EMB-8 AN EVALUATION OF THE DISCREPANCY BETWEEN EXPERIMENT AND THEORY FOR A TYPICAL PRESSURE DISTRIBUTION TEST AT A MACH NUMBER OF 1.93 by W.H. Dorrance

ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN Re port No. EMB-8 Copy No. _ AN EVALUATION OF THE DISCREPANCY BETWEEN EYPERIMENT AND THEORY FOR A TYPICAL PRESSURE DISTRIBUTION TEST AT A MACH NUMBER OF 1.93. Pre pared bv,.; W. H, Dorraxoce Approved by 2', 14 i November 29, 1948

,l/ -n s: 2?`

U ANIVERSIT OF M ICHIGA NE 4TA-bj OF CO!TEWTS Intrcnu ticn * *. * o * * * * a a.. o * ~ ~ * 1 S 3ir v 3 * * a a a 4 a a a a a a a a a a a a * a o 2 Siynbs C.$... c * *. * * * * * *.. * * * * ~ * * 4 Discus:sici e a a.. a a a. a a *.. 0 0 0 4 The Effect+s of Msach Nwber Vaiation o on Pressures Coefficient..... * * * 5 The Effects of P P ande Variation on Pressure Coeffic- ent q. o. 0 6 The Effects of -Anule of Attack Deviation on Prossure Coefficient 0 0 o ~ ~ ~ ~ ~ o ~ ~ 8 The Effects of Vertex Angle Deviation on Fressure C oeftiolent 0 *.. * a.0 o a o 0 * * * * 8 The Effect of Bcundary Layer on Pressure Coefficiont..* * + 0 0., 0 j *.. a a a. a o 9 A Check on Test; Data Cosselncy.. * ~ ~ 1) SummXry of Conclusions 0 * *. * * * 0 ~ ~ o. 12 References.*. ~ * * * ~ ~ ~ * ~ * * * ~ ~ ~14

ENGINEERING RESEARCH INSTITUTE. EMB UNIVERSITY OF AMICHIGAN ge In+troduo ti on Er~,,ri;:att&al Dressure di,~tribation o ver supersonic models ar3 being condutead at a Maohl Nu-iber of 1.93 at the Univwrsity of Miohigan Supersonio Wind Tunnel*. oncuzront167 w~ith tihes toes s theorotical pressure distributions are beizn dotormined using the linoarized theories, Taylor and Macooll theory for cones and ho e thl dimensional method of characteristios. The fir4t of the series of tests wire run on the simple model of a 2Co incrllided anglo cono. An analysis is mado in this report of the di soropea:cy present bot-woen theor3otical.ld oX rimen-*l1 values of yreassureo cofficient for -the. 20~ cone rmodel1

On the basis of the investigation reported herein the following conclusions are drawn regarding pressure test variables in the 200 cone test. 1. The effects of viscosity which are neglected by theory account for about 30% of the deviation in pressure coefficient values between experiment anti theory. 2. Tunmel Maoh Nuxber variation is slight in the region of the cone model and had very little effect on the values of presstre coefficient. 3. The variation of Po and Po versus test section position q Pa along the centerline of the model can effect values of pressure coefficient sigraf'icantly. 4. The effects of incorrect reading or deviation of angle of attack can be counteracted to a reasonable extent by averaging values of pressure coefficient diametrically opposed at each station. This report examines.the test parameters discussed abo7e and evaluates their effects upon the experimentally determined values of pressure coefficient, On the basis of this analysis it was conoludod that an error exists in the experimental values of pressure coefficient possibly due to erroneous recorded values of the pressure ratios _, Po and L ~L q Pa Po 4

ENGINEERING RESEARCH INSTITUTE ]EM-8 tUNIVERSITY OF MITCfHIGAN Page 3 symbol. Cp - Pea preessure coefficOi ent q CPT~: Taylor-Maccoll tleoretical pressure coefficient mD - CPT r s drag coefficient of cone given by M*I.T. tables 2 1 m lenigtb of cone model surfsae element M u free etrezan Mach Number p u loctO static pressure p = free stream static pressure q = Q V2 = free stensm dynamnc pressure R a V1 Reynolos Ntu.boe of cone srfaoe V m freo streao ve loci ty'X angle of attack:- 1.4C05 ratio of specific heats for air $'q "angle of roll measured from vertical reference plane Gs - semi-vertex angle of cone p = fr*ee stream density I" C coo off ~ci ent of Vi sCOsit? I, II, III, IV, V =:eridian planes at 00, 45~ 900, 1350 and 180 res pectively

ENGINEERING RESEARCH iNSTIIWTE Pag Ebl~EMB-,UNIRVERSITY OF MI4CHIG(AN i. 4 Dis t; u) It A sesries of proessure dist.rib.lution tests was run orn a 200 included arnje coo;- e rrodel at a Mac. Ntrber of 1*9. and was reported in Reference 1. Included in these tests were rius at about 00 anile of attack. The theoretical values of pressure coefficient as dterrmined by the exactf Taylor4-'aecol) t}l or>; and the linearized theory were determined and conpared rC t }t the exserirental vliues. (Figure 1) Ex&arina-tion of thlle plot oF pressure coeffici.ent C vereus axial station for the 20~ cone r veals a dscrt)paicy of ACp 0.022. (Figure 1) An investigation was ma8de into the t est rameters that affect the surf~ace pressures and the pressure coeffio ennto Pressure coefficient as plotted in Reference I was based on the follo,wing expressiono. Pa whEere: M -:.9 (average value) u = 1.406 In this formnu1 P/Pa: j_ X Po Po Pa whore nrzmare value at each station along the tunnel oonterline. Since this corrected value of Po was used it is believed that the Pa largest source of deviation lies in the choice of the average value of M s 1*3. To check the value of Cp obtained by using formula (1) an alternative formula for Cp was used. This ist (2) Cp P'0 P P I In this formulsa tihe plots of the variation Pa aid q along the Po Po length of thet modi.el were prepared by the wirnd tunn-el group and used throughout the data reduction process.* It was decided, however, to use a mean value of. to reduce labor and time oorismingS calculations. P0

EMB-8 ~ENGINEERING RESEARCH INSTITUTE l, FB-3[8 UNIVERSITY OF'MICHIGAN The list of test variables which can affect the values of pressure coefficient as expressed by equations (1) and/or (2) and the experiment;al values of pressure are listed below with their rawges of variati on 1o Mach N=mbeM M l.lbs = M,.93 Average M 1 93 at model centerline 2. Stagnation to ambient pressure ratio Po Pa 6o980S Po- 7.030 Average Po - 70050 P& Pa 3. Stagnation to dynamic pressure ratio Po q 2.68 S Po 5 2o695 Average Po 2.686 q q 4. Angle of attack variation 00 < <2 5* Vertex angle variation 200001 28, - 200091 6. Boundary layer increasing the effective cone angle. Each of these parareters will be disoussed in the following text..i#.e Effecte of 40W iinizaeber on Pres sure Croeffiient. The effeot of Mac'r variation in equation (1) is apparent when the s8arlleet possible value of M 1in the region of the model is used to calculate pressure ooeffioiento The variation of M in the region of the nodel is shown in the following sketcho

ENGINEERING RESEARCH INSTITUTE! Patge.........,UNIVERSITY OF MICHIGAN,Page / --- 3 S. ~-1 / 3 M=/5 Z M "13 M —/.?-S/s. The value of Cp based on M' 1*93 showrn in Figure 1 is Ptm c -.129 If the extroeme value of M 1.915 is taken the value of the mean Cp becomes9 p 1.-31 This yields a ACC C.002 ai'd is no+ eonsidered a sigrificnt change in C P The E4'focts of, Pt an Psn Pressure Coefficient The effects of variattiol., in stagnittion to anr mbient pressure ratio Po and stagnation to dynanic pressure ratio Po are discussed Pa q together. The ranges on these parameters are given below. 6.980 o. 7.030 a,

ENGINEERING RESEARCH I]NSTITUTE EM-B._8 UNIVERSITY OF MtIC-liG;AN 7 and, 2oe380 4 Po 2.695 q Using extremal values of these parameters in the expression for pressure coefficient (2) an idea of the range of values in expexi'mental Cp can be obtained. Cp - PP: The values of P/Po from test data fell into the following range when values straying obviously from the mean were neglected..1890,.192 Average p A s1907 P0 P0 Using extremal values to determine the experimental range of C there results; 1 C max 1 - (l1327 P p 2.95 C miln i 1890 - 60980) =.12257 P 1 2.68 Henee, the experimental pressure ooefficient lies within the range, Figure 1.12.257 C 1327 Usini mean values of P taken from experiment along with mean values of Po and PQ will give a mean experimental value of Cp to Pa q compare wi.th the mean value plotted on Figure 1 obtained in Reference 1 using equation (1)o This is, 1 a,% pmean U 1907 =;o * 1286 This value is substscnztlly the same as that founr using expression (1I) whi h $tri

ENGINEERING RESEARCH INSTITUTE EMB-.8e NUNIVERSITY OF'MICHIGAN 8 C mean- ~~ \- 2 a o129 ave0 1.405S x 1j.9S Sinoo mean values for P, P0 and P were taken throughout in the calculations to deterrmine Cp mean above it is concluded the figiure represented by Cp o12"9 is as correct as oan be reasonably determiined using the data made available. the *f e- of An le oM.,- k vitLo iocn rerssur'Coooeffcicen There was a rsvxige of angle of attack variation which is oiven beI rat.at w i This renge was obltined by measuring the aigle between the cent erl i.ne of the cone and a vertical reference lire in the Schlieren photographs.I Reference 3 8as shown that tajling the mean Nvaluet of two pressure re8dilngs on a cone sxrface at twoe points diametruically opposed when the cone e at a4 slitht a l-e of attack will yield the zero angle of attack value. Since readings were taken at 0O roll and 1800 untder similar conditions it is reasonable to assume under the hypothesis above that the mean value ofb is close to the correct vslme. Thus the effect; o` sligiht amew cf e -i-tWrk is r. lCd Iel ii'te. st'*3 c-J~ * f {t.&tX 6awl The<ia-/ c-z.t 1m?Presireu Cte>f> 5 ct e-nt.+ The theoretdoil vl!ue of Cp for a 200 vertex angle cone at a Maoh NtUmber 1.93 was extrapolated from tables given in Reference 4. These tables were assembled from calculations based on thc acclrate TaylorMaceooll theory for cones. According tc Reference 4 such extrapolation is permissible. The value of Cp thus determined and plotted In Figure 1 is givon belcVwo Cp a.10672 Since it is impractical to expect the true cone angle of t1he model to be exactly 200 a series of measurements was made of the vertex angle. Readings were taken in the planes illustrated below as the model ras clamped rigidly in a lathe chuck. Readings (1) and (2) were taken in planes diametrically opposedo Readings (3) and (4) were also taken 1800 apart and 90~ fromr the plane of readings (1) and (2). Readings (5), (6), and (7) were taken in the orifice planes of the model as sketched below. ( 3 ) - _ _ _

ENGINEERING RESEARCH INSTITUTiF P EM3- 8 t:NI\,Er:R:u',,TY (M)o M:ICHIFIGA.N 9 The mean of readings (1). (2), (3), and (4) was taken and compared with tre mean of readings (5), (6) and (7)* On the basis of these readings it was dectided that the true vertex angle was 2'3 s 0 20~ 61 Usitng thdis value for 20 t-he theoretical value of Cp for TM' 1.93 wae deteorartdned againo This value was The if rtArnce bertweorn thdis value a,.nd t1e Ienl e:Xtl ri;:oitaIl Value was attributed to boeuntry lyer growth. Tids differeucoe I, ~:tfc,f So,~dLxL0 Laxe' 1 on Praucro Coef>fi'i exit On the basis of the experimental value of Cp -,1286 the effective oone angle can be determined for M m 1e93. Using the Taylor-Maccoll theory the apparent effective cone angle is, (e8) a 11l180 effective From whdch the apparent &0 a due to boundary layer is determined. This is AOG s (es) s0 )' 11.180 10l050 effective measured AO: 1.130 On the basis of this apparent Ahs a boundary layer thickoness oan be determined. This is, for the cone model, where: 1 - length of corne surface element C 3.10 6 boundary layer thickness at end of Ocrne element 51'- toanAs A 3,10 x ttan 1.10 It is apparent that the boundary layer thickness 5 nust be thds value if the experimental values of C p are to be consistent with the theoretical values of Cp.

ENGINEERING RESEARCH INSTITUTI g ]/B-8 } UNIVERSiTY OF MICHIGAN 1.0 Referenoes 5 and 6 have determined that boundary layer formulas for laminar and turbulent flow are unaffected by Mach Number variation in the low supersonic range. Using the faniliar expressions for boundary layer thick8esss for laminar ard turbulent flow over flat plates an order of magnitude of the thickness of the boundary layer to be expected over the cone can be determined. These formulas are given below including the numerical calculations, The Reynolds Ntmber of the wind tunnel test section is given as: R/ft = 3.92 x 106/ft The Reynolds Number of the cone model is then; R 2 3.92 x 106 x 1 =-3.92 x 106 x 3.10 3 1.012 x 106 12 For laminar flow &: 5.2*1: 5.2 x 3.10 _.01602".;7Br ~100 x 16 for w hich B3, = tan'l.01602 -.2930 3010 %nd, a aO$ + 08.*29 + 10.05 I 10.34~ effective the theoretical pressure coefficient for this cone angle is: (Figure 2) C _.11302 PT-M For turbulent flow 5 z * 76 -,_.376 x 3*10.0737" (R)1/5 (io0)12 X (1.012)02 for which - tal-.-0737? 1o360 3.10 and 8Os - Z3 + 0 - 1136.10.05 - 11.41~ effective

ENGINEERING RESEA4RCH INSTITUTE EMB-8 UNIVERSITY OF -MIC1HIGANI The theoretical pressure coefficient for this corne angle is: (Figure 2) CP -.1329 T3Eil - Thus the experimental value of Cp -.129 lies between the value for pressure coefficient including an allowance for a laminar boundary layer and the value for pressure coefficient including an allowance for turbulent boundary layero (Figure 2) That is, C + (ac) PT-M p laminar BoL. 0113 (C ) -': o129 P mear. experimental | CG + (ac ) o133 P turbulent B.L. Examination of a typical Schlierern photograph of the cone tests indioates that the boundary ap[!..ra to'oe linar,. Expertir?,*stz: urin b+, th NACA reported in Referenes 5 at, Rseynolds Nmbiors inaluding and excee3ding the Reynolds Number of the cone test showed that the boundary layer was laminar over bodies of revolution placed in a Mach Number 1.5 stream. Experiments reported in Reference 7 reported boundary layer thicknesses over models at Mach Numbers tabulated belowo Model 1058 M a 1*86 5:.020"n-.33" Model 22-588 M 1075 5:. 04" Model 11058 M: lo96 5 -.02" + Q04" Experiments over a cone in a Mach 1.75 free jet reported in Reference 9 found boundary layer thicknesses indicated below. 200 cone M 175 a m.0298" 300 cone 1M 1.75 58.0248" 40 cone M * l75 8.0294" These values are lear the value for a laminar bounda*ry layer over the surfaces tested. On the basi.e (o isf information atrid t-e: ays-is abover it is conzwc-lded t}mt the bo;ulndaryr layer over the cone modet was ne* a r l.n-iar rin char. btero A Check on. Test Dat.a'Jonristain. A chLeck was made tc deterine if' the d{icreeancye in pressure coef fi6c'r.nt was cons stnt in more recent testn s Po?l:u~ tap Cra t e 19E6.~ conicali nose o'~ awtih.t...r mede! t,$se- >,,,er' th; con no toi-e. at." a l slpied:'la.ou, XU,, cmp.,'isos 3.uar:.;seso The crileotr on this vostn were lccated as Shc;w in thi e QcI cw6ir sketch.

:/so g _4 _^w _ __ I _E Readings were taken at meridian planes I, II, III, IV, and V for seven iifferrlt rus at about zero angle of attack and averaged to yield a mean value. Table 1 gives the values of Cp for these readings. The mean value of experimental Cn p was C..123 The Taylor-4aoooll value for a 19oO0 cone was, Cp',10396 T-M To his theoretical value of C must be added an allowance for boundary layer effects and other ePfects included in the increment apparently present in the previous cone test made in similar circumstances. The nose of the bioonic model was tlhe same langth as the cone model so that the sa$ie discrepancy should be apparent if a consistant discrepanoy is present. This value of ACp was found to be ACp Y.0200 Adding this to the theoretical value C0PT- will give a vale for Cp which should be close to the experimental mean value. The two values are given belto (C) 01o23 P experimental mean QpT t (ACp) A.1C 040 +.0205.1245 The two values agree closely and the conclusion is made that the Iame discrepancy appears in both tes+s. Because a larger boundary layvr tdclkness then can reasonably be expected frot a near laminar boundary layer is needed to increase the

effetive cone angla to a valuae necessary to yield thle experimental press-ure coefficient it is concluded that the discrepancy between exrerimental and theoretical pressure coefficients canLot be completely accotulted for by viscous effectso The error between the experimental valise and the theoretical value based on a laminar bomndary layer is in tlhe region of ACp -013. The experimental scatter about the mean value of experimental Cp isA+AC "V.004 and - ACp.Q006. As illustrated in Figure 1. On the basis of this analyses a table of percentage error can be assembled for the cone testo The percents are expressed as percent of mean experimental pressure ooefficient. Percent discrepancy between experimental pressure 3< ooefficitent and Taylor-Maccoll prassure co fficient / Percent discrepancy between experimental pressure corw)fficient and theoretical press-uee coefficient Iz 1% corrected for a lam iar boundary layer, Percent error possibl3 using extremal experimental (+3.19%J val.as of FoP, I, anrd P7, q PG Pa On the basis of this evidence it is concluded that some unfore3ien quawlitty is affect-ing tne pressure data. This quantti ty may be present in t;he form of erroneous recordings of pross're ratios Po, P, and q_ *'"~~~D1

References 1. "Pressure Distribution and Force Coefficients on a 200 Cone Using Experimental and Theoretical Methods at Mach Number 1.93", by W. H. Dorranoe, University of Michigan Report EMB-5. 20 "Final Calibration Report on the Mach 2 Configuration, Excluding Balance System", by WO H. Curry, University of Michigan, U.M.E.R.I. Supersonio Wind Tunnel iPport WTM-45o 3. "Pressure Distributions Over a Cylinder with Conical or fIemispherioal Nose", by T. L. Cronvich, Applied Physics Laboratory, The Johns Hopkins University Report TG-10-4. 4o "Supersonic Flow of Air Around Cones", by Z. Kopal, Massachusetts Institute of Technology Report TR-1. 5< "Experimental Investigation of the Effectse of Viscosity on the Drag of Bodies of Revolution at a Mach Number of 1.5", by Chapman and Perkins, NACA RM A7A3l.. 6, "Experiments on Drag of Rievolving Discs, Cjylinders and Streamline Rods at High Speeds", by Theodorsen and Rezier, NACA ACR L4FI18 7. "Data on Boundar~y Layer Thiclkess for Models", by A. C. G. Mitchell, Applied Physics Laboratory, The Johns Hopkins University, Report APL-C F-118-N 8. "Experimental Determination of Pressure on the Surface of a Cone in a Supersonic Stream", by F. K. Hill, Applied Physics Laboratory, The Johns Hopkins University, Report APL-CF-53Q0-N. 9. "Pressure Survey on Cones in the Two-Dimensional 1.75aM Free Jet at F.G.S.", by F. Ko Hill, Applied Physics Laboratory, The Johns Hopkins University Report APL-CF-716-N.

~: F':'Tf~~rfi: 747717T,.t*r*' ~I? —-;~..; i~:~'-T'-J * -!-':-4-.'''! ——. —... 1'? 4 ~~ ~~~~~~~~~~~~~~-. -.- l — 1 — I~.'. ~t'i'~ - - ~ -"~ i~:'~'~-~'f;i.1. K- F;-f ~-"4: 4+ —.-~._ 1,..... i: - -~~~~~~~~~~~~~~~~~~~~~,.!-'-'..... 1~~~~~~~~~~~~~~~~~~~~' t'i"., [,.. I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. J. T __~_.. 1 4~~-! —F.4 "~ I-~~ ~ ~ ~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~ -'[ I I::~~~ ~~- 4-.1: 4 4 4 1 4 4 1 1~~~~~~~~~~~~~~~~~~'.....!-:,: i — — ~;-~i~: —— ~.....

I I.1..... ___ __ - - __ ___ -__ I. - -'..4;.I I,:-I- I- _'..1.'I-. 11 - —, 4- - :4_ -1 — __'II.I..I-; —dI -!.I, 71"_r'r.1.. -.- I -.- - -,I.-- -, f- - - I , -I.-' — =- —, — - -, :,i'tIIt I.I II-T' q.,,,-- II.'I-t 11'II-4- -1IIli,_-.1. + I:I.II.t-,%- 2- —, —, - 4 -II. —I,'!1 _4...,- I_''i -i,. ' -4'I - -. -. Irl11; -IIr... — r-I.-.I,.I- I_ - I. i-I11,;iTi..I. -'''.L:4-1'.. .',.',qI.7-7-I-...- _.c'.__ -'.. 11. —....III -11I'.Ii ",._4 -i _; -.''.' — _ -. —— I _ —,.,. -"..-— __. - - _- -4.-__ —- —..-__ - f —7 - -.-'t- -t —— LII ..II.IIS4111- II." - -I'..I-Ir-f -I... - 1. _.Ii.-..-,I.-,I. -I..,-,. t;t-. -, l-, -, —,-I:I —1, ".'7.",,..__.'-..4.,i.I. I —il'_I-. _.i,,i -+-. -_ -..iI'I;fi-T'-.I,,,1,,I,-III..I....-,,.,4",I;,i..I v1-,-A. — I- t I.. -.r.I.,I,,.. I..- It.I't_ —-. -...-_ II-t,-t,:L _.I'.I-IIo.._.- I:.I.t,--'-.. I.i_.''.:..- 7'''-I- -,. -1 -, - i,... I - ....;, -_-I. -I I -I! —...1;I —-, ...-, I. —-f — -II. - i "-", ,.I.t.-i, I.I -II-.I I,-.IL:4. -t —:. -. —.-I.I-T -_.-:.t. -I-1-T.,'- -_fI_.. _j"_ -4..'. -,I. — -I.I;tI,-:,4L-,I I.-';,- 1, — .1 -___ - -.1 __-. -I_'_ —II,.I4.II.`"'7 _' —11,I- -I 1--__,4 __'-_t;___, — — F_...I -_ —- -_ I..- I. —I-". _; v_.;' I4 -fi —— __.. -..I ——.. —.-I.-, I —-,I...'..- -i-..;4.p'_' ..I-. I..I: - _.I-'.-_ _- I- -_II -, _ I';:II-_ IIII'' —i-.7+I I.'.I.. -.-I.I —- -.I+ - —— I-.,-I.I.. I.I,I.1"I-..,-,.IliI._:-_.--I-, i-I-I.. I —I..4-, _' _i'.* — _ -, --:- f.. ..._'."_ I.1-1;_'l _- I. -..-I.Ii.III II I1 - j.,..L...:. . -j -,,.-. _ '..,-.,-I-. II- I."-.. — — I. —-, —I;..- I —,-i —4 _'', -I.I., - _ i —- -_.IIII -—.'''I..-'_ II —-.7,.I'.... +4 -4-t-. r.-. 11-. - - I .II.-... I- 11 —_..I. I41 -,. ".-Ii,..+..1.11 - il —.-..I!_-,- - -.14 -,.,...IIi.1I:I,,I I.' I.- _F_ Ii - t- -It -,,_.__'___4_ 'A-, —, ——, It I —-, —- --— '_ -I I. -1.I —- I,.II,, —:'; il-"- -'-'; -1-1: I,,- ___-_!_ - ___,_ ___'..t —,IMi I.-.,.... II-1.M.1.-.- ,I-_rl _. -. - -I-,! —'_'.-___.. - __'_ - -I.-__,I- _._ __ __;I..II.II-I II I -MMl _I- I..- _ L.MMd.M.I.rI.IMiM.MIII..I- r-1. —,,:. —— I a_'r:!.'I-II; I- 7 -.-_I1MII-M..,MI —I - II.M-'I.,__.!-!, —--- p,4IiI —I...1 1..I I.-.I-S.;_4 —-, _ -, I-1 im 4.,-I- fl-'.. - r. - I-,I —-— I — - i71II.MI-.I,-f -—.I —I.f-M - -I.- -._w 4_' -. M.'_ — I1III.M.:II;IM. -. I-:-I..-..- I- M,.III M.I. I:I1.-.4 —'-1, - M,-i.,,,,I.._'- L..+ f -t --r r 4-Lf- +. -.- I.- _ ---.-_.M MI.-'".I -MI ..I-a:,MIMiuIII -.T.IM1..:II.;IIM- IM.. .-IM; — .1..-,,M. I-M;-_I —1-I —It —.,..,-Ii. -_II i"I. —-,-, -IM- -, - - I-i -- -tM!II-I Ii''i-t'MI''-M.!-I;_-I -,-.- -T___l_ __iI - _1__I.I,I. --— It-:Ia:,, -__-I-T-.__ -..__ __-_____ I.M.'II-I ML-I-_..t-,.:,'M,M-_-,__"MI';. -.I..-- —.1 -1. . H_..1 -,M% IMI-,:;I.I I.- 4,-I.,,.-. I, IM-.M -4 t.,--, — 777" I — -- -_I..- — 1-. M..II.-, —- L-'AJL.I I.'w-I+_I_4II- -- It.M,I...MM.I,-I.I,-,-L......, m.+.. -. _; - . -.-,.,,-. M — I-I;, i-,I..I.-1..M,.-f___. - M-',. j- '-_iI'iA II!.I'Mt, —I. —. .' - " M-I- -I.M:. I,+,'IL-'II-.1-,I I.-.+- -..I-L - 4 -,- -'MiI-,. -.. — M. 1..-M,....1...-. IM-M-.- ml 1.-!_ -.4 -I.,;IIIIiaM — — --— I- --- - i, — 4- -.II,. —_!... IItIII..-,. II- _-.4- -,.,I I4-,rl-.....' 7 -,,- t. — -,, ---—, _ - M.-I-II - --- -—:..,MIIi.I1+I'.- - __ - -- ----:_LM -- - __-_ — _ I1I;IM-II.'-6 —-. —_ —_I-I-. -.'I,.;-mi - -II-M-7- -,I__J -.II —M..II-I I- -1. -.1. I-7 _.T-1 1 -1I- -_ .;.-.I_- _- --, 'II.i-.- I.MI. MIII,-.-4- ;!, Mt_; -,-. — _! — — M; - .-I —I-__ I -o- t:I -— I.- -II I+7-,7.... _' - — mm I.!M., — -1c I"rmrM I-.fI.:.4 M,4-,?q — -.'!M.I..-II.m,;' 4-I.,.-,. j,"L-: —?,'-'-',M-I11 II:' - - M!;'-,M --, +1 4,, -1-,4:1:I1 - _,'-,-I iI-'k,_.."i-.-. - , 4.- —, - -.M-i.__.,,'. -,.I-a-,: -..,'Ai1,,'I1,'x-.i;.,!,I.__ -,. -M. ',I.1, —— 1.-I11!.I__ . i'.7 I,.-'_ I M- I - IM.I.rMI,-. -.-,-.MI-.M._-'t- --'-,, -mlr:....I'.-M,- 1.I.17'_' M.,I. —-— I'-,I -_.-LII_;.1 t.,. 4w__.-_ Lm "-* —_ M-_i-M- i...-.II —.- _ 4-i.-, II-:I,," 1, - i- - -I J -.,!tv-:I-I -', I. ,- — -1- —,_ _ -,t- - f — -' - 4-, -;,,. -1I-IM-.... __ _= m-M- -— M:!; I-IIM-I-II.-I. -.Is.IJ;r;II'M-. —-II:-M —— II i .-I-I - — [ —- M''-, ".r.....I.-M- _...l. __ - -,-1,. _.,M.,..-iIIL'1-I:MI. —_r:.:I.II!'-I:;; — I.-:_'.I. I I III —.M I-'''-tI —— I --',.'-I —- It:'. .i.",. -II. ,-t !.-.-,-. - II.-' I -_-, It,!" I+ i.I,-II - IM.-M.,!-M.! IMII I,.M.II -- tI-,-rI-,-I.II -I-o- _-M I. —,.-M -,.I.!-I4. I.-I". II —-L-4-IIF'':IM- 4,t --— + I- -i I -a M —.-'2'- - 4,, -_+ 4 - _-, -M.,-.- I,. I.-Iv-.Ii.Mmi'j I -I-. -,,M!..,,II —1 IIII:II-!4r-III-,I!-M-, ;-'. — I..-.,. - _. —4-i- M,- -1 1. M.. I-" —. -I -I,TII:-I J-I.I,.iI_I-.."I — -+, —_:.; -4 i11 - --- - -. -1.' % —- --, -—.-M -M-I'L -,-, —, —M:;.-.1-M. —I-IIIIIM —;1.-.;-,,I. i,,L I+' M,''I'' -:- i M - iM.. ML- -''.I-II!-0 MIII I-I .. II,.- - t_; - ;7-iI-_-_ I 4-r- -6. o__ —_-..-_ - --- -I.- M-:-MII.I-I -_ "- - -I- -___- + _ —II --— t i. i'+ I _t -1,7-, —i-I-'- - -I!.'i- -- -I, MI- w -'1, —..-I4. -- II-..I,.4- t1 -4 _, M, I-! —I;I-f' -:!'-II.IIIII ——, -iI. II, I..r M -.I.-I..-.I-II,,,.- - I. -.II-I-I!,., — MI,,.i-:_ I,.,.,,i — — + —- -.,-Mi- - 4.. —. '.,-1.M--.. -, —,, w,.,MII,,I-1., —-.-: —,;! —_,-,,.I —.-.I-oI,;I.M0.IM. -I..I —IM:I't''.'mII-.-,4-4.i i:'.I..I.-....I. m.-_,M, I.t 1..L!.kM.;-.._(.- __'. . .1-IIi - t..I.. 1_1- 4 +.-_ -1,-_ It-I- i.I'. o'-, —--,,'-,1;.II M-IM.-:-I,M: -.I + -- -'-'Tr,_'l. -,-. 11 _;-M I.M. -,..-'IiII, M..I.I-I-t.m7-,- I.I-.,A.II-",t-,.. -111t-:i —-, -..MM.. —! —.II- -_I..- -,.i, - I — L -_..I. — Ii-.. __.-I.-.-.-.-,, —:-...-, - -..-I -."-4,II:.. T —, -.- I-1 - -.. - IMIIII I+-I- —.,'t 'M- — M.1 - MI —- I- ' _ T-'[ I,'..,_l!'i —t._- _mn Al:_,.f.-M.,_ I -I71-71III- -- - -7 -'-" t- --— :.-I _ -I.I,-IM -.I:I.'-1,-II — MI._.;I-....- I. -I;;I,,ImI-.I,I - :. - I4.I-T."I- -_4 M- m- r M M_,r —.-w, -M-.-,I.-i. —i.-J- - -.- I -4 -.4. -_-I- 4..-,,. , I.I.IMI.I-1 M.;M-..i -- 7i I-1-, +-I.i.,1 — - L- - t - -M I- III _ . __, M', i. -.. -- __i —-- " — -__ - —.'. --- __ _.: - I. —MI+.- -— +- I-I4- - +.-.....: _ - 4 1 -, -.!-....,..-'MI4II' —''' II-4.M11. —I-%M-4 — 4, —wI —- 4-' L- _.-.M-.-..!_.. -M.:;:" -I-4--'I-',,, w,.- -, -_ M-:I -t--:-,-, _;..-I4,-,, —-—, _ _+l I.Itt,tMI- —t-f-, i _I - 14 —11I-'L tI-t I, T`,I- r,.IIIMI t iI:' -4 II IM.,.MI — M —-- — II.;AII.t11L.i.-.I I.II I -7-1 -- m - - m m —-'-Z -M,!-711I -.- -m-c,.4 - -M-t.I. —,.I. LI - I-_.4 -._M,+_.._ii.: r'M,,_'r.1.. M- Ii_-IJ.-.-_ — - 4.-' 7-t-. 1. _Mi.M, ,-.Ir___-M7:II','.- ii'_.1 7.-_t -'-.. -"'- - -- —'L-II 'iI-,.II-.I -!IfI, —IIIMI II - — _;M' 4 -;-i -..M -I1-I.. i, I. -. ...'.- -L,, -, -I - -, -,__', — L,,+ —-i-4- i —l —-47-, - -+ -, — m + -- + —,-: -'.- - III-;+-4-I — MM.-I —, --,I -I . -I- 14II. -II-,._.,. IJ'I''T ., IT.%I.I-, —, _k_._..__,_. __._,TM-. _! -t. -I. —,-,-, -f- - ----.4 -I — f-.-. —'- f —7 —I-11III. -I-I. — T 7-,, —,- -:-- a1; -I- -1- 17 - I- -L-.- L I.-.,,-,..:.I...I..:.M,J.MI -i-:-,- -. —'r$1-'- - _11-tI - +_I!.i- - MM'_ -..'. -4- II, - .4-, —,-M - -4-t- r — TI,T-.- "-, 7itI.I.TII.iII- r4L —.,M.I.-f -- - —-M - -M- -M; II",.,,MI. I''M-1- M-,i_II:f-, --.- --- --.I- -..M.-.., i. -I; --- r. — 7;T'.. — —'- - T —7 —,1- f- —r M,-4 -I —.t II -M.I .-mmmI:.T 7IT-. - I: — +- I - I. - 4. - IMi. —4- I_ II I,:MM.,-,,,-II'.II. I_ ' -+ M-.,,-- --.. —-_"_-,.. -1 - . - M -. MI..IM. —i.- -- - _- i- VI.II_m L -. t-,..,,;iIII, 4-..' ..-.. —- I__IIIMIII --.i___ M-T.:';:, M- -.- -,.,,-,M —.-_ i - I- -. -_ 7..M..I..., —- r.II-!- --—:- -M-,..I. I-7. -T -.I - __ - tI-t- _111-ir _-.- - - —,-,- ._; -,-I _-, -,,_ -I.I _1 -_ -;- I.- - —....14 - 4-MM- —,-T - -,- — t i -'i' -. - t_. -,- I--tl -I- ,,-t'.,- --,!,-_'., - ,_ "_ - - -. . L!fiI.1,,,t —t417... r T —.L — I. M i - +. Ii'.. r #-IM -- T!- i-, I- M7 -1.,_ T1, -I- - 7-3, —-._-._ -.-.. — -_. - __. _+_'i- - - - 1. _+ -— 4-1- M -I- -.-Mq-o — I.iMII_77-'r, _7 - I- f- Tk)I.-. +lm! _1I' I,.., -.Lt_: I= -II --- - 11 _. .-..,- --,,,_1 -t- I' -H,, -I'II 7., —- — 1 —M _.;.- __'j~.-, ' -t —.7-..:..*-M-,.' 1 M L_.-1 - -- -,. I,"-I., rI- -- — I I — _4-I -1 -1;_ _ .I] -- _11!-` —t-'I.-4. III —-- -__".. — - -.Ii.I,-," --i- II -,;-. — t- -4- - . —." _ —;-. - 4 —-- -. III'' -I' MMMI-Ml-.+ Mt - - -T- - t-, -t-M. -,I,1 —4!-Ml -:,4 —4_r iII,.Mi..IiI AI.,.7 --- -MI-_41..- - -iI -:-I1.I_, -, - 4 - -4 - - -,-1-I:' v — — -. .-I - I-.-.-- ' — -- ---- I — I-I I'';I.?MFI-..-.4.- - t_ i- I1 _4 1 -M —I- IIM- tM —- _'.4I —! — t-.'- L-_. —i —4- +-,_M-.M-.M. Ii.' II-.I-IM -1.M-. -M.I_ —m 1.I-.-_I..+.. -.. 1. MI I-.41 I I-.,,It.. Ii -4-11i —'4 - I - L."_: 1. —Mw__'I.M.-II,:-,-:!,-,:- --;,.Iw-I ._ -4,_ 1 ,.MI14. M4.-,' f —i+-", —-,-.6.I-: -. —..I IMI.II-i 'GIiI'II i -- -. -_ -M-M.IITf.MI —, M.-I — IM.I — -— g- -4i17'-_I,,-IIIi:I'.-,-,I — _- -I T7, --— I —-, I -- -.1. __ - . -I —1-_; __ M -_ -I — 1 ! _: - .-.I- 77, - -.,- +_III,-+4- I-- --' —4" -4 -I - I,I —-' _' ---..- ---.1 -. MI(''-T''IIMt't-II I'I_-;II - _L —M --, -4-,", L..!m.. - I-_ M. -1 -I. I- I — I-,-4-,-, - — MM;,...ti IMI.IMI M-. -' -,M --'-i,_TI- 4 —,_;M. -I -- - ,.-,-- .. -—,,- -i,,-II,;_. - _..,',_.Ii.,- ..1IIJ-.+_ - M M.- - II iH "... - + I-4 -, -, -+- - M-, - I1. —'-I- + -T- -,''-' -.'- — —' -t- +_ MiI!-:',-,-,-, —- --- -L- -__.. _Mt: M. -, 4.M-, I --'_. -!_ I'_'_ -_.-m -i!,-M 2m- MIM I1... t- j, -,, - 6-_ - t-:;- - lr.,- ---- — il —-..,II" - -- 4,Ir.r — 4 — r,I;Ir T' "'-t.-_ I' I.;I-t,!.- -1,t-,.;.I "m. __ .__'_.I - -- M-_'- -----— I;..' r-r II.- --—, -, -,-,'T.rI!- -. —,: —17I -' —1 4 4-! —, 4-'-'I- - ..I..I.,I..,'II __ -fi' -;'i -L — ---- _ —, -L!:;=,-1 MIM1-t....II.I-I.I-I. -, M,--+-._-: —---.-.-I -1,.__-,L- T..7" T..-_-I -TI.I —_ —.-177'-.I-+ - -_-__i4]___ i-I.-I —1,I.,--' -"-,:i --. -. 1, -1 4- - 11,.. -M _ _; - -MI_. -I —,'4, 4-V- 4.4 - M-Mt- -- I.+.iIIIII.III.,r It:.,.- I- -- t- — I.I-I+,.IM' -. —...IIi- - M —I — -.'1111,I I —- .,.- -,-1,t. —tM-I — Ii _#.., L,, 4-. -_;_-, --.-.IItMf- —,- — I-II —-'-m;I_ I.7 -. -_ . -,-III - ,- I';-.1 —-. — 1-.IMIM!I —-- 'M. -I,,'.M,_t 4-1t"_.I _t -—.'..i.:.;'; -..-". -1 — I -''4. —-,... -.z- -— __, -.1..'_._ —-1. — 4 —, M.Mi''.1 -',,M-,,,.. —_. _I.. _.-I.. _.- ——.;.._ —4 MI.-,,ILI'.;zM___t;I, -. IIt-1-,- i__, -:- ,.',-,. 1 —t,-I..-.-.. _: -.- _ :4- -4 —., -,,a., — I I' —TImmrI:I.-I- i -!-.,. M. _'.....: t,,I,"`M4.I.;- - -I1-4 —- - — 4. - — - -, -- -I- LIMJ -,-+M,t- 11 -,.[-. I.- IiIIiII,-*-I-iII I..4.M a:M-MI,4 __ -4 —1 I — IM.; ;II, i IT..I -T —'-.M —-7-IM-.6- - -— IiII;I.-4-0-. — I....4 1 6 1 M i. 1 . ; I-, I-.M q....I,..I.- - —. M-.-m:_, ''-',, —. . —tm,I.-,.. MiI-;_. J'% —-- I II —.-.."- -4, —_ - - ,,T -I.-IM -, -—, —-t t-rl i.IiI;- i- , " —,-rt.11;j, r -- -,::II;.I.;pI. I_ - -.,_. -., —- M,:,';I I1M`VI.i-,-1 - 4-1- -f- 4 M.- I., tII - -II__ -— I.II!.'i -1-.' -!I - M;I —,..-'.I- -— M -, -M-1 - .. -1 - 7- It.I- _' M-._ -,-II.I.I. _'. I:,.-M.,J,'q.II,,-- "-t-,- ,I I-r -..M"M — -.T I I- -- I1., I.1.:,i-MMI —tI IMI- -!'-'-;.4-4 —-IM- ItI,IIIt;11M.rMI.__'.III I-,- -,, I- -- .1.4..a —_ -; - -..-. _.,,..-...-MI —1"I,.-V-,-..' —.--',mi.. - —.'IIt - -—,1 —.- I —;:TM+-. 1. -t-'i -_ -;M.+Ii; —. I' -'!MMIL.,IzqM" r-:4 - r -1-i-;,,-Ii4- r'_ -.,, -II, —II1ItM. — -— ItIIII t!'.' .__ mm — t- M -_1 — ___ —.- -,__ __ — _.ii--1;I-II4- I-r-I I..-.,IIIF:-,I IMv..I..4-, —.....','- — I,!....4-_ -." _-.4 -,.i-11-1 -.-1 - t- r _-'.-t.-,-~,,. II,IM.IRT.;..I -_ - -f- 4-.-_III.-1-1 ——, -,,- 4-.'-. -I - 1..'-..,- - II. - -.'.i -4-1f- 41rM -— - — *- f-+ -t — -- -,-Ir, I —- — r-T -f4-t _f.- 4,,;"_,.- f -I-! tI -.MIfl —.JL.-I. - -M- —? I;,-4 --;;.- -_ T'II;Lt+IMrI. I-,,. I —_' -1-,,__,..II, -1 -t M-,-:,- T- .__'iIIII IMI-:i.,I':MI.1 -1.-.. — -I-,.-_-.: -.- -1I-I+ _.. IM.-I. r';MMMr..'+:.__ - __o M - 4 __ - -__ta-i7' IM-I — - —, - -- - -I-,-,II. - 4 - _...I JI, —.-..-,.- I.- _.M.: o.t. — T —"'_,;-,, ,-T;!- -, m- - f4-,iI.I-.,Ii;4 1_r__ I:,.I ,, l.IIIr_4.M-. -.. -I.I - IM -- -- - - -,4-'-,. —T 4_-.Ii --- - -,.I —.Ii'!iI-II. — I-.-.I-.-t-LM.Ii- -.M-i- I-.-M, —, -WI —-.; — I-I,I- -M M-...M.. +_-77 - r77-M-I-.- --...7 -Z_ -- -'M..- 1.." -.m' __ IJ -..- i _i-.A. —I -. - 4-4-, —-..I - I I.;-M'_ i M--i "-, —-— tstIII —,Mo!-11..i.I..-I,-,:.II.. -4_. it- __F.M.-.+-l'-_ -.;_, -:-f!- M, _.- -— —- --,M.1.-.II__._I...-IT...-..Iw-..M.- -":_ j.-_._',... _'.I -—.-.- -, M, _4 -11 — i ,M.-.' MIMi I-II:I.II.;..M1t. -Ir-I-,I.I_7" -;-..1I,;_ M4. -,I.; - P_ l - . -,,-M!, — -!. 1-MI - -.IM,,, -,;. -t" — 1 -, -- i- -,,.',: M:,7,!-, -- M.-, 4 4. i.I ---,.4 -,.T_' _7.L M M.It.+ I.- - — T.::'.,-.-.- -4v -,.I M.I.....I:I —i.I.-.M-I-i1741.I-;I I;11I —-.. 1. 11-.4-,.,Il-.! I _.,1 -.ifIM.___i M —-- I11.I-I. — 1;_ - -,, — — I. -1 _!. — -t- - - —', 4.I.. I.-I"-_ 11,IIi- M., - :i-; —,!,M-_. 4 _+ -7- —.-:_ - -- -__iIi-IIi-t.-T- 11_ & _..-,! o.-!_: M-IIIII.--I-,, -- -—, - —1 - — t. -MI?,-;;',,'4-Ir-. - _'.Mi —MMj, IM,.I;MIM+.I-,. I- I....M..4..1.-... - _'.;. - 47 -—, --,,-%,.. M;'44.. ,,It-, w I. _- II-, -:, --- -,,-. -- -4- t + 4 -, -4- - —, I:'. I.. I.rI- -., - 11I —,:1 - +1 I. -.-'f. t,II;.' -I. II!-.-I,.:_.-+ JL I - -f I —-11 ;M" - ,I- - -. —1.,, -, --I-T-4ziMM.I 6'. — -_t,1 1 — T,-4M..I-.41, 'I.,,.,-. —.-_,7mIMIaIT-j.M..! -I — I:- - -I,.-M —.t- —,, - .,.-;-_-.IIi' . -I - -— - — M,,-I..' -.! -1,IM. .,4I — I-I.'. - I -Mm ' -., -4-,..t.+ —.M -, —- - - _ — _ _; -__.:-_'' 4....-.- r - - I.I,..!;" II-I- I.M.4i IMII. MI — I..I1MI! -I. __.!II..--.. —, -tL —- -,I,-11.I' t'm.I-1.1._' - -'i,-.,-._. t++'_-".--i -1,..r - II -I __.Iti:.II-III.,.-! -. I"?I..I T ", it'II.. -...,"M - ---- ---,-I-MI - -_ -,q-,__MI.MIMI MM-M.i';.:.: mI-_-II.:7 - - -I. —_. - M.p-,L.,- I.IM.v4 —..I-.1 "_.I-l.M-.- I- — _;.-1 -L,_-MI- - -' I. -I,.- - -:.1, —- -_.,. —.- 4_',_ _.._._,.IMIIMi1.,:-1I-_.-; I I --.- - I, M . i-!II- - -.Mf —-..-II,....,-M v_*- - -v - - .i. -I;.-II_! m-4 —-I.;'i — i — L -- -... —.. MI_, — " .-I I,_I —--— I_.-I-i-I- I...I- 4I __''I T!.IIi- I-I.rl I1. - -; —I -,w+_ I.4 - -IIM,-,. — - -''a.II _r " -M; i,:-! -1,,.bMI,M....-,-._m -L-,,M.II. — I:-, - I`-..' -:;I.I -I.-; -;- -4- -,, -t.-.,.I.I..,II;I', I-.. —- IIM-1...-I- -. -.IIqr.I-...'1'II14!-;+ +- —.-,, IIIII..MI-M...., —-I.1Ii. i _2,-IMII-_' -:II-iI-_t' -- __TMT:i IIIM!I-. - —.-. —-IM..,,i'',I -1 - -.- M -.,I - __ — 7 -"* —'.. —' — iMI —-.- -1f,;.,_ —. — -. _''M —,IlaMI -_, -— II-I-...I MQI -I-M' I;.MM —..I — _,.II -n1iI-;I-7 "'I.- I..`-.- I.I-M, -....-.-"M I- II''.- —.,+. -II.,mr- i —Ii',-.:._:',-1-11II I-'' — 4. - 4,,' ----- - I _-__-M-;,,-:. —.'_, —_+ - -,,- -..M —,.I-1I'.I M.qI:,.M!M — - 1-. . I-m 4m -.II. I, Iil _ __.l_.' _ _ -L , -,.!-. -1.,.,- -: _ -1 .'LL.' -M.I-t-I-.M-,It,-!- -. —..M-_ _ - :--1.IT'-,,I-__ -'_, IJI III.I -. -1-__ - —M._-,I-, —.qII I —.-, -,M —.II —9... tt-;II,i' - 1 i.,I II-III.-,..II-If'I-,MIIi,.'+ i_-,... — I —.I — — 1-I; —_ _i.",,,MII;II.I I - I-I IIII__-.I.:4.. I11T-. —, ,. -— 77-1.T_..M i-,-. — _ltp —-I-1, J_ -, I..II.-. M;.M-z.M -,I —.I.'_m- _"'M. L___- -I —--- I;M.'IMM.tI —- —,- ------ -- — .-!I - II..I IM.-.__ —- -_ I1 ,I. - _ - -..-1-1 -I-,,- "-:..- _i1-III_ -.;II —'- ---— 4- -; 4 —I-MI-__, —I*41 - M MM7'!.t-Ic -r-I4i —:.IM.-M1.;_;M.- ---,M - 11I___ I-1 —I —- 7 I -.Ir-.-M I,14, -- -, —_-,- - — 11,I. -.- _. L __ .-I-1 —I - 1. —-17iI., - .,."- — IIMWI;-.I.I-.7 'IM I-I.- - -.- —.-I-1 -1--..TI.II-.- - -, - Ii —-17_tj-,, 1 -,, —T' -f - -, -— I. i — M 1. -..- M I- -. — -.M - - - 1-1. - -__' - __ - -, — -—,. - -"T-..:_ A,"I.-IMI1: iII —-, —, - i — -**IL.;*IItI-;i. -I -IMI.-, -...r- _., -! -7,-I -i'.,I I- 4T, 2. - 71..; r _. - —' i-L-_.I-,711- - -I .z,. ;Is IT_-II.. —-_ -,,..';___l I -I-.; +_ - -.".' _.I -i-1. ,. _ -. —. v L I-' t-1-IIm -- - ':.- — --IfIi.M't I-.. I.I,,-..-I —,, —- I- I-T.I.i; 7I- -z —, —-III; MIII -I -, I'4+.1,-L....MI -_.- -IIIr,'I, II — I —-, 4iT- ---— i..M MrM-_ _._ —._ - - Iitr-:LIII.t7- " - - -'-'-.I_7- I_ -,,I _ 11. -, 7 -- M i M-t-.;I; -,I. __ +- -- -l.M-...I. — — IIIi;-T- - i____'''-'I,-, —'' -'I-II —. I-.'..I -r.r.-.,I, .I-.M.,.-_ _.II.-,._4 — I-,-..-I'-' i_7ri — IIM...I;M I IMI1 7 - -I.-,I____,M - f M4 1iI I

oQ= /~~~~ / X ago~~~~~~~~~~~~~~~~~~~t be/ 0=/,o81= ~5 //'f 8 /1 -9ot/' / ft-5//-t9*. we' /'/ 7bOj'' */ II O6/SJE' ~/ QS//~8 O//p IoSV,' 8 // 1t,/'..$/,,-/ f, O = p ~' 5/', / 0Q~9~ Q..ydf' 4I-' //-j 6 z/i'.~/ // oO L5 p. 0 9/' 8 //'?5//' / /2' 9 - #' —X, C 6z~/'../ 1/ ~0_ g O?/* 3 /1 Ct d'/' / /1 ~ee/' / /Z-/-B;#,,),.'~ /,, sO7E~,? 6&6/-d4 Z~7*I RWv) o99'6/ 9~z/.f7,;/=02 R t- 0 ~tM 7~tw~Tt

UNIVERSITY OF MICHIGAN 3 9015 02653 5875