WftCftL-i^'^^'' . / 
 
 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 
 
 WARTIME REPORT 
 
 ORIGINALLY ISSUED 
 
 Fetrtiary 19^14- as 
 Advance Restricted Report 4B21| 
 
 EXTENDED TABLES OF STUFTIESS AND CARRY-OVER FACTOR 
 FOR STRUCTURAL MEMBERS UNDER AXIAL LOAD 
 
 By Eugene E. Lxmdqulst and W. D. Kroll 
 
 Langley Memorial Aeronautical Laboratory 
 Langley Field, Va. 
 
 ^ UNIVERSITY OF FLORIDA 
 DOCUMENTS DEPARTMENT 
 120 MARSTON SCIENCE LIBRARY 
 P.O. BOX 117011 
 GAINESVILLE, FL 32611-7011 USA 
 
 KACA 
 
 ' WASHINGTON 
 
 NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of 
 advance research results to an authorized group requiring them for the war effort. They were pre- 
 viously held under a security status but are now unclassified. Some of these reports were not tech- 
 nically edited. All have been reproduced without change in order to expedite general distribution. 
 
 L - 255 ' 
 
i'^HO^Xi.i^ 3^c;<.i-t7 
 
 NATIONAL ADVISORY COWIITTSE FOR AERONAUTICS 
 
 ADVANCE R23TRICTI::D REPORT 
 
 EXTENDED TABLr":8 OF STIPFNI^SS AND CARRY-OVER FACTOR 
 FOR STRUCTURAL ItEMBERS UNDER AXIAL LOAD 
 B7/ Eugene E. Liind.q\;ist and 7/. D. Kroll 
 
 SUMMARY 
 
 The tables of stiffness and carrT-over factor that 
 vv-ere presented, in NACA Technical I-ote No. 652 have been 
 extended to Include the stiffness of a nienber with the 
 far end subjected to a noment equal and opnosite to the 
 noment applied at the near end. These tables are of use 
 in solving proolers in the stabllit;/ of structural members 
 under axial load as well as in the usual applications of 
 the Cross method of moment distribution when the effects 
 of a::ial load in the mer.bers are considered. The values 
 presented are for structural members in v/hich the cross 
 section and the axial load do not vary along the length 
 of the member. The interval between successive values 
 of the argument is small enough to make interpolation 
 unnecessary in engineering calculations. 
 
 INTRODUCTION 
 
 The tables of stiffness and carry-over factor given 
 in reference 1 have been found useful in the applications 
 of mom.ent-distribution metliods to a number of structural 
 problems. Recent studies have shown the desirability of 
 including in these tables an additional stiffness that 
 was not formerly presented. The present paper has 
 therefore been written to include in the tables values 
 for this additional stiffness as well as the material of 
 reference 1 and consequently supersedes reference 1. 
 
 The method of m.om.ent distribution developed by Nardy 
 Cross (reference 2) can frequently be used to advantage 
 In the stress analysis of continuous beams, continuous 
 frames, and rigid joint trusses, some of "/hich occur in 
 aeronautical structures. In reference 5, James summ.arized 
 the principles of the Cross riethod and showed how the 
 effects of axial load in the members m.ay be considered in 
 a moment-distribTition analysis. In reference 4, it was 
 shown how the principles of mom.ent distribution may be 
 
used tc solve problenn in the stafcllitj- o± structural 
 ireiTiber? uiider axirl loed. 
 
 In the stability calculations as veil as in the r.ore 
 usual type of morent-distribution analysis in v/hich the 
 effects of axial load are considered, it is desirable to 
 have tables piving the stiffness and the carry-over factor 
 as a function of the axial load and properties of the 
 member. Such a set of tables was presented in refer- 
 ence 1. 
 
 Ik the use of the principles of moment distribution 
 as applied to the stability of p-lates (reference 5) the 
 stiffness of a plate vn* th the far edge subjected to a 
 moment equal and opposite to the mojnent applied at the 
 near edge v/as found useful in stability problems in which 
 the assembly of plates was s;>rrun6trical about a plate. 
 Because the equations that must be satisfied for the sta- 
 bility of plates are identical in their general for;"i to 
 those for bars under arial load, a corresponding stiffness 
 for bars is desirable. As is the case for plates, this 
 stiffness is designated 3^^'^, and values are presented 
 herein. 
 
 The ta'':le3 apply to members for which th.e cross 
 section and axial load do not vary along the length of 
 the member. The interval between successive values of 
 the argument was made rufflciently small that interpola- 
 tion Vvould be urmecerrary f'cr uiost engineering calcula- 
 tions . 
 
 SYMBOLS 
 
 E modulus of ela-.ticity 
 
 E effective modulus oi elasticity for stresses beyond 
 the elastic range 
 
 I mom.ent of inertia of cross section about centroidal 
 axis perpendicular to plane of bending 
 
 I. length of member 
 
 P axial load in m.em.ber (absolute value) 
 
ITS 
 
 cvi 
 I 
 
 L L -, 
 
 —CSC — - 1 
 
 a = b 
 
 (. SL 
 
 [ 1 / 
 
 v3/ 
 
 1 - ^ cot ii 
 
 6 = 5 
 
 J 
 
 J 
 
 J/ 
 
 2 
 
 -N 
 
 V 
 
 f 
 
 ^ 
 
 For conpreasion rfiCxiib'jrs 
 
 a = 6 
 
 L , L . 
 — cech — - J. 
 J J 
 
 
 P = 5 
 
 1 - -. coth ^ 
 
 J J 
 
 
 /- 
 
 For tension members 
 
 • _ , ^ -I- 
 
 -^ - V T 
 
 j "^'^i 
 
 .' p 
 
 1 / Vtpt 
 
 Effective values of a and p are obtained byy 
 
 tut ion of (L/j) „^ for l/ j . 
 
 exf 
 
 s ub s 1 1 - 
 
k 
 
 The s^TTibols lAsed to designate the stiffness and 
 c&rry-over factor for the different typee: of restraint 
 at the far una ai-e given in the follo'ving tahle and 
 corresncnd tc there Msed In reference '•'-): 
 
 j Carry-ovor ( 
 Sbiffness , factor ! 
 
 C 
 
 Conditions n t far end 
 Far end fixed agaizist rotation. 
 
 3I 
 
 oil 
 
 r.-'-- = n 
 
 Frv end elastically restrained 
 against rotation. 
 
 No restraint egainet rotation 
 at far end. 
 
 rv 
 
 -1 j I'-ar end suojected to a rioment 
 
 e'lual and opposite to that 
 aioplied at near end 
 
 I 
 
 . I nT Q 1 T 
 
 II 
 
 The quantities C-^, C^, S-^S and C-^-^ oi' this paper 
 
 are the quantities S', c', ?', and c", respectively, 
 of rix'erences 1 and 4. 
 
 DEFINITIO'^S 
 
 The followinrr def i niti'-^ns of carry-ovei' factor arxd 
 stiffness p.re thf.- sa-ne as those f^;lven in reference I4., 
 
 Crr r v-over f ac to-p . - I*" a rneiaher :-.s on lUiyielding 
 supports at each end arc a r.icment is applied at the near 
 end, the ratno of the r-.c.-aent developed at the far end to 
 the -nonent applied at the near end is called the carry- 
 over f^-'Ctor, 
 
 Stif ^ges g .- If a riemb^r is on unyielding supports 
 at each end, the rrc.nent at one end nscessa^^* to produce 
 a rotrtlon of one-fourth radian of that end is called 
 the stiffness. 
 
The stiffness of a member cciti'Duted according to this 
 definition is one-fourth that corriputeQ according to the 
 definition used "by Cross (reference 2). In the Gross 
 method, the relative stiffness of the members is of im- 
 portance and not the absolute value. The foregoing 
 definition was selected so that the stiffness of a member 
 of constant cross section with no ajcial load and fixed at 
 the far end would be EI/L instead of J4.EI/L. 
 
 Sign convent ion.- The sign convention used in this 
 report is the same as that used in references h. and 5* 
 A clockwise moment acting on tlie end of a member is 
 positive. An external moment applied at a joint is 
 considered to act on the joint; a counterclockwis© 
 moment acting on a joint is positive. 
 
 rpflPT tPQ 
 
 Tables I and II do not give directly the values of 
 stiffness bub_give. Instead, values of stiffness divided 
 by a factor EI/L. The actual stiffnesses are therefore 
 obtained by multiplying the values in the tables by EI/L, 
 The value of C is read directly from the tables. 
 
 ;i/l' 
 
 Form-ulas used in calculation .- The quantities 
 
 qll c IV 
 
 ~ ', ~ , and G are tabulated for values of 
 
 ei/l ei/l 
 
 (L/j)^P^ in tables I and II for compression and tension, 
 respectively. The stiffness 3-^ and carry-over 
 factor C^ that apply when the far end of the member is 
 elastically restrained are dependent on the restraint at 
 the far end and can be computed by the formulas given in 
 reference I|. or 5 • 
 
 In the elastic range of the material comnrising the 
 
 - - / ^ '' I T \ 
 
 m.embers, E = E and l^] ^^ ' -^ I. Above the elastic 
 
 X .1 .pf f. \ 1 ■■• 
 
 range, however, it is necessary to use a reduced modulus 
 which is called the effective modulus. A method for ob- 
 taining the effective modulus from the accepted coliyTin 
 formula for the material is described in I'eference Ij.. 
 
The forr'ulas usod In calculatirn; the second, third, 
 fovirth, end sT.venth coli^rirs In tables I rnd II are; 
 
 -^ 
 
 (1) 
 
 All .J. 
 
 ki/l k{i 
 
 (2) 
 
 hi/i. ei/l ii - c^i 
 
 L-" 
 
 (3) 
 
 ^1 
 et/l 
 
 3TI 
 
 7"r /t 
 
 -■^ ci 
 
 (i;) 
 
 Equation? fl) and ^2) ,;ere first presented by James 
 in reference ?. Equation (J) fo"^ lov»s rrom equation (1?) 
 of reference li, and equation (h,-) > fnora equation ill;.) of 
 reference 5« 
 
 The fifth and si-x^-.h coli-iT'ins in tables I and TI were 
 obtained fror.' the preceding colu:nn3, as indicated by 
 their headings. '^hcse colunii? a-^e included as a con- 
 venience because tTiey are of u.?3 in some stability 
 calculations (reference h.) . 
 
 Ac cur 
 used in fa 
 presented 
 Equations 
 second, th 
 fifth colu 
 The s Ix \.h 
 column and 
 colu2nn v;as 
 columns . 
 fi^;ures an, 
 taken; in 
 order i^^;re 
 where irre 
 
 ac 
 
 c- or eg 
 are ac 
 
 (1), ( 
 
 ird, sn 
 
 :'an VvT.s 
 
 coluir.n 
 
 mu],ti 
 
 there 
 
 All V 
 
 d the 
 
 sorr^e c 
 
 used. 
 
 £ulcri 
 
 of tablen.- The tables of reference 6 ii'ere 
 arr tion of tables I and II. All values 
 c'uj^ate to tiie nu:nber of places given. 
 2), and (5) v/ere u.sed to calculate the 
 i jToui'th coluinns, respectively. The 
 
 ootamed oy squaring-- "cl 
 
 e second column. 
 
 obtained by sqi'saring the fourth 
 
 v/aj 
 
 plying bv tbe fifth colurrn. The sixth 
 fore ;:3ade to aepend on ail preceding 
 a lues were tabulated to six significant 
 differences for the last col'^ir;u? wei-e 
 ases differences as hi^h as the fourth 
 
 The diff'jrencas v/ere studied and, 
 ties occurred, the tables were checked. 
 
An independent cVieck -Nat^ also made of a series of values 
 
 oIV 
 
 throughout the tables. The ^-^alues for z~r were 
 
 ei/l 
 
 computed from equation (1^) and were independently checked. 
 
 Langley I-'^etnorial Aeronautical Laboratory, 
 
 National Advisory Committee for Aeronautics, 
 Langley Field, Va. 
 
 1. Lundquist, Eu.geKO E., end ICroll, '*"/. D. : Tables of 
 
 Stiffness and Carry-Over Factor for Structural 
 ^1elnbers under Axial Load. T.N. ilo. 652, 
 NACA, 1938. 
 
 2. Cross, Hardy: Analysis of Continuous Frames by 
 
 Di s tr Ibut ing Fixe d-End Moment s . Trans . A . o . C . E . , 
 Vol. 96, 1952, pp. 1-10. 
 
 5. James, Benjamin viylle : Principal iilffects of /i:<ial 
 Load on T-foment- Distribution Analysis of Rigid 
 Structures. T.N. Vo . y^k, NACA, 1935. 
 
 Ij.. Lundquist, Eugene S.: Stability of Structvtral 
 Members londer Axial Load. T.y. No. 617, 
 NACA, 1957. 
 
 5. Lundquist, E\igene ^., Stov-ell, I-nbridre Z., and 
 
 Schuette, Evan li. : Principles of Moment Distri- 
 bution Applied to otabilitv of Structiores Composed 
 of Rars or Plates. K ". JA AFJi No. 3K06, Nov. 19^+3. 
 
 6. '-'ayashi, T'eiichi: Sieben- und mehrstellige Tafeln 
 
 der Freis- und Kyperbelfunktionen und deren 
 Produckte so'.vie der ("-ammal'unktion. 
 Julius Springer (Berlin), I926. 
 
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 rH ONO^rH_d" 
 rHCO ONJ-rH 
 
 NO OJ o^. C^U^ - • - 
 
 U-\3'fM rH O O^CO C^U-Xd" fOOj rH O On 
 
 , -f d -d-d— d toKNfOtofO tOfOfOtocM 
 
 f\J-dt*-rHNO 
 
 rH ON ONOJ NO 
 coco ONrH OJ 
 CO [^-•-OnO lP- 
 
 oj OJ <M rg CM 
 
 rH U^a^rH OJ 
 tr.rH H_:^CO 
 
 _4noco oco 
 
 _dKNCM OJ rH 
 
 r\J f>j CM OJ OJ 
 
 iH C^rH rHCO 
 _d- rHrH CM J- 
 irXO rH_:^T^ 
 O CTnO-CO t^ 
 
 O ON-dWNCO 
 ON-dfV rH rH 
 03CQCM'-0 
 f-^O LTNiA-d 
 rH r~i rH rH^ 
 
 r-rHCO ONO 
 N^C^rHCO to 
 0_^ONfOCO 
 ^J-tOfM CM rH 
 
 lOr-CM O rH 
 _J-.J>0 O^KN 
 tooD ^^^co_d■ 
 
 rH O O ONON 
 rH r^ rH O C> 
 
 rHrH rH rH rH rH rH rH rH rH rH rH rH rH rH 
 
 I I I I I I I I I I I I I I I 
 
 I I I I I 
 
 t I I I I 
 
 rHfMKVd"*^ NO C*-00 OnO 
 
 -d-_d'^-d--d- -d-d--d-d-'J^ ^^ 
 
 ITMOLOlOtO LfN lO l/N LPvtO 
 
 KVd-LO 
 
 i/nlTnlO 
 
 • • • • • 
 
 lOUPiLfMOt/N 
 
 NO C^-OO OnO 
 I/NLP iOI/nnO 
 
 NO r-co onO 
 
 irMOlOU^U^ LOiPlpvLPU^ lOlOlTMOlO lOUNlOU-MO lOlOlOtTMO U^lO U" iP- lO . 
 
14 
 
 TABLE II.- TENSION 
 
 VjJeff 
 
 c 
 
 s" 
 
 EI/L 
 
 s 
 
 El/L 
 
 C^ 
 
 S2c2 
 
 siv 
 
 El/L 
 
 (EI/L)2 
 
 
 .1 
 .2 
 
 i 
 
 .5 
 
 0.500000 
 
 •499757 
 .1+99001 
 .1+97760 
 .1+96053 
 .1+93831 
 
 0.750000 
 .750512 
 .75I996 
 
 .751+468 
 .757? 61+ 
 .762412 
 
 1.00000 
 1.00056 
 1.00133 
 1.00500 
 1.00552 
 1.00831 
 
 0.250000 
 
 ■ 21+9757 
 .21+9002 
 .2L7765 
 .2I+60I+9 
 .2I+3&69 
 
 0.250000 
 .249936 
 .21+9665 
 .21,9252 
 
 ,2U6675 
 .21+7937 
 
 0.500000 
 .5OOI122 
 .501666 
 ,50371+4 
 .5O66I+? 
 .510374 
 
 .6 
 
 ■I 
 
 .q 
 
 1.0 
 
 .1+91167 
 .l+e8os7 
 . 1+81+ s 19 
 .1+80575 
 .1+7621+6 
 
 .767818 
 .771+165 
 
 .7611+31 
 .789595 
 .798652 
 
 I.OII9I+ 
 1.01623 
 1.02116 
 1.02672 
 1.05291 
 
 .2I12I+5 
 .258200 
 .251+759 
 .250955 
 .226810 
 
 .21+701+2 
 
 .21+5991+ 
 .21+1+798 
 
 .21+5U59 
 .21+1985 
 
 .514911 
 .520252 
 
 .526386 
 .540988 
 
 1.1 
 
 1.2 
 
 1:1 
 
 1.5 
 
 .1+71556 
 .1+66550 
 .I+6119I+ 
 
 .j;55575 
 .i+i+9699 
 
 .808515 
 .819215 
 
 .650703 
 .81+291+9 
 .855921 
 
 1.05971 
 l.Ot+712 
 
 1.05515 
 1.06372 
 1.07289 
 
 .222565 
 .217651 
 .212700 
 .20751+8 
 .202229 
 
 .21+0376 
 .2 56 61+6 
 .256799 
 .231+845 
 • 252765 
 
 .5491+28 
 .558608 
 .568510 
 .579118 
 .5901+13 
 
 1.6 
 
 u 
 
 1-9 
 
 2.0 
 
 .14^5591+ 
 .U37286 
 .1+50802 
 
 .1+21+167 
 .l+171+oi 
 
 .869586 
 .685915 
 .898873 
 .911+1+29 
 .930553 
 
 1.08262 
 1.09290 
 1.10371 
 1.11505 
 1.12689 
 
 .196775 
 .191219 
 • 185 590 
 .179918 
 .174229 
 
 .250653 
 .228396 
 .226081 
 •223697 
 .221251 
 
 .602376 
 
 .6149^9 
 .628230 
 .61+2080 
 
 ,656518 
 
 2.1 
 2.2 
 
 2.S 
 
 ,1+1051+8 
 .1+05610 
 .396616 
 .589568 
 .58251+t 
 
 .9I+721I+ 
 .961+380 
 .982021+ 
 
 1.00012 
 1.01865 
 
 1.15925 
 1.15205 
 
 1.16554 
 1.17908 
 
 1.19325 
 
 .160550 
 .162901 
 .157505 
 .151779 
 .l465l+0 
 
 ,216751 
 .216205 
 
 .213621 
 .211006 
 
 .208566 
 
 .671522 
 
 .607071 
 
 • 703145 
 
 • n9723 
 . 7567^2 
 
 2.6 - 
 
 ^:^ 
 
 2.9 
 5.0 
 
 ! 5 681+80 
 .5611+92 
 .5,^1+555 
 .51+7676 
 
 1.05751+ 
 1.05683 
 I.O76I+6 
 
 i.oq61i2 
 1.11668 
 
 1.20765 
 1.22287 
 1.25827 
 I.25I+06 
 1.27022 
 
 .iiaoo2 
 
 .155777 
 .150677 
 .125708 
 .120878 
 
 .205709 
 .20501j2 
 .200^69 
 
 • 197697 
 ,195052 
 
 .754395 
 .772264 
 .790646 
 .S09429 
 .82S594 
 
 3.1 
 5.2 
 
 3.5 
 
 . 5I+O67I 
 
 .551+ 1U9 
 .327520 
 .520990 
 .511+566 
 
 1.15722 
 I.I5S05 
 1.17° 09 
 
 1.20057 
 1.221S8 
 
 1.28675 
 1.^0558 
 1.52076 
 1.55826 
 1,55606 
 
 .116195 
 .111656 
 .107269 
 .105054 
 .0989519 
 
 ,102378 
 .IS97I+O 
 .187122 
 .161+ 529 
 .161963 
 
 .34s 120 
 .867991 
 .868188 
 .908693 
 .929491 
 
 3.6 
 
 1:1 
 
 .508255 
 ..502062 
 .295990 
 .29001+2 
 .281+221 
 
 1.21+556 
 1.2651+7 
 
 1.26754 
 
 1.50976 
 
 1.55211+ 
 
 1.57416 
 1.39255 
 1.41117 
 1.1+5007 
 1.1+4921 
 
 .0950211+ 
 .09121+15 
 .0876098 
 . 08I+1242 
 .0607615 
 
 .1 79429 
 .176929 
 .171)466 
 .17201+2 
 .169658 
 
 .950564 
 .971S98 
 
 •993477 
 1.01529 
 
 l^0573l 
 
 
 .270529 
 .272967 
 
 .267555 
 .26225!+ 
 .257065 
 
 I.35U66 
 
 1.37751 
 1.40009 
 1.1+2297 
 1.1+4597 
 
 l.i+6659 
 l,l+d820 
 1.50602 
 1,52605 
 1.51+828 
 
 .0775763 
 .0745108 
 
 ! 0667666 
 .0660815 
 
 ,167318 
 .165022 
 .162771 
 .160566 
 
 .156409 
 
 1^05955 
 1.08197 
 
 1.10457 
 1.12735 
 1.15028 
 
 l;.9 
 5.0 
 
 .252022 
 .2II7IIO 
 .21+2521+ 
 .25766k 
 .255128 
 
 l.l+6q07 
 1.1+9225 
 
 1.55689 
 
 1.5b232 
 
 I.56S7O 
 1.58950 
 1.61008 
 ' 1.63101 
 1.65211 
 
 .0635151 
 .0610651 
 .0567210 
 
 .0561+81+3 
 .05I+5I+06 
 
 .156300 
 .151+238 
 .152225 
 .150260 
 
 .i4e3i4 3 
 
 1^17535 
 1.19657 
 1.21992 
 l.2k338 
 1.26696 
 
15 
 
 t-H 
 
 IW 
 
 O IS\0 LTNO 
 
 o oj Lr>c^o 
 
 LTnO LTnO LfN 
 
 CVJ LTN C~~ O CM 
 
 rH rH rH r^ O 
 O LT'O LTNO 
 
 irst~o c\i ws 
 
 O O O O O 
 
 Lr^O LTsO LTv 
 
 OtJD OD UD 00 
 
 O LTNO LTNO 
 
 CNcrNaNONO 
 
 o o o o o 
 
 lPsO iTnO U> 
 
 OJ LP r— o r\j 
 
 O O O r-t rH 
 
 ra OJ OJ OJ rH 
 
 o o o oo 
 o ltno lr^o 
 irst — o po lt-^ 
 
 rH rH OJ OJ OJ 
 
 iH iH »H i-H i-t 
 O O O O O 
 
 LPvO Lr>0 U~N 
 
 c^o OJ m^- 
 oj ^o^N>,^f^^"\ 
 
 fH r-4 i-H rH rH ' 
 O O O O O 
 O LTNO LTNO ■ 
 
 ojojojf\jr\j ojojojojCM ojoj>-vjojoj (Mojryojoj f\)f\jf\jojrc\ N^^^^N^K^K^ NArorr\pr\ro\ K^^f^K^K^^^^ 
 
 ^O OJ O rH_^ 
 
 ON cr\ ctn ON ON 
 o o o o o 
 
 _^^-0 O OJ 
 
 ONL^^^^\r^ ON 
 O LfNrHa:) LfN 
 O LnrHM3 OJ 
 C— nOnO lTM/N 
 
 ON O ON ON ON 
 
 o o o o o 
 
 LT'^t^r-i OJ 
 l^-LTOJ CTvd- 
 
 LO ^ O NO OJ 
 
 On ON ON ON cn 
 
 o o o o o 
 
 C~^CTnOnC~-O0 
 
 ojNO rH i>-_d- 
 
 nj CM OJ (-H rH 
 
 CO rONONO O 
 
 _3-_zi-0 NN,N^ 
 H ON'TD O-C— 
 
 OJO) LfNfNJ ON 
 rH O O O CTN 
 CnOnc?nC7VX) 
 
 o o o o o 
 
 C^_trH_H-K\ 
 
 X) O ■O H o 
 
 r~-aNO K%MD 
 
 VO K^rHCO LfN 
 
 (JnonOnCOiT) 
 '-0 CO CO OD CO 
 
 o o o o o 
 
 C^OJ ONLfNO 
 
 _d-_:Jcoco N'\ 
 cr.KNC^rvjco 
 CM O C^LfNCM 
 
 coco i>-r~-c^ 
 
 O' J CO CO CO 
 
 o o o o o 
 
 rHCO ON^O 
 OJ LTNrrNvD rTA 
 J-O [>-_d-iM 
 Geo ir\tr\r-\ 
 C—-^ vO NO ^ o 
 COiXt'Ororo 
 O O O O O 
 
 rONAKNrrNNN | 
 
 CO mrH_itJ- i 
 r<\CO t— ONLfS 
 O O C— £>vD 
 ONNO_;jTM O 
 lTn i/n ir\ ltn i/N 
 ■TD O'O'O-O 
 O O O O O 
 
 C^^CMnO ro» 
 LfNO l/nonKN 
 COCO CO ONCM 
 _::J-rH O l/Nf<N 
 t^rr\oj OJ OJ 
 
 r-i ,-A r-t r-i r^ 
 
 o o o o o 
 
 COCO O O ITN 
 lP'NO^O r^C^ 
 
 LTNOVZi-ONO 
 
 o o o o o 
 
 OJ cr.rM -Ono 
 
 C V C~- K"^ j CM 
 
 K\i-\ O C" ON 
 CONO-Zj-rH C-. 
 O O O O Q- 
 rH rH >-f rH O 
 O O O O O 
 
 CO O ON_zfC*- 
 NO ifNO OnO 
 
 c^^o fM_±-o 
 f^-NO^rvj O 
 
 o o o o o 
 
 CO O a>co ro 
 rH O pr\0 O 
 -^ <-* 0-j±oj 
 
 C^^ !<> I>^ rH NO 
 
 CO C—LTV^tOJ 
 
 .-O ' O ■ "O CO rO 
 
 o o o o o 
 o o o o o 
 
 _^KO rH O N-N 
 
 O OnC—iH o 
 J-ONOnN^O 
 7-lvJD CM CT-NO 
 
 i-t Oni OnO LfN 
 
 CO ^-^-^-[^- 
 o o o o o 
 
 o o o o o 
 
 rOiOco [^-NO 
 
 WN O '. J NO _d- 
 _^| KN, rH o ON 
 
 o o o o o 
 o o o o o 
 
 -d- CT.OJ rH LTN 
 
 C■f^O^^^^0N 
 OJ <H O O (- , 
 
 CO r~-%o LnN-N 
 
 vO^OsOnOO 
 
 o o o o o 
 o o o o o 
 
 ONK^C^LPOO 
 ^f^ND r-t (y>CO 
 'X) CTnKVOnO 
 ON,_ ^O O rH 
 CM rH (H O On 
 nO ^-O sO ^-O LfN 
 O O O O O 
 O O O O O 
 
 M 
 
 ONLTNOJ {M_d- 
 
 nood o ojI3- 
 
 LfNON_d<0 CM 
 T-i K>nOCO rH 
 
 r-c~-r^r--co 
 
 t>-f\J ONCO ON 
 NO ONrH^C-- 
 nO O LTvONtOv 
 KNNO CO O H-\ 
 
 cotoco cr.cr. 
 
 rH_:H-ONtrNN-N OJN^L^>COCM 
 
 rHl3-r-^u-N onnn,c~-hno 
 
 1,/J CM NO rH LfN pvJ--0 rOC^ 
 
 LfXO O N~Mj-. f--0 OJ ifNC— 
 
 ONOnOOO O r-i i-i r-i r-i 
 
 V^^r^ O ON 
 
 O LfNO LfN(7\ 
 OJVO r-i UNON 
 
 o CM LPs c^ cr> 
 OJ r^ OJ OJ OJ 
 
 OrH_d-C— rH 
 LfNO LTNOnO 
 ^0\tC\CQ OJ 
 CM-ii-t^ONCM 
 
 C^CM CNr~-Lr. 
 •-{ C^c\|co_:J- 
 
 [:~-rHNO O LfN 
 
 J-C--o-'C\J-cJ- 
 
 ^^-C^-LT LfN 
 
 _ij-_zTLrNNOco 
 O'-O CMco.^ 
 
 0_J-ONrO.O 
 
 ^-c^•'-'_^o 
 
 Lp>LfNNO ^-x: 
 
 O roC^CM C^ 
 rH C— k>Ono 
 fOvC^Oj l>-rH 
 
 ONrH-^JNO CN 
 
 vO C--C--|>-[>- 
 
 OJOjnjCMOJ OJCMOJOJCM ojojN.rr.N", NNrfMO»K>rC\ ^^^^<^^<~^N^^<^ ^r^K^N^^r^K^ hOrtAKNN^, rr, hr\rr\KNN"\rO. NN»KN^rNh(Arf\ 
 
 
 M 
 
 C— .J-rH cTnCO 
 O t^-::tO C— 
 0\tc\..x) rC\V~~ 
 tr^O OJ Lr>C^ 
 NO C~-C— t-^f- 
 
 C-~-t"-C0 O OJ 
 ^j^rH CO NO KN 
 OJ r~-rHNO i-i 
 
 o f\j ir-c— o 
 
 CO CO CO CO cr- 
 
 _J-C^rH LfNO 
 
 o C~-LrvcM o 
 
 so O LfNO lTn 
 CM Lpr^O CM 
 
 cr. ON ON o o 
 
 C--LJ-NOJ O CO 
 
 -ct■^-a-^f^J^ 
 
 O O O i-t r-i 
 
 CO NO LTV^KN 
 LfNKNrH CIN^~ 
 
 trsco ro,C^oj 
 
 r-ONOj^r- 
 
 rH rH CM OJ OJ 
 
 OJ OJ OJ K>»_:j- 
 Lr\N-\rH ONt~-- 
 r— OJ C~-rHNO 
 
 ONOJ-d-^-CT 
 OJ K%f<\KM^\ 
 
 LfNKNrH OCO 
 rHvO HnD O 
 oO-d-t^cr OJ 
 
 NO CJNrr\NO O 
 
 vO.jj-rorH o 
 
 IPO LfNO LfN 
 
 -itr^ONCM-d- 
 
 ltnlTnlTvonO 
 
 
 OJ OJ OJ fM OJ OJ CM OJ OJ OJ OJ OJ OJ N^^^^ rr\rr\rr\K>N~\ ^cs rr\ ro\ fo* tc\ ^r^^^^^^^^f^N^ t<Nfr\K\K-.K , knkm^mtnn-n N"\NAf«(^t<M«rN 
 
 CO^O KNCO O 
 OJ O rH^d-rH 
 
 *Hco Lr\oj o 
 
 NO_zf'<NOJ 1-i 
 
 Onn^OJnO cm 
 G -»-* U^.,-t O 
 t— -O^KNCM 
 O\O0 C— NO iT- 
 
 O o o o o 
 
 f-{ r-i r-i i-i r-* 
 
 OJ nnno onnn, 
 rH_::tONNOND 
 rH O CT QNON 
 ^Ht-i O ON 
 O O O O On 
 rH fH rH f-l O 
 
 C^OJ OJ K^cr^ 
 NO QnO CfNLfN 
 C^OnO OJ r~i 
 OnO O rH rvj 
 coco ["-NO lTs 
 
 ON 
 
 S-&&0 & 
 
 "OCO OJ f^t^ 
 OnONnDCO LfN 
 rH r^-^^-OJ ON 
 
 Kvjt LJ^ r~-oo 
 
 _j-rr\ry i-i O 
 CJnOnOnOn 
 
 o o o o 
 
 OCO t^KVzt 
 CO-d-LT OCO 
 C--C--CO >-i^ 
 
 o r\j-d^~ON 
 o ONCO ^-NO 
 g>oocococo 
 o o o o o 
 
 NO LTNX) C\i~Zt 
 CT MNCrCOCO 
 C-NO N^CM OJ 
 rH^ t^O N-\ 
 
 NO lr\J:t-d■^c■^ 
 
 CO CO CO CO CO 
 
 o o o o o 
 
 fM OJ (M OnO 
 O ^f^^-^H C^ 
 
 -dN-o o wd-ON 
 
 NO OnCMnO CJn 
 
 .^^-CO_d-K> 
 CM ^-CM C~-rH 
 NO hOvoj i-i CM 
 
 K>(>-rH ITNCN 
 On^O'T) C--NO 
 
 o oo O O 
 
 NO f-oo o^.o 
 
 CTnOnCNOnO 
 
 rH OJ hrvdiJ" 
 
 o o o o o 
 
 NO C^-CO OnO 
 O O O O fH 
 
 ,_^LfN NO C-- CO ONO 
 
 r-i (M KVd" LfN 
 OJ OJ CM fM OJ 
 
 NO t-co OnO 
 
 (M CM OJ CM K^ 
 
 r-t OJ K^_d-LJ^ 
 pr\N>rr\K\rr\ 
 
 NO C^-CO OnO 
 
 I Iw 
 
 _d-cu ONi/xo 
 ^o^rv) OJ ry 
 
 O_3C0 CM NO 
 ONr-( KNnOCO 
 OJ KNKNrfNrrN 
 
 0\i^r-i O LfN 
 HMJXO rH_d" 
 0_dCO NAt^ 
 ^-^ N-,Lf~XX) O 
 
 _d J -d-_d- LP 
 
 NO O O P<NO> 
 CO KNCO fCVX) 
 rHsO O LPvC ^ 
 KNLfNQ^ O CM 
 LfN LP> LPvVO VO 
 
 O n~\OnX) on 
 
 LTNrH C^^rH 
 -dpNKNOO KN 
 
 LT. f— O CM LfN 
 
 ^Ovo c— t— r— 
 
 K^cJN^-*oco 
 ON^J3-d"0j o 
 
 C— CM ^-CM C^ 
 
 r— o OJ LTNt^ 
 £r—-0 X) CO -O 
 
 o_d-o ^-^ 
 
 CTN (T-^sO _d" N^ 
 r-\--4J rH^O rH 
 O OJ LPC—O 
 
 ONO^cr-o^o 
 
 NNKSKVd't^ 
 CM »-< O CJnCO 
 
 vO rHvO O LfN 
 
 OJ lt-C^O cm 
 
 O O O rH rH 
 
 ONCMNO rHNO 
 t^t~--vONO LfN 
 O LfNO IP>0 
 
 lTsC^O (M lP 
 
 i-H rH fM OJ OJ 
 
 rHNO KNONnO 
 LfNJ-_d-KNKN 
 LfNO iTNO ITN 
 f^O OJ LfNC^ 
 CM KNKNKNKN 
 
 HfM 
 
 (MCMfVJOJfM OJOJCMOJOJ CMOJOJCMOJ 
 
 IW 
 
 m_d-o KNcxj 
 c— trvo LT c^ 
 
 _dNOCO rH_d- 
 NO_d-(M rH ON 
 
 _4-3-_d-_d- KN 
 7h rH rH H rH 
 
 NO LfXO MNrH 
 N->_dONONKN 
 
 iJO CM NO rH C— 
 C"-NO^KNrH 
 K~\K'vKNKNKi 
 r-i t-t f-i i~i r-t 
 
 O OCO LfNO 
 
 r-i KNCO 'X) OJ 
 
 K\o>Lr>oj o 
 
 O O C^-^ LfN 
 
 K-.OJ OJ CM OJ 
 
 -H C--CO (MCO 
 
 OnCJNNA rH rH 
 
 t— UTv-d '^ ^ OJ 
 KNfM rH O ON 
 OJ OJ CM OJ H 
 f-t t~i r~i r-i r-^ 
 
 LfNCVj OJ LTnO 
 
 i rH OJ 
 
 J LTvd- 
 
 ONCO CM O OJ 
 U) On K\ CTN V— 
 CM KN Lr '-O CO 
 KNCV) r-\ O CI-. 
 M rH M rH O 
 
 f^ 
 
 C^O Lp.oj I 
 O H ^lT'-J r-i 
 Q ,( O [""-NO -^ 
 
 O O O o o 
 
 KNfM CD OJ WN 
 
 OJ tPo--NO„d- 
 _-j-r^o_^ J 
 LTvrr-tKNfM 
 o o o o o 
 
 '-0 
 rH^KNl^_d- 
 _d- LfN 3 CM ■ O 
 
 OJ NO O LP. ON 
 
 OJ rH rH O {JN 
 
 O O O O o- 
 rH rH rH rH O 
 
 t^-d-_d-ONX» 
 
 ONKNl/NrHCO 
 OnO O KNK^ 
 KNKNLPC^O 
 CM OCO NO LP. 
 
 LpMi^^_d-_d- 
 o o o o o 
 
 o 
 
 lr^_d■ON^- 1-^ 
 
 OJ CTNLPCO,^ 
 OJ C^O ON LfN 
 
 3co^fo-NNO 
 
 KN rH OCO C^ 
 
 ^_d-d-KNK^ 
 o o o o o 
 
 NO r—o onon 
 o KNrH a^f~ 
 
 KNrH c;>*JD C^ 
 \0 LP'K\C\J r-t 
 
 KNKNKNKNKN 
 O O O O O 
 
 NO LP>\OC0 O 
 CM I-H (M KNKN 
 IPiC— KNKNC^ 
 C~-t"-CO ONO 
 O OnX) F-t>- 
 
 _d-(M C^KNlP. 
 COCO o_j-c— 
 _d-Li^o c^c-^ 
 OJ J-t^crNfM 
 
 sO LrN_d'K\KN 
 OJ CM CM OJ OJ 
 
 o o o o o 
 
 ONrH C"-NO C-- 
 
 (XI r-O'JD ON 
 
 OnO lT lPCO 
 nO O .KN^-rH 
 CM rH rH O O 
 OJ CM OJ OJ OJ 
 O O O O O 
 
 C^C^I>-CO o 
 
 CMNO O KNLfN 
 
 _ZJtH rH (M LP> 
 nO rHNO t-i-^ 
 CT.O COCO c^ 
 
 LPNO lP,^t^ 
 
 K\UO t' - LP LfN 
 
 ONO_d--d-LfN 
 
 OJ ^-KNONL^ 
 
 IS^ONO LfNLfN 
 
 OOOOO OOOOO 
 
 C^OnnO knlP 
 
 ctnnono X) r-^ 
 
 r~- rH ^ OJ O 
 rHO_d-»H O 
 U-N_-t3-.d-KN 
 r-t >-\^ H rH 
 OOOOO 
 
 HH 
 
 ^OnO cr«LfN_d" 
 KNC— CM OnI-- 
 KN_d-^ E--ON 
 f—ONrH KNLP- 
 
 NO NO r-c^c^ 
 
 NO CO OJnO o 
 
 NO NO CO O-d" 
 
 r-i KNLPCO O 
 
 CO o oj-d^- 
 
 t—co CO iX) CO 
 
 CO KN r^^NO ^d" 
 
 CM LP r-O K\ 
 
 0^,rH KN^OCO 
 
 CO ONOnO-. (Tn 
 
 knC^c^^c— 
 
 KNOJ r\j KN_d" 
 
 --0 cr^oJ iT-co 
 
 O OJ iPiC^CTN 
 OOOOO 
 
 t~-KN_d-0 CM 
 NO gnOJnO o 
 rH_d-X) r-i LP. 
 CMld'-^ C^.rH 
 rH rH rH rH nj 
 
 OnOnO t*-rH 
 _dO U-^r^CO 
 'X) OJ LPONf\J 
 KNnOCO O KN 
 f\J OJ OJ K\KN 
 
 O OJ O^CO CM 
 
 lpncm o^^~^J^ 
 
 NO O K>C^rH 
 iT^CD O OJ LP 
 KN-KN_d--3--d 
 
 coco rH^O ir\ 
 _d'K>f^ ^fM OJ 
 LP■0'^^*^^^rH 
 
 c^o .f\i-dt^ 
 _d"-:r ITS LP LfN 
 
 sO OnO lPnO 
 (M KNKVd-LP 
 LPfjNKNC^rH 
 0>'-H_dNO o-^ 
 lP-^O nO no ^O 
 
 OJtMfMOJOJ OJiMOjrXJOJ OJfNJOJCMCM OJfMfMfUOJ CMCMOJfXJC^J (MiNJCMOJOJ 
 
 
 iw 
 
 K\ o -^_d ON c^vd-.d- cr^ t^ 
 
 C0_dO C^^ OJ rH O ONON 
 
 LP ON K\nO O _dC0 CM LP ON 
 
 COOKNlPCO OOJLP^t^CT 
 
 HPnnO nOnOnO C^C^t — t^r- 
 
 OnO LPCO_d" KNlPsO C-nO COOJCOnOvO COrHvOKNrH rHCM LPCO K^ 
 
 O O rH OJ_d nOCO rH KNnO CT^KN^O 0_d' 'X) KNt— OJ C^ OJ t— CM C^KN 
 
 _d^.O C\J ^O O J"CO KnC— rH l/NO^d'O'.^'^ r~-OJNOrHLP O^a KNCO 
 
 CM-d'C^CTNfM -3^^ (y\'-i^ no ONrH K\NO d) r-i KnnOCO rH K ifNCO O 
 
 COCOCO Jn On CrsONCTsO O O O i~i t-i i~( rHCMOJCMOJ KNN",fr.KN_d 
 
 ONt^LPU-NLP NO ONCMnO r-\ 
 
 rO_d-OsOfM fX)_d<-H t^_d- 
 
 (Mt^OjNOrH lPO LPCT^^ 
 
 KNlPCO O K^ LP.X) O OJ LP 
 
 _d"-d'-d" LP LfN tTN LP\J3 --O nO 
 
 < OJ OJ OJ CM OJ CM CM OJ OJ fM OJ OJ OJ CM CM fM CM CM CM CVJ OJ CM C\J CM OJ CM CM 
 
 ►Jl' 
 
 KNCO CNND_d- 
 »H t-i KNC^OJ 
 C^-d-fM '-^f>J 
 C03-OnO OJ 
 C\J CM C\J rH H 
 CM OJ OJ OJ CM 
 
 f-i CM K\JLP 
 LP LP^ LP' LP IP 
 
 fH LPfxj rHCO rHNO CM LTVd 
 
 coj-rHco_d- f-i^-^ '--i.^iu> 
 
 KNNOO_dO C--_:J-rr\cM CM 
 
 co_d-rHr-.d- oc-_d'-<co 
 
 O O O O-ON O. CO CO '"'J c^ 
 
 OJOJOJrHrH r-< r-t i-i r-i r-i 
 
 NO r-co ono 
 
 LP lP^ IP LP*nO 
 
 iH OJ KVd"iP* 
 
 NO NO NO vO NO 
 
 _d--d-cj_d'ON 
 
 nO^O K>K\ 
 
 K\lP<:0 r-i LP 
 
 LPOj a>^--d" 
 
 C^t^-NO\ONO 
 
 NO c~-co cr^o 
 NO NO 'sO NO r— 
 
 K\NO_d'^ o 
 
 r-i IP.VJ3 K C>- 
 
 O LfNtHCO U~- 
 CM ONt^^3-CM 
 vO lP LP i/nlP 
 
 r-i OJ KVd'LP^ 
 
 CM KNiH lPoJ 
 rH C~-On tP'NO CM CM t^ 
 KNCM rH O O rHcM-d'^CO 
 
 oco^£j_df\ ocoNO_d-oj 
 
 tPvd-_^l_d-_d- _d K^ H^ »<> N^ 
 rH rH r^ rH rH (H rH »H rH rH 
 
 NO C^-CO O O rH OJ KX^ Ln 
 
 c-t^r^c-co cococococo 
 
 pj-du^i^oj ^_d"C^fMO 
 
 NO cJnnO t^CM O OJ r— ^oco 
 
 rH_d^X) C\J C^ fM^-CMCO-d 
 
 rH ON C^-nO J- KNrHOCOt- 
 
 KNCXJ CMCMCM fXjCMOJrHrH 
 
 i~i r-i r-i r-i r-i r-i r-i r-i r-i r-t 
 
 NO tXO (TnO 
 CO CO CO CO CT^ 
 
 r-i C\J KN_dU^ 
 CTn CTN CT\ CTn CTn 
 
16 
 
 ltd I 
 
 u 
 
 oo o o o 
 o o o o o 
 
 O lT O lTvO 
 
 o o o o o 
 
 o o o o o 
 o o o o o 
 
 lT'O lTnO lTi 
 
 1.0 0\r-\ ITSO 
 
 ooo o o 
 
 o o o o o 
 o o o o o 
 
 O ir\0 lTaO 
 
 a^o^a.o^o 
 
 rH OJ N^V^J-O 
 
 L^^_J■K^(^J r-i 
 ^- 1-- 1>- C^ [-- 
 
 o o o o o 
 
 o o o o o 
 
 o o o o o 
 
 o o o o o 
 
 LTNO LTNO it- 
 
 _ri-OvO c\j OJ 
 O Lr^lH O OJ 
 
 NAMD n\t<\co 
 
 i>-i>-c— ^-t^- 
 o o c o o 
 
 o o o o o 
 o o o o o 
 o o o o o 
 
 O LT-O iTsO 
 
 Lr-[>-0 Oy Lf> 
 
 o o o o o 
 o o o o o 
 o o o o o 
 ltno Lr\o Lr> 
 t~--o c»a LTvt^ 
 
 sij vO t^ C^ C— C--CO JD -O CO 
 
 O O LTOj t-— 
 LT OcO 0_U- 
 
 N ■ OJ OJ OJ iH 
 
 o o o o o 
 
 CO r-l_^-^ LTv 
 
 r^ <H OJ Lr.O 
 
 ^ r-lO O O 
 
 o o o o o 
 
 oo o oo 
 oo o oo 
 oo o oo 
 o irvo uno 
 
 O CM LT.C^ • 
 
 . - . .o 
 
 c O'.CNCrs'-i 
 
 OJ o-^jd-_j-«-( 
 
 CTsvO C^cTnOJ 
 
 0'0^_zJ-Oj 
 O c'^0^''f^cr^ 
 
 O OO OO 
 
 o o o o o 
 o o o o o 
 lt-O ltao Lr> 
 f\j Lr«c~-o f\j 
 
 o o o o o 
 o o o o o 
 
 O LTsO iTvO 
 d^r— O OJ ir^ 
 
 OOOrHrH f-(iHOJ 
 
 nO rcvrr\ rH OJ 
 t--o_y-ov^ 
 
 O CTNt^u'Vd' 
 OvjD CO r O CO 
 •O vO "O ^O ^43 
 O O O O O 
 
 <H OJ OJ OJ 
 rH rH r-4 r-t 
 
 O O asKNCO 
 i-i 0\C\i OJVO 
 rH C^LTNKArH 
 K\r-{ O ONCO 
 
 CO coco c^c— 
 
 vO O v£) sO M3 
 
 O O o o o 
 
 O rr\ C*- o OJ 
 ro,o> rH 0_-J- 
 CO »-* ^O rH -i) 
 
 OJ cr>Lr^ojvO 
 
 OJ rH rH rH O 
 
 O O O O o 
 
 o o c o o 
 
 J-OnO^^.jD 
 OJ '-0 ^-O fO» rH 
 t-'^'-HCO L/^OJ 
 O O CT.ONON 
 w .rooj OJ OJ 
 O O O o o 
 o o o o o 
 
 rH CO rc\t--X) 
 ir\\o rr\_j-0 
 O c^O^O^O 
 
 CMTNOJ C^t^ 
 
 ODCO O ^-C- 
 t\i OJ OJ OJ OJ 
 
 o o o o o 
 o o o o o 
 
 O C^OJ^O rH 
 O LfVrH fOrH 
 
 o r~-^£) o^o 
 
 O O -D CTstr\ 
 LT'fM 0(0 C^ 
 OJ OJ OJ rH rH 
 O O O O O 
 
 O o o o o 
 
 O CTv:J-rH\D 
 O <M C^lT^O 
 O OrH lT^O^ 
 
 o t~-c-t^^ 
 
 ^0_4-^f^^J rH 
 I-i r-i r-i r-k r-\ 
 
 o o o o o 
 o o o o o 
 
 NX-=fr\j 
 
 rH UD^O {^LTN 
 
 l-^ lt iTNoj o 
 
 rH O vO JO U~^ 
 rH_^[-^rHSO 
 rH O OnO""^ 
 rH rH O O O 
 
 O O o o o 
 o o o o o 
 
 vO LnO r-l OJ 
 OJ O^ OJ^O 
 
 ■O rH O OJ C^ 
 
 o oo oo 
 O OO o o 
 o o o o o 
 
 0_j-KArOv(Ts 
 O CO CTN rTN OJ 
 O O'OCO lTn 
 LTVjjvO O^O 
 r\j c^^X)_:±'H 
 
 -O LfMXM/>LfN 
 
 O O o o o 
 o o o o o 
 o o o o o 
 
 c^o_cfoo N^ 
 OJ ctnOnoj cr« 
 
 N-\oi f\j_:J-^^ 
 
 o o o o o 
 o o o o o 
 o o o o o 
 
 
 OJ^fvO O -M 
 rH O^r^LOJ- 
 
 KMT f- O OJ 
 
 C OnO o o 
 
 _d-c^o j-r- 
 
 oj O c^C— LP. 
 LTstr-o OJ LP- 
 
 O O rH rH rH 
 
 i-t lPCTsKAOD 
 _zJ-OJ O ONf- 
 
 oD fO»:o OJ f>- 
 
 t—O OJ L/Nt^ 
 rH ,-\J OJ OJ OJ 
 
 OJ O rH rTN^ 
 ^f \ O cO C-- 1^ 
 vj3 LrM>r\oj r-\ 
 OJ 1>-(M C^OJ 
 Lr\r— o OJ t/> 
 
 rOvO K\0J^J3 
 
 CO o OJ uNx) 
 
 O O OM-O ^~ 
 C^OJ^O rHvi) 
 
 ^-o OJ u" c^ 
 
 OJVO rHS£> rH 
 
 r-l'-O rH'-O r-f 
 O Oj lP^-O 
 
 T Ln-m 
 
 lT LP-LTM-Tm 
 
 LnLTM/^u^u^ LP-LP^iD^'^ Nor-r— f-'C^ gococo'X)c> 
 
 rH ONCTMi^OJ 
 C^r\l„0 K\fr\ 
 -TT-d-N^rHsD 
 sO rH'-D O OJ 
 
 OJ Lr\[~— • • 
 • • • oo 
 
 a.C^^O^'H rH 
 
 CO lt^oj on^^ 
 
 CNJ OJ OJ rH rH 
 rHsO rHvX) rH 
 LPt^O OJ Lf^ 
 
 rH O O O 
 C^ O f\j l^^t^- 
 
 O rH rH rH 
 
 en 
 < 
 
 Eh 
 
 
 o OJ LT r^o^ 
 
 OJ rH O a CO 
 r-^ rOvOCO <-H 
 
 c o>o-c^o 
 
 ■ O C— J3 iJ*N lPn 
 
 '"O kvj:) k>' o 
 
 hPvvOcO <-H rOv 
 
 O O O rH rH 
 
 _d-t^O ^^^^^ 
 3'^<>'^f\l "-H 
 fC\rO S"\cO "^ 
 X) OD rH rTN^ 
 <-H rH OJ OJ OJ 
 
 O OM3 [^OJ 
 iP-axKAcO-^ 
 OJ rH rH O O 
 r-t\0 rH^JD rH 
 LTNt^-O OJ LP 
 
 O OJVO K",C\J 
 O^O OJ O^O 
 O OCTsCOCO 
 •O O lPO LP' 
 C^O OJ LPC-- 
 
 fTN^sO rHCO LP 
 rPv O CO LP fP* 
 
 O LPO IP'O 
 O OJ iPt^ O 
 
 _-j-lP lPLP^lPlPlP lPiPslPlP-lPi lP.u^v£)v^nO vOt"~r^C^C^ COCLtCOU^O^ 
 
 r-^ovo o LP 
 
 lP«0 lPO OJ 
 
 OJ L^^^- • • 
 . . .o o 
 
 O^CT^O^rH rH 
 
 rrsrHOCOC^ ^O _d- N~N OJ rH 
 
 ^O^O*^ LP LP lP^lPlPLPlP 
 
 O iTvO lPO lPO lPO lP> 
 
 Lr\t>-o OJ LP. c^o OJ LP t~- 
 
 O O rH rH rH • 
 
 rH c\j OJ r\j r\j 
 
 OJ ojcD c^•Lr^ 
 
 CO [^ p^ LP LP- 
 
 rH cr r~--o LT-- 
 
 a")_l' rHCO LP 
 vD^i3>JD LP LP\ 
 
 LPlT lT LPlP 
 
 o o o o o 
 
 ^ OtJDCO O 
 QD Lrv:H-C--_d- 
 
 j-_j-!3-j-Lj^ 
 
 rrM^tP\oj OJ 
 
 LP« lP> LP. LP. LP 
 
 O O O O O 
 
 O O lPKnC^ 
 O cr-^±C0^-D 
 O rH LP t-^O 
 Ovo_J-_::tNO 
 O c~~ir^K\t~i 
 
 o o o o o 
 
 C lPO NACO 
 OrH l^_cf(\J 
 O -JD K".rHCO 
 0_ziO C-- H- 
 
 oco f^ip3 
 
 -z^hP.K rrsKA 
 
 o o o o o 
 
 tc\f~i O OCO 
 fTsCO O t<\r^ 
 
 fPiLPLPO rH 
 
 hT^OJ OJ rP,_:J- 
 N~\OJ rH O O^. 
 hr\hPrc*fp\OJ 
 O C O O O 
 
 _:iCOOGOO 
 H C^r^lPvrH 
 C-t-OJ r-i^ 
 lPC^ O r^\sO 
 
 CO C — [^^J3 LP 
 OJ OJ OJ OJ OJ 
 O O O o o 
 
 O OJ lPCO KN OJ >~i^O KNOJ 
 
 O O ON LP C^ OJ O-^O fCiCO 
 
 O CTnO iP-OJ OJKAC-»C\0 
 
 o KAco OJ t^ ftj r~-ojco_d' 
 
 LTvJd" tPvKNOJ OJrHrHOO 
 
 ojojojojoj ojrvjojojoj 
 
 OOOOO OOOOO 
 
 IJI- 
 
 ^^ C^-CO onO 
 
 rH OJ rP^^LP. \0 E^-CO On 
 OnONOnOnOn CTvOCTvOnO 
 
 ^o r^xi a\o 
 
 fVJ OJ OJ C\J KA 
 
 *HOJK>_zi-LP 'sO C--CO ONO rHOJKVctlP. 
 
 K\KAfO.»OKN K\KNrr»KV::t -z}-_jd'_:t_3'-d' 
 
 ^o c-co o>o 
 
 «1 rH 
 
 llw 
 
 rHO O O O 
 OOOOO 
 lP-O lPO lP. 
 OJ lTnC^O OJ 
 
 LP^LPLPn^^ 
 
 OOOOO 
 OOOOO 
 
 O LPO LP>0 
 LPiC^O OJ LP 
 
 OOOOO 
 OOOOO 
 
 LPO LT O LP 
 
 t—O OJ iP.t^ 
 O-UDCOCOCO 
 
 OOOOO 
 OOOOO 
 O LTNO LP-O 
 O OJ LP'C^O 
 O^O^CTnONO 
 
 OOOOO 
 O O O o o 
 
 LPO LPO LPi 
 OJ lP^ C^ O OJ 
 O O O rH rH 
 
 OOOOO OOOOO OOOOO 
 
 OOOOO OOOOO OOOOO 
 
 O LPO lPO iP*0 LPO LPv O lPO LPO 
 
 lpc^o OJ LP. r~-oojLP.c^ o OJ LP\C— o 
 
 rH rH OJ OJ OJ OJ rP\r0.tC\NA _z}--d'-d'-^ l/^ 
 
 o o o o o 
 
 OOOOO 
 LP>0 LPO LP. 
 OJ LnC^O OJ 
 
 LP- LP LP'"'^ "^ 
 
 ^p.N■^K^^p^^P\ K^K^^P.^^\K^ KM>r\fr»rrNto, 
 
 NA KA K> rr\_d- -d"— 
 
 OJ 
 
 o 
 
 I:j 
 
 iH rHvO LP.LP 
 
 LPcO-d--::l-l>- 
 
 lO -jj„-j-oj O 
 
 C O O O o 
 
 C^O hPxLPiT^ 
 rr\K\LPO J3 
 
 rH t-TMPvJD O 
 
 CNt-^Lr>rP\oj 
 
 ^r^^P^^P,^<^^p^ 
 O^ OCO CO TO 
 OOOOO 
 
 _^<7NrH O rf\ 
 ONf\J ONDD ON 
 rP.r~-O_d-C0 
 O .o t^u^ rp\ 
 ^f^OJ OJ OJ OJ 
 CO i,XJ ^-O rO (-0 
 OOOOO 
 
 rH_d-0 ONrH 
 rP^O-OJCO OJ 
 rPvC^oj t— hP. 
 OJ O ONt-^i) 
 c\j <r\j >~t 1-^ r-\ 
 
 ro G3 CO CO ':o 
 
 OOOOO 
 
 _:J-Ov0^rH 
 C^LPuzf^J^ O 
 
 K^D-J-O --O N-% 
 
 ^NA^ O CN 
 r-t r-< <-{•-* <D 
 
 'O'-O o^oco 
 OOOOO 
 
 CO-cfO ^PLi^ 
 LP^^P^^^v^^- 
 f>vO rP.O C— 
 f~-vo Lr\_ctoj 
 
 OOOOO 
 lOiOCOCOCO 
 OOOOO 
 
 LP\OJ tXO LP 
 OJ ONf— C^CTs 
 lP\OJ 0>XJ'-C» 
 
 rH o c^^-NO 
 o o (T\o\(y^ 
 coco c^[--r-- 
 
 OOOOO 
 
 CO r^rH ^ IT' 
 
 OJ t^_;toj i-t 
 
 lP.rP\OJ rH O 
 iPvd-NNOJ t-i 
 0''^CT^Os On ON 
 
 OOOOO 
 
 hPvo i»p\fc\r^ 
 
 O^CO C~-^j3 LP 
 
 CO CO CO CO CO 
 
 OOOOO 
 
 
 OJ ONfPvONrH 
 OngnO onCO 
 
 vO CO KNTD '-0 
 OJ hPLPvOCO 
 
 CO t— O lPvJ- 
 lP.lPlPlPlP 
 OOOOO 
 OOOOO 
 
 rPvOco r-i LPv 
 _d--OCO-^ (Ts 
 
 NO C^O LTNrH 
 
 o OJ LPr— o 
 
 ^KNCNJ I-i I-i 
 
 LP LP LP. LfN LP. 
 
 OOOOO 
 OOOOO 
 
 CO OJ r-i^r-\ 
 
 a . c. o OJ ^jD 
 
 OJ LP.ONOJ IPN 
 
 O crvX)aj t— 
 
 vOvO_^C^-H 
 OJsO KNOJ_;+ 
 ^ C— iP^Id- 
 
 ONOj^o o_d^ 
 
 C^oj o Lp.rP\ 
 
 LPCO rH vD OJ 
 iVJ OJ ^- rH ^O 
 r.r>N'\OJ OJ r-t 
 
 OOOOO 
 O O C O O 
 
 OJ_J-LPK>_d- 
 r-t ON^-Lr^oJ 
 
 CN~-0 LPVLPM3 
 O LP.O iPvO 
 rH O O ONON 
 
 _d--d-^fONN 
 
 OOOOO 
 OOOOO 
 
 t^ONCO OJ ON 
 
 X) rPit^O Q 
 C~-0 rr\co r^ 
 
 LPrHNO r-i t— 
 COUD C~-[--^X> 
 ^p^^p^K^K^K^ 
 OOOOO 
 OOOOO 
 
 c--_ifco t^o 
 cr>o O OJ OJ 
 
 CO ir-tf\r~i o 
 ojcO-rtONO 
 v^ lPlPlPvjij- 
 
 ^fM■P fPv NN N". 
 OOOOO 
 OOOOO 
 
 L^^O_ 
 
 CO OJ oj o- f^ 
 
 CTnO rH OJ LP 
 rH CO -J-O^O 
 -JN-NNANNOJ 
 
 ^<N^p^p n .ro, 
 OOOOO 
 OOOOO 
 
 1 t-* 
 
 OJCO LP.OJ O 
 
 fP\aN^-o fp\0 
 
 nO O lPO lP 
 rH_j^-0 CNrH 
 COCO CO CO ON 
 
 CO r'-'.x>'vONO 
 
 NO rPvO f~-_J- 
 
 ON-j-ONrP.CO 
 KNnOCO rH KN 
 ONONO^O O 
 
 r-co aNrH_t 
 
 rHCO LP^PO 
 NN^~f\J t^OJ 
 vOCO rH K\N0 
 Q O i-i i-i t-^ 
 
 NO O I^C-- rH 
 C^lPOJ OvC^ 
 NO rHNO O LP 
 CO i-t rovN£)co 
 rH (\J CM OJ CvJ 
 
 NO rHNO OJCO 
 
 _d-fM ot^J- 
 o LP- a v-J- cr. 
 
 rH NN LP. O O 
 
 rP,rriNNr<N^ 
 
 LP.rHC0NO ^P^ r-i O^CO C—-X> uP-LPlPM/^LrN nOnOC^QnO 
 
 OJ O C— iP^^P rHLX)NO_^fM O'TDNO^oj OcONO_rl NN, 
 
 _d■C^^^P^CO rr\ CO OJ C— OJ C^ OJNOrHNOrH -sOOlPOLPn 
 
 m^lTncO O nn LPCO O KNLP CO O ^P\ iPCO O rP\u~vCO O 
 
 _ J-_^_d" LP. LP LPU-^NOvDNO NO C^C^t— C^ COODCO-L'ON 
 
 rr\ .f . ro ro N^ na kn fr\_d-_:t 
 
 ^^^ 
 
 
 t-H 
 
 CO-J-ONOOJ COLPOJ ON'O KNrH CO NO _d- OJ rH OnCO t^ 
 
 O Cr<ONO lP« K~\0J rH ONCO t— NO _rt l"*^ OJ f-* OCO t— NO 
 
 -JlfX) rPvCO K\ CO KNCO OJ [^ CM ^~OJ C~-f\) C^CMnO rHNO 
 
 ONrH_jNO CT^ i-t^lt^ O^r-i _^NO ONrH_d' "^ 0NrH_:H-O 
 
 f-COOaCOCO C7NONONCr-0 OOOrHrH rHrHCMCMOJ 
 
 NO LP\_zfrO,KN 
 Lrvd-rP.C\J rH 
 rHNO rH^O r-i 
 CJNrH_:tNO ON 
 
 f\j rP,rPr<NKN 
 
 KN CM CM OJ OJ NN rP\_:j-_^ lP. no C-CO (T'.t-i CM kn lp- r— on 
 
 O OVX) ^~-nO lP-J-KNOJ r-i O ONCO l>-r^ NO LP_rtKNOJ 
 
 NO o LfN o LP. o lpo lpo Lp.cr_j- c^^d" ON-rt ON-it ON 
 
 rH_jjNO ONrH _;iNO ONrH-d" NO CO rH KNnO CO iH r><NsO 00 
 
 _^3"-d'-=tLP ip.lpip.nono nond r-c^t^ t-cocooaco 
 
 rr\K~\KNiOiNA ^^^N^^p^^r^_d■ 
 
 _d_^_^_=J--^ 
 
 rr\rHNO C^O _d<D O C^ON _4-OnO O rH CO ONKNCO-d CTnKNKXCJnO 
 
 ^iJno no LrNK^ co ^-i rc\ i-i v^ r-lcMO -^ u> cm '^ t^ knno j- o^ o-^i^no 
 
 KNlPOD CM C^ CM ON^-O^+CM OJ OJ CMJ^nO (TsCM'^rHNO CMCOU^f<NrH 
 
 fC\D~-rHNO O ITN CN^d" ONJ- ON-d'O-wd'O^- _:j-Ol/N,HNO rMt^lCNONtP. 
 
 '-O LP LPvJ-_zl- KNCMOJrHrH OOC CTCO CO CO ^~ C"-^0 nO LP iT^^^zt 
 
 C^C^C^C^r— [*-C^r~C^t-^ C^C^-.OnOnD nOnOnOnOnD nOnO^nOnO 
 
 OOOOO OOOOO OOOOO OOOOO OOOOO 
 
 .jj-rH O O C7N C^KNNOnOO 
 
 CM -d" rH rCi C7N rHCO ONLPnO 
 
 O CTnCTnONCTv rHfM_d-t^O 
 
 rHNOOJCO_d- rHC^KN QnNO 
 
 _d-KNrP>CM OJ CM rH rH O O 
 
 nOnO -OnOnO n^nXJnOnOnO 
 
 OOOOO OOOOO 
 
 O^fMCO^ LP 
 O O KNrH rr\ 
 _d<0 CM t^fM 
 CM CO ON rHCO 
 O OCT'OnCC 
 nO IP LPLTNip, 
 OOOOO 
 
 UMrs_d- CM CO 
 O^O^tf\i-i CM 
 
 P-NNO r^-d" 
 
 _rJ-'H CO _d-rH 
 
 COCO t--c— r^ 
 
 IfN LfN IP^ l^^ LP 
 OOOOO 
 
 CM f<N_d-Lr. 
 
 NO C-OO CrO rH CM KVd-LP NO t^-CO OnO rH CM f'Vd' "^ 
 
 _d-^_H-_d--:t -d"-d"-d"-d" U^ ip.irvLPip.LP LP^tPipviT^NO vOnOnOnOnO 
 .-—1—1—1—1 Ti^^I^-^-^ ^ ^^^^^ ^ r•^ rt f-^ f-i ^r^r^t-ir^ 
 
 nOC-COOnO r-i c\i rc\^ tr^ 
 
 nOnOnOnO t""- 
 r-i I-i ,~i >-i r-t 
 
 ^-o r-co ono 
 
 CO CO CD CO CO 
 
I lyil'yiRSITY OF FLORIDA 
 
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