03560.00393 231.00 71.00.33809.00659 231.00 172.00.99775.00013 235.70 22.00.03902.00323 231.00 72.00.34456.00710 231.00 173.00.99775.00050 235.70 23.00.04206.00330 231.00 73.00.35229.00710 231.00 174.00.99875.0001.9 235.70 24.00.04561.00380 231.00 74.00.35876.00672 231.00 175.00.99812 -.00006 235.70 25.00.04967.00374 231.00 75.00.36573.00685 231.00 176.00.99862.00025 235.70 26.00.05309.00374 231.00 76.00.37245.00678 231.00 177.00.99862 -.00013 235.70 27.00.05715.00412 231.00 77.00.37930.00672 231.00 178.00.99837.00019 235.70 28.00.06133.00431 231.00 78.00.38589.00697 231.00 179.00.99900.00031 235.70 29.00.06577.00450 231.00 79.00.39324.00691 231.00 180.00.99900.00006 235.70 30.00.07033.00450 231.00 80.00.39971.00691 231.00 181.00.99912.00013 235.70 31.00.07477.00463 231.00 81.00.40706.00691 231.00 182.00.99925.00025 235.70 32.00.07959.00520 231.00 82.00.41353.00685 231.00 183.00.99962.00031 235.70 33.00.08517.00526 231.00 83.00.42075.00710 231.00 184.00.99987.00019 235.70 34.00.09011.00475 231.00 84.00.42773.00716 231.00 185.00 1.00000.00000 235.70 35.00.09467.00507 231.00 85.00.43508.00691 231.00 36.00.10025.00532 231.00 86.00.44155.00666 231.00 37.00.10532.00551 231.00 87.0u.44839.00697 231.00 38.00.11128.00596 231.00 88.01).45549.00678 231.00 39.00.11724.00590 231.00 89.00.46196.00666 231.00 40.00.12307.00545 231.00 90.00.46880.00672 231.00 41.00.12814.00590 231.00 91.00.47540.00659 231.00 42.00.13486.00640 231.00 92.00.48199.00659 231.00 43.00.14095.00602 231.00 93.00.48858.00647 231.00 44.00.14691.00615 231.00 94.00.49492.00678 231.00 45.00.15325.00615 231.00 95.00.50215.00710 231.00 46.00.15921.00634 231.00 96.00.50912.00697 231.00 47.00.16593.00685 231.00 97.00.51609.00653 231.00 48.00.17290.00716 231.00 98.00.52218.00647 231.00 49.00.18025.00697 231.00 99.00.52902.00678 231.00 NORMALIZED DATA FROM RUN 53 (CONT'D) NORMALIZED DATA FROM RUN 53 (CONT'D) NORMALIZED DATA FROM RUN 53 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN' OF MIN MIN' OF MIN MIN OF 100.00.53574.00678 231.00 150.00.80183.00361 230.80 200.00.93495.00152 230.80 101.00.54259.00666 231.00 151.00.80551.00387 230.80 201.00.93634.00177 230.80 102.00.54905.00647 231.00 152.00.80956.00374 230.80 202.00.93850.00171 230.80 103.00.55552.00602 231.00 153.00.81299.00323 230.80 203.00.93977.00095 230.80 104.00.56110.00690 231.00 154.00.81603.00311 230.80 204.00.94040.00114 230.80 105.00.56933.00735 230.90 155.00.81920.00336 230.80 205.00.94205.00158 230.80 106.00.57579.00628 230.90 156.00.82275.00361 230.80 206.00.94357.00139 230.80 107.00.58188.00628 230.90 157.00.82643.00342 230.80 207.00.94484.00133 230.80 108.00.58835.00602 230.90 158.00.82960.00342 230.80 208.00.94623.00171 230.80 109.00.59392.00609 230.90 159.00.83327.00342 230.80 209.00.94826.00133 230.80 110.00.60052.00640 230.90 160.00.83644.00336 230.80 210.00.94890.00133 230.80 111.00.60673.00609 230.90 161.00.83999.00330 230.80 211.00.95092.00146 230.80 112.00.61269.00609 230.90 162.00.84303.00330 230.80 212.00.99181.00139 230.80 113.00.61890.00628 230.90 163.00.84658.00342 230.80 213.00.95371.00152 230.80 114.00.62524.00609 230.90 164.00.84988.00323 230.80 214.00.95485.00120 230.80 115.00.63107.00583 230.90 165.00.85305.00317 230.80 215.)0.95612.00133 230.80 _16.00.63690.00545 230.90 166.00.85622..00317 230.80 216.00.95752.00120 230.80 117.00.64197.00571 230.90 167.00.85939.0031) 230.80 217.00.95853.00120 230.80 118.00.64831.00571 230.90 168.00.86256.00298 230.80 218.00.95993.00114 230.80 119.00.65338.00551 230.90 169.00.86535.00260 230.80 219.00.96081.00108 230.80 120.00.65934.00590 230.90 170.00.86776.00285 230.80 220.00.96208.00120 230.80 121.00.66517.00564 230.90 171.00.87105.00304 230.80 221.00.96322.00108 230.80 122.00.67063.00627 230.90 172.00.87384.00279 230.80 222.00.96424.00095 230.80 123.00.67771.00640 230.80 173.00.87663.00266 230.80 223.00.96512.00095 230.80 124.00.68342.00551 230.80 174.00.87917.00254 230.80 224.00.96614.00032 230.80 125.00.68874.00520 230.80 175.00.88170.00254 230.80 225.00.96577.00032 230.90 126.00.69381.00526 230.80 176.00.88424.00260 230.80 226.00.96678.00101 230.90 127.00.69927.00545 230.80 177.00.88690.00260 230.80 227.00.96780.00095 230.90 128.00.70472,00513 230.80 178.00.88944.00247 230.80 228.00.96869.00089 230.90 129.00.70953.00482 230.80 179.00.89184.00241 230.80 229.00.96957.00095 230.90 130.00.71435.00520 230.80 180.00.89425.00228 230.80 230.00.97059.00101 230.90 131.00.71993.00526 230.80 181.00.89641.00228 230.80 231.00.97160.00089 230.90 132.00.72488.00475 230.80 182.00.89882.00235 230.80 232.00.97236.00089 230.90 133.00.72944.00463 230.80 183.00.90110.00222 230.80 233.00.97338.00095 230.90 134.00.73413.00475 230.80 184.00.90325.00222 230.80 234.00.97426.00095 230.90 135.00.73895.00501 230.80 185.00.90554.00235 230.80 235.00.97528.00070 230.90 136.00.74415.00488R 230.80 186.00.90795T.00228 230.80 236.00.97566.00063 230.90 137.00.74871.00456 230.80 187,00.91010.00209 230.80 237.00.97655.00076 230.90 138.00.75327.00444 230.80 188.00.91213.00203 230.80 238.00.97718.00051 230.90 139.00.75758.00444 230.80 189.00.91416.00216 230.80 239.00.97756.00057 230.90 140.00.76215.00437 230.80 190.00,91644.00209 230.80 240.00.97832.00057 230.90 141.00,.76633.00425 230.80 191.00.91834.00177 230.80 241.00.97870.00057 230,90 142.00.77064.00406 230.80 192.00.91999.00197 230.80 242.00.97946.00082 230.90 143.00.77445.00374 230.80 193.00.92227.00177 230.80 243.00.98035.00089 230.90 144.00.77812,00393 230.80 194,00.92354.00209 230.80 244.00.98124.00070 230.90 145.00.78231.00418 230.80 195.00.92646.00203 230.80 245.00.98174.00044 230.90 146.00.78649.00380 230.80 196.00.92760.00165 230.80 246.00.98212.0044 230.90 147.00.7899.1.00387 230.80 197.00.92975.00184 230.80 247.00.98263.00051 230.90 148.00.79422.00418 230.80 198.00.93127.00177 230.80 248.00.98314.00063 230.90 149.00.79828.00380 230.80.199.00.93330.00184 230.80 249.00.98390.00051 230.90

-287NORMALIZED DATA FROM RUN 53 (CONT'D) NORMALIZEID DATA FROM RUN 53 (CONT'D) NORMALIZED DATA FROM RUN 54 TIME ALPHA RATE TEMP. TI ME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF MIN IN' OF M I N MIN-' OF 250.00.98415.00057 230.90 300.00.99835.00006 230.90.00.00000.00044 230.90 251.00.98504.00070 230.90 301.00.99848.00013 230.90 1.00.00088.00082 230.90 252.00.98555.00038 230.90 302.00.99861.00019 230.90 2.00.00165.00102 230.90 253.00.98580.00032 230.90 303.00.99886.00019 230.90 3.00.00292.00127 230.90 254.00.98618.00044 230.90 304.00.99899.00006 230.90 4.00.00419.00121 230.90 255.00.98669.00038 230.90 305.00.99899.00013 230.90 5.00.00533.00133 230.90 256.00.98694.00032 230.90 306.00.99924.00038 230.90 6.00.00686.00133 230.90 257.00.98732.00032 230.90 307.00.99975.00013 230.90 7.00.00800.00127 230.90 258.00.98758.00032 230.90 308.00.99949.00000 230.90 8.00.00940.00102 230.90 259.00.98796.00025 230.90 309.00.99975.00019 230.90 9.00.01004.00089 230.90 260.00.98808.00032 230.90 310.00.99987.00013 230.90 10.00.01118.00146 230.90 261.00.98859.00025 230.90 311.00 1.00000 -.00069 230.90 11.00.01296.00178 230.90 262.00.98859.00032 230.90 12.00.01474.00159 230.90 263.00.98922.00032 230.90 13.00.01614.00159 230.90 264.00.98922.00032 230.90 14.00.01792.00172 230.90 265.00.98986.00057 230.90 15.00.01957.00165 230.90 266.00.99036.00038 230.90 16.00.02122.00184 230.90 267.00.99062.00038 230.90 17.00.02325.00197 230.90 268.00.99113.00038 230.90 18.00.02516.00197 230.90 269.00.99138.00044 230.90 19.00.02720.00216 230.90 270.00.99201.00044 230.90 20.00.02948.00216 230.90 271.00.99227.00019 230.90 21.00.03152.00210 230.90 272.00.99239.00025 230.90 22.00.03368.00210 230.90 273.00.99277.00044 230.90 23.00.03571.00229 230.90 274.00.99328.00057 230.90 24.00.03825.00242 230.90 275.00.99391.00038 230.90 25.00.04054.00235 230.90 276.00.99404.00019 230.90 26.00.04296.00261 230.90 277.00.99429.00032 230.90 27.00.04575.00254 230.90 278.00.99468.00025 230.90 28.00.04804.00254 230.90 279.00.99480.00013 230.90 29.00.05084.00267 230.90 280.00.99493.00019 230.90 30.00.05338.00299 230.90 281.00.99518.00025 230.90 31.00.05681.00292 230.90 282.00.99544.00032 230.90 32.00.05923.00261 230.90 283.00.99582.00032 230.90 33.00.06202.00324 230.90 284.00.99607.00013 230.90 34.00.06571.00318 230.90 285.00.99607.00025 230.90 35.00.06838.00235 230.90 286.00.99658.00025 230.90 36.00.07041.00235 230.90 287.00.99658.00006 230.90 37.00.07308.00324 230.90 288.00.99670.00025 230.90 38.00.07690.00343 230.90 289.00.99708.00044 230.90 39.00.07995.00330 230.90 290.00.99759.00051 230.90 40.00.08351.00362 230.90 291.00.99810.00006 230.90 41.00.08719.00343 230.90 292.00.99772 -.00019 230.90 42.00.09037.00343 230.90 293.00.99772.00000 230.90 43.00.09406.00350 230.90 294.00.99772.00013 230.90 44.00.09736.00350 230.90 295.00.99797.00025 230.90 45.00.10105.00375 230.90 296.00.99823.00006 230.90 46.00.10486.00369 230.90 297.00.99810.00000 230.90 47.00.10842.00375 230.90 298.00.99823.00013 230.90 48.00.11236.00375 230.90 299.00.99835.00006 230.90 49.00.11592.00362 230.90 NORMALIZED DATA FROM RUN 54 (CONT'D) NORMALIZED DATA FROM RUN 54 (CONT'ID) NORMALIZED DATA FROM RUN 54 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN'' OF MIN MIN-I OF MIN MIN-' OF 50.00.11961.00400 230.90 100.00.34484.00464 230.80 150.00.57174.00458 230.80 51.00.12393.00413 230.90 101.00.34752.00426 230.90 151.00.57467.00464 230.90 52.00.12787.00432 230.90 102.00.35336.00464 230.80 152.00.58102.00451 230.80 53.00.13257.00400 230.90 103.00.35680.00489 230.90 153.00.58370.00426 230.90 54.00.13588.00413 230.90 104.00.36315.00458 230.80 154.00.58954.00458 230.80 55.00.14083.00445 230.90 105.00.36595.00432 230.90 155.00.59285.00458 230.90 56.00.14478.00388 230.90 106.00.37179.00439 230.80 156.00.59869.00451 230.80 57.00.14859.00426 230.90 107.00.37472.00439 230.90 157.00.60187.00458 230.90 58.00.15329.00432 230.90 108.00.38056.00458 230.80 158.00.60784.00445 230.80 59.00.15723.00400 230.90 109.00.38387.00464 230.90 159.00.61077.00419 230.90 60.00.16130.00419 230.90 110.00.38984.00451 230.80 160.00.61623.00407 230.80 61.00.16562.00419 230.90 111.00.39290.00483 230.90 161.00.61891.00445 230.90 62.00.16969.00413 230.90 112.00.39950.00470 230.80 162.00.62513.00426 230.80 63.00.17388.00419 230.90 113.00.40231.00483 230.90 163.00.62742.00426 230.90 64.00.17808.00400 230.90 114.00.40916.00496 230.80 164.00.63364.00439 230.80 65.00.18189.00495 230.90 115.00.41222.00445 230.90 165.00.63619.00419 230.90 66.00.18799.00464 230.80 116.00.41806.00432 230.80 166.00.64203.00413 230.80 67.00.19117.00464 230.90 117.00.42086.00451 230.90 167.00.64446.00439 230.90 68.00.19726.00419 230.80 118.00.42708.00445 230.80 168.00.65080.00445 230.80 69.00.19956.00331 230.90 119.00.42976.00445 230.90 169.00.65335.00413 230.90 70.00.20388.00464 230.90 120.00.43598.00470 230.80 170.00.65907.00419 230.80 71.00.20884.00521 230.90 121.00.43917.00477 230.90 171.00.66174.00439 230.90 72.00.21430.00445 230.80 122.00.44552.00451 230.80 172.00.66784.00394 230.80 73.00.21774.00375 230.90 123.00.44819.00426 230.90 173.00.66963.00388 230.90 74.00.22181.00439 230.90 124.00.45403.00445 230.80 174.00.67559.00394 230.80 75.00.22651.00445 230.90 125.00.45709.00451 230.90 175.00.67751.00413 230.90 76.00.23070.00439 230.90 126.00.46306.00451 230.80 176.00.68385.00477 230.80 77.00.23528.00572 230.90 127.00.46612.00451 230.90 177.00.68704.00426 230.90 78.00.24214.00496 230.80 128.00.47208.00439 230.80 178.00.69237.00388 230.80 79.00.24519.00337 230.90 129.00.47489.00439 230.90 179.00.69479.00407 230.90 80.00.24888.00432 230.90 130.00.48085.00451 230.80 180.00.70051.00413 230.80 81.00.25384.00407 230.90 131.00.48391.00451 230.90 181.00.70306.00394 230.90 82.00.25702.00477 230.90 132.00.48988.00464 230.80 182.00.70839.00407 230.80 83.00.26337.00540 230.90 133.00.49319.00470 230.90 183.00.71119.00432 230.90 84.00.26782.00470 230.90 134.00.49929.00445 230.80 184.00.71703.00400 230.80 85.00.27278.00477 230.90 135.00.50209.00458 230.90 185.00.71920.00388 230.90 86.00.27735,.00483 230.90 136.00.50844.00426 230.80 186.00.72478.00388 230.80 87.00.28244.00458 230.90 137.00.51061.00445 230.90 187.00.72695.00375 230.90 88.00.28651.00432 230.90 138.00.51734.00483 230.80 188.00.73228.00388 230.80 89.00.29108.00458 230.90 139.00.52027.00477 230.90 189.00.73471.00400 230.90 90.00.29566,.00470 230.90 140.00.52687.00470 230.80 190.00.74029.00388 230.80 91.00,.30049.00483 230.90 141.00.52967.00445 230.90 191.00.74246.00375 230.90 92.00.30532,00483 230.90 142.00,53577.00445 230.80 192.00.74779.00407 230.80 93.00.31015.00470 230.90 143.00.53857.00477 230.90 193.00.75060.00375 2301.90 94.00,31473.00477 230.90 144.00.54530.00470 230.80 194.00.75529.00350 230,80 95.00.31968.00464 230.90 145.00,54798.00413 230.90 195.00.75759.00369 230.90 96.00,32400,00464 230.90 146.00.55356.00419 230.80 196.00.76266.00362 230.80 97.00.32896.00565 230,90 147.00.55637.00502 230.90 197.00.76483.00356 230.90 98.00.33531.00464 230.80 148.00.56360.00458 230.80 198.00.76978,00369 230.80 99,00.33824.00477 230.90 149.00.56552.00407 230.90 199.00.77221.00394 230.90

-288NORMALIZED DATA FROM RUN 54 (CONT'D) NORMALIZED DATA FROM RUN 54 (CONT'D) NORMALIZED DATA FROM RUN 54 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIM E ALPHA RATE TEMP. IM IN M I NN- OF MIN MI I N~1 oF 200.00.77766.00337 230.80 250.00.90694.00197 230.80 300.00.96670.00083 231.00 201.00.77894.00330 230.90 251.00.90733.00197 230.90 301.00.96759.00089 231.00 202.00.78427.00356 230.80 252.00.91088.00165 230.80 302.00.96848.00070 231.00 203.00.78606.00337 230.90 253.00.91063.00083 230.90 303.00.96898.00083 231.00 204.00.79101.00311 230.80 254.00.91254.00172 230.90 304.00.97013.00089 231.00 205.00.79229.00337 230.90 255.00.91406.00153 230.90 305.00.97076.00057 231.00 206.00.79775.00362 230.80 256.00.91559.00172 230.90 306.00.97127.00064 231.00 207.00.79953.00324 230.90 257.00.91750.00191 230.90 307.00.97204.00089 231.00 208.00.80423.00324 230.80 258.00.91940.00172 230.90 308.00.97305.00070 231.00 209.00.80602.00330 230.90 259.00.92093.00165 230.90 309.00.97343.00057 231.00 210.00.81084.00324 230.80 260.00.92271.00172 230.90 310.00.97420.00089 231.00 211.00.81250.00350 230.90 261.00.92436.00140 230.90 311.00.97521.00083 231.00 212.00.81783.00311 230.80 262.00.92550.00133 230.90 312.00.97585.00057 231.00 213.00.81873.00280 230.90 263.00.92703.00165 230.90 313.00.97636.00044 231.00 214.00.82342.00311 230.80 264.00.92881.00165 230.90 314.00.97674.00051 231.00 215.00.82496.00305 230.90 265.00.93033.00140 230.90 315.00.97737.00070 231.00 216.00.82952.00267 230.80 266.00.93161.00127 230.90 316.00.97814.00064 231.00 217.00.83030.00273 230.90 267.00.93288.00172 230.90 317.00.97864.00038 231.00 218.00.83499.00299 230.80 268.00.93504.10089 230.90 318.00.97890.00032 231.00 219.00.83627.00191 230.90 269.00.93466.00045 231.00 319.00.97928.00057 231.00 220.00.83881.00254 230.90 270.00.93593.00159 231.00 320.00).98004.00051 231.00 221.00.84135.00248 230.90 271.00.93784.00146 231.00 321.00.98030.00057 231.00 222.00.84377.00242 230.90 272.00.93886.00133 231.00 322.00.98119.00051 231.00 223.00.84619.00261 230.90 273.00.94051.00153 231.00 323.00.98131.00032 231.00 224.00.84898.00261 230.90 274.00.94191.00108 231.00 324.00.98182.00057 231.00 225.00.85140.00330 230.90 275.00.94267.00102 231.00 325.00.98246.00051 231.00 226.00.85558.00248 230.80 276.00.94394.00127 231.00 326.00.98284.00032 231.00 227.00.85635.00159- 230.90 277.00.94521.00114 231.00 327.00.98309.00038 231.00 228.00.85877.00242 230.90 278.00.94623.00108 231.00 328.00.98360.10044 231.00 229.00.86118.00324 230.90 279.00.94738.00114 231.00 329.00.98398.00025 231.00 230.00.86524.00242 230.80 280.00.94852.00114 231.00 330.00.98411.00013 231.00 231.00.86601.00248 230.90 281.00.94966.00108 231.00 331.00.98424.00032 231.00 232.00.87020.00222 230.80 282.00.95068.00089 231.00 332.00.98475.00064 231.00 233.00.87046.00134 230.90 283.00.95144.00095 231.00 333.00.98551,.00064 231.00 234.00.87288.00261 230.90 284.00.95259.00102 231.00 334.00.98602.00044 231.00 235.00.87568.00248 230.90 285.00.95348.00102 231.00 335.00.98640.00038 231.00 236.00.87784.00197 230.90 286.00.95462.00102 231.00 336.00.98678.00044 231.00 237.00.87962.00216 230.90 287.00.95551.00095 231.00 337.00.98729.00038 231.00 238.00.88216.00261 230.90 288.00.95653.00102 231.00 338.00.98754.00032 231.00 239.00.88483.00235 230.90 289.00.95754.00114 231.00 339.00.98792.00025 231.00 240.00.88686.00191 230.90 290.00.95882.00114 231.00 340.00.98805.00025 231.00 241.00.88864.00247 230.90 291.00.95983.00064 231.00 341.00.98843.00038 231.00 242.00.89181.00172 230.80 292.00.96009.00044 231.00 342.00.98881.00032 231.00 243.00.89207.00172 230.90 293.00.96072.00083 231.00 343.00.98907.00032 231.00 244.00.89524.00191 230.80 294.00.96174.00089 231.00 344.00.98945.00038 231.00 245.00.89589.00134 230.90 295.00.96250.00070 231.00 345.00.98983.00032 231.00 246.00.89792.u0j78 230.90 296.00.96314.00083 231.00 346.00.99009.00025 231.00 247.00.89945.002350F 230.90 297.00.96415.00095 231.00 347.00.99034.00019 231.00 248.00.90300.00197 230.80 298.00.96504.00089 231.00 348.00.99047.00019 231.00 249. O0.90339.00197 230.90 299.00.96593.00083 231.00 349.00.99072.00013 231.00 NORMALIZED DATA FROM RON 54 (CONTD) NORMALIZED DATA FROM RUN 54 (CONTID) NORMALIZED DATA FROM RUN 55 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MI 1 MINN OF MIN MIN-' OF MIN MIN- OF 350.00.99072.00019 231.00 400.00.99936.00006 231.00.00.00000.00777 244.40 351.00.99110.00051 231.00 401.00.99949.00006 231.00.50.00777.01259 244.30 352.00.99174.00038 231.00 402.00.99949.00006 231.00 1.00.01259.00654 244.40 353.00.99186.00013 231.00 403.00.99962.00013 231.00 1.50.01431.00907 244.70 354.00.99199.00025 231.00 404.00.99975.00000 231.00 2.00.02166.01699 244.70 355.00.99237.00025 231.00 405.00.99962 -.00013 231.00 2.50.03130.01821 244.60 356.00.99250.00013 231.00 406.00.99949.00019 231.00 3.00.03988.01609 244.60 357.00.99263.00013 231.00 407.00 1.00000.00006 231.00 3.50.04739.01781 244.70 358.00.99275.00032 231.00 4.00.05768.02201 244.70 359.00.99326.00038 231.00 4.50.06940.02311 244.60 360.00.99352.00013 231.00 5.00.08080.02365 244.60 361.00.99352.00013 231.00 5.50.09305.02475 244.60 362.00.99377.00032 231.00 6.00.10554.02573 244.60 363.00.99415.00019 231.00 6.50.11878.02695 244.60 364.00.99415.00013 231.00 7.00.13250.03022 244.60 365.00.99441.00019 231.00 7.50.14899.03193 244.50 366.00.99453.00019 231.00 8.00.16443.03557 244.50 367.00.99479.00038 231.00 8.50.18456.03883 244.30 368.00.99530.00025 231.00 9.00.20326.03801 244.20 369.00.99530.00006 231.00 9.50.22257.03924 244.10 370.00.99542.00013 231.00 10.00.24250.04177 244.00 371.00.99555.00006 231.00 10.50.26434.04095 243.80 372.00.99555.00013 231.00 11.00.28345.03847 243.80 373.00.99581.00025 231.00 11.50.30281.04063 243.80 374.00.99606.00013 231.00 12.00.32408.04409 243.70 375.00.99606.00019 231.00 12.50.34690.04470 243.50 376.00.99644.00019 231.00 13.00.36878.04315 243.40 377.00.99644.00006 231.00 13.50.39005.04173 243.30 378.00.99657.00013 231.00 14.00.41051.04222 243.30 379.00.99670.00013 231.00 14.50.43227.04149 243.20 380.00.99682.00019 231.00 15.00.45200.03920 243.20 381.00.99708.00000 231.00 15.50.47148.03884 243.20 382.00.99682 -.00006 231.00 16.00.49084. 03965 243.20 383.00.99695.00019 231.00 16.50.51113.03737 243.10 384.00,.99720.00013 231.00 17.00.52820.03675 243.20 385.00.99720.00006 231.00 17.50.54788.03565 243.10 386.00,99733.00019 231.00 18,00.56385.03504 243.20 387.00.99758,00019 231.00 18,50.58292.03862 243.10 388.00.99771.00013 231,00 19.00.60247.03492 243.00 389.00.99784.00006 231.00 19.50.61784.03276 243.10 390.00.99784.00013 231.0020.00.63523.03430 243.10 391.00.99809.00019 231.00 20.50.65214.03332 243.10 392.00.99822.00006 231.00 21.00.66856.03426 243.10 393.00.99822.00006 231.00 21.50.68640.03222 243.00 394.00.99835.00032 231.00 22.00.70078.02957 243.10 395.00.99886.00038 231.00 22.50.71597.03002 243.10 396.00.99911.00019 231.00 23.00.73079.03002 243.10 397.00.99924.00006 231.00 23.50.74599.02810 243.10 398.00.99924.00006 231.00 24.00.75890.02774 243.20 399.00.99936.00006 231.00 24.50.77372.02904 243.20

-289NORMALIZED DATA FROM RUN 55 (COINT'D) NURIALIZEO DATA FR611- RU 55 (CiUsT'O) NORMALIZED DATA FRUM RUN 58 TIME ALPHA RATE TEMP. T I E ALHA HATE I EP. t ALPHA RATE TEMP. MIN MIN-' O M I IM OF I Il I N- OF 25.00.78793.02732 243.20 50.00.99195 -.00009 246.20.00.00()000.0)0071 256.90 25.50.80104.02516 243.20 50.50.99293.00290 246.20 1.00.00142.00199 256.90 26.00.81310.02215 243.30 51.00.99485.(00061 246.10 2.00.00399.00274 256.90 26.50.82319.02450 243.40 51.50.99354 -.00070 246.20 3.(.00690.(00398 256.90 27.00.83760.02426 243.30 52.00.99416.00086 246.20 4.00 ().01195.00379 256.80 27.50.84745.02100 243.40 52.50.99440.00229 246.20 5.00)).01449.00438 256.90 28.00.85860.01847 243.40 53.00.99645.,0241 246.10,, 0.).02070.00455 256.80 28.50.86592.01619 243.60 53.50.99681 -.)00(02 246.10 7.00.02360.00608 256.90 29.00.87478.01867 243.70 54.00.99563.(.0074 246.20 8.()O.032R6.00784 256.70 29.50.88458.01720 243.70 54.50.99755.0()025 246.11) 9.00.0392H.00665 256.70 30.00.89198.01251 243.80 55.()00.995871.()0025 246.20 10(.),0.04617.00730 256.70 30.50.89709.01344 244.00 55.50.99779.00049 246.10 11.0) 0 ()538.00994 256.70 31.00.90542.01401 244.00 56. (0.99636.000)(37 246.2 (1 2. 00. 0 6606.101011 256.50 31.50.91110.01148 244.10 55.5).99816.00049 246.10 1 3. ().07409.01246 25 6. 60 32.00.91691.01160 244.20 57.00.9956H.00061 246.20 14.00.09()99.01316 256.20 32.50.92271.01266 244.30 57.550.9H77.0(012 246.10 15.00.10042.01250 256.30 33.00.92957.01107 244.30 58.()0.99697,0(012 24.20 16.00.11599.01384 256.10 33.50.93378.01033 244.40 58.50.999.99.00025 246.10 17.00.12H11.01484 256.20 34, 00,.93990.00687 244.40 59.00.99722.00012 246.20) 18.100.14566.01665 256.00 34.50.94064.00984 244.70 59.50.999)02.00049 246.1)) 19.00.16142.01853 256.00 35.00.94975.01282 244.50 6)1.00.99771.00037 246.20) 20.00.18272.01882 255.70 35.50.95346.00646 244.60 60.50.99939.00180 246.10 21.00.19907.01781 255.70 36.00.95620.00405 244.70 61.()0.99951.00000 246.10 22.00.21835.01786 255.60 36.50.95751.00776 244.90 61.50.99939 -.00131 246.10 23.00.23479.01939 255.70 37.0(1.6396h.I)7) 744.x i 62.00.99820.00025 246.20 24.00.25712.02009 255.50 37.50.96466.00270 245.00 62.50.99963 -.00012 246.10 25.00.27497,.02180 255.60 38.00.96666.00400 245.10 53.00.99808.00025 246.20) 26.00).30072.02132 255.20 38.50.96866.00543 245.20 6350.99988.0()012 246.10) 27.00.31761.02037 255.40 39.)0.97209.00674 245.20 64.00..9982)0 -.00()336 246.20 28.00.34146.02237 255.20 39.50.97540.00506 245.20 64.50.99652.00025 246.30 29.00.36235.02331 255.20 40.00.97715.00314 245.30 65.00.99844.00348 246.20 30.00.38807.02241 255.00 40.50.97854.00384 245.40 65.50) 1.00000 -.00168 246.10 31.00.40718.02341 255.20 41.00.98099.00466 245.40 32.00.43490.02541 254.90 41.50.9 8319.00273 245.40 33.00.45801.02335 254.90 42.00.98372 -.00074 245.50 34.00.48159.02270 254.90 42.50.98245.00212 245.70 35.00.50341.02500 255.00 43.00.98585.00237 245.60 36.00.53159.02552 254.70 43.50.98482.00081 245.80 37.00.55445.02422 254.80 44.00.98666.00151 245.80 38.00.58003,.02399 254.70 44.50.98633.00257 245.90 39.00.60243.02335 254.80 45.00.98923.00425 245.80 40.00.62673.02318 254.70 45.50.99058.00257 245.80 41.00.64879.02300 254.70 46.00.99180.00257 245.80 42.00.67274.02001 254.60 46.50.99315.00208 245.80 43.00.68882.01861 254.80 47.00.99388.00004 245.80 44.00.70996.01815 254.70 47.50.99319 -.00152 245.90 45.00.72511.01815 254.90 48.00.99237 -.00176 246.00 46.00.74625.01891 254.80 48.50.99142.00135 246.10 47.00.76293.01727 254.90 49.00.99371.00159 246.00 48.00.78079.01609 254.90 49.50.99302 -.00176 246.10 49.00.79512.01563 255.10 NORMALIZED DATA FROM RUN 58 (CONIT'D) NORMALIZED DATA FROm RUN 58 (CONT'D) NORMALIZED) DATA FROM RUN 59 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF MIN MIN-1 F PM11 NMIN) OF 50.00.81205.01534 255.10 100.00.99580.00035 256.90.00.01000).00081 250.10 51.00.82581.01518 255.20 101.00.99603.00006 256.90 1.00).00163.00141 250.00 52.00.84240).01323 255.10 102.00.99591.00000 256.90 2.00.00281.00318 250.00 53.00.85227.01324 255.40 103.00.99603.00029 256.90 3.10.00799.00213 249.80 54.00.86888.01142 255.20 104.00.99650.00023 256.90 4.00.00706.00160 249.90 55.00.87512.01132 255.60 105.00.99650.00018 256.90 5.00.01120.00278 249.80 56.00.89151.01144 255.30 106.00.99685.00035 256.90 6.)00,1262.00260 249.80 57.00.898(0.01003 255.60 107.00.99720.00012 256.90 7.00.01640.00208 249.70 58.00.91158.00892 255.40 108.00.99708.00006 256.90 8.00.01677.00120 249.80 59.00.91584.00686 255.70 109.00.99732.00023 256.90 9.00.01879.00225 249.80 60.00.92530.00899 255.70 110.00.99755.00018 256.90 10.00.02128.00355 249.80 61.00.93382.00717 255.70 111.00.99767.00000 256.90 11.00.02589.00373 2.49.70 62.00.93964.00499 255.80 112.00.99755.00006 256.90 12.00.02874.00285 249..70 63.00.94380.00648 256.00 113.00.99778.00023 256.90 13.00.03159.00209 249.70 64.00.95260.00595 255.80 114.00.99802.00006 256.90 14.00.03292.00338 249.80 65.00.95571.00413 256.00 115.00.99790.00000 256.90 15.00.03835.00350 249.70 66.00.96085.00408 256.00 116.00.99802.00018 256.90 16.00.03992.00274 249.80 67.00.96386.00361 256.10 117.00.99825.00018 256.90 17.00.04383.00409 249.80 68.00.96807.00143 256.10 118.00.99837.00012 256.90 18.00.04811.00668 249.80 69.00.96672.00090 256.40 119.00.99848.00012 256.90 19.00.05720.00586 249.60 70.00.96987.00208 256.40 120.00).99860.00012 256.90 20.00.05983.00469 249.70 71.00.97088.00350 256.60 121.00.99872.00023 256.90 21.00.06658.00(1598 249.60 72.00.97688.00251 256.40 122.1)0.99907.00018 256.90 22.00.07180.00552 249.60 73.00.97590.00233 256.60 123.00.99907 -.00012 256.90 23.00).07761.00605 249.60 74.00.98155.00157 256.40 124.00.99883.00006 256.90 24.00.08390.00741 249.60 75.00.97903 -.00021 256.70 125.0(.99918.00023 256.90 25.00.09242.00747 249.50 76.00.98113.00228 256.70 126.00.99930.00023 256.90 26.00.09883.00647 249.50 77.00.98358.00281 256.70 127.00.99965.00018 256.90 27.00.10536.00589 249.50 78.00.98676.00134 256.60 128.00.99965 -.00006 256.90 28.00.11061.00618 249.60 79.00.98627.00028 256.70 129.00.99953.00012 256.90 29.00.11773.00736 249.60 80.00.98732.00123 256.70 130.00.99988.00006 256.90 30.00.12532.00795 249.60 81.00.98872.00217 256.70 131. 00.99965.0100)16 256.9)) 31.00.13363.00813 249.60 82.00.99166 -.00043 256.60 132.00 1.0000.00006 256.9) 32.00.14158.01024 249.60 83.00.98786 -.00078 256.90 33.00.15411.01042 249.40 84.00.99010.00064 256.80 34.00.16242.00966 249.40 85.00.98914.00093 256.90 35.00.17344.01019 249.30 86.00.99197.00070 256.80 36.00).18281.00885 249.30 87.00.99054.00047 256.90 37.()(00).19114.0)792 249.40 88.00.99290.00058 256.80 38.00.19864.01019 249.50 89.00,.99171.00053 256.90 39.00.21153.01220 249.30 90.00.99395.0(058 256.80 40.00.22304.1)1110 249.30 91.00.99288.00041 256.90 41.00.23373.0)1092 249.30 92.00.99477.00035 256.80 42.00.244H6.0118() 249.30 93.00.99358.00064 256.90 43.00.25732.0)1285 249.20 94.,0.99605.00064 256.80 44.00.2705H.1)1327 249.10 95,00.99486.00023 256.90 45.,0,28385.)01245 249.00 96.00.99652 -.00006 256.80) 46.100.29548.(11093 249. 00 97.00.99475 -.00006 256.90 47.00.30571.01017 249.10 98.00.99640.00029 256.80 48.,0.31553.01216 249.20 99.00.99533 -.00030 256.90 49.00.33004.01286 249.10

-290NORMALIZED DATA FROM RUN 59 ICONTO) NORMALIZED DATA FROM RUN 59 (CONT'D) NORMALIZED DATA FROM RUN 59 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN' OF MIN MI N- OF MIN MIN- OF 50.00.34156.01304 249.10 100.00.90562.00647 249.00 150.00.99798.00012 249.60 51.00.35613.01364 249.00 101.00.91191.00629 249.00 151.00.99786.00006 249.60 52.00.36883.01475 249.00 102.00.91820.00587 249.00 152.00.99810.00012 249.60 53.00.38563.01481 248.80 103.00.92366.00522 249.00 153.00.99810.00006 249.60 54.00.39844.01112 248.80 104.00.92864.00522 249.00 154.00.99822.00024 249,.60 55.00.40787.01206 249.00 105.00.93410.00423 249.00 155.00.99858.00018 249.60 56.00.42256.01469 248.90 106.00.93710).00399 249.10 156.00.99858.00012 249.60 57.00.43725.01230 248.80 107.00.94208.00287 249.10 157.00.99881.00024 249.60 58.00.44716.01359 249.00 108.00.94284.00240 249.30 158.00.99905.00018 249.60 59.00.46443.01470 248.80 109.00.94688.00404 249.30 159.00.99917.00006 249.60 60.00.47656.01383 248.90 110.00.95091..00386 249.30 160.00.99917.00006 249.60 61.00.49208.01441 248.80 111.00.95459.00344 249.30 161.00.99929.00012 249.60 62.00.50537.01329 248.80 112.00.95780.00326 249.30 162.00.99941.00030 249.60 63.00.51867.01184 248.80 113.00.96112.00326 249.30 163.00.99988.00024 249.60 64.00.52905.01160 249.00 114.00.96432.00297 249.30 164.00.99988.00000 249.60 65.00.54186 401481 249.00 115.00.96705.00291 249.30 165.00.99988.00000 249.60 66.00.55866.01429 248.80 116.00.97014.00273 249.30 166.00.99988.00006 249.60 67.00.57044.01329 248.90 117.00.97251.00237 249.30 167.00 1.00000 -.00006 249.60 68.00.58525.01363 248.80 118.00.97489.00237 249.30 69.00.59771.01246 248.80 119.00.97726.00225 249.30 70.00.61017.01439 248.80 120.00.97940.00160 249.30 71.00.62649.01234 248.60 121.00.98046.00108 249.30 72.00.63485.01111 248.80 122.00.98156.00161 249.40 73.00.64871.01163 248.70 123.00.98369.00166 249.40 74.00.65812.01181 248.80 124.00.9848R.00131 249.40 75.00.67233.01252 248.70 125.00.98630.00043 249.40 76.00.68316.01199 248.80 126.00.98573.00031 249.50 77.00.69630.01169 248.70 127.00.98692.00131 249.50 78.00.70654.01081 248.80 128.00.98835.00025 249.50 79.00.71793.01133 248.80 129.00.98742.00001 249.60 80.00.72921.01139 248.80 130.00.98837.00095 249.60 81.00.74072.01127 248.80 131.00.98932.00083 249.60 82.00.75176.01086 248.80 132.00.99003.00095 249.60 83.00.76244.01062 248.80 133.00.99122.00083 249.60 84.00.77300.01044 248.80 134.00.99169.00059 249.60 85.00.78332.01021 248.80 135.00.99240.00059 249.60 86.00.79341.00997 248.80 136.00.99288.00053 249.60 87.00.80326.00961 248.80 137.00.99347.00089 249.60 88.00.81264.00838 248.80 138.00.99466.00059 249.60 89.00.82002.00850 248.90 139.00.99466.00012 249.60 90.00.82964.00920 245.90 140.00.99490.00036 249.60 91.00.83842.00825 248.90 141.00.99537.00024 249.60 92.00.84613.00855 248.90 142.00.99537.00012 249.60 93.00.85551.00878 248.90 143.00.99561.00042 249.60 94.00.86370.00825 248.90 144.00.99620.00065 249.60 95.00.87201.00684 248.90 145.00.99691.00042 249.60 96.00.87737.00648 249.00 146.00.99703.00012 249.60 97.00.88497.00760 249.00 147.00.99715.00012 249.60 98.00.89256.00700 249.00 148.00.99727.00024 249.60 99.00.89897.00653 249.00 149.00.99763.00036 249.60 NORMALIZED DATA FROM RUN 60 NORMALIZED DATA FROM RUN 60 (CONTI'D) NORMALIZED DATA FROM RUN 61 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF MIN MIN-' Of MIN MIN-' OF.00.00000.00168 248.60 50.00.99359.00036 249.60.00.00000.00186 245.10 1.00.00335.00706 248.90 51.00.99371.00006 249.60 1.00.00372.00308 245.00 2.00.01413.01476 248.90 52.00.99371.00018 249.60 2.00.00616.00352 245.10 3.00.03288.01834 248.70 53.00.99407.00006 249.60 3.00.01077.00534 245.10 4,00.05080.02318 248.80 54.00.99383 -.00012 249.60 4.00.01683.00661 245.10 5.00.07923.03109 248.60 55.00.99383 -.00157 249.60 5.00.02399.00807 245.10 6.00.11299.03689 248.40 56.00.99069.00036 249.80 6.00.03297.00970 245.10 7.00.15302.04353 248.00 57.00.99456.00018 249.60 7.00.04340.01423 245.10 8.00.20006.04927 247.60 58.00.99105.00018 249.80 8.00.06143.01714 244.80 9.00.25156.05110 247.20 59.00.99492.00200 249.60 9.00.07767.01751 244.70 10.00.30225.05316 247.00 60.00.99504.00024 249.60 10.00.09646.02000 244.60 11.00.35788.05533 246.70 61.00.99540.00018 249.60 11.00.11767.02477 244.50 12.00.41292.05809 246.50 62.00.99540.00000 249.60 12.00.14599.02785 244.10 13.00.47407.05485 246.00 63.00.99540.00000 249.60 13.00.17338.02745 243.90 14.00.52263.04891 246.10 64.00.99540.00012 249.60 14.00.20089.02999 243.80 15.00.57188.04648 246.00 65.00.99565.00036 249.60 15.00.23335.03132 243.50 16.00.61560.04461 246.10 66.00.99613.00018 249.60 16.00.26353.03296 243.40 17.00.66109.04316 246.00 67.00.99601.00000 249.60 17.00.29926.03490 243.10 18.00.70191.04002 246.10 68.00.99613.00097 249.60 18.00.33332.03376 243.00 19.00.74113.03448 246.10 69.00.99794 -.00091 249.50 19.00.36678.03352 242.90 20.00.77087.03291 246.50 70.00.99432 -.00091 249.70 20.00.40036.03358 242.80 21.00.80695.03372 246.50 71.00.99613.00097 249.60 21.00.43394.03352 242.70 22.00.83832.02842 246.60 72.00.99625.00097 249.60 22.00.46740.03201 242.60 23.00.86378.02413 246.80 73.00.99807.00000 249.50 23.00.49797.03057 242.60 24.00.88657.02224 247.00 74.00.99625 -.00091 249.60 24.00.52854.03002 242.60 25.00.90826.01843 247.10 75.00.99625.00000 249.60 25.00.55802.02978 242.60 26.00.92344.01522 247.40 76.00.99625.00091 249.60 26.00.58810.02882 242.60 27.00.93870.01496 247.50 77.00.99807 -.00091 249.50 27.00.61566.02863 242.70 28.00.95335.01032 247.50 78.00.99444.00097 249.70 28.00.64536.02886 242.60 29.00.95934.00676 247.90 79.00 1.00000.00097 249.40 29.00.67338.02735 242.60 30.00.96686.00596 248.10 30.00.70007.02567 242.60 31.00.97125.00348 248.40 31.00.72471.02410 242.70 32.00.97382.00371 248.70 32.00.74827.02445 242.80 33.00.97867.00261 248.80 33.00.77362.02384 242.80 34.00.97905.00249 249.10 34.00.79594.02010 242.80 35.00.98365.00442 249.10 35.00.81382.01853 243.00 36.00.98788.00254 249.10 36.00.83300.01845 243.10 37.00.98873 -.00036 249.20 37.00.85071.01543 243.10 38.00.98717.00224 249.40 38.0)0.86386.01440 243.30 39,00.99321.00206 249.20 39.00.8795().01420 243.30 40.00.99128 -.00127 249.40 40.00.8922:.01167 243.40 41.00.99068 -.00072 249,50 41.00.9'0285.01058 243.60 42.00.98984.00000 249.60 42.00.91342.01045 243.70 43.00.99068.00097 249.60 43.00.92375.00954 243.80 44.00.99177.00061 249.60 44.00.93251.00833 243.90 45.00.99189.00115 249.60 45.00.94041.00748 244.00 46.00.99407.00109 249.50 46.00.94746.00777 244.10 47.00.99407.00006 249.5047.00.95595.00657 244.10 48.00.99419 -.00054 249.50 48.00.96059.00457 244.30 49,00.99298 -.00030 249.60 49.00.96510.00426 244.40

-291NORMALIZED DATA FROM RUN 61 (CONT'D) NORMALIZED DATA FROM RUN 62 NORMALIZED DATA FROM RUN 62 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' oF MIN MIN-' OF MIN MIN-' OF 50.00.96912.00450 244.50.00.00000.00018 245.10 250.00.92186.00221 244.70 51.00.97409.00371 244.50 5.00.00180.00012 245.00 255.00.93170.00180 244.70 52.00.97653.00250 244.60 10.00.00119.00022 245.10 260.00.93986.00151 244.80 53.00.97909.00304 244.70 15.00.00396.00026 245.00 265.00.94683.00130 244.80 54.00.98261.00315 244.70 20.00.00384.00035 245.10 270.00.95283.00132 244.80 55.00.98540.00189 244.70 25.00.00744.00044 245.00 275.00.96003.00106 244.80 56.00.98639.00152 244.80 30.00.00828.00054 245.10 280.00.96339.00100 244.90 57.00.98845.00134 244.80 35.00.01284.00080 245.00 285.00.96999.00082 244.80 58.00.98907.00086 244.90 40.00.01632.00102 245.10 290.00.97155.00065 244.90 59.00.99016.00158 244.90 45.00.02304.00119 245.00 295.00.97647.00071 244.80 60.00.99222.00164 244.90 50.00.02820.00152 245.10 300.00.97863.00067 244.90 61.00.99344 -.00023 244.90 55.00.03529.00200 245.00 305.00.98320.00048 244.80 62.00.99176 -.00029 245.10 60.00.04825.00218 245.00 310.00.98344.00040 244.90 63.00.99286 -.00059 245.10 65.00.06013.00257 245.00 315.00.95716.00037 244.80 64.00.99058.00037 245.30 70.00.07394.00287 245.00 320.00.98716.00017 244.90 65.00.99360.00109 245.20 75.00.08882.00332 245.00 325.00.98884.00018 244.90 66.00.99276.00145 245.30 80.00.10719.00370 244.90 330.00.98896.00023 245.00 67.00.99650.00049 245.10 85.00.12579.00387 244.90 335.00.99112.00018 244.90 68.00.99373.00145 245.30 90.00.14584.00435 244.90 340.00.99076.00022 245.00 69.00.99939.00205 245.00 95.00.16924.00469 244.80 345.00.99328.00010 244.90 70.00.99783 -.00066 245.10 100.00.19277.00490 244.80 350.00.99172.00013 245.00 71.00.99807.00018 245.10 105.00.21822.00515 244.80 355.00.99460.00034 244.90 72.00.99819 -.00084 245.10 110.00.24426.00534 244.80 360.00.99508.00013 244.90 73.00.99639 -.00265 245.20 115.00.27163.00546 244.80 365.00.99592.00012 244.90 74.00.99289.00012 245.40 120.00.29888.00567 244.80 370.00.99628.00010 244.90 75.00.99663.00259 245.20 125.00.32829.00573 244.70 375.00.99688 -.00002 244.90 76.00.99807.00169 245.10 130.00.35614.00549 244.70 380.00.99604.00005 245.00 77.00 1.00000 -.00060 245.00 135.00.38314.00561 244.70 385.00.99772.00005 244.90 140.00.41219.00561 244.60 390.00.99652.00005 245.00 145.00.43920.00559 244.60 395.00.99520.00026 244.90 150.00.46813.00571 244.60 400.00.99916.00012 244.90 155.00.49634.00571 244.60 405.00.99940.00005 244.90 160.00.52527.00583 244.60 410.00.99964.00002 244.90 165.00.55467.00579 244.60 415.00.99964.00004 244.90 170.00.58312.00576 244.60 420.00 1.00000 -.00012 244.90 175.00.61229.00573 244.60 180.00.64038.00568 244.60 185.00.66907.00574 244.60 190.00.69775.00541 244.60 195.00.72320.00510 244.60 20(.00.74877.00485 244.60 205.00.77170.00447 244.60 210.00.79342.00385 244.60 215.00.81023.00365 244.70 220.00.82991.0)0383 244.70 225.00.84852.00364 244.70 230.00.86628.00344 244.70 235.00.88297.00306 244.70 240.00.89689.00266 244.70 245.00.90961.00250 244.70 NORMALIZED DATA FROM RUN 63 NORMALIZED DATA FROM IRUN 64 NIORMALIZED DATA FROM RUN 64 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF MIN MIN-' OF MIN MIN-' OF.00.00500.00365 262.80.00.00000.00046 267.30 50.00.99771.00086 269.40 1.00.00731.00632 262.60 1.00.00092.00498 267.70 51.00.99943.00000 269.30 2.00.01264.00880 262.70 2.00.00996.01217 267.90 52.00.99771 -.00086 269.40 3.00.02491.01069 262.50 3.00.02526.01808 267.90 53.00.99771.00017 269.40 4.00.03402.01298 262.60 4.00.04612.02740 267.90 54.00.99805.00028 269.40 5.00.05088.01663 262.40 5.00.08007.03677 267.50 55.00.99828.00000 269.40 6.00.06727.02138 262.40 6.00.11966.04601 267.20 56.00.99805.00086 269.40 7.00.09364.02605 262.00 7.00.17209.05668 266.60 57.00 1.00000.00011 269.30 8.00.11938.02960 261.90 8.00.23301.06488 266.00 9.00.15285.03364 261.50 9.00.30185.06843 265.30 10.00.18667.03668 261.30 10.00.36988.07221 264.90 11.00.22621.03874 260.90) 11.00.44628.07459 264.30 12.00.26414.04040 260.70 12.00.51905.06693 263.90 13.00.30700.04123 261.30 13.00.58014.06126 263.80 14.00.34660.04218 260.20 14.00.64158.06069 263.70 15.00.39135.04344 259.90 15.00.70153.05373 263.60 16.00.43347.04475 259.80 16.00.74903.04959 264.00 17.00.48085.04384 259.50 17.00.80071.04511 264.00 18.00.52116.04307 259.60 18.00.83925.03797 264.40 19.00.56700.04267 259.40 19.00.87665.03070 264.60 20.00.60650.04241 259.50 20.00.90066.02418 265.20 21.00.65182.03958 259.20 21.001.92501.02083 265.50 22.00.68565.03423 259.40 22.00.94232.01777 266.00 23.00.72028.03234 259.40 23.00.96055.01305 266.20 24.00.75033.03213 259.60 24.00.96843.00959 266.80 25.00.78454.02982 259.50 25.00.97974.00761 267.00 26.00.80996.02616 259.80 26.00.98364.00323 267.50 27.00.83685.02415 259.90 27.00.98619.00181 267.90 28.00.85825.02308 260.20 28.00.98726.00365 268.30 29.00.88302.01970 260.20 29.00.99350.00206 268.30 30.00.89766.01712 260.70 30.00.99139.00150 268.70 31.00.91727.01709 260.70 31.00.99651.00243 268.60 32.00.93183.01442 260.90 32.00.99624.00037 268.80 33.00.94611.01053 261.00 33.00.99725 -.00043 268.90 34.00.95289.00892 261.40 34.00.99539 -.00025 269.10 35.00.96395.00826 261.50 35.00.99675.00056 269.10 36.00.96940.00614 261.80 36.00.99651.0)033 269.20 37.00.97622.00482 261.90 37.00.99741.00079 269.20 38.00.97903.00433 262.20 38.00.99809.00068 269.20 39.00.98488.00461 262.20 39.00.99877 -.00041 269.20 40.00.98826.00292 262.30 40.00.99728.00040 269.30 41.00.99072.00057 262.40 41.00.99957.00034 269.20 42.00.98940 -.00012 262.70 42.00.99796 -.00075 269.30 43.00.99048.00258 262.80 43.00.99807 -.00058 269.30 44.00.99456.00267 262.70 44.00.99681.00023 269.40 45.00.99582 -.00006 262.70 4.00.99853.00011 269.30 46.00.99444 -.00017 262.90 46.00.99703.00011 269.40 47.00.99547.00014 262.90 47.00.99875 -.00069 269.30 48.00.99472.00158 263.00 48.00.9956 -.00052 269.50 49.00.99862 -.00081 262.80 49.00.99771.0(103 269.40 50.00.99311.00069 263.20 51.00 1.00000.00184 262.80

-292NORMALIZED DATA FROM RUN 66 NORMALIZED 1ATA PROM RUN 66 (CONT'D) NORMALIZED DATA FROM RUN 66 (CONTID) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF MIN MIN' OF MIN MIN' OF.0.00000.00001 325.8 500.0.18527.00076 325.9 1000.0.67923.00120 325.8 10.0.00017.00003 325.8 510.0.19288.00076 325.9 1010.0.69078.00111 325.7 20.0.00056.00001 325.7 520.0.20050.00074 325.9 1020.0.70135.00102 325.7 30.0.00029.00004 325.7 530.0.20778.00074 325.9 1030.0.71126.00097 325.7 40.0.00133.00010 325.7 540.0.21539.00079 325.9 1040.0.72085.00097 325.7 50.0.00237 -.00001 325.7 550.0.22366.00076 325.9 1050.0.73076.00111 325.7 60.0.00111 -.00011 325.7 560.0.23062.00078 326.0 1060.0.74297.00117 325.7 70.0.00018 -.00003 325.7 570.0.23922.00083 326.0 1070.0.75419.00099 325.7 80.0.00057.00010 325.7 580.0.24716.00081 326.0 1080.0.76279.00088 325.7 90.0.00227.00009 325.7 590.0.25543.00083 326.0 1090.0.77172.00102 325.7 100.0.00233.00005 325.7 600.0.26370.00083 326.0 1100.0.78327.00101 325.7 110.0.00337,.00002 325.7 610.0.27196.00081 326.0 1110.0.79187.00088 325.6 120.0.00277.00009 325.8 620.0.27991.00093 326.0 1120.0.80080,.00096 325.6 130.0,.00512.00025 325.8 630.0.29047,.00107 326.0 1130.0.81104,.00101 325.6 140.0.00781.00028 325.8 640.0.30137.00099 326.0 1140.0.82095.00093 325.6 150.0.01082.00020 325.8 650.0.31030,.00094 326.0 1150.0.82955.00093 325.6 160.0.01186.00017 325.8 660.0.32021.00089 325.8 1160.0.83946.00096 325.6 170.0.01422.00027 325.8 670.0.32815.00088 325.8 1170.0.84872.00086 325. 6 180.0.01723.00025 325.8 680.0.33773.00104 325.8 1180.0.85666.00076 325.6 190.0.01926.00020 325.8 690.0.34896.00097 325.8 1190.0.86394.00084 325.6 200.0.02129.00022 325.8 700.0.35723.00094 325.8 1200.0.87352,.00089 325.6 210.0.02365.00028 325.8 710.0.36780.00101 325.8 1210.0.88179.00074 325.5 220.0.02699.00038 325.8 720.0.37738.10089 325.8 1220.0.88842.00073 325.5 230.0.03131.00032 325.8 730.0.38565.00088' 325.8 1230.0.89636.00076 325.5 240.0.03334.00024 325.8 740.0.39491.00097 325.8 1240.0.90364.00076 325.5 250.0.03603.00035 325.8 750.0.40515.00106 325.8 1250.0.91159.00079 325.5 260.0.04035.00056 325.8 760.0.41604.00116 325.9 1260.0.91953.00065 325.5 270.0.04731.00056 325.8 770.0.42826.00107 325.9 1270.0.92451.00061 325.5 280.0.05164.00040 326.0 780.0.43751.00094 325.9 1280.0.93179.00070 325.5 290.0.05531.00045 326.0 790.0.44709.00106 325.9 1290.0.93842.00051 325.5 300.0.06062.00050 326.0 800.0.45865.00099 325.9 1300.0.94209.00048 325.5 310.0.06528.00048 326.1 810.0.46692.00106 325.8 1310.0.94806.00050 325.8 320.0.07026.00050 326.1 820.0.47979.00112 325.8 1320.0.95206.00048 325.8 330.0.07524.00051 326.1 830.0.48937.00099 325.8 1330.0.95770.00040 325.8 340.0.08056.00053 326.1 840.0.49961.00104 325.8 1340.0.96006.00037 325.8 350.0.08587.00048 326.1 850.0.51018.00104 325.8 1350.0.96504.00043 325.8 360.0.09020.00051 326.0 860.0.52042.00102 325.8 1360.0.96871.00033 325.7 370.0.09617.00058 326.0 870.0.53066.00097 325.8 1370.0.97173.00028 325.7 380.0.10181.00068 326.0 880.0.53992.00096 325.8 1380.0.97441.00037 325.7 390.0.10975.00074 326.0 890.0.54983.00104 325.8 1390.0.97907.00040 325.7 400.0.11670.00066 326.0 900.0.56073.00104 325.8 1400.0.98241.00028 325.7 410.0.12300.00066 326.0 910.0.57064.00106 325.8 1410.0.98476.00019 325.5 420.0.12996.00066 326.0 920.0.58186.00120 325.8 1420.0.98613.00019 325.5 430.0.13626.00060 326.0 930.0.59473.00116 325.8 1430.0.98849.00025 325.5 440.0.14190.00058 326.0 940.0.60497.00106 325.8 1440.0.99118.00025 325.5 450.0.14787.00065 326.0 950.0.61587.00127 325.8 1450.0.99353.00010 325.5 460.0.15482.00071 325.9 960.0.63038.00135 325.8 1460.0.99326 -.00001 325.5 470.0.16211.00079 325.9 970.0.64292.00120 325.8 1470.0.99332.00010 325.5 480.0.17070.00078 325.9 980.0.65448.00119 325.8 1480.0.99534.00033 325.5 490.0.17766.00073 325.9 990.0.66669.00124 325.8 1490.0 1.00000.00023 325.5 NORMALIZED DATA PROM R U N 68 NORMALIZED DATA FROM RUN 68 (CONT'D) NORMALIZED DATA FROM RUN 69 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' oF MIN MIN-i OF MIN MIN-i OF.00.00000,.00014 326.10 250.00.45283.00384 326.40.00.00000.00007 325.80 5.00.00142,.00020 326.00 255.00.47296.00390 326.40 5.00.00066.00015 325.80 10.00.00203.00012 326.00 260.00.49187.00375 326.40 10.00.00154.00026 325.80 15.00,.00264.00015 326.00 265.00,.51047.00384 326.40 15.00,.00330.00026 325.80 20.00.00356.00018 326.00 270.00.53029.00415 326.40 20.00.00418.00018 325.80 25.00.00447,.00018 326.00 275.00.55194.00415 3.26.40 25.00.00505.00015 325.80 30.00.00539.00012 326.00 280.00.57176.00366 326.40 30.00.00564.00015 325.80 35.00.00569,.00021 326.00 285.00.58853.00354 326.40 35.00,.00652,.00006 325.80 40.00.00752.00024 326.00 290.00.60713.00403 326.40 40.00.00622 -.00003 325.80 45.00.00813.00018 326.00 295.00.62878.00396 326.40 45.00.00622.00003 325.80 50.00.00935.00034 326.00 300.00.64677.00378 326.40 50.00.00652.00023 325.80 55.00.01149.00030 326.00 305.00.66659.00433 326.40 55.00.00857.00020 325.80 60.00.01240.00034 326.00 310.00.69007.00393 326.40 60.00.00857.00000 325.80 65.00.01484.00058 326.00 315.00.70593.00424 326.40 65.00.00857.00003 325.80 70.00.01819.00058 326.00 320.00.73246.00506 326.40 70.00.00886.00015 325.80 75.00.02063.00046 326.00 325.00.75655.00476 326.40 75.00.01003.00015 325.80 80.00.02277.00070 326.00 330.00.78003.00467 326.40 80.00.01032.00018 325.80 85.00.02765.00098 326.00 335.00.80320.00457 326.40 85.00.01179.00038 325.80 90.00.03253.00095 326.00 340.00.82576.00436 326.40 90.00.01413.00056. 325.80 95.00.03710.00116 326.00 345.00.84680.00439 326.40 95.00.01735.00067 325.80 100.00.04411.00146 326.00 350.00.86967.00467 326.40 100.00.02086.00064 325.80 105.00.05174.00165 326.00 355.00.89346.00473 326.40 105.00.02379.00073 325.80 110.00.06058.00174 326.00 360.00.91694.00436 326.40 110.00.02818.00082 325.80 115.00.06912.00180 326.00 365.00.93706.00372 326.40 115.00.03198.00082 325.80 120.00.07857.00226 326.00 370.00.95414.00323 326.40 120.00.03637.00114 325.80 125.00.09168.00229 326.00 375.00.96939.00238 326.40 125.00.04340.00132 325.80 130.00.10144.00226 326.00 380.00.97793.00203 326.40 130.00.04954.00149 325.80 135.00.11425.00265 326.00 385.00.98973.00178 326.30 135.00.05833.00170 325.80 140.00.12797.00271 326.00 390.00.99573.00084 326.20 140.00.06652.00179 325.80 145.00.14139.00281 326.00 395.00.99817.00015 326.20 145.00.07618.00190 325.80 150.00.15602.00290 326.00 400.00.99726.00018 326.20 150.00.08555.00208 325.80 155.00.17035.00311 326.00 405.00 1.00000.00024 326.20 155.00.09696.00258 325.80 160.00.18713.00239 326.00 160.00.11131.00269 325.80 165.00.19426.00215 326.10 165.00.12389.00275 325.80 170.00.20859.00290 326.10 170.00.13882.00296 325.80 175.00.22323.00233 326.10 175.00.15346.00296 325.80 180.00.23188.00236 326.20 180.00.16838.00316 325.80 185.00.24682.00296 326.20 185.00.18507.00337 325.80 190.00.26146.00287 326.20 190.00.20204.00325 325.80 195.00.27548.00248 326.20 195.00.21756.00354 325.80 200.00.28625.00269 326.30 200.00.23746.00383 325.80 205.00.30242.00332 326.30 205.00.25590.00309 325.80 210.00.31949.00326 326.30 210.00.26841.00321 325.90 215.00.33504.00338 326.30 215.00.28802.00398 325.90 220.00.35334.00357 326.30 220.00.30821.00359 325.90 225.00.37072.00335 326.30 225.00.32394.00377 326.00 230.00.38688.00348 326.30 230.00.34589.00445 326.00 235.00.40548.00297 326.30 235.00.36843.00397 326.00 240.00.41655.00291 326.40 240(.00.38561.00394 326.10 245.00.43454.00363 326.40 245.00.40785.00436 326.10

-293NORMALIZED DATA FROM RUN 69 (CONT'I) NOIRMALIZED DATA HRUM RUN 70 NOIRMALIZED DATA FROM RUN 71 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF M I MI N- OF M I MIN- OF 250.00.42922.00424 326.10.00.00000.00022 338.20.00.00000.00022 338.60 255.00.45030.00427 326.10 5.00.00224.00046 338.20 0.00.00222.00037 338.60 260.00.47196.00454 326.10.10.00.00457.00047 338.20 10.00.00369.00029 338,.60 265.00.49567.00457 326.10 15.00.00690.00061 338.20 15.00.00515.00044 338.60 270.00.51762.00462 326.10 20.00.01069.00087 338.20 20.00.00808.00050 338.60 275.00.54191.00489 326.10 25.00.01564.00108 338.20 25.00.01013.00056 338.60 280.00.56650.00483 326.10 30.00.02146.00137 338.20 30.00.01365.00094 338.60 285.00.59021.00580 326.10 35.00.02933.00175 338.20 35.00.01951.00126 338.60 290.00.62446.00594 326.10 40.00.03.894.00227 338.20 40.00.02625.00141 338.60 295.00.64963.00501 326.10 45.00.05204.00259 338.20 45.00.03358.00161 338.60 300.00.67451.00486 326.10 50.00.06485.00240 338.20 50.00.04237.00149 338.60 305.00.69822.00489 326.10 55.00.07609.00281 338.30 55.00.04846.00130 338.70 310.00.72339.00509 326.10 60.00.09297.00390 338.30 60.00.05542.00228 338.80 315.00.74915.00509 326.10 65.00.11511.00437 338.30 65.00.07125.00343 338.80 320.00.77432.00518 326.10 70.00.13666.00401 338.30 70.00.08971.00399 338.80 325.00.80096.00515 326.10 75.00.15516.00409 338.50 75.00.11111.00443 338.80 330.00.82584.00492 326.10 80.00.17758.00498 338.50 80.00.13397.00475 338.80 335.00.85013.00495 326.10 85.00.20496.00556 338.50 85.00.15858.00495 338.80 340.00.87531.00495 326.10 90.00.23320.00559 338.50 90.00.18350.00513 338.80 345.00.89960.00506 326.10 95.00.26087.00580 338.50 95.00.20987.00528 338.80 350.00.92595.00498 326.10 100.00.29116.00591 338.50 100.00.23625.00587 338.80 355.00.94936.00442 326.10 105.00.31999.00591 338.50 105.00.26856.00602 338.70 360.00.97014.00340 326.10 110.00.35028.00609 338.50 110.00.29640 \.00560 338.70 365.00.98332.00228 326.10 115.00.38086.00620 338.50 115.l0.32454.00563 338.70 370.00.99298.00114 326.10 120.00.41231.00641 338.50 120.00.35267.00580 338.70 375.00.99473.00047 326.10 125.00.44493.00652 338.50 125.00.38256.00607 338.70 380.00.99766.00029 326.10 130.00.47754.00652 338.50 130.00.41334.00559 338.70 385.00.99766.00003 326.10 135.00.51016.00670 338.50 135.00.43847.00556 338.80 390.00.99795.00006 326.10 140.00.54452.00676 338.50 140.00.46895.00621 338.80 395.00.99824.00006 326.10 145.00.57772.00606 338.50 145.00.50060.00633 338.80 400.00.99854.00003 326.10 150.00.60510.00591 338.50 150.00.53225.00636 338.80 405.00.99854.00015 326.10 155.00.63684.00681 338.50 155.00.56420.00648 338.80 410.00 1.00000.00015 326.10 160.00.67325.00711 338.50 160.00.59702.00633 338.80 165.00.70790.00702 338.50 165.00.62750.00627 338.80 170.00.74343.00716 338.50 170.00.65974.00648 338.80 175.00.77954.00711 338.50 175.00.69227.00385 338.80 180.00.81449.00681 338.50 180.00.69829.00686 339.30 185.00.84769.00670 338.50 185.00.76085.00939 338.80 190.00.88147.00649 338.50 190.00.79221.00651 338.80 195.00.91263.00600 338.50 195.00.82591.00654 338.80 200.00.94146.00533 338.50 200.00.85757.00662 338.80 205.00.96593.00419 338.50 205.00.89215.00677 338.80 210.00.98340.00291 338.50 210.00.92527.00621 338.80 215.00.99505.00157 338.50 215.00.95428.00528 338.80 220.00.99913.00044 338.50 220.00.97802.00366 338.80 225.00.99942.00009 338.50 225.00.99091 -.00086 338.80 230.00 1.00000.00003 338.50 230.00.96938.00073 339.30 235.00.99824.00306 338.80 240.00 1.00000.00015 338.80 NORMALIZED DATA FROM RUN 72 NORMALIZED DATA FROM RUN 72 (CONT'D) NORMALIZED DATA FROM RUN 73 TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN-' OF MIN MIN-' OF MIN MIN-' OF.0.00000.00001 339.1 500.0.31536.00142 338.9.00.00000.00040 347.70 10.0.00023.00006 339.1 510.1.32902.00158 338.9 5.00.00404.00081 347.70 20.0.00119.00021 339.1 520.0.34701.00183 339.1 10.00.00814.00005 347.70 30.0.00447.00020 339.1 530.0.36558.00177 339.1 15.00.00451 -.00009 347.80 40.0.00515.00013 339.0 540.0.38241.00177 339.1 20.00.00724.00044 347.80 50.0.00698.00015 339.0 550.0.40098.00173 339.1 25.00.00888 -.00012 347.80 60.0.00823.00017 339.0 560.0.41695.00176 339.1 30.00.00606 -.00006 347.90 70.0.01036.00015 339.0 570.0.43609.00187 339.1 35.00.00825.00055 347.90 80.0.01132.00017 339.0 580.0.45437.00184 339.1 40.00.01153.00066 347.90 90.0.01373.00023 339.0 590.0.47294.00193 339.1 45.00.01481.00093 347.90 100.0.01585.00024 339.0 600.0.49295.00199 339.1 50.00.02083.00211 347.90 110.0.01855.00026 339.0 610.0.51267.00196 339.1 55.00.03594.00263 347.80 120.0.02096.00023 339.0 620.0).53210.00190 339.1 60.00.04715.00254 347.80 130.0.02308.00023 339.0 630.0.55067.00212 339.1 65.00.06137.00303 347.80 140.0.02549.00024 338.9 640.0.57443.00229 339.1 70.00.07750.00394 347.80 150.0.02790.00027 338.9 650.0.59646.00215 339.1 75.00.10073.00492 347.80 160.0.03089.00034 338.9 660.0.61733.00204 339.1 80.00.12670.00552 347.80 170.0.03474.00036 338.9 670.0.63734.00209 339.1 85.00.15595.00610 347.80 180.0.03802.00041 338.9 680.0.65908.00210 339.1 90.00.18766.00670 347.80 190.0.04302.00053 338.9 690.0.67938.00204 339.1 95.00.22292.00719 347.80 200.0.04860.00044 338.9 700.0.69997.00204 339.1 100.00.25955.00688 347.80 210.0.05188.00050 338.9 710.0.72026.00194 339.1 105.00.29172.00685 347.90 220.0.05862.00050 338.9 720.0.73883.00191 339.1 110.00.32808.00733 347.90 230.0.06189.00044 338.9 730.0.75855.00187 339.1 115.00.36499.00749 347.90 240.0.06748.00062 338.9 740.0.77625.00178 339.1 120.00.40298.00771 347.90 250.0.07421.00054 338.9 750.0.79424.00160 339.1 125.00.44207.00793 347.90 260.0.07835.00037 338.9 760.0.80819.00157 339.1 130.00.48226.00859 347.90 270.0.08163.00052 338.9 770.0.82561.00164 339.1 135.00.52799.00867 347.80 280.0.08866.00062 338.9 780.0.84100.00155 339.1 140.00.56900.00806 347.80 290.0.09395.00054 339.0 790.0.85668.00150 339.1 145.00.60863.00834 347.80 300.0.09953.00066 339.0 800.0.87092.00141 339.1 150.00.65237.00872 347.80 310.0.10714.00072 339.0 810.0.88487.00138 339.1 155.00.69584.00888 347.80 320.0.11387.00066 339.0 820.0.89853.00118 339.1 160.00.74121.00894 347.80 330.0.12032.00067 339.0 830.0.90844.00101 339.1 165.00.78522.00902 347.80 340.0.12735.00085 339.0 840.0.91864.00101 339.1 170.00.83142.00852 347.80 350.0.13726.00093 339.0 850.0.92855.00102 339.1 175.00.87043.00830 347.90 360.0.14602.00082 339.0 860.0.93904.00106 339.1 180.00.91444.00831 347.90 370.0.15362.00088 339.0 870.0.94982.00092 339.1 185.00.95353.00664 347.90 380.0.16353.00103 339.0 880.0.95742.00062 339.1 190.00.98086.00391 347.90 390.0.17431.00108 339.1 890.0.96214.00054 339.1 195.00.99262.00167 347.90 400.0.18509.00112 339.1 900.0.96830.00059 339.1 200.00.99754.00068 347.90 410.0.19673.00119 339.1 910.0.97388.00059 339.1 205.00.99945.00025 347.90 420.0.20895.00122 338.9 920.0.98004.00047 339.1 210.00 1.00000 -.00003 347.90 430.0.22117.00119 338.9 930.0.98332.00036 339.1 440,0.23281.00124 338.9 940.0.98717.00027 339.1 450.0.24589.00135 338.9 950.0.98872.00018 339.1 460.0,25984.00132 338.9 960.0.99084.00026 339.1 470.0.27235.00128 338.9 970.0.99382.00024 339.1 480.0.28544.00141 338.9 980.0.99566.00017 339.1 490.0.30054.00150 338.9 990.0.99720.00018 339.1 1.000.0.99932.00014 339.1 1010.0 1.00000.00003 339.1

-29k4NORMALIZED DATA FROM RUN 75 NORMALIZED DATA FROM RUN 75 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN- OF OMIN MIN-' OF.00.00000.00021 347.60 250.00.99795 -.00006 347.70 5.00.00213.00035 347.60 255.00.99684 -.00003 347.70 10.00.00351.00033 347.60 260.00.99767.00032 347.70 15.00.00544.00010 347.60 265.00 1.00000.00004 347.60 20.00.00450.00018 347.70 25.00.00727 -.00033 347.70 30.00.00118 -.00039 347.70 35.00.00339.00066 347.70 40.00.00782.00105 347.70 45.00.01390.00166 347.70 50.00.02441.00241 347.70 55.00.03796.00299 347.70 60.00.05427.00365 347.70 65.00.07445.00418 347.70 70.00.09602.00434 347.70 75.00.11786.00418 347.70 80.00.13777.00346 347.70 85.00.15243.00357 347.70 90.00.17344.00451 347.70 95.00.19749.00433 347.70 100.00.21678.00455 347.80 105.00.24304.00539 347.80 110.00.27069.00550 347.80 115.00.29807.00559 347.80 120.00.32662.00554 347.70 125.00.35344.00509 347.70 130.00.37749.00514 347.70 135.00.40487.00561 347.70 140.00.43362.00498 347.70 145.00.45464.00398 347.70 150.00.47344.00418 347.70 155.00.49639.00451 347.70 160.00.51851.00445 347.70 165.00.54090.00411 347.70 170.00.55963.00447 347.80 175.00.58562.00539 347.80 180.00.61355.00570 347.80 185.00.64258.00619 347.80 190.00.67548.00739 347.80 195.00.71648.00819 347.70 200.00.75740.00827 347.70 205.00.79915.00885 347.70 210.00.84588.00932 347.70 215.00.89233.00885 347.70 220.00.93436.00735 347.70 225.00.96588.00495 347.70 230.00.98385.00252 347.70 235.00.99104.00122 347.70 240.00.99602.00064 347.70 245.00.99740.00019 347.70 NORMALIZED DATA FROM RUN 76 NORMALIZED DATA FROM RUN 76 (CONT'D) TIME ALPHA RATE TEMP. TIME ALPHA RATE TEMP. MIN MIN OF MIN MIN-' OF.0.00000.00002 347.0 500.0.62017.00275 346.8 10.0.00031.00010 347.0 510.0.64737.00269 346.8 20.0.00205.00016 347.0 520.0.67398.00257 346.8 30.0.00351.00012 347.0 530.0.69881.00256 346.8 40.0.00437.00009 347.0 540.0.72513.00257 346.8 50.0.00523.00013 347.0 550.0.75026.00239 346.7 60.0.00697.00009 347.0 560.0.77302.00202 346.7 70.0.00695.00013 347.0 570.0.79075.00207 346.7 80.0.00958.00034 347.0 580.0.81440.00214 346.7 90.0.01370.00034 347.0 590.0.83361.00197 346.8 100.0.01633.00032 347.0 600.0.85370.00174 346.8 110.0.02015.00040 347.0 610.0.86847.00164 346.8 120.0.02427.00037 347.0 620.0.88650.00171 346.8 130.0.02750.00044 347.0 630.0.90275.00149 346.8 140.0.03309.00054 347.0 640.0.91634.00124 346.8 150.0.03839.00049 347.0 650.0.92756.00115 346.8 160.0.04280.00046 347.0 660.0.93937.00100 346.8 170.0.04751.00043 347.1 670.0.94763.00090 346.8 180.0.05133.00050 347.1 680.0.95736.00081 346.8 190.0.05752.00071 347.1 690.0.96385.00072 346.8 200.0.06548.00074 347.1 700.0.97181.00074 346.8 210.0.07226.00081 347.1 710.0.97859.00054 346.8 220.0.08170.00093 347.1 720.0.98271.00046 346.8 230.0.09085.00086 347.1 730.0.98771.00046 346.8 240.0.09881.00078 347.1 740.0.99182.00046 346.8 250.0.10648.00094 347.1 750.0.99683.00031 346.8 260.0.11770.00112 347.0 760.0.99798.00007 346.8 270.0.12892.00118 346.9 770.0.99825.00010 346.8 280.0.14132.00130 346.9 780.0 1.00000.00009 346.8 290.0.15491.00130 346.9 300.0.16731.00131 346.9 310.0.18119.00146 346.9 320.0.19655.00167 346.9 330.0.21458.00168 346.9 340.0.23024.00164 346.9 350.0.24738.00174 346.9 360.0.26511.00186 346.9 370.0.28461.00213 346.9 380.0.30767.00220 346.9 390.0.32865.00216 346.9 400.0.35082.00231 346.8 410.0.37477.00241 346.8 420.0.39901.00245 346.8 430.0.42384.00254 346.8 440.0.44986.00278 346.8 450.0.47943.00290 346.8 460.0.50781.00282 346.8 470.0.53590.00278 346.8 480.0.56340.00282 346.8 490.0.59238.00284 346.8

APPENDIX U OBSERVED EXPERIMENTAL DATA OBSERVED EXPERIMENTAL DATA FROM RUN 6 OBSERVED EXPERIMENTAL DATA FROM RUN 6 (CONT'D) TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN oF CM MIN OF CM.0 79.4 -. — 50.0 259.8 17.210 100.0 259.8 22.470 150.0 259.8 26.280 173.0 260.0 27.105 196.0 260.0 27.560 1.0 125.0 -. — 51.0 259.8 17.320 101.0 259.8 22.570 151.0 259.8 26.325 174.0 259.9 27.135 197.0 260.0 27.580 2.0 158.0 -. —- 52.0 259.8 17.420 102.0 259.8 22.670 152.0 259.8 26.375 175.0 260.0 27.170 198.0 260.0 27.590 3.0 183.0 -. 53.0 259.8 17.540 103.0 259.8 22.760 153.0 259.8 26.420 176.0 259.9 27.190 199.0 260.0 27.600 4.0 199.7 8.230 54.0 259.8 17.640 104.0 259.8 22.855 154.0 259.8 26.465 177.0 260.0 27.210 200.0 260.0 27.610 5.0 213.0 9.580 55.0 259.8 17.750 105.0 259.8 22.950 155.0 259.8 26.500 178.0 260.0 27.240 201.0 260.1 27.620 6.0 222.6 10.690 56.0 259.8 17.860 106.0 259.8 23.040 156.0 259.8 26.555 179.0 260.0 27.255 202.0 260.0 27.635 7.0 231.2 11.550 57.0 259.8 17.970 107.0 259.8 23.140 157.0 259.8 26.588 180.0 260.0 27.280 203.0 260.1 27.640 8.0 237.0 12.235 58.0 259.8 18.075 108.0 259.8 23.225 158.0 259.8 26.630 181.0 260.0 27.300 204.0 260.0 27.650 9.0 242.0 12.770 59.0 259.8 18.180 109.0 259.8 23.320 159.0 259.8 26.670 182.0 260.0 27.320 205.0 260.2 27.655 10.0 245.7 13.198 60.0 259.8 18.285 110.0 259.8 23.410 160.0 259.9 26.705 183.0 260.0 27.330 206.0 260.1 27.670 11.0 249.0 13.525 61.0 259.8 18.400 111.0 259.8 23.500 161.0 259.9 26.740 184.0 260.0 27.360 207.0 260.2 27.680 12.0 251.0 13.780 62.0 259.8 18.500 112,0 259.8 23.590 162.0 259.9 26.785 185.0 260.0 27.380 208.0 260.1 27.685 13.0 253.0 13.991 63.0 259.8 18.605 113.0 259.8 23.680 163.0 259.9 26.810 186.0 260.0 27.400 209.0 260.2 27.690 14.0 254.2 14.145 64.0 259.8 18.710 114.0 259.8 23.760 164.0 259.9 26.855 187.0 260.0 27.410 210.0 260.1 27.695 15.0 255.6 14.270 65.0 259.8 18.820 115.0 259.8 23.855 165.0 260.0 26.880 188.0 260.0 27.440 211.0 260.2 27.700 16.0 256.6 14.370 66.0 259.8 18.925 116.0 259.8 23.930 166.0 259.9 26.900 189.0 260.0 27.455 212.0 260.1 27.702 17.0 257.1 14.440 67.0 259.8 19.025 117.0 259.8 24.010 167.0 260.0 26.935 190.0 260.0 27.470 213.0 260.2 27.708 18.0 257.7 14.495 68.0 259.8 19.140 118.0 259.8 24.110 168.0 259.9 26.965 191.0 260.0 27.480 214.0 260.1 27.710 19.0 258.1 14.545 69.0 259.8 19.250 119.0 259.8 24.190 169.0 260.0 27.000 192.0 260.0 27.500 215.0 260.2 27.715 20.0 258.3 14.585 70.0 259.8 19.350 120.0 259.8 24.270 170.0 259.9 27.030 193.0 260.0 27.510 216.0 260.1 27.720 21.0 258.9 14.620 71.0 259.8 19.460 121.0 259.8 24.350 171.0 260.0 27.060 194.0 260.0 27.530 217.0 260.2 27.725 22.0 259.0 14.660 72.0 259.8 19.560 122.0 259.8 24.425 172..0 259.9 27.085 195.0 260.0 27.555 218.0 260.2 27.730 23.0 259.2 14.700 73.0 259.8 19.665 123.0 259.8. 24.505 24.0 259.2 14.755 74.0 259.8 19.775 124.0 259.8 24.590 25.0 259.5 14.805 75.0 259.8 19.885 125.0 259.8 24.665 26.0 259.6 14.875 76.0 259.8 19.990 126.0 259.8 24.745 27.0 259.7 14.950 77.0 259.8 20.098 127.0 259.8 24.810 28.0 259.8 15.020 78.0 259.8 20.200 128.0 259.8 24.895 29.0 259.8 15.100 79.0 259.8 20.310 129.0 259.8 24.970 30.0 259.8 15.185 80.0 259.8 20.420 130.0 259.8 25.040 31.0 259.8 15.270 81.0 259.8 20.525 131.0 259.8 25.120 32.0 259.8 15.355 82.0 259.8 20.630 132.0 259.8 25.190 33.0 259.8 15.450 83.0 259.8 20.735 133.0 259.8 25.240 34.0 259.8 15.548 84.0 259.8 20.840 134.0 259.8 25.338 35.0 259.8 15.645 85.0 259.8 20.945 135.0 259.8 25.400 36.0 259.8 15.745 86.0 259.8 21.055 136.0 259.8 25.470 37.0 259.8 15.850 87.0 259.8 21.160 137.0 259.8 25.530 38.0 259.8 15.950 88.0 259.8 21.265 138.0 259.8 25.600 39.0 259.8 16.055 89.0 259.8 21.375 139.0 259.8 25.655 40.0 259.8 16.1.60 90.0 259.8 21.475 140.0 259.8 25.710 41.0 259.8 16.260 91.0 259.8 21.570 141.0 259.8 25.788 42.0 259.8 16.365 92.0 259.8 21.675 142.0 259.8 25.840 43.0 259.8 16.470 93.0 259.8 21.780 143.0 259.8 25.900 44.0 259.8 16.575 94.0 259.8 21.880 144.0 259.8 25.955 45.0 259.8 16.685 95.0 259.8 21.975 145.0 259.8 26.010 46.0 259.8 16.792 96.0 259.8 22.070 146.0 259.8 26.085 47.0 259.8 16.895 97.0 259.8 22.170 147.0 259.8 26.110 48.0 259.8 17.000 98.0 259.8 22.270 148.0 259.8 26.170 49.0 259.8 17.100 99.0 259.8 22.385 149.0 259.8 26.220 OBSERVED EXPERIMENTAL DATA FROM RUN 7 OBSERVED EXPERIMENTAL DATA FROM RUN 8 TIME TEMP. HEIGHT TIME TE.MP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN oE CM MIN OF CM.0 80.0 —. —- 34.0- 257.5 24.510 68.0 258.0 30.435.0 80.0 —. —- 29.0 257.2 29.180 58.0 257.0 35.430 1.0 130.1 —. —- 35.0 257.1 24.745 69.0 258.0 30.485 1.0 146.0 16.300 30.0 257.3 29.430 59.0 257.0 35.530 2.0 163.2 10.810 36.0 257.0 24.980 70.0 258.0 30.530 2.0 173.0 18.600 31.0 257.0 29.685 60.0 257.0 35.640 3.0 185.1 13.450 37.0 256.9 25.230 71.0 258.0 30.560 3.0 192.0 20.450 32.0 257.0 29.950 61.0 257.0 35.730 4.0 201.7 15.460 38.0 256.8 25.478 72.0 258.2 30.590 4.0 206.7 21.960 33.0 256.9 30.220 62.0 257.2 35.810 5.0 213.8 17.060 39.0 256.8 25.735 73.0 258.2 30.620 5.0 217.9 -23.120 34.0 256.9 30.490 63.0 257.2 35.880 6.0 223.5 18.310 40.0 256.6 25.990 74.0 258.3 30.655 6.0 226.9 24.060 35.0 256.5 30.750 64.0 257.4 35.950 7.0 231.0 19.310 41.0 256.4 26.260 75.0 258.3 30.680 7.0 233.3 24.800 36.0 256.7 31.020 65.0 257.4 36.010 8.0 237.0 20.135 42.0 256.2 26.500 76.0 258.3 30.700 8.0 239.0 25.360 37.0 256.6 31.300 66.0 257.6 36.080 9.0 241.2 20.790 43.0 256.1 26.755 77.0 258.3 30.725 9.0 243.0 25.830 38.0 256.6 31.560 67.0 257.5 36.110 10.0 245.3 21.310 44.0 256.1 27.000 78.0 258.4 30.745 10.0 246.3 26.185 39.0 256.4 31.810 68.0 257.9 36.160 11.0 248.0 21.710 45.0 256.1 27.240 79.0 258.4 30.758 11.0 248.7 26.460 40.0 256.5 32.080 69.0 257.8 36.205 12.0 250.2 22.020 46.0 256.1 27.470 80.0 258.5 30.770 12.0 250.9 26.670 41.0 256.4 32.320 70.0 258.0 36.240 13.0 252.0 22.260 47.0 256.1 27.700 81.0 258.5 30.780 13.0 252.2 26.825 42.0 256.5 32.565 71.0 258.0 36.270 14.0 253.4 22.450 48.0 256.1 27.915 82.0 258.7 30.795 14.0 253.9 26.970 43.0 256.4 32.800 72.0 258.0 36.300 15.0 254.3 22.590 49.0 256.1 28.125 83.0 258.6 30.810 15.0 254.8 27.080 44.0 256.4 33.040 73.0 258.1 36.320 16.0 255.2 22.708 50.0 256.1 28.330 84.0 258.7 30.820 16.0 255.4 27.170 45.0 256.3 33.260 74.0 258.2 36.350 17.0 256.0 22.790 51.0 256.1 28.520 85.0 258.6 30.830 17.0 256.2 27.250 46.0 256.4 33.480 75.0 258.1 36.360 18.0 256.9 22.860 52.0 256.1 28.700 86.0 258.7 30.840 18.0 256.8 27.340 47.0 256.2 33.685 76.0 258.4 36.380 19.0 257.0 22.920 53.0 256.2 28,880 87.0 258.6 30.845 19.0 257.0 27.440 48.0 256.3 33.880 77.0 258.2 36.390 20.0 257.3 22.960 54.0 256.5 29.040 88.0 258.5 30.850 20.0 257.3 27.540 49.0 256.3 34,080 78.0 258.4 36.400 21.0 257.8 22.990 55.0 256.6 29.200 89.0 258.6 30.870 21.0 257.4 27.650 50.0 256.4 34.260 79.0 258.2 36.410 22.0 258.0 23.030 56.0 256.7 29.350 90.0 258.7 30.875 22.0 257.6 27.780 51.0 256.3 34.440 80.0 258.6 36.420 23.0 258.1 23.080 57.0 256.9 29.480 91.0 258.7 30.875 23.0 257.7 27.930 52.0 256.3 34.600 81.0 258.3 36.430 24.0 258.2 23.130 58.0 257.0 29.605 92.0 258.7 30.880 24.0 257.8 28.100 53.0 256.3 34.760 82.0 258.7 36.435 25.0 258.2 23.190 59.0 257.0 29.720 93.0 258.7 30.880 25.0 257.8 28.285 54.0 256.6 34.910 83.0 258.5 36.440 26.0 258.2 23.260 60.0 257.0 29.835 94.0 258.7 30.890 26.0 257.8 28.490 55.0 256.5 35.060 84.0 258.7 36.440 27.0 258.2 23.360 61.0 257.0 29.940 95.0 258.8 30.890 27.0 257.8 28.700 56.0 256.8 35.190 28.0 258.2 23.460 62.0 257.2 30.025 96.0 258.8 30.892 28.0 257.8 28.930 57.0 256.8 35.310 29.0 258.1 23.600 63.0 257.3 30.110 97.0 258.9 30.894 30.0 258.0 23.750 64.0 257.5 30.185 98.0 258.9 30.896 31.0 258.0 23.910 65.0 257.6 30.255 99.0 258.9 30.898 32.0 257.9 24.100 66.0 257.6 30.325 100.0 258.9 30.900 33.0 257.7 24.300 67.0 257.7 30.380 -295

-296OBSERVED EXPERIMENTAL DATA FROM RUN 9 OBSERVED EXPERIMENTAL DATA FROM RUN 10 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM.0 79.2 -. —- 28.0 259.5 17.040 56.0 257.1 22.910.0 81.3 —. —- 28.0 258.0 32.450 56.0 256.0 38.480 1.0 133.1 -. —- 29.0 259.5 17.120 57.0 257.1 23.100 1.0 139.3 —. —- 29.0 258.0 32.555 57.0 256.0 38.560 2.0 163.0 5.970 30.0 259.4 17.220 58.0 257.1 23.270 2.0 171.0 —. —- 30.0 258.0 32.675 58.0 256.2 38.810 3.0 185.4 8.180 31.0 259.5 17.330 59.0 257.2 23.435 3.0 192.4 —. —- 31.0 258.0 32.810 59.0 256.0 38.980 4.0 202.0 9.890 32.0 259.3 17.460 60.0 257.2 23.600 4.0 207.3 23.140 32.0 258.0 32.960 60.0 256.2 39.110 5.0 215.0 11.309 33.0 259.2 17.600 61.0 257.3 23.750 5.0 218.5 25.100 33.0 257.9 33.180 61.0 256.2 39.255 6.0 224.2 12.360 34.0 259.0 17.780 62.0 257.5 23.890 6.0 227.4 26.610 34.0 257.8 33.320 62.0 256.8 39.360 7.0 232.0 13.270 35.0 259.0 17.950 63.0 257.7 24.000 7.0 233.1 27.810 35.0 257.6 33.525 63.0 256.7 39.460 8.0 238.0 14.000 36.0 258.9 18.140 64.0 257.8 24.120 8.0 238.6 28.750 36.0 257.5 33.745 64.0 256.9 39.565 9.0 242.4 14.600 37.0 258.7 18.350 65.0 258.0 24.220 9.0 242.4 29.480 37.0 257.2 33.970 65.0 256.9 39.655 10.0 246.0 15.070 38.0 258.2 18.580 66.0 258.0 24.320 10.0 246.0 30.045 38.0 257.1 34.210 66.0 257.1 39.780 11.0 249.0 15.445 39.0 258.2 18.810 67.0 258.0 24.400 11.0 248.3 30.510 39.0 256.9 34.450 67.0 257.0 39.800 12.0 251.0 15.740 40.0 258.0 19.045 68.0 258.1 24.480 12.0 250.5 30.845 40.0 256.9 34.700 68.0 257.6 39.860 13.0 253.0 15.990 41.0 258.0 19.290 69.0 258.3 24.550 13.0 252.0 31.125 41.0 256.8 34.955 69.0 257.5 39.910 14.0 254.2 16.185 42.0 257.8 19.550 70.0 258.3 24.600 14.0 253.2 31.350 42.0 256.8 35.210 70.0 257.9 39.960 15.0 255.3 16.320 43.0 257.8 19.800 71.0 258.6 24.660 15.0 254.1 31.665 43.0 256.4 35.475 71.0 257.9 40.000 16.0 256.3 16.435 44.0 257.4 20.070 72.0 258.7 24.710 16.0 255.0 31.760 44.0 256.4 35.740 72.0 258.0 40.020 17.0 257.0 16.530 45.0 257.4 20.320 73.0 258.9 24.745 17.0 256.2 31.850 45.0 256.1 35.990 73.0 258.0 40.050 18.0 257.5 16.610 46,0 257.1 20.590 74.0 259.0 24.780 18.0 257.0 31.910 46.0 256.2 36.250 74.0 258.2 40.080 19.0 258.0 16.660 47.0 257.1 20.850 75.0 259.0 24.800 19.0 257.0 31.960 47.0 256.1 36.500 75.0 258.1 40.100 20.0 258.2 16.710 48.0 257.1 21.100 76.0 259.1 24.830 20.0 257.0 32.010 48.0 256.2 36.750 76.0 258.4 40.110 21.0 258.7 16.740 49.0 257.1 21.350 77.0 259.2 24.850 21.0 257.0 32.050 49.0 256.0 37.000 77.0 258.2 40.120 22.0 258.9 16.780 50.0 257.1 21.600 78.0 259.1 24.860 22.0 257.3 32.080 50.0 256.0 37.300 78.0 258.6 40.130 23.0 259.0 16.810 51.0 257.1 21.820 79.0 259.3 24.880 23.0 257.3 32.110 51.0 256.0 37.460 79.0 258.4 40.140 24.0 259.1 16.840 52.0 257.1 22.070 80.0 259.3 24.880 24.0 257.7 32.180 52.0 256.0 37.690 80.0 258.8 40.140 25.0 259.3 16.880 53.0 257.1 22.290 81.0 259.4 24.890 25.0 257.7 32.220 53.0 256.0 37.900 81.0 258.9 40.150 26.0 259.5 16.910 54.0 257.1 22.500 26.0 258.0 32.280 54.0 256.0 38.105 82.0 259.0 40.160 27.0 259.5 16.980 55.0 257.i 22.710 27.0 258.0 32.350 55.0 256.0 38.300 OBSERVED EXPERIMENTAL DATA FROM RUN 11 OBSERVED EXPERIMENTAL DATA FROM RUN 12 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM.0 81.0 —. —- 29.0 259.5 25.290 58.0 257.0 31.300.0 83.0 -. —- 29.0 260.0 25.200 58.0 257.4 31.440 1.0 135.0 ----- 30.0 259.5 25.380 59.0 257.0 31.460 1.0 131.9 9.030 30.0 260.0 25.250 59.0 257.5 31.655 2.0 160.9 12.450 31.0 259.5 25.490 60.0 257.2 31.640 2.0 162.8 11.830 31.0 260.0 25.305 60.0 257.6 31.840 3.0 183.0 15.000 32.0 259.3 25.610 61.0 257.3 31.785 3.0 184.9 14.500 32.0 260.0 25.375 61.0 257.8 32.002 4.0 199.9 17.085 33.0 259.2 25.745 62.0 257.6 31.920 4.0 201.0 16.670 33.0 260.0 25.460 62.0 257.9 32.160 5.0 213.2 18.775 34.0 259.0 25.910 63.0 257.8 32.040 5.0 213.0 18.409 34.0 260.0 25.570 63.0 258.0 32.300 6.0 222.5 20.125 35.0 259.0 26.085 64.0 257.9 32.160 6.0 222.9 19.800 35.0 259.9 25.690 64.0 258.1 32.420 7.0 231.0 21.210 36.0 258.8 26.280 65.0 258.0 32.265 7.0 230.8 20.912 36.0 259.9 25.835 65.0 258.2 32.525 8.0 236.3 22.065 37.0 258.7 26.475 66.0 258.1 32.355 8.0 236.0 21.789 37.0 259.8 25.995 66.0 258.5 32.615 9.0 241.2 22.760 38.0 258.2 26.685 67.0 258.3 32.430 9.0 240.8 22.478 38.0 259.8 26.182 67.0 258.7 32.700 10.0 245.0 23.270 39.0 258.2 26.910 68.0 258.6 32.510 10.0 245.0 23.020 39.0 259.4 26.382 68.0 258.9 32.765 11.0 248.1 23.680 40.0 258.0 27.140 69.0 258.8 32.570 11.0 247.6 23.461 40.0 259.2 26.610 69.0 259.0 32.815 12.0 250.4 24.000 41.0 258.0 27.375 70.0 258.9 32.620 12.0 250.0 23.826 41.0 259.0 26.850 70.0 259.1 32.870 13.0 252.3 24.250 42.0 257.8 27.620 71.0 259.0 32.680 13.0 252.3 24.104 42.0 258.9 27.100 71.0 259.2 32.906 14.0 254.0 24.440 43.0 257.8 27.860 72.0 259.0 32.710 14.0 254.0 24.325 43.0 258.7 27.360 72.0 259.5 32.940 15.0 255.0 24.590 44.0 257.3 28.110 73.0 259.2 32.740 15.0 255.2 24.500 44.0 258.5 27.630 73.0 259.6 32.956 16.0 256.0 24.700 45.0 257.4 28.370 74.0 259.1 32.775 16.0 256.3 24.633 45.0 258.4 27.910 74.0 259.7 32.980 17.0 256.9 24.780'46.0 257.3 28.610 75.0 259.3 32.790 17.0 257.1 24.740 46.0 258.0 28.200 75.0 259.8 32.990 18.0 257.2 24.850 47.0 257.2 28.860 76.0 259.2 32.810 18.0 257.8 24.822 47.0 257.9 28.490 76.0 259.8 33.000 19.0 257.9 24.910 48.0 257.1 29.110 77.0 259.4 32.820 19.0 258.2 24.885 48.0 257.9 28.786 77.0 259.9 33.010 20.0 258.1 24.950 49.0 257.1 29.355 78.0 259.5 32.845 20.0 258.7 24.935 49.0 257.7 29.080 78.0 260.0 33.020 21.0 258.7 24.975 50.0 257.0 29.600 79.0 259.6 32.850 21.0 259.0 24.978 50.0 257.7 29.370 79.0 260.0 33.025 22.0 258.9 25.000 51.0 257.0 29.825 80.0 259.6 32.860 22.0 259.3 25.015 51.0 257.6 29.660 80.0 260.0 33.030 23.0 259.0 25.030 52.0 257.0 30.070 81.0 259.7 32.865 23.0 259.4 25.040 52.0 257.4 29.944 81.0 260.0 33.030 24.0 259.1 25.060 53.0 257.0 30.290 82.0 259.7 32.870 24.0 259.8 25.060 53.0 257.3 30.221 82.0 260.0 33.035 25.0 259.2 25.080 54.0 257.0 30.510 83.0 259.8 32.880 25.0 259.8 25.090 54.0 257.4 30.475 83.0 260.0 33.035 26.0 259.2 25.115 55.0 257.0 30.720 84.0 259.8 32.885 26.0 259.8 25.110 55.0 257.3 30.740 84.0 260.0 33.040 27.0 259.5 25.160 56.0 257.0 30.910 85.0 259.8 32.890 27.0 259.9 25.140 56.0 257.3 30.990 28.0 259.5 25.225 57.0 257.0 31.110 28.0 260.0 25.170 57.0 257.3 31.215

-297OBSERVED EXPERIMENTAL DATA FROM RUN 13 OBSERVED EXPERIMENTAL DATA FROM RUN 14 TIME TEMP. HEIGHT TIME'TEMP. HEIGHT TIME TEMP,. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM' MIN OF CM MIN OF CM MIN OF CM MIN OF CM.0 85.0 -. —- 26,0 259,9 26.340 52.0 258.0 30.610.0 7. ---- 26.0 260.1 22.885 52.0 258.6 28.365 1.0 127.0 8.133 27.0 259.9 26.370 53.0 258.0 30.830 1.0 137.0 6.510 27.0 260.2 22.970 53.0 258.7 28.550 2.0 158.3 11.367 28.0 260.0 26.400 54.0 258.0 31.020 2.0 166.3 9.800 28.0 260.2 23.060 54.0 258.8 28.725 3.0 181.0 14.600 29.0 260.0 26.450 55.0 258.2 31.200 3.0 187.9 12.450 29.0 260.2 23.190 55.0 259.0 28.880 4.0 198.3 16.980 30,0 260.0 26.510 56.0 258.4 31.360 4.0 203.7 14.570 30.0 260.2 23.340 56.0 259.0 29.025 5.0 211.5 18.870 31.0 260.0 26.580 57.0 258.6 31.500 5.0 216.0 16.260 31.0 260.1 23.505 57.0 259.1 29.150 6.0 222.0 20.205 32.0 260.0 26.660 58.0 258.8 31.628 6.0 225.7 17.650 32.0 260.0 23.700 58.0 259.1 29.270 7.0 230.0 21.640 33.0 260.0 26.741 59.0 259.0 31.742 7.0 233.4 18.730 33.0 260.0 23.900 59.0 259.8 29.370 8.0 236.2 22.610 34.0 260.0 26.840 60.0 259.2 31.840 8.0 239.0 19.595 34.0 259.8 24.110 60.0 259.8 29.445 9.0 241.2 23.410. 35.0 260.0 26.960 61.0 259.4 31.920 9.0 244.0 20.270 35.0 259.5 24.300 61.0 259.9 29.525 10.0 245.1 24.050 36.0 259.8 27.099 62.0 259.6 31.988 10,0 247,0 20.800 36.0 259.3 24.565 62.0 260.0 29.590 11.0 248.0 24.545 37.0 259.5 27.240 63.0 259.8 32.042 11.O0 250.0 21.250 37.0 259.1 24.800 63.0 260.0 29.630 12.0 251.0 24.940 38.0 259.2 27.400 64.0 259.9 32.088 12.0 252.1 21.595 38.0 259.0 25.040 64.0 260.1 29.690 13.0 253.0 25.237 39.0 259.0 27.570 65.0 259.9 32.125 13.0 254.0 21.860 39.0 259.0 25.280 65.0 260.2 29.710 14.0 254.2 25.430 40.0 259.0 27.772 66.0 260.0 32.150 14.0 255.3 22.070 40.0 258.8 25.525 66.0 260.3 29.750 15.0 255.3 25.631 41.0 258.8 27.972 67.0 260.0 32.172 15.0 256.7 22.225 41.0 258.8 25.775 67.0 260.4 29.770 16.0 256.5 25.790 42.0 258.5 28.200 68.0 260.0 32.190 16.0 257.3 22.350 42.0 258.4 26.020 68.0 260.5 29.790 17.0 257.1 25.910 43.0 258.2 28.432 69.0 260.1 32.200 17.0 258.0 22.450 43.0 258.4 26.280 69.0 260.7 29.800 18.0 257.9 26.000 44.0 258.1 28,678 70.0 260.1 32.210 18.0 258.6 22.525 44.0 258.4 26.530 70.0 260.7 29.805 19.0 258.2 26.080 45.0 258.0 28.925 71.0 260.1 32.220 19.0 259.0 22.590 45.0 258.4 26.780 71.0 260.8 29.815 20.0 258.9 26.138 46.0 258.0 29.180 72.0 260.2 32.228 20.0 259.4 22.620 46.0 258.3 27.025 72.0 260.9 29.825 21.0 259.0 26.189 47.0 258.0 29.430 73.0 260.2 32.230 21.0 259.8 22.680 47.0 258.3 27.270 73.0 261.0 29.830 22.0 259.5 26.225 48.0 258.0 29.690 74.0 260.3 32.235 22.0 259.9 22.720 48.0 258.2 27.505 74.0 261.0 29.835 23.0 259.5 26.251 49.0 258.0 29.930 75.0 260.3 32.240 23.0 260.0 22.750 49.0 258.2 27.745 75.0 261.0 29.840 24.0 259.8 26.286 50.0 258.0 30.170 76.0 260.4 32.242 24.0 260.0 22.790 50.0 258.2 27.958 25.0 259.9 26.305 51.0 258.0 30.400 77.0 260.5 32.245 25*0 260.1 22.825 51.0 258.4 28.171 OBSERVED EXPERIMENTAL DATA FROM RUN 15 OBSERVED EXPERIMENTAL DATA FROM RUN 16 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM IN OF CM MIN OF CM.0 85.0 -. —- 32.0 258.9 17.880 64.0 257.1 24.800.0 88.0 -. —- 34.0 260.0 13.940 68.0 258.8 20.310 1.0 128.6 3.750 33.0 258.9 18.000 65.0 257.2 24.930 1.0 132.0 -. — 35.0 260.0 14.100 69.0 258.8 20.440 2.0 158.4 5.500 34.0 258.9 18.130 66.0 257.4 25.050 2.0 162.0 -. —- 36.0 260.0 14.280 70.0 258.9 20.560 3.0 186.0 7.250 35.0 258.9 18.290 67.0 257.8 25.165 3.0 183.9 3.150 37.0 259.9 14.470 71.0 259.0 20.670 4.0 198.0 9.350 36.0 258.8 18.450 68.0 257.9 25.260 4.0 200.5 5.200 38.0 259.9 14.645 72.0 259.1 20.770 5.0 211.1 11.050 37.0 258.8 18.640 69..0 258.0 25.340 5.0 213.2 6.870 39.0 259.7 14.830 73.0 259.1 20.850 6.0 221.6 12.400 38.0 258.8 18.840 70.0 258.0 25.405 6.0 223.8 8.230 40.0 259.7 15.020 74.0 259.3 20.925 7.0 229.8 13.500 39.0 258.8 19.050 71.0 258.0 25.470 7.0 231.6 9.310 41.0 259.4 15.200 75.0 259.4 20.990 8.0 235.9 14.390 40.0 258.2 19.260 72.0 258.2 25.510 8.0 238.0 10.180 42.0 259.6 15.390 76.0 259.6 21.040 9.0 240.5 15.085 41.0 258.1 19.485 73.0 258.6 25.560 9,0 242.3 10.870 43.0 259.3 15.570 77.0 259.7 21.090 10.0 244.5 15.620 42.0 258.0 19.710 74.0 258.7 25.595 10.0 246.1 11.400 44.0 259.3 15.750 78.0 259.9 21.130 11.0 247.1 16.050 43.0 257.9 19.950 75,0 258.8 25.620 11.0 249.0 11.835 45.0 259.1 15.925 79.0 260.0 21.160 12.0 249.9 16.385 44.0 257.8 20.180 76.0 258.9 25.645 12.0 251.3 12.180 46.0 259.1 16.100 80.0 260.0 21.190 13.0 251.6 16.640 45.0 257.7 20.420 77.0 259.0 25.660 13.0 253.0 12.440 47.0 259.0 16.280 81.0 260.0 21.210 14.0 253.0 16.840 46.0 257.2 20.670 78.0 258.9 25.680 14.0 254.8 12.655 48.0 259.0 16.450 82.0 260.1 21.230 15.0 254.2 17.000 47.0 257.2 20.920 79.0 259.0 25.690 15.0 255.8 12.815 49.0 258.9 16.630 83.0 260.1 21.250 16.0 255.1 17.130 48.0 257.1 21.178 80.0 259.0 25.700 16.0 257.0 12.950 50.0 258.9 16.805 84.0 260.1 21.260 17.0 256.0 17.230 49.0 257.0 21.430 81.0 259.0 25.700 17.0 257.2 13.050 51.0 258.7 17.000 85.0 260.1 21.265 18.0 256.7 17.305 50.0 257,0 21.690 82.0 259.0 25,.705 18.0 258.0 13.140 52.0 258.8 17.190 86.0 260.1 21.280 19.0 257.1 17.370 51.0 257.0 21.950 83.0 259.1 25.708 19.0 258.2 13.195 53.0 258.4 17.380 87.0 260.1 21.290 20.0 257,2 17.420 52.0 257.0 22.215 84.0 259.0 25.710 20.0 258.9 13.250 54.0 258.6 17.580 88.0 260.2 21.299 21.0 257.8 17.450 53.0 257.0 22.4-75 85.0 259.2 25.720 21.0 259.0 13.285 55.0 258.4 17.790 89.0 260.2 21.300 22.0 258.0 17.490 54.0 256.9 22.730 86.0 259.1 25.730 22.0 259.2 13.310 56.0 258.5 18.000 90.0 260.2 21.300 23.0 258.1 17.510 55.0 257.0 22.990 87.0 259.2 25.735 23.0 259.2 13.340 57.0 258.1 18.205 91.0 260.2 21.302 24.0 258.2 17.530 56.0 256.9 23.225 88.0 259.2 25.740 24.0 259.7 13.360 58.Q 258.2 18.420 92.0 260.3 21.305 25.0 258.3 17.550 57.0 257.0 23.460 89.0 259.3 25.750 25.0 259.8 13.380 59.0 258.1 18.640 93.0 260.2 21.305 26.0 258.4 17.570 58.0 256.9 23.690 90.0 259.2 25.750 26.0 259.9 13.400 60.0 258.2 18.851 94.0 260.3 21.310 27.0 258.5 17.590 59.0 257.0 23.910 91.0 259.2 25.760 27.0 259.9 13.410 61.0 258.1 19.066 95.0 260.3 21.310 28.0 258.6 17.620 60.0 256.9 24.110 92.0 259.2 25.760 28.0 260.0 13.440 62.0 258.2 19.270 96.0 260.5 21.315 29.0 258.8 17.660 61.0 257.0 24.300 93.0 259.5 25.765 29.0 260.0 13.470 63.0 258.1 19.470 97.0 260.4 21.315 30.0 258.8 17.720 62.0 257.0 24.520 94.0 259.3 25.768 30.0 260.0 13.520 64.0 258.2 19.650 98.0 260.5 21.320 31.0 258.9 17.790 63.0 257.0 24.650 95.0 259.5 25.770 31.0 260.0 13.590 65.0 258.2 19.830 99.0 260.4 21.320 32.0 260.0 13.688 66.0 258.3 20.000 33.0 260.0 13.800 67.0 258.4 20.115

-298OBSERVED EXPERIMENTAL DATA FROM RUN 19 OBSERVED EXPERIMENTAL DATA FROM RUN 19 (CONT'D) TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM.0 94.8 ---- 50.0 250.5 17.885 100.0 250.0 20.845 150.0 249.6 25.437 176.0 250.0 26.385 202.0 250.0 26.550 1.0 129.7 2.847 51.0 250.7 17.889 101.0 250.0 20.946 151.0 249.8 25.498 177.0 250.0 26.396 203.0 250.1 26.551 2.0 156.7 5.779 52.0 250.6 17.900 102.0 249.9 21.044 152.0 249.7 25.558 178.0 250.0 26.408 204.0 250.2 26.551 3.0 177.5 8.189 53.0 250.6 17.907 103.0 250.0 21.143 153.0 249.8 25.614 179.0 250.0 26.419 205.0 250.2 26.554 4.0 193.2 10.156 54.0 250.6 17.912 104.0 249.9 21.239 154.0 249.8 25.663 180.0 250.0 26.429 206.0 250.2 26.554 5.0 205.6 11.745 55.0 250.6 17.925 105.0 250.0 21.336 155.0 249.8 25.719 181.0 250.1 26.442 207.0 250.3 26.558 6.0 215.1 13.026 56.0 250.5 17.933 106.0 249.9 21.442 156.0 249.9 25.768 182.0 250.1 26.448 208.0 250.3 26.557 7.0 222.6 14.053 57.0 250.6 17.955 107.0 249.9 21.539 157.0 249.9 25.819 183.0 250.1 26.461 209.0 250.3 26.559 8.0 228.3 14.856 58.0 250.5 17.969 108.0 249.8 21.639 158.0 249.8 25.868 184.0 250.0 26.467 210.0 250.3 26.561 9.0 233.2 15.510 59.0 250.6 17.981 109.0 249.9 21.744 159.0 249.9 25.908 185.0 250.0 26.477 211.0 250.3 26.561 10.0 236.5 16.011 60.0 250.5 18.002 110.0 249.8 21.843 160.0 249.9 25.950 186.0 250.0 26.484 212.0 250.2 26.562 11.0 239.7 16.410 61.0 250.6 18.029 111.0 249.8 21.950 161.0 249.9 25.991 187.0 250.0 26.495 213.0 250.3 26.563 12.0 241.6 16.716 62.0 250.5 18.054 112.0 249.8 22.049 162.0 249.9 26.021 188.0 250.0 26.499 214.0 250.3 26.563 13.0 243.6 16.962 63.0 250.6 18.080 113.0 249.8 22.151 163.0 249.9 26.060 189.0 250.0 26.506 215.0 250.3 26.563 14.0 244.8 17.153 64.0 250.4 18.112 114.0 249.8 22.254 164.0 249.9 26.096 190.0 250.0 26.507 216.0 250.3 26.564 15.0 246.0 17.300 65.0 250.6 18.142 115.0 249.8 22.352 165.0 249.9 26.120 191.0 250.0 26.510 217.0 250.3 26.568 16.0 246.9 17.419 66.0 250.4 18.180 116.0 249.8 22.456 166.0 249.9 26.159 192.0 250.0 26.517 218.0 250.2 26.571 17.0 247.5 17.510 67.0 250.6 18.218 117.0 249.9 22.559 167.0 250.0 26.188 193.0 250.0 26.520 219.0 250.3 26.569 18.0 248.0 17.581 68.0 250.4 18.263 118.0 249.8 22.656 168.0 250.0 26.216 194.0 250.0 26.526 220.0 250.2 26.571 19.0 248.7 17.638 69.0 250.6 18.315 119.0 249.9 22.760 169.0 250.0 26.242 195.0 250.0 26.532 221.0 250.3 26.569 20.0 248.8 17.679 70.0 250.4 18.364 120.0 249.8 22.862 170.0 250.0 26.264 196.0 250.0 26.530 222.0 250.2 26.571 21.0 249.3 17.717 71.0 250.6 18.416 121.0 249.9 22.963 171.0 250.0 26.286 197.0 250.0 26.538 223.0 250.3 26.571 22.0 249.4 17.742 72.0 250.3 18.475 122.0 249.8 23.061 172.0 250.0 26.313 198.0 250.0 26.538 224.0 250.2 26.572 23.0 249.7 17.765 73.0 250.5 18.535 123.0 249.9 23.162 173.0 250.0 26.328 199.0 250.0 26.538 225.0 250.3 26.572 24.0 249.8 17.785 74.0 250.3 18.601 124.0 249.8 23.260 174.0 250.0 26.347 200.0 250.0 26.542 226.0 250.3 26.572 25.0 249.9 17.796 75.0 250.5 18.669 125.0 249.8 23.356 175.0 250.1 26.359 201.0 250.0 26.548 26.0 250.0 17.810 76.0 250.3 18.739 126.0 249.8 23.461 27.0 250.0 17.816 77.0 250.6 18.809 127.0 249.8 23.553 28.0 250.1 17.823 78.0 250.3 18.886 128.0 249.7 23.651 29.0 250.1 17.825 79.0 250.5 18.958 129.0 249.8 23.749 30.0 250.2 17.833 80.0 250.2 19.041 130.0 249.7 23.845 31.0 250.3 17.839 81.0 250.4 19.116 131.0 249.8 23.938 32.0 250.3 17.841 82.0 250.1 19.197 132.0 249.6 24.032 33.0 250.4 17.841 83.0250.3 19.286 133.0 249.8 24.124 34.0 250.3 17.844 84.0 250.2 19.367 134.0 249.7 24.213 35.0 250.5 17.847 85.0 250.2 19.457 135.0 249.8 24.305 36.0 250.3 17.853 86.0 250.2 19.545 136.0 249.8 24.394 37.0 250.4 17.851 87.0 250.2 19.635 137.0 249.8 24.481 38.0 250.3 17.856 88.0 250.2 19.721 138.0 249.7 24.556 39.0 250.4 17.858 89.0 250.2 19.818 139.0 249.8 24.646 40.0 250.3 17.859 90.0 250.0 19.909 140.0 249.7 24.726 41.0 250.4 17.856 91.0 250.1 20.000 141.0 249.8 24.811 42.0 250.3 17.860 92.0 250.0 20.090 142.0 249.8 24.884 43.0 250.5 17.862 93.0 250.1 20.184 143.0 249.8 24.963 44.0 250.4 17.866 94.0 250.0 20.276 144.0 249.7 25.037 45.0 250.4 17.864 95.0 250.0 20.371 145.0 249.8 25.108 46.0 250.4 17.670 96.0 250.0 20.468 146.0 249.7 25.185 47.0 250.6 17.872 97.0 250.1 20.564 147.0 249.8 25.245 48.0 250.5 17.874 98.0 250.0 20.662 148.0 249.6 25.313 49.0 250.7 17.879 99.0 250.0 20.754 149.0 249.8 25.379 OBSERVED EXPERIMENTAL DATA FROM RUN 20 OBSERVED EXPERIMENTAL DATA FROM RUN 20 (CONT'D) TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN op CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM.0 94.3 -. — 50.0 249.8 22.194 100.0 249.3 25.384 150.0 249.2 29.951 173.0 249.9 30.518 196.0 249.8 30.639 1.0 127.1 6.749 51.0 249.8 22.217 101.0 249.5 25.494 151.0 249.4 29.990 174.0 249.8 30.534 197.0 249.9 30.638 2.0 154.6 9.687 52.0 249.8 22.234 102.0 249.3 25.606 152.0 249.2 30.040 175.0 249.9 30.543 198.0 249.8 30.641 3.0 176.0 12.192 53.0 249.8 22.252 103.0 249.6 25.715 153.0 249.4 30.086 176.0 249.8 30.549 199.0 249.9 30.640 4.0 191,8 14,165 54.0 249,8 22.272 104.0 249.3 25.827 154.0 249.2 30.125 177.0 249.9 30.561 200.0 249.8 30.645 5.0 204.4 15.849 55.0 249.8 22.291 105.0 249.6 25.941 155.0 249.5 30.159 178.0 249.9 30.567 201.0 249.9 30.648 6.0 213.8 17.165 56.0 249.8 22.315 106.0 249.3 26.054 156.0 249.3 30.192 179.0 249.9 30.572 202.0 249.8 30.649 7.0 221.6 18.204 57.0 249.8 22.341 107.0 249.3 26.172 157.0 249.5 30.220 180.0 249.9 30.576 203.0 249.9 30.650 8.0 227.2 19.032 58.0 249.8 22.364 108.0 249.2 26.285 158.0 249.4 30.253 181.0 250.0 30.582 204.0 249.8 30.649 9.0 232.1 19.688 59.0 249.8 22.390 109.0 249.3 26.396 159.0 249.6 30.281 182.0 249.8 30.588 205.0 249.9 30.650 10.0 235.6 20.195 60.0 249.8 22.418 110.0 249.1 26.515 160.0 249.4 30.309 183.0 249.9 30.595 206.0 249.8 30.647 11.0 238.5 20.598 61.0 249.9 22.448 111.0 249.2 26.622 161.0 249.6 30.332 184.0 249.8 30.599 207.0 249.9 30.648 12.0 240.7 20.906 62.0 249.8 22.482 112.0 249.1 26.735 162.0 249.4 30.362 185.0 249.9 30.601 208.0 249.9 30.647 13.0 242.5 21.153 63.0 249.8 22.514 113.0 249.3 26.851 163.0 249.6 30.381 186.0 249.8 30.607 209.0 249.9 30.648 14.0 244.2 21.346 64,0 249.8 22.548 114.0 249.1 26,962 164.0 249.4 30.403 187.0. 249.9 30.612 210.0 249.9 30.649 15.0 245.3 21.500 65.0 249.8 22.589 115.0 249.2 27.070 165.0 249.7 30.417 188.0 249.8 30.617 211.0 249.9 30.653 16.0 246,3 21.614 66,0 249.8 22.627 116.0 249.0 27.181 166.0 249.5 30.434 189.0 249.9 30.618 212.0 249.8 30.652 17.0 247.0 21.713 67.0 249.9 22.669 117.0 249.2 27.290 167.0 249.8 30.452 190.0 249.8 30.619 213.0 249.8 30.654 18.0 247,4 21.785 68.0 249.9 22.715 118.0 249.0 27.393 168.0 249.6 30.467 191.0 249.9 30.622. 214.0 249.8 30.654 19.0 247.8 21.844 69.0 249.9 22.765 119.0 249.2 27.502 169.0 249.8 30.481 192.0 249.8 30.623 215.0 249.8 30.655 20.0 248.3 21.891 70.0 249.9 22.810 120.0 249.0 27.609 170.0 249.7 30.495 193.0.249.9 30.632 216.0 249.8 30.655 21.0 248.5 21.927 71.0 249.9 22.865 121.0 249.2 27.711 171.0 249.9 30.506 194.0 249.8 30.635 217.0 249.9 30.655 22.0 248.8 21.952 72.0 249.8 22.918 122.0 249.0 27.818 172.0 249.8 30.513 195.0 249.9 30.637 23.0 249.0 21.976 73.0 249.9 22.975 123.0 249.2 27.917 24.0 249.1 21.996 74.0 249.8 23.035 124.0 249.1 28.016 25.0 249.2 22.008 75.0 249.9 23.099 125.0 249.3 28.116 26,0 249.3 22.018 76.0 249.9 23.163 126.0 249.1 28.215.27.0 249.5 22.027 77.0 249.9 23.230 127.0 249.3 28.314 28.0 249.5 22,031 78.0 249.8 23.302 128.0 249.1 28.409 29.0 249.5 22.037 79.0 249.9 23.373 129.0 249.3 28.499 30.0 249.7 22.046 80.0 249.8 23.451 130.0 249.1 28.590 31.0 249.8 22.050 81.0 249.8 23.525 131.0 249.3 28.680 32.0 249.8 22.056 82.0 249.8 23.609 132.0 249.0 28.768 33.0 249.8 22.055 83.0 249.8 23,688 133.0 249.3 28.851 34.0 249.8 22.059 84.0 249.8 23.775 134.0 249.1 28.932 35.0 249.8 22.067 85.0 249.8 23.861 135.0 249.3 29.015 36.0 249.8 22.071 86.0 249.8 23.949.136.0 249.0 29.093 37.0 249.8 22.076 87.0 249.8 24.040 137.0 249.2 29.170 38.0 249.8 22.078 88.0 249.8 24.133 138.0 249.1 29.244 39.0 249.8 22.082 89.0 249.8 24.230 139.0 249.3 29.312 40.0 249.9 22.089 90.0 249.7 24.326 140.0 249.1 29.383 41.0 249.8 22.094 91.0 249.8 24.425 141.0 249.3 29.451 42.0 249.8 22,102 92.0 249.7 24.521 142.0 249.1 29.517 43.0 249.8 22.111 93.0 249.8 24.629 143.0 249.3 29.575 44.0 249.8 22.119 94.0 249.6 24.733 144.0 249.1 29.638 45.0 249.8 22.132 95.0 249.8 24.837 145.0 249.4 29.698 46.0 249.8 22.142 96.0 249.3 24.943 146.0 249.2 29.754 47.0 249.8 22.152 97.0 249.5 25.051 147.0 249.4 29.806 48.0 249.8 22.169 98.0 249.3 25.159 148.0 249.2 29.854 49.0 249.8 22.186 99.0 249.5 25.268 149.0 249.4 29.906

-299OBSERVED EXPERIMENTAL DATA FROM RUN 21 OBSERVED EXPERIMENTAL DATA FROM RUN 21 (CONT'D) TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM.0 91.1 -. — 50.0 250.1 22.515 100.0 249.9 26.470 150.0 250.0 30.459 166.0 250.0 30.796 182.0 250.1 30.899 1.0 125.0 6.985 51.0 250.1 22.531 101.0 249.9 26.566 151.0 250.0 30.493 167.0 250.1 30.808 183.0 250.2 30.900 2.0 152.9 10.004 52.0 250.1 22.554 102.0 249,9 26.658 152.0 250.0 30.522 168.0 250.0 30.813 184.0 250.2 30.901 3.0 174.0 12.460 53.0 250.1 22.577 103.0 249.9 26.758 153.0 250.0 30.541 169.0 250.0 30.823 185.0 250.3 30.903 4.0 190.1 14.483 54.0 250.1 22.603 104.0 250.0 26.852 154.0 250.0 30.578 170.0 250.0 30.828 186.0 250.2 30.904 5.0 202.8 16.128 55.0 250.1 22.634 105.0 249.9 26.952 155.0 250.0 30.608 171.0 250.0 30.835 187.0 250.3 30.905 6.0 213.1 17.463 56.0 250.1 22.670 106.0 250.0 27.051 156.0 250.0 30.627 172.0 250.0 30.843 188.0 250.2 30.909 7.0 221.1 18.521 57.0 250.1 22.713 107.0 249.9 27.146 157.0 250.0 30.648 173.0 250.0 30.844 189.0 250.3 30.910 8.0 226.9 19.362 58.0 250.1 22.760 108.0 249.9 27.244 158.0 250.0 30.676 174.0 250.0 30.846 190.0 250.2 30.914 9.0 231.7 20.023 59.0 250.1 22.809 109.0 249.9 27.347 159.0 250.0 30.690 175.0 250.0 30.862 191.0 250.3 30.914 10.0 235.8 20.546 60.0 250.1 22.862 110.0 249.9 27.441 160.0 250.0 30.709 176.0 250.0 30.868 192.0 250.2 30.917 11.0 238.5 20.952 61.0 250.1 22.923 111.0 249.8 27.548 161.0 250.1 30.729 177.0 250.1 30.871 193.0 250.3 30.918 12.0 240.8 21.270 62.0 250.1 22.986 112.0 249.8 27.646 162.0 250.0 30.739 178.0 250.1 30.879 194.0 250.2 30.918 13.0 242.7 21.526 63.0 250.1 23.053 113.0 249.8 27.746 163.0 250.0 30.755 179.0 250.1 30.883 195.0 250.3 30.918 14.0 244.1 21.720 64.0 250.1 23.127 114.0 249.8 27.843 164.0 250.0 30.772 180.0 250.1 30.886 15.0 245.4 21.871 65,0 250.0 23.206 115.0 249.8 27.947 165.0 250.1 30.784 181.0 250.2 30.893 16.0 246.4 21.995 66.0 250.0 23.287 116.0 249.8 28.044 17.0 247.2 22.088 67.0 250.0 23.367 117.0 249.8 28.145 18.0 247.7 22.160 68.0 250.0 23.452 118.0 249.8 28.239 19.0 248.3 22.213 69.0 250.0 23.542 119.0 249.8 28.334 20.0 248.7 22.262 70.0 250.0 23.636 120.0 249.8 28.435 21.0 248.9 22.300 71.0 250.0 23.729 121.0 249.8 28.526 22.0 249.2 22.331 72.0 250.0 23.823 122.0 249.8 28.618 23.0 249.4 22.352 73.0 250.0 23.919 123.0 249.8 28.715 24.0 249.6 22.373 74.0 250.0 24.017 124.0 249.8 28.806 25.0 249.8 22.388 75.0 250.0 24.114 125.0 249.9 28.894 26.0 249.8 22.399 76.0 250.0 24.211 126.0 249.8 28.984 27.0 249.9 22.408 77.0 250.0 24.309 127.0 249.9 29.068 28.0 249.9 22.413 78.0 250.0 24.412 128.0 249.9 29.151 29.0 249.9 22.418 79.0 250.0 24.506 129.0 249.9 29.231 30.0 250.0 22.418 80.0 250.0 24.605 130.0 249.8 29.313 31.0 250.0 22.428 81.0 249.9 24.699 131.0 249.9 29.395 32.0 250.0 22.430 82.0 249.9 24.798 132.0 249.9 29.472 33.0 250.1 22.435 83.0 249.9 24.892 133.0 249.9 29.546 34.0 250.1 22.435 84.0 249.9 24.988 134.0 249.8 29.616 35.0 250.1 22.436 85.0 249.9 25.076 135.0 249.9 29.688 36.0 250.1 22.435 86.0 249.9 25.173 136.0 249.8 29.755 37.0 250.1 22.440 87.0 249.9 25.264 137.0 249.9 29.817 38.0 250.1 22.439 88.0 249.9 25.357 138.0 249.8 29.887 39.0 250.1 22.440 89.0 249.9 25.453 139.0 249.9 29.941 40.0 250.1 22.444 90.0 249.9 25.537 140.0 249.9 30.006 41.0 250.1 22.444 91.0 249.9 25.629 141.0 249.9 30.064 42.0 250.1 22.448 92.0 250.0 25.724 142.0 249.9 30.115 43.0 250.1 22.450 93.0 249.9 25.818 143.0 250.0 30.166 44.0 250.1 22.456 94.0 250.0 25.909 144.0 249.9 30.213 45.0 250.1 22.464 95.0 249.9 26.003 145.0 250.0 30.263 46.0 250.1 22.469 96.0 250.0 26.097 146.0 249.9 30.307 47.0 250.1 22.476 97.0 249.9 26.188 147.0 250.0 30.342 48.0 250.1 22.486 98.0 249.9 26.285 148.0 249.9 30.387 49.0 250.1 22.500 99.0 249.9 26.375 149.0 250.0 30.420 OBSERVED EXPERIMENTAL DATA FROM RUN 22 OBSERVED EXPERIMENTAL DATA FROM RUN 22 (CONT'D) TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM.0 90.1 ----- 50.0 250.0 30.863 100.0 249.3 34.385 150.0 249.2 38.438 171.0 249.8 38.807 192.0 249.8 38.877 1.0 123.7 14.648 51.0 250.0 30.901 101.0 249.3 34.491 151.0 249.3 38.437 172.0 249.7 38.811 193.0 249.9 38.878 2.0 152.3 17.856 52.0 249.9 30.922 102.0 249.2 34.604 152.0 249.2 38.472 173.0 249.8 38.814 194.0 249.8 38.878 3.0 174.6 20.503 53.0 250.0 30.940 103.0 249.2 34.708 153.0 249.3 38.506 174.0 249.8 38.819 195.0 249.9 38.886 4.0 190.9 22.626 54.0 250.0 30.968 104.0 249.2 34.817 154.0 249.2 38.528 175.0 249.8 38.827 196.0 249.8 38.885 5.0 203.8 24.329 55.0 250.0 30.996 105.0 249.2 34.928 155.0 249.3 38.555 176.0 249.8 38.834 197.0 249.9 38.887 6.0 213.8 25.692 56.0 250.0 31.019 106.0 249.2 35.035 156.0 249.2 38.586 177.0 249.8 38.838 198.0 249.8 38.889 7.0 221.7 26.759 57.0 250.0 31.047 107.0 249.2 35.143 157.0 249.3 38.605 178.0 249.8 38.841 199.0 250.0 38.893 8.0 227.3 27.692 58.0 250.0 31.079 108.0 249.1 35.254 158.0 249.2 38.623 179.0 249.8 38.844 200.0 249.9 38.893 9.0 232.2 28.245 59.0 250.0 31.114 109.0 249.2 35.360 159.0 249.3 38.643 180.0 249.7 38.849 201.0 250.0 38.893 10.0 236.0 28.756 60.0 250.0 31.148 110.0 249.1 35.470 160.0 249.3 38.663 181.0 249.8 38.855 202.0 249.9 38.895 11.0 238.7 29.144 61.0 250.0 31.182 111.0 249.2 35.573 161.0 249.6 38.684 182.0 249.8 38.858 203.0 250.0 38.896 12.0 240.9 29.463 62.0 250.0 31.219 112.0 249.1 35.677 162.0 249.5 38.703 183.0 249.8 38.867 204.0 249.9 38.897 13.0 242.7 29.715 63.0 250.0 31.263 113.0 249.2 35.782 163.0 249.7 38.717 184.0 249.8 38.868 205.0 250.0 38.898 14.0 244.2 29.894 64.0 250.0 31.308 114.0 249.0 35.886 164.0 249.7 38.729 185.0 249.8 38.873 206.0 249.9 38.897 15.0 245.5 30.037 65.0 250.0 31.351 115.0 249.2 35.992 165.0 249.7 38.743 186.0 249.8 38.869 207.0 250.0 38.898 16.0 246.4 30.140 66.0 250.0 31.405 116.0 249.1 36.095 166.0 249.7 38.753 187.0 249.9 38.869 208.0 249.9 38.896 17.0 247.1 30.244 67.0 250.0 31.455 117.0 249.2 36.192 167.0 249.8 38.764 188.0 249.8 38.874 209.0 250.0 38.897 18.0 247.7 30.314 68.0 250.0 31.511 118.0 249.1 36.293 168.0 249.7 38.773 189.0 249.9 38.872 210.0 249.9 38.897 19.0 248.0 30.367 69.0 250.0 31.568 119.0 249.2 36.386 169.0 249.8 38.781 190.0 249.8 38.880 20.0 248.4 30.410 70.0 250.0 31.619 120.0 249.1 36.491 170.0 249.7 38.798 191.0 249.8 38.878 21.0 248.7 30.444 71.0 250.0 31.685 121.0 249.2 36.580 22.0 249.0 30.474 72.0 249.9 31.750 122.0 249.1 36.674 23.0 249.2 30.496 73.0 249.9 31.823 123.0 249.2 36.764 24.0 249.3 30.523 74.0 249.9 31.888 124.0 249.0 36.847 25.0 249.4 30.522 75.0 249.9 31.962 125.0 249.1 36.938 26.0 249.7 30.538 76.0 249.9 32.033 126.0 249.1 37.021 27.0 249.7 30.545 77.0 249.9 32.110 127.0 249.2 37.109 28.0 249.8 30.559 78.0 249.9 32.194 128.0 249.0 37.198 29.0 249.9 30.560 79.0 249.9 32.278 129.0 249.2 37.274 30.0 249.9 30.569 80.0 249.9 32.366 130.0 249.0 37.347 31.0 250.0 30.572 81.0 249.9 32.439 131.0 249.0 37.422 32.0 250.0 30.583 82.0 249.9 32.543 132.0 249.0 37.501 33.0 250.0 30.589 83.0 249.9 32.629 133.0 249.1 37.569 34.0 250.0 30.598 84.0 249.9 32.722 134.0 249.0 37.639 35.0 249.9 30.606 85.0 249.9 32.820 135.0 249.2 37.705 36.0 249.9 30.615 86.0 249.8 32.918 136.0 249.1 37.765 37.0 249.9 30.627 87.0 249.8 33.016 137.0 249.1 37.832 38.0 249.9 30.636 88.0 249.8 33.111 138.0 249.1 37.889 39..0 249.9 30.642 89.0 249.7 33.215 139.0 249.2 37.950 40.0 250.0 30.654 90.0 249,7 33.317 140.0 249.1 38.006 41.0 250.0 30.669 91.0 249.7 33.420 141.0 249.1 38.056 42.0 250.0 30.684 92.0 249.5 33.522 142.0 249.1 38.110 43.0 250.0 30.705 93.0 249.5 33.627 143.0 249.1 38.156 44.0 250.0 30.723 94.0 249.4 33.739 144.0 249.0 38.205 45.0 250.0 30.736 95.0 249.3 33.842 145.0 249.0 38.247 46.0 250.0 30.760 96.0 249.4 33.953 146.0 249.0 38.272 47.0 250.0 30.782 97.0 249.5 34.058 147.0 249.0 38.326 48.0 250.0 30.827 98.0 249.4 34.169 148.0 249.1 38.358 49.0 250.0 30.845 99.0 249.4 34.274 149.0 249.2 38.398

-300OBSERVED EXPERIMENTAL DATA FROM RUN 23 OBSERVED EXPERIMENTAL DATA FROM RUN 23 (CONT'D) TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM' MIN OF CM MIN O CM MIN OF CM.0 89.2 —. —- 50.0 249.8 27.346 100.0 249.4 30.298 150.0 249.3 34.813 166.0 249.7 35.369 182.0 249.9 35.585 1.0 122.7 —. —- 51.0 249.8 27.363 101.0 249.4 30.404 151.0 249.3 34.861 167.0 249.8 35.389 183.0 249.9 35.590 2.0 150.8 14.510 52.0 249.8 27.383 102.0 249.4 30.515 152.0 249.3 34.909 168.0 249.8 35.409 184.0 249.8 35.598 3.0 172.4 17.039 53.0 249.8 27.404 103.0 249.5 30.626 153.0 249.4 34.951 169.0 249.8 35.428 185.0 249.9 35.604 4.0 190.0 19.113 54.0 249.8 27.423 104.0 249.4 30.734 154.0 249.3 34.989 170.0 249.8 35.447 186.0 249.9 35.609 5.0 202.1 20.906 55.0 249.7 27.447 105.0 249.4 30.846 155.0 249.3 35.026 171.0 249.8 35.460 187.0 249.9 35.613 6.0 212.2 22.167 56.0 249.8 27.473 106.0 249.4 30.957 156.0 249.3 35.067 172.0 249.8 35.478 188.0 249.9 35.617 7.0 220.0 23.253 57.0 249.8 27.498 107.0 249.5 31.073 157.0 249.3 35.108 173.0 249.8 35.496 189.0 249.9 35.620 8.0 226.1 24.103 58.0 249.8 27.521 108.0 249.4 31.185 158.0 249.3 35.141 174.0 249.8 35.507 190.0 249.9 35.622 9.0 231.2 24.776 59.0 249.8 27.551 109.0 249.5 31.297 159.0 249.3 35.174 175.0 249.9 35.515 191.0 250.0 35.626 10.0 234.9 25.305 60.0 249.8 27.579 110.0 249.5 31.406 160.0 249.3 35.209 176.0 249.9 35.527 192.0 249.9 35.625 11.0 237.8 25.718 61.0 249.7 27.611 111.0 249.5 31.516 161.0 249.4 35.238 177.0 249.9 35.539 193.0 249.9 35.625 12.0 240.2 26.040 62.0 249.8 27.640 112.0 249.4 31.631 162.0 249.4 35.268 178.0 249.8 35.550 194.0 249.9 35.625 13.0 242.0 26.293 63.0 249.7 27.671 113.0 249.4 31.741 163.0 249.5 35.294 179.0 249.9 35.564 195.0 250.0 35.626 14.0 243.5 26.491 64.0 249.8 27.710 114.0 249.4 31.851 164.0 249.6 35.316 180.0 249.9 35.572 196.0 249.9 35.627 15.0 244.8 26.652 65.0 249.8 27.740 115.0 249.3 31.957 165.0 249.7 35.342 181.0 249.9 35.579 16.0 245.6 26.773 66.0 249.8 27.777 116.0 249.2 32.061 17.0 246.6 26.876 67.0 249.8 27.814 117.0 249.3 32.171 18.0 247.1 26.953 68.0 249.8 27.854 118.0 249.3 32.276 19.0 247.5 27.009 69.0 249.8 27.888 119.0 249.2 32.374 20.0 247.8 27.056 70.0 249.8 27.929 120.0 249.2 32.485 21.0 248.3 27.093 71.0 249.8 27.979 121.0 249.2 32.586 22.0 248.5 27.121 72.0 249.8 28.029 122.0 249.2 32.685 23.0 248.6 27.146 73.0 249.8 28.078 123.0 249.2 32.782 24.0 248.8 27.168 74.0 249.8 28.123 124.0 249.2 32.883 25.0 249.2 27.184 75.0 249.8 28.182 125.0 249.2 32.981 26.0 249.2 27.194 76.0 249.8 28.239 126.0 249.2 33.078 27.0 249.3 27.203 77.0 249.7 28.304 127.0 249.2 33.171 28.0 249.3 27.207 78.0 249.7 28.360 128.0 249.2 33.265 29.0 249.4 27.216 79.0 249.8 28.423 129.0 249.2 33.354 30.0 249.3 27.218 80.0 249.7 28.491 130.0 249.2 33.437 31.0 249.3 27.224 81.0 249.8 28.560 131.0 249.1 33.531 32.0 249.5 27.230 82.0 249.8 28.629 132.0 249.2 33.616 33.0 249.5 27.232 83.0 249.8 28.708 133.0 249.3 33.698 34.0 249.5 27.234 84.0 249.7 28.779 134.0 249.2 33.777 35.0 249.5 27.235 85.0 249.6 28.863 135.0 249.3 33.860 36.0 249.5 27.237 86.0 249.7 28.946 136.0 249.2 33.940 37.0 249.5 27.240 87.0 249.5 29.020 137.0 249.2 34.013 38.0 249.5 27.243 88.0 249.6 29.114 138.0 249.2 34.088 39.0 249.5 27.248 89.0 249.6 29.203 139.0 249.3 34.159 40.0 249.5 27.256 90.0 249.5 29.293 140.0 249.2 34.226 41.0 249.6 27.260 91.0 249.4 29.391 141.0 249.3 34.298 42.0 249.7 27.262 92.0 249.4 29.479 142.0 249.2 34.360 43.0 249.7 27.275 93.0 249.4 29.577 143.0 249.3 34.422 44.0 249.8 27.278 94.0 249.4 29.676 144.0 249.2 34.487 45.0 249.8 27.292 95.0 249.4 29.774 145.0 249.2 34.547 46.0 249.8 27.299 96.0 249.4 29.873 146.0 249.2 34.600 47.0 249.8 27.309 97.0 249.4 29.981 147.0 249.3 34.659 48.0 249.7 27.319 98.0 249.4 30.085 148.0 249.2 34.711 49.0 249.7 27.333 99.0 249.4 30.190 149.0 249.3 34.766 OBSERVED EXPERIMENTAL DATA FROM RUN 24. OBSERVED EXPERIMENTAL DATA FROM RUN 24 (CONT'D) TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM.0 93.3 -. —- 50.0 249.7 24.453 100.0 249.2 27.303 150.0 249.0 31.625 179.0 249.2 32.471 208.0 249.5 32.657 1.0 130.9 9.118 51.0 249.5 24.480 101.0 249.0 27.396 151.0 249.0 31.676 180.0 249.2 32.485 209.0 249.5 32.660 2.0 159.7 12.168 52.0 249.8 24.509 102.0 249.2 27.502 152.0 249.0 31.721 181.0 249.2 32.497 210.0 249.5 32.663 3.0 180.5 14.614 53.0 249.4 24.533 103.0 249.0 27.600 153.0 249.0 31.767 182.0 249.2 32.509 211.0 249.4 32.663 4.0 195.5 16.581 54.0 249.5 24.555 104.0 249.1 27.700 154.0 249.0 31.811 183.0 249.2 32.517 212.0 249.5 32.662 5.0 206.6 18.148 55.0 249.4 24.585 105.0 249.0 27.804 155.0 249.0 31.853 184.0 249.2 32.530 213.0 249.4 32.666 6.0 215.3 19.408 56.0 249.6 24.612 106.0 249.1 27.909 156.0 249.0 31.898 185.0 249.2 32.537 214.0 249.5 32.663 7.0 222.5 20.414 57.0 249.4 24.643 107.0 249.0 28.013 157.0 249.0 31.934 186.0 249.2 32.545 215.0 249.4 32.665 8.0 228.5 21.219 58.0 249.6 24.667 108.0 249.1 28.115 158.0 249.0 31.970 187.0 249.2 32.556 216,0 249.5 32.665 9.0 232.7 21.853 59.0 249.4 24.694 109.0 249.0 28.218 159.0 249.0 32.009 188.0 249.2 32.560 217.0 249.4 32.666 10.0 236.3 22.348 60.0 249.6 24.721 110.0 249.1 28.325 160.0 249.0 32.043 189.0 249.3 32.569 218.0 249.5 32.665 11.0 238.8 22.730 61.0 249.4 24.753 111.0 249.0 28.425 161.0 249.0 32.076 190.0 249.3 32.574 219.0 249.5 32.667 12.0 241.0 23.035 62.0 249.6 24.783 112.0 249.1 28.528 162.0 249.0 32.109 191.0 249.3 32.582 220.0 249.5 32.668 13.0 242.4 23.272 63.0 249.5 24.813 113.0 249.0 28.630 163.0 249.0 32.138 192.0 249.3 32.588 221.0 249.5 32.666 14.0 243.8 23.454 64.0 249.6 24.845 114.0 249.2 28.734 164.0 249.0 32.165 193.0 249.3 32.596 222.0 249.5 32.667 15.0 244.8 23.597 65.0 249.4 24.878 115.0 249.0 28,.836 165.0 249.0 32.192 194.0 249.3 32.601 223.0 249.5 32.670 16.0 245,9 23.709 66.0 249.5 24.913 116.0 249.1 28.943 166.0 249.0 32.215 195.0 249.3 32.605 224.0 249.5 32.670 17.0 246.2 23.798 67.0 249.4 24.954 117.0 249.0 29.044 167.0 249.1 32.244 196.0 249.3 32.610 225.0 249.5 32.673 18.0 247.2 23.869 68.0 249.7 24.987 118.0 249.1 29.148 168.0 249.1 32.264 197.0 249.3 32.614 226.0 249.5 32.672 19.0 247.3 23.920 69.0 249.4 25.031 119.0 249.0 29.242 169.0 249.2 32.287 198.0 249.3 32.620 227.0 249.4 32.671 20.0 247.8 23.954 70.0 249.6 25.074 120.0 249.0 29.343 170.0 249.2 32.315 199.0 249.3 32.626 228.0 249.5 32.674 21.0 248.0 24.000 71.0 249.4 25.119 121.0 249.0 29.440 171.0 249.2 32.333.200.0 249.3 32.630 229.0 249.4 32.674 22.0 248.5 24.023 72.0 249.6 25.166 122.0 249.0 29.535 172.0 249.3 32.354 201.0 249.3 32.634 230.0 249.4 32.675 23.0 248.8 24.045 73.0 249.4 25.212 123.0 249.0 29.633 173.0 249.2 32.374 202.0 249.3 32.639 231.0 249.3 32.674 24.0 248.8 24.062 74.0 249.5 25.263 124.0 249.0 29.719 1.74.0 249.3. 32.394 203.0 249.3 32.639 232.0 249.4 32.675 25.0 248.8 24.077 75.0 249.4 25.314 125.0 249.0 29.817 175.0 249.2 32.410 204.0 249.4 32.644 233.0 249.3 32.674 26.0 249.0 24.088 76.0 249.6 25.374 126.0 249.0 29.913 176.0 249.3 32.423 205.0 249.4 32.647 234.0 249.4 32.674 27.0 248.9 24.099 77.0 249.6 25.432 127.0 249.0 30.002 177.0 249.2 32.440 206.0 249.5 32.653 235.0 249.3 32.674 28.0 249.1 24.109 78.0 249.7 25.488 128.0 249.0 30.094 178.0 249.3 32.452 207.0 249.4 32.652 29.0 249.1 24.114 79.0 249.6 25.550 129.0 248.9 30.178 30.0 249.3 24.117 80.0 249.6 25.610 130.0 249.0 30.267 31.0 249.1 24.123 81.0 249.5 25.677 131.0 249.0 30.352 32.0 249.3 24.129 82.0 249.6 25.740 132.0 249.0 30.433 33.0 249.3 24.133 83.0 249.4 25.814 133.0 249.0 30.513 34.0 249.6 24.142 84.0 249.6 25.889 134.0 249.0 30.594 35.0 249.3 24.148 85.0 249.4 25.959 135.0 249.0 30.672 36.0 249.6 24.157 86.0 249.4 26.039 136.0 249.0 30.743 37.0 249.3 24.167 87.0 249.2 26.119 137.0 249.0 30.818 38.0 249.6 24.183 88.0 249.3 26.201 138.0 249.0 30.892 39.0 249.5 24.193 89.0 249.2 26.281 139.0 248.9 30.959 46.0 249,8 24.208 90.0 249.3 26.360 140.0 248.9 31.027 41.0 249.5 24.223 91.0 249.2 26.451 141.0 248.9 31.099 42.0 249.8 24.247 92.0 249.3 26.532 142.0 248.9 31.168 43.0 249.7 24.270 93.0 249.2 26.627 143.0 248.9 31.226 44.0 249.7 24.295 94.0 249.3 26,718 144.0 248.9 31.290 45.0 249.6 24.316 95.0 249.2 26.814 145.0 248.9 31.352 46,0 249.7 24.341 96.0 249.3 26.909 146.0 249.0 31.406 47.0 249.5 24.366 97.0 249.2 27.003 147.0 249.0 31.463 48.0 249.7 24.395 98.0 249.2 27.102 148.0 249.0 31.518 49,0 249.5 24.421 99.0 249.1 27.193 149,0 249.0 31.573

-301OBSERVED EXPERIMENTAL DATA FROM RUN 25 OBSERVED EXPERIMENTAL DATA FROM RUN 25 (CONT'D) TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OP CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM.0 91.2 -. —- 50.0 249.8 19.852 100.0 248.8 24.479 150.0 249.6 27.169 183.0 250.0 27.566 216.0 250.0 27.634 1.0 125.8 3.784 51.0 249.8 19.922 101.0 249.0 24.563 151.0 249.8 27.195 184.0 250.0 27.570 217.0 250.0 27.637 2.0 154.2 6.775 52.0 249.7 19.994 102.0 248.8 24.650 152.0 249.7 27.216 185.0 250.0 27.574 218.0 249.9 27.639 3.0 175.9 9.438 53.0 249.8 20.064 103.0 249.0 24.734 153.0 249.8 27.233 186.0 249.9 27.582 219.0 250.0 27.642 4.0 192.1 11.243 54.0 249.7 20.141 104.0 248.8 24.817 154.0 249.8 27.252 187.0 250.0 27.583 220.0 249.9 27.640 5.0 204.8 12.856 55.0 249.7 20.216 105.0 249.0 24.894 155.0 249.8 27.273 188.0 250.0 27.587 221.0 250.0 27.640 6.0 214.2 14.148 56.0 249.7 20.297 106.0 248.8 24.980 156.0 249.8 27.289 189.0 250.1 27.590 222.0 249.9 27.643 7.0 222.0 15.180 57.0 249.7 20.376 107.0 249.0 25.057 157.0 249.9 27.312 190.0 250.0 27.597 223.0 250.0 27.643 8.0 227.9 16.007 58.0 249.4 20.461 108.0 248.8 25.135 158.0 249.8 27.327 191.0 250.0 27.599 224.0 249.9 27.644 9.0 232.7 16.640 59.0 249.5 20.538 109.0 248.9 25.2.13 159.0 249.9 27.340 192.0 250.0 27.602 225.0 250.0 27.644 10.0 236.1 17.144 60.0 249.3 20.624 110.0 248.8 25.286 160.0 249.8 27.356 193.0 250.0 27.606 226.0 249.9 27.645 11.0 238.9 17.542 61.0 249.5 20.714 111.0 249.0 25.358 161.0 249.9 27.371 194.0 250.0 27.606 227.0 250.0 27.644 12.0 241.0 17.854 62.0 249.2 20.798 112.0 248.8 25.431 162.0 249.8 27.386 195.0 250.0 27.610 228.0 249.9 27.643 13.0 242.8 18.092 63.0 249.5 20.891 113.0 249.0 25.504 163.0 249.9 27.396 196.0 250.0 27.612 229.0 249.9 27.644 14.0 244.2 18.279 64.0 249.2 20.981 114.0 248.8 25.569 164.0 249.8 27.413 197.0 250.0 27.614 230.0 249.9 27.644 15.0 245.8 18.428 65.0 249.5 21.074 115.0 249.1 25.636 165.0 249.9 27.421 198.0 250.0 27.616 231.0 250.0 27.643 16.0 246.4 18.545 66.0 249.3 21.172 116.0 249.0 25.702 166.0 249.8 27.436 199.0 250.0 27.616 232.0 249.9 27.644 17.0 247.3 18.637 67.0 249.4 21.268 117.0 249.1 25.768 167.0 249.9 27.445 200.0 250.0 27.618 233.0 250.0 27.646 18.0 247.6 18.714 68.0 249.2 21.355 118.0 249.0 25.830 168.0 249.8 27.458 201.0 250.0 27.619 234.0.249.9 27.649 19.0 248.3 18.767 69.0 249.3 21.456. 119.0 249.1 25.895 169.0 249.9 27.470 202.0 250.0 27.619 235.0 250.0 27.649 20.0 248.5 18.817 70.0 249.2 21.554 120.0 249.0 25.954 170.0 249.9 27.478 203.0 250.0 27.620 236.0 249.9 27.649 21.0 248.7 18.852 71.0 249.3 21.653 121.0 249.2 26.018 171.0 250.0 27.491 204.0 250.0 27.621 237.0 250.0 27.650 22.0 248.9 18.881 72.0 249.1 21.753 122.0 249.1 26.073 172.0 249.9 27.498 205.0 250.0 27.627 238.0 249.9 27.650 23.0 249.2 18.913 73.0 249.2 21.856 123.0 249.2 26.131 173.0 250.0 27.506 206.0 250.0 27.628 239.0 250.0 27.650 24.0 249.2 18.932 74.0 249.1 21.956 124.0 249.2 26.188 174.0 249.9 27.515 207.0 250.0 27.630 240.0 249.9 27.651 25.0 249.4 18.952 75.0 249.3 22.049 125.0 249.4 26.242 175.0 250.0 27.519 208.0 250.0 27.631 241.0 249.9 27.652 26.0 249.4 18.965 76.0 249.0 22.154 126.0 249.3 26.294 176.0 250.0 27.524 209.0 250.0 27.632 242.0 249.9 27.653 27.0 249.7 18.981 77.0 249.3 22.255 127.0 249.4 26.341 177.0 250.0 27.534 210.0 249.9 27.631 243.0 249.9 27.651 28.0 249.7 19.005 78.0 249.0 22.354 128.0 249.2 26.396 178.0 250.0 27.537 211.0 250.0 27.632 244.0 249.9 27.651 29.0 249.8 19.020 79.0 249.2 22.458 129.0 249.5 26.449 179.0 250.0 27.542 212.0 250.0 27.633 245.0 249.9 27.651 30.0 249.8 19.036 80.0 248.8 22.558 130.0 249.2 26.493 180.0 250.0 27.549 213.0 250.0 27.633 246.0 249.9 27.653 31.0 249.8 19.056 81.0 249.0 22.662 131.0 249.5 26.536 181.0 250.0 27.555 214.0 250.0 27.633 247.0 249.9 27.652 32.0 249.9 19.077 82.0 248.9 22.764 132.0 249.4 26.584 182.0 250.0 27.559 215.0 250.0 27.634 248.0 249.9 27.651 33,0 249.9 19.103 83.0 249.0 22.868 133.0 249.7 26.619 34.0 249.9 19.127 84.0 248.9 22.964 134.0 249.4 26.661 35.0 250.0 19.155 85.0 249.0 23.064 135.0 249.7 26.701 36.0 250.0 19.179 86.0 248.9 23.164 136.0 249.4 26.743 37.0 250.0 19.217 87.0 249.0 23.265 137.0 249.6 26.780 38.0 250.0 19.251 88.0 248.8 23.359 138.0 249.4 26.816 39.0 250.0 19.289 89.0 249.0 23.457 139.0 249,8 26.852 40.0 250.0 19.330 90.0 248.8 23.556 140.0 249.5 26.889 41.0 250.0 19.372 91.0 249.0 23.652 141.0 249.8 26.917 42.0 250.0 19.418 92.0 248.8 23.750 142.0 249.5 26.948 43.0 250.0 19.465 93.0 249.0 23.843 143.0 249.8 26.982 44.0 250.0 19.516 94.0 248.8 23.937 144.0 249.7 27.011 45.0 250.0 19.567 95.0 249.0 24.029 145.0 249.8 27.040 -46.0 249.9 19.618 96.0 248.8 24.121 146.0 249.6 27.068 47.0 249.9 19.685 97.0 249.0 24.208 147.0 249.8 27.090 48.0 249.8 19.729 98.0 248.8 24.297 148.0 249.6 27.114 49.0 249.8 19.792 99.0 249.0 24.385 149.0 249.8 27.144 OBSERVED EXPERIMENTAL DATA FROM RUN 26 OBSERVED EXPERIMENTAL DATA FROM RUN 26 (CONT'D) TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN- OF CM MIN OF' CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM.0 91.3 -. —- 50.0 249.8 19.514 100.0 249.4 20.864 150.0 248.9 24.800 200.0 249.4 27.434 250.0 249.5 27.889 1.0 129.3 4.581 51.0 249.9 19.515 101.0 249.6 20.944 151.0 249.0 24.879 201.0 249.5 27.455 251.0 249.5 27.893 2.0 157.5 7,563 52.0 249.8 19.518 102.0 249,4 21.001 152.0 249.0 24.959 202.0 249.5 27.479 252.0 249.5 27.896 3.0 178,.8 9.993 53.0 249.9 19.522 103.0 249.6 21.062 153.0 249.1 25.037 203.0 249.6 27.498 253.0 249.5 27.899 4.0 195.6 11.960 54.0 249.8 19.524 104.0 249.3 21.120 154.0 249.0 25.113 204.0 249.7 27.515 254.0 249.5 27.903 5.0 206.8 13.561 55.0 249.9 19.530 105.0 249.5 21.198 155.0 249.1 25.191 205.0 249.7 27.533 255.0 249.5 27.905 6.0 215.7 14,833 56.0 249.7 19,536 106.0 249.3 21.273 156.0 249.0 25.269 206.0 249.7 27.557 256.0 249.5 27.907 7.0 223.0 15.844 57.0 249.9 19.541 107.0 249.5 21.343 157.0 249.1 25.344 207.0 249.7 27.572 257.0 249.5 27.909 8.0 228.5 16.644 58.0 249,8 19.544 108.0 249.2 21.415 158.0 249.0 25,.418 208.0 249.6 27.587 258.0 249.6 27.911 9.0 233.3 17.265 59.0 249.9 19.550 109.0 249.4 21.489 159.0 249.1 25.495 209.0 249.6 27.603 259.0 249.7 27.913 -0.0 236.6 17.750 60.0 249.8 19.556 110.0 249.2 21.561 160.0 249.0 25.567 210.0 249.6 27.616 260.0 249.8 27.916 11.0 239.4 18.128 61.0 249.9 19.562 111.0 249.4 21.636 161.0 249.1 25.635 211.0 249.5 27.630 261.0 249.9 27.920 12.0 241,2 18.431 62.0 249.8 19.573 112.0 249.1 21.713 162.0 249.0 25,.705 212.0 249.5 27.643 262.0 249.8 27.926 13.0 243.1 18.663 63.0 249.8 19.580 113.0 249.3 21.788 163.0 249.1 25.772 213.0 249.5 27.655 263.0 249.8 27.928 14.0 244.2 18.839 64.0 249,7 19.591 114.0 249.2 21.867 164.0 249.0 25,.842 214.0 249.5 27.663 264.0 249.8 27.930 15.0 245.6 18.982 65.0 249.9 19.599 115.0 249.3 21.943 165.0 249.1 25.906 215.0 249.5 27.673 265.0 249.8 27.935 16.0 246.2 19.093 66.0 249.7 19.608 116.0 249.2 22.019 166.0 249.0 25.971 216.0 249.4 27.689 266.0 249.8 27.937 17.0 247.0 19.177 67.0 249.8 19.624 117.0 249.3 22.099 167.0 249.1 26.035 217.0 249.4 27.700 267.0 249.9 27.940 18.0 247.3 19.240 68.0 249.7 19.638 118.0 249.2 22.179 168.0 249.0 26.098 218.0 249.4 27.707 268.0 249.8 27.941 19.0 247.8 19.296 69.0 249.9 19.652 119.0 249.3 22.258 169.0 249.2 26.157 219.0 249.5 27.718 269.0 249.8 27.945 20.0 248.0 19.335 70.0 249.6 19.665 120.0 249.1 22.339 170.0 249.1 26.218 220.0 249.5 27.729 270.0 249.8 27.945 21.0 248.4 19.369 71.0 249.7 19.684 121.0 249.3 22.417 171.0 249.2 26.279 221.0 249.5 27.736 271.0 249.8 27.946 22.0 248,5 19.397 72.0 249.5 19.702 122.0 249.2 22.499 172.0 249.1 26,336 222.0 249.5 27.745 272.0 249.8 27.944 23.0 248.8 19.418 73.0 249.7 19.721 123.0 249.3 22.581 173.0 249.2 26.395 223.0 249.5 27.750 273.0 249.8 27.945 24.0 248.8 19.431 74.0 249.5 19.742 124.0 249.2 22.662 174.0 249.1 26.450 224.0 249.5 27.755 274.0 249.8 27.946 25.0 248.9 19.445 75.0 249.7 19.763 125.0 249.3 22.742 175.0 249.2 26.503 225.0 249.5 27.767 275.0 249.9 27.949 26.0 249.1 19.456 76.0 249.6 19.788 126.0 249,2 22.827 176.0 249.0 26.557 226.0 249.5 27.766 276.0 249.8 27.953 27.0 249.2 19.465 77.0 249.8 19.814 127.0 249.3 22.919 177.0 249.1 26.606 227.0 249.6 27.769 277.0 249.8 27.957 28.0 249.2 19.469 78.0 249.5 19.839 128.0 249.1 22.991 178.0 249.1 26.657 228.0 249.6 27.786 278.0 249.8 27.955 29.0 249.3 19.475 79.0 249.8 19.865 129.0 249.2 23.074 179.0 249.1 26.706 229.0 249.5 27.793 279.0 249.9 27.959 30.0 249.2 19.478 80.0 249.5 19.897 130.0 249.2 23.159 180.0 249.0 26.756 230.0 249.6 27.802 280.0 249.8 27.960 31.0 249.6 19.480 81.0 249.7 19.931 131.0 249.3 23.237 181.0 249.1 26.802 231.0 249.5 27.807 281.0 249.9 27.962 32.0 249.4 19.486 82.0 249.6 19.965 132.0 249.2 23.319 182.0 249.0 26.845 232.0 249.5 27.812 282.0 249.8 27.964 33.0 249.5 19.487 83.0 249.8 20.004 133.0 249.3 23.404 183.0 249.2 26.893 233.0 249.5 27.817 283.0 249.8 27.968 34.0 249.4 19.493 84.0 249.5 20.028 134.0 249.2 23.487 184.0 249.1 26.930 234.0 249.5 27.820 284.0 249.8 27.969 35.0 249.6 19.495 85.0 249.7 20.074 135.0 249.3 23.570 185.0 249.2 26.974 235.0 249.6 27.828 285.0 249.8 27.970 36.0 249.5 19.495 86.0 249.5 20.120 136.0 249.2 23.654 186.0 249.1 27.012 236.0 249.5 27.831 286.0 249.8 27.971 37.0 249.6 19.495 87.0 249.7 20.161 137.0 249.3 23.736 187.0 249.2 27.051 237.0 249.5 27.840 287.0 249.8 27.973 38.0 249.6 19.498 88.0 249.4 20.206 138.0 249.1 23.820 188.0 249.3 27.093 238.0 249.5 27.842 288.0 249.8 27.973 39.0 249.7 19.499 89.0 249.6 20.250 139.0 249.3 23.905 189.0 249.4 27.122 239.0 249.5 27.846 289.0 249.8 27.976 40.0 249.7 19.498 90.0 249.4 20.301 140.0 249.0 23.988 190.0 249.3 27.159 240.0 249.6 27.851 290.0 249.8 27.976 41.0 249.8 19.498 91.0 249.6 20.351 141.0 249.0 24.073 191.0 249.5 27.190 241.0 249.5 27.855 291.0 249.8 27.979 42.0 249.8 19.500 92.0 249.4 20.402 142.0 248.9 24.154 192.0 249.4 27.219 242.0 249.7 27.859 292.0 249.9 27.982 43.0 249.8 19.500 93.0 249.6 20.455 143.0 249.0 24.234 193.0 249.5 27.253 243.0 249.6 27.865 293.0 249.9 27.983 44,0 249,8 19,503 94,0 249.4 20,509 144.0 248.9 24.317 194.0 249.4 27.282 244.0 249,5 27.870 294.0 249.9 27.983 45,0 249,9 19.504 95.0 249.7 20,564 145.0 249.0 24.402 195.0 249,5 27.308 245.0 249.6 27.874 295.0 249.9 27.983 46.0 249.9 19.505 96.0 249.4 20.620 146.0 248.9 24.482 196.0 249.4 27.339 246.0 249.6 27.875 296.0 249.9 27.984 47.0 249.9 19.507 97.0 249.6 20.680 147.0 249.0 24.559 197.0 249.5 27.366 247.0 249.6 27.879 297.0 249.9 27.984 48.0 249.8 19.511 98.0 249.4 20.740 148.0 248.9 24.642 198.0 249.5 27.388 248.0 249.5 27.880 298.0 249.9 27.985 49.0 249.9 19.513 99.0 249.6 20.804 149.0 249.0 24.728 199.0 249.6 27.411 249.0 249.5 27.885 299.0 249.9 27.986

-502OBSERVED EXPERIMENTAL DATA FROM RUN 26 (CONT'D) OBSERVED EXPERIMENTAL DATA FROM RUN 27 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OP CM MIN O cm CMIN oF CM BIN OF CM 81\1 OF CM MIN OF CM 300.0 249.9 27.986 303.0 249.9 27.987 306.0 249.9 27.987'.0 87.4 —. —- 50.0 250.2 29.257 100.0 249.8 31.211 301.0 249.9 27.990 304.0 249.9 27.987 307.0 249.9 27.989 1.0 128.8 13.567 51.0 250.1 29.265 101.0 249.8 31.298 302.0 249.9 27.985 305.0 249.9 27.988 2.0 157.7 16.715 52.0 250.2 29.270 102.0 249.8 31.388 3.0 178.6 19.273 53.0 250.1 29.278 103.0 249.7 31.473 4.0 193.9 21.317 54.0 250.2 29.286 104.0 249.8 31.559 5.0 205.9 22.978 55.0 250.1 29.295 105.0 249.6 31.648 6.0 214.9 24.298 56.0 250.2 29.307 106.0 249.8 31.741 7.0 222.0 25.374 57.0 250.1 29.314 107.0 249.6 31.827 8.0 228.2 26.219 58.0 250.2 29.322 108.0 249.8 31.911 9.0 232.8 26.878 59.0 250.1 29.338 109.0 249.6 32.014 10.0 236.6 27.390 60.0 250.2 29.350 110.0 249.8 32.108 11.0 239.2 27.796 61.0 250.1 29.363 111.0 249.7 32.206 12.0 241.6 28.110 62.0 250.2 29.379 112.0 249.8 32.299 13.0 243.2 28.359 63.0 250.1 29.396 113.0 249.4 32.392 14.0 244.8 28.447 64.0 250.2 29.411 114.0 249.6 32.486 15.0 245.8 28.691 65.0 250,1 29.428 115.0 249.3 32.583 16.0 246.9 28.809 66.0 250.2 29.447 116.0 249.5 32.679 17.0 247.3 28.899 67.0 250.1 29.466 117.0 249.3 32.774 18.0 247.9 28.971 68.0 250.2 29.489 118.0 249.5 32.870 19.0 248.4 29.026 69.0 250.1 29.509 119.0 249.3 32.966 20.0 248.7 29.075 70.0 250.2 29.536 120.0 249.4 33.064 21.0 249.0 29.104 71.0 250.2 29.565 121.0 249.3 33.159 22.0 249.3 29.133 72.0 250.2 29.595 122.0 249.4 33.256 23.0 249.4 29.156 73.0 250.2 29.622 123.0 249.3 33.350 24.0 249.8 29.176 74.0 250.2 29.657 124.0 249.5 33.444 25.0 249.8 29.193 75.0 250.2 29.690 125.0 249.2 33.541 26.0 249.9 29.204 76.0 250.2 29.726 126.0 249.4 33.632 27.0 249.9 29.214 77.0 250.1 29.767 127.0 249.3 33.727 28.0 249.9 29.217 78.0 250.2 29.805 128.0 249.5 33.815 29.0 250.0 29.225 79.0 250.0 29.847 129.0 249.3 33.909 30.0 250.0 29.231 80.0 250.0 29.889 130.0 249.5 33.998 31.0 249.9 29.230 81.0 250.0 29.936 131.0 249.3 34.089 32.0 250.1 29.238 82.0 250.0 29.986 132.0 249.5 34.176 33.0 249.9 29.240 83.0 249.9 30.042 133.0 249.3 34.261 34.0 250.0 29.243 84.0 250.0 30.094 134.0 249.5 34.349 35.0 250.0 29.242 85.0 249.9 30.145 135.0 249.3 34.432 36.0 250.1 29.243 86.0 250.0 30.203 136.0 249.4 34.518 37.0 250.0 29.244 87.0 249.9 30.266 137.0 249.3 34.606 38.0 250.1 29.247 88.0 250.1 30.325 138.0 249.4 34.690 39.0 250.1 29.247 89.0 249.9 30.388 139.0 249.3 34.770 40.0 250.2 29.249 90.0 250.0 30.455 140.0 249.4 34.847 41.0 250.1 29.251 91.0 249.9 30.517 141.0 249.3 34.931 42.0 250.2 29.252 92.0 250.0 30.589 142.0 249.4 35.011 43.0 250.1 29.242 93.0 249.9 30.663 143.0 249.3 35.088 44.0 250.2 29.230 94.0 249.9 30.736 144.0 249.5 35.163 45.0 250.1 29.222 95.0 249.8 30.811 145.0 249.3 35.236 46.0 250.2 29.229 96.0 249.9 30.892 146.0 249.6 35.308 47.0 250.2 29.235 97.0 249.8 30.967 147.0 249.3 35.381 48.0 250.2 29.244 98.0 249.9 31.051 148.0 249.6 35.449 49.0 250.2 29.251 99.0 249.8 31.129 149.0 249.3 35.519 OBSERVED EXPERIMENTAL DATA FROM RUN 27 (CONT'D) OBSERVED EXPERIMENTAL DATA FROM RUN 28 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN Or CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM 150.0 249.5 35.588 187.0 249.7 37.158 224.0 250.0 37.515.0 87.3 —. —- 50.0 249.1 26.780 100.0 249.2 27.708 151.0 249.3 35.654 188,0 249,8 37.180 225.0 250.0 37.515 1.0 125.7 11.215 51.0 249.2 26.783 101.0 249.4 27.754 152.0 249.5 35.721 189.0 249.8 37.200 226.0 250.0 37.518 2.0 154.0 14.239 52.0 249.1 26.784 102.0 249.2 27.808 153.0 249.3 35.785 190.0 249.8 37.216 227.0 249.9 37.520 3.0 175.2 16.754 53.0 249.2 26.787 103.0 249.3 27.854 154.0 249.4 35.848 191.0 249.8 37.233 228.0 250.0 37.525 4.0 191.2 18.809 54.0 249.1 26.790 104.0 249.1 27.909 155.0 249.3 35.910 192.0 249.9 37.253 229.0 249.9 37.525 5.0 203.9 20.464 55.0 249.2 26.794 105.0 249.2 27.958 156.0 249.3 35.970 193.0 249.9 37.270 230.0 250.0 37.531 6.0 213.4 21.796 56.0 249.1 26.800 106.0 249.0 28.016 157.0 249.3 36.027 194.0 249.9 37.287 231.0 249.9 37.532 7.0 221.2 22.855 57.0 249.2 26.806 107.0 249.2 28.068 158.0 249.4 36.087 195.0 249.9 37.302 232.0 250.0 37.531 8.0 227.1 23.692 58.0 249.1 26.813 108.0 249.0 28.124 159.0 249.3 36.139 196.0 249.9 37.317 233.0 250.0 37.535 9.0 231.6 24.342 59.0 249.3 26.816 109.0 249.2 28.180 160.0 249.4 36.194 197.0 249.8 37.329 234.0 250.0 37.536 10.0 235.0 24.863 60.0 249.1 26.822 110.0 249.0 28.239 161.0 249.3 36.246 198.0 249.9 37.345 235.0 250.0 37.537 11.0 238.1 25.270 61.0 249.3 26.827 111.0 249.2 28.303 162.0 249.5 36.295 199.0 249.9 37.357 236.0 250.0 37.539 12.0 240.2 25.588 62.0 249.1 26.834 112.0 249.0 28.367 163.0 249.4 36.343 200.0 249.8 37.367 237.0 250.0 37.539 13.0 242.0 25.831 63.0 249.2 26.842 113.0 249.2 28.430 164.0 249.5 36.392 201.0 249.8 37.379 238.0 250.0 37.540 14.0 243.2 26.020 64.0 249.1 26.850 114.0 249.0 28.492 165.0 249.4 36.448 202.0 249.9 37.391 239.0 249.9 37.541 15.0 244.5 26.176 65.0 249.2 26.858 115.0 249.2 28.558 166.0 249.6 36.498 203.0 249.9 37.402 240.0 250.0 37.542 16.0 245.3 26.293 66.0 249.1 26.868 116.0 248.9 28.619 167.0 249.4 36.536 204.0 249.9 37.411 241.0 249.9 37.544 17.0 246.2 26.389 67.0 249.2 26.879 117.0 249.0 28.692 168.0 249.6 36.576 205.0 249.9 37.418 242.0 250.0 37.544 18.0 246.7 26.460 68.0 249.1 26.886 118.0 249.8 28.763 169.0 249.5 36.615 206.0 249.9 37.429 243.0 250.0 37.546 19.0 247.2 26.519 69.0 249.2 26.897 119.0 249.9 28.832 170.0 249.6 36.653 207.0 249.8 37.435 244.0 250.0 37.546 20.0 247.3 26.571 70.0 249.0 26.908 120.0 249.8 28.904 171.0 249.4 36.692 208.0 249.9 37.442 245.0 250.0 37.548 21.0 247.7 26.605 71.0 249.3 26.918 121.0 249.0 28.976 172.0 249.5 36.730 209.0 249.8 37.448 246.0 250.0 37.547 22.0 247.8 26.637 72.0 249.1 26.932 122.0 248.8 29.051 173.0 249.5 36.766 210.0 249.9 37.456 247.0 250.0 37.548 23.0 248.2 26.658 73.0 249.3 26.945 123.0 248.9 29.123 174.0 249.7 36.800 211.0 249.8 37.460 248.0 250.0 37.550 24.0 248.3 26.676 74.0 249.1 26.959 124.0 248.7 29.197 175.0 249.6 36.834 212.0 249.8 37.469 249.0 250.0 37.550 25.0 248.6 26.689 75.0 249.3 26.976 125.0 248.9 29.274 176.0 249.7 36.865 213.0 249.8 37.473 250.0 250.0 37.550 26.0 248.4 26.699 76.0 249.2 26.989 126.0 248.7 29.351 177.0 249.7 36.901 214.0 249.9 37.478 251.0 250.0 37.551 27.0 248.6 26.709 77.0 249.5 27.009 127.0 248.8 29.430 178.0 249.7 36.930 215.0 249.8 37.484 252.0 250.0 37.552 28.0 248.5 26.717 78.0 249.3 27.024 128.0 248.6 29.508 179.0 249.7 36.959 216.0 249.8 37.491 253.0 250.0 37.551 29.0 248.7 26.725 79.0 249.5 27.045 129.0 248.7 29.587 180.0 249.7 36.988 217.0 249.8 37.498 254.0 250.0 37.552 30.0 248.7 26.727 80.0 249.3 27.069 130.0 248.6 29.666 181,0 249.7 37.014 218.0 249.9 37.498 255.0 250.0 37.553 31.0 248.8 26.735 81.0 249.5 27.087 131.0 248.8 29.746 182.0 249.8 37.041 219.0 249.9 37.503 256.0 250.1 37.552 32.0 248.8 26.736 82.0 249.3 27.106 132.0 248.6 29.826 183.0 249.7 37.070 220.0 250.0 37.507 257.0 250.0 37.551 33.0 248.9 26.739 83.0 249.5 27.127 133.0 248.8 29.908 184.0 249.8 37.094 221.0 250.0 37.508 258.0 250.1 37.551 34.0 248.9 26.740 84.0 249.3 27.152 134.0 248.6 29.987 185.0 249.8 37.114 222.0 250.0 37.510 259.0 250.0 37.552 35.0 249.0 26.745 85.0 249.4 27.178 135.0 248.7 30.073 186.0 249.8 37.137 223.0 250.0 37.515 260.0 250.0 37.552 36.0 249.0 26.749 86.0 249.3 27.205 136.0 248.6 30.151 37.0 249.1 26.748 87.0 249.4 27.234 137.0 248.7 30.236 38,0 249,0 26.753 88.0 249.3 27.261 138.0 248.5 30.314 39.0 249.2 26.753 89.0 249.4 27.293 139.0 248.7 30.395 40.0 249.1 26.753 90.0 249.2 27.322 140.0 248.5 30.477 41.0 249.2 26.757 91.0 249.4 27.358 141.0 248.7 30.558 42.0 249.1 26.758 92.0 249.2 27.390 142.0 248.5 30.639 43.0 249.2 26.758 93.0 249.5 27.425 143.0 248.7 30.720 44.0 249.1 26.759 94.0 249.3 27.459 144.0 248.5 30.806 45.0 249.3 26.766 95.0 249.5 27.500 145.0 248.7 30.878 46.0 249.2 26.769 96.0 249.3 27.539 146.0 248.5 30.960 47.0 249.2 26.771 97.0 249.5 27.078 147.0 248.7 31.045 48.0 249.1 26.773 98.0 249.2 27.619 148.0 248.6 31.120 49.0 249.2 26.776 99.0 249.5 27.663 149.0 248.7 31.202

-303OBSERVED EXPERIMENTAL DATA FROM RUN 28 (CUNT'D) OBSERVED EXPERIMENTAL DATA FROM RUN 29 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OP CM MIN OF CM MIN OF CM MIN OF CM 150.0 248.5 31.284 197.0 248.7 34.082 244.0 249.1 34.989.0 83.7 —. —- 50.0 249.4 3D.599 100G. 249.2 21.951 151.0 248.7 31.361 198.0 248.8 34.116 245.0 249.1 34.998 1.0 122.4 —. —- 51.0 249.5 30.606 101.0 249.3 32.010 152.0 248.5 31.439 199.0 248.8 34.153 246.0 249.1 35.006 2.0 151.0 17.729 52.0 249.4 30.613 102.0 249.2 32.078 153.0 248.8 31.515 200.0 248.8 34.187 243.0 249.1 35.010 3.0 173.4 20.335 53.0 249.5 30.617 103.0 249.X 32.140 154.0 248.5 31.593 201.0 248.R 34.223 24R.0 249.2 35.017 4.0 188.8 22.461 54.0 249.4 30.620 104.0 249.2 22.206 155.0 248.7 31.670 202.0 248.8 34.254 249.0 249.2 35.022 5.0 201.4 24.165 55.0 249.5 30.632 105.0 249.3 32.274 156.0 248.4 31.746 203.0 249.0 34.285 25D.0 249.2 35.D26 6.0 211.6 25.545 56.0 249.3 30.636 1D6.D 249.1 32.240 157.0 248.7 31.818 204.0 248.9 34.320 251.0 249.3 35.032 7.0 219.8 26.643 57.0 249.4 30.644 107.0 249.2 32.407 158.0 248.4 31.R95 205.0 248.9 34.349 252.0 249.3 35.037 8.0 226.1 27.5D4 5R.0 249.3 30.655 108.0 249.0 32.476 159.0 248.6 31.963 206.0 24R.9 34.376 253.0 249.3 35.040 9.0 231.3 28.175 59.0 249.5 30.664 109.0 249.0 32.545 160.0 248.4 32.038 207.0 249.0 34.405 254.0 249.3 35.046 10.0 234.9 28.702 60.0 249.4 30.672 110.0 24R.9 32.618 161.0 248.5 32.112 208.0 248.9 34.428 255.0 249.4 35051 11.0 238.0 29.113 61.0 249.5 30.681 111.0 249.0 32.691 162.0 248.4 32.183 209.0 249.0 34.453 256.0 249.3 35.056 12.0 240.0 29.433 62.0 249.4 30.694 112.0 248.8 32.766 163.0 248.5 32.252 210.0 24R.9 34.480 257.0 249.4 35.061 13.0 242.0 29.681 63.0 249.6 30.704 113.0 249.0 32.837 164.0 248.4 32.223 211.0 249.0 34.509 258.0 249.3 35.066 14.0 243.3 29.876 64.0 249.4 30.715 114.0 248.9 32.915 165.0 248.5 32.391 212.0 24R.9 34.533 259.0 249.4 35.066 15.0 244.8 30.019 65.0 249.6 30.729 115.0 249.0 32.991 166.0 248.4 32.45R 213.0 249.0 34.555 260.0 249.3 35.069 16.0 245.5 30.133 66.0 249.5 30.744 116.0 248.9 23.066 167.0 248.5 32.527 214.0 248.9 34.576 261.0 249.3 35.070 17.0 246.4 30.214 67.0 249.6 30.760 117.0 249.0 33.141 16R.0 248.5 32.594 215.0 249.0 34.601 262.0 249.3 35.074 1R.0 246.8 30.282 68.0 249.5 30.777 118.0 248.9 33.216 169.0 248.5 32.661 216.0 248.9 34.623 263.0 249.4 35.07R 19.0 247.3 30.333 69.0 249.6 20.791 119.0 249.0 33.295 170.0 248.4 32.726 217.0 249.0 34.644 264.0 249.3 35.083 20.0 247.7 30.370 70.0 249.5 30.810 120.0 248.9 33.375 171.0 248.5 32.784 218.0 249.0 34.658 265.0 249.3 35.084 21.0 248.1 30.405 71.0 249.5 30.826 121.0 249.0 33.452 172.0 248.4 32.851 219.0 249.1 34.678 266.0 249.3 35.088 22.0 248.2 30.434 72.0 249.4 30.R43 122.0 248.9 33.531 073.0 248.5 32.912 220.0 249.1 34.695 267.0 249.3 35.089 23.0 248.5 30.458 73.0 249.6 30.868 123.0 249.0 33.611 174.0 248.4 32.962 221.0 249.2 34.713 268.0 249.3 35.088 24.0 248.6 30.474 74.0 249.4 30.888 124.0 248.9 33.697 175.0 248.4 33.033 222.0 249.1 34.730 269.0 249.3 35.090 25.0 248.7 30.4R6 75.0 249.6 30.911 125.0 249.0 33.775 176.0 248.4 33.090 223.0 249.1 34.742 270.0 249.3 35.093 26.0 248.8 30.498 76.0 249.5 30.934 126.0 248.9 33.854 177.0 248.4 33.146 224.0 249.1 34.761 271.0 249.3 35.094 27.0 249.0 30.506 77.0 249.6 30.961 127.0 249.0 33.935 178.0 248.4 33.207 225.0 249.1 34.778 272.0 249.3 35.093 28.0 248.9 30.515 78.0 249.5 30.984 128.0 248.7 34.010 179.0 248.5 33.259 226.0 249.1 34.792 273.0 249.4 35.094 29.0 249.1 30.522 79.0 249.6 31.010 129.0 248.8 34.096 180.0 248.4 33.308 227.0 249.2 34.808 274.0 249.3 35.095 30.0 249.1 30.525 80.0 249.5 31.043 130.0 248.6 34.178 181.0 248.5 33.363 22R.0 249.1 34.819 275.0 249.4 35.096 31.0 249.2 30.528 81.0 249.7 31.072 131.0 248.8 34.259 182.0 248.5 33.415 229.0 249.1 34.833 276.0 249.3 35.099 32.0 249.1 30.533 82.0 249.4 31.104 132.0 248.7 34.338 183.0 248.5 33.466 230.0 249.1 34.845 277.0 249.3 35.100 33.0 249.2 30.538 83.0 249.7 31.137 132.0 24R.8 34.416 184.0 248.5 33.516 231.0 249.1 34.859 279.0 249.3 35.100 34.0 249.1 30.539 84.0 249.5 31.171 134.0 248.7 34.495 185.0 248.5 33.56R 232.0 249.1 34.R72 279.0 249.3 35.101 35.0 249.3 30.543 85.0 249.6 31.210 135.0 248.8 34.579 186.0 248.5 33.615 233.0 249.0 34.884 290.0 249.3 35.101 36.0 249.2 30.545 86.0 249.4 31.247 136.0 248.7 34.659 187.0 249.6 33.659 234.0 249.1 34.89R 281.0 249.3 35.102 37.0 249.3 30.545 83.0 249.7 31.291 137.0 248.8 24.739 188.0 248.5 33.708 235.0 249.1 34.909 282.0 249.2 35.104 38.0 249.2 30.549 89.0 249.4 31.330 138.0 248.7 34.813 189.0 248.5 33.752 236.0 249.1 34.921 283.0 249.2 35.106 39.0 249.3 30.551 89.0 249.7 31.376 139.0 248.8 34.894 190.0 248.5 33.800 237.0 249.0 34.933 284.0 249.2 35.105 40.0 249.2 30.555 90.0 249.3 31.418 140.0 248.7 34.975 191.0 248.5 33.R37 238.0 249.1 34.942 2R5.0 249.3 35.104 41.0 249.3 30.558 91.0 249.6 31.46R 141.0 248.8 35.047 192.0 248.5 33.879 239.0 249.1 34.951 286.0 249.3 35.105 42.0 249.2 30.561 92.0 249.3 31.515 142.0 248.7 35.127 193.0 24R.6 33.923 240.0 249.1 34.959 287.0 249.7 35.106 43.0 249.3 30.563 93.0 249.6 31.563 143.0 248.8 35.203 194.0 248.6 33.965 241.0 249.1 34.968 288.0 249.8 35.105 44.0 249.2 30.570 94.0 249.2 31.615 144.0 248.7 35.281 195.0 248.6 34.006 242.0 249.1 34.973 45.0 249.4 30.573 95.0 249.5 31.667 145.0 248.7 35.358 196.0 248.6 34.044 243.0 249.1 34.981 46.0 249.4 30.581 96.0 249.2 31.724 146.0 248.6 35.427 47.0 249.5 30.586 97.0 249.3 31.781 147.0 248.7 35.503 48.0 249.5 30.589 98.0 249.2 31.838 148.0 248.7 35.569 49.0 249.6 30.593 99.0 249.3 31.897 149.0 248.8 35.645 OBSERVED EXPERIMENTAL DATA PROM RUN 29 (CONT'D) OBSERVED EXPERIMENTAL DATA PROM RUN 30 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OP' CM MIN OF CM MIN OP CM MIN OP CM MIN OP CM 150.0 248.7 35.715 194.0 248.8 37.839 238.0 249.1 38.416.0 86.0 -. —- 50.0 249.3 23.961 100.0 249.3 24.632 151.0 248.8 35.787 195.0 248.8 37.867 239.0 249.0 38.421 1.0 127.6 8.398 51.0 249.3 23.964 101.0 249.2 24.671 152.0 248.7 35.854 196.0 248.8 37.892 240.0 249.0 38.425 2.0 155.5 11.436 52.0 249.3 23.965 102.0 249.3 24.716 153.0 248.8 35.923 197.0 248.8 37.915 241.0 249.0 39.427 3.0 177.9 13.972 53.0 249.3 23.970 103.0 249.3 24.757 154.0 248.7 35.992 198.0 248.7 37.939 242.0 249.1 38.431 4.0 192.8 16.035 54.0 249.4 23.970 104.0 249.3 24.808 155.0 248.8 36.056 199.0 248.8 37.962 243.0 249.0 38.431 5.0 205.6 17.696 55.0 249.4 23.974 005.0 249.3 24.853 156.0 248.7 36.112 200.0 248.7 37.986 244.0 249.1 38.435 6.0 215.0 19.'028 56.0 249.5 23.975 106.0 249.3 24.905 157.0 248.9 36.190 201.0 248.8 38.008 245.0 249.1 38.436 7.0 221.8 20.080 57.0 249.5 23.974 107.0 249.3 24.955 158.0 248.8 36.253 202.0 248.8 38.027 246.0 249.1 38.439 8.0 227.5 20.919 S8.0 249.5 23.978 108.0 249.3 25.008 159.0 248.9 36.311 203.0 248.8 38.048 247.0 249.1 38.441 9.0 232.0 21.673 59.0 249.5 23.983 109.0 249.3 25.065 160.0 248.8 36.367 204.0 248.8 38.067 248.0 249.1 38.442 10.0 235.5 22.087 60.0 249.5 23.984 110.0 249.2 25.123 161.0 248.9 36.469 205.0 248.8 38.080 249.0 249.1 38.447 11.0 238.2 22.483 61.0 249.5 23.985 111.0 249.3 25.179 162.0 248.8 36.506 206.0 248.8 38.097 250.0 249.1 38.447 12.0 240.8 22.799 62.0 249.5 23.992 112.0 249.3 25.243 163.0 248.8 36.558 207.0 248.8 38.118 251.0 249.0 38.450 13.0 242.1 23.044 63.0 249.5 23.994 113.0 249.2 25.305 164.0 248.8 36.615 208.0 248.8 38.133 252.0 249.0 38.450 14.0 243.6 23.234 64.0 249.5 23.996 114.0 249.2 25.371 165.0 248.8 36.670 209.0 248.9 38.150 253.0 249.0 38.452 15.0 244.7 23.379 65.0 249.5 24.000 115.0 249.2 25.436 166.0 248.8 36.727 210.0 248.9 38.165 254.0 249.0 38.450 16.0 245.9 23.497 66.0 249.5 24.007 116.0 249.1 25.503 167.0 248.9 36.780 211.0 249.0 38.182 255.0 249.0 38.453 17.0 246.3 23.587 67.0 249.5 24.012 117.0 249.1 25.573 168.0 248.8 36.835 212.0 249.0 38.192 256.0 249.0 38.455 18.0 247.2 23.590 68.0 249.6 24.016 118.0 249.0 25.645 169.0 248.9 36.889 213.0 249.0 38.208 257.0 249.0 38.455 19.0 247.2 23.661 69.0 249.6 24.021 119.0 249.1 25.718 L10.0 248.8 36.938 214.0 248.9 38.219 258.0 049.0 38.456 20.0 248.0 23.717 70.0 249.5 24.028 120.0 249.0 25.790 171.0 248.9 36.987 215.0 249.0 38.233 259.0 249.0 38.458 21.0 248.2 23.765 71.0 249.6 24.031 121.0 249.0 25.867 172.0 248.8 37.036 216.0 248.9 38.246 260.0 249.0 38.460 22.0 248.3 23.799 72.0 249.6 24.038 122.0 249.0 25.947 173.0 248.9 37.084 217.0 249.0 38.258 261.0 249.0 38.463 23.0 248.4 23.828 73.0 249.5 24.046' 123.0 249.0 26.027 174.0 248.8 37.133 218.0 249.0 38.271 262.0 249.0 38.464 24.0 248.7 23.851 74.0 249.6 24.055 124.0 249.1 26.107 175.0 248.9 37.177 219.0 249.0 38.286 263.0 249.0 38.464 25.0 248.9 23.871 75.0 249.5 24.064 125.0 249.0 26.190 176.0 248.8 37.221 220.0 249.0 38.297 264.0 249.0 38.465 26.0 249.0 23.884 76.0 249.5 24.076 126.0 249.0 26.269 177.0 249.0 37.272 221.0 249.0 38.306 265.0 249.0 38.466 27.0 248.9 23.895 77.0 249.5 24.086 127.0 249.0 26.358 178.0 248.8 37.306 222.0 249.0 38.315 266.0 249.0 38.468 28.0 249.0 23.909 78.0 249.5 24.099 128.0 249.0 26.444 179.0 248.9 37.345 223.0 249.0 38.324 267.0 249.0 38.470 29.0 249.0 23.913 79.0 249.4 24.113 129.0 248.9 26.527 180.0 248.8 37.387 224.0 249.0 38.333 268.0 249.0 38.471 30.0 249.1 23.921 80.0 249.5 24.124 130.0 248.9 26.618 181.0 248.9 37.424 225.0 249.0 38.339 269.0 249.0 38.471 31.0 249.1 23.926 81.0 249.5 24.137 131.0 248.9 26.707 182.0 248.8 37.464 226.0 249.0 38.351 270.0 248.9 38.474 32.0 249.1 23.930 82.0 249.5 24.155 132.0 248.9 26.801 183.0 248.8 37.502 227.0 249.0 38.356 271.0 248.9 38.474 33.0 249.1 23.933 83.0 249.5 24.170 133.0 248.9 24.887 184.0 248.8 37.535 228.0 249.0 38.363 272.0 248.8 38.475 34.0 249.1 23.935 84.0 249.5 24.187 134.0 248.9 26.977 18S.0 248.8 37.568 229.0 249.0 38.368 273.0 248.9 38.477 35.0 249.1 23.939 8S.0 249.4 24.204 135.0 248.8 27.070 186.0 248.8 37.403 230.0 249.0 38.376 274.0 248.8 38.477 34.0 249.2 23.944 86.0 249.4 24.224 136.0 248.8 27.165 187.0 248.8 37.637 231.0 249.0 38.385 275.0 248.9 38.477 37.0 249.2 23.944 87.0 249.4 24.243 137.0 248.8 27.260 188.0 248.8 37.466 232.0 249.0 38.390 276.0 248.9 38.478 38.0 249.3 23.944 88.0 249.4 24.265 138.0 248.8 27.353 189.0 248.9 37.694 233.0 249.0 38.396 277.0 248.9 38.478 39.0 249.3 23.944 89.0 249.4 24.286 139.0 248.7 27.449 190.0 248.8 37.728 234.0 249.0 38.400 278.0 248.9 38.479 40.0 249.4 23.948 90.0 249.4 24.313 140.0 248.8 27.547 191.0 248.8 37.756 235.0 249.0 38.406 279.0 248.9 38.478 41.0 249.3 23.950 91.0 249.4 24.340 141.0 248.8 27.640 192.0 248.8 37.784 236.0 249.0 38.411 280.0 248.9 38.479 42.0 249.3 23.950 92.0 249.4 24.343 142.0 248.8 27.734 193.0 248.8 37.813 237.0 249.0 38.414 43.0 249.3 23.9S0 93.0 249.4 24.389 143.0 248.8 27.832 44.0 249.4 23.9S5 94.0 249.3 24.421 144.0 248.9 27.925 45.0 249.3 23.995 99.0 249.3 24.447 14S.0 248.8 28.02S 46.0 249.3 23.95S 96.0 249.4 24.482 144.0 248.8 28.119 47.0 249.3 23.9S7 97.0 249.3 24.919 147.0 248.8 28.219 48.0 249.3 23.958 98.0 249.3 24.5S5 148.0 248.8 28.317 49.0 249.3 23.958 99.024.2459 1.0488840

-504OBSERVED EXPERIMENTAL DATA FROM RUN 30 (CONTID) OBSERVED EXPERIMENTAL DATA FROM RUN 31 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN Op CM MIN OP CM MIN OF CM MIN OP CM 150.0 248.9 28.508 186.0 248.8 31.224 222.0 249.2 32.187.0 87.0.000 50.0 249.8 21.611 100.0 249.9 22.954 151.0 248.8 28.590 187.0 248.7 31.270 223.0 249.2 32.198.0 87.0 -. — 50.0 249.8 21.611 100.0 249.9 22.954 152.0 248.8 28.688 188.0 248.8 31.318 224.0 249.3 32.205 1.0 124.9 6.115 51.0 249.8 21.613 101.0 249.9 23.028 153.0 248.8 28.780 189.0 248.7 31.366 225.0 249.2 32.213 2.0 154.5 9.129 52.0 249.8 21.616 102.0 249.9 23.099 154.0 248.9 28.873 190.0 248.8 31.412 226.0 249.3 32.221 3.0 175.1 11.648 53.0 249.9 21.617 103.0 249.9 23.179 155.0 248.7 28.963 191.0 248.8 31.454 227.0 249.2 32.228 4.0 191.9 13.707 54.0 249.8 21.622 104.0 249.8 23.256 156.0 248.8 29.057 192.0 248.8 31.491 228.0 249.3 32.234 5.0 204.4 15.364 55.0 249.9 21.623 105.0 249.8 23.336 157.0 248.8 29.150 193.0 248.7 31.537 229.0 249.2 32.237 6.0 214.8 16.697 56.0 249.8 21.630 106.0 249.8 23.418 158.0 248.8 29.236 194.0 248.8 31.571 230.0 249.4 32.243 7.0 222.3 17.748 57.0 249.9 21.635 107.0 249.8 23.502 159.0 248.8 29.325 195.0 248.8 31.613 231.0 249.3 32.249 8.0 228.1 18.569 58.0 249.8 21.637 108.0 249.8 23.588 160.0 248.8 29.413 196.0 248.8 31.648 232.0 249.4 32.253 9.0 232.8 19.218 59.0 249.9 21.643 109.0 249.8 23.676 161.0 248.7 29.503 197.0 248.8 31.679 233.0 249.3 32.255 10.0 236.2 19.778 60.0 249.9 21.648 110.0 249.8 23.766 162.0 248.8 29.582 198.0 248.9 31.714 234.0 249.5 32.260 11.0 239.0 20.131 61.0 249.9 21.654 111.0 249.8 23.853 163.0 248.8 29.670 199.0 248.9 31.746 235.0 249.3 32.265 12.0 241.0 20.448 62.0 249.9 21.665 112.0 249.8 23.948 164.0 248.8 29.751 200.0 249.0 31.772 236.0 249.4 32.269 13.0 243.2 20.696 63.0 249.9 21.673 113.0 249.6 24.042 165.0 248.8 29.833 201.0 248.9 31.808 237.0 249.3 32.273 14.0 244.3 20.894 64.0 249.9 21.682 114.0 249.5 24.138 166.0 248.8 29.913 202.0 248.9 31.832 238.0 249.5 32.276 15.0 245.6 21.040 65.0 249.9 21.692 115.0 249.5 24.236 167.0 248.8 29.990 203.0 248.9 31.861 239.0 249.3 32.278 16.0 246.3 21.158 66.0 249.9 21.704 116.0 249.5 24.336 168.0 248.9 30.075 204.0 248.9 31.884 240.0 249.5 32.281 17.0 247.1 21.256 67.0 249.9 21.719 117.0 249.6 24.440 169.0 248.8 30.154 205.0 248.9 31.913 241.0 249.3 32.284 18.0 247.5 21.327 68.0 249.9 21.730 118.0 249.5 24.535 170.0 248.9 30.232 206.0 249.0 31.931 242.0 249.5 32.285 19.0 248.0 21.385 69.0 249.9 21.748 119.0 249.5 24.640 171.0 248.8 30.306 207.0 248.9 31.955 243.0 249.3 32.288 20.0 248.2 21.426 70.0 249.9 21.754 120.0 249.5 24.742 172.0 248.8 30.373 208.0 248.9 31.972 244.0 249.4 32.289 21.0 248.6 21.459 71.0 249.9 21.776 121.0 249.5 24.845 173.0 248.8 30.445 209.0 248.9 32.014 245.0 249.3 32.290 22.0 248.8 21.490 72.0 249.9 21.791 122.0 249.4 24.948 174.0 248.8 30.515 210.0 249.0 32.034 246.0 249.3 32.292 23.0 249.0 21.513 73.0 249.9 21.808 123.0 249.4 25.056 175.0 248.8 30.579 211.0 248.9 32.049 247.0 249.3 32.293 24.0 249.1 21.533 74.0 250.0 21.827 124.0 249.3 25.164 176.0 248.7 30.647 212.0 249.0 32.066 248.0 249.4 32.295 25.0 249.4 21.544 70.0 250.0 21.849 125.0 249.2 25.270 177.0 248.7 30.718 213.0 248.9 32.083 249.0 249.3 32.298 26.0 249.3 21.558 76.0 250.0 21.871 126.0 249.2 25.378 178.0 248.7 30.776 214.0 249.0 32.097 250.0 249.5 32.301 27.0 249.4 21.566 77.0 250.0 21.894 127.0 249.2 25.487 179.0 248.7 30.838 215.0 248.9 32.115 251.0 249.3 32.305 28.0 249.6 21.574 78.0 250.0 21.919 128.0 249.2 25.594 180.0 248.8 30.902 216.0 249.0 32.128 252.0 249.4 32.306 29.0 249.8 21.579 79.0 250.0 21.942 129.0 249.2 25.701 181.0 248.8 30.956 217.0 249.0 32.136 253.0 249.3 32.305 30.0 249.8 21.583 80.0 250.1 21.973 130.0 249.2 25.810 182.0 248.8 31.014 218.0 249.0 32.147 254.0 249.4 32.304 31.0 249.8 21.585 81.0 250.1 21.999 131.0 249.2 25.917 183.0 248.8 31.065 219.0 249.0 32.161 255.0 249.3 32.304 32.0 249.8 21.588 82.0 250.0 22.028 132.0 249.2 26.020 184.0 248.8 31.122 220.0 249.0 32.169 33.0 249.8 21.588 83.0 250.1 22.063 133.0 249.2 26.126 185.0 248.8 31.170 221.0 249.1 32.176 34.0 249.8 21.592 84.0 250.0 22.099 134.0 249.2 26.236 35.0 249.8 21.592 85.0 250.0 22.139 135.0 249.2 26.342 36.0 249.8 21.592 86.0 250.0 22.164 136.0 249.2 26.449 37.0 249.8 21.595 87.0 250.0 22.219 137.0 249.2 26.549 38.0 249.8 21.595 88.0 249.9 22.260 138.0 249.2 26.653 39.0 249.8 21.596 89.0 249.9 22.305 139.0 249.2 26.759 40.0 249.8 21.596 90.0 249.9 22.353 140.0 249.1 26.860 41.0 249.8 21.595 91.0 249.9 22.405 141.0 249.2 26.964 42.0 249.8 21.596 92.0 249.9 22.455 142.0 249.2 27.064 43.0 249.8 21.598 93.0 249.9 22.511 143.0 249.2 27.159 44.0 249.8 21.598 94.0 249.9 22.567 144.0 249.2 27.264 45.0 249.8 21.600 95.0 249.9 22.626 145.0 249.2 27.360 46.0 249.8 21.600 96.0 249.9 22.685 146.0 249.1 27.460 47.0 249.8 21.603 97.0 249.9 22.749 147.0 249.2 27.559 48.0 249.8 21.606 98.0 249.9 22.815 148.0 249.2 27.650 49.0 249.8 21.607 99.0 249.9 22.882 149.0 249.1 27.740 OBSERVED EXPERIMENTAL DATA FROM RUN 31 (CONT'D) OBSERVED EXPERIMENTAL DATA FROM RUN 32 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OP cm MIN OF cm MIN OP cm MI0 OF CM MIN OF CM MIN OF CM 150.0 249.1 27.833 179.0 249.4 29.622 208.0 250.0 30.074.0 89.9 -. —- 50.0 249.8 22.700 100.0 249.9 22.909 151.0 249.1 27.920 180.0 249.5 29.655 209.0 250.0 30.077 1.0 128.8 7.494 51.0 249.6 22.700 101.0 249.9 22.924 152.0 249.1 28.006 181.0 249.6 29.687 210.0 250.0 30.080 2.0 158.3 10.520 52.0 249.7 22.700 102.0 249.9 22.941 153.0 249.0 28.093 182.0 249.6 29.718 211.0 250.0 30.088 3.0 178.6 12.994 53.0 249.6 22.700 103.0 249.9 22.959 154.0 249.0 28.178 183.0 249.7 29.746 212.0 250.0 30.089 4.0 194.8 15.026 54.0 249.7 22.700 104.0 249.9 22.983 155.0 249.1 28.259 184.0 249.7 29.772 213.0 250.0 30.093 5.0 206.5 16.652 55.0 249.6 22.700 105.0 249.9 23.006 156.0 249.1 28.340 185.0 249.8 29.798 214.0 249.9 30.095 6.0 215.8 17.960 56.0 249.8 22.699 106.0 249.9 23.027 157.0 249.0 28.413 186.0 249.8 29.818 215.0 250.0 30.096 7.0 223.0 18.988 57.0 249.6 22.698 107.0 249.9 23.051 158.0 249.1 28.489 187.0 249.8 29.840 216.0 249.9 30.098 8.0 228.9 19.813 58.0 249.8 22.697 108.0 249.9 23.078 159.0 249.0 28.565 188.0 249.8 29.864 217.0 249.9 30.099 9.0 233.1 20.453 59.0 249.6 22.696 109.0 249.8 23.104 160.0 249.1 28.638 189.0 249.8 29.880 218.0 250.0 30.102 10.0 236.6 20.948 60.0 249.8 22.692 110.0 249.8 23.131 161.0 249.0 28.709 190.0 249.8 29.899 219.0 250.0 30.107 11.0 239.3 21.334 61.0 249.6 22.692 111.0 249.8 23.158 162.0 249.0 28.777 191.0 249.8 29.911 220.0 249.9 30.109 12.0 241.3 21.633 62.0 249.8 22.691 112.0 249.9 23.190 163.0 249.0 28.842 192.0 249.8 29.924 221.0 249.9 30.110 13.0 242.9 21.858 63.0 249.6 22.692 113.0 249.9 23.220 164.0 249.0 28.908 193.0 249.8 29.938 222.0 250.0 30.114 14.0 244.3 22.033 64.0 249.8 22.690 114.0 249.9 23.254 165.0 249.1 28.964 194.0 249.8 29.953 223.0 250.0 30.116 15.0 245.3 22.178 65.0 249.7 22.691 115.0 249.9 23.289 166.0 249.1 29.026 195.0 249.8 29.964 224.0 250.0 30.117 16.0 246.3 22.289 66.0 249.8 22.696 116.0 249.9 23.328 167.0 249.0 29.082 196.0 249.8 29.977 225.0 250.1 30.120 17.0 246.8 22.374 67.0 249.7 22.697 117.0 249.9 23.362 168.0 249.2 29.142 197.0 249.9 29.992 226.0 250.0 30.120 18.0 247.3 22.445 68.0 249.7 22.700 118.0 249.9 23.404 169.0 249.2 29.194 198.0 249.9 30.007 227.0 250.0 30.120 19.0 247.6 22.498 69.0 249.7 22.702 119.0 249.8 23.443 170.0 249.3 29.245 199.0 249.9 30.013 228.0 250.0 30.120 20.0 248.1 22.540 70.0 249.8 22.704.120.0 249.8 23.484 171.0 249.3 29.296 200.0 249.9 30.021 229.0 250.0 30.120 21.0 248.2 22.573 71.0 249.8 22.709 121.0 249.8 23.523 172.0 249.3 29.344 201.0 249.9 30.030 230.0 250.0 30.120 22.0 248.5 22.598 72.0 249.8 22.711 122.0 249.9 23.569 173.0 249.4 29.389 202.0 249.9 30.038 231.0 250.0 30.124 23.0 248.7 22.620 73.0 249.8 22.711 123.0 249.8 23.613 174.0 249.3 29.437 203.0 249.9 30.044 232.0 250.0 30.124 24.0 248.9 22.633 74.0 249.9 22.713 124.0 249.9 23.657 175.0 249.3 29.472 204.0 249.9 30.051 233.0 250.0 30.124 25.0 248.8 22.647 75.0 249.8 22.711 125.0 249.8 23.707 176.0 249.3 29.513 205.0 250.0 30.057 234.0 250.0 30.124 26.0 249.2 22.660 76.0 249.9 22.716 126.0 249.9 23.755 177.0 249.3 29.551 206.0 250.0 30.063 235.0 250.0 30.124 27.0 249.2 22.667 77.0 249.9 22.717 127.0 249.8 23.806 178.0 249.3 29.588 207.0 250.0 30.068 28.0 249.5 22.673 78.0 249.9 22.719 128.0 249.9 23.853 29.0 249.2 22.677 79.0 249.9 22.721 129.0 249.8 23.909 30.0 249.4 22.682 80.0 250.0 22.725 130.0 249.9 23.950 31.0 249.3 22.688 81.0 249.9 22.729 131.0 249.8 24.006 32.0 249.6 22.689 82.0 249.9 22.732 132.0 249.8 24.056 33.0 249.4 22.693 83.0 249.9 22.738 133.0 249.8 24.113 34.0 249.6 22.697 84.0 250.0 22.743 134.0 249.8 24.168 35.0 249.4 22.697 85.0 249.9 22.750 135.0 249.8 24.223 36.0 249.6 22.698 86.0 250.0 22.754 136.0 249.8 24.281 37.0 249.4 22.698 87.0 249.9 22.759 137.0 249.8 24.340 38.0 249.6 22.697 88.0 250.0 22.768 138.0 249.8 24.400 39.0 249.4 22.697 89.0 249.9 22.776 139.0 249.8 24.457 40.0 249.7 22.697 90.0 250.0 22.787 140.0 249.8 24.511 41.0 249.4 22.698 91.0 249.9 22.792 141.0 249.8 24.577 42.0 249.7 22.698 92.0 250.0 22.800 142.0 249.8 24.637 43.0 249.5 22.698 93.0 249.9 22.813 143.0 249.8 24.699 44.0 249.7 22.698 94.0 200.0 22.823 144.0 249.8 24.760 45.0 249.6 22.699 95.0 249.9 22.835 145.0 249.8 24.826 46.0 249.7 22.699 96.0 250.0 22.847 146.0 249.8 24.890 47.0 249.0 22.699 97.0 249.9 22.863 147.0 249.8 24.954 48.0 249.8 22.700 98.0 250.0 22.874 148.0 249.8 25.022 49.0 249.6 22.700 99.0 249.9 22.892 149.0 249.8 25.088

-505-OBSERVED EXPERIMENTAL DATA FROM RUN 32 (CONT'D) OBSERVED EXPERIMENTAL DATA FROM RUN 32 (CONT'D) TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CMm MIN OP cm RIN OF CM MIN OF CM MIN OF CM MIN op CM 150.0 249.8 25.157 200.0 249.3 28.744 250.0 249.8 30.628 300.0 249.8 30.999 306.0 249.7 31.006 312.0 249.6 31.009 151.0 249.7 25.225 201.0 249.3 28.797 251.0 249.7 30.643 301.0 249.7 31.000 307.0 249.6 31.008 313.0 249.E 31.009 152.0 249.8 25.295 202.0 249.3 28.862 252.0 249.7 30.657 302.0 249.8 31.000 308.0 249.8 31.008 314.0 249.T 31.010 153.0 249.7 25.364 203.0 249.3 28.922 253.0 249.7 30.675 303.0 249.6 31.000 309.0 249.6 31.008 315.0 249.6 31.011 154.0 249.7 25.435 204.0 249.3 28.978 254.0 249.7 30.689 304.0 249.8 31.002 310.0 249.7 31.008 316.0 249.6 31.013 155.0 249.7 25.509 205.0 249.3 29.030 255.0 249.7 30.705 305.0 249.6 31.004 311.0 249.6 31.008 317.0 249.4 31.014 156.0 249.7 25.576 206.0 249.4 29.085 256.0 249.7 30.720 157.0 249.6 25.649 207.0 249.3 29.133 257.0 249.7 30.732 158.0 249.6 25.720 208.0 249.4 29.193 258.0 249.7 30.749 159.0 249.6 25.793 209.0 249.4 29.248 259.0 249.5 30.760 160.0 249.6 25.868 210.0 249.5 29.296 260.0 249.7 30.774 161.0 249.6 25.940 211.0 249.4 29.348 261.0 249.6 30.786 162.0 249.6 26.014 212.0 249.5 29.398 262.0 249.7 30.796 163.0 249.5 26.090 213.0 249.4 29.449 263.0 249.6 30.807 164.0 249.5 26.164 214.0 249.5 29.497 264.0 249.5 30.817 165.0 249.5 26.238 215.0 249.3 29.541 265.0 249.6 30.826 166.0 249.5 26.313 216.0 249.5 29.587 266.0 249.6 30.834 167.0 249.6 26.387 217.0 249.4 29.632 267.0 249.5 30.847 168.0 249.6 26.467 218.0 249.5 29.673 268.0 249.6 30.853 169.0 249.7 26.545 219.0 249.4 29.717 269.0 249.6 30.862 170.0 249.6 26.617 220.0 249.5 29.759 270.0 249.7 30.872 171.0 249.7 26.693 221.0 249.5 29.807 271.0 249.5 30.881 172.0 249.7 26.770 222.0 249.6 29.847 272.0 249.7 30.887 173.0 249.6 26.843 223.0 249.6 29.885 273.0 249.6 30.896 174.0 249.7 26.916 224.0 249.7 29.924 274.0 249.6 30.904 175.0 249.7 26.994 225.0 249.7 29.963 275.0 249.6 30.910 176.0 249.7 27.073 226.0 249.8 30.000 276.0 249.7 30.916 177.0 249.7 27.150 227.0 249.8 30.035 277.0 249.6 30.919 178.0 249.6 27.226 228.0 249.8 30.069 27R.0 249.6 30.924 179.0 249.6 27.299 229.0 249.8 30.104 279.0 249.6 30.929 180.0 249.6 27.372 230.0 249.8 30.137 280.0 249.6 30.938 181.0 249.5 27.445 231.0 249.8 30.169 281.0 249.6 30.938 182.0 249.5 27.521 232.0 249.8 30.201 282.0 249.6 30.943 183.0 249.4 27.595 233.0 249.7 30.230 283.0 249.6 30.948 184.0 249.4 27.670 234.0 249.7 30.260 284.0 249.7 3C.950 185.0 249.4 27.738 235.0 249.8 30.291 285.0 249.6 30.954 186.0 249.4 27.811 236.0 249.8 30.319 286.0 249.7 30.958 187.0 249.3 27.884 237.0 249.8 30.343 287.0 249.6 30.961 188.0 249.3 27.952 238.0 249.8 30.369 288.0 249.7 30.968 189.0 249.4 28.020 239.0 249.8 30.395 289.0 249.6 30.970 190.0 249.4 28.090 240.0 249.8 30.419 290.0 249.8 30.973 191.0 249.4 28.160 241.0 249.8 30.442 291.0 249.6 30.975 192.0 249.4 28.228 242.0 249.8 30.468 292.0 249.7 30.977 193.0 249.3 28.296 243.0 249.8 30.490 293.0 249.6 30.981 194.0 249.3 28.360 244.0 249.8 30.509 294.0 249.7 30.984 195.0 249.3 28.427 245.0 249.8 30.532 295.0 249.6 30.958 196.0 249.4 28.490 246.0 249.8 30.556 296.0 249.8 30.990 197.0 249.3 28.553 247.0 249.8 30.568 297.0 249.7 30.991 198.0 249.3 28.615 248.0 249.8 30.590 298.0 249.7 30.993 199.0 249.3 28.680 249.0 249.8 30.608 299.0 249.7 30.998 OBSERVED EXPERIMENTAL DATA FROM RUN 33 OBSERVED EXPERIMENTAL DATA FROM RUN 33 (CONT'D) TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM.0 86.2 -. — 100.0 249.6 20.682 200.0 249.3 21.010 300.0 249.4 22.909 400.0 249.4 24.921 500.0 249.2 27.934 2.0 155.1 8.193 102.0 249.6 20.683 202.0 249.3 21.039 302.0 249.4 22.948 402.0 249.4 24.972 502.0 249.2 27.986 4.0 192.9 12.831 104.0 249.7 20.680 204.0 249.3 21.071 304.0 249.4 22.987 404.0 249.4 25.014 504.0 249.2 28.043 6.0 214.6 15.870 106.0 249.7 -20.679 206.0 249.3 21.103 306.0 249.4 23.018 406.0 249.4 25.061 506.0 249.2 28.097 8.0 228.2 17.768 108.0 249.7 20.679 208.0 249.3 21.139 308.0 249.4 23.058 408.0 249.4 25.111 508.0 249.2 28.146 10.0 236.2 18.919 110.0 249.7 20.680 210.0 249.3 21.174 310.0 249.4 23.095 410.0 249.4 25.151 510.0 249.2 28.193 12.0 240.2 19.610 112.0 249.6 20.680 212.0 249.3 21.213 312.0 249.4 23.134 412.0 249.4 25.199 512.0 249.2 28.239 14.0 244.2 20.016 114.0 249.6 20.681 214.0 249.3 21.252 314.0 249.4 23.163 414.0 249.4 25.253 514.0 249.2 28.281 16.0 246.1 20.268 116.0 249.6 20.679 216.0 249.3 21.288 316.0 249.4 23.207 416.0 249.4 25.304 516.0 249.2 28.321 20.0 247.9 20.518 120.0 249.6 20.670 220.0 249.3 21.372 318.0 249.4 23.242 418.0 249.4 25.349 518.0 249.2 28.358 18.0 247.2 20.420 118.0 249.7 20.675 218.0 249.3 21.331 320.0 249.4 23.278 420.0 249.4 25.398 520.0 249.2 28.388 22.0 248.4 20.583 122.0 2492.6 20.670 222.0 249.3 21.417 322.0 249.4 23.316 422.0 249.4 25.451 522.0 249.2 28.427 24.0 248.8 20.621 124.0 249.7 20.668 224.0 249.3 21.463 324.0 249.4 23.353 424.0 249.4 25.503 524.0 249.2 28.458 26.0 248.8 20.647 126.0 249.7 20.668 226.0 249.3 21.505 326.0 249.4 23.385 426.0 249.4 25.555 526.0 249.2 28.489 28.0 249.0 20.663 128.0 249.7 20.670 228.0 249.3 21.545 328.0 249.4 23.433 428.0 249.4 25.607 528.0 249.2 28.517 30.0 249.2 20.670 130.0 249.6 20.669 230.0 249.3 21.586 330.0 249.4 23.464 430.0 249.4 25.658 530.0 249.2 28.544 32.0 249.3 20.678 132.0 249.7 20.668 232.0 249.3 21.629- 332.0 249.4 23.506 432.0 249.4 25.713 532.0 249.2 28.571 34.0 249.3 20.680 134.0 249.6 20.665 234.0 249.3 21.666 334.0 249.4 23.540 434.0 249.4 25.770 534.0 249.2 28.595 36.0 249.3 20.686 136.0 249.6 20.665 236.0 249.3 21.720 336.0 249.4 23.579 436.0 249.4 25.821 536.0 249.2 28.616 38.0 249.3 20.686 138.0 249.6 20.667 238.0 249.3 21.762 338.0 249.4 23.617 438.0 249.4 25.881 538.0 249.2 28.637 40.0 249.5 20.687 140.0 249.6 20.670 240.0 249.3 21.803 340.0 249.4 23.654 440.0 249.4 25.932 540.0 249.2 28.658 42.0 249.6 20.686 142.0 249.6 20.667 242.0 249.3 21.843 342.0 249.4 23.698 442.0 249.4 25.988 542.0 249.2 28.685 44.0 249.6 20.688 144.0 249.6 20.672 244.0 249.3 21.883 344.0 249.4 23.740 444.0 249.4 26.048 544.0 249.2 28.701 46.0 249.6 20.689 146.0 249.6 20.669 246.0 249.3 21.926 346.0 249.4 23.778 446.0 249.4 26.103 546.0 249.2 28.723 48.0 249.7 20.689 148.0 249.6 20.670 248.0 249.3 21.965 348.0 249.4 23.821 448.0 249.4 26.163 548.0 249.2 28.742 50.0 249.7 20.688 150.0 249.5 20.673 250.0 249.3 22.003 350.0 249.4 23.857 450.0 249.3 26.221 550.0 249.2 28.763 52.0 249.8 20.689 152.0 249.5 20.671 252.0 249.3 22.048 352.0 249.4 23.898 452.0 249.2 26.283 552.0 249.2 28.779 54.0 249.8 20.689 154.0 249.5 20.673 254.0 249.3 22.082 354.0 249.4 23.937 454.0 249.1 26.339 554.0 249.2 28.796 56.0 249.8 20.688 156.0 249.5 20.672 256.0 249.3 22.125 356.0 249.4 23.974 456.0 249.1 26.397 556.0 249.2 28.809 58.0 249.8 20.688 158.0 249.4 20.672 258.0 249.3 22.165 358.0 249.4 24.015 458.0 249.1 26.464 558.0 249.2 28.824 60.0 249.8 20.686 160.0 249.4 20.673 260.0 249.3 22.197 360.0 249.4 24.059 460.0 249.1 26.524 560.0 249.2 28.833 62.0 249.8 20.687 162.0 249.4 20.677 262.0 249.3 22.236 362.0 249.4 24.099 462.0 249.1 26.590 562.0 249.2 28.842 64.0 249.8 20.683 164.0 249.4 20.679 264.0 249.3 22.270 364.0 249.4 24.143 464.0 249.1 26.656 564.0 249.2 28.853 66.0 249.8 20.684 166.0 249.4 20.688 266.0 249.4 22.306 366.0 249.4 24.186 466.0 249.1 26.722 566.0 249.2 28.863 68.0 249.8 20.684 168.0 249.3 20.696 268.0 249.4 22.341 368.0 249.4 24.224 468.0 249.1 26.792 568.0 249.2 28.869 70.0 249.8 20.684 170.0 249.3 20.709 270.0 249.4 22.377 370.0 249.4 24.264 470.0 249.1 26.863 570.0 249.2 28.880 72.0 249.8 20.686 172.0 249.3 20.718 272.0 249.4 22.412 372.0 249.4 24.306 472.0 249.1 26.933 572.0 249.2 28.884 74.0 249.8 20.687 174.0 249.3 20.733 274.0 249.4 22.451 374.0 249.4 24.347 474.0 249.1 27.004 574.0 Z749.2 28.891 76.0 249.8 20.684 176.0 249.3 20.747 276.0 249.4 22.483 376.0 249.4 24.389 476.0 249.1 27.083 576.0 249.2 28.898 78.0 249.8 20.683 178.0 249.3 20.757 278.0 249.4 22.514 378.0 249.4 24.429 478.0 249.1 27.163 578.0 249.2 28.901 80.0 249.8 20.684 180.0 249.3 20.778 280.0 249.4 22.549 380.0 249.4 24.472 480.0 249.1 27.239 580.0 249.2 28.908 82.0 249.8 20.683 182.0 249.3 20.792 282.0 249.4 22.585 382.0 249.4 24.513 482.0 249.1 27.315 582.0 249.2 28.909 84.0 249.7 20.681 184.0 249.3 20.813 284.0 249.4 22.624 384.0 249.4 24.555 484.0 249.1 27.394 584.0 249.2 28.910 86.0 249.8 20.682 186.0 249.3 20.829 286.0 249.4 22.658 386.0 249.4 24.604 486.0 249.1 27.469 586.0 249.2 28.914 88.0 249.7 20.683 188.0 249.3 20.854 288.0 249.4 22.690 388.0 249.4 24.648 488.0 249.1 27.542 588.0 249.2 28.917 90.0 249.7 20.682 190.0 249.3 20.825 290.0 249.4 22.729 390.0 249.4 24.692 490.0 249.5 27.609 590.0 249.2 28.919 92.0 249.7 20.680 192.0 249.3 20.899 292.0 249.4 22.767 392.0 249.4 24.738 492.0 249.1 27.681 592.0 249.2 28.920 94.0 249.6 20.682 194.0 249.3 20.925 294.0 249.4 22.801 394.0 249.4 24.783 494.0 249.1 27.746 594.0 249.2 28.921 96.0 249.6 20.681 196.0 249.3 20.949 296.0 249.4 22.839 396.0 249.4 24.832 496.0 249.1 27.809 596.0 249.2 28.921 98.0 249.5 20.683 198.0 249.3 20.978 298.0 249.4 22.873 398.0 249.4 24.878 498.0 249.1 22.872 598.0 249.2 28.922

-506OBSERVED EXPERIMENTAL DATA FROM RUN 33 (CONTOD) OBSERVED EXPERIMENTAL DATA FROM RUN 34 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN Op CM 600.0 249.2 28.921 610.0 249.2 28.926 620.0 249.2 28.927.0 85.0 -. — 50.0 249.5 17.150 100.0 249.3 19.379 602.0 249.2 2R.922 612.0 249.2 28.92R 622.0 249.2 28.927 1.0 122.0 -. — 51.0 249.5 17.153 101.0 249.3 19.480 604.0 249.2 28.922 614.0 249.2 28.930 624.0 249.2 28.924 2.0 151.3 4.488 52.0 249.5 17.157 102.0 249.3 19.580 606.0 249.2 28.923 616.0 249.2 28.930 3.0 173.3 6.938 53.0 249.5 17.164 103.0 249.2 19.687 608.0 249.2 28.925 618.0 249.2 28.929 4.0 190.2 8.981 54.0 249.5 17.169 104.0 249.2 19.789 5.0 203.9 10.656 55.0 249.5 17.178 105.0 249.0 19.894 6.0 213.0 12.012 56.0 249.5 17.188 106.0 249.0 20.003 7.0 220.9 13.096 57.0 249.5 17.194 107.0 249.0 20.112 8.0 226.8 13.959 58.0 249.5 17.206 108.0 249.0 20.223 9.0 231.7 14.638 59.0 249.5 17.219 109.0 249.0 20.329 10.0 235.2 15.178 60.0 249.5 17.232 110.0 249.0 20.439 11.0 238.0 15.593 61.0 249.5 17.249 111.0 249.0 20.550 12.0 240.5 15.923 62.0 249.5 17.260 112.0 249.0 20.659 13.0 242.1 16.179 63.0 249.5 17.279 113.0 248.9 20.774 14.0 243.8 16.379 64.0 249.5 17.299 114.0 248.9 20.881 15.0 244.8 16.534 65.0 e49.5 17.316 115.0 248.9 20.995 16.0 245.8 16.657 66.0 249.5 17.335 116.0 248.9 21.108 17.0 246.4 16.755 67.0 249.5 17.355 117.0 248.9 21.217 18.0 247.0 16.827 68.0 249.5 17.387 118.0 248.9 21.335 19.0 247.3 16.888 69.0 249.5 17.412 119.0 248.9 21.446 20.0 247.9 16.934 70.0 249.5 17.439 120.0 248.9 21.559 21.0 248.0 16.973 71.0 249.5 17.470 121.0 248.9 21.669 22.0 248.3 17.000 72.0 249.5 17.500 122.0 248.9 21.779 23.0 248.5 17.015 73.0 249.5 17.534 123.0 248.9 21.889 24.0 248.9 17.039 74.0 249.5 17.574 124.0 248.9 22.004 25.0 248.9 17.053 75.0 249.5 17.613 125.0 248.9 22.114 26.0 249.0 17.063 76.0 249.5 17.652 126.0 248.9 22.216 27.0 249.0 17.072 77.0 249.5 17.696 127.0 248.9 22.324 28.0 249.1 17.078 78.0 249.5 17.745 128.0 248.9 22.431 29.0 249.1 17.079 79.0 249.5 17.793 129.0 248.9 22.531 30.0 249.2 17.092 80.0 249.5 17.842 130.0 248.9 22.638 31.0 249.2 17.092 81.0 249.5 17.899 131.0 248.9 22.743 32.0 249.4 17.096 82.0 249.5 17.953 132.0 248.9 22.846 33.0 249.4 17.097 83.0 249.5 18.013 133.0 248.9 22.940 34.0 249.4 17.104 84.0 249.5 18.069 134.0 248.9 23.039 35.0 249.4 17.104 85.0 249.5 18.131 135.0 248.9 23.134 36.0 249.5 17.104 86.0 249.5 18.203 136.0 248.9 23.235 37.0 249.5 17.108 87.0 249.5 18.274 137.0 248.9 23.327 38.0 249.5 17.113 88.0 249.5 18.347 138.0 248.9 23.415 39.0 249.5 17.117 89.0 249.5 18.418 139.0 248.9 23.509 40.0 249.5 17.115 90.0 249.5 18.496 140.0 248.9 23.598 41.0 249.5 17.119 91.0 249.5 18.573 141.0 248.9 23.687 42.0 249.5 17.120 92.0 249.5 18.655 142.0 248.9 23.769 43.0 249.5 17.124 93.0 249.5 18.736 143.0 248.9 23.853 44.0 249.5 17.128 94.0 249.5 18.823 144.0 248.9 23.936 45.0 249.5 17.129 95.0 249.3 18.907 145.0 248.9 24.019 46.0 249.5 17.135 96.0 249.3 19.001 146.0 248.9 24.093 47.0 249.5 17.138 97.0 249.3 19.095 147.0 248.9 24.168 48.0 249.5 17.142 98.0 249.3 19.189 148.0 248.9 24.243 49.0 249.5 17.145 99.0 249.3 19.283 149.0 248.9 24.315 OBSERVED EXPERIMENTAL DATA FROM RUN 34 (CONTOD) OBSERVED EXPERIMENTAL DATA FROM RUN 35 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF I CM MIN OF CM MIN OF CM MIN OF CM MIN Op cM 150.0 248.9 24.385 184.0 249.0 25.635 218.0 249.5 25.791.0 77.0 —. —- 50.0 248.8 22.508 100.0 248.5 23.878 151.0 248.9 24.451 185.0 249.0 25.648 219.0 249.5 25.792 1.0 118.1 —. —- 51.0 248.8 22.514 101.0 248.5 23.942 152.0 248.9 24.517 186.0 249.0 25.657 220.0 249.5 25.794 2.0 149.0 11.900 52.0 248.9 22.514 102.0 248.5 24.006 153.0 248.9 24.578 187.0 249.0 25.672 221.0 249.5 25.791 3.0 171.0 14.031 53.0 248.9 22.516 103.0 248.5 24.071 154.0 248.9 24.641 188.0 249.2 25.677 222.0 249.5 25.795 4.0 188.0 15.777 54.0 248.9 22.525 104.0 248.5 24.139 155.0 248.9 24.695 189.0 249.2 25.688 223.0 249.5 25.792 5.0 201.0 17.192 55.0 248.9 22.529 105.0 248.5 24.206 156.0 248.9 24.753 190.0 249.2 25.693 224.0 249.5 25.795 6.0 210.5 18.324 56.0 248..9 22.538 106.0 248.5 24.274 157.0 248.9 24.812 191.0 249.2 25.703 225.0 249.5 25.798 7.0 218.9 19.225 57.0 248.9 22.544 107.0 248.5 24.348 158.0 248.9 24.860 192.0 249.2 25.710 226.0 249.5 25.794 8.0 225.5 19.926 58.0 248.9 22.552 108.0 248.5 24.418 159.0 248.9 24.912 193.0 249.2 25.718 227.0 249.5 25.796 9.0 230.0 20.482 59.0 248.9 22.558 109.0 248.5 24.492 160.0 248.9 24.963 194.0 249.2 25.720 228.0 249.5 25.796 10.0 234.0 20.921 60.0 248.9 22.573 110.0 248.5 24.565 161.0 248.9 25.009 195.0 249.2 25.728 229.0 249.5 25.795 11.0 236.5 21.255 61.0 248.9 22.575 111.0 248.5 24.640 162.0 248.9 25.052 196.0 249.2 25.734 230.0 249.5 25.791 12.0 239.2 21.520 62.0 248.9 22.587 112.0 248.5 24.718 163.0 248.9 25.095 197.0 249.2 25.741 231.0 249.5 25.795 13.0 240.8 21.725 63.0 248.9 22.600 113.0 248.5 24.793 164.0 248.9 25.136 198.0 249.2 25.743 232.0 249.5 25.796 14.0 242.5 21.888 64.0 248.9 22.611 114.0 248.5 24.875 165.0 248.9 25.179 199.0 249.2 25.750 233.0 249.5 25.798 15.0 243.4 22.009 65.0 248.9 22.623 115.0 248.5 24.950 166.0 248.9 25.216 200.0 249.2 25.750 234.0 249.5 25.794 16.0 244.6 22.108 66.0 248.9 22.638 116.0 248.5 25.032 167.0 248.9 25.250 201.0 249.2 25.754 235.0 249.5 25.799 17.0 245.1 22.180 67.0 248.9 22.647 117.0 248.5 25.116 168.0 248.9 25.286 202.0 249.2 25.762 236.0 249.5 25.796 18.0 246.0 22.246 68.0 248.8 22.668 118.0 248.5 25.196 169.0 248.9 25.320 203.0 249.2 25.764 237.0 249.5 25.800 19.0 246.2 22.289 69.0 248.8 22.681 119.0 248.5 25.280 170.0 248.9 25.351 204.0 249.3 25.766 238.0 249.5 25.799 20.0 246.8 22.327 70.0 248.8 22.696 120.0 248.5 25.362 171.0 248.9 25.383 205.0 249.3 25.769 239.0 249.5 25.798 21.0 247.0 22.355 71.0 248.8 22.715 121.0 248.4 25.445 112.0 249.0 25.404 206.0 249.3 25.772 240.0 249.5 25.798 22.0 247.2 22.376 72.0 248.8 22.733 122.0 248.4 25.536 173.0 249.0 25.432 207.0 249.3 25.773 241.0 249.5 25.797 23.0 247.5 22.393 73.0 248.8 22.754 123.0 248.4 25.613 174.0 249.0 25.459 208.0 249.3 25.777 242.0 249.5 25.799 24.0 247.7 22.410 74.0 248.8 22.775 124.0 248.4 25.700 175.0 249.0 25.480 209.0 249.4 25.776 243.0 249.5 25.799 25.0 247.8 22.416 75.0 248.8 22.800 125.0 248.3 25.780 176.0 249.0 25.503 210.0 249.4 25.778 244.0 249.5 25.797 26.0 248.0 22.429 76.0 248.8 22.823 126.0 248.3 25.872 177.0 249.0 25.524 211.0 249.4 25.782 245.0 249.5 25.800 27.0 247.8 22.442 77.0 248.8 22.849 127.0 248.3 25.956 178.0 249.0 25.543 212.0 249.4 25.783 246.0 249.5 25.800 28.0 248.0 22.446 78.0 248.8 22.876 128.0 248.3 26.045 179.0 249.0 25.558 213.0 249.4 25.786 247.0 249.5 25.800 29.0 248.0 22.455 79.0 248.8 22.907 129.0 248.3 26.129 180.0 249.0 25.574 214.0 249.4 25.786 248.0 249.5 25.797 30.0 248.1 22.462 80.0 248.8 22.936 130.0 248.3 26.217 181.0 249.0 25.589 215.0 249.4 25.786 249.0 249.5 25.798 31.0 248.0 22.463 81.0 248.8 22.969 131.0 248.3 26.301 182.0 249.0 25.608 216.0 249.4 25.787 250.0 249.5 25.800 32.0 248.1 22.471 82.0 248.8 23.003 132.0 248.3 26.391 183.0 249.0 25.619 217.0 249.5 25.789 33.0 248.2 22.469 83.0 248.8 23.039 133.0 248.2 26.480 34.0 248.3 22.475 84.0 248.8 23.075 134.0 248.2 26.562 35.0 248.3 22.479 85.0 248.8 23.113 135.0 248.2 26.652 36.0 248.5 22.483 86.0 248.8 23.154 136.0 248.2 26.738 37.0 248.5 22.483 87.0 248.8 23.197 137.0 248.1 26.822 38.0 248.5 22.487 88.0 248.8 23.240 138.0 248.1 26.911 39.0 248.5 22.485 89.0 248.7 23.284 139.0 248.1 26.991 40.0 248.5 22.485 90.0 248.7 23.328 140.0 248.0 27.079 41.0 248.5 22.490 91.0 248.7 23.374 141.0 248.0 27.170 42.0 248.6 22.490 92.0 248.7 23.425 142.0 248.0 27.253 43.0 248.6 22.490 93.0 248.7 23.478 143.0 248.0 27.339 44.0 248.7 22.492 94.0 248.7 23.529 144.0 248.0 27.424 40.0 248.7 22.492 95.0 240.6 23.584 145.0 248.0 27.511 46.0 248.7 22.499 96.0 248.6 23.640 146.0 248.0 27.593 47.0 240.7 22.502 97.0 240.6 23.700 147.0 248.0 27.681 48.0 248.8 22.004 98.0 240.6 23.759 148.0 248.0 27.763 49.0 248.8 22.506 99.0 248.6 23.815 149.0 248.0 27.849

-507OBSERVED EXPERIMENTAL DATA FROM RUN 35 (CONT'D) OBSERVEDEXPERIMENTAL DATA',FROM RUN 36 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN' F CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM 150.0 248.0 27.926 184.0 248.0 30.122 218.0 248.5 30.884.0 79.9 —. —- 32.0 245.3 30.612 64.0 248.9 35.054 151.0 248.0 28.013 185.0 248.0 30.164 219.0 248.5 30.893 1.0 118.3 —. —- 33.0 245.3 31.003 65.0 248.9 35.058 152.0 248.0 28.093 186.0 248.0 30.202 220.0 248.5 30.894 2.0 148.0 14.078 34.0 245.2 31.380 66.0 248.9 35.060 153.0 248.0 28.173 187.0 248.0 30.240 221.0 248.5 30.901 3.0 170.8 16.665 35.0 245.2 31.745 67.0 248.9 35.062 154.0 248.0 28.250 188.0 248.0 30.275 222.0 248.5 30.909 4.0 187.8 18.787 36.0 245.2 32.089 68.0 248.9 35.064 155.0 248.0 28.329 189.0 248.0 30.314 223.0 248.5 30.916 5.0 201.1 20.500 37.0 245.2 32.412 69.0 249.0 35.063 156.0 248.0 28.402 190.0 248.0 30.348 224.0 248.6 30.922 6.0 211.1 21.879 38.0 245.2 32.710 70.0 249.0 35.069 157.0 248.0 28.483 191.0 248.0 30.382 225.0 248.6 30.930 7.0 219.5 22.967 39.0 245.3 32.988 71.0 249.0 35.067 158.0 248.0 28.560 192.0 248.0 30.416 226.0 248.6 30.932 8.0 225.2 23.818 40.0 245.3 33.247 72.0 249.0 35.068 159.0 248.0 28.636 193.0 248.0 30.445 227.0 248.6 30.935 9.0 230.4 24.495 41.0 245.7 33.487 73.0 249.0 35.071 160.0 248.0 28.712 194.0 248.0 30.466 228.0 248.7 30.935 10.0 234.3 25.024 42.0 245.9 33.700 74.0 249.0 35.069 161.0 248.0 28.783 195.0 248.1 30.501 229.0 248.7 30.943 11.0 237.3 25.436 43.0 246.0 33.891 75.0 249.0 35.073 162.0 248.0 28.856 196.0 248.1 30.529 230.0 248.7 30.946 12.0 239.6 25.755 44.0 246.2 34.063 76.0 249.0 35.075 163.0 248.0 28.927 197.0 248.1 30.553 231.0 248.7 30.950 13.0 241.6 26.007 45.0 246.7 34.212 77.0 249.0 35.074 164.0 248.0 28.997 198.0 248.1 30.580 232.0 248.7 30.952 14.0 242.9 26.202 46.0 246.8 34.349 78.0 249.0 35.073 165.0 248.0 29.067 199.0 248.1 30.603 233.0 248.7 30.955 15.0 244.1 26.357 47.0 247.0 34.460 79.0 249.0 35.074 166.0 248.0 29.135 200.0 248.2 30.628 234.0 248.7 30.959 16.0 245.0 26.486 48.0 247.2 34.558 80.0 249.0 35.074 167.0 248.0 29.204 201.0 248.2 30.647 235.0 248.7 30.962 17.0 246.0 26.587 49.0 247.5 34.648 81.0 249.0 35.075 168.0 248.0 29.269 202.0 248.2 30.672 236.0 248.7 30.962 18.0 246.3 26.683 50.0 247.6 34.720 82.0 249.0 35.073 169.0 248.0 29.327 203.0 248.2 30.689 237.0 248.7 30.968 19.0 246.9 26.780 51.0 247.9 34,780 83.0 249.0 35.075 170.0 248.0 29.393 204.0 248.2 30.709 238.0 248.7 30.968 20.0 247.0 26.882 52.0 247.9 34.829 84.0 249,0 35.076 171.0 248.0 29.454 205.0 248.2 30.727 239.0 248.7 30.969 21.0 247.3 27.009 53.0 248.0 34.875 85.0 249.0 35.075 172.0 248.0 29.508 206.0 248.3 30.739 240.0 248.7 30.969 22.0 247.3 27.172 54.0 248.1 34.910 86.0 249.0 35.075 173.0 248.0 29.567 207.0 248.3 30.760 241.0 248.8 30.968 23.0 247.3 27.374 55.0 248.2 34.942 87.0 249.0 35.073 174.0 248.0 29.629 208.0 248.3 30.774 242.0 248.8 30.969 24.0 247.3 27.617 56.0 248.3 34.970 88.0 249.0 35.075 175.0 248.0 29.682 209.0 248.3 30.783 243.0 248.8 30.969 25.0 247.2 27.909 57.0 248.5 34.990 89.0 249.0 35.073 176.0 248.0 29.737 210.0 248.3 30.798 244.0 248.8 30.968 26.0 246.8 28.233 58.0 248.6 35.003 90.0 249.0 35.073 177.0 248.0 29.790 211.0 248.3 30.812 245.0 248.8 30.969 27.0 246.6 28.600 59.0 248.7 35.018 91.0 249.0 35.073 178.0 248.0 29.842 212.0 248.4 30.825 246.0 248.8 30.970 28.0 246.0 28.988 60.0 248.8 35.030 92.0 249.0 35.074 179.0 248.0 29.889 213.0 248.4 30.836 247.0 248.8 30.969 29.0 246.0 29.389 61.0 248.9 35.039 93.0 249.0 35.072 180.0 248.0 29.941 214.0 248.4 30.845 248.0 248.8 30.970 30.0 245.7 29.799 62.0 248.9 35.045 94.0 249.0 35.070 181.0 248.0 29.988 215.0 248.4 30.857 249.0 248.8 30.969 31.0 245.6 30.211 63.0 248.9 35.050 95.0 249.0 35.070 182.0 248.0 30.036 216.0 248.4 30.868 250.0 248.9 30.969 183.0 248.0 30.075 217.0 248.4 30.878 OBSERVED EXPERIMENTAL DATA FROM RUN 37 OBSERVED EX-PERIMENTAL DATA FROM RUN 38 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MN F CM MI N OF CM MIN OF CM MN OF CM MIN OF CM.0 80.0 -. — 17.5 238.5 23.701 35.0 248.0 25.986.0 77.3 -. — 47.0 239.0 22.588 94.0 239.7 28.293.5 106.9 -. —- 18.0 239.0 23.977 35.5 248.0 25.989 1.0 115.6 -. —- 48.0 239.0 22.780 95.0 239.7 28.318 1.0 125.2 -. — 18.5 239.5 24.227 36.0 248.1 25.990 2.0 143.7 8.784 49.0 239.0 22.964 96.0 239.7 28.346 1.5 142.1 7.15 5 19.0 240.0 24.457 36.5 248.1 25.990 3.0 165.0 11.092 50.0 238.9 23.156 97.0 239.7 28.374 2.0 155.5 8.586 19.5 240.5 24.665 37.0 248.1 25.994 4.0 181.4 12.972 51.0 238.9 23.347 98.0 239.8 28.399 2.5 167.1 9.819 20.0 241.0 24.850 37.5 248.1 25.994 5.0 194.1 14.500 52.0 238.9 23.537 99.0 239.8 28.414 3.0 177.0 10.889 20.5 241.6 25.010 38.0 248.1 25.995 6.0 203.8 15,739 53.0 238.9 23.727 100.0 239.8 28.434 3.5 185.3 11.827 21.0 242.1 25.157 38.5 248.1 25.994 7.0 211.3 16.725 54.0 238.9 23.917 101.0 239.8 28.449 4.0 193.0 12.656 21.5 242.7 25.283 39.0 248.1 25.997 8.0 217.4 17.505 55.0 238.9 24.104 102.0 239.8 28.462 4.5 199.0 13.391 22.0 243.2 25.386 39.5 248.1 26.000 9.0 222.1 18.123 56.0 238.8 24.296 103.0 239.8 28.480 5.0 205.1 14.044 22.5 243.7 25.478 40.0 248.1 26.000 10.0 225.8 18.610 57.0 238.8 24.476 104.0 239.9 28.485 5.5 209.9 14.636 23.0 244.0 25.558 40.5 248.1 26.000 11.0 228.6 18.997 58.0 238.7 24.653 105.0 239.9 28.500 6.0 214.1 15.042 23.5 244.6 25.622 41,0 248.1 26.00.3 12.0 231.1 19.293 59.0 238.7 24.832 106.0 239.9 28.511 6.5 218.1 15.691 24.0 245.025.677 41.5 248.1 26.002 13.0 233.0 19.525 60.0 238.7 25.000 107.0 239.9 28.519 7.0 221.4 15.987 24.5 245.5 25.722 42.0 248.1 26.002 14.0 234.5 19.715 61.0 238.7 25.177 108.0 239.9 28.526 7.5 224.7 16.335 25.0 245.8 25.761 42.5 248.1 26.003 15.0 235.6 19.860 62.0 238.7 25.341 109.0 239.9 28.535 8.0 227.2 16.651 25.5 246.0 25.793 43.0 248.1 26.004 16.0 236.5 19.973 63.0 238.7 25.505 110.0 239.9 28.541 8.5 229.3 16.959 26.0 246.2 25.818 43.5 248.1 26.004 17.0 237.1 20.059 64.0 238.7 25.667 111.0 239.9 28.553 9.0 231.2 17.265 26.5 246.6 25.840 44.0 248.1 26.006 18.0 237.8 20.129 65.0 238.7 25.817 112.0 239.9 28.553 9.5 232.6 17.594 27.0 246.8 25.863 44.5 248.1 26.006 19.0 238.3 20.191 66.0 238.7 25.966 113.0 239.9 28.559 10.0 233.3 17.954 27.5 247.0 25.880 45.0 248.1 26.007 20.0 238.5 20.231 67.0 238.7 26.108 114.0 239.9 28.565 10.5 234.1 18.341 28.0 247.1 25.890 45.5 248.1 26.006 21.0 238.9 20.270 68.0 238.7 26.250 115.0 239.9 28.563 11.0234.5 18.746 28.5 247.2 25.904 46.0 248.1 26.005 22.0 239.0 20.300 69.0 238.726.387 116.0 239.9 28.570 11.5 234.9 19.157 29.0 247.3 25.915 46.5 248.1 26.004 23.0 239.3 20.322 70.0 238.8 26.517 117.0 239.9 28.570 12.0 235.1 19.573 29.5 247.4 25.928 47.0 248.1 26.006 24.0 239.4 20.348 71.0 238.8 26.638 118.0 239.9 28.575 12.5 235.2 19.993 30.0, 247.6 25.937 47.5 248.1 26.005 25.0 239.5 20.373 72.0 238.8 26.762 119.0 239.9 28.577 13.0 235.7 20.415 30.5 247,7 25.945 48.0 248.1 26.006 26.0 239.7 20.400 73.0 238.8 26.877 120.0 239.9 28.578 13.5 236.0 20.833 31.0 247.8 25.952 48.5 248.1 26.005 27.0 239.8 20.423 74.0 238.8 26.991 121.0 239.9 28.581 14.0 236.2 21.240 31.5 247.8 25.961 49.0 248.1 26.004 28.0 239.8 20.451 75.0 238.9 27.098 122.0 239.9 28.580 14.5 236.5 21.642 32.0 247.9 25.965 49.5 248.1 26.006 29.0 239.8 20.490 76.0 238.9 27.199 123.0 239.9 28.583 15.0 236.8 22.026 32.5 247.9 25.967 50.0 248.1 26.005 30.0 239.9 20.526 77.0 238.9 27.289 124.0 239.8 28.585 15.5 237.1 22.397 33.0 248.0 25.973 50.5 248.1 26.005 31.0 239.9 20.577 78.0 238.9 27.378 125.0 239.8 28.584 16.0 237.6 22.753 33.5 248.0 25.974 51.0 248.1 26.005 32.0 239.9 20.632 79.0 239.0 27.469 126.0 239.8 28.588 16.5 237.8 23.090 34.0 248.0 25.980 33.0 239.9 20.694 80.0 239.0 27.548 127.0 239.8 28.588 LT.0 238.2 23.407 34,5 248.0 25.984 34.0 239,9 20.769 81.0 239.0 27.628 128.0 239.8 28.588 35.0 239.9 20.849 82.0 239.0 27.700 129.0 239.8 28.589 36.0 239.9 20.946 83.0 239.1 27.770 130.0 239.8 28.583 37.0 239.9 21.051 84.0 239.2 27.835 131.0 239.8 28.588 38.0 239.9 21.165 85.0 239.2 27.900 132.0 239.8 28.586 39.0 239.8 21.292 86.0 239.2 27.952 133.0 239.8 28.585 40.0 239.7 21.429 87.0 239.2 28.006 134.0 239.8 28.583 41.0 239.6 21.563 88.0 239.3 28.055 135.0 239.8 28.584 42.0 239.5 21.726 89.0 239.4 28.104 136.0 239.8 28.585 43.0 239.4 21.890 90.0 239.5 28.142 137.0 239.8 28.589 44.0 239.2 22.055 91.0 239.5 28.188 138.0 239.8 28.580 45.0 239.1 22.227 92.0 239.5 28.224 139.0 239.8 28.585 46.0 239.1 22.407 93.0 239.6 28.258 140.0 239.9 28.585

-508OBSERVED EXPERIMENTAL DATA FROM RUN 39 OBSERVED EXPERIMENTAL DATA FROM RUN 40 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OP CM MIN OF CM MIN OF CM.0 75.0 —. —- 43.0 237.5 27.641 86.0 240.3 30.355.0 75.5 -. —-- 21.5 235.7 28.158 43.0 239.5 33.099 1.0 114.2 —. —- 44.0 237.5 27.868R 87.0 240.3 30.354.5 96.3 ------ 22.0 235.7 28.376 43.5 239.8 33.111 2.0 143.2 10.948 45.0 237.5 28.088 88.0 240.3 30.358 1.0 118.5 ------ 22.5 235.7 28.593 44.0 239.8 33.125 3.0 165.0 13.323 46.0 237.6 28.291 89.0 240.3 30.360 1.5 137.7 14.718 23.0 235.7 28.809 44.5 239.8 33.134 4.0 181.7 15.239 47.0 237.6 28.483 90.0 240.4 30.360 2.0 150.0 15.887 23.5 235.7 29.026 45.0 239.8 33.148 5.0 194.4 16.768 48.0 237.7 28.667 91.0 240.4 30.363 2.5 1,60.0 16.945 24.0 235.7 29.237 45.5 239.9 33.152 6.0 204.2 17.982 49.0 237.8 28.834 92.0 240.5 30.363 3.0 169.4 17.915 24.5 235.7 29.442 46.0 240.0 33.159 7.0 211.8 18.950 50.0 238.0 28.992 93.0 240.5 30.359 3.5 177.9 18.768 25.0 235.7 29.646 46.5 240.0 33.169 8.0 217.8 19.713 51.0 238.0 29.140 94.0 240.5 30.362 4.0 185.0 19.550 25.5 235.7 29.846 47.0 240.0 33.174 9.0 222.3 20.316 52.0 238.1 29.275 95.0 240.5 30.363 4.5 191.1 20.242 26.0 235.7 30.040 47.5 240.1 33.178 10.0 226.1 20.788 53.0 238.2 29.398 96.0 240.5 30.363 5.0 196.7 20.865 26.5 235.7 30.226 48.0 240.1 33.183 11.0 229.0 21.157 54.0 238.4 29.509 97.0 240.5 30.359 5.5 201.7 21.417 27.0 235.7 30.413 48.5 240.1 33.188 12.0 231.4 21.446 55.0 238.5 29.610 98.0 240.5 30.362 6.0 206.1 21.919 27.5 235.7 30.585 49.0 240.1 33.188 13.0 233.1 21.674 56.0 238.5 29.701 99.0 240.5 30.362 6.5 209.9 22.360 28.0 235.7 30.761 49.5 240.1 33.194 14.0 234.6 21.847 57.0 238.7 29.785 100.0 240.5 30.370 7.0 213.3 22.754 28.5 235.7 30.925 50.0 240.2 33.194 15.0 235.7 21.990 58.0 238.9 29.863 101.0 240.5 30.372 7.5 216.2 23.100 29.0 235.7 31.087 50.5 240.2 33.196 16.0 236.6 22.100 59.0 239.0 29.927 102.0 240.5 30.375 8.0 219.0 23.411 29.5 235.8 31.238 51.0 240.2 33.200 17.0 237.3 22.195 60.0 239.1 29.984 103.0 240.5 30.379 8.5 221.3 23.687 30.0 236.0 31.383 51.5 240.3 33.200 18.0 237.8 22.274 61.0 239.2 30.036 104.0 240.5 30.387 9.0 223.2 23.929 30.5 236.0 31.519 52.0 240.5 33.203 19.0 238.2 22.348 62.0 239.3 30.077 105.0 240.5 30.386 9.5 225.0 24.142 31.0 236.2 31.650 52.5 240.5 33.206 20.0 238.4 22.422 63.0 239.3 30.122 106.0 240.5 30.385. 10.0 227.0 24.337 31.5 236.4 31.765 53.0 240.5 33.205 21.0 238.7 22.503 64.0 239.5 30.154 107.0 240.5 30.385 10.5 228.5 24.509 32.0 236.7 31.894 53.5 240.5 33.208 22.0 238.9 22.590 65.0 239.6 30.184 108.0 240.5 30.389 11.0 229.6 24.661 32.5 236.7 32.005 54.0 240.5 33.211 23.0 239.0 22.698 66.0 239.7 30.209 109.0 240.5 30.395 11.5 230.7 24.800 33.0 236.7 32.110 54.5 240.5 33.209 24.0 239.0 22.827 67.0 239.7 30.234 110.0 240.5 30.397 12.0 231.8 24.923 33.5 236.9 32.208 55.0 240.5 33.210 25.0 239.0 22.972 68.0 239.8 30.249 111.0 240.5 30.395 12.5 232.4 25.039 34.0 237.1 32.299 55.5 240.5 33.212 26.0 239.0 23.148 69.0 239.9 30.267 112.0 240.5 30.398 13.0 233.3 25.161 34.5 237.2 32.386 56.0 240.5 33.216 27.0 239.0 23.346 70.0 240.0 30.282 113.0 240.5 30.397 13.5 234.1 25.275 35.0 237.5 32.464 56.5 240.5 33.213 28.0 239.0 23.558 71.0 240.0 30.294 114.0 240.5 30.397 14.0 234.7 25.397 35.5 237.7 32.537 57.0 240.5 33.214 29.0 238.7 23.788 72.0 240.0 30.305 115.0 240.5 30.394 14.5 235.0 25.520 36.0 238.0 32.603 57.5 240.5 33.216 30.0 238.7 24.046 73.0 240.0 30.313 116.0 240.5 30.399 15.0 235.2 25.659 36.5 238.1 32.666 58.0 240.6 33.215 31.0 238.5 24.322 74.0 240.0 30.319 117.0 240.6 30.400 15.5 235.3 25.800 37.0 238.1 32.721 58.5 240.6 33.213 32.0 238.2 24.600 75.0 240.0 30.327 118.0 240.7 30.400 16.0 235.7 25.960 37.5 238.3 32.772 59.0 240.6 33.215 33.0 238.0 24.888 76.0 240.1 30.332 119.0 240.7 30.401 16.5 235.7 26.126 38.0 238.6 32.822 59.5 240.6 33.218 34.0 238.0 25.179 77.0 240.1 30.337 120.0 240.8 30.402 17.0 235.7 26.308 38.5 238.7 32.863 60.0 240.6 33.215 35.0 237.9 25.473 78.0 240.1 30.334 121.0 240.8 30.403 17.5 235.8 26.490 39.0 238.7 32.904 60.5 240.6 33.217 36.0 237.8 25.773 79.0 240.1 30.340 122.0 240.8 30.401 18.0 235.9 26.681 39.5 238.9 32.938 61.0 240.7 33.218 37.0 237.7 26.054 80.0 240.1 30.343 123.0 240.8 30.401 18.5 235.8 26.878 40.0 239.1 32.970 61.5 240.7 33.216 38.0 237.6 26.341 81.0 240.1 30.345 124.0 240.8 30.404 19.0 235.7 27.077 40.5 239.1 32.998 62.0 240.7 33.219 39.0 237.5 26.617 82.0 240.1 30.345 125.0 240.8 30.402 19.5 235.7 27.293 41.0 239.2 33.023 62.5 240.7 33.218 40.0 237.5 26.888 83.0 240.2 30.348.126.0 240.8 30.403 20.0 235.7 27.506 41.5 239.3 33.042 63.0 240.7 33.219 41.0 237.5 27.151 84.0 240.2 30.349 127.0 240.8 30.403 2?. 235.7?t.Q(u 4. 239. 33.067 42.0 237.5 27.400 85.0 240.2 30.355 128.0 240.8 30.403 21.3 233.7 27.941 42.5 233.5 33.084 OBSERVED EXPERIMENTAL DATA FROM RUN 41 OBSERVED EXPERIMENTAL DATA FROM RUN 42 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OP CM MIN OF CM MIN OP CM.0 83.1 -. — 21.5 229.8 22.838 43.0 234.4 26.621.078.0 ------ 500.0 239.4 20.970 1000.0 239.7 25.517.5 101.3 -. — 22.0 230.0 23.026 43.5 234.3 26.633 10.0 226.2 15.991 510.0 239.4 21.139 1010.0 239.7 25.533 1.0 118.3 7.528 22.5 230.0 23.205 44.0 234.4 26.648 20.0 237.6 17.814 520.0 239.3 21.305 1020.0 239.7 25.550 1.5 132.8 8.987 23.0 230.1 23.387 44.5 234.5 26.659 30.0 239.0 18.0164 530.0 239.3 21.484 1030.0 239.6 25.565 2.0 145.2 10.274 23.5 230.1 23.556 45.0 234.7 26.666 40.0 239.6 18.056 540.0 239.3 21.654 1040.0 239.6 25.579 2.5 156.0 11.388 24.0 230.2 23.728 45.5 234.7 26.680 50.0 239.7 18.072 550.0 239.3 21.823 1050.0 239.6 25.593 3.0 165.4 12.354 24.5 230.3 23.893 46.0 234.9 26.680 60.0 239.8 18.0764 560.0 239.3 21.996 1060.0 239.7 25.613 3.5 173.4 13.200 25.0 230.6 24.055 46.5 234.9 26.689 70.0 239.7 18.069 570.0 239.3 22.167 1070.0 239.7 25.629 4.0 180.9 13.955 25.5 230.7 24.203 47.0 235.0 26.694 80.0 239.6 18.070 580.0 239.3 22.332 1080.0 239.7 25.640 4.5 187.0 14.616 26.0 230.8 24.354 47.5 235.0 26.700 90.0 239.6 18.078 590.0 239.3 22.497 1090.0 239.7 25.658 5.0 192.5 15.207 26.5 231.0 24.497 48.0 235.1 26.706 100.0 239.6 18.073 600.0 239.3 22.659 1100.0 239.6 25.469 5.5 197.3 15.734 27.0 231.0 24.638 48.5 235.2 26.709 110.0 239.7 18.075 610.0 239.3 22.824 1110.0 239.6 25.685 6.0 201.7 16.200 27.5 231.1 24.770 49.0 235.2 26.715 120.0 239.8 18.077 620.0 239.3 22.981 1120.0 239.6 25.696 6.5 205.2 16.607 28.0 231.2 24.893 49.5 235.1 26.718 130.0 239.8 18.079 630.0 239.4 23.134 1130.0 239.6 25.700 7.0 208.8 16.969 28.5 231.4 25.016 50.0 235.2 26.720 140.0 239.7 18.085 640.0 239.4 23.284 1140.0 239.7 25.716 7.5 211.6 17.297 29.0 231.5 25.134 50.5 235.2 26.724 150.0 239.7 18.090 650.0 239.4 23.422 1150.0 239.7 25.730 8.0 214.0 17.579 29.5 231.6 25.249 51.0 235.2 26.722 160.0 239.8 18.106 660.0 239.5 23.559 1160.0 239.7.25.739 8.5 216.6 17.832 30.0 231.9 25.354 51.5 235.2 26.728 170.0 239.8 18.110 670.0 239.5 23.695 1170.0 239.7 25.752 9.0 218.8 18.056 30.5 231.9 25.449 52.0 235.2 26.729 180.0 239.9 18.113 680.0 239.5 23.815 1180.0 239.7 25.768 9.5 220.2 18.259 31.0 232.0 25.548 52.5 235.2 26.731 190.0 239.9 18.123 690.0 239.6 23.940 1190.0 239.7 25.773 10.0 222.1 18.435 31.5 232.1 25.636 53.0 235.2 26.733 200.0 239.9 18.132 700.0 239.6 24.053 1200.0 239.8 25.790 10.5 223.3 18.601 32.0 232.2 25.721 53.5 235.2 26.733 210.0 239.8 18.143 710.0 239.6 24.169 1210.0 239.8 25.800 11.0 224.8 18.762 32.5 232.3 25.800 54.0 235.2 26.733 220.0 239.8 18.164 720.0 239.6 24.275 1220.0 239.8 25.821 11.5 225.4 18.910 33.0 232.4 25.875 54.5 235.2 26.734 230.0 239.8 18.182 730.0 239.6 24.370 1230.0 239.8 25.833 12.0 226.7 19.064 33.5 232.6 25.943 55.0 235.2 26.736 240.0 239.8 18.204 740.0 239.5 24.439 1240.0 239.8 25.840 12.5 227.1 19.227 34.0 232.8 26.001 55.5 235.2 26.738 250.0 239.8 18.229 750.0 239.4 24.537 1250.0 239.8 25.853 13.0 227.7 19.400 34.5 232.9 26.067 56.0 235.2 26.736 260.0 239.8 18.262 760.0 239.4 24.622 1260.0 239.7 25.869 13.5 227.9 19.583 35.0 233.0 26.120 56.5 235.2 26.738 270.0 239.8 18.295 770.0 239.4 24.700 1270.0 239.7 25.883 14.0 228.3 19.773 35.5 233.1 26.179 57.0 235.2 26.737 280.0 239.8 18.332 780.0 239.4 24.766 1280.0 239.7 25.894 14.5 228.4 19.978 36.0 233.2 26.224 57.5 235.1 26.739 290.0 239.8 18.386 790.0 239.4 24.828 1290.0 239.7 25.913 15.0 228.6 20.185 36.5 233.3 26.275 58.0 235.2 26.740 300.0 239.8 18.445 800.0 239.4 24.887 1300.0 239.7 25.928 15.5 228.6 20.390 37.0 233.5 26.315 58.5 235.2 26.738 310.0 239.8 18.510 810.0 239.5 24.943 1310.0 239.8 25.940 16.0 228.9 20.600 37.5 233.6 26.360 59.0 233.2 26.739 320.0 240.0 18.590 820.0 239.5 24.994 1320.0 239.9 25.958 16.5 229.0 20.811 38.0 233.7 26.396 59.5 235.1 26.739 330.0 240.0 18.673 830.0 239.5 25.045 1330.0 239.9 25.970 17.0 229.0 21.022 38.5 233.8 26.427 60.0 235.3 26.739 340.0 240.0 18.766 840.0 239.8 25.085 1340.0 240.0 25.982 17.5 229.1 21.233 39.0 233.9 26.456 60.5 235.2 26.738 350.0 240.0 18.866 850.0 239.8 25.126 1350.0 240.0 25.993 18.0 229.2 21.441 39.5 234.0 26.486 61.0 235.2 26.739 360.0 240.0 18.972 860.0 239.8 25.159 1360.0 240.0 26.006 18.5 229.3 21.651 40.0 234.1 26.509 61.5 235.2 26.739 370.0 240.0 19.085 870.0 239.7 25.198 1370.0 240.0 26.017 19.0 229.4 21.856 40.5 234.1 26.535 62.0 235.2 26.739 380.0 239.8 19.192 880.0 239.6 25.232 1380.0 240.0 26.035 19.5 229.5 22.058 41.0 234.2 26.553 62.5 235.2 26.739.390.0 239.8 19.311 890.0 239.6 25.262 1390.0 240.0 26.048 20.0 229.8 22.261 41.5 234.2 26.570 63.0 235.2 26.739 400.0 239.8 19.444 900.0 239.5 25.288 1400.0 240.0 26.063 20.5 229.8 22.455 42.0 234.4 26.590 410.0 239.8 19.577 910.0 239.5 25.317 1410.0 240.0 26.075 21.0 229.9 22.649 42.5 234.3 26.608 420.0 239.8 19.710 920.0 239.5 25.342 1420.0 240.0 26.087 430.0 239.8 19.856 930.0 239.5 25.3721430.0 240.0 26.102 440.0 239.8 20.011 940.0 239.4 25.3946 440.0 240.0 26.120 450.0 239.8 20.170 590.0 239.4 25.4201450.0 240.0 26.135 460.0 239.8 20.320 960.0 239.4 25.4411460.0 240.0 26.151 470.0 239.7 20.479 970.0 239.5 25.4591470.0 240.0 26.162 480.0 239.7 20.644 980.0 239.6 25.4821480.0 240.0 26.171 490.0 239.5 20.802 990.0 239.6 25.4971490.0 240.0 26.180

-509OBSERVED EXPERIMENTAL DATA FROM RUN 42 (CONTID) OBSERVED EXPERIMENTAL DATA FROM RUN 43 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM 1500.0 240.0 24.193 1580.0 240.0 26.264 1660.0 240.0 26.293.0 79.2 —. —- 50.0 239.7 26.270 100.0 239.3 28.459 1510.0 240.0 24.205 1590.0 240.0 26.269 1670.0 240.0 26.295 1.0 110.8 —. —- 51.0 239.7 26.282 101.0 239.3 28.531 1520.0 240.0 26.214 1600.0 239.9 26.275 1680.0 239.9 26.295 2.0 143.9 13.973 52.0 239.7 26.288 102.0 239.3 28.610 1530.0 240.0 2E.225 1610.0 239.9 26.276 1690.0 239.9 26.300 3.0 164.8 16.427 53.0 239.7 26.300 103.0 239.3 28.690 1540.0 240.0 24.234 1620.0 239.9 26.278 1700.0 239.9 26.296 4.0 181.3 18.434 54.0 239.7 26.312 104.0 239.3 28.771 1550.0 240.0 26.238 1630.0 240.0 26.283 1710.0 239.9 26.296 5.0 193.8 20.063 55.0 239.7 26.325 105.0 239.3 28.848 1560.0 240.0 26.242 1640.0 240.0 26.288 1720.0 240.0 26.294 6.0 203.4 21.370 56.0 239.7 26.339 106.0 239.3 28.927 1570.0 240.0 26.250 1650.0 240.0 26.290 7.0 211.1 22.407 57.0 239.7 26.350 107.0 239.3 29.010 8.0 217.2 23.229 58.0 239.7 26.367 108.0 239.3 29.093 9.0 222.0 23.870 59.0 239.7 26.384 109.0 239.3 29.169 10.0 225.4 24.372 60.0 239.7 26.407 110.0 239.3 29.246 11.0 228.3 24.768 61.0 239.6 26.424 111.0 239.3 29.331 12.0 230.5 25.076 62.0 239.6 26.443 112.0 239.3 29.410 13.0 232.6 25.318 63.0 239.5 26.463 113.0 239.2 29.488 14.0 234.1 25.503 64.0 239.5 26.490 114.0 239.2 29.564 15.0 235.1 25.650 65.0 239.5 26.518 115.0 239.2 29.648 16.0 236.0 25.768 66.0 239.5 26.545 116.0 239.2 29.732 17.0 236.7 25.857 67.0 239.5 26.575 117.0 239.2 29.810 18.0 237.4 25.926 68.0 239.5 26.604 118.0 239.2 29.890 19.0 237.7 25.980 69.0 239.5 26.639 119.0 239.2 29.968 20.0 238.2 26.020 70.0 239.5 26.670 120.0 239.2 30.048 21.0 238.5 26.056 71.0 239.5 26.706 121.0 239.2 30.128 22.0 238.6 26.085 72.0 239.5 26.744 122.0 239.2 30.203 23.0 238.8 26.108 73.0 239.5 26.785 123.0 239.2 30.279 24.0 239.0 26.122 74.0 239.5 26.828 124.0 239.2 30.357 25.0 239.1 26.139 75.0 239.5 26.864 125.0 239.2 30.432 26.0 239.2 26.150 76.0 239.5 26.910 126.0 239.3 30.506 27.0 239.3 26.162 77.0 239.5 26.957 127.0 239.3 30.578 28.0 239.4 26.170 78.0 239.5 27.002 128.0 239.3 30.645 29.0 239.4 26.179 79.0 239.5 27.058 129.0 239.3 30.718 30.0 239.5 26.186 80.0 239.5 27.110 130.0 239.3 30.787 31.0 239.5 26.189 81.0 239.5 27.165 131.0 239.3 30.861 32.0 239.7 26.195 82.0 239.5 27.222 132.0 239.3 30.934 33.0 239.7 26.196 83.0 239.5 27.278 133.0 239.4 31.003 34.0 239.7 26.203 84.0 239.5 27.340 134.0 239.4 31.073 35.0 239.7 26.205 85.0 239.5 27.400 135.0 239.4 31.135 36.0 2 39.7 26.209 86.0 239.5 27.465 136.0 239.4 31.204 37.0 239.7 26.209 87.0 239.5 27.525 137.0 239.4 31.269 38.0 239.7 26.215 88.0 239.5 27.593 138.0 239.4 31.339 39.0 239.7 26.220 89.0 239.5 27.658 139.0 239.4 31.409 40.0 239.7 26.220 90.0 239.5 27.730 140.0 239.4 31.469 41.0 239.7 26.220 91.0 239.5 27.800 141.0 239.4 31.530 42.0 239.7 26.226 92.0 239.5 27.867 142.0 239.4 31.598 43.0 239.7 26.228 93.0 239.5 27.936 143.0 239.4 31.655 44.0 239.7 26.233 94.0 239.5 28.005 144.0 239.4 31.717 45.0 239.7 26.239 95.0 239.4 28.080 145.0 239.4 31.776 46.0 239.7 26.244 96.0 239.4 28.150 146.0 239.4 31.837 47.0 239.7 26.247 97.0 239.4 28.228 147.0 239.4 31.900 48.0 239.7 26.257 98.0 239.4 28.303 148.0 239.4 31.954 49.0 239.7 26.262 99.0 239.3 28.381 149.0 239.4 32.008 OBSERVED EXPERIMENTAL DATA FROM RUN 43 (CONT'D) OBSERVED EXPERIMENTAL DATA FROM RUN 44 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF cm MIN OF cm MI\ OF CM MIN OP CM MIN OP CM MIN OP CM 150.0 239.4 32.063 200.0 239.3 33.808 250.0 239.0 34.224.0 77.0 —. —- 100.0 239.9 24.642 200.0 239.9 27.596 151.0 239.4 32.108 201.0 239.3 33.826 251.0 239.0 34.232 2.0 149.3 —. —- 102.0 239.9 24.662 202.0 239.9 27.679 152.0 239.4 32.164 202.0 239.3 33.843 252.0 239.0 34.233 4.0 185.2 17.617 104.0 239.9 24.684 204.0 239.9 27.760 153.0 239.4 32.224 203.0 239.3 33.858 253.0 239.0 34.235 6.0 206.2 20.426 106.0 239.8 24.704 206.0 239.9 27.846 154.0 239.4 32.276 204.0 239.3 33.874 254.0 239.0 34.235 8.0 219.0 22.176 108.0 239.9 24.727 208.0 239.9 27.926 155.0 239.4 32.331 205.0 2 39.3 33.891 255.0 239.0 34.235 10.0 226.6 23.233 110.0 239.8 24.756 210.0 239.9 28.009 156.0 239.4 32.385 206.0 239.3 33.902 256.0 239.0 34.238 12.0 231.5 23.845 112.0 239.9 24.783 212.0 239.9 28.091 157.0 239.3 32.432 207.0 239.3 33.915 257.0 239.0 34.239 14.0 234.5 24.207 114.0 239.9 24.815 214.0 239.9 28.179 158.0 239.3 32.484 208.0 239.3 33.932 258.0 239.0 34.241 16.0 236.4 24.414 116.0 239.9 24.850 216.0 239.9 28.256 159.0 239.3 32.530 209.0 2 39.2 33.945 259.0 239.0 34.244 18.0 237.5 24.526 118.0 239.9 24.884 218.0 239.8 28.341 160.0 239.3 32.580 210.0 2 39.2 33.957 260.0 23 9.0 34.245 20.0 238.2 24.585 120.0 239.9 24.920 220.0 239.8 28.426 161.0 239.3 32.622 211.0 239.2 33.971 261.0 239.0 34.247 22.0 238.6 24.605 122.0 239.9 24.959 222.0 239.8 28.505 162.0 239.3 32.667 212.0 239.2 33.981 262.0 239.0 34.250 24.0 239.0 24.620 124.0 239.9 25.002 224.0 239.8 28.592 163.0 239.3 32.710 213.0 239.2 33.997 263.0 239.0 34.253 26.0 239.2 24.616 126.0 239.9 25.045 226.0 239.8 28.673 164.0 239.3 32.756 214.0 239.2 34.006 264.0 239.0 34.255 28.0 239.4 24.605 128.0 239.9 25.089 228.0 239.8 28.754 165.0 239.3 32.802 215.0 239.2 34.017 265.0 239.0 34.260 30.0 239.5 24.594 130.0 239.9 25.136 230.0 239.8 28.834 166.0 239.3 32.843 216.0 239.2 34.026 266.0 239.0 34.259 32.0 239.5 24.584 132.0 239.9 25.185 232.0 239.8 28.917 167.0 239.3 32.885 217.0 239.2 34.036 267.0 239.0 34.261 34.0 239.5 24.570 134.0 239.9 25.233 234.0 239.8 28.996 168.0 239.3 32.924 218.0 239.2 34.048 268.0 239.0 34.263 36.0 239.7 24.557 136.0 239.9 25.281 236.0 239.8 29.076 169.0 239.3 32.964 219.0 239.2 34.053 269.0 239.0 34.266 35.0 239.7 24.548 138.0 239.9 25.337 238.0 239.8 29.157 170.0 239.3 32.997 220.0 239.2 34.062 270.0 239.0 34.263 40.0 239.7 24.538 140.0 239.9 25.393 240.0 239.8 29.236 171.0 239.3 33.038 221.0 239.2 34.074 271.0 239.0 34.265 42.0 239.7 24.524 142.0 239.9 25.452 242.0 239.7 29.315 172.0 239.3 33.073 222.0 239.2 34.080 272.0 239.0 34.266 44.0 239.7 24.518 144.0 239.9 25.511 244.0 239.7 29.383 173.0 239.3 33.114 223.0 239.2 34.088 273.0 239.0 34.270 46.0 239.7 24.508 146.0 239.9 25.569 246.0 239.7 29.462 174.0 239.3 33.153 224.0 239.2 34.096 274.0 239.0 34.270 48.0 239.9 24.502 148.0 239.9 25.632 248.0 239.7 29.539 175.0 239.3 33.190 225.0 239.2 34.104 275.0 239.0 34.273 50.0 239.9 24.494 150.0 239.9 25.694 250.0 239.7 29.614 176.0 239.3 33.224 226.0 239.2 34.111 276.0 239.0 34.277 52.0 240.0 24.490 152.0 239.9 25.755 252.0 239.6 29.691 177.0 239.3 33.263 227.0 239.2 34.119 277.0 239.0 34.279 54.0 240.0 24.484 154.0 239.9 25.823 254.0 239.6 29.768 178.0 239.3 33.293 228.0 239.2 34.126 278.0 239.0 34.279 56.0 240.0 24.480 156.0 239.9 25.890 256.0 239.5 29.841 179.0 239.3 33.319 229.0 239.2 34.133 279.0 239.0 34.281 58.0 239.9 24.477 158.0 239.9 25.959 258.0 239.5 29.912 180.0 239.3 33.348 230.0 239.2 34.139 280.0 239.0 34.278 60.0 239.9 24.474 160.0 239.9 26.026 260.0 239.5 29.989 181.0 239.3 33.380 231.0 239.2 34.144 281.0 239.0 34.279 62.0 239.9 24.472 162.0 239.9 26.100 262.0 239.5 30.059 182.0 239.3 33.410 232.0 239.2 34.151 282.0 239.0 34.279 64.0 239.9 24.474 164.0 239.9 26.173 264.0 239.6 30.132 183.0 239.3 33.439 233.0 239.2 34.153 283.0 239.0 34.282 66.0 239.9 24.472 166.0 239.9 26.246 266.0 239.6 30.203 184.0 239.3 33.467 234.0 239.2 34.162 284.0 239.1 34.282 68.0 239.9 24.472 168.0 239.9 26.323 268.0 239.6 30.274 185.0 239.3 33.495 235.0 239.2 34.164 285.0 239.1 34.285 70.0 239.9 24.475 170.0 239.9 26.395 270.0 239.6 30.341 186.0 239.3 33.517 236.0 239.2 34.170 286.0 239.1 34.285 72.0 239.9 24.482 172.0 239.9 26.470 272.0 239.6 30.403 187.0 239.3 33.544 237.0 239.2 34.174 287.0 239.1 34.285 74.0 239.9 24.488 174.0 239.9 26.546 274.0 239.6 30.470 188.0 239.3 33.569 238.0 239.2 34.179 288.0 239.2 34.285 76.0 239.8 24.492 176.0 239.9 26.625 276.0 239.5 30.533 189.0 239.3 33.591 239.0 239.2 34.182 289.0 239.2 34.287 78.0 239.8 24.500 178.0 239.9 26.703 278.0 239.5 30.600 190.0 239.3 33.614 240.0 239.2 34.190 290.0 239.2 34.285 80.0 239.9 24.506 180.0 239.9 26.778 280.0 239.5 30.659 191.0 239.3 33.635 241.0 239.2 34.193 291.0 239.2 34.287 82.0 239.9 24.515 182.0 239.9 26.858 282.0 239.5 30.719 192.0 239.3 33.657 242.0 239.2 34.200 292.0 239.2 34.286 84.0 239.9 24.524 184.0 239.9 26.938 284.0 239.5 30.780 193.0 239.3 33.678 243.0 239.0 34.208 293.0 239.2 34.289 86.0 239.9 24.535 186.0 239.9 27.019 286.0 239.5 30.839 194.0 239.3 33.694 244.0 239.0 34.208 294.0 239.3 34.291 88.0 239.9 24.548 188.0 239.9 27.103 288.0 239.5 30.895 195.0 239.3 33.716 245.0 239.0 34.213 295.0 239.3 34.289 90.0 239.9 24.560 190.0 239.9 27.184 290.0 239.5 30.950 196.0 239.3 33.735 246.0 239.0 34.213 296.0 239.3 34.289 92.0 239.8 24.573 192.0 239.9 27.269 292.0 239.5 31.003 197.0 239.3 33.754 247.0 239.0 34.217 297.0 239.3 34.293 94.0 239.9 24.584 194.0 239.9 27.347 294.0 239.5 31.063 198.0 239.3 33.770 248.0 239.0 34.217 298.0 239.3 34.288 96.0 239.9 24.603 196.0 239.9 27.432 296.0 239.5 31.114 199.0 239.3 33.793 249.0 239.0 34.224 299.0 239.3 34.290 98.0 239.9 24.625 198.0 239.9 27.515 298.0 239.4 31.167 300.0 239.7 34.291

-510OBSERVED EXPERIMENTAL DATA FROM RUN 44 (CONT'D)I OBSERVED EXPERIMENTAL DATA FROM RUN 45 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM. MI O cm IN OF CM MIN OF CM MIN OF CM MIN OF CM 300.0 239.3 31.219 368.0 239.3 32.366 436.0 239.5 32.642.0 83.0 -. —- 50.0 239.1 28.304 100.0 237.8 34.111 302.0 239.3 31.270 370.0 239.3 32.385 438.0 239.5 32.646 1.0 121.3 13.774 51.0 239.0 28.347 101.0 237.9 34.211 304.0 239.3 31.318 372.0 239.3 32.400 440.0 239.5 32.646 2.0 148.2 16.674 52.0 239.0 28.386 102.0 237.8 34.306 306.0 239.3 31.369 374.0 239.3 32.413 442.0 239..5 32.654 3.0 169.0 19.048 53.0 239.1 28.427 103.0 237.8 34.396 308.0 239.3 31.412 376.0 239.3 32.427 444.0 239.5 32.655 4.0 184.1 20.954 54.0 239.1 28.484 104.0 237.8 34.485 310.0 239.3 31.463 378.0 239.3 32.441 446.0 239.5 32.657 5.0 196.1 22.475 55.0 239.1 28.534 105.0 237.9 34.573 312.0 239.3 31.508 380.0 239.3 32.455 448.0 239.5 32.659 6.0 205.1 23.678 56.0 239.0 28.593 106.0 237.9 34.655 314.0 239.3 31.552 382.0 239.3 32.469 450.0 239.5 32,663 7.0 212.1 24.625 57.0 239.0 28.660 107.0 238.0 34.734 316.0 239.3 31.595 384.0 239.3 32.482 452.0 239.5 32.669 8.0 217.4 25.379 58.0 239.0 28.735 108.0 237.9 34.813 318.0 239.3 31.634 386.0'239.3 32.496 454.0 239.5 32.670 9.0 222.2 25.963 59.0 239.0 28.815 109.0 237.9 34.886 320.0 239.3 31.680 388.0 239.3 32.505 456.0 239.5 32.673 10.0 225.9 26.422 60.0 239.0 28.905 110.0 237.9 34.958 322.0 239.3 31.723 390.0 239.3 32.514 458.0 239.5 32.673 11.0 228.5 26.782 61.0 239.0 28.994 111.0 238.0 35.025 324.0 239.3 31.760 392.0 239.3 32.525 460.0 239.5 32.675 12.0 230.4 27.066 62.0 238.9 29.095 112.0 237.9 35.084 326.0 239.3 31.798 394.0 239.3 32.537 462.0 239.6 32.672 13.0 232.5 27.288 63.0 239.0 29.202 113.0 238.0 35.149 328.0 239.3 31.835 396.0 239.3 32.546 464.0 239.6 32.672 14.0 233.6 27.459 64.0 238.6 29.308 114.0 238.0 35.209 330.0 239.3 31.874 398.0 239.3 32.556 466.0 239.6 32.674 15.0 234.6 27.594 65.0 238.6 29.425 115.0 238.0 35.261 332.0 239.3 31.907 400.0 239.3 32.559 468.0 239.6 32.675 16.0 235.4 27.700 66.0 238.3 29.548 116.0 238.0 35.316 334.0 239.3 31.939 402.0 239.3 32.569 470.0 239.7 32.676 17.0 236.1 27.781 67.0 238.5 29.677 117.0 238.0 35.366 336.0 239.3 31.969 404.0 239.3 32.575 472.0 239.7 32.677 18.0 236.8 27.850 68.0 238.2 29.807 118.0 238.0 35.414 338.0 239.3 32.006 406.0 239.3 32.580 474.0 239.7 32.677 19.0 237.0 27.897 69.0 238.3 29.940 119.0 238.0 35.459 340.0 239.3 32.035 408.0 239.3 32.587 476.0 239.7 32.679 20.0 237.5 27.935 70.0 238.1 30.082 120.0 238.0 35.505 342.0 239.3 32.066 410.0 239.3 32.597 478.0 239.7 32.677 21.0 238.0 27.970 71.0 238.0 30.222 121.0 238.0 35.540 344.0 239.3 32.091 412.0 239.3 32.602 480.0 239.7 32.678 22.0 238.0 27.999 72.0 238.0 30.369 122.0 238.0 35.579 346.0 239.3 32.121 414.0 239.3 32.608 482.0 239.8 32.679 23.0 238.2 28.015 73.0 238.0 30.516 123.0 238.1 35.615 348.0 239.3 32.147 416.0 239.3 32.615 484.0 239.8 32.679 24.0 238.3 28.031 74.0 238.0 30.664 124.0 238.1 35.648 350.0 239.3 32.173 418.0 239.3 32.619 486.0 239.8 32.679 25.0 238.6 28.046 75.0 238.0 30.811 125.0 238.1 35.684 352.0 239.3 32.197 420.0 239.3 32.621 488.0 239.8 32.680 26.0 238.8 28.059 76.0 237.9 30.964 126.0 238.1 35.711 354.0 239.3 32.220 422.0 239.3 32.623 490,0 239.8 32.681 27.0 238.9 28.065 77.0 238.0 31.111 127.0 238.1 35.737 356.0 239.3 32.245 424.0 239.4 32.626 492.0 239.8 32.683 28.0 238.8 28.076 78.0 237.9 31.261 128.0 238.1 35.765 358.0 239.3 32.267 426.0 239.4 32.628 494.0 239.8 32.681 29.0 238.9 28.079 79.0 238.0 31.414 129.0 238.2 35.791 360.0 239.3 32.290 428.0 239.4 32.632 496.0 239.8 32.679 30.0 238.8 28.088 80.0 237.9 31.568 130.0 238.2 35.815 362.0 239.3 32.310 430.0 239.5 32.634 498.0 239.8 32.683 31.0 238.9 28.093 81.0 238.0 31.710 131.0 238.3 35.839 364.0 239.3 32.330 432.0 239.5 32.633 500.0 239.9 32.683 32.0 238.9 28.096 82.0 237.8 31.860 132.0 238.3 35.857 366.0 239.3 32.353 434.0 239.5 32.636 33.0 239.0 28.100 83.0 237.9 32.008 133.0 238.4 35.867 34.0 238.9 28.104 84.0 237.6 32.148 134.0 238.4 35.895 35.0 239.0 28.108 85.0 237.9 32.290 135.0 238.5 35.910 36.0 238.9 28.114 86.0 237.7 32.430 136.0 238.5 35.925 37.0 238.9 28.116 87.0 237.8 32.571 137.0 238.4 35.939 38.0 238.9 28.121 88.0 237.7 32.707 138.0 238.4 35.955 39.0 239.1 28.130 89.0 237.8 32.837 139.0 238.4 35.967 40.0 239.0 28.138 90.0 237.6 32.971 140.0 238.4 35.978 41.0 239.2 28.143 91.0 237.9 33.097 141.0 238.3 35.988 42.0 239.1 28.155 92.0 237.6 33.224 142.0 238.4 36.002 43.0 239.2 28.164 93.0 237.9 33.345 143.0 238.4 36.010 44.0239.1 28.178 94.0 237.9 33.462 144.0 238.4 36.016 45.0 239.2 28.195 95.0 237.6 33.581 145.0 238.5 36.025 46.0 239.2 28.213 96.0 237.6 33.689 146.0 238.4 36.032 47.0 239.2 28.234 97.0 237.8 33.800 147.0 238.4 36.038 48.0 239.1 28.258 98.0 237.8 33.908 148.0 238.4 36.044 49.0 239.1 28.283 99.0 237.8 34.008 149.0 238.5 36.048 OBSERVED EXPERIMENTAL DATA FROM RUN 45 (CONT'D) OBSERVED EXPERIMENTAL DATA FROMRUN 47 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN PF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM 150.0 238.4 36.050 160.0 238.5 36.075 170.0 238.8 36.082.089.5 -. —- 23.0 239.8 20.956 46.0 239.6 27.787 151.0 238.4 36.054 161.0 238.6 36.075 171.0 238.7 36.081 1.0 121.9 -. —- 24.0 239.6 21.256 47.0 240.0 27.873 152.0 238.5 36.058 162.0 238.6 36.075 172.0 238.8 36.081 2.0 152.8 9.883 25.0 239.5 21.594 48.0 240.0 27.948 153.0 238.5 36.060 163.0 238.7 36.079 173.0 238.8 36.082 3.0 172.1 11.974 26.0 239.1 21.959 49.0 240.1 28.009 154.0 238.5 36.062 164.0 238.6 36.080 174.0 238.8 36.083 4.0 187.6 13.674 27.0 238.9 22.344 50.0 240.5 28.060 155.0 238.5 36.066 165.0 238.8 36.078 175.0 238.8 36.082 5.0199.3 15.045 28.0 238.5 22.747 51.0 240.5 28.097 156.0 238.5 36.069 166.0 238.8 36.080 176.0 238.6 36.082 6.0 208.1 16.132 29.0 238.1 23.153 52.0 240.8 28.129 157.0 238.6 36.071 167.0 238.8 36.082 177.0 238,6 36.082 7.0 215.3 17.000 30.0 238.0 23.562 53.0 241.0 28.154 158.0 238.5 36.072 168.0 238.6 36.082 178.0 238.7 36.084 8.0221.0 17.672 31.0 238.0 23.968 54.0 241.0 28.174 159.0 238.5 36.075 169.0 238.8 36.082 9.0 225.1 18.209 32.0 238.0 24.365 55.0 241.1 28.192 10.0 228.5 18.625 33.0 238.0 24.748 56.0 241.0 28.211 11.0 231.2 18.952 34.0 237.8 25.112 57.0 241.2 28.219 12.0 233.2 19.204 35.0 237.8 25.463 58.0 241.2 28.228 13.0 234.9 19.403 36.0 237.8 25.786 59.0 241.2 28.228 14.0 236.1 19.562 37.0 237.8 26.093 60.0 241.2 28.230 15.0 237.3 19.688 38.0 237.9 26.369 61.0 241.3 28.238 16.0 238.0 19.800 39.0 237.9 26.622 62.0 241.3 28.232 17.0 238.8 19.901 40.0 238.0 26.854.63.0 241.4 28.236 18.0 239.0 20.014 41.0 238.1 27.067 64.0 241.4 28.234 19.0 239.4 20,138 42.0 238.3 27.253 65.0 241.4 28.238 20.0 239.6 20.286 43.0 238.8 27.413 66.0 241.4 28.240 21.0 239.6 20.473 44.0 239.0 27.559 22.0 239.7 20.693 45.0 239.3 27.681

-511OBSERVED EXPERIMENTAL DATA FROM RUN 48 OBSERVED EXPERIMENTAL DATA FROM RUN 49 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM PIN OF CM RIN 0F cm MIS OF cm HN OF CM.0 89.0 -. — 25.0 237.4 25.378 50.0 241.9 29.366.0 89.1 —. —- 29.0 241.0 28.576 58.0 239.9 35.377.5 104.8 -. — 25.5 237.3 25.611 50.5 241.9 29.366 1.0 127.8 —. —- 30.0 240.7 28.744 59.0 240.1 35.460 1.0 121.9 --- 26.0 237.3 25.843 51.10 241.9 29.369 2.0 153.5 17.4013 31.10 240(.5 28.944 60.0 240.2 35.531 1.5 136.6 9.741 26.5 237.1 26.066 51.5 242.0 29.373 3.0 173.6 19.656 32.0 240.0 29.168 61.0 240.4 35.593 2.0 149.0 11.071 27.0 237.1 26.284 52.0 242.0 29.373 4.0 188.2 21.456 33.0 239.9 29.421 62.0 240.4 35.647 2.5 161.6 12.240 27.5 237.1 26.494 52.5 242.0 29.376 5.0 200.0 22.983 34.0 239.5 29.694 63.0 240.8 35.685 3.0 170.0 13.223 28.0 237.1 26.697 53.0 242.0 29.378 6.0 208.6 24.012 35.0 239.4 29.989 64.0 240.8 35.732 3.5 178.5 14.205 28.5 237.1 26.890 53.5 242.0 29.377 7.0 215.9 24.900 36.0 239.0 30.300 65.0 241.0 35.762 4.0 186.0 15.030 29.0 237.1 27.072 54.0 242.0 29.378 8.0 221.1 25.602 37.0 238.9 30.606 66.0 241.0 35.788 4.5 187.1 15.767 29.5 237.2 27.258 54.5 242.0 29.378 9.0 225.5 26.149 38.0 238.5 30.927 67.0 241.0 35.813 5.0 198.0 16.419 30.0 237.3 27.423 55.0 242.0 29.381 10.0 228.7 26.565 39.0 238.5 31.245 68.0 241.0 35.830 5.5 203.1 17.002 30.5 237.3 27.585 55.5 242.0 29.383 11.0 231.6 26.897 40.0 238.4 31.569 69.0 241.1 35.846 6.0 207.4 17.519 31.0 237.5 27.737 56.0 242.0 29.383 12.0 233.5 27.153 41.0 238.4 31.883 70.0 241.2 35.855 6.5 212.0 17.975 31.5 237.7 27.880 56.5 242.0 29.386 13.0 235.3 27.350 42.0 238.1 32.191 71.0 241.4 35.865 7.0 214.8 18.379 32.0 238.0 28.014 57.0 242.0 29.382 14.0 236.5 27.501 43.0 238.1 32.495 72.0 241.5 35.875 7.5 217.7 18.739 32.5 238.0 28.143 57.5 242.0 29.387 15.0 237.8 27.619 44.0 238.0 32.785 73.0 241.6 35.880 8.0 220.4 19.056 33.0 238.1 28.267 58.0 242.0 29.388 16.0 238.3 27.716 45.0 238.0 33.069 74.0 241.6 35.888 8.5 222.8 19.343 33.5 238.3 28.370 58.5 242.0 29.388 17.0 239.1 27.784 46.0 238.0 33.329 75.0 241.6 35.888 9.0 225.1 19.589 34.0 238.7 28.475 59.0 242.0 29.390 18.0 239.4 27.842 47.0 238.2 33.584 76.0 241.6 35.890 9.5 227.0 19.808 34.5 238.8 28.570 59.5 242.0 29.390 19.0 240.0 27.885 48.0 238.2 33.819 77.0 241.6 35.891 10.0 228.9 20.000 35.0 238.9 28.658.60.0 242.0 29.390 20.0 240.1 27.925 49.0 238.5 34.042 78.0 241.6 35.894 10.5 230.0 20.178 35.5 239.1 28.736 60.5 242.0 29.389 21.0 240.6 27.965 50.0 238.6 34.249 79.0 241.6 35.895 11.0 231.4 20.329 36.0 239.5 28.811 61.0 242.0 29.390 22.0 240.6 28.003 51.0 238.9 34.436 80.0 241.6 35.897 11.5 232.9 20.465 36.5 239.5 28.875 61.5 242.0 29.390 23.0 240.9 28.043 52.0 238.9 34.614 81.0 241.7 35.898 12.0 233.8 20.585 37.0 239.7 28.935 62.0 242.0 29.391 24.0 240.9 28.095 53.0 239.1 34.776 82.0 241.7 35.899 12.5 234.5 20.698 37.52 39.9 28.989 62.5 242.0 29.391 25.0 241.0 28.151 54.0 239.1 34.922 83.0 241.8 35.898 13.0 235.2 20.793 38.0 240.0 29.036 63.0 242.0 29.394 26.0 241.0 28.226 55.0 239.5 35.060 84.0 241.8 35.898 13.5 236.0 20.887 38.5 240.2 29.080 63.5 242.0 29.395 27.0 241.0 28.318 56.0 239.6 35.176 85.0 241.8 35.896 14.0 236.9 20.974 39.0 240.3 29.115 64.0 242.0 29.395 28.0 241.0 28.434 57.0 239.9 35.284 86.0 241.8 35.896 14.5 237.1 21.068 39.5 240.5 29.147 64.5 242.0 29.395 15.0 237.8 21.160 40.0 240.8 29.181 65.0 242.0 29.396 15.5 238.1 21.264 40.5 240.9 29.206 65.5 242.0 29.398 16.0 238.5 21.379 41.0 240.9 29.233 66.0 242.0 29.398 16.5 238.5 21.512 41.5 241.0 29.249 66.5 242.0 29.400 17.0 238.5 21.664 42.0 241.1 29.267 67.0 242.0 29.400 17.5 238.5 21.827 42.5 241.1 29.280 67.5 242.0 29.400 18.0 238.6 22.014 43.0 241.2 29.287 68.0 242.1 29.400 18.5 238.6 22.212 43.5 241.4 29.307 68.5 242.1 29.400 19.0 238.6 22.425 44.0 241.5 29.314 69.0 242.1 29.400 19.5 238.6 22.653 44.5 241.5 29.323 69.5 242.1 29.400 20.0 238.6 22.887 45.0 241.5 29.329 70.0 242.1 29.400 20.5 238.5 23.125 45.5 241.5 29.336 70.5 242.1 29.400 21.0 238.4 23.374 46.0 241.5 29.338 71.0 242.1 29.401 21.5 238.2 23.627 46.5 241.5 29.348 71.5 242.1 29.402 22.0 238.0 23.876 47.0 241.6 29.350 72.0 242.1 29.403 22.5 237.8 24.132 47.5 241.7 29.353 72.5 242.1 29.402 23.0 237.7 24.389 48.0 241.9 29.359 73.0 242.1 29.404 23.5 237.7 24.638 48.5 241.9 29.362 73.5 242.1 29.402 24.0 237.7 24.885 49.0 241.9 29.361 74.0 242.1 29.402 24.5 237.4 25.124 49.5 241.9 29.365 74.5 242.1 29.402 75.0 242.1 29.403 OBSERVED EXPERIMENTAL DATA FROM RUN 50 OBSERVED EXPERIMENTAL DATA FROM RUN 51 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM.0 86.8 —. —- 42.0 240.9 25.081 84.0 240.5 31.906.0 82.2 —. —- 50.0 235.0 21.229 100.0 234.3 23.184 1.0 126.4 10.217 43.0 240.9 25.215 85.0 240.5 31.956 1.0 122.3 —. —- 51.0 235.0 21.240 101.0 234.3 23.272 2.0 153.1 13.105 44.0 240.7 25.383 86.0 240.5 32.001 2.0 148.0 10.515 52.0 235.0 21.241 102.0 234.3 23.361 3.0 173.0 15.413 45.0 240.7 25.559 87.0 240.8 32.045 3.0 168.1 12.719 53.0 235.0 21.242 103.0 234.2 23.449 4.0 187.8 17.262 46.0 240.5 25.736 88.0 240.8 32.096 4.0 181.8 14.486 54.0 235.0 21.252 104.0 234.1 23.538 5.0 198.9 18.740 47.0 240.1 25.930 89.0 240.9 32.118 5.0 193.2 15.918 55.0 235.0 21.259 105.0 234.0 23.628 6.0 207.6 19.923 48.0 240.0 26.139 90.0 240.9 32.151 6.0 202.0 17.063 56.0 235.0 21.263 106.0 234.0 23.717 7.0 214.8 20.857 49.0 240.0 26.350 91.0 240.9 32.179 7.0 209.1 17.965 57.0 235.0 21.266 107.0 234.0 23.807 8.0 220.4 21.595 50.0 240.0 26.569 92.0 241.0 32.205 8.0 214.5 18.678 58.0 235.0 21.277 108.0 234.0 23.903 9.0 224.9 22.170 51.0 240.0 26.796 93.0 241.0 32.229 9.0 218.6 19.235 59.0 235.0 21.286 109.0 234.0 23.992 10.0 228.0 22.620 52.0 239.9 27.027 94.0 241.0 32.248 10.0 222.0 19.669 60.0 235.0 21.296 110.0 234.0 24.090 11.0 230.7 22.972 53.0 239.9 27.252 95.0 241.0 32.269 11.0 224.9 20.009 61.0 235.0 21.306 111.0 234.0 24.180 12.0 232.8 23.246 54.0 239.8 27.488 96.0 241.0 32.284 12.0 226.7 20.269 62.0 235.0 21.317 112.0 234.0 24.276 13.0 234.7 23.461 55.0 239.8 27.713 97.0 241.0 32.296 13.0 228.4 20.479 63.0 235.0 21.326 113.0 234.0 24.369 14.0 235.9 23.628 56.0 239.7 27.938 98.0 241.0 32.310 14.0 229.7 20.638 64.0 235.0 21.342 114.0 234.0 24.467 15.0 237.0 23.758 57.0 239.7 28.168 99.0 241.0 32.324 15.0 230.8 20.763 65.0 235.0 21.360 115.0 234.0 24.560 16.0 237.8 23.860 58.0 239.7 28.394 100.0 241.0 32.335 16.0 231.6 20.862 66.0 235.0 21.373 116.0 234.0 24.654 17.0 238.5 23.943 59.0 239.6 28.608 101.0 241.0 32.340 17.0 232.1 20.935 67.0 235.0 21.394 117.0 234.0 24.745 18.0 238.9 24.003 60.0 239.5 28.819 102.0 241.0 32.352 18.0 232.8 20.999 68.0 235.0 21.414 118.0 234.0 24.843 19.0 239.3 24.053 61.0 239.5 29.025 103.0 241.0 32.363 19.0 233.1 21.046 69.0 235.0 21.439 119.0 234.0 24.933 20.0 239.6 24.088 62.0 239.5 29.229 104.0 241.0 32.366 20.0 233.5 21.079 70.0 235.0 21.458 120.0 234.0 25.025 21.0 240.0 24.120 63.0 239.5 29.427 105.0 241.2 32.375 21.0 233.9 21.110 71.0 235.0 21.484 121.0 234.0 25.118 22.0 240.1 24.144 64.0 239.5 29.614 106.0 241.2 32.380 22.0 234.0 21.131 72.0 235.0 21.511 122.0 234.0 25.209 23.0 240.2 24.165 65.0 239.5 29.800 107.0 241.3 32.385 23.0 234.1 21.150 73.0 235.0 21.539 123.0 233.9 25.302 24.0 240.3 24.185 66.0 239.5 29.973 108.0 241.3 32.390 24.0 234.3 21.164 74.0 235.0 21.569 124.0 233.9 25.392 25.0 240.5 24.198 67.0 239.5 30.141 109.0 241.4 32.392 25.0 234.5 21.176 75.0 235.0 21.604 125.0 233.9 25.484 26.0 240.5 24.212 68.0 239.5 30.300 110.0 241.4 32.400 26.0 234.6 21.185 76.0 235.0 21.641 126.0 233.9 25.569 27.0 240.6 24.230 69.0 239.5 30.454 111.0 241.5 32.400 27.0 234.7 21.193 77.0 235.0 21.680 127.0 233.9 25.656 28.0 240.7 24.244 70.0 239.5 30.584 112.0 241.5 32.405 28.0 234.8 21.198 78.0 235.0 21.718 128.0 233.9 25.742 29.0 240.7 24.259 71.0 239.6 30.733 113.0 241.5 32.405 29.0 234.9 21.203 79.0 235.0 21.765 129.0 233.9 25.831 30.0 240.8 24.279 72.0 239.6 30.860 114.0 241.5 32.408 30.0 234.9 21.206 80.0 235.0 21.808 130.0 233.9 25.915 31.0 240.9 24.300 73.0 239.7 30.979 115.0 241.5 32.407 31.0 234.9 21.208 81.0 234.9 21.857 131.0 233.9 26.000 32.0 240.9 24.326 74.0 239.8 31.100 116.0 241.5 32.411 32.0 234.9 21.208 82.0 234.8 21.909 132.0 233.9 26.086 33.0 240.9 24.355 75.0 239.9 31.210 117.0 241.5 32.411 33.0 234.9 21.211 83.0 234.7 21.960 133.0 233.9 26.169 34.0 240.9 24.396 76.0 239.9 31.312 118.0 241.5 32.414 34.0 234.9 21.214 84.0 234.7 22.019 134.0 233.9 26.254 35.0 240.9 24.442 77.0 239.9 31.404 119.0 241.5 32.415 35.0 234.9 21.215 85.0 234.6 22.076 135.0 233.9 26.334 36.0 240.9 24.496 78.0 240.0 31.494 120.0 241.5 32.414 36.0 235.0 21.215 86.0 234.6 22.139 136.0 233.9 26.414 37.0 240.9 24.564 79.0 240.1 31.573 121.0 241.5 32.418 37.0 235.0 21.216 87.0 234.6 22.200 137.0 233.9 26.496 38.0 240.9 24.628 80.0 240.1 31.650 122.0 241.5 32.419 38.0 235.0 21.219 88.0 234.6 22.266 138.0 233.9 26.572 39.0 240.9 24.730 81.0 240.2 31.723 123.0 241.5 32.418 39.0 235.0 21.217 89.0 234.5 22.336 139.0 233.9 26.650 40.0 240.9 24.824 82.0 240.2 31.787 124.0 241.5 32.417 40.0 235.0 21.219 90.0 234.5 22.407 140.0 233.9 26.729 41.0 240.9 24.950 83.0 240.4 31.847 125.0 241.5 32.420 41.0 235.0 21.219 91.0 234.5 22.470 141.0 233.9 26.801 42.0 235.0 21.219 92.0 234.5 22.548 142.0 233.9 26.874 43.0 235..0 21.220 93.0 234.5 22.620 143.0 233.9 26.950 44.0 235.0 21.219 94.0 234.5 22.697 144.0 233.9 27.020 45.0 235.0 21.222 95.0 234.5 22.777 145.0 233.9 27.088 46.0 235.0 21.225 96.0 234.5 22.856 146.0 233.9 27.157 47.0 235.0 21.230 97.0 234.4 22.934 147.0 233.9 27.223 48.0 235.0 21.229 98.0 234.4 23.019 148.0 233.9 27.2911 49.0 235.0 21.229 99.0 234.3 23.103 149.0 233.9 27.353

-512OBSERVED EXPERIMENTAL DATA FRUM RUN 51 (CUNTOD) OBSERVED EXPERIMENTAL DATA FROM RUN 52 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEI(GHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF cm MIN OF C iI5N OF CM MIN OF CM MIN OF CM 150.0 233.9 27.434 192.0 234.0 29.040 234.0 234.4 29.363.0 80.0 -. — 50.0 234.9 19.426 100.0 234.0 24.165 151.0 233.9 27.486 193.0 234.0 29.056 235.0 234.4 29.364 1.0 117.0 5.005 51.0 234.9 19.501 101.0 234.0 24.240 152.0 233.9 2T.544 194.0 234.0 29.074 236.0 234.4 29.367 2.0 143.6 7.712 52.0 234.9 19.580 102.0 234.0 24.313 153.0 233.9 2T.605 195.0 234.0 29.091 237.0 234.4 29.365 3.0 163.9 9.914 53.0 234.9 19.660 103.0 234.0 24.387 154.0 233.9 2 7.662 196.0 234.0 29.104 238.0 234.4 29.267 4.0 179.5 11.706 54.0 234.7 19.745 104.0 234.0 24.456 155.0 233.9 2.720 197.0 234.0 29.121 239.0 234.4 29.269 5.0 191.3 13.150 55.0 234.7 19.830 105.0 234.0 24.526 156.0 233.9 2 7.775 198.0 234.0 29.135 240.0 234.4 29.369 6.0 200.4 14.305 56.0 234.5 19.920 106.0 234.0 24.595 157.0 233.9 27.832 199.0 234.1 -29.152 241.0 234.4 29.373 7.0 207.6 15.228 57.0 234.5 20.010 107.0 234.0 24.663 158.0 233.9 27.885 200.0 234.1 29.162 242.0 234.4 29.373 8.0 213.2 15.958 58.0 234.5 20.104 108.0 234.0 24.728 159.0 233.9 27.938 201.0 234.1 29.175 243.0 234.4 29.378 9.0 217.8 16.527 59.0 234.5 20.197 109.0 234.0 24.796 160.0 233.9 27.991 202.0 234.1 29.188 244.0 234.4 29.379 10.0 221.3 16.978 60.0 234.5 20.293 110.0 234.0 24.859 161.0 233.9 28.040 203.0 234.2 29.199 245.0 234.5 29.379 11.0 224.1 17.325 61.0 234.5 20.390 111.0 234.0 24.918 162.0 233.9 28.090 204.0 234.2 29.211 246.0 234.5 29.378 12.0 226.1 17.600 62.0 234.5 20.482 112.0 234.0 24.979 163.0 233.9 28.138 205.0 234.2 29.217 247.0 234.5 29.380 13.0 228.0 17.818 63.0 234.5 20.589 113.0 234.0 25.036 164.0 233.9 28.184 206.0 234.2 29.228 248.0 234.5 29.383 14.0 229.4 17.9854 64.0 234.5 20.693 114.0 234.0 25.092 165.0 233.9 28.229 207.0 234.3 29.239 249.0 234.5 29.382 15.0 230.7 18.118 65.0 234.4 20.794 115.0 234.0 25.155 166.0 233.9 28.273 208.0 234.3 29.247 250.0 234.5 29.380 16.0 231.4 18.220 66.0 234.3 20.896 116.0 234.0 25.200 167.0 233.9 28.315 209.0 234.3 29.257 251.0 234.5 29.384 17.0 232.0 18.300 67.0 234.2 21.001 117.0 234.0 25.251 168.0 233.9 28.357 210.0 234.3 29.266 252.0 234.5 29.386 18.0 232.7 18.364 68.0 234.2 21.108 118.0 23 4-.0 25.301 169.0 233.9 28.399 211.0 234.3 29.273 253.0 234.5 29.387 19.0 233.1 18.415 69.0 234.2 21.211 119.0 234.0 25.358 170.0 233.9 28.436 212.0 234.3 29.279 254.0 234.5 29.384 20.0 233.5 18.454 70.0 234.2 21.317 120.0 234.0 25.402 171.0 233.9 28.477 213.0 234.3 29.285 255.0 234.5 29.386 21.0 233.9 18.483 71.0 234.2 21.421 121.0 234.0 25.450 172.0 233.9 28.504 214.0 234.3 29.294 254.0 234.5 29.382 22.0 234.0 18.510 72.0 234.1 21.526 122.0 234.0 25.495 173.0 233.9 28.548 215.0 234.4 29.302 257.0 234.5 29.384 23.0 234.1 18.530 73.0 234.1 21.630 123.0 234.0 25.542 174.0 233.9 28.583 216.0 234.4 29.309 258.0 234.5 29.382 24.0 234.2 18.550 74.0 234.1 21.739 124.0 234.0 25.587 175.0 233.9 28.614 217.0 234.4 29.313 259.0 234.5 29.382 25.0 234.4 18.563 75.0 234.0 21.840 125.0 234.0 25.627 176.0 233.9 28.644 218.0 234.4 29.317 260.0 234.5 29.387 26.0 234.5 18.578 76.0 234.0 21.943 126.0 234.0 25.663 177.0 233.9 28.677 219.0 234.4 29.318 261.0 234.5 29.386 27.0 234.7 18.590 77.0 234.0 22.049 127.0 234.0 25.703 178.0 233.9 28.712 220.0 234.4 29.322 262.0 234.5 29.386 28.0 234.8 18.601 78.0 234.0 22.149 128.0 234.0 25.741 179.0 233.9 28.740 221.0 234.4 29.328 263.0 234.5 29.383 29.0 234.9 18.613 79.0 234.0 22.253 129.0 234.0 25.777 180.0 233.9 28.769 222.0 234.4 29.330 264.0 234.5 29.386 30.0 234.9 18.630 80.0 234.0 22.354 130.0 234.0 25.819 181.0 233.9 28.796 223.0 234.4 29.332 265.0 234.5 29.384 31.0 234.9 18.642 81.0 234.0 22.458 131.0 234.0 25.857 182.0 233.9 28.820 224.0 234.4 29.337 266.0 234.5 29.384 32.0 234.9 18.660 82.0 234.0 22.557 132.0 234.0 25.891 183.0 234.0 28.846 225.0 234.4 29.340 267.0 234.5 29.382 33.0 234.9 18.680 83.0 234.0 22.657 133.0 234.0 25.923 184.0 234.0 28.870 226.0 234.4 29.343 268.0 234.5 29.383 34.0 234.9 18.701 84.0 234.0 22.757 134.0 234.0 25.952 185.0 234.0 28.895 227.0 234.4 29.346 269.0 234.5 29.383 35.0 234.9 18.724 85.0 234.0 22.849 135.0 234.0 25.982 186.0 234.0 28.917 228.0 234.4 29.349 270.0 234.5 29.385 36.0 234.9 18.747 86.0 234.0 22.949 136.0 234.0 26.015 187.0 234.0 28.940 229.0 234.4 29.348 271.0 234.5 29.386 37.0 234.9 18.775 87.0 234.0 23.044 137.0 234.1 26.042 188.0 234.0 28.960 230.0 234.4 29.357 272.0 234.5 29.385 38.0 234.9 18.807 88.0 234.0 23.137 138.0 234.1 26.071 189.0 234.0 28.981 231.0 234.4 29.258 273.0 234.5 29.384 39.0 234.9 18.840 89.0 234.0 23.231 139.0 234.1 26.096 190.0 234.0 29.003 232.0 234.4 29.358 274.0 234.5 29.386 40.0 234.9 18.865 90.0 234.0 23.321 140.0 234.1 26.122 191.0 234.0 29.020 233.0 234.4 29.360 275.0 235.0 29.385 41.0 234.9 18.915 91.0 234.0 23.415 141.0 234.3 26.148 42.0 234.9 18.957 92.0 234.0 23.503 142.0 234.3 26.176 43.0 234.9 19.004 93.0 234.0 23.589 143.0 234.3 26.202 44.0 234.9 19.050 94.0 234.0 23.675 144.0 234.3 26.226 45.0 234.9 19.106 95.0 234.0 23.760 145.0 234.3 26.248 46.0 234.9 19.164 96.0 234.0 23.847 146.0 234.4 26.269 47.0 234.9 19.223 97.0 234.0 23.929 147.0 234.4 26.289 48.0 234.9 19.287 98.0 234.0 24.006 148.0 234.4 26.310 49.0 234.9 19.357 99.0 234.0 24.084 149.0 234.4 26.329 OBSERVED EXPERIMENTAL DATA FROM RUN 52 (CONT'ID) OBSERVED EXPERIMENTAL DATA FROM RUN 53 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OP CM 150.0 234.4 26.348 176.0 234.7 26.647 202.0 234.8 26.745.0 76.4 —. —- 50.0 230.1 24.673 100.0 230.1 26.712 151.0 234.4 26.366 177.0 234.7 26.650 203.0 234.8 26.749 1.0 116.0 11.339 51.0 230.1 24.690 101.0 230.1 26.765 152.0 234.4 26.384 178.0 234.7 26.657 204.0 234.8 26.750 2.0 142.9 14.027 52.0 230.1 24.709 102.0 230.1 26.822 153.0 234.4 26.398 179.0 234.7 26.663 205.0 234.8 26.750 3.0 162.2 16.184 53.0 230.1 24.729 103.0 230.1 26.880 154.0 234.4 26.415 180.0 234.7 26.669 206.0 234.8 26.752 4.0 177.1 17.921 54.0 230.1 24.745 104.0 230.1 26.934 155.0 234.4 26.430 181.0 234.7 26.673 207.0 234.8 26.752 5.0 188.4 19.283 55.0 230.1 24.764 105.0 230.1 26.993 156.0 234.4 26.445 182.0 234.7 26.676 208.0 234.8 26.760 6.0 196.9 20.363 56.0 230.1 24.788 106.0 230.1 27.050 157.0 234.4 26.458 183.0 234.7 26.681 209.0 234.8 26.755 7.0 203.8 21.210 57.0 230.1 24.808 107.0 230.1 27.106 158.0 234.4 26.472 184.0 234.7 26.684 210.0 234.8 26.759 8.0 208.6 21.874 58.0 230.1 24.823 108.0 230.1 27.166 159.0 234.4 26.486 185.0 234.7 26.690 211.0 234.8 26.759 9.0 212.8 22.384 59.0 230.1 24.859 109.0 230.1 27.221 160.0 234.5 26.500 186.0 234.8 26.696 212.0 234.8 26.757 10.0 215.8 22.777 60.0 230.1 24.887 110.0 230.1 27.275 161.0 234.5 26.514 187.0 234.8 26.705 213.0 234.8 26.762 11.0 218.9 22.928 61.0 230.1 24.911 111.0 230.1 27.338 162.0 234.5 26.523 188.0 234.8 26.707 214.0 234.8 26.762 12.0 221.1 23.273 62.0 230.1 24.940 112.0 230.1 27.392 163.0 234.5 26.535 189.0 234.8 26.706 215.0 234.8 26.763 13.0 222.9 23.537 63.0 230.1 24.973 113.0 230.1 27.449 164.0 234.5 26.548 190.0 234.8 26.711 216.0 234.8 26.764 14.0 224.1 23.750 64.0 230.1 25.000 114.0 230.1 27.505 165.0 234.5 2 6.558 191.0 234.8 26.715 217.0 234.8 26.766 15.0 225.2 23.918 65.0 230.1 25.033 115.00230.1 27.561 166.0 234.5 26.568 192.0 234.8 26.716 218.0 234.8 26.768 16.0 226.1 24.053 66.0 230.1 25.067 116.0 230.1 27.616 167.0 234.5 26.580 193.0 234.8 26.719 219.0 234.8 26.769 17.0 227.0 24.153 67.0 230.1 25.103 117.0 230.1 27.676 168.0 234.5 26.588 194.0 234.8 26.723 220.0 234.8 26.768 18.0 227.6 24.233 68.0 230.1 25.139 118.0 230.1 27.730 169.0 234.5 26.594 195.0 234.8 26.724 221.0 234.8 26.769 19.0 228.0 24.291 69.0 230.1 25.175 119.0 230.1 27.790 170.0 234.5 26.602 196.0 234.8 26.728 222.0 234.8 26.769 20.0 228.2 24.343 70.0 230.1 25.214 120.0 230.1 27.842 171.0 234.5 26.611 197.0 234.8 26.734 223.0 234.8 26.768 21.0 228.8 24.382 71.0 230.1 25.258 121.0 230.1 27.899 172.0 234.5 26.619 198.0 234.8 26.732 224.0 234.8 26.766 22.0 229.0 24.403 72.0 230.1 25.298 122.0 230.1 27.954 173.0 234.7 26.625 199.0 234.8 26.738 225.0 234.9 26.765 23.0 229.2 24.435 73.0 230.1 25.334 123.0 230.1 28.012 174.0 234.7 26.635 200.0 234.8 26.746 24.0 229.3 24.458 74.0 230.1 25.378 124.0 230.1 28.063 175.0 234.7 26.643 201.0 234.8 26.741 25.0 229.5 24.467 75.0 230.1 25.419 125.0 230.1 28.117 26.0 229.8 24.485 76.0 230.1 25.466 126.0 230.1 28.173 27.0 229.9 24.492 77.0 230.1 25.513 127.0 230.1 28.224 28.0 229.9 24.500 78.0 230.1 25.560 128.0 230.1 28.278 29.0 230.0 24.505 79.0 230.1 25.600 129.0 230.1 28.330 30.0 230.0 24.511 80.0 230.1 25.653 130.0 230.1 28.382 31.0 230.0 24.518 81.0 230.1 25.702 131.0 230.1 28.434 32.0 230.0 24.524 82.0 230.1 25.749 132.0 230.1 28.483 33.0 230.0 24.528 83.0 230.1 25.799 133.0 230.1 28.539 34.0 230.0 24.532 84.0 230.1 25.847 134.0 230.1 28.593 35.0 230.0 24.534 85.0 230.1 25.899 135.0 230.1 28.646 34.0 230.0) 24.542 86.0 230.1 25.951 136.0 230.1 28.693 37.0 230.0 24.546 857.0 230.1 26.0037 137.0 230.1 28.746 35.0 230.0 24.555 88.0 230.1 26.057 138.0 230.1 28.798 39.0 230.0 24.560 89.0 230.1 26.105 139.0 230.1 28.851 40.0 230.0 24.569 90.0 230.1 26.159 140.0 230.1 28.900 41.0 230.0 24.573 91.0 230.1 26.217 141.0 230.1 25.950 42.0 230.0 24.581 92.0 230.1 26.270 142.0 230.1 25.993 43.0 230.0 24.593 93.0 230.1 26.318 143.0 230.0 29.044 44.0 230.0 24.600 94.0 230.1 26.376 144.0 230.0 29.094 45.0 230.1 24.611 95.0 230.1 26.429 145.0 230.0 29.140 46.0 230.1 24.622 96.0 230.1 26.487 146.0 230.0 29.185 47.0 230.1 24.634 97.0 230.1 26.544 147.0 230.0 29.230 45.0 230.1 24.6458 98.0 230.1 26.603 145.0 230.0 29.280 49.0 230.1 24.660 99.0 230.1 26.657 149.0 230.0 29.326

-513OBSERVED EXPERIMENTAL DATA FROM RUN 53 (CONT'D) OBSERVED EXPERIMENTAL DATA FROM RUN 53 (CONTID) TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM 150.0 230.0 29.371 200.0 229.9 31.147 250.0 229.9 31.993 300.0 230.0 32.288 319.0 230.0 32.337 338.0 230.0 32.360 151.0 230.0 29.418 201.0 229.9 31.175 251.0 229.9 32.007 301.0 230.0 32.293 320.0 230.0 32.339 339.0 230.0 32.361 152.0 230.0 29.465 202.0 229.9 31.200 252.0 229.9 32.016 302.0 230.0 32.293 321.0 230.0 32.341 340.0 230.0 32.362 153.0 230.0 29.509 203.0 229.9 31.225 253.0 229.9 32.026 303.0 230.0 32.298 322.0 230.0 32.343 341.0 230.0 32.364 154.0 230.0 29.553 204.0 229.9 31.250 254.0 229.9 32.037 304.0 230.0 32.301 323.0 230.0 32.343 342.0 230.0 32.365 155.0 230.0 29.591 205.0 229.9 31.275 255.0 229.9 32.045 305.0 230.0 32.303 324.0 230.0 32.347 343.0 230.0 32.365 156.0 230.0 29.639 206.0 229.9 31.300 256.0 229.9 32.055 306.0 230.0 32.307 325.0 230.0 32.347 344.0 230.0 32.366 157.0 230.0 29.677 207.0 229.9 31.322 257.0 229.9 32.062 307.0 230.0 32.309 326.0 230.0 32.348 345.0 230.0 32.370 158.0 230.0 29.722 208.0 229.9 31.340 258.0 229.9 32.072 308.0 230.0 32.313 327.0 230.0 32.351 346.0 230.0 32.368 159.0 230.0 29.766 209.0 229.9 31.366 259.0 229.9 32.081 309.0 230.0 32.315 328.0 230.0 32.354 347.0 230.0 32.370 T60.0 230.0 29.808 210.0 229.9 31.388 260.0 229.9 32.089 310.0 230.0 32.316 329.0 230.0 32.358 348.0 230.0 32.371 161.0 229.9 29.850 211.0 229.9 31.410 261.0 229.9 32.095 311.0 230.0 32.319 330.0 230.0 32.355 349.0 230.0 32.372 162.0 229.9 29.893 212.0 229.9 31.430 262.0 229.9 32.103 312.0 230.0 32.323 331.0 230.0 32.355 350.0 230.1 32.373 163.0 229.9 29.934 213.0 229.9 31.450 263.0 230.0 32.113 313.0 230.0 32.327 332.0 230.0 32.355 351.0 230.1 32.373 164.0 229.9 29.973 214.0 229.9 31.469 264.0 230.0 32.121 314.0 230.0 32.328 333.0 230.0 32.357 352.0 230.1 32.373 165.0 229.9 30.014 215.0 229.9 31.490 265.0 230.0 32.129 315.0 230.0 32.330 334.0 230.0 32.359 353.0 230.1 32.373 T66.0 229.9 30.056 216.0 229.9 31.510 266.0 230.0 32.135 316.0 230.0 32.333 335.0 230.0 32.358 354.0 230.1 32.373 167.0 229.9 30.093 217.0 229.9 31.529 267.0 2.30.0 32.142 317.0 230.0 32.334 336.0 230.0 32.359 168.0 229.9 30.130 218.0 229.9 31.548 268.0 230.0 32.150 318.0 230.0 32.335 337.0 230.0 32.360 169.0 229.9 30.172 219.0 229.9 31.565 269.0 230.0 32.158 170.0 229.9 30.210 220.0 229.9 31.583 270.0 230.0 32.164 171.0 229.9 30.245 221.0 229.9 31.601 271.0 230.0 32.172 172.0 229.9 30.281 222.0 229.9 31.618 272.0 230.0 32.178 173.0 229.9 30.318 223.0 229.9 31.636 273.0 230.0 3.2.186 174.0 229.9 30.358 224.0 229.9 31.655 274.0 230.0 32.189 175.0 229.9 30.395 225.0 229.9 31.671 275.0 230.0 32.196 176.0 229.9 30.431 226.0 229.9 31.687 276.0 230.0 32.201 177.0 229.9 30.466 227.0 229.9 31.703 277.0 230.0 32.204 178.0 229.9 30.502 228.0 229.9 31.720 278.0 230.0 32.210 179.0 229.9 30.536 229.0 229.9 31.735 279.0 230.0 32.213 180.0 229.9 30.570 230.0 229.9 31.748 280.0 230.0 32.218 181.0 229.9 30.601 231.0 229.9 31.765 281.0 230.0 32.225 182.0 229.9 30.630 232.0 229.9 31.775 282.0 230.0 32.232 183.0 229.9 30.664 233.0 229.9 31.797 283.0 230.0 32.236 184.0 229.9 30.697 234.0 229.9 31.806 284.0 230.0 32.239 185.0 229.9 30.725 235.0 229.9 31.823 285.0 230.0 32.243 186.0 229.9 30.759 236.0 229.9 31.835 286.0 230.0 32.247 187.0 229.9 30.792 237.0 229.9 31.850 287.0 230.0 32.253 188.0 229.9 30.820 238.0 229.9 31.863 288.0 230.0 32.255 189.0 229.9 30.850 239.0 229.9 31.874 289.0 230.0 32.261 190.0 229.9 30.882 240.0 229.9 31.890 290.0 230.0 32.265 191.0 229.9 30.910 241.0 229.9 31.900 291.0 230.0 32.267 192.0 229.9 30.934 242.0 229.9 31.905 292.0 230.0 32.270 193.0 229.9 30.959 243.0 229.9 31.918 293.0 230.0 32.274 194.0 229.9 30.988 244.0 229.9 31.929 294.0 230.0 32.276 195.0 229.9 31.017 245.0 229.9 31.939 295.0 230.0 32.279 196.0 229.9 31.042 246.0 229.9 31.950 296.0 230.0 32.281 197.0 229.9 31.070 247.0 229.9 31.965 297.0 230.0 32.284 198.0 229.9 31.095 248.0 229.9 31.970 298.0 230.0 32.285 199.0 229.9 31.123 249.0 229.9 31.986 299.0 230.0 32.288 OBSERVED EXPERIMENTAL DATA FROM RUN 54 OBSERVED EXPERIMENTAL DATA FROM RUN 54 (CONT'D) TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM.0 82.0 -. — 50.0 229.8 20.360 100.0 230.0 20.415 150.0 230.0 21.021 200.0 230.0 22.631 250.0 230.0 24.460 1.0 118.1 7.484 51.0 229.8 20.360 101.0 230.0 20.415 151.0 230.0 21.052 201.0 230.0 22.666 251.0 229.9 24.497 2.0 143.1 10.037 52.0 229.8 20.360 102.0 230.0 20.419 152.0 230.0 21.074 202.0 230.0 22.704 252.0 230.0 24.533 3.0 163.1 12.139 53.0 229.8 20.360 103.0 230.0 20.424 153.0 230.0 21.091 203.0 230.0 22.739 253.0 229.9 24.572 4.0 177.0 13.834 54.0 229.8 20.366 104.0 230.0 20.427 154.0 230.0 21.113 204.0 230.0 22.779 254.0 230.0 24.602 5.0 187.9 15.200 55.0 229.8 20.365 105.0 230.0 20.432 155.0 230.0 21.144 205.0 230.0 22.810 255.0 229.9 24.643 6.0 196.8 16.295 56.0 229.8 20.361 106.0 230.0 20.439 156.0 230.0 21.170 206.0 230.0 22.846 256.0 230.0 24.680 7.0 203.5 17.160 57.0 229.8 20.363 107.0 230.0 20.444 157.0 230.0 21.-199 207.0 230.0 22.881 257.0 229.9 24.720 8.0 208.8 17.846 58.0 229.9 20.367 108.0 230.0 20.450 158.0 230.0 21.230 208.0 230.0 22.919 258.0 230.0 24.756 9.0 213.1 18.385 59.0 229.8 20.366 109.0 230.0 20.455 159.0 230.0 21.256 209.0 230.0 22.956 259.0 229.9 24.792 00.0 216.7 18.815 60.0 229.9 20.363 110.0 230.0 20.460 160.0 230.0 21.285 210.0 230.0 22.993 260.0 230.0 24.827 11.0 219.1 19.143 61.0 229.8 20.364 111.0 230.0 20.465 161.0 230.0 21.312 211.0 230.0 23.029 261.0 229.9 24.868 12.0 221.4 19.406 62.0 229.9 20.363 112.0 230.0 20.473 162.0 230.0 21.341 212.0 230.0 23.067 262.0 230.0 24.903 13.0 223.0 19.611 63.0 229.8 20.366 113.0 230.0 20.479 163.0 230.0 21.372 213.0 230.0 23.101 263.0 229.9 24.935 14.0 224.4 19.771 64.0 229.9 20.367 114.0 230.0 20.487 164.0 230.0 21.400 214.0 230.0 23.139 264.0 230.0 24.971 15.0 225.2 19.897 65.0 229.9 20.368 115.0 230.0 20.494 165.0 230.0 21.432 215.0 229.9 23.176 265.0 229.9 25.016 16.0 226.3 19.993 66.0 229.9 20.365 116.0 230.0 20.500 166.0 230.0 21.460 216.0 230.0 23.211 266.0 230.0 25.044 17.0 227.0 20.077 67.0 229.9 20.367 117.0 230.0 20.509 167.0 230.0 21.490 217.0 229.9 23.250 267.0 229.9 25.081 18.0 227.6 20.136 68.0 229.9 20.368 118.0 230.0 20.517 168.0 230.0 21.524 218.0 230.0 23.284 268.0 230.0 25.118 19.0 227.8 20.186 69.0 229.8 20.366 119.0 230.0 20.523 169.0 230.0 21.556 219.0 229.9 23.318 269.0 229.9 25.156 20.0 228.1 20.203 70.0 229.9 20.368 120.0 230.0 20.533 170.0 230.0 21.593 220.0 230.0 23.358 270.0 230.0 25.191 21.0 228.2 20.253 71.0 229.9 20.365 121.0 230.0 20.543 171.0 230.0 21.620 221.0 229.9 23.395 271.0 229.9 25.224 22.0 228.8 20.274 72.0 229.9 20.366 122.0 230.0 20.552 172.0 230.0 21.659 222.0 230.0 23.430 272.0 230.0 25.263 23.0 228.9 20.294 73.0 229.9 20.366 123.0 230.0 20.564 173.0 230.0 21.691 223.0 229.9 23.464 273.0 229.9 25.297 24.0 229.1 20.307 74.0 229.9 20.369 124.0 230.0 20.573 174.0 230.0 21.721 224.0 230.0 23.500 274.0 230.0 25.335 25.0 229.1 20.320 75.0 229.9 20.370 125.0 230.0 20.585 175.0 230.0 21.759 225.0 229.9 23.533 275.0 229.9 25.369 26.0 229.3 20.330 76.0 229.9 20.374 126.0 230.0 20.590 176.0 230.0 21.790 226.0 230.0 23.572 276.0 230.0 25.405 27.0 229.2 20.335 77.0 229.9 20.377 127.0 230.0 20.600 177.0 230.0 21.823 227.0 229.9 23.606 277.0 229.9 25.436 28.0 229.3 20.335 78.0 229.9 20.378 128.0 230.0 20.614 178.0 230.0 21.857 228.0 230.0 23.644 278.0 230.0 25.470 29.0 229.4 20.344 79.0 229.8 20.382 129.0 230.0 20.629 179.0 230.0 21.890 229.0 229.9 23.683 279.0 229.9 25.506 30.0 229.6 20.348 80.0 229.9 20.383 130.0 230.0 20.641 180.0 230.0 21.923 230.0 230.0 23.718 280.0 230.0 25.538 31.0 229.6 20.353 81.0 229.8 20.380 131.0 230.0 20.655 181.0 230.0 21.956 231.0 229.9 23.759 281.0 229.9 25.574 32.0 229.6 20.359 82.0 229.9 20.385 132.0 230.0 20.669 182.0 230.0 21.987 232.0 230.0 23.797 282.0 230.0 25.607 33.0 229.6 20.361 83.0 229.9 20.383 133.0 230.0 20.683 183.0 229.9 22.022 233.0 229.9 23.830 283.0 229.9 25.640 34.0 229.7 20.365 84.0 229.9 20.387 134.0 230.0 20.700 184.0 230.0 22.060 234.0 230.0 23.865 284.0 230.0 25.673 35.0 229.6 20.366 85.0 229.8 20.386 135.0 230.0 20.715 185.0 229.9 22.095 235.0 229.9 23.903 285.0 229.9 25.710 36.0 229.7 20.360 86.0 229.9 20.385 136.0 230.0 20.732 186.0 230.0 22.127 236.0 230.0 23.938 286.0 230.0 25.743 37.0 229.7 20.360 87.0 229.9 20.386 137.0 230.0 20.751 187.0 230.0 22.161 237.0 229.9 23.976 287.0 229.9 25.775 38.0 229.8 20.360 88.0 229.9 20.386 138.0 230.0 20.768 188.0 230.0 22.200 238.0 230.0 24.016 288.0 230.0 25.810 39.0 229.8 20.363 89.0 229.9 20.392 139.0 230.0 20.786 189.0 229.9 22.230 239.0 229.9 24.054 289.0 229.9 25.845 40.0 229.9 20.362 90.0 229.9 20.395 140.0 230.0 20.803 190.0 230.0 22.271 240.0 230.0 24.090 290.0 230.0 25.872 41.0 229.9 20.362 91.0 229.9 20.395 141.0 230.0 20.824 191.0 230.0 22.303 241.0 229.9 24.124 291.0 229.9 25.904 42.0 229.9 20.366 92.0 230.0 20.395 142.0 230.0 20.843 192.0 230.0 22.340 242.0 230.0 24.163 292.0 230.0 25.931 43.0 229.9 20.365 93.0 230.0 20.400 143.0 230.0 20.863 193.0 230.0 22.374 243.0 229.9 24.199 293.0 229.9 25.967 44.0 229.8 20.360 94.0 230.0 20.401 144.0 230.0 20.886 194.0 230.0 22.410 244.0 230.0 24.237 294.0 230.0 26.003 45.0 229.8 20.36S5 95.0 230.0 20.403 145.0 230.0 20.905 195.0 229.9 22.451 245.0 229.9 24.273 295.0 229.9 26.031 46^.0 229.8 20.360 96.0 230.0 20.407 146.0 230.0 20.928 196.0 230.0 22.488 246.0 230.0 24.310 296.0 230.0 26.062 47.0 229.8 20.362 97.0 230.0 20.404 147.0 230.0 20.949 197.0 230.0 22.518 247.0 229.9 24.345 297.0 229.9 26.093 48.0 229.8 20.360 98.0 230.0 20.409 148.0 2311.0 20.978 198.0 230.0 22.S57 248.0 230.0 24.354 298.0 230.0 26.124 49.0 229.8 20.360 99.01 230.0 20.410 149.0 230.0 20.998 199.0 230.0 22.582 249.0 229.9 24.419 299.0 229.9 26.152

OBSERVED EXPERIMENTAL DATA FROM RUN 54 (CONT'D) OBSERVED EXPERIMENTAL DATA FROM RUN 54 (CONT'D) TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM 300.0 230.0 26.186 350.0 230.0 27.424 400.0 230.1 28.091 450.0 230.1 28.359 476.0 230.1 28.420 502.0 230.1 28.451 301.0 229.9 26.217 351.0 230.0 27.444 401.0 230.1 28.100 451.0 230.1 28.363 477.0 230.1 28.422 503.0 230.1 28.452 302.0 230.0 26.246 352.0 230.0 27.467 402.0 230.1 28.107 452.0 230.1 28.366 478.0 230.1 28.422 504.0 230.1 28.454 303.0 229.9 26.276 353.0 230.0 27.485 403.0 230.1 28.116 453.0 230.1 28.369 479.0 230.1 28.424 505.0 230.1 28.455 304.0 230.0 26.305 354.0 230.0 27.500 404.0 230.1 28.123 454.0 230.1 28.373 480.0 230.1 28.427 506.0 230.1 28.456 305.0 229.9 26.333 355.0 230.0 27.520 405.0 230.1 28.131 455.0 230.1 28.375 481.0 230.1 28.427 507.0 230.1 28.456 306.0 230.0 26.363 356.0 230.0 27.542 406.0 230.1 28.139 456.0 230.1 28.378 482.0 230.1 28.429 508.0 230.1 28.458 307.0 229.9 26.393 357.0 230.0 27.559 407.0 230.1 28.149 457.0 230.1 28.379 483.0 230.1 28.430 509.0 230.1 28.459 308.0 230.0 26.422 358.0 230.0 27.574 408.0 230.1 28.157 458.0 230.1 28.382 484.0 230.1 28.432 510.0 230.1 28.459 309.0 229.9 26.450 359.0 229.9 27.586 409.0 230.1 28.159 459.0 230.1 28.385 485.0 230.1 28.436 511.0 230.1 28.460 310.0 230.0 26.483 360.0 230.0 27.602 410.0 230.1 28.164 460.0 230.1 28.387 486.0 230.1 28.436 512.0 230.1 28.464 311.0 229.9 26.507 361.0 229.9 27.615 411.0 230.1 28.172 461.0 230.1 28.390 487.0 230.1 28.437 513.0 230.1 28.466 312.0 230.0 26.537 362.0 230.0 27.633 412.0 230.1 28.178 462.0 230.1 28.393 488.0 230.1 28.438 514.0 230.1 28.467 313.0 229.9 26.563 363.0 230.0 27.650 413.0 230.1 28.183 463.0 230.1 28.395 489.0 230.1 28.438 515.0 230.1 28.467 314.0 230.0 26.593 364.0 230.0 27.663 414.0 230.1 28.191 464.0 230.1 28.397 490.0 230.1 28.440 516.0 230.1 28.468 315.0 229.9 26.618 365.0 229.9 27.678 415.0 230.1 28.198 465.0 230.1 28.398 491.0 230.1 28.442 517.0 230.1 28.468 316.0 230.0 26.649 366.0 230.0 27.695 416.0 230.1 28.205 466.0 230.1 28.400 492.0 230.1 28.442 518.0 230.1 28.469 317.0 229.9 26.679 367.0 229.9 27.711 417.0 230.1 28.211 467.0 230.1 28.400 493.0 230.1 28.445 519.0 230.1 28.469 318.0 230.0 26.701 368.0 230.0 27.728 418.0 230.1 28.218 468.0 230.1 28.403 494.0 230.1 28.445 520.0 230.1 28.470 319.0 229.9 26.729 369.0 229.9 27.743 419.0 230.1 28.225 469.0 230.1 28.408 495.0 230.1 28.446 521.0 230.1 28.471 320.0 230.0 26.756 370.0 230.0 27.755 420.0 230.1 28.229 470.0 230.1 28.409 496.0 230.1 28.447 522.0 230.1 28.470 321.0 229.9 26.781 371.0 230.0 27.770 421.0 230.1 28.238 471.0 230.1 28.410 497.0 230.1 28.448 523.0 230.1 28.469 322.0 230.0 26.804 372.0 230.0 27.783 422.0 230.1 28.243 472.0 230.1 28.413 498.0 230.1 28.450 524.0 230.1 28.473 323.0 229.9 26.833 373.0 230.0 27.796 423.0 230.1 28.247 473.0 230.1 28.414 499.0 230.1 28.448 525.0 230.1 28.470 324.0 230.0 26.859 374.0 230.0 27.811 424.0 230.1 28.253 474.0 230.1 28.415 500.0 230.1 28.449 325.0 229.9 26.883 375.0 230.0 27.826 425.0 230.1 28.261 475.0 230.1 28.416 501.0 230.1 28.451 326.0 230.0 26.909 376.0 230.0 27.838 426.0 230.1 28.264 327.0 229.9 26.934 377.0 230.0 27.852 427.0 230.1 28.270 328.0 230.0 26.959 378.0 230.0 27.865 428.0 230.1 28.278 329.0 229.9 26.987 379.0 230.0 27.874 429.0 230.1 28.283 330.0 230.0 27.007 380.0 230.0 27.886 430.0 230.1 28.287 331.0 229.9 27.030 381.0 230.0 27.900 431.0 230.1 28.290 332.0 230.0 27.055 382.0 230.0 27.912 432.0 230.1 28.295 333.0 229.9 27.077 383.0 230.0 27.922 433.0 230.1 28.301 334.0 230.0 27.096 384.0 230.0 27.932 434.0 230.1 28.305 335.0 229.9 27.119 385.0 230.0 27.949 435.0 230.1 28.307 336.0 230.0 27.143 386.0 230.1 27.959 436.0 230.1 28.310 337.0 230.0 27.164 387.0 230.1 27.969 437.0 230.1 28.316 338.0 230.0 27.185 388.0 230.1 27.984 438.0 230.1 28.318 339.0 230.0 27.204 389.0 230.1 27.992 439.0 230.1 28.325 340.0 230.0 27.224 390.0 230.1 28.005 440.0 230.1 28.326 341.0 230.0 27.247 391.0 230.1 28.016 441.0 230.1 28.330 342.0 230.0 27.267 392.0 230.1 28.022 442.0 230.1 28.335 343.0 229.9 27.288 393.0 230.1 28.032 443.0 230.1 28.338 344.0 230.0 27.308 394.0 230.1 28.042 444.0 230.1 28.340 345.0 230.0 27.328 395.0 230.1 28.050 445.0 230.1 28.344 346.0 230.0 27.348 396.0 230.1 28.059 446.0 230.1 28.347 347.0 229.9 27.368 397.0 230.1 28.068 447.0 230.1 28.348 348.0 230.0 27.388 398.0 230.1 28.077 448.0 230.1 28.349 349.0 229.9 27.408 399.0 230.1 28.085 449.0 230.1 28.353 OBSERVED EXPERIMENTAL DATA FROM RUN 55 OBSERVED EXPERIMENTAL DATA FROM RUN 55 (CONT'D) TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM.0 84.1 -. —- 25.0 243.6 20.916 50.0 243.1 27.360 75.0 245.1 28.364 80.0 245.1 28.374 85.0 245.4 28.380.5 104.2 -. — 25.5 243.6 21.034 50.5 243.2 27.424 75.5 245.2 28.367 80.5 245.2 28.378 85.5 245.3 28.380 1.0 122.6 -. —- 26.0 243.5 21.161 51.0 243.3 27.488 76.0 245.1 28.369 81.0 245.1 28.376 86.0 245.2 28.379 1.5 138.1 6.950 26.5 243.5 21.293 51.5 243.3 27.547 76.5 245.2 28.368 81.5 245.2 28.377 86.5 245.3 28.379 2.0 151.3 8.366 27.0 243.3 21.432 52.0 243.4 27.597 77.0 245.1 28.370 82.0 245.1 28.378 87.0 245.4 28.379 2.5 162.9 9.643 27.5 243.2 21.573 52.5 243.4 27.649 77.5 245.2 28.370 82.5 245.2 28.378 87.5 245.2 28.379 3.0 173.0 10.784 28.0 243.1 21.719 53.0 243.7 27.698 78.0 245.1 28.371 83.0 245.3 28.378 88.0 245.2 28.379 3.5 181.3 11.813 28.5 243.0 21.870 53.5 243.5 27.747 78.5 245.2 28-.374 83.5 245.2 28.380 88.5 245.3 28.378 4.0 188.9 12.721 29.0 242.8 22.023 54.0 243.6 27.793 79.0 245.1 28.374 84.0 245.1 28.379 4.5 195.4 13.547 29.5 242.8 22.180 54.5 243.7 27.830 79.5 245.1 28.375 84.5 245.3 28.380 5.0 201.2 14.276 30.0 242.8 22.339 55.0 243.9 27.868 5.5 206.2 14.935 30.5 242.7 22.500 55.5 243.8 27.907 6.0 210.8 15.516 31.0 242.5 22.659 56.0 244.0 27.940 6.5 214.7 16.033 31.5 242.4 22.821 56.5 244.1 27.970 7.0 218.1 16.490 32.0 242.3 22.979 57.0 244.2 28.000 7.5 221.1 16.897 32.5 242.3 23.143 57.5 244.2 28.028 8.0 223.9 17.262 33.0 242.2 23.307 58.0 244.2 28.055 8.5 226.3 17.578 33.5 242.2 23.469 58.5 244.3 28.083 9.0 228.4 17.860 34.0 242.2 23.629 59.0 244.4 28.108 9.5 230.2 18.109 34.5 242.2 23.788 59.5 244.4 28.128 10.0 231.8 18.326 35.0 242.1 23.943 60.0 244.4 28.146 10.5 233.3 18.521 35.5 242.2 24.104 60.5 244.5 28.164 11.0 234.4 18.693 36.0 242.1 24.257 61.0 244.7 28.181 11.5 236.0 18.846 36.5 242.2 24.408 61.5 244.6 28.195 12.0 236.9 18.979 37.0 242.1 24.556 62.0 244.8 28.214 12.5 237.8 19.098 37.5 242.0 24.706 62.5 244.8 28.229 13.0 238.5 19.205 38.0 242.1 24.848 63.0 244.9 28.240 13.5 239.1 19.299 38.5 242.1 24.993 63.5 244.8 28.250 14.0 239.9 19.378 39.0 242.1 25.134 64.0 244.8 28.261 14.5 240.4 19.457 39.5 242.1 25.270 64.5 244.8 28.271 15.0 241.0 19.526 40.0 242.0 25.403 65.0 244.8 28.282 15.5 241.2 19.587 40.5 242.1 25.535 65.5 244.8 28.288 16.0 241.6 19.641 41.0 242.1 25.660 66.0 244.9 28.296 16.5 242.2 19.693 41.5 242.1 25.782 66.5 245.0 28.303 17.0 242.5 19.744 42.0 242.1 25.905 67.0 245.1 28.309 17.5 242.8 19.794 42.5 242.2 26.020 67.5 245.0 28.314 18.0 243.0 19.845 43.0 242.2 26.136 68.0 245.1 28.322 18.5 243.4 19.894 43.5 242.2 26.247 68.5 245.2 28.327 19.0 243.3 19.947 44.0 242.2 26.350 69.0 245.2 28.335 19.5 243.4 20.001 44.5 242.3 26.457 69.5 245.1 28.337 20.0 243.7 20.056 45.0 242.4 26.551 70.0 245.2 28.340 20.5 243.7 20.116 45.5 242.3 26.652 70.5 245.2 28.345 21.0 243.6 20.182 46.0 242.4 26.744 71.0 245.2 28.347 21.5 243.6 20.252 46.5 242.4 26.833 71.5 245.1 28.350 22.0 243.7 20.328 47.0 242.6 26.918 72.0 245.1 28.353 22.5 243.7 20.412 47.5 242.7 27.002 72.5 245.2 28.357 23.0 243.6 20.495 48.0 242.7 27.080 73.0 245.1 28.359 23.5 243.6 20.589 48.5 242.8 27.154 73.5 245.2 28.3b9 24.0 243.6 20.694 49.0 243.0 27.226 74.0 245.1 28.361 24.5 243.6 20.802 49.5 243.0 27.298 74.5 245.2 28.363

-515OBSERVED EXPERIMENTAL DATA FROM RUN 56 OBSERVED EXPERIMENTAL DATA FROM RUN 57 TIME TEMP. HEIGHT TIME TEMP, HEIGHT TIME TEMP. HEIGHT TIME TFMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM.0 81.8 —. —- 41.0 229.8 32.803 82.0 229.7 32.798.0 79.9 -. — 41.0 230.0 16.424 82.0 230.1 16.423 1.0 119.2 19.858 42.0 229.8 32.800 83.0 229.7 32.798 1.0 116.8 3.430 42.0 230.2 16.424 83.0 229.9 16.423 2.0 144.0 22.489 43.0 229.8 32.800 84.0 229.7 32.797 2.0 142.8 5.991 43.0 229.9 16.420 84.0 230.1 16.424 3.0 163.3 24.639 44.0 229.6 32.800 85.0 229.7 32.796 3.0 162.0 8.081 44.0 230.1 16.420 85.0 229.9 16.424 4.0 177.8 26.366 45.0 229.8 32.803 86.0 229.7 32.794 4.0 176.8 9.789 45.0 229.9 14.420 86.0 230.1 16.421 5.0 189.0 27.744 46.0 229.5 32.802 87.0 229.8 32.797 5.0 188.8 11.192 46,0 230.2 16.427 87.0 229.9 16.424 6.0 197.6 28.829 47.0 229.8 32.802 88.0 229.8 32.795 6.0 197.3 12.304 47.0 229.9 16.424 88.0 230.1 16.420 7.0 204.4 29.689 48.0 229.8 32.803 89.0 229.8 32.794 7.0 204.3 13.194 48.0 230.1 16.424 89.0 229.9 16.420 8.0 209.8 30.372 49.0 229.5 32.802 90.0 229.8 32.793 8.0 209.8 13.893 49.0 229.9 16.424 90.0 230.1 16.420 9.0 213.8 30.898 50.0 229.8 32.802 91.0 229.8 32.792 9.0 214.1 14.445 50.0 230.0 16.424 91.0 230.0 16.420 10.0 217.1 31.312 51.0 229.7 32.802 92.0 229.8 32.793 10.0 217.7 14.888 51.0 230.0 16.420 92.0 230.0 16.420 11.0 219.9 31.634 52.0 229.8 32.801 93.0 229.8 32.792 11.0 220.0 15.218 52.0 229.9 16.422 93.0 229.9 16.418 12.0 221.8 31.886 53.0 229.8 32.800 94.0 229.7 32.790 12.0 222.5 15.485 53.0 230.0 16.421 94.0 230.1 16.418 13.0 223.4 32.080 54.0 229.7 32.799 95.0 229.8 32.792 13.0 223.8 15.693 54.0 229.9 16.426 95.0 230.0 16.419 14.0 224.7 32.230 55.0 229.8 32.798 96.0 229.8 32.792 14.0 225.3 15.858 55.0 230.0 16.424 96.0 230.0 16.414 15.0 225.7 32.354 56.0 229.7 32.799 97.0 229.7 32.791 15.0 226.2 15.984 56.0 230.2 16.425 97.0 229.9 16.417 16.0 226.4 32.449 57.0 229.7 32.799 98.0 229.7 32.791 16.0 227.2 16.080 57.0 230.0 16.425 98.0 230.0 16.414 17.0 227.2 32.525 58.0 229.7 32.799 99.0 229.7 32.790 17.0 227.6 16.157 58.0 230.2 16.427 99.0 230.0 16.415 18.0 227.6 32.585 59.0 229.7 32.801 100.0 229.7 32.791 18.0 228.3 16.213 59.0 230.0 16.427 100.0 230.0 16.415 19.0 228.2 32.632 60.0 229.7 32.800 101.0 229.7 32.790 19.0 228.4 16.260 60.0 230.1 16.430 101.0 230.0 16.414 20.0 228.3 32.669 61.0 229.7 32.800 102.0 229.7 32.789 20.0 229.0 16.294 61.0 230.0 16.430 102.0 230.0 16.414 21.0 228.7 32.704 62.0 229.7 32.800 103.0 229.7 32.790 21.0 229.0 16.322 62.0 230.2 16.429 103.0 229.9 16.415 22.0 228.8 32.723 63.0 229.8 32.800 104.0 229.7 32.792 22.0 229.3 16.342 63.0 230.0 16.431 104.0 230.0 16.412 23.0 229.1 32.743 64.0 229.7 32.800 105.0 229.7 32.790 23.0 229.3 16.364 64.0 230.0 16.433 105.0 229.9 16.412 24.0 229.0 32.753 65.0 229.7 32.800 106.0 229.7 32.789 24.0 229.7 16.375 65.0 230.0 16.432 106.0 229.9 16.410 25.0 229.3 32.766 66.0 229.7 32.799 107.0 229.8 32.787 25.0 229.7 16.386 66.0 230.0 16.433 107.0 229.9 16.410 26.0 229.2 32.771 67.0 229.7 32.800 108.0 229.8 32.788 26.0 229.8 16.396 67.0 230.0 16.431 108.0 230.0 16.411 27.0 229.4 32.7.77 68.0 229.7 32,800 109.0 229.7 32.788 27.0 229.8 16.405 68,0 229.9 16.431 109.0 230.0 16.412 28.0 229.3 32.788 69.0 229.7 32.799 110.0 229.7 32.788 28.0 229.9 16.410 69.0 230.0 16.430 110.0 230.0 16.410 29.0 229.6 32.791 70.0 229.7 32.799 111.0 229.7 32.788 29.0 229.8 16.415 70.0 230.2 16.430 111.0 230.0 16.412 30.0 229.4 32.796 71.0 229.6 32.799 112.0 229.8 32.789 30.0 230.0 16.420 71.0 229.9 16.429 112.0 230.1 16.410 31.0 229.7 32.798 72.0 229,7 32.798 113.0 229.7 32.788 31.0 229.9 16.420 72.0 229.9 16.431 113.0 230.0 16.413 32.0 229.5 32.801 73.0 229.7 32.798 114.0 229.8 32.787 32.0 230.0 16.424 73.0 230.0 16.429 114.0 230.0 16.414 33.0 229.7 32.801 74.0 229.7 32.797 115.0 229.7 32.787 33.0 229.9 16.427 74.0 229.9 16.428 115.0 230.0 16.411 34.0 229.6 32.804 75.0 229.7 32.796 116.0 229.7 32.788 34.0 230.2 16.429 75.0 230.0 16.426 116.0 230.0 16.413 35.0 229.8 32.805 76.0 229.7 32.796 117.0 229.7 32.787 35.0 229.9 16.430 76.0 229.9 16.429 117.0 229.9 16.411 36.0 229.4 32.805 77.0 229.7 32.795 118.0 229.8 32.787 36.0 230.2 16.428 77.0 229.9 16.429 118.0 229.9 16.411 37.0 229.7 32.804 78.0 229.8 32.795 119.0 229.7 32.788 37.0 229.9 16.431 78.0 230.1 16.430 119.0 229.9 16.411 38.0 229.7 32.804 79.0 229.7 32.795 120.0 229.7 32.788, 38.0 230.0 16.431 79.0 229.9 16.429 120.0 230.0 16.409 39.0 229.7 32.804 80.0 229.7 32.794 39.0 230.0 16.428 80.0 230.1 16.426 40.0 229.8 32.805 81.0 229.7 32.797 40.0 230.2 16.426 81.0 229.9 16.423 OBSERVED EXPERIMENTAL DATA FROM RUN 58 OBSERVED EXPERIMENTAL DATA FROM RUN 58 (CONTID) TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF C IN O CM MIN OF CM MIN OF CM.0 81.8 -. — 50.0 255.1 23.011 100.0 255.5 29.952 150.0 256.0 30.285 157.0 256.0 30.292 164.0 256.0 30.295 1.0 122.3 5.243 51.0 254.8 23.149 101.0 255.5 29.978 151.0 256.0 30.286 158.0 256.0 30.294 165.0 256.0 30.294 2.0 152.5 8.390 52.0 254.8 23.288 102.0 255.7 30.014 152.0 256.0 30.287 159.0 256.0 30.294 166.0 256.0 30.292 3.0 175.6 11.048 53.0 254.7 23.440 103.0 255.5 30.037 153.0 256.0 30.290 160.0 256.0 30.293 167.0 256.0 30.294 4.0 193.3 13.226 54.0 254.8 23.596 104.0 255.7 30.056 154.0 256.0 30.290 161.0 256.0 30.296 168.0 256.0 30.293 5.0 206.9 14.996 55.0 254.6 23.760 105.0 255.5 30.075 155.0 256.0 30.288 162.0 256.0 30.294 169.0 256.0 30.293 6.0 217.8 16.421 56.0 254.7 23.931 106.0 255.8 30.096 156.0 256.0 30.291 163.0 256.0 30.297 170.0 256.0 30.293 7.0 226.0 17.558 57.0 254.3 24.103 107.0 255.8 30.113 8.0 232.4 18.456 58.0 254.5 24.283 108.0 255.8 30.134 9.0 237.2 19.160 59.0 254.3 24.468 109.0 255.7 30.146 10.0 241.2 19.720 60.0 254.3 24.652 110.0 255.8 30.156 11.0 244.8 20.155 61.0 254.1 24.849 111.0 255.8 30.165 12.0 247.0 20.486 62.0 254,3 25.045 112.0 255.8 30.176 13.0 248.9 20.750 63.0 254.0 25.244 113.0 255.7 30.187 14.0 250.6 20.954 64.0 254.0 25.444 114.0 256.0 30.197 15.0 251.8 21.118 65.0 254.0 25.647 115.0 255.9 30.201 16.0 252.8 21.242 66.0 254.1 25.850 116.0 256.0 30.207 17.0 253.3 21.338 67.0 253.8 26.042 117.0 255.9 30.217 18.0 254.0 21.415 68.0 253.9 26.243 118.0 256.0 30.219 19.0 254.3 21.470 69.0 253.8 26.440 119.0 255.9 30.225 20.0 254.8 21.514 70.0 253.9 26.640 120.0 256.0 30.229 21.0 254.9 21.555 71.0 253.8 26.830 121.0 255.9 30.233 22.0 255.2 21.586 72.0 253.8 27.015 122.0 256.0 30.238 23.0 255.3 21.610 73.0 253.7 27.207 123.0 255.9 30.240 24.0 255.6 21.630 74.0 253.9 27.380 124.0 256.0 30.244 25.0 255.7 21.649 75.0 253.8 27.555 125.0 255.9 30.251 26.0 255.8 21.667 76.0 254.0 27.720 126.0 256.0 30.255 27.0 255.8 21.683 77.0 253.9 27.891 127.0 255.9 30.255 28.0 256.0 21.695 78.0 254,0 28.048 128.0 256.0 30.254 29.0 255.9 21.714 79.0 254.0 28.201 129.0 255.9 30.254 30.0 256.1 21.731 80.0 254.2 28.352 130.0 256.0 30.259 31.0 256.0 21.751 81.0 254.2 28.496 131.0 256.0 30.262 32.0 256.0 21.768 82.0 254.3 28.625 132.0 256.0 30.264 33.0 256.0 21.790 83.0 254.2 28.750 133.0 256.0 30.263 34.0 256.0 21.815 84.0 254.5 28.874 134.0 256.0 30.264 35.0 255.9 21.845 85.0 254.3 28.985 135.0 256.0 30.268 36.0 256.0 21.881 86.0 254.7 29.093 136.0 256.0 30.268 37.0 255.9 21.921 87.0 254.4 29.186 137.0 256.0 30.271 38.0 256.0 21.960 88.0 254.7 29.280 138.0 256.0 30.274 39.0 255.8 22.012 89.0 254.5 29.363 139.0 256.0 30.273 40.0 255.8 22.067 90.0 254.8 29.439 140.0 256.0 30.275 41.0 255.8 22.127 91.0 254.8 29.516 141.0 256.0 30.277 42.0 255.8 22.193 92.0 254.8 29.585 142.0 256.0 30.278 43.0 255.6 22.270 93.0 254.9 29.646 143.0 256.0 30.277 44.0 255.7 22.353 94.0 255.1 29.707 144.0 256.0 30.279 45.0 255.3 22.442 95.0 254.9 29.753 145.0 256.0 30.281 46.0 255.4 22.538 96.0 255.1 29.806 146.0 256.0 30.20( 47.0 255.2 22.642 97.0 255.1 29.849 147.0 256.0 30.281 48.0 255.3 22.758 98.0 255.2 29.887 148.0 256.0 30.283 49.0 255.1 22.878 99.0 255.2 29.922 149.0 256.0 30.284

-516OBSERVED EXPERIMENTAL DATA FROM RUN 59 OBSERVED EXPERIMENTAL DATA FROM RUN 59 (CONT'D) TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OP cm MIN OF cm MIN OF CM MIN OF CM MIN OF CM MIN OF CM.0 88.1 -. — 50.0 249.0 15.821 100.0 248.2 19.088 150.0 248.2 23.566 172.0 248.7 24.103 194.0 248.8 24.213 1.0 129.4 -. — 51.0 249.0 15.833 101.0 248.1 19.198 151.0 248.3 23.607 173.0 248.7 24.115 195.0 248.8 24.216 2.0 159.7 3.260 52.0 248.9 15.849 102.0 248.0 19.307 152.0 248.3 23.650 174.0 248.8 24.123 196.0 248.8 24.215 3.0 181.2 5.797 53.0 249.0 15.868 103.0 248.2 19.421 153.0 248.5 23.688 175.0 248.8 24.132 197.0 248.8 24.218 4.0 196.7 8.870 54.0 249.0 15.885 104.0 248.0 19.534 154.0 248.5 23.722 176.0 248.8 24.140 198.0 248.8 24.218 5.0 208.5 9.531 55.0 249.0 15.906 105.0 248.1 19.651 155.0 248.5 23.756 177.0 248.8 24.146 199.0 248.8 24.219 6.0 217.1 10.863 56.0 248.9 15.929 106.0 248.0 19.765 156.0 248.5 23.788 178.0 248.8 24.157 200.0 248.8 24.222 7.0 224.6 11.916 57.0 248.9 15.953 107.0 248.0 19.876 157.0 248.5 23.815 179.0 248.8 24.161 201.0 248.8 24.222 8.0 229.4 12.742 58.0 248.9 15.977 108.0 248.0 19.988 158.0 248.5 23.843 180.0 248.8 24.167 202.0 248.8 24.224 9.0 233.8 13.389 59.0 249.0 16.004 109.0 248.2 20.108 159.0 248.5 23.870 181.0 248.8 24.172 203.0 248.8 24.226 10.0 236.8 13.899 60.0 248.9 16.033 110.0 248.2 20.217 160.0 248.5 23.894 182.0 248.8 24.177 204.0 248.8 24.227 11.0 239.5 14.290 61.0 249.0 16.062 111.0 248.0 20.328 161.0 248.5 23.921 183.0 248.8 24.187 205.0 248.8 24.227 12.0 241.3 14.603 62.0 249.0 16.095 112.0 248.1 20.443 162.0 248.5 23.942 184.0 248.8 24.187 206.0 248.8 24.228 13.0 243.1 14.849 63.0 249.0 16.131 113.0 248.0 20.553 163.0 248.5 23.963 185.0 248.8 24.189 207.0 248.8 24.229 14.0 244.5 15.036 64.0 248.8 16.1.75 114.0 248.0 20.663 164.0 248.5 23.984 186.0 248.8 24.193 208.0 248.8 24.233 15.0 245.6 15.181 65.0 248.9 16.213 115.0 248.0 20.773 165.0 248.5 24.003 187.0 248.8 24.193 209.0 248.8 24.233 16.0 246.2 15.296 66.0 248.8 16.254 116.0 247.8 20.885 166.0 248.5 24.012 188.0 248.8 24.196 210.0 248.8 24.233 17.0 246.8 15.385 67.0 248.8 16.297 117.0 248.0 20.993 167.0 248.6 24.039 189.0 248.8 24.201 211.0 248.8 24.233 18.0 247.2 15.453 68.0 248.8 16.346 118.0 247.9 21.099 168.0 248.6 24.058 190.0 248.8 24.207 212.0 248.8 24.234 19.0 247.8 15.504 69.0 248.8 16.399 119.0 248.0 21.199 169.0 248.6 24.068 191.0 248.8 24.208 213.0 248.8 24.232 20.0 248.1 15.550 70.0 248.7 16.454 120.0 247.9 21.307 170.0 248.6 24.081 192.0 248.8 24.209 214.0 248.8 24.233 21.0 248.3 15.580 71.0 248.7 16.508 121.0 248.0 21.415 171.0 248.7 24.092 193.0 248.8 24.210 215.0 248.8 24.233 22.0 248.6 15.609 72.0 248.7 16.562 122.0 247.9 21.512 23.0 248.7 15.628 73.0 248.8 16.622 123.0 248.0 21.615 24.0 248.8 15.644 74.0 248.8 16.683 124.0 248.0 21.713 25.0 249.0 15.656 75.0 248.8 16.748 125.0 248.0 21.809 26.0 249.0 15.668 76.0 248.8 16.819 126.0 248.0 21.908 27.0 249.1 15.678 77.0 248.8 16.887 127.0 248.0 22.002 28.0 249.2 15.684 78.0 248.6 16.962 128.0 248.0 22.092 29.0 249.2 15.687 79.0 248.6 17.033 129.0 248.0 22.182 30.0 249.2 15.689 80.0 248.5 17.111 130.0 248.0 22.270 31.0 249.2 15.695 81.0 248.5 17.191 131.0 248.0 22.355 32.0 249.2 15.700 82.0 248.6 17.278 132.0 248.0 22.439 33.0 249.2 15.705 83.0 248.7 17.360 133.0 248.0 22.519 34.0 249.2 15.706 84.0 248.5 17.439 134.0 248.1 22.597 35.0 249.2 15.709 85.0 248.5 17.539 135.0 248.1 22.676 36.0 249.0 15.716 86.0 248.5 17.632 136.0 248.1 22.749 37.0 249.2 15.717 87.0 248.5 17.729 137.0 248.1 22.813 38.0 249. 1.5.720 88.0 248.4 17.820 138.0 248.1 22.891 39.0 249.4 15.723 89.0 248.3 17.919 139.0 248.1 22.959 40.0 249.2 15.728 90.0 248.2 18.018 140.0 248.1 23.028 41.0 24Q.2 15.233 91.0 248.2 18.119 141.0 248.2 23.088 42.0 249.2 1:.739 92.0 248.3 18.225 142.0 248.2 23.151 43.0 249.3 15.746 93.0 248.4 18.329 143.0 248.2 23.214 44.0 249.0 15.756 94.0 248.3 18.436 144.0 248.2 23.268 45.0 249.3 15.765 95.0 248.3 18.536 145.0 248.2 23.325 46.0 249.2 15.772 96.0 248.2 18.646 146.0 248.2 23.378 47.0 249.2 15.782 97.0 248.2 18.754 147.0 248.2 23.431 48.0 249.0 15.794 98.0 248.0 18.866 148.0 248.2 23.478 49.0 249.1 15.802 99.0 248.0 18.976 149.0 248.2 23.520 OBSERVED EXPERIMENTAL DATA FROM RUN 60 OBSERVED EXPERIMENTAL DATA FROM R8)N 61 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF cm MIN Op cm MIS OF cm MIN OP cm MIN OF CM MIN OF CM.0 77.3 -. — 50.0 247.1 27.633 100.0 248.6 28.201.0 77.0 -. — 35.0 243.9 21.019 70.0 243.1 28.015 1.0 124.1 4.709 51.0 247.3 27.730 101.0 248.8 28.201 1.0 134.1 -. — 36.0 243.8 21.168 71.0 243.2 28.094 2.0 154.3 7.723 52.0 247.6 27.814 102.0 248.8 28.203 2.0 162.1 9.940 37.0 243.7 21.334 72.0 243.3 28.166 3.0 177.7 10.198 53.0 247.9 27.880 103.0 248.8 28.204 3.0 181.9 12.143 38.0 243.3 21.515 73.0 243.3 28.236 4.0 194.1 12.217 54.0 248.0 27.935 104.0 248.8 28.204 4.0 196.0 13.890 39.0 243.1 21.716 74.0 243.5 28.302 5.0 206.7 13.840 55.0 248.3 27.983 105.0 248.9 28.205 5.0 206.4 15.274 40.0 243.0 21.932 75.0 243.6 28.353 6.0 215.9 15.141 56.0 248.3 28.021 106.0 248.8 28.205 6.0 214.8 16.374 41.0 242.7 22.160 76.0 243.7 28.400 7.0 223.0 16.166 57.0 248.3 28.056 107.0 248.8 28.206 7.0 221.1 17.242 42.0 242.6 22.397 77.0 243.7 28.441 8.0 228.8 16.970 58.0 248.4 28.078 108.0 248.8 28.207 8.0 226.2 17.921 43.0 242.3 22.650 78.0 243.8 28.475 9.0 233.0 17.616 59.0 248.6 28.095 109.0 248.9 28.208 9.0 230.0 18.459 44.0 242.2 22.913 79.0 243.9 28.509 10.0 236.3 18.094 60.0 248.4 28.115 110.0 248.8 28.209 10.0 233.0 18.878 45.0 242.1 23.171 80.0 243.9 28.537 11.0 239.0 18.478 61.0 248.6 28.129 111.0 248.9 28.209 11.0 235.3 19.201 46.0 242.0 23.434 81.0 243.9 28.560 12.0 241.0 18.776 62.0 248.7 28.139 112.0 248.8 28.208 12.0 237.3 19.456 47.0 241.9 23.699 82.0 244.0 28.581 13.0 242.8 19.004 63.0 248.8 28.147 113.0 248.9 28.209 13.0 238.8 19.656 48.0 241.8 23.966 83.0 244.0 28.598 14.0 244.1 19.179 64.0 248.8 28.154 114.0 248.8 28.211 14.0 240.1 19.815 49.0 241.8 24,230 84.0 244.1 28.616 15.0 245.2 19.314 65.0 248.8 28.163 115.0 248.9 28.213 15.0 240.9 19.935 50.0 241.8 24.494 85.0 244.1 28.625 16.0 245.8 19.417 66.0 248.8 28.164 116.0 248.8 28.213 16.0 241.8 20.033 51.0 241.8 24.743 86.0 244.1 28.642 17.0 246.5 19.498 67.0 248.7 28.167 117.0 248.8 28.215 17.0 242.2 20.108 52.0 241.8 24.997. 87.0 244.1 28.651 18.0 246.9 19.568 68.0 248.7 28.167 118.0 248.8 28.213 18.0 242.8 20.170 53.0 241.9 25.243 88.0 244.3 28.665 19.0 247.5 19.622 69.0 248.7 28.168 119.0 248.9 28.215 19.0 243.0 20.217 54.0 241.8 25.476 89.0 244.3 28.674 20.0 247.7 19.675 70.0 248.8 28.173 120.0 248.7 28.214 20.0 243.5 20.256 55.0 241.8 25.709 90.0 244.5 28.683 21.0 247.8 19.735 71.0 248.8 28.178 121.0 248.9 28.216 21.0 243.6 20.285 56.0 241.8 25.927 91.0 244.4 28.693 22.0 248.1 19.807 72.0 248.8 28.179 122.0 248.9 28.216 22.0 244.0 20.315 57.0 241.9 26.136 92.0 244.5 28.700 23.0 248.1 19.895 73.0 248.8 28.179 123.0 248.9 28.219 23.0 244.0 20.335 58.0 242.0 26.335 93.0 244.3 28.703 24.0 247.9 20.021 74.0 248.8 28.182 124.0 248.9 28.221 24.0 244.1 20.356 59.0 242.0 26.537 94.0 244.5 28.708 25.0 248.0 20.185 75.0 248.8 28.180 125.0 248.9 28.219 25.0 244.3 20.376 60.0 242.0 26.717 95.0 244.2 28.713 26.0 247.8 20.391 76.0 248.8 28.180 126.0 248.9 28.221 26.0 244.3 20.396 61.0 242.2 26.888 96.0 244.3 28.714 27.0 247.6 20.645 77.0 249.0 28.184 127.0 248.9 28.219 27.0 244.2 20.427 62.0 242.3 27.056 97.0 244.3 28.716 28.0 247.2 20.930 78.0 248.8 28.186 128.0 248.9 28.220 28.0 244.3 20.461 63.0 242.3 27.203 98.0 244.3 28.717 29.0 246.8 21.276 79.0 249.0 28.187 129.0 248.9 28.222 29.0 244.3 20.500 64.0 242.5 27.346 99.0 244.4 28.716 30.0 246.4 21.648 80.0 248.8 28.189 130.0 248.9 28.219 30.0 244.3 20.550 65.0 242.5 27.481 100.0 244.6 28.715 31.0 246.2 22.042 81.0 248.8 28.190 131.0 248.9 28.220 31.0 244.3 20.611 66.0 242.6 27.605 101.0 244.4 28.718 32.0 245.9 22.460 82.0 248.8 28.193 132.0 248.9 28.217 32.0 244.3 20.689 67.0 242.8 27.725 102.0 244.3 28.716 33.0 245.7 22.881 83.0 248.8 28.193 133.0 248.9 28.216 33.0 244.3 20.780 68.0 242.9 27.830 103.0 244.2 28.718 34.5 245.2 23.308 84.0 248.8 28.193 134.0 248.9 28.217 34.0 244.0 20.893 69.0 243.0 27.929 104.0 244.4 28.720 35.0 245.3 23.726 85.0 248.8 28.193 135.0 248.9 28.220 36.0 245.2 24.131 86.0 248.8 28.195 136.0 248.9 28.223 37.0 245.3 24.524 87.0 248.8 28.199 137.0 248.9 28.225 38.0 245.2 24.894 88.0 248.8 28.198 138.0 248.9 28.227 39.0 245.3 25.253 89.0 248.8 28.199 139.0 248.9 28.227 44.0 245.3 25.580 90.0 248.7 28.199 140.0 248.9 28.227 41.0 245.7 25.886 91.0 248.9 28.199 141.0 248.9 28.226 42.0 245.7 26.172 92.0 248.8 28.199 142.0 248.9 28.228 43.0 245.8 26.435 93.0 248.8 28.200 143.0 248.9 28.228 44.0 246.0 26.669 94.0. 248.7 28.200 144.0 248.9 28.228 45.0 246.2 26.882 95.0 248.8 28.200 145.0 248.9 28.227 46.0 246.3 27.071 96.0 248.8 28.200 146.0 248.9 28.228 47.0 246.6 27.245 97.0 248.8 28.200 147.0 248.9 28.227 48.0 246.7 27.393 98.0 248.7 28.200 148.0 248.9 28.226 49.0 246.7 27.519 99.0 248.9 28.200 149.0 248.9 28.225

-517OBSERVED EXPERIMENTAL DATA FROM RUN 62 OBSERVED EXPERIMENTAL DATA FROM RUN 63 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN oF CM MIN OF CM MIN OF CM.0 73.3 —. —- 165.0 244.0 32.863 330.0 244.1 38.568.0 75.2 -. — 32.0 261.0 22.553 64.0 261.2 30.324 5.0 199.2 24.457 170.0 244.0 33.079 335.0 244.0 38.608 1.0 121.9 4.234 33.0 260.9 22.760 65.0 261.3 30.367 10.0 230.9 28.847 175.0 243.9 33.299 340.0 244.1 38.635 2.0 153.3 7.588 34.0 260.6 22.990 66.0 261.4 30.404 15.0 239.9 30.137 180.0 243.9 33.522 345.0 244.0 38.661 3.0 178.0 10.424 35.0 260.4 23.253 67.0 261.7 30.436 25.0 243.9 30.632 190.0 243.8 33.988 355.0 244.0 38.713 4.0 196.1 12.756 36.0 260.0 23.542 68.0 261.8 30.461 30.0 244.3 30.673 195.0 243.8 34.219 360.0 244.1 38.728 5.0 210.8 14.644 37.0 259.8 23.846 69.0 261.7 30.482 35.0 244.2 30.688 200.0 243.8 34.458 365.0 244.0 38.744 6.0 221.8 16.171 38.0 259.4 24.176 70.0 261.7 30.493 40.0 244.3 30.692 205.0 243.8 34.691 370.0 244.1 38.757 7.0 230.8 17.388 39.0 259.3 24.522 71.0 261.9 30.511 45.0 244.2 30.696 210.0 243.8 34.930 375.0 244.1 38.770 8.0 237.3 18.350 40.0 259.0 24.878 72.0 261.9 30.520 20.0 242.9 30.518 185.0 243.9 33.753 350.0 244.1 38.691 9.0 242.8 19.104 41.0 258.9 25.238 73.0 262.0 30.528 50.0 244.3 30.696 215.0 243.8 35.173 380.0 244.2 38.784 10.0 246.8 19.694 42.0 258.6 25.611 74.0 261.8 30.533 55.0 244.2 30.702 220.0 243.8 35.408 385.0 244.1 38.788 11.0 250.1 20.159 43.0 258.7 25.974 75.0 262.2 30.543 60.0 244.3 30.712 225.0 243.8 35.641 390.0 244.2 38.798 12.0 252.7 20.519 44.0 258.5 26.331 76.0 261.8 30.545 65.0 244.2 30.721 230.0 243.8 35.865 395.0 244.1 38.805 13.0 254.8 20.810 45.0 258.6 26.679 77.0 262.0 30.546 70.0 244.3 30.734 235.0 243.8 36.093 400.0 244.2 38.806 14.0 256.3 21.029 46.0 258.3 27.022 78.0 262.0 30.550 75.0 244.2 30.750 240.0 243.8 36.321 405.0 244.1 38.815 15.0 257.6 21.197 47.0 258.5 27.354 79.0 262.2 30.556 80.0 244.3 30.772 245.0 243.8 36.523 410.0 244.1 38.819 16.0 258.5 21.336 48.0 258.5 27.670 80.0 262.0 30.555 85.0 244.2 30.796 250.0 243.8 36.728 415.0 244. 38.825 17.0 259.5 21.438 49.0 258.7 27.967 81.0 262.2 30.559 90.0 244.3 30.840 255.0 243.8 36.929 420.0 244.1 38.828 18.0 259.9 21.521 50.0 258.6 28.251 82.0 262.0 30.563 95.0 244.2 30.882 260.0 243.8 37.120 425.0 244.1 38.833 19.0 260.6 21.587 51.0 258.9 28.515 83.0 262.2 30.561 100.0 244.3 30.940 265.0 243.9 37.283 430.0 244.2 38.839 20.0 260.8 21.635 52.0 259.0 28.758 84.0 262.0 30.561 105.0 244.2 31.011 270.0 243.9 37.451 435.0 244.1 38.839 21.0 261.1 21.679 53.0 259.3 28.983 85.0 262.2 30.562 110.0 244.2 31.093 275.0 243.9 37.602 440.0 244.2 38.843 22.0 261.3 21.718 54.0 259.3 29.191 86.0 262.0 30.565 115.0 244.2 31.192 280.0 243.9 37.747 445.0 244.1 38.843 23.0 261.5 21.755 55.0 259.8 29.381 87.0 262.1 30.565 120.0 244.2 31.306 285.0 243.9 37.882 450.0 244.1 38.850 24.0 261.6 21.790 56.0 259.8 29.544 88.0 262.0 30.567 125.0 244.2 31.429 290.0 243.9 37.996 455.0 244.1 38.852 25.0 261.8 21.832 57.0 260.0 29.693 89.0 262.3 30.565 130.0 244.1 31.567 295.0 243.9 38.100 460.0 244.1 38.854 26.0 261.6 21.881 58.0 260.1 29.827 90.0 262.0 30.561 135.0 244.1 31.719 300.0 243.9 38.200 465.0 244.1 38.854 27.0 261.7 21.943 59.0 260.5 29.941 91.0 262.2 30.565 140.0 244.1 31.882 305.0 243.9 38.281 470.0 244.1 38.857 28.0 261.5 22.022 60.0 260.6 30.048 92.0 262.1 30.564 145.0 244.0 32.059 310.0 244.0 38.361 475.0 244.2 38.858 29.0 261.6 22.117 61.0 260.8 30.136 93.0 262.2 30.564 150.0 244.0 32.251 315.0 244.0 38.418 480.0 244.1 38.857 30.0 261.4 22.235 62.0 260.9 30.208 94.0 262.1 30.563 155.0 244.0 32.449 320.0 244.0 38.467 31.0 261.4 22.380 63.0 261.2 30.274 160.0 244.0 32.651 325.0 244.0 38.526 OBSERVED EXPERIMENTAL DATA FROM RUN 64 OBSERVED EXPERIMENTAL DATA FROM RUN 66 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN OF CM.0 81.9 -.. 27.0 264.3 25.449 54.0 268.2 32.088.0 82.3 —. —- 500.0 324.5 33.686 1000.0 324.4 34.750 1.0 126.6 4.945 28.0 263.9 25.987 55.0 268.2 32.095 10.0 -—.- ----- 510.0 324.6 33.698 1010.0 324.3 34.771 2.0 158.9 8.499 29.0 263.3 26.549 56.0 268.2 32.101 20.0 315.0 32.163 520.0 324.6 33.710 1020.0 324.3 34.807 3.0 183.9 11.486 30.0 262.9 27.117 57.0 268.2 32.107 30.0 323.1 33.548 530.0 324.6 33.722 1030.0 324.3 34.833 4.0 202.7 13.931 31.0 262.8 27.665 58.0 268.3 32.109 40.0 324.0 33.644 540.0 324.6 33.736 1040.0 324.3 34.861 5.0 217.2 15.913 32.0 262.7 28.198 59.0 268.2 32.114 50.0 324.1 33.650 550.0 324.6 33.749 1050.0 324.3 34.889 6.0 228.7 17.405 33.0 262.6 28.706 60.0 268.3 32.115 60.0 324.0 33.645 560.0 324.533.760 060.0 324.3 34917 7.0 237.3 18.760 34.0 263.0 29.172 61.0 268.3 32.116 70.0 324.4 33.641 570.0 324.5 33.775 1070.0 324.3 34.945 8.0 244.2 19.746 35.0 263.0 29.606 62.0 268.4 32.120 80.0 324.3 33.637 580.0 324.5 33.789 1080.0 324.3 34.970 9.0 249.3 20.523 36.0 263.4 29.992 63.0 268.3 32.120 90.0 324.4 33.632 590.0 324.5 33.811 1090.0 324.3 34.996 10.0 253.7 21.132 37.0 263.6 30.341 64.0 268.4 32.122 100.0 324.3 33.627 600.0 324.5 33.830 1100.0 324.3 35.026 11.0 256.9 21,602 38.0 264.2 30.648 65.0 268.3 32.122 110.0 324.3 33.624 610.0 324.5 33.846 1110.0 324.3 35.053 12.0 259.4 21.973 39.0 264.5 30.912 66.0 268.5 32.125 120.0 324.3 33.618 620.0 324.5 33.865 1120.0 324.3 35.084 13.0 261.1 22.256 40.0 265.0 31.140 67.0 268.4 32.128 130.0 324.3 33.614 630.0 324.5 33.881 1130.0 324.3 35.119 14.0 262.7 22.479 41.0 265.2 31.329 68.0 268.4 32.128 140.0 324.3 33.606 640.0 324.5 33.896 1140.0 324.3 35.147 15.0 263.9 22.658 42.0 265.8 31.488 69.0 268.3 32.128 150.0 324.3 33.603 650.0 324.5 33.911 1150.0 324.3 35.177 16.0 265.0 22.796 43.0 266.0 31.617 70.0 268.4 32.128 160.0 324.3 33.600 660.0 324.4 33.930 1160.0 324.3 35.217 17.0 265.7 22.909 44.0 266.5 31.725 71.0 268.4 32.128 170.0 324.3 33.598 670.0 324.4 33.949 1170.0 324.3 35.252 18.0 266.3 23.010 45.0 266.9 31.806 72.0 268.4 32.131 180.0 324.3 33.597 680.0 324.4 33.973 1180.0 324.3 35.284 19.0 266.7 23.107 46.0 267.3 31.875 73.0 268.4 32.132 190.0 324.3 33.596 690.0 324-4 33.992 1190.0 324.3 35.317 20.0 266.9 23.215 47.0 267.3 31.928 74.0 268.4 32.131 200.0 324.3 33.594 700.0 324.4 34.012 1200.0 324.43 3.5352 21.0 266.9 23.351 48.0 267.7 3A.969 75.0 268.3 32.132 210.0 324.3 33.592 710.0 324.4 34.033 1210.0 324.2 35.3824 22.0 266.9 23.536 49.0 267.6 31.999 76.0 268.4 32.132 220.0 324.2 33.590 720.0 324.4 34.053 1220.0 324.2 35.412 23.0 266.5 23.776 50.0 267.8 32.026 77.0 268.3 32.132 230.0 324.2 33.585 730.0 324.4 34.073 1230.0 324.2 35.439 24.0 266.2 24.091 51.0 267.9 32.049 78.0 268.5 32.132 240.0 324.2 33.585 740.0 324.4 34.094 1240.0 324.2 35.465 25.0 265.6 24.480 52.0 268.1 32.063 79.0 268.3 32.131 250.0 324.2 33.585 750.0 324.4 34.116 1250.0 324.2 35.491 26.0 265.0 24.939 53.0 268.1 32.075 260.0 324.2 33.578 760.0 324.5 34.135 1260.0 324.42 35.523 270.0 324.2 33.572 770.0 324.5 34.158 1270.0 324.2 35.553 280.0 324.2 33.570 780.0 324.5 34.180 1280.0 3243.2 35.575 290.0 324.2 33.572 790.0 324.5 34.202 1290.0 324.2 35.598 300.0 324.2 33.569 800.0 324.5 3354.224 1300.0 324.2 340 5.628 310.0 324.2 33.569 810.0 324.5 34.245 1310.0 324.1 35.650 320.0 324.3 33.564 820.0 324.5 34.266 1320.0 3242.1 35.673 330.0 324.3 33.568 830.0 324.5 34.295 1330.0 324.1 35.700 340.0 324.3 33.573 840.0 324.5 34.325 1340.0 324.1 35.725 350.0 324.3 33.579 850.0 324.5 34.349 1350.0 324.1 35.747 360.0 324.3 33.579 86(0.0 324.3 34.375 1360.0 324.1 35.773 370.0 324.3 33.583 870.0 324.3 34.396 1370.0 324.1 35.797 380.0 324.3 33.590 880.0 324.3 34.422 1380.0 324.1 35.817 390.0 324.3 33.593 890.0 324.3 34.453 1390.0 324.1 35.835 400.0 324.3 33.569 900.0 324.3 34.475 1400.0 324.1 35.860 410.0 324.3 33.6009 910.0 324.3 34.503 1410.0 324.0 35.881 420.0 324.3 33.6074920.0 324.3 34.529 1420.0 324.0 35.897 430.0 324.3 33.6178 930.0 324.3 34.551 1430.0 324.0 35.917 440.0 324.3 33.6203940.0 324.3 34.576 1440.0 324.0 35.935 450.0 324.3 33.626 950.0 324.3 34.604 1450.0 324.0 35.955 460.0 324.3 33..636 960.0 324.4 34.633 1460.0 324.0 35.975 470.0 324.3 33.654 970.0 324.4 34.667 1470.0 324.0 35.987 480.0 324.5 33.665 9 80.0 324.4 34.692 1480.0 324.0 36.005 490.0 324.5 33.673 990.0 324.4 34.718 1490.0 324.0 36.021

-318OBSERVED EXPERIMENTAL DATA FROM RUN 66 (CONT'D) OBSERVED EXPERIMENTAL DATA FROM RUN 68 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN 0F CM MIN OF CM MIN OF CM 1500.0 324.0 36.029 1580.0 324.2 36.098 1660.0 324.0 36.129.0 80.9 -. —- 175.0 324.5 33.313 350.0 324.9 34.923 1510.0 324.3 36.043 1590.0 324.2 36.109 1670.0 324.0 36.126 5.0 —.- ---- 180.0 324.5 33.329 355.0 324.9 34.983 1520.0 324.3 36.052 1600.0 324.2 36.116 1680.0 324.0 36.129 10.0 297.0 29.094 185.0 324.5 33.343 360.0 324.9 35.048 1530.0 324.3 36.065 1610.0 324.0 36.119 1690.0 324.0 36.139 15.0 317.8 32.047 190.0 324.5 33.365 365.0 324.9 35.118.1540.0 324.3 36.069 1620.0 324.0 36.120 1700.0 324.0 36.127 20.0 322.6 32.830 195.0 324.5 33.389 370.0 324.9 35.183 1550.0 324.3 36.080 1630.0 324.0 36.124 1710.0 324.0 36.127 25.0 323.8 33.059 200.0 324.5 33.416 375.0 324.9 35.237 1560.0 324.2 36.088 1640.0 324.0 36.129 30.0 324.2 33.129 205.0 324.5 33.443 380.0 324.9 35.298 1570.0 324.2 36.094 1650.0 324.0 36.133 35.0 324.2 33.167 210.0 324.5 33.473 385.0 324.9 35.368 40.0 324.3 33.185 215.0 324.5 33.514 390.0 324.9 35.426 45.0 324.3 33.194 220.0 324.5 33.547 395.0 324.9 35.490 50.0 324.3 33.206 225.0 324.5 33.591 400.0 324.9 35.563 55.0 324.3 33.212 230.0 324.5 33.637 405.0 324.9 35.613 60.0 324.4 33.216 235.0 324.5 33.682 410.0 324.9 35.696 65.0 324.4 33.220 240.0 324.5 33.732 415.0 324.9 35.771 70.0 324.5 33.225 245.0 324.5 33.780 420.0 324.9 35.845 75.0 324.5 33.226 250.0 324.5 33.837 425.0 324.9 35.917 80.0 324.5 33.226 255.0 324.6 33.882 430.0 324.9 35.988 85.0 324.5 33.226 260.0 324.6 33.931 435.0 324.9 36.054 90.0 324.6 33.231 265.0 324.6 33.980 440.0 324.9 36.125 95.0 324.5 33.231 270.0 324.7 34.031 445.0 324.9 36.199 100.0 324.5 33.233 275.0 324.7 34.081 450.0 324.9 36.273 105.0 324.5 33.235 280.0 324.7 34.131 455.0 324.9 36.336 110.0 324.5 33.238 285.0 324.7 34.178 460.0 324.9 36.389 115.0 324.5 33.241 290.0 324.8 34.234 465.0 324.9 36.437 120.0 324.5 33.244 295.0 324.8 34.286 470.0 324.9 36.464 125.0 324.5 33.245 300.0 324.8 34.342 475.0 324.8 36.481 130.0 324.5 33.250 305.0 324.8 34.392 480.0 324.7 36.480 135.0 324.5 33.252 310.0 324.8 34.452 485.0 324.7 36.488 140.0 324.5 33.256 315.0 324.8 34.508 490.0 324.7 36.485 145.0 324.5 33.263 320.0 324.8 34.561 495.0 324.7 36.493 150.0 324.5 33.266 325.0 324.8 34.622 500.0 324.7 36.492 155.0 324.5 33.273 330.0 324.9 34.678 505.0 324.7 36.492 160.0 324.5 33.284 335.0 324.9 34.737 510.0 324.7 36.493 165.0 324.5 33.291 340.0 324.9 34.796 515.0 324.7 36.488 170.0 324.5 33.298 345.0 324.9 34.862 520.0 324.7 36.487 OBSERVED EXPERIMENTAL DATA FROM RUN 69 OBSERVED EXPERIMENTAL DATA FROM RUN 70 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM MIN OF CM MIN 0F CM MIN OF CM.0 80.1 ----- 165.0 324.3 37.781 330.0 324.6 39.639.0 80.7 —. — 110.0 336.6 39.715 220.0 336.9 41.566 5.0 —.- -. —- 170.0 324.3 37.804 335.0 324.6 39.750 5.0 —.- -. — 115.0 336.6 39.740 225.0 336.9 41.678 10.0 288.2 32.446 175.0 324.3 37.825 340.0 324.6 39.831 10.0 319.2 34.946 120.0 336.6 39.771 230.0 336.9 41.770 15.0 315.5 36.243 180.0 324.3 37.854 345.0 324.6 39.913 15.0 329.8 38.344 125.0 336.6 39.814 235.0 336.9 41.876 20.0 321.7 37.233 185.0 324.3 37.881 350.0 324.6 39.996 20.0 334.2'39.228 130.0 336.6 39.856 240.0 336.9 41.991 25.0 323.3 37.514 190.0 324.3 37.914 355.0 324.6 40.083 25.0 335.7 39.473 135.0 336.7 39.908 245.0 336.9 42.101 30.0 324.0 37.605 195.0 324.3 37.945 360.0 324.6 40.173 30.0 336.0 39.551 140.0 336.7 39.967 250.0 336.9 42.214 35.0 324.1 37.635 200.0 324.3 37.983 365.0 324.6 40.260 35.0 336.1 39.587 145.0 336.7 40.045 255.0 336.9 42.328 40.0 324.3 37.649 205.0 324.3 38.031 370.0 324.6 40.353 40.0 336.2 39.601 150.0 336.7 40.120 260.0 336.9 42.439 45.0 324.3 37.657 210.0 324.3 38.073 375.0 324.6 40.439 45.0 336.3 39.610 155.0 336.9 40.215 265.0 336,9 42.546 50.0 324.3 37.662 215.0 324.3 38.123 380.0 324.6 40.523 50.0 336.3 39.620 160.0 336.9 40.294 270.0 336.9 42.655 55.0 324.3 37.665 220.0 324.3 38.172 385.0 324.6 40.611 55.0 336.3 39.630 165.0 336.9 40.389 275.0 336.9 42.755 60.0 324.3 37.670 225.0 324.3 38.223 390.0 324.6 40.696 60.0 336.6 39.639 170.0 336.9 40.488 280.0 336.9 42.848 65.0 324.3 37.673 230.0 324.3 38.279 395.0 324.6 40.788 65.0 336.6 39.638 175.0 336.9 40.585 285.0 336.9 42.927 70.0 324.3 37.676 235.0 324.3 38.336 400.0 324.6 40.870 70.0 336.6 39.637 180.0 336.9 40.691 290.0 336.9 42.983 75.0 324.3 37.678 240.0 324.3 38.388 405.0 324.6 40.942 75.0 336.6 39.636 185.0 336.9 40.792 295.0 336.9 43.021 80.0 324.3 37.681 245.0 324.3 38.455 410.0 324.6. 40.988 80.0 336.6 39.645 190.0 336.9 40.898 300.0 336.9 43.034 85.0 324.3 37.680 250.0 324.3 38.517 415.0 324.6 41.022 85.0 336.6 39.652 195.0 336.9 41.006 305.0 336.9 43.035 90.0 324.3 37.680 255.0 324.4 38.575 420.0 324.6 41.028 90.0 336.6 39.660 200.0 336.9 41.116 310.0 336.9 43.037 95.0 324.3 37.681 260.0 324.4 38.640 425.0 324.6 41.038 95.0 336.6 39.667 205.0 336.9 41.230 315.0 336.9 43.036 100.0 324.3 37.688 265.0 324.4 38.706 430.0 324.6 41.038 100.0 336.6 39.680 210.0 336.9 41.340 320.0 336.9 43.033 105.0 324.3 37.688 270.0 324.5 38.771 435.0 324.6 41.039 105.0 336.6 39.696 215.0 336.9 41.450 110.0 324.3 37.688 275.0 324.5 38.841 440.0 324.6 41.040 115.0 324.3 37.689 280.0 324.5 38.913 445.0 324.6 41.041 120.0 324.3 37.693 285.0 324.6 38.982 450.0 324.6 41.041 125.0 324.3 37.694 290.0 324.6 39.053 455.0 324.6 41.047 130.0 324.3 37.699 295.0 324.6 39.121 460.0 324.6 41.046 135.0 324.3 37.707 300.0 324.6 39.188 465.0 324.6 41.045 140.0 324.3 37.717 305.0 324.6 39.257 470.0 324.6 41.044 145.0 324.3 37.729 310.0 324.6 39.333 475.0 324.6 41.044 150.0 324.3 37.739 315.0 324.6 39.404 480.0 324.6 41.044 155.0 324.3 37.753 320.0 324.6 39.483 160.0 324.3 37.766 325.0 324.6 39.562

-519OBSERVED EXPERIMENTAL DATA FROM RUN 71 OBSERVED EXPERIMENTAL DATA FROM RUN 72 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT. TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN ~ c CM MI OF CM m F CMI O CM MIN OF CM.0 82.1 —. —- 115.0 337.0 34.185 230.0 337.2 35.939.0 84.9 ------ 500.0 337.5 40.432 1000.0 337.5 41.330 5.0. —-.- —. —- 120.0 337.0 34.208 235.0 337.2 36.043 10.0 -—.- —. —- 510.0 337.4 40.427 1010.0 337.5 41.380 10.0 308.8 29.440 125.0 337.0 34.233 240.0 337.2 36.150 20.0 331.3 39.341 520.0 337.4 40.426 1020.0 337.5 41.436 15.0 329.9 32.813 130.0 337.0 34.262 245.0 337.2 36.249 30.0 336.9 40.639 530.0 337.4 40.423 1030.0 337.5 41.483 20.0 335.0 33.673 135.0 337.1 34.302 250.0 337.2 36.354 40.0 337.4 40.734 540.0 337.4 40.423 1040.0 337.5 41.541 25.0 336.0 33.946 140.0 337.2 34.345 255.0 337.2 36.460 50.0 337.5 40.742 550.0 337.4 40.419 1050.0 337.5 41.596 30.0 336.6 34.043 145.0 337.2 34.398 260.0 337.7 36.571 60.0 337.5 40.744 560.0 337.4 40.420 1060.0 337.5 41.652 35.0 336.7 34.074 150.0 337.2 3^4.461 265.0 337.2 36.683 70.0 337.5 40.736 570.0 337.4 40.420 1070.0 337.5 41.713 40.0 336.8 34.087 155.0 337.2 34.533 270.0 337.2 36.794 80.0 337.5 40.730 580.0 337.4 40.422 1080.0 337.5 41.773 45.0 336.9 34.099 160.0 337.2 34.611 275.0 337.2 36.915 90.0 337.5 40.720 590.0 337.4 40.423 1090.0 337.5 41.832 50.0 336.9 34.109 165.0 337.2 34.694 280.0 337.2 37.029 100.0 337.5 40.716 600.0 337.4 40.423 1100.0 337.5 41.886 55.0 337.0 34.108 170.0 337.2 34.778 285.0 337.2 37.153 110.0 337.6 40.710 610.0 337.3 40.424 1110.0 337.5 41.955 60.0 337.0 34.108 175.0 337.2 34.868 290.0 337.2 37.272 120.0 337.6 40.700 620.0 337.3 40.425 1120.0 337.5 42.019 65.0 337.0 34.108 180.0 337.2 34.957 295.0 337.2 37.376 130.0 337.7 40.695 630.0 337.3 40.428 1130.0 337.5 42.079 70.0 337.0 34.110 185.0 337.1 35.047 300.0 337.2 37.456 140.0 337.7 40.682 640.0 337.3 40.434 1140.0 337.5 42.136 75.0 337.0 34.113 190.0 337.1 35.141 305.0 337.2 37,499 150.0 337.7 40.675 650.0 337.3 40.438 1150.0 337.5 42.199 80.0 337.0 34.115 195.0 337.1 35.236 310.0 337.7 37.522 160.0 337.7 40.669 660.0 337.3 40.448 1160.0 337.5 42.257 85.0 337.0 34.124 200.0 337.1 35.331 315.0 337.2 37.524 170.0 337.7 40.662 670.0 337.3 40.460 1170.0 337.5 42.316 90.0 337.0 34.130 205.0 337.1 35.432 320.0 337.2 37.530 180.0 337.7 40.651 680.0 337.3 40.465 1180.0 337.5 42.374 95.0 337.0 34.135 210.0 337.1 35.534 325.0 337.2 37.529 190.0 337.7 40.645 690.0 337.3 40.481 1190.0 337.5 42.427 100.0 337.0 34.145 215.0 337.2 35.634 330.0 337.2 37.528 200.0 337.7 40.640 700.0 337.3 40.485 1200.0 337.5 42.484 105.0 337.0 34.152 220.0 337.2 35.733 335.0 337.2 37.526 210.0 337.7 40.630 710.0 337.3 40.497 1210.0 337.5 42.534 110.0 337.0 34.165 225.0 337.2 35.836 220.0 337.7 40.625 720.0 337.3 40.513 1220.0 337.5 42.586 230.0 337.7 40.615 730.0 337.3 40.520 1230.0 337.5 42.625 240.0 337.7 40.610 740.0 337.3 40.524 1240.0 337.5 42.674 250.0 337.7 40.607 750.0 337.3 40.542 1250.0 337.5 42.717 260.0 337.6 40.595 760.0 337.4 40.553 1260.0 337.5 42.762 270.0 337.6 40.588 770.0 337.4 40.565 1270.0 337.5 42.801 280.0 337.6 40.581 780.0 337.4 40.585 1280.0 337.5 42.839 290.0 337.6 40.580 790.0 337.4 40.601 1290.0 337.5 42.877 300.0 337.6 40.573 800.0 337.4 40.616 1300.0 337.5 42.902 310,0 337.5 40.569 810.0 337.4 40.634 1310.0 337.5 42.929 320.0 337.5 40.560 820.0 337.4 40.661 1320.0 337.5 42.954 330.0 337.5 40.557 830.0 337.4 40.685 1330.0 337.5 42.981 340.0 337.5 40.552 840.0 337.4 40.704 1340.0 337.5 43.009 350.0 337.5 40.548 850.0 337.4 40.732 1350.0 337.5 43.027 360.0 337.6 40.540 860.0 337.5 40.762 1360.0 337.5 43.036 370.0 337.6 40.531 870.0 337.5 40.793 1370.0 337.5 43.049 380.0 337.6 40.494 880.0 337.5 40.827 1380.0 337.5 43.060 390.0 337.6 40.484 890.0 337.3 40.863 1390.0 337.5 43.074 400.0 337.6 40.480 900.0 337.3 40.898 1400.0 337.5 43.078 OBSERVED EXPERIMENTAL DATA FROM RUN 73 410.0 337.6 40.470 910.0 337.3 40.932 1410.0 337.5 43.085 420.0 337.6 40.464 920.0 337.3 40.971 1420.0 337.5 43.082 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT 430.0 337.6 40.462 930.0 337.3 41.013 1430.0 337.5 43.082 MIN OF CM MIN OF CM MIN OF CM 440.0 337.6 40.457 940.0 337.3 41.050 1440.0 337.5 43.086 450.0 337.6 40.450 950.0 337.3 41.088 1450.0 337.5 43.085.0 81.1 —. —- 90.0 346.1 26.277 180.0 346.1 28.378 460.0 337.5 40.436 960.0 337.3 41.134 1460.0 337.5 43.083 5.0 -—.- —. —- 95.0 346.1 26.316 185.0 346.1 28.536 470.0 337.5 40.435 970.0 337.3 41.179 1470.0 337.5 43.082 10.0 325.2 22.429 100.0 346.1 26.366 190.0 346.1 28.691 480.0 337.5 40.432 980.0 337.3 41.220 1480.0 337.5 43.077 15.0 341.1 25.183 105.0 346.1 26.423 195.0 346.1 28.854 490.0 337.5 40.428 990.0 337.5 41.274 20.0 344.1 25.671 110.0 346.1 26.505 200.0 346.1 29.011 25.0 345.1 25.948 115.0 346.1 26.597 205.0 346.1 29.174 30.0 345.8 26.050 120.0 346.1 26.702 210.0 346.2 29.329 35.0 346.0 26.117 125.0 346.1 26.815 215.0 346.2 29.482 40.0 346.0 26.145 130.0 346.1 26.941 220.0 346.2 29.619 45.0 346.0 26.160 135.0 346..1 27.072 225.0 346.2 29.714 50.0 346.1 26.166 140.0 346.2 27.213 230.0 346.2 29.756 55.0 346.1 26.176 145.0 346.2 27.352 235.0 346.2 29.773 60.0 346.1 26.182 150.0 346.2 27.493 240.0 346.2 29.780 65.0 346.2 26.191 155.0 346.2 27.639 245.0 346.2 29.782 70.0 346.2 26.199 160.0 346.2 27.788 250.0 346.2 29.779 75.0 346.2 26.211 165.0 346.2 27.936 255.0 346.2 29.780 80.0 346.2 26.222 170.0 346.1 28.083 260.0 346.2 29.778 85.0 346.2 26.243 175.0 346.1 28.233 265.0 346.2 29.776 OBSERVED EXPERIMENTAL DATA FROM RUN 76 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT MIN OF CM MIN OF CM MIN OF CM.0 79.6 —. —- 380.0 345.3 40.783 760.0 345.1 41.892 10.0 322.5 37.515 390.0 345.3 40.781 770.0 345.1 41.965 20.0 343.8 40.786 400.0 345.3 40.773 780.0 345.1 42.050 30.0 345.1 41.016 410.0 345.3 40.774 790.0 345.1 42.132 40.0 345.2 41.035 420.0 345.3 40.780 800.0 345.1 42.212 50.0 345.3 41.033 430.0 345.3 40.781 810.0 345.1 42.290 60.0 345.3 41.029 440.0 345.3 40.786 820.0 345.1 42.373 70.0 345.3 41.026 450.0 345.3 40.792 830.0 345.1 42.453 80.0 345.3 41.019 460.0 345.3 40.795 840.0 345.1 42.532 90.0 345.3 41.017 470.0 345.3 40.806 850.0 345.1 42.609 100.0 345.3 41.005 480.0 345.3 40.817 860.0 345.1 42.680 oUAI r-KOM RUN 75 110.0 345.3 40.997 490.0 345.3 40.824 870.0 345.1 42.756 120.0 345.3 40.988 500.0 345.4 40.832 880.0 345.0 42.828 TIME TEMP. HEIGHT TIME TEMP. HEIGHT TIME TEMP. HEIGHT 130.0 345.3 40.980 510.0 345.4 40.837 890.0 345.0 42.893 MIN OF CM MIN OF CM MIN OF CM 140.0 345.3 40.971 520.0 345.4 40.850 900.0 345.0 42.942 150.0 345.3 40.942 530.0 345.4 40.870 910.0 345.0 43.009.0 81.8 —. —- 110.0 346.0 40.132 220.0 346.1 42.013 160.0 345.3 40.932 540.0 345.4 40.885 920.0 345.1 43.063 5.0 ----- —. —- 115.0 346.0 40.212 225.0 346.1 42.110 170.0 345.3 40.928 550.0 345.4 40.910 930.0 345.1 43.124 10.0 329.7 35.626 120.0 346.0 40.286 230.0 346.1 42.220 180.0 345.3 40.917 560.0 345.4 40.933 940.0 345.1 43.167 15.0 339.6 38.686 125.0 346.0 40.339 235.0 346.0 42.345 190.0 345.3 40.911 570.0 345.4 40.953 950.0 345.1 43.222 20.0 344.0 39.471 130.0 346.0 40.417 240.0 346.0 42.482 200.0 345.3 40.901 580.0 345.4 40.971 960.0 345.1 43.270 25.0 345.4 39.689 135.0 346.0 40.505 245.0 346.0 42.624 210.0 345.3 40.888 590.0 345.3 41.002 970.0 345.1 43.309 30.0 345.9 39.743 140.0 346.1 40.590 250.0 346.0 42.782 220.0 345.3 40.874 600.0 345.2 41.032 980.0 345.1 43.339 35.0 345.9 39.763 145.0 346.1 40.687 255.0 346.0 42.940 230.0 345.3 40.865 61,0.0 345.2 41.067 990.0 345.1 43.372 40.0 345.9 39.773 150.0 346.1 40.789 260.0 346.0 43.085 240.0 345.3 40.864 620.0 345. 4.106 1000.0 345.1 43. 93.45.0 345.9 39.711 155.0 346.1 40.190 265.0 346.0 43.201 250.0 345.3 40.857 630.0 345.2 41.141 1010.0 345.1 43.418 50.0 345.9 39.786 160.0 346.0 40.982 270.0 346.0 43.268 260.0 345.3 40.844 640.0 345.2 41.180 1020.0 345.1 43.432 55.0 345.9 39.792 165.0''346.0 41.081 275.0 346.0 43.294 270.0 345.3 40.841 650.0 345.2 41.225 1030.0 345.1 43.452 60.0 346.0 39.802 170.0 346.0 41.170 280.0 346.0 43.313 280.0 345.3 40.833 660.0 345.2 41.277 1040.0 345.1 43.467 65.0 346.0 39.811 175.0 346.0 41.269 285.0 346.0 43.318 290.0 345.3 40.828 670.0 345.2 41.321 1050.0 345.1 43.473 70.0 346.0 39.790 180.0 346.0 41.371 290.0 346.0 43.320 300.0 345.3 40.820 680.0 345.2 41.370 1060.0 345.1 43.483 75.0 346.0 39.798 185.0 346.0 41.446 295.0 346.0 43.316 310.0 345.3 40.816 690.0 345.2 41.421 1070.0 345.1 43.489 80.0 346.0 39.813 190.0.346.0 41.513 300.0 346.0 43.319 320.0 345.3 40.808 700.0 345.2 41.478 1080.0 345.1 43.498 15.0 346.0 39.834 195.0 346.0 41.594 305.0 345.9 43.314 330.0 345.3 40.800 710.0 345.2 41.547 1090.0 345.1 43.494 90.0 346.0 39.870 200.0 346.0 41.673 310.0 345.9 43.307 340.0 345.3 40.798 720.0 345.2 41.609 1100.0 345.1 43.487 95.0 346.0 39.919 205.0 346.0 41.753 315.0 345.9 43.304 350.0 345.3 40.796 730.0 345.1 41.675 1110.0 345.1 43.485 100.0 346.0 39.979 210.0 346.1 41.832 360.0 345.3 40.793 740.0 345.1 41.747 105.0 346.0 40.053 215.0 346.1 41.920 370.0 345.3 40.788 750.0 345.1 41.820

REFERENCES 1. Atoji, M., "Anhydrite Obtained by the Dehydration of Gypsum", J. Chem. Phys., 30, 341-2 (1959). 2. Atoji, M. and Rundle, R. E., "Neutron Diffraction Study of Gypsum, CaSO4.2H20", J. Chem. Phys., 29, 1306-11 (1958). 5. Avrami, M., "Kinetics of Phase Change. I", J. Chem. Phys.o 7, 1103-12 (1939). 4. Avrami, M., "Kinetics of Phase Change. II", J. Chem. Phys., 8, 212-23 (1940). 5. Avrami, M., "Kinetics of Phase Change. III", J. Chem. Phys., 9, 177-84 (1941). 6. Barshad, I., "Calibration of Differential Thermal Analysis Apparatus", Am. Mineral., 37, 667-94 (1952). 7. Biltz, W., "The Volume of Water in Calcium Sulfate Hydrates", Z. anorg. allgem. Chem., 143, 231-2 (1925), C. A., 19, 1978 (19257. 8. Bradley, R. S., Colvin, J., and Hume, J., "On the Mass Rate of Reactions in Solids", Proc. Royal Soc. London, 137A, 531-41 (1932)o 9. Bragg, W. L., Atomic Structure of Minerals, Cornell University Press, Ithaca, N.Y., 1937, PP. 128-31. 10. Braggs, W. L., and Claringbull, G. F., The Crystalline State, Vol. 4, "Crystal Structure of Minerals", Cornell University Press, Ithaca, N.Y., 1965, pp. 139-42. 11. Budnikoff, P. P., "The Rate of Dehydration of Calcium Sulfate at Different Temperatures", Kolloid-Z, 56, 97-99 (1929). 12. Budnikoff, P. P., and Schtschukareva, L. A., "Concerning the Kinetics of Calcium Sulfate Dehydration", Kolloid-Z, 73, 334-39 (1935). 135 Bunn, C. W., Chemical Crystallography, Oxford University Press, London, 1945, pp. 74-77, 14. Caspari, W. A., "Calcium Sulfate Hemihydrate", Nature, 155, 648 (1934). 15. Caspari, W. A., "Calcium Sulphate Hemihydrate and the Anhydrites, I-Crystallography", Proc. Royal Soc. Londo A155 41-48 (1936). -320

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