T F UC-NRLF SB 31b LIBRARY OF THE UNIVERSITY OF CALIFORNIA. Class RAILROAD CURVE TABLES CONTAINING A COMPREHENSIVE TABLE OF FUNCTIONS OF A ONE-DEGREE CURVE, WITH COR- RECTION QUANTITIES GIVING EXACT VALUES FOR ANY DEGREE OF CURVE TOGETHER WITH VARIOUS OTHER TABLES AND FORMULAS, INCLUDING RADII, NATURAL SINES, COSINES, TANGENTS, COTANGENTS, ETC. TO WHICH IS ADDED A METHOD OF FINDING ANY FUNCTION OF A CURVE OF ANY DEGREE OR RADIUS WITHOUT A FIELD BOOK By R. S. HENDERSON OF THE UNIVERSITY OF NEW YORK THE ENGINEERING NEWS PUBLISHING Co. 1906 eENEHAL COPYRIGHT, 1906, BY R. s. HP:NDERSON. J. F. TAPLEY CO., BOOK MANUFACTURERS, NEW YORK. PREFACE. This little volume is intended to supplement existing field books. Consequently the usual theoretical discussions have been omitted and the book reduced in size as much as possible. It is believed, however, that these tables will prove amply sufficient to meet the demands of the field engineer. The correction quantities are original in that they are applicable to any function of a curve and are independent of the central angle. The rectangular co-ordinates, X and Y, are believed to be entirely new. The appendix, "Field Engineering Without a Field Book," is here presented for the first time. The computations have been made with extreme care. The approximation of 5,730 feet for the radius of a one- degree curve, used in several previous books, has not been permitted in the preparation of the present volume. While every effort has been made "to secure absolute accuracy in the tables, the author makes no claim to infalli- bility. Should any errors be discovered, however slight, a favor will be conferred by reporting -the same to the pub- lishers. Chicago, July, 1906. R. S. HENDERSON. 204109 CONTENTS. PAGE. Explanation of Terms 1 Use of Tables 2 Table I. Minutes in Decimals of a Degree and Length of a 1 Curve 9 Table II. Functions of a 1 Curve 10 Table III. Correction Quantities 52 Table IV. Curves Designated by Radius 55 Table V. Radii 56 Table VI. Natural Sines and Cosines .- 58 Table VII. Natural Tangents and Cotangents GO Table VIII. Frogs and Switches 61 Table IX. Standard Rail Sections 61 Table X. Inches in Decimals of a Foot 61 Table XL Trigonometrical Formulas 62 Trigonometrical Formulas 62 Miscellaneous Formulas and Their Application 63 Appendix. Field Engineering Without a Field Book. . . 66 TABLES EXPLANAT/ON OF TERMS. FORMULAS FOR A I CURVE. f&dios * R T = Eternal Secant - E = F? exsec^ A Middle Ordinote = M= Recton^ular Co-ordinate X = Rsin A Rectangular Co-ordinate Y= F?vers A Length of Curve = l_ = 100 A RAILROAD CURVE TABLES /. To f.orf For a J curve.. T-25Z6.I Cor - 0.19 E = S3Z.14- Cor. = 0.04 C = 46221.8 Cor. = 0.34 M = 4-S6.9/ Cor. = 0.04 X = 4-Z30.0 Cor.= 0.3/ U5E OP TABLES. functions of a <5 curve if A -4-7-35. (Tables I, II anJ HI.) For o 6 curve . E = C~ = 4ti.2\ + 0.04= o8.73 - 81.19 + 0.14- =3/0.% L =47X100+5833= 4/S8.33 2. To f/W T^e functions of o curve of 22o' radius if (Table* I, II and IV.) For o /* curve. r=S973.l E- 2547. 2 C =8269.7 M = /7^3.3 No correcti'on required. Degree of curve -26-t6A J5Y.62 For o curve of 22o rcruxjs . T -5973.1 X .038397 - 229.35 E = ^54 7. a X .038397 = 97 9O C = 829.7 X .038397= ^17.^3 .038397= 67.71 /f chaining begins at C/?G ens in poss ing obstacles- (Tables I, II an', W/^ transit at P.I. (after A has been /Treasured) set P.C. at station 4O+8O.5 and sef P.T. on for- ward tangent 73/-/' from PI. W,'fJi transit at PC. set stations 41 and AZ by chi lection s . O/? accou/jf of obstacles on l/fle. stations 43, 44, 45 and 46 are invisible from P.C . Central angle to station 4-3 = 2 y(4-5(>') - 9- 5?'. RAILROAD CURVE TABLES For & = 9S2' X, - 981. 81 y,= 54.75 d-alting PC. station set Q pcxnt A of 2-A/8.2 on svbtongznt. Set station 4-3 by measuring 18.23' irom A ond foo' frc/r? slo t/on 42. Centra/ angle to station 4*4 = (9-S2')+(4*-Jo) * /4-22 For 4 = I4'-Z2 X, = 14-21.7 = 3/5.3 ~~ 5e/ Q poinf B at slaf/c/r J//5T9 on subtangent. 5e/ 44- by measuring 39.92 fro/7? B and^ /oo' from slat/on imilarl for station 45, A - /8-52\ X.^/SSz.?, X 4 ., = 4//.T t =30783 j \, ~ 68.41 5et o po'/ot f of station 4+//.7 o For stat.'on 47, A = 27-S2' C, - 27533 ^"f^ ~ 6/3 - ; 8 Cor - = -^ 6/3.18 + O.tS - 6/3. 33 = C 4 ., , Set station 47 by chord distance. 6/J.53' //v/? /?C. ?/7w measunna jroiT) station 4-4 or 46. W/'/fr "transit at F se~f station 45 by meos- ur/nQ (?$.4-l' of r/qht a/r(j>nf . W/"M transit at station 4~7 jef static/75 4-6 and 48 by Jet/ec- t~i F4 C 4 . }0 . AT, = 70. f 4 -- = /ff.68 - /K-,o Set station SI bu chore/ 398. 4(>' from sfat~icii 4-7 and ^er/ec//o/7 5- O fro/77 f0/?t~ at sla'ton 4 7. Set a po/r?f H on the cJrord IOO' Jrctn static* 47 and measure. c//s/bflce fro/77 )-/ fo staf/on 4-8. Set o po//jt tf on J/>e chore/ IOO' from stot/ofi SI. Set static/? SO 6 RAILROAD CURVE TABLES from station SI aae curve HZ 's proc/uce 58 -QK -TV. o cury^ o tral Bisect chore/ 0G o/ A/ Connect H an^ F. 243.3 Draw P2 perpendicular to chor\ar /b cliord fff/'t/d/e point" Q. T/ros tj swcce55/^e ' plotted or? tie curve. <7/?y numher of points may be 6. Use of X, Y a aj C in plott,ng a curve of small central angle. Given a 3 curve. A=2'-/7'. uireJ t plot points or> the curve. So opari- 'too P.C, station gives the following values oi X.Yand C -for one half of 1he. curve: +50 +50 3- A-3O 6- 7-30 9- 5OO /OO.O S49.8 199.6 249.3 Z38.S 3*8.0 Y 07 1.1 /O.S" ai 3?.0 /oo.o If 0.0 199.9 249.8 299.7 349.5" Calling P.T station O use the- same. Makes of X, V and C for the other half of the curve. RAILROAD CURVE TABLES 7. Use of long cKorc/s m plotting a Transit line. Required ~)b plot the following notes: Tangent Length 4.79/6 Total Angle C, for Ttrfo/ Anjte f I SfOO' 397? 800 5631 382 > 37#4 28-32' R. I6-/9 L. 38-44 L. 4o-54 R 47- 16 U. ^83ZR. 12-13 f?. 26- 3 L. /4-23R 32- i-3 L. 2924.0' /2I9.4- 2628. /4-J4..6 3243.4- T/ie length o/>W circ/e (/row a ///>e parallel to tangent 6, the circumference at point t>. mop circle sco/e to circle YV .8333 83.33 // .1833 /33 3/ .5/67 51.67 5/ .8500 85.00 /a .20OO 20.00 3a .5333 53.33 52 -8667 S 67 /3 2/67 21.67 33 .5500 55.00 53 .9833 88-33 !2333 23.33 34- .5667 56-67 54- .9000 9O.OO /5 .500 25.00 35 .5833 58.33 55 .9/67 91.67 / G .2667 26.67 36 .600O 6OOO 56 -93J3 93.33 17 .2833 28.33 37 .6/67 6/.67 57 .9500 95.00 18 .3000 30.00 39 .6333 63.33 58 .9667 19 .3/67 31.67 39 65 OO 59 .9833 90.33 POSITIVE CORRECTION FOR LENGTH OF SUB-CHORD FOR A 10* CURVE. T/;e correc'/on varies as the. square of $e c/e.gnee of curve. Thus for a 15 curve e7/?o / soA-c/joro 7 of 7& /^e correction 10 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE / r T E C M X Y T E c M y Y o.oo o.ooo o.oo o.ooo 000 0.000 50.00 0.2/8 IOO.OO OZI8 roo.oo 0.873 1 0.83 o.ooo /.67 o.ooo 1.67 o.ooo 50.84 0.226 01.67 0.226 0/.66 0.902 2 /.67 o.ooo 3.33 o.ooo 3.33 O.OOI 5/.67 0.233 03.33 O.233 05.33 0.932 3 2.50 O.OOI 5.00 O.OOI S.OO 0.002 52. SO 0.241 OS. 00 0.241 0500 0.962 4 3.33 O.OOI 6.67 O.OOI 6.67 0.004 53.34- 0.248 06.67 0.248 06.66 0.993 5 4.)7 0.002 8.33 0.002 9.33 0.006 S4-.I7 0.256 08.33 0.2^6 08.33 /.024 6 5.00 0.002 /O.OO O.O02 /O.OO 0.009 55.00 0.264 10.00 0264 09.99 1.056 7 5. 83 0.003 11.67 O1003 11.67 O.OIZ 55.84 0.272 11.67 0.272 1166 1.088 8 6.67 O.004 13.33 0.004 13.33 0.016 56.67 0290 13.33 O.?80 13.33 A/2/ 9 7.50 0.005 IS.OO O.OO5 15.00 O.020 57.50 0.283 fs.oo 0.289 14.99 1.154 10 9.33 O.OO6 /6.67 O.OO6 16.67 0.024 59. 34 0.297 116.67 O.Z97 116.66 I.I 88 II 9.17 O.007 19.33 0.007 19.33 0.029 59./7 0.306 18.33 0306 18.33 1.222 12. 10.00 0.003 20.00 0.009 2o.oo 0.035 60.00 0.3/4 20.00 0.3/4 19.99 1.257 13 10.83 o.o/o ZI.67 O.O/O 21.67 0.041 60.84 0.323 21.67 a 32 3 21.66 1.292 14- It. 67 0.012 23.33 0.0/2 23.33 0.048 61.67 0.332 23.33 0.332 23.33 1.327 If 12.50 0.0/4 25.00 0.0/4 25.00 0.055 62.50 0.341 25.00 0341 24.99 1.364 16 /3.33 0.016 26.67 O.O/6 26.67 0.062 63.34 0.350 26.67 0.350 26.66 1.400 17 14.17 O.OI8 28.33 0.0/8 2933 0.07O 64.17 0.359 28.3? 0.359 28.32 1.437 18 15.00 0.020 30.OO 0.020 3O.OO 0.079 65.00 0.369 30.00 0.369 29.99 I47S 19 15.93 0.022 J/.67 0.022 31.67 0.088 65.94 0.378 31.67 0.378 31.66 1.513 20 16.67 0,024 33.33 0.024 33.33 0.037 66.67 0.388 133.33 0.388 133.32 I.5S-I 2/ /7.50 0.027 35.00 0.027 35.00 O./07 67.50 O.398 35.00 0.398 34.99 I.59O 22 19.33 0.029 36.67 0.029 36.67 o.m 69.34 0.408 36.67 0.408 36.66 1.630 23 19.17 0.032 38.33 0.032 38.31 0.128 69.17 0.418 38.33 0.4/8 38.32 1.670 24 20.00 0.035" 40.00 0.035 4O.OO 0.140 70.0O 0.419 4o.oo O428 39.99 1-7/0 25 20.93 0.038 41.67 0.038 41.67 0.152 70.94 0.438 41.66 0.438 41.65 1.75-1 26 ZI.67 0.0 A 1 43.33 0.04/ 43.33 0.164 71.67 0.448 43.33 0.448 43.32 1793 27 22.50 0.044 45.00 0.044- 45.00 0.177 72.50 0.459 45.00 0.459 44.99 1-935 28 23.33 0.048 46.67 0.048 46.67 0.190 7*34 0.469 46U 0.469 46.65 1.877 29 24. )7 0.051 49.33 0.05/ 48.33 0.204 74. 1 7 0.480 48.33 0.480 4932 I.9ZO 30 25.00 0.0 SS 50.00 0.055 50.00 0.218 7f.0l 0.49/ 1 50.00 0.49 / 149.98 1.963 3/ 2583 0.059 51.67 0.058 5/.S7 0.233 75.94 0.502 5J.66 0.502 51.65 2.007 32 26-67 0.062 53.33 0.062 53.33 0.248 76.67 0.5/3 53.33 0.5/3 53.32 2.052 J3 27.50 0.066 55.00 0.066 55.00 0.264 77.51 0.524 5500 0.524 54.98 2.096 34 28.33 O.O7O 56.67 0.070 56.67 0.280 78.34 0.536 56.66 0.535 56.65 2.I4Z 35 29./7 0.074 58.33 O.074. 58.33 0.297 79.17 0.547 58.33 0.547 58.32 Z.I98 36 30.00 0.079 60.00 0.079 60.00 0.3/4- 20.01 0.559 60.00 0.559 59.98 2.234 37 30.93 0.093 6/.67 0.083 6/.67 0.332 90.94 0.570 61.66 O.57O 6/.65 2.281 3* 31.67 0.088 63.33 0.099 63.33 0.350 91.67 0.582 63.33 0.582 63.3; 2.328 39 32.50 0.092 65.00 0.092 65.00 0.369 92.51 0.594 65.00 0.594 64.98 2.376 40 33.33 0.097 66.67 0097 66.67 0.388 83.34 0.606 166.66 0.606 166.65 2.424 4' 34.17 0.102 68.33 0./02 68.33 0.408 84.17 0.618 69.33 0.6/8 68.31 2-473 4-2 35.00 O.IO7 70.00 O./O7 70.00 0.428 95.01 0.631 70.00 0.630 69.98 "2.522 43 35.93 0.//2 7/.67 O.//2 71.67 0.448 85.94 0.643 7166 0.643 7A64 2.572 44 36.67 0.117 73.33 O.I 17 73.33 0.469 86.67 0.656 73.33 0.655 73.31 2.622 45 37.50 0.123 75.00 0.123 75.00 0.49/ 97.51 0.668 75.00 0.668 7498 2.672 46 39.33 0.129 76.67 0.129 76.67 O.5/3 89.34 O.68/ 76.66 068/ 76.64 2.124 47 39.17 0.134 78.33 0.134 78.33 0.5J5 89.17 0.694 78.33 0.694 78.31 2.775" 4? 40.00 0./40 80.00 O./4O 80.0O 0.559 90.01 0.707 79.99 0707 79.97 2.927 49 40.93 0.146 S/.67 0./46 81.66 0.582 90.84 0.72O 81.66 0.720 91.64 2.880 50 41.67 0.152. 83.33 0./52 93.33 0.606 91.68 0.773 183.33 0.733 183.30 2 9?3 5/ 42.50 0.1*8 85.00 0./58 85.00 0.630 92.51 0.747 84.99 0.74-7 94.97 2.987 52 43-33 0.164 86.67 0./64 96.66 0.655 93.34 0.76O 86.66 0.76O 86.64 3.041 53 44. 17 0.170 88.33 0.1 70 88.33 0.68 / 94.18 0.774 88.33 0.774 88.30 3.095 54 45.0O 0.177 9O.OO 0.177 90.00 0.707 95.01 0.788 89.99 6.738 89.97 3./50 55 45.83 0.193 91.67 0.183 91.66 0.733 95.84 0.902 9A66 0.802 91.63 3.206 56 46.67 O.I 90 93.33 0.190 93.33 0.76O 96.68 0.816 93.33 0.8/6 93.30 3.262 57 47.50 0.197 95.00 0.197 95.00 0.788 97. SI O.830 94.99 0.830 94.96 3.3/8 58 48-34 0.204 96.67 0.204 96.66 0.8/6 93.34 0.844 96.66 0.844 96.63 3.375 59 49. 17 0.211 98.33 0.211 98.33 0.844 99.18 09S8 98.33 O.858 98.30 3.432 TABLE II. FUNCTIONS OF A ONE-DEGREE CUR V K 11 2 3 / T E c M X y T E C M X y 100.01 0.873 199.99 0373 199.96 3.490 |5"o.o4 1.964 Z.9997 1.963 299.87" 7.8SZ O 00.85 0.887 20/.G6 0.887 201.63 3549 50.87 1.986 30/64 \.99S 301.53 7.94-0 \ 01.68 0902 03.33 0.902. 03 29 3.608 51.70 2.008 03.30 2.007 03.20 9.02.8 i 02.5-; 0.9 J 7 04.99 0.917 04.96 3.667 52.54 2.O30 04.97 2.029 04.86 3.116 3 03.35 0.3 32 06.66 0.932 06.62 3.727 55.37 2.052 06.63 2.052 06.52 8.2of A- 04-. 18 0.947 08.32 0.947 08.29 3.787 54.2 1 2.07S 08.30 2.074 08.19 Z.Z9A 5 05.01 0962- 03.99 0962 09.96 ?-84.8 55.04 2.097 09.97 2.096 09.85 9.384 6 05:85 0378 11.66 0977 /A 62 3.909 55.97 2.120 11.63 2. 1 19 11.52 9.4,75 7 06.68 0.993 13.32 0.993 13.29 3.97/ F6.7/ 2.143 13.30 2.14-i 13. IB 9.566 8 07.51 I.oo9 14.99 1 ooy 14-95 4-.013 57.54 2.l(,(, I4-.96 2.165 14.85 9.657 9 } 09.3 5 1.024- 21666 1.02.4 2/6.62 4.096 158.38 2.1 3d 316.63 2.188 3/6.51 9.749 to 09.18, I.O4O 13.12 1.040 18. 28 4.159 59.21 2.212 Id. 30 2.211 19.17 8.94-1 n IO.OI /.OS 6 19.99 I.OS6 /9.95 4 223 60.04- 2.235 J9.9(, 2.234 I9.V4 8.934 12 10.95 1.072. 21.66 1.072 ZI.6I 4.287 60.88 2.258 21.63 2.257 2150 9.027 13 II. 68 /.089 23.3Z I.03Z 23.28 4.352 61.71 2.282 23.29 2.2?/ Z3./7 9.121 14 /Z.52 /./Off 24.99 I.lo4 24.95 4.4/7 62.55 2.305 24.96 2.304 24-33 9.2/F 15 /3.?5 I./2I 2665 1.121 26.61 4.483 63.38 Z.129 26.63 2.328 26.49 9.310 16 A4./8 l.i '39 28.32 1.137 28.28 4.549 64-.2I 1.353 28.29 2.352 Z8.l(, 9.405 17 /5T02 /./S4 29.99 1154 29.94 4.6/6 65.05 2.377 29.96 2.376 29.82 9.501 18 /5.85 1.171 31.65 A/7/ 3/.6Y 4.683 65. 88 2.401 3/.6Z 2.400 3S.49 9.597 19 / /6.69 //#9 232.32 1.188 233.27 4.7 f/ 166.72 ?.425 333.29 2.424 333./S 9.694 20 (752 I.ZOS J4-.99 l.2o? 34.94 4.8/9 67.55- 2.449 34.96 2.448 34.81 9.791 21 1835 /222 36.65 1.222. 36.60 4.887 68.38 2.474 36.62 24-73 36.48 9.888 21 13.19 / 24O 38.32 I.Z39 38.27 4.956 69.22. 2.498 3829 2.4-97 38/4 9.987 23 20.02 1.257 39.99 A 2 57 39.93 026 70.0? 2.52J 39.95 2.522 39.90 10.09 24 20.85 1.274- 4-1.65 1.274- 41.60 5.096 70.99 2.54g 41.62- 2.547 41.4-7 10.18 25 2/.69 1.292 43.32. 1.Z92 43.26 5.166 71.72 2.573 43.29 2.572 43.13 10.28 26 2Z.52 1.3/0 44.98 1.3/0 44.9/ 5.237 72.55 2.598 4495 2597 44.80 10.39 27 23.35 1.329 46.65 1.327 46.59 5.309 73.39 2.62,3 46.62 2.622 46.46 M.4S 28 24-. 19 /.346 48.32 1345 48.Z6 5.38 / 74. Z2 2.64$ 48.28 2.647 48. tZ to. 59 29 125,02 1.364 249.98 1.364 24992 5.4-53 ; 75:06 2.674- 34995" 2.672 349.79 10.69 30 as. 86 /.3g2 51.65 1.382 si. 5-9 5.526 75. 89 2.699 51.62. 2698 51.4-5- 10.79 31 26.69 l.4&o 53. 32. l.4oo 53.25 5.600 76.72 2.725 53.28 2.7^4 53.11 10.89 32 27.Hl /.4/9 54.98 1.419 54-92 5.674 77.56 2.7S-/ 54.95 2.7*9 54.7? JA9* 33 28-36 1.4-19 -56.65 1.437 56.58 5.74-3 78.39 2.776 56.61 2.77f 56.44- II./O 34 29./9 /.456 58.31 1.4 56 58.1S 5.823 79.23 2.903 58.29 2.901 5810 //.ZO 35 30.02 1.4-75 59.98 1.475 59.91 5898 80.06 2.829 59.95 2317 59.77 //.3I 36 30.86 1.494 6I.& 1.434. 61.58 f.974 80.90 2.85 f 6/.6I 2.854 (,1.4-3 '/.4I 37 J/.69 1.513 6331 1.513 6*24 6.050 91.73 2.881 63.28 2.880 63.09 //. Si 38 52.55 /.S32 64.98 1.532 64.91 6.127 82.56 2.908 64.94 2.906 64.76 H.6Z 39 J33.36 1.55-2 266.65 1.5 SI 266.57 6.205 |8?.40 2.934- 3*6.67 2.933 366.42 11.7) 40 34. /9 I.S7/ 60. 31 1.571 69.-z.4- 6.282 8423 2.961 68.27 2.960 68.08 11.84 41 75.03 /.S9I 69.98 1590 69.90 6.36 1 85.07 2988 69.94 2.987 69.7S 11.94 42 35.96 1.6 II 7/64 1.610 7/.S7 6439 990 3.0/5 7/.6I 3.014 7/.4/ I2.0S 43 36.69 1.630 73.31 t.63o 73.Z3 6..5V9 86.74 704-2 73-17 3.0*1 73.07 12.16 44 37 53 l.65o 74.99 1.650 74.90 6.598 87.^7 3.069 74.94 3.06,9 74.74 /2.Z7 45 38.36 /.670 76.64 1.670 76. 5& 6.679 88.40 3.097 76.60 3.095 7640 /2.38 46 39. /9 1.691 78.31 /.690 78:23 6.759 89.24 3.|24 79 27 3.123 78.06 12.4,5 47 40.03 1.7/1 79.98 1.710 79. 89 6.940 90.07 3.152 79.94- 3.150 79.73 12. 6O 48 40.96 /.73I 81.64 17 3 1 81.56 6.92? 90.91 3.190 9i.6o 3.178 S/.39 12.71 49 14-1.70 1.751 Z83.3/ 175-1 2S3.22 7.004 191.74 3.207 383.27 3.206 383. of 32 SO 4-2.53 1.773 94.97 1.7 72 04.89 7.087 91.58 3.235- 84.93 3.234 84.72 12.93 51 43.37 1.793 86.64 1.793 86.55 7.170 93.4-1 3263 t60 3.262 86.38 13.04. 52 44.20 /8/4 88.31 1.314 88.Z2 7254 94.24 3292 26 3.290 88 o4 '3.16 5? 45.03 /S3S 89.97 1835 89.08 7.338 95.08 3.32O 89.93 3.3/9 $9'.7O '3.27 54 45.87 1.157 91.64 1356 9 154 7.4-22 95.91 3.348 9/.60 3.347 91.37 13.38 55 46.70 1.978 93.31 1.977 93.ZI 7.507 9675 3.377 936 3.37S 93.03 13.50 56 47.53 1-399 94.97 1.993 9 4 .87 7.533 97.58 3.406 94.9 J 3-404 9469 /1.6I 57 48.37 I.9ZI 96.64 1.920 96.54 7.679 99.42 3.4-34- 96.59 34X 96.35 13 73 58 49.20 /. 942 38.30 /.94Z 98.20 7.765 9925 3.46? 98.26 ?,*/ 9?pt 'A'* 59 1:2 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE / 4 5 T E c M X y T E C M X Y 200.08 3492 399.^2 3.49o 39968 13.96 250.IG 5.459 499.85 5453 499.37 21.90 1 00.92 J 522 40/59 3.520 401.34 I4-.07 Sl.oo 5.4-95 50/.5/ 5.490 501.03 2I.9S 2 0/.7f 3.551 03. ?6 3.549 03.01 /4./9 51.31 -5532 oJ. / B 5.526 02 69 2lp9 3 02.59 3.590 04.92 3.S39 0467 /4.3/ 52.67 5568 04.84 5.563 04.35 Z2.Z4 4 0342 3.6/0 06.59 3.608 06.33 M.43 53.50 5.605 06.51 S.600 0601 22.39 5 04.26 -?.64o 08.25 3.637 0799 /454 54W 5642 08.17 5637 07.67 22.54 6 05.09 3669 09.92 3.667 O9.66 /4.66 55. / 7 5.679 09.84 5.67* 09.33 Z2.<# 7 05.92 3.699 //.58 3.697 11.32 14.78 56.01 5.717 11.50 5711 10.99 2?.3 06.76 3.72? /3.25 3.727 '2.98 1490 Sb.84 5.752 13.17 5.748 72.6? 22.98 0759 3.760 /4.9/ 3.757 /464 15.02 S7.68 5.797 14.93 5.78 S 14.31 23.13 IO 208.43 3.790 4-16.58 3.787 4/6.3o \5.)4 2585' .f.?29 5 16. So 5823 5/5.97 23.28 n 09.26 3.820 '8.25 3.8/8 1797 ,15.2.7 59.35 5.867 18.16 5861 17.63 23.43 12 10.10 3.85X /9.9I 3848 19.63 15.39 60.18 5.9^4 19.83 5898 '9.2') 23.58 13 IO.93 3-887 2153 3879 2129 15. SI 61.02 5942 21.49 5936 20.95 23.73 14 11.77 S.9/Z 23.24 3.909 22.95 15.6? 61.95 5^90 23.16 5.927 22.6' 23.88 15 12.60 3.943 24.91 3.940 24.62 /5.76 62.69 6.0/9 24.83 6.0/2 24.27 24.04 IB 13.43 3.9** 26.57 3.971 26.28 '5.88 63.52 6.057 26.49 6.050 2593 24./9 17 14.27 4-.005 28.24 4.002 2794 /6.OO 64.36 6.095 28.15 6.089 27.59 #.34 18 IS.fO 4.0i6 29.90 4033 29.60 /6.J3 65. 19 6.734 2982 6./27 29.25 245o 9 1*94- 4.063 3/.57 4065 3X26 16.25 66,03 6.173 37.4* 6./66 30.91 24.6S" 2.0 216.77 4.099 43324 4.096 432.9? 16.38 266.06 6.211 533.AT 6.20S 532.57 248o i\ 17.61 4.131 34,90 4MB J4-.59 16.51 67.70 6.250 34.8/ 6.243 3423 24.96 2.2. 8.44 4.163 36.57 4.159 3625 16.63 68.53 6.289 36.48 6.282 35.89 25.12 23 19.28 4.194 33.23 4.191 379/ 16.76 69.37 6.328 38. /4 6.3P/ 3755 25.27 24 20.11 4.226 39.90 4.223 39.57 16.89 70.20 6.368 39.8/ 6.367 39.21 25.43 25 20.95 4.259 4/56 4.255 41.23 17.01 7/.04 6Ao7 4/.47 (,400 40.87 2559 26 21.78 A.&l 43.23 4.2g7 4230 /7.I4 7/.87 6.447 4-3.14 6.439 42.53 25.74 27 22.61 4.323 44.89 4.320 44.56 17.27 72.71 6.486 44.80 6.479 44-.9 25.90 28 23.45 435S 46.56 4.?52 46.22 17.40 73.54 6.526 46.47 6.5/9 4-5.84 26.06 29 24*8 4.388 48.22 4.385 478 '7.5} 7438 6.566 48.13 6.558 47.5o 26.2? 30 225. It 4421 4-49.89 4-.4-I7 449. 54 17.66 275-.2I 6606 5W.80 6.598 S49.K, 26.38 31 25.95 4.4*4 51.56 4.450 5/.20 17.79 76.0* 6.646 5-1.46 6.638 50.82 26.54 32 26.79 4.4-87 53.22 448J 52.87 17.93 76.99 6.686 53.13 6.679 52.48 26-70 33 276* 4.52O 54.89 4.5/6 54.53 15.06 77.72 6.727 54.79 6.7/9 54. 14 26.86 34 28.46 4.553 56. 55 4.54.9 56.19 IB.19 79.56 6.76-7 56.45 6.7S9 S5.SO 27.01 35 29.29 4.586 58.22 4.5S^ 5785" 18.32 79.39 6.808 58./Z 6.800 57.46 21.18 36 30. 13 4.620 5988 4.6/6 59. 5V 1846 80.23 6.849 59.78 6.840 59.12 27.35 37 30.96 4.653 6/.55 4.649 6/./7 /8.S9 8/.O6 6.890 6/.45 6.881 60.77 275/ 33 37.80 4.687 63.21 4)683 62.83 18.72 81.90 6.930 63. // 6.92? 62.43 2767 39 32.63 4.721 6488 4.7/7 64.50 18.96 82.73 6.972 64.75 6.963 64.09 27.84 40 233.47 4.755 466.54 4.757 466.16 18.99 2J33.S7 7.0/3 -5-66.44- 7004 565.75 28.00 4i 34.30 4.789 69.ZI 47P5- 67.82 19.13 4.4o 7.0S4 68. H 7.046 67.41 2*.I6 4E 35. 13 4.923 69.87 4.819 69.48 19.2.7 85.24 7.036 69.77 7.087 69.07 28.33 4-3 35.97 4857 7/.S4 4.853 71.14- 19.40 96.07 7.137 71.44 7.122 70.73 2350 44 36.80 4391 73.20 4.887 72.^0 /9.S4 96.91 7.179 73.10 7.170 72.38 2S.66 4-5 3764 4.926 74.07 4.922 74.46 (9.68 67.74 7.2ZI 74.77 7.212 74.04 2993 46 39.47 4.96 / 76. 54 4956 76.12 /9.82 88518 7.263 76.43 7.254 7S.70 900 47 39. 3 1 4.995 79.20 4.99/ 7778 /9.96 #9.42 7.305 78.10 7.296 77.36 29.16 48 40.14- 5.*3o 79.06 5.026 7944 20.09 90.? 5 r.iA7 79.7<, 7.330 79.02 2933 49 40.98 5.065 81.53 5.06/ 91.11 20.23 41.09 7.389 31.42 73*0 80.68 29.50 5-0 241.31 5. loo 483.20 5.0^6 492.77 0.37 2.91.92 7.432 583.09 7422 502.33 29.67 SI 42.65 5. 136 84.86 5.131 84.43 20.52 92.76 7.474 84.7S 7.465 83.99 W.84 52 43.48 5.171 86.53 5./66 86.09 20.66 93.59 7.5/7 86.41 7.507 85.6$ 3o.oi 53 4432 5.207 88. 19 5.202 37.7J- 208o 94.43 7560 88.08 7.550 87.31 30.18 54 45.15 5-242 89 36 5.237 89.4/ 20.94- 95".26 7603 89.75 7.593 83.97 30.3? -# 45.99 5.278 9/.52 5.273 91.07 21.08 96 to 7646 9/.4/ 7.636 90.62' 30.52 56 46.82 5.3/4 93J9 5.309 32.73 21.23 96.94 7.689 93-^8 7679 92.28 30.69 57 4766 5.350 9485 5.345 94.39 21.37 97.77 7.732 94.74 7.722 93.94 30.87 59 48.49 5-386 96.52 5.38; 36.05 Zi 51 9&6/ 7.776 96.40 7765 95.60 3/04 59 49.3? 5.422 98. 1 8 5.4/7 tt?! 2/66 99.44 7.8/9 98.07 7.809 97.25 3/.ZI TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE 6 7 / T E C M X Y T E c M X Y 300.29 7863 59973 7.052 598.91 31.39 *S0.44 10.71 699..F7 /0.69 698.Z? 42.71 O 01.11 7-907 601.40 7.896 600.57 3/.S6 5V. 29 10.76 70/.24 10.74- 99.92 42.91 01.35 7.9f/ O3.o6 794o 02.13 3i.n 52. // 10.91 0290 /0.79 701.58 43.12 a 02.79 7935 04.73 7.98^ 03.99 Jl.91 52.9IT /0.96 04.56 0.94 03.23 A3. 32 3 03.62 8.039 06.39 R028 05.54 32 09 53.70 /04I 06.23 0.89 04-.& 4-3.52 4 04.46 9.083 08.06 8.072 07.2,0 32.26 5462 /0.% 07.89 10.94 06.54 43. 7/ 5 OS. 29 8.129 09.72 9.1/6 08.86 3; 44 55.44 J/.02 03. sr to 99 09.19 43.94

9.7/ 9.384 /8.30 31.51 60.48 //.? /9.S4 //.3/ 19.12 4 5- >8 12 11.14 5.442 Zi.37 14JO 20.44, 31.63 61.3? It. 39 21.20 t/.*6 /977 45.39 13 11.98 .4*7 23.03 8475 2.2 II JJ.87 62.15 V.43 2286 /f4< 21.4-2. 45.60 /4 1291 8.533 24.70 9.510 23.77 ^4.06 62.99 11.49 24 Si H:46 Zi.09 4-5.81 15 13.65 8.578 26.36 3.566 2543 34X4 63.83 U.S4 2J9 //.Si Z4-.71 46.02 16 14.49 .624 29.o3 S.6>/ 27.08 34-41 64.64 /t.S9 27.95 ".57 26.38 46.2.3 17 /S.32 8.670 29.69 8.6S7 2874 34.60 65.50 l/.GS 29.52 11.62 28.04 4644 18 16.16 8.7/6 31.35 9703 30.40 34.7? 66.1& 11.70 3I./8 It. 68 29.69 46.65 19 3/6.99 8762 (,33.02 8.749 632.05 34.97 367/7 If. 7 5 732.94 H73 731.34 46.87 20 17 83 8.808 34.68 8795 33. 71 3SJ5 68 01 I/.2I 34.5-1 //.78 33.0O 47.08 Zl 19.67 3.855 36.35 8.941 3S.S7 35.34 6885 I/. 86 36.17 /'.34* 34.65 4-7.29 22 19 So 8.901 38.0f 8.997 37.02 35.52 69. 6 & H 91 3783 11.89 36.30 47.51 2.3 20. 54 8.348 39.68 8.934 38.68 35. 71 77 38 #. 9.662 64.64 9645 63.52 38.55 83.07 /2.T9 ^4.44 IZ.7( 62.74 51.00 39 33J.7/ 9.7/0 616.30 9.694 66S~/7 3S.74 383.91 /2.9S 766. 10 12.92 76439 5722 40 34.55 9.7.T9 6796 9.742 66%3 .39.94 84 7S /z.90 67.77 11.97 66.04 57.^4 41 te.T) 9.5og 69.63 9791 6848- 39.) 3 5.59 12.96 69.4-J 1293 <>7.(>9 5/66 42. 36.22 9.85-7 71.29 9.340 70.14 J9.32 642 /3 oi 71.09 '299 &>JS 57.89 43 J7.0& 9.9o(, 72.95 9.888 7/79 39.52 87.26 13.07 72.76 11.04. 7/00 52.11 44 3790 9.955 74.62 993? 7345 J9.72 88.10 'J 13 7442 13.10 72. (,5 5,?.H 45 38 7) 10.00 76.2? 9.987 75/O 39.91 88.91 S3./9 76 08 /J.i6 74. 3O 5^.56 44 39.57 /O.Q5 7795 to. oa 7676 4c.lt 89.77 /?.?* 7774 /1.2> 75 9 f 52.79 47 4o.4o IO.IO 73.61 10.09 7g4l 4o.3l 90.61 /3 3O 79.0-1 /3.17 7760 53 01 4g 4/.24 10.15 SI. 27 IOJ3 9oo7 40. 50 9 /.4S /?Jt 8/.O7 /3.33 79.Z5 53.24 49 34-2.09 10. 2o 68294 ioj8 691.72 40.70 J928 /J.4/ 782 gj /3 38 780 9 1 5^.46 5O 4Z.9/ 10.25 84-60 /02} %3.38 40,90 93. rt I3A7 8443 1344 8256 fJ69 r/ 4?. 75" 1030 8626 to.29 &5.0? 4/./O 93.96 /3.S) 96.06 13 SO $a?-' 53.92 52 44 59 IO.35 87.93 /o.3J . fo.69 4 /JO 94.79 /3S9 7 7 ? I3.K tiS-86 54/5 S3 4542 #.40 89. f 9 '0.& 98. w 4l.fo 95.63 /1 64 8938 /?.(,< 87. $> 54.39 54 4626 1045 9/26 /0*1) 9o.oo 4170 96.47 /3.7Q ^1 Of 13.67 89/(, 54 f>l 5S 4709 10.50 9292 /0.48 9l.f,5 4-1 9o 9T.3/ X3.76" 91. 7 f IS.7) 9O.9I 14.84 56 47. 9J /O.SS 945? /0.53 9). 11 42.10 9S./4 /3.&Z 94 J/ //. 7g 9244, 5 07 S7 477 10. (,1 96.25- IO.59 94% 42.10 9? .99 13.97 96.04 /)34 94.11 55.30 -58 49 60 '066 979/ /0(>4 9662 42 SI 9992 '393 9770 13.90 9576 SS53 5? 11 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE / 8 9 T E c M X Y r E C M X \y 400.66 /3.99 799.36 //96 797.41 S5-.76 450.93 77.72 89909 7766 896.31 ^.54 1 01.4-9 /4.05 80J.02 14.02 99.06 *5.99 SI. 77 17.78 900.75 /7.7* 579^ 70.ft> 2 02.33 /4./I 02.69 14-07 800.71 S6.23 FZ.bl r /7.S5 02.4-1 17.79 99.61 7/.O6 3 05.17 14.17 04.35 14.13 0236 XA.6 5JAS 17.92 C4-.07 '7.36 901.25 7/33 4 04-.OI 14.2$ 06.01 14.19 04.01 56.69 $4.Z9 /7.98 os. i y 17.93 02.90 77.59 5 04.84 14.2% 07.67 14.25 05.66 &.91 ff./3 1805 07.39 17.99 04.54 77.85 6 05.68 tf.34 09.34 14.31 07.31 57.16 55.96 18.11 09.06 /8SX> 06.)9 7^. // 7 06. 5 a 14-Ao 11.00 14.37 08.96 57.40 S6.80 '8.18 10.72 18. \2 07M 7 29.29 '5-.CZ 27/7 60.OI 66-03 #92 28.99 ISM as.9j 7S.3I )9 16.57 /S.I2 30.95 IS. OS 28176 60.25 66.97 18.99 3o.6f /8.93 27.58 7S.58 20 4-17.41 &J8 83261 1F.I4 830AI 60.50 467.71 /9.06 932.31 1299 929.22 75.85 21 18.25 /S25 34.Z7 IS. 20 32.06 60.74 f>8.fS &.I3 33.97 19.06 30.?7 76.12 22 19.08 /S.3I 15.93 IS.Z7 33.71 60.98 69.39 /9.I9 3563 79.? 32.51 763) 23 19.92 tf.17 37.60 /5.33 35.36 61.22 70.22 19.26 37. 3O 19.20 34.16 76. 6C 24 20.76 /S.43 30.26 /S.39 37.00 6/.47 7/.06 /9.33 38.96 19.27 35.S0 7694 25 21.60 tf.49 40.92 15.45 38.65 61.71 71.90 /94o 40.62 79.33 37.44 77.21 26 12.43 I5-.SS 4-2.58 15. SI 40.10 6l-9f 72.74 I9A7 42.28 79.40 39-09 77.4? 27 23.17 15.61 44.24 15.57 41.95- 6220 73.58 /9.54 4?.94 19.47 40.73 77.76 2* 24.11 /f.67 45.9 / 15.63 43.60 62.44- 7442 /9.6I 45.60 19.54 42.38 78.03 29 24.95 /S.74 4.7.S7 15.69 45.25 62.69 7y.Z6 /9.68 47.2.6 19.61 44.02 7g30 30 425.79 15,80 849.23 1S.76 846.90 62.94 476.10 I3.7S 948.92 I9.6B 945.67 70.58 31 26.62 15.86 S0.89 IS.22 48.59- 6J.I8 76.9A 79.82 50.59 19.1 T 47.31 78.85 32. 2.7.46 /S.92 52.56 'S.88 So.19 63.43 77. 78 79.89 -T2.25 /9.82 48.95 79.13 33 29.30 '5.99 54.22 15.94 51.84 6368 78.61 19.96 5331 /9.89 50.60 79.4-1 34 29.14 /6.0S SS.88 16.00 53.49 all 79.45 Z0.03 SS.57 '9.96 52.24 79.68 35 29.98 16. M S7.f4 /6.07 SSI/4 64.17 80.29 20.10 57.23 20.03 33.88 79.96 36 30.91 /6.I7 SB. 20 16.13 5679 6442 81.1? 20.17 S8.99 20.09 5553 &>.& 37 31.65 /6.24 60.87 16.19 58.43 6467 $1.97 20.24 6o.5S 20.16 57/7 80.5Z 38 32.49 16.30 62.5) /6.2? 60.08 64.92 8Z.8I W.3I 61.21 20.23 S8.8I 80.79 39 33.33 16,36 64.19 /6.32 61.73 6S-.I7 83.65 20.38 63.87 20.30 60.46 VI. 07 40 434.; r I6A1 365.85 16.38 863.38 65.42 484.49 20.45 965.53 20.37 962.10 St. 3 5 41 35.01 /649 67.51 76.44 6S.oi 6567 8533 20.52 67/9 ^o.44 63.74- gl.63 42 35.94 76.55 69. 13 16. SI 66.67 65.93 86-17 20.55 68.85 20. SZ 65.39 81.91 43 36.6? 16.61 70.84 16.57 68.32 66.18 87.01 20.66 70.51 20.59 67.03 92.20 44 J7.52 fc.68 7250 16.63 69.97 66.43 87.8 f 20.73 72.18 20.66 68.67 82.48 45 MX /6.74 74.16 16.70 7/.6I 66.68 88.69 10.80 73.94 20.73 70.31 8276 46 39.20 1631 75.82 16.76 73.Z6 66.94 89 S3 20.87 7fo Z0.80 71.96 83.04- 47 4003 16.^7 7748 16.92 74.91 67./9 9o.36 20.95 77/6 20.87 73.60 8332 48 4o.l7 /6.94 79.15 16. V) 76.56 67.45 9l.2o 21.02 78.82 20.94 7S.24 83.61 49 41.71 17.00 a>.8/ 16.95 7&20 67.70 92M Z/.09 80.48 21.01 76.98 83.89 50 442.55 17.07 982.47 17.01 879.85 67.96 492.88 ZI.I6 982. 14 21.0$ 97ff.fi 84. 18 ft 43.39 17.1-5 84/3 17.08 S'.so 68.21 93.72 ZI.23 83.80 21. IS 80.17 4.46 2 4423 I7.'9 35.79 17.14 83.f4 68.47 94.56 21.30 5.46 Zt.23 81-81 4.75 S3 45.06 I7.2t> 6746 1721 84.79 68.73 9S.40 21.38 87./2 Z/.3O 83.45 85.03 54- 45.90 17.32 89.12 17.27 86.44 68.99 96.24 2 IAS 88.78 2/.37 95.03 #5.32 ff 46.74 17.39 9078 /7.34 88.0% 69.24 97.08 21.52 90.44- 2/.44 86.74 85.61 S6 4Z58 '7.46 92.44 17.40 0973 69.50 97.9* 21.59 92.10 21. SI 8S.38 85 89 57 4&4Z /7.51 94./0 17.1(7 9/.3S 9.76 98.76 2.1.61 93.76 2/.S9 90.02 #6.18 58 49.26 I7.S9 9S.7(, n.n 93.02 70.02 99.60 21.74 95.42 2.1.66 91.66 86.47 S? 50,o? 17.65 97.42 ,740 94,67 70.28 &0.4& Zt.81 97.0$ 21.73 93.30 86.76 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE 10 11 / T B c M Y Y T E C M X Y JO/. 28 2/.89 938.74 ZUSO 99494 87.05- 5.57.70 2kSO 10983 26.38 O93.3 /05.Z 7 02.12 2/.9fe looo.q- 1.68 96 SS 3734 52.54 26.58 noo.o 26.46 94.9 0559 1 oz.96 22.03 OZ.I ZI35 923 07.6} Si. 39 Z6.66 01.6 26.54 96.5 05.9/ 2 03.80 22.'/ 03.7 22.02 9287 87.K 54.23 2674 03.3 26.6Z 98.1 06.23 3 04.64 Z2.I8 05.4 22 .09 / 22.40 lOfl- 22.3/ 06.4- $9.08 J759 27.0 f 09.9 26.94 04.7 07.51 7 08.00 22.48 K.O 22.39 08. 1 89.38 58.43 27 J 5 //. 2702 06.4 07.93 g 08.34 22.55 '3.7 225% 09.7 89.b7 59.27 27-2? /3.^ 27./0 08.0 08.15 9 5Y?9.68 22.62 0/5-.3 22.54 10 II. 4- 89.96 5"6O.// 27.31 II 14-3 Z7./8 /A>9.6 108.4-7 to /0.S2 22.70 /70 226/ 13.0 90.26 60.96 27.39 16.6 27.26 //. ? 08.90 n 11.3k 22.77 /0.7 22.68 /4.6 90.SS 6 /.go 27.48 I8.z 27.75 /2.9 09. IZ 12. 12.20 22.85 20.3 22.76 /6.3 Sb.85 6Z.64 27.56 19.9 27.43 14. 5 09.44 n 13.04 22.92 22.o 22.83 /7.9 91.14. 63.48 2764 21.5 27. 5/ 16.2 09.77 14- 13.98 23.0O 2*6 Z2.9I /9-6 9144 64.32 27.72 23.2 27.59 17.8 /0.09 15 14.72 23.0? 25.3 22.9? 2/.2 9174 65./6 27.81 24.9 2767 19.4 10.4,2 '16 IS.5S, Si. IS 270 23.06 22.8 92.04 66.00 27.99 26.5 27.75 Zl.l /0.74 17 164-0 33.22 286 2J./3 24.5 32.33 66#5 27.97 28.2 27?4 22.7 11 .07 19 17.24 2J.30 *>. 3 23.20 26.1 92.63 6769 28.OS 9.8 Z7W Z4.3 11.40 19 518.09 30. 6/ 76.6 22.lt 51 44.97 25. 86 S5-./ 25.74 VO.Z 02.74 9547 30.g6 84.6 30.69 78.2 22.45 52 45". g2 25.94 86.7 ZS82. ?/.8 0306 96.3/ 30.95 86 Z 3o7s 798 22.79 53 4&Ct 26.02 884. 25 90 83.5 03.37 97/6" 3/.03 879 3o.87 91.5 23.14 54 47.50 26JO 90.0 2S.9S 85.1 0369 9^.00 3l.lt 89.5 3o.9S 83. / 23.4$ 55 48.34 26. 18 91.7 2606 86.7 O&oo 38.84 3/.*l 9/.2 3/.04 84.7 23.82 56 49. (8 26.26 93.3 26.14- ZS.4 043i 99.68 3/.30 9?.9 31.13 86.4 24.17 57 5J.02 26.34 9*0 Z6.Z2 90.0 04.63 600.51 3/.38 94.5 3l.il 88.0 24.52 58 -50.86 26.42 9fe.7 Z630 9/6 04.95 01.37 3/47 9fe.2 3/.30 89.6 ?4.95 57.03 37.55 05.5 37.30 970 48.73 6 07Z7 32.03 078 3/.9I IZOI.O 27.29 f788 37.64 07.2 37.40 98.6 4-9.11 7 09. // 32./8 09.4 32.00 02.7 Z7M 59.72 37.74 083 37.43 1300.3 49.49 e 08.95 32.Z7 /// 32.09 04.3 27.99 59.57 37.84- 10.5 37.S9 01.9 49.84 9 .7* 52.36 X2.7 32.18 or.9 20.34 60.41 3793 I2.\ 37.69 03.5 ,57.24 )o 6/0.64 3245 /2/4.4 &.zt \207.6 I28-7O 661.25 38.03 1313.8 37.78 13 OS./ I&.6Z II 11.48 32.54 /6./ 3^.^f 09.Z 29.05 62. (O 38.13 5.4 37. gg 06.7 SI.OO /z 12.32 32.63 /7.7 32.44 10.8 29.40 62.94 39.23 17.1 3797 08.4 5/38 n 13.17 32.72 /*4 32.53 124 29.75 63.79 39.32 18.8 3807 10 5776 14 14.01 32.81 21.0 32.62 14.1 30. to 64.63 38.4* 204 38. 1 6 11.6 52.15 15 14.95 32.90 22.7 32. 71 15.7 30.46 65.48 38.52 22.1 38.26 /3.2 52.W 16 IS.69 52.99 243 32.90 /7.3 30.8/ 66.32 38.61 23.7 38.36 14.9 52.91 17 16.54 I?.0g 26.0 32.9) /9.0 3/J7 67. /7 38.71 254 38.45 16.5 53.29 18 19 17.38 19.22 33.17 33.26 27.7 29.* 32.98 33.06 20.6 22.Z 31.52 31-99 68.01 68.86 38.91 30.91 270 28.7 3&SS 38.65 IB.I '9.7 SSL 7-6 619.07 33.35 J25/.0 5/lS IZ23.8 1 32.23 669.70 39.01 1330.3 38.74 /32A3 A54.44 Zl 19.91 33.44 32.6 33.24 25.5 32.59 70.54- 39.10 320 38.84 23.0 54.83 2t 20.75 33.H 34.3 33.33 27J J2.94 7/.39 39.20 33.7 38.94 24.6 55. z/ 23 ZI.6O 33.62 35.9 33.41 28.7 J3.30 72.23 39.30 35.3 39.03 26.2 5560 24 25 22.44 23.28 .7/ 33.80 376 39.3 33.W 33.60 30.4 32.0 33.66 34.02 73.08 73.92 39^40 39.50 37.0 38.6 39. 13 3923 27g 29.5 55.98 56.37 26 24.13 33.99 40.9 33.69 3J.G 3438 74.77 39.60 44.3 39.32 31.1 56.76 27 24.97 33.96 42.6 33.78 J5.2 34.74 7S.6I 39.70 41.9 39.4? 32.7 57. If 28 25.8 ; 34.09 44.2 33*7 J6.9 35./0 76.46 39.79 43.6 39.52 34.3 57.53 & 6.66 34.17 45.9 3-3.96 38.5 35.46" 77.30 39.99 45.2 39.6? 353 579? JO 627.50 34.26 /Z47.5 34.06 24o.l /^5.82 679.15 39.99 '346.9 39.7,? 1337.6 158.31 31 2S.34 34.35 49.2 34.15 41.8 36.19 79.99 4009 4#.6 39.SI 39.2 59.70 32 29. /9 34 44 Jfc.9 34*4 43.4 36.54 79.84 40. 19 50.2 39.9; 40.8 59.09 33 1003 3453 525 34.33 45.0 36.90 80.69 40.29 51.9 40.01 42.4 59.48 34 30.87 34.63 S4.Z 34.42 46.6 3726 9153 40.39 -5J.5 40.11 44.0 59.87 35 3A72 34.72 55.9 34.51 49.3 37.63 92.37 40.49 552 40.11 45.7 60.26 36 32.56 J4.? 57.5 34.60 49-9 3799 #3.22 40.59 5S.8 40.31 47-3 60.65 37 33.40 34.90 59. \ 34.69 51.5 38.35 8J4-06 469 59.5 40.40 48.9 61. 05 38 34.25 35.00 60S 34.78 53.1 3972 54.91 40.79 60.1 40.50 -S-0.5 6/.44 39 35.09 35.09 624 34.88 54.9 39.08 95.76 40. 89 61.8 40.60 52.1 61.83 4o 635:95 35/8 #64.1 34.97 1156.4 139.45 626.60 40.99 1363.4- 40.70 35*8 I62-.Z3 41 36.7? 35. 28 6 8 35T06 58.0 39.91 87.45 4l.o9 65. / 4o.go 55.4 62.62 42 37.62 35.37 674 35.15 59.6 40.18 88.29 4/./9 66.9 40.90 57.0 63.01 43 39.46 35.46 69. / 3S.24 61.3 4o.5F 89.14 4/-29 684 4/.00 SZ6 63.41 44 39.31 35.56 70.7 35. )4 62-9 40.9/ 89.98 4/.40 70.I 41.10 6o.2 63.90 45 40.15 35.65 72.4 35.43 64.5 41.28 9a8J 4/.50 71.7 4/.20 6/.9 64.20 4G 41.00 35.74 74.0 35.52 66.1 4I.K 91.67 41.60 73.4 4110 6J.F 6460 47 4/84 35.94 7S7 35. 61 67.8 42DZ 92.52 41.70 75.0 4/40 6S-.I 6499 48 4ZM 35.93 77.4 35.71 69.4 42.39 93.36 41.90 767 41.50 66.7 65.39 49 43.53 36.03 79.0 3S.90 7f.o 42.76 94.21 41.90 78.3 41.60 68.3 65.79 .TO 644.37 36.12 /2B0.7 3589 IZ72& 143.13 695.06 42.00 1390.0 4-1.70 1370.0 166.19 5/ 45.21 36-ZI 8^3 ^5-99 74.3 43.50 959o 42.JI 91.6 41.80 7/.6 66.59 52 4606 36.31 4.0 J6.Gg 7S.9 43.87 96.75 42.21 83.3 4V. 9o 73.Z 66 98 53 46^0 34.40 56 36.17 77.5 44.24 97.59 42.31 95.0 4200 74. 8 67.38 54 47.7^ 36.50 87.3 36Z7 79. / 44.61 98.44 42.4 / 86.6 42.10 76. .4 67.78 55 4. 36.59 !*.9 36.36 80.8 44.98 99.28 42.51 88-3 42.20 78.0 68.18 J"6 49.43 36.69 9fl6 3645 824 4*.3J 700. / 3 426? 89.9 42.30 79.7 68.59 57 AJEI 36.71? 9EJ 36.55 P4.o 45.7* 00.98 42.72 91. 6 42/W 81.3 68.99 58 5/./Z 3fe98 93.9 J664 856 46-10 0/.8Z 42.82 93.2 42.51 92.9 6939 5? 5A97 ,?6.,97 ?*h ?6.74 87.3 *4fl8 02.67 W3 ?4.9 42.61 84,? 69.79 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE 17 |4? 15 / T E c M X Y T C M y Y 7O3.5I 43.03 1396.5 42.7/ I386./ \7O2P 7f4.32 49.44 )49S7 49.02 1482.9 I9f.23 O 04.36 43.13 90.Z 42.81 877 70.60 SS.'7 49.55 97.4 49. 13 #4.6 95:66 1 Of.ZO 43.24 99.8 4291 99.4 71.oo 56.02. 49.66 99.0 49.24 06.2 96. lo 2 06.05 43.34 1401.5 43.0 / 91 o 7/.4I S6.97 49.77 1500.7 49.34 979 96.53 3 0690 4*44 03.2 43.12. 92.6 7/.8I S7.7/ 49.88 02.3 49.45 89.4 96.96 4 07.74 A3. 55 04.8 43.2Z 94.Z 72.22 5&S(, So.oo 04.0 49.56 9/.0 97.40 5 08 S ~9 43.65 06.5 43.32 95.8 72.62 5-9.41 SO. II 057 49.67 9Z.(, 97.83 6 09.4-3 43.75 02.1 4)42 97.4 73.03 60.26 So ZZ 07.3 49.78 94.2 98.26 7 to.i* 43.86 09.8 43.52 99J 73.44 61.11 So.33 09.0 49.89 9f.S 98.70 8 11.13 43.96 11.4 43.63 14007 73.94 6I.3S S044 /o.t, 50.00 974 99.13 9 7//97 44.07 1413.1 43.73- 14021 174.25 76Z30 S0.55 If/23 50.11 1499.0 199.57 /O /2.8Z 44.17 14.7 43.93 03.9 74.66 63.65 So 67 '3.9 50.22 15-006 ZOO.OI // '3.67 4427 '6.4 43.94 Of. 5 75:07 64.50 SoT8 '*.<> So.33 02.3 00.44 /2 14.5-1 -44.3? /g.O 44.04 07. f 7JI48 65.35 So.99 17.Z 50.44- 03.9 00.88 /3 '$-.36 44.48 19.7 44.14 08.8 7S.89 66.20 5/.00 '8.9 50.55 05.5 0/32 14 16. 20 44.?9 21.3 44.24 '0.4 76.30 67O4 s/n ZO.S &.(>(, 07. / 01.76 fS 17.0 f 4469 3 o 44.35 I2.o 76.71 67.99 S/.23 22.2 S0.77 Og.7 02.19 '6 17 90 44". 80 24.7 44.4-5 13.6 77.12. 68.74 S'M 23.8 S0.88 /0.3 02.63 17 '9.74 44.90 26.3 44.56 15.2. 77.53 69.59 S'.*S 25.? f/.OO If. 9 03.07 '8 f9.59 45. o; 28.o 44.66 I6.B 7/94 70.44 S/.S7 27.1 f/./> 13.5 03.51 '9 72O.44 45.12 J49.6 44.76 14184 170.35 77/.Z9 S/.(,8 15-28.8 S/.ZZ /&5.I 2.03.95 Z-0 21,28 4-5:22 31.3 4427 20. \ 79.77 72.13 51.79 30.4 51.33 X6-.7 04.39 21 22. 13 4S.33 32.9 4497 21.7 79.18 72.98 fl.9t 32.1 S/.44 /8.3 04.84 22 22.98 45.43 34-6 45.08 23.3 79.59 73.^3 52.02 33.7 S/.SS 19.9 OS.18 23 23 82 45.54 362 45. 18 24.9 SO.oi 74.68 52.13 35.4 S/.66 ZI.5 05.72 24 4.67 45.65 37.9 4S.2S 265 8042 Tf.53 52.25 37-0 S/.77 23.2 06. /6 25 25.52 4S.7S 39.5- 45.39 23. / 80.84 7638 52.36 38.7 S/.89 24.8 06.61 26 2636 45.6 41.2 4S49 29.7 81-25 77.23 52.47 4o.3 SZ.oo 264 07.05 27 2.7.21 45.96 42$ 45.60 31.4 81.67 78.07 5259 42.o 52.11 80 07.49 28 2?. 06 46.07 44.5 4S.70 33.0 82.09 78.9 a 52.70 43.6 52.22 29.6 07.94 -Z9 723.90 46.18 14462 45.91 1434 .6 18250 779.77 ,52.82 1545.3 5234 Ittl.Z 208.38 30 29.75 46.2? 478 45.91 36.2 82.92 80.62. 52.93 469 52.45 323 09S3 31 30.60 46.39 49. f 46 02 37.8 83.34 21.47 53.05 48.6 5J.S6" 34.4 09.28 32 J/.44 46.50 51.1 46.>2 39.4 31.76 9232 53.16 50.3 52.67 ?6.0 09.72 33 J2.29 4-6.61 52.8 46.23 4-1 O 84.18 83.17 5/28 SI. 9 52.79 37.6 10.17 34 33. /4 46.71 54.4 46.34 42.7 84.60 84 02 5339 &.(, 52.90 39. 2 I0.6Z 35 33.99 Af>2l 56.1 4644 44.3 85.02 84.96 53.51 55.2 S3.0\ 40.8 11.07 36> 34.33 46.93 577 46.55 45.9 8544 85.7/ 5*6? 56.9 53.12 42.4 )L5I 37 35.6? 47.04 59.4 46.6? 47 S 85.96 86.56 53.74 58.5 53.24 44.0 /t.96 30 3653 47. 15 6l.o 46.76 49.1 86.28 74/ 53.95 60.? 33.35 45.6 12.41 39 73737 47.25 1462.7 44.87 14*0.7 18670 78.26 5337 I5-6I.S S3.46 M7.Z 2/2.86 40 38.22 47.36 64-? 46.97 52.3 87.12 89.11 54.08 63.5 S3.SB 48.8 13.31 41 39.07 4747 66.0 47*0 53.9 87.54 89.96 54. *0 65.1 53.69 50.4- 13.76 4Z J9.9Z 47.5* 67.6 47/9 55.6 87.97 90.91 54. 32. 66.9 S3.SI &] I4.ZI 43 40.76 47.69 69.3 4729 57.? 08.33 97.66 54.4-3 68.4 53.92 5-J.7 X4.67 44 4-1.61 4780 70.9 47.40 58$ 98.92 92.5"' 54.55 70.1 54.03 5^3 IS. IZ 45 42.46 47 #> 72.6 47.51 60.4 89.24 93.3 5-4.67 7t.7 54 .15 6\9 I5-.S7 46 43.?o 48.01 743 47.61 620 89.67 94.ZI 5478 73.4 5-4.26 5R5 16.02 47 44. >5 42.12. 7f.9 4-7.72 63.6 90.09 9J-.05 54.90 75-.0 54.3* 60.1 16.49 48 45.00 48.23 776 47.83 65JJ 70.52 95.90 55;oz ~%.7 S4.49 61.7 S6.93 49 745.F5- 48.34 1479.2. 47.94 )4668 190.9^ 796.75" &.I3 1578.3 54f>\ 15633 2/7.39 fO 46.69 48.45 80.9 48.04 68A 9137 97.60 55.ZS 80.0 54.72. 64.9 17.24- 51 47.54 48.56 82.5 48. IS 70.1 91.80 9*.*$- 55.37 8t.G 54X4 66.5 18.30 52 49.39 48.67 84.2 48.26 71.7 92.23 39.30 5S148 83.3 5495 68.1 I8.7S S3 4-9Z4 48.78 85.8 48.37 73.3 92.65 800./5 55.60 84.9 55.07 69.7 V.2I 54 So.08 48.81 37.S 49*8 749 93.08 OI.OO 55.72 86.6 5S.I8 71.3 /9.67 55 So 93 49.00 99.1 48.58 76.5 93.51 01. SS 55.94 98.2 55.30 72.9 20.12. 5-6 5/.7* 4^11 90.8 4*69 7g.l 93.94 02.70 55.9S 89.9 SS.4I 74.5" 20.5-8 S7 52.63 4922 92.4 48.80 79.7 9437 03.55 56.07 9/.5 55.53 Tf.t 21.04 5S 53.48 49.33 941 48.91 9 1.3 94.80 04.40 56.19 932 55.64 77.7 21. SO 59 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE , 16 \r T E C M X Y T E C M X Y 805.25 56.31 1594.8 J5.76 I57S>3 2Z/.96 856 3O 63.63 163J.S 62 94 16/5" 2 25036 / 06. 10 56.43 96.5 55.88 80.9 57.15 63.76 95.4 6*06 76.8 $0.85 2 0& QB S6.5S 98.1 55.93 815 22.89 58.01 63.89 97.1 63. 18 78.4 513} 3 07.90 56.66 56.11 84.1 ^3.34 58.86 6401 98.7 63.31 Boo 51. 81 4 08.65 56. 7g 1601.4 S6.Z3 85.7 23.90 5971 64.1 A 1700.4 63.43 8/6 S2.3I 5 09.50 56.90 03.1 56.34 87? 24.26 . 60.56 64.27 02.0 63.55 83.2 fl.80 6 10. 35 57.02 04.7 S6.4(, 98.9 24.73I 1 255-.2S II 14.60 5762 13.0 S7.04 96.9 27.04 65.68 65.03 11.9 64.30 32.7 55.75 IZ. I5.4f 57.74 I4A 9.5 27-50 66.53 65.15 13 (, 64.4Z 94.3 56.Z4 13 16.30 57.96 16.3 S7.23 \6oo.l 27.97 ^38 & 5" 2.% 15. 2 64.55 95.3 56.73 14 17.15- 57.98 17.3 S7.40 01.7 2843 68.23 65.41 /69 64.67 97.5 5723 15 18.00 19.6 57.51 OJ.3 28.90 69.09 65.54 /8.5 6400 99.1 57.72 /G 19.95 58.22 2/.2 57.6) 04.9 29.37 69.94 65.67 20.? 64.92 I7O0.7 Sg.ZI /7 13.70 5834 22.9 S7.75 06.5 29 93 70.73 65.79 21.9 65.05 02.3 /8 2o.F5 59.46 24.S 57.37 08.1 3030 7/.64 65.92 2*5 65.17 03.9 f9.ZO /9 2/.4o 58.58 26.2. S7-99 09.7 30.77 7f.5o 66.05 2.5-.I 65.30 S9..70 20 8ZZ.25 50.70 ;62.78 50.10 161 1.3 Z3I.24 97J.3F 66. 18 1726.8 642 1707.0 260.20 2 1 23. 10 58.92 29.5 58.22 /2 3 31.71 74.20 66.31 28.4 65.5-j 08k 60.69 ez Z3.9S SB. 94 31.1 58.34 H's 32.18 75.05 66.44 30.0 65.67 61. 19 23 2*J QO 59.06 32-8 58.46 16.1 32.65 7*9 1 6.6.56 31.7 65.80 U'-9 61.69 4 66 59.19 34.4 17.7 33. 12 76.76 6669 33.3 65. 93 13.4 t>2.\3 25 26.5-7 59.31 36.1 57.70 19.3 33.59 77.6 \ 66.82 35.0 66.05 15.0 62.69 G 27.36 59.43 37.7 53.82 20.9 34.06 78.47 66.95 66./g /6.6 *>*.)% 27 22.ZI 59. 5 f 33.4 22.5 34.53 79.32 67.08 38.3 66.30 19.2 63.68 29 29.06 5967 4l.o 5*9.06 24- / 35.00 80.17 67.21 39.3 66.4J 19-9 64.18 29 59.79 4Z.7 59. n 257 35.48 81.02 6734 4/6 66.56 2.1.3 64.68 3o 830.76 S9.9I 1644.3 .59.29 16273 235.95 891.88 67.47 1743.2 66 6g 17223 265.19 31 3/.6I >o 04 46.0 59.41 28.9 36.42 82.73 67.60 44.3 66'.gl 24.5 65.69 32 3246 60.16 47.6 59.53 30 f 36.90 83.58 67.73 46.5 66.94 Zf>.\ 66.19 33 3J.3/ 60.28 4-9.3 5*65 3SJ 3737 84.44 67.86 48.2 6707 27.7 6669 314 3A./6 60.40 F09 S9.77 33.7 3795 85.29 67*9 49.8 67(9 2.9-3 67/9 315 J!5" 01 fyC 5*3 52.6 35.3 38.32 86.14 68.12 51.5 7 ?2 30.9 6770 36 35-87 60 '65 54-2 60.01 36.9 58.80 #700 68.25 53.1 6745 32.5 68.20 37 36.7* 60.77 SS9 60.17 38.5 39.27 87.8S 8.38 548 67.57 34.1 6871 39 37-57 60.99 60. zs 4o.l 39.75" 88.70 68.51 564 67.70 35.7 69.21 39 38.41 6 (.02 59 S Z 60.38 41.7 40.23 99. 5 6 68.64 58.1 6793 372 69.71 40 839.27 61.14 1660.9 60.50 1643.3 240 71 990.41 68.77 1759.7 67.96 1738.9 Z70.ZI 41 4o.lZ /-2& 61.5 60.6Z 44.9 41.19 91.2k 6891 61.3 68.09 4o.4 70.73 AZ 40.97 61.39 64.1 60.74 46.5 4-1.66 92.12 69.04 63.0 68.21 Atp 43 4/.|J 61.51 65.8 60.96 4-8J 42.14 92.97 69.17 64.6 6J4 43.6 71.74 44 / 64 674 60.98 49.7 42.6Z 9J.82 f>9 3o 66.3 68.47 45. Z 72.25 45 43'.53 6l'.76 69. 1 61.10 51.3 43.10 94.68 69.43 679 68.60 46.8 72.76 46 44.38 61.98 70.7 6I.ZZ 52.9 43.5? 95.53 69.56 69.6 68.73 48.4 7j 26 47 4S.2.3 62.01 72.4 61.34 54.5 44.06 96.39 69.69 71.2 68.86 49.9 7J.77 48 46-08 6Z.I3 74.0 61.47 56 1 44.54 97.24 6983 72.9 68.99 SI. 5 74.28 49 46.93 62.26 75:7 61.59 S7.6 4-5.03 98.09 69.96 74.5 69.11 53.1 7479 So 847.78 62.38 1677.3 61.71 1659.2. 245. 51 898.95 70.09 177*. 2 69.24 I7F47 2753o 51 4% 64 62-5' 79.0 61.81 60.8 45.99 99.80 70. 21 778 69.37 56.3 7$ "81 52 49.'49 61.95 62.4 46.48 900.65 7036 79.5 69.50 57.9 7*32 53 fO.34 6Z76 82.3 62.08 64.0 OI.5/ 70.49 91.1 69.63 59.5 7^.84 54 5V. /9 6z.es 93.3 62.20 65.6 47.44 02.36 70.62 82.8 69.76 61.0 77.35 55 52.04- 63.01 85.5 62.32 67.2. 47.93 03.2Z 70.75- 844 69.89 62.6 77.96 56 S2.99 63.13 6244 68.8 48.4-1 04.07 a?.89 86.0 70.ot 64.2 76.37 57 53.75 63.26 99% 62.57 70.4 49.90 04.92 71.01 877 70.15 65.9 78.89 58 S4.60 63.30 49.38 05.78 7A/5 85.3 7o 28 674 79.40 5"9 63.51 9Z.I 62.8' 74.6 49.97 O6.63 7/.29 91.0 /fc4l 69.0 79.91 UNIVERSH TAB! ^FUNCTIONS OF A ONE-DEGREE CURVE 18 19 / T E c M X V T E C M X Y 907.49 71.41 I792.& 70.S4 n?o.(= 290.43 9S8.BI 7967 1891.3 78.58 J565.4 312.16 O 08.34 7/.5S 94.3 70.67 72.1 80.94 59.67 79.81 930 7872 67.o 12.70 O9.2O 7/.69 95:9 70.80 73.7 81.46 60.*] 79.95 94.6 7835 68. S 13.25 2 lo.os 7/.S2 976 709) 7Z.3 81.98 61.38 90.) '0 963 78.99 70.1 13.79 3 IO.9O 7/% 99. 2 7/.06 76.9 8Z.49 6f.Zt- $014 97.9 79.13 71.7 14.31 4 11.76 72.03 800.9 7/./9 78. 5 83 .01 6i.lo 8o.)9 995 79. Z7 73.3 /4.98 5 12.61 72.22 02.5 7/.J* $0.1 83.53 63.96 80.52 1901. 2 79.41 748 15.42 6 13.47 72.X, 04.2 7'Af, 91.7 84.05 6431 90.66 028 79.54 76.4 IS 97 7 14.31 72.4") 05.8 7/5"? m 84.57 65.67 BO.BI 04.5 79.68 78.0 16.51 8 15.18 72.63 07.4 7/72 84.8 85.08 66.53 go.95 06.1 79.8Z 79.6 17.06 9 91603 72.76 S09.I 7/.r 78(>4 285.60 967.38 g/.09 1907.8 7996 1891. 1 3>7.6I /o 16.89 72.90 10.7 7/98 8B.O 86./2 68.24 8/.23 094 80.10 827 /8.I6 // 17.74 73.03 12.4- 72.11 89.6 6.64 69. to 61.38 If-/ 8o.l4 84.3 18.70 12 18.60 73.17 I4.o 72.25 91.2 87.16 69.96 $1.52 12.7 $0.3% 85.9 19.25 13 19.4-5 73.30 IS. 7 72.38 92.7 87.69 70.91 S/.66 143 80.52 87.4 19.90 14 20.31 7344 17.3 72.51 943 88.21 71.67 81.81 16.0 #0.66 89.0 20.35 15 21. It 7J.S8 19.0 72.64 959 88.73 7Z.S3 8f.9S 17.6 00.79 90.6 Z0.90 Ik 22 02 73.71 20.6 72.78 97.5 e9.2S 73.38 82.09 19.1 S0.13 92.2 21.45 n 22.87 73.25 22.3 72 9/ 99.1 8977 74.24 82.2* 20.9 21.07 93.7 22.00 19 23.73 73:98 23.9 7J.04 BOO.G 90.30 75. 10 02.38 22.6 21. 21 9X3 2155 /9 924.58 74.it ;825.6 73. / 7 802 a 23o$2 97*96 82.53 /924Z 8/.3f 8969 323.10 20 25.44 74.26 27Z 73. 31 03.8 97.35" 76.91 9t.er 25J8 8149 98.5 23.66 21 26.29 7*39 28.8 73.44- 05.4 91.27 77.67 82.21 17.5 81.63 9oo.o 24.21 2t 27. 15 7*53 305 7357 07. 92.40 7853 82.96 29.1 21.77 01.6 24.76 23 29.00 74.67 32.1 73.70 08.6 92.92 79.39 8J.IO 30.g 81.91 03.1 25.31 24 28.86 7480 33.8 7*84 10.1 93.45 SO 24 83.25 32.4 82.05 04.7 25.87 25 -29.7/ 7494 35.4- 73.97 11.7 93.98 8/./0 83.39 34.1 82.20 06.3 26.42 26 3057 Tf.08 37.1 74.11 13.3 94. fo 81.96 83.54 35.7 82.34 079 26.98 27 3/.4Z Tf.21 38.7 74.24 14.9 95.03 8E.2 83.62 37? 82.48 09.5 "27.53 28 32.28 7S.35 4o.4 74.37 /6.S 95. S6 83.68 83.83 39.0 8Z.62 ll.o 28.09 29 933.13 7*49 1842.0 74.51 J8/8.0 296.09 984.53 83.97 /94o.fc 32.76 J9J2.6 318.64 30 33.39 7#-63 43.6 74.64 19.6 96.61 85.39 84.12. 42-3 82.90 14.2 29.20 31 54.84 7f.76 45.3 74.77 21.2 97.15 86.25 84.26 43.9 83.04- 15.7 29.76 32 35.70 7X90 4&9 74.91 22.3 97.68 87. II 84.V 45.6 B3.IS 17? 30.32 33 36.55 76.04 4-3.G 7JT.04 Z4.4 98.21 97.97 84. 5T 472 $3.32 18.7 30.87 34- 37.41 76.18 50.2 75 19 2 9 99.74- $832 94.70 4-8.9 8347 20.S 31.43 35 38.27 76.32 SO 75.31 27.5 99.27 89.68 34.85 50.5 83. 61 22p 31.99 36 39./Z 76.45 53.5 75.45 29. / 99.90 90.54 9499 52.. 1 33.75 236 32.55 37 39.98 4o.93 7659 76.73 55.2 56.8 75.58 75.72 30.7 32.3 300.33 00.87 9/.40 92.26 85.14 95.28 53.9 S5.4. 33.99 94.03 25T.2 26.7 33-H 33.67 38 39 941.69 76.37 IS58.4 7f.3S /833.S 301.40 993. K 85.43 I9f7./ 84.1S 1928.3 334.23 4-0 42.55 77.oi 60.1 7f99 35.4 OI.93 93.37 85.58 59.7 84.32 29.9 34.79 41 43.40 77.15 (,1.7 76.lt 370 02.47 34%3 85.72 60.3 S4.4S 3/.4 35J5 4-t 4426 77.29 63.4 76.26 3B.(, 03.00 95.69 S5.87 62.0 94.60 33.0 35. 9? 43 4-5.11 77.43 65.0 76.39 40.Z 03.54 9&S5 86.02 63.6 84.7S 34.6 36.49 44 45.97 7757 66.7 76.53 41.7 04.07 97.4; V6J7 6f.3 84.89 367 37.04 45 46.83 77.70 69.3 76.66 43.3 04.61 98.27 96.31 66.9 85.03 377 3760 46 47.68 77.94 70.O 763,0 443 05.14 99. 13 86.46 68-5 f.|8 39.3 38.17 47 48.54 77.98 7L6 76.94. 46.5 05.68 99.98 86.61 70.Z 8S.32 40.9 38.73 M 43. 39 Tg.lZ 73.2 77.07 4*0 06.22 1000.8 86.76 7t.3 85.46 42.4 39.30 49 950.25 78.26 1*743 77.21 1849.6 306.76 IOOI.7 86.90 1973.5 85.61 J944.0 339.86 so 5/.M 78.40 76.5 77 35 5U 0729 02.6 0705 7F.I 97S 455 40.43 51 SI 96 78.54 78* 77.49 52.8 07.8? 03.4 87.20 768 85.89 4.7.1 A039 52 52.82 70.62 79.9 77. 61 54.4 08.37 04.3 8735 78.4 86.04 48.7 41.56, 5*68 78 8? 81.5 77. 76 5J.9 08.9/ 05.1 3750 Bo.o 96.18 50.3 42.13 54 Jaw 78.97 83.1 77.99 575 09.45" 06.0 8764 81.7 86.32 51.8 42.70 SS SS.39 79.11 84.9 79.03 59. / 09.99 06.9 8779 93.3 et.47 5*4 43.26 .56 5624 79.25 86.4 78.\7 60.7 /0.53 07.7 8794 850 96.61 55.0 43.83 5? 57/o 79.39 88.0 79.30 62.2 11.07 08.6 88.09 866 86.76 56.5 44.4o 58 57.9fe 79.53 89.7 78.44 63.8 II.6Z 09.4 88.24 8V.Z 869o 58.1 44.97 59 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE / 21 T E c M X Y T E C M X Y 10/0.3 8339 19893 "B7.0F 1959.7 34554 IO6/.9 9752? 20883 95.94 053.3 3gQ56 / 11.2 8854 9/5 S7./9 6/.Z 46. // 62.9 977/ 89.9 96./.3 59.44 ^OOI.4 88.06 70.6 49.5 A 68.0 W68 99.8 97.01 64.2 94.75 S 17. 2 89.59 O3.o 99 Zl 722 50.12 688 98.84 Z\o\A 97/6 65.8 85.X 9 I8P 8974 04.7 98.35 73.7 50.69 69.7 990) 03.0 97.32 673 85.95 IO 1018.9 89.89 2oo63 SSSo '97S3 3?/.6 J070.6 99.15 2/04.7 97.47 2068.9 386.56 11 197 90.04 07.9 88.15 76.9 51.84 7/4 9931 06.3 9762 704 87.16 IZ 206 9o.l9 09.6 88.79 7g.4- 5241 72.3 95.47 O8.o 9777 72.0 87.76 /) 21.5 9o.H 11.2 88.94 ?0.o 5239 73. / 99.63 09.6" 979? 73.5 88.36 it- 223 90.49 12.9 89.08 g/.6 53.57 74P 99.79 11.2. 9*08 7SJ 88.97 is- Z3-2 9o.64 14. S 89.23 83./ 54.14 74.9 99.95 72.9 98.2? 76.6 $9.57 /6 24.0 9079 16.1 ?93g ?4.7 54.72 7J7 100.11 74*5" 98.39 78.2 90. 1? 17 24.9 9o.94 178 89.52 96.3 55.30 76.6 00.17 /6.7 9?54 79.7 90.78 J8 25.8 91.10 /9.4 99.67 S78 5587 77. S 00.43 /7.g 9S70 81.3 9/38 /9 26.6 91. ZS 2/.I 99.92. 89.4 ft.4y 70.3 00.59 19.4 5>8.'8S 82.9 97.99 ZO IOZ7.S 91.40 2022.7 89.96 1990.9 357.03 /079.Z I00.7S 2121. 1 99.00 2084.4 392.60 it 28.3 9I.SS 24.3 90.11 92.S 57.61 SO.o 00.91 22.7 991k 86.0 93.20 2Z 29.2 91.70 26.0 90.26 94.1 S8.\9 80.9 01.07 *4.3 99.31 87.5 93.87 3 30.1 91.86 76 90.41 95.6 58.77 81.8 0/.23 26.0 9947 99. 1 94.42 24 J0.9 92.01 29.5 9o. SS 97.Z 59. JF 82.6 0/.39 276 99.6Z 90.6 9f.03 25 3l.g 92.16 J0.9 9070 388 539 83.5 0/.55 29.2 99.78 92.2 95.63 26 32.6 92.31 32.5 90.85 2000.3 60. S 4.4- 0171 30.9 99.93 93.7 76.24 27 33.5 93.47 34.2. 91.00 0/.9 61.10 85.2 01. S 7 32.5 JOO.O9 95.3 96.85 29 34.4 92.62 35.8 91.14 03.4 6I&8 86. \ 02.03 34-2 O0.24 96.8 9746 29 3 92.77 375 91.29 05.0 62.26 f(>.9 02.J9 353 0040 98.4 98.07 3& /036.I #.92 2039. 9/.44 2006.6 362.85 1097.9 /02.35 27374 /00.SS 20999 398.68 3/ 370 93.08 40.7 9/.S9 OS.I 63.43 88.7 02.51 39.1 00.11 ZIOI. 5 99.29 3i 37 93.23 4z* 9A74 09.7 64.0/ 89. 5 0267 4o.-7 00.86 03.0 9991 33 38.7 93.38 44.0 9/.89 n.z 64.60 90.4 02>3 42.3 0/.02 04.6 400.52 34 335 93.54 4F.7 9204 72.8 65. /8 913 02.99 44.0 01.18 06.1 01.13 35 4o.4 93.69 47.3 92 (8 /4.4 65.77 92.1 03.16 45.6 01.33 077 01.74 36 41.3 93.85 48.9 9Z.33 'f.9 6636 93.0 0332 473 O/.49 09.Z 02.36 37 42.1 94-.oo 506 92.48 '7. S 6694 93.9 .7 9ST.W 67.0 W.98 33. \ 72.83 02.5 OS.\\ 65!3 03 .21 26.3 09. J 3 4 5/.6 95:70 6g 94.13 34.6 73.43 03.4 05.27 669 03.37 27.8 0975 44 .524 ar.86 7* 94.29 36.t 74.02 04.2 05.43 eg.f 03.53 29.4 10.37 SO 7053.3 96.0| 207/.9 14.41 20378 374.6 ( 05. 1 /.34 70.1 18.25 92.2 /5.96 464 5874 5 /$*) 09.23 96.4 06.23 556 20.97 70.9 1842 94.4 16.01. 490 59.39 6 /s'g 0844 98.0 06.39 S7Z. 21.59 7/.g 18.60 96.0 /b.\9 49S 6005 7 20.7 02.56 99.6 06.55 587 22.22 72.7 1877 97.7 51.0 60.70 8 21.5 08.73 tZOI. 3 0671 60.3 22.35 77.5 1894 99.3 /6.52 6136 9 //224 (08.90 2202.9 106.87 2/6/.S 423.46 //74.4 J19.I2 23009 1/669 2254 / 46101 /0 23.2 09.06 04,5 07.03 63.4 Z4.ll 7f.3 19.29 02.6 16.86 55.6 62.67 H 24. / 09.23 06.2 07.19 64.9 24.74 76.1 19.47 O4.2. 17.03 571 63.33 / 25.0 09.40 07.8 07.35 66.4 25.37 77.0 19.64 05.8 I7./9 587 63. 98 13 25.8 09. 56 09.4 07.51 68.0 26.00 77.9 07.5 17.36 60.2 64.64 /4 26.7 09.73 II. / 07.67 69.5 2643 1939 09.1 /7.S3 61.7 65.30 IS 276 09.90 /2 7 07.23 71.1 27.26 79.(> 20.17 '0.7 17.70 63.3 6594 /& 294 10.06 14.3 07.99 72S, 27.09 90S 124 17*7 64.8 6&62 17 29.3 IO.Z3 16.0 08.15 742 2*52 20.52 140 12.03 66.3 67.27 3o.i /0.4O '7.6 08.31 7S.7 29. IS 82.Z 20.69 IS.G, 679 67 93 /9 113 1.0 3/.9 110.57 10.73 2219.2 20.9 03.64 2,177.2 79.9 429.79 3041 83.9 21.04 23/73 19.9 U837 W.S4 2269.4 70.9 468.59 6925 20 2.1 32.8 10.90 22.5 08.80 $0.3 31.06 21.22 20.5 19.71 7t.S 69.9' ZZ 33.6 II O7 24.2 08.96 81.9 3/.69 95.7 21.40 ZZ.Z 18.88 74.0 70.58 23 345 11.24 25{? 09.12 634 32.32 86> 21.57 Z3.8 I9.0S 755 24 35.4 11.41 27.4 09.19 84.9 3? 96 874 25.4 19.11 77.0 7I9O W 362 11.58 29. / 09.44 36.5 336O 21.92 27. / /9.18 786 7256 26 37.1 11.74 J0.7 09.61 89.0 34.23 99.2 22.10 297 19. 55 8o.l 7J.23 27 32.0 11.91 32.3 09.77 896 34.87 90,0 22.28 303 19. 72 81.6 73.29 23 38.8 '2.08 .o 09.9} 91.1 35.51 90.9 22.45 32.0 19.99 83.Z 74.55 9 1139.7 112.25 2235.6 110.09 2192.6 4-36.14 1/9 /? /Z2.63 2333.6 \VDjO6 2284.7 473T22- 30 40'6 '2.42 372 IO ?6 94. Z 36.78 22.81 35.2. 20.23 86.1 7SB8 31 41.4 12.59 38.9 10.41 95 7 37.4Z 93.5 22.99 36.9 2040 97.7 76.55 3Z 42.3 12.76 40.5 /O.S8 973 38.06 94.4 23J6 20.57 89.3 77.21 33 43.2 12.93 42.1 1074 98.8 38.70 9S.Z 23.34 40.1 20.74 908 34 44o n.io 43.8 tO 9/ 2200.3 39.34 96.1 23.52 4-1J8 20.9/ 5123 ~7S 5*5" 44.9 13.27 454 //.07 01.9 39.98 97.0 23.70 43.4 21.08 9*9 79. 11 36 45.8 /3.44 470 // 23 03.4 4o.62 979 23.27 21.25 93-4 7928 97 46 13.61 42.7 11.40 O5.0 4/.26 24.05 46k 21.42 969 80.55 47.5 13.78 & 3 . //.56 06.5 41.90 99.6 24.23 48.3 11.59 98* 81.22 39 114-8.4 113.95 2251.9 ///73 2208.0 44254 /200.5 124.41 2349.9 111.77 23000 481.88 40 49.2 14.12 Si 6 1129 09.6 43.19 01.3 2459 SI. 5 21.94- 01.5 92.55 4-1 oj 14.19 55.2 12.05 // / OZ-.Z 24.77 53.2 22.11 03.0 83.22 4-t SI.O 51.8 1446 14.63 IIJ /2tt /232 12.6 14.2 4447 45.12 03.1 03.9 24.94- 25.12 S4.S 56.4 22.22 2245 04.5 06.\ 83.89 84.56 4-3 4-4 52.7 I4.d0 601 /2.S5 157 45.76 048 25.30 581 2XJ6Z 07.6 4S 53.6 14.97 6/J /2.7I 17.3 4641 05.7 ZS 48 597 22.79 09.1 ?5.9? 44, 54.4 /5.I4 634 47.05 06.6 Z5\b6 61.3 22.96 10.6 86.58 4-7 55.3 15 3/ 65.0 /3.04 20.3 47.70 074 25.84 63.0 23.14 122 9725 49 56.2 15.43 66.6 13.20 2/.9 48.34 08.3 26.02 64.6 23.31 13.7 8792 49 J/570 115.66 2268.3 1/3.37 22234 442.99 /2.09.2 12620 2*662 123.48 23/512 499.60 So 57.9 15.83 69.9 13 53 24.9 49.64 lO.o 26.39 67.9 23.65 '6.7 89.27 fl 58.8 16.00 7/5 /3.70 2.6.5 50.28 10.9 26.56 69.5 9994 52 59.6 16.17 73.Z 13.96^ Z2.o 50.93 IIS 26.74 71.1 24.00 19.2 90.6Z- 53 6(4 16.35 16.52 74.8 76.5 14.20 31.1 52.23 12.6 13.5 26.92 27/0 72.7 74.4 24.17 2434 Z<3 222 9/.M 9/97 54 SS 62.? 16 69 78. 1 14.36 32.6 52.88 I4A 27.2g 7*0 24.52 24.4 9^.65 S6 63.1 16.86 79.7 14.53 $4. 1 S3.S3 27.46 776 2469 159 9J.3Z S7 64.0 17.04 81.4 14.69 35.7 16.1 27.64 79.3 24.26 274 94.00 SV 64.8 17.21 83.0 J4.8& 372 5A**> I7A Z7.8Z 809 289 9468 59 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE , 24 25 T E C M X Y T E C M y Y IZI7.9 1*8:00 23825 \25.tl 2330.S 49F.3/ 1 17O "2. f39.H E400.Z 115.82 2421.5 53682 1 J8.7 28.19 84.2. 25.38 32.0 96.03 71 1 39.30 81.9 36.00 23.0 3/53 z 19.6 29.37 gs.z 2555 33.5 72.0 39.49 83. S 36.18 245 3 20.5 28.55 <&7.4 25.73 35 O 97:39 39.68 8 S.I 36.36 26.0 3094 A 21.4 28.73 89.0 25.90 36. 5 98. 07 73.7 39.27 86.8 3654 275 39.64 5 222 2?.9/ 90.7 26.07 38.1 98.75 74.6 40.06 88.4 36.72 29.0 4035 6 23. / 29.09 92.3 26.2f 39.6 99.43 75.5 40.25 90JO 36.90 305 4/.06 7 2.4.0 29.27 93.9 26.42 fOO.II 76.4 9L6 37.08 32.0 4A76 8 24 29.45 956 26.60 42.6 00.79 77-z- 40.63 93.3 32 26 33.5 42,47 9 257 29.64 972 26.77 44.2 01.47 40.82 94.9 37.44 35.o /o '226 fe 129.82 2398 S JZ6.95 2345.7 502.16 /279.0 14-101 24965 / 37.63 24366 543.89 // 27.5 30.00 240015 27/2 472 02.84 70.9 4/.'*0 98J 378/ 3S.I 44.60 /2 28.3 30.19 02 ( 27.39 48.7 03.52 90.7 4/.39 99.8 3799' 39.6 4S.3I /3 29.2 30.37 03.7 27.47 50 Z 04.20 6V.6 41.58 250/.4- 3RI7 41.1 46.02 14 3O.I 30.55 05.3 2764 51.8 04.89 52.5 41.75 03.0 38.35" 42.6 46.73 /5 309 30.74 O7.0 27.82 5J!3 05.57 83.4 4/.97 046 38.53 44.1 47.44 3/.F 30.92 086 2799 06.26 84.2 42. 16 06.3 3872 456 48.15 /7 32.7 31.10 /0.2 28. 7 56.3 06.94 42.35 07.9 38.90 47. / 48.86 / 33.6 3/.Z9 /A9 28.34 578 07.63 86.0 42.54 09.5 39.08 486 49.57 (9 34.4 31.47 /J.5 28. SZ J-9.4 08. 3/ #6.9 42.73 11-2 39.26 SO.I sort 2o J235.3 /3/ 65 24/5J IZ9.70 2360.9 509.00 1287.7 /42.9Z 2SI28 /3945 245/6 551.00 2/ 36.2 31.84 /6.7 2887 62.4 09.69 43.J2 14.4 39.63 53.; 51.71 22 370 32.02 /8.4 29.05 63.9 /0.37 89.'5 43.31 16.0 39.81 54.6 52.43 Z3 379 32.20 2o.o 29.22 65.4 11.06 43.50 177 40.00 56 / 53.14 24 388 32.39 2/.6 29.4252.8 135.36 24477 13273 239;.2 522.82 '305.3 /46.79 2545.3 /43J3 24SI.7 565.35 4/ 53.6 35.54 49.3 92.7 23.52 06.1 46.99 46.9 43.3; 83.2 66.07 42 54.5 35.73 50.9 32! 59 94.2 24.22. 07.O 47.18 485 43.50 847 6679 43 55.4 35.92 52.6 32.77 95.7 2491 079 47.38 50.2 43.68 16.1 67.52 44 56.3 J6 to 32.94 973 25.61 088 4757 SI. 8 4J.87 87.7 68.24 45 57./ 36 2$ 558 33.12 9*.8 26. 3/ 09.6 47.77 534 44.0F 89.2 46 58.0 36.48 575 33.30 2400.3 27.0| IO.S 4796 550 4424 90.7 69.69 47 58.9 59. / 33.48 01.8 27.70 H.4- 56.7 44.4Z 922 48 59-7 36.85 6o.7 33.66 033 28.40 I2..3 48.35 44.61 93.7 71.14 49 37.04 62.3 33.84 04.8 Z9.IO 13.1 48.55 59.9 44.80 95.2 71.86 50 ;26/.5 J3723 2464.0 / 34.02 406.3 529.80 1314.0 14875 2561.5 / 44.98 2496.7 572.59 51 624 3742 6S-.6 34.TLO 079 305o J4.9 48.94 63.2 4S./7 98 ^ 73.32 52 672 34.38 09.4 3/.20 J 5" 8 49.14 64.8 4535 99.7 74.04 64.1 37.79 68.9 34.56 /o.9 37.90 167 49.33 66.4 45.54 74.77 54 65.0 37.98 34.74 /2.4 32.60 17.5 4953 68.0 45.7J 02.7 7f 5o 55 659 18.17 721 34.92 / ^ 9 33.3/ 18.4 49.73 69.7 04.2 76.23 56 667 73.7 35.; 15.4 34 01 49.92 71.3 46. lo 05.7 76.96 57 67.6 sail 75.4 35.28 34.71 2o\ 50. IZ 72.9 46.25 07* 77.68 5 68.5 694 38.74 38.92 77.0 78,6 35.46 3S.64 18.4 19.9 3S.42 36.IZ 2.1.0 50.32 50.52 74.5 76 z 464? 46.66 087 78.41 79.14 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE ^6 o 7 / r E c M y Y T E C M X Y I3ZZ.8 150.71 Z577.8 146.95 2511.7 579.87 |375"6 162.91 Z67f./ > 59.11 260/.Z. 624. SO Z3.7 50.9 1 79.4 47c?4 I3.Z 80.61 76.4 6307. 767 585-1 02.7 25.Z5 1 24.? f/.// 8l.o 4723 /47 81.34 77. J 63.ZZ 78.4 58.70 04.2 26.01 Z 254 f/-J/ 2.7 47.4/ I6.Z 8Z07 78 Z 63A3 80.0 f87 22.2 8500 81.7 64.25 86.5 59.68 H.6 29.80 7 29? S23o 90.8 48.35 23.7 SS.73 Qi.f, 64.46 98.1 59.87 13.1 30.56 f 307 32.50 924 46.54 25.2 86.47 83.S 6467 89.7 60.07 I4J6 3/. 9 J33/.G IS2.U) 2594.0 149.73 2526.7 S87ZO 13844 164.^7 Z63I.3 /60.26 26)6.0 632.08 10 3Z5 52.89 956 48.92 29.Z 8794 9f.3 65.08 9^.9 6o.4t 17.5 32.84 II 333 53.09 97.3 49.11 29.7 88.67 86.1 6J-.29 946 60.65 19.0 33.61 IZ 34 : ^ 53.29 98.9 4.9.30 3\.Z 89.41 87.0 65.ro 96.1- 60.85 ZOf 34.37 13 35.1 53A1 26005" 4949 32.7 90.15 87.9 65.70 97.8 61.05 22.0 35.13 14- 360 S3 69 02. 49.68 34.-L 90.88 88.8 65.9' 99.4 67.24 235 35.89 If 36.8 5389 03.9 49.86 35.7 9/62 89.7 66. IZ 270/.0 61.44 24.9 36.66 16 177 5409 05.4 $0.05 37.1 92.36 90.6 66.33 02.7 1.63 26.4 3742 17 38.6 5429 07.0 5-0.24 39.6 93. 10 9/.4 66.54 04.3 6I.8S 279 38. 18 18 39.5 -54.49 08.6 50.43 401 93.84 92.3 66.74 OS.9 62.03 29.4 38.95" 19 1 340.4 J54.69 26/03 /50.62 Z54/.6 S94.57 1393.1 /66.95 2707S 762.23 26 30.9 6J9.7/ zo 41.2 54.89 11.9 50.81 43.1 9J.3I 94.1 67/6 09.1 QZ.41 J2.3 40.48 Zl 42 ./ 55.09 I3.f 51.00 44.6 96.05 95.0 6737 IDA 6Z.6Z 33.8 4US ^^ 4*o 5529 >5~/ 51.19 4(,l 96.79 95.9 67-58 IZ4 62.82 3 f.3 4-E.OI 23 43.9 55.49 '6.7 J-/.38 47.6 97W 96.7 67.79 14.0 63.01 36.8 42.78 24 *4S 55-69 '8.4 5/.S7 49.1 9g.2g 976 68.00 lf.6 63.it *8.3 43.55 25 456 .5.89 zo.o 51-76 S0.6 99.01 98.5 68 il IZ2 6J.4-I 39.7 443/ 26 465 56.09 ZI.6 SI. 96 5Z.I 99.76 99.4 68.41 189 63.61 4I.Z 45.08 27 474 56.30 Z3.Z 52.15 S3.6 6 00 SO I4oo.3 68.62 ZQS 63.80 4-27 45.85- 28 48J 5(5.So Z4.9 5234 SS.I OI.Z5 OI.Z 68.83 2Z.I 64-00 4-A.1 46.62 29 '349.2 /5&70 %26.? /52.M 2556.6 601.99 1402.0 ) 69.04 27,237 1 64.20 264-5.7 647.39 3O 500 5*.?0 28.1 .52.72 se.o 02.73 02.9 6925 253 64.40 47.1 48.16 31 50.9 57.10 29.7 &.3I WS 03.48 03.9 ^9.44 2-70 ^460 4-8.6 48.9? ?2 57 S730 31.3 S3.IO 61.0 04 Z2 04.7 69.67 Z96 64.79 5 O.I 49.70 33 527 53.6 57.51 57.71 33.0 J?4.6 S3?9 S3A9 62.5 64.0 0497 05. 71 056 065 69.S9 7o.ro 30.Z 31.8 64.9* 65. 19 51.6 53.0 5047 51.24 34 35 544 S7.9/ 26.2 S3.& 65:5 06.46 073 70.31 33.4 6S.39 ?4.S SZ.OI 36 55.? S8.ll 378 53. 87 67.0 07.2/ 03. Z 70.51 35.0 65.59 S6.o 52.79 37 56. Z 58.3Z 39.5 54.06 68.5 07.95 09.1 70.7) 36.7 65.79 f7f 55.56 38 5-77 5852 4-1.1 f4ZS 70.0 08.70 10.0 7094 J8.3 65-. 99 59.0 54.33 39 1358.0 >^8.7^ 26427 154-44 2S7/.5 605.45 /4/0.9 /7/./S 27/99 /66J9 26*0.4- 65f.ll 4o 58.8 S8.93 44.3 _f464 ?3.0 10.20 /t.8 7/36 4/5 66.39 6/.9 55.88 41 59.7 5913 459 548J 74 A '0.94 lt.6 7X.5-7 43.1 66.59 63.4- 56.65 42 60.6 59.33 476 550t 7f9 //.69 13.5 7/.T9 448 66.78 6*9 5743 43 6/.5 59.53 49.2 5SZ\ 77.4 /^.44 14.4 72.oo 46.4 6198 66.3 58.20 44 62.4 59.74- 508 5fA\ 733 13.19 IS- 3 7Z.ZI 48.0 67.18 67? 58.98 45 6?.2 59.94 524 S3~.60 $o4 13.94 /6.Z 7Z4Z 4-9.6 67.3? 69.3 59.76 46 64' 6e>.i5 54o 55.79 SI.9 /4.69 >7. 1 7Z6) 5V.2 67.58 748 60.53 47 650 6o3 5 55.7 5539 93.4 /545 17.9 7^%5 5-28 6778 72.Z 6/.3J 48 659 60 55 573 56./g 849 16.20 '8.9 7J.06 5VJ.5- 67.98 73.7 62.03 49 I36fe.8 ICO '76 2658.9 156.37 2586.3 6/C.95- W9.7 173.27 275-6.J 168.18 Z67SZ fefe2.87 SO 67 G 6096 60.5 5*.5fc 87.8 I7.7O 20.6 75.43 5-77 68.39 767 6*64 SI 6S5 61.17 62.7. 56.76 ?9.3 /8.4S z>. s 73.7O 59.3 6859 781 64A2 52 69.4 61.37 63.5 56.95 90.8 '9 Zl 28.4 71.91 609 69.79 79.6 65.20 53 7*3 61.58 6S-4 57/5 92.3 19.91 23.3 7412- 626 68.99 81.1 65.98 54 7/.Z 61.78 670 ^7.34 93.8 2o. 7^ 24 1 74.34 64.Z 69.; 9 82.5 6676 ss 720 6/99 63.6 5753 053 Zt.47 25.0 74.55 65.8 69.^9 840 6754 56 729 62.19 703 5773 96.8 22.23 2?9 74.76 674 69.59 85-5 68.32 57 7^.8 CZ40 7/.9 579? 98.2 2298 %.g 74.99 69.0 69. 79 87.0 69 10 5-8 7V. 7 62.60 73.5 58./Z 99.7 23.74 277 751/9 706 70.00 38.4 9.89 59 TAHLE II. FUNCTIONS OF A ONE-DEGREE CURVE / 28 29 T E c M X V T C M x- Y o 1428.6 I7S4/ 2772.3 170.20 26899 67^>67 /48A 18851 286 9. Z /8250 27778 7/^8 1 29.4 75. 6 Z "73.9 70.40 9/.4 7/.4^ ?2.7 9873 70.9 82>/ 79.2 11.19 2 Jo. 3 75.83- 75.5 70.60 92.9 72.23 83.6 38.9 F 7Z.4 82.92 So.r ^ooo 3 3/.2 76.05 77./ 70X0 94.3 73.0? 84.5 89 \ 8 74O 83.13 82 2 20.81 4 72 / 76.26 787 71.00 95.8 7J.ZO 85.3 9.40 7J-.6 8330- 83.6 2/62 S 33.b 76.48 0.3 7/.e/ 97.3 74*9 86.2 89.62 77.2 83-55 85. / ?243 6 333 7K.69 82.0 7>.4/ 987 7f37 87. / 99.85 78.9 8376 865 ?3Z 85P #U>7 80.5- 83.97 8F 93.4 9/.4I 90.2 85.23 96.7 28.93 14 4l.O 78.41 949 73.0) /0.5 8/.67 94Z 9/.64 9/.8 85:44 9R Z 2974 15 41.8 78.63 96.5 7/.C3 12.0 82.46 9f./ 9/-?6 9*4 8^.65 996 3(3.5^ /6 42.7 75.85 9/ 7^.44 13.4 83.24 960 92.0? 95.0 ?5.6 2gO/ 1 3/37 17 4-3.6 79.07 99.7 7J.W 149 8403 ^6.9 92.3) 96.6 86.07 025 M.I8 18 44.5 79.28 280/.4 7^?4 /64 8482 978 92.54 98.Z 86.28 040 3300 19 454 79.50 03.0 74.05 /7.'? 85.61 98.7 92.76 99.8 86.49 054 33.91 20 /4463 179.72 2804.6 /74E5 Z7/9.3 686.40 /499.6 1 31.99 290/4 186.70 28069 734.63 2/ 472 79.94 06 .e 7446 20.8 870 /500.5 93.ZI 03.1 86.9, ttfi 35.45 2Z 48. / 9f./5 078 74.66 22.2 87.?9 01.4 9344 047 87/2 09.8 36.26 23 48.9 80.37 09.4 7*86 23.7 5S.7,? 013 93.67 06.3 87.33 11.3 37.08 24 4*? 90.59 U.l 7f.07 25! ? 3957 03.1 93.89 079 8754 127 3/90 25" 50.7 80. 80 12.7 75.27 266 90.36 04.0 94 IZ 09. 5T S7.7* I4-.Z 38.72 26 5V.6 81.01 /4.3 7f.4S 28./ 9/./6 049 94.34- U.l 8797 I5(> 3954 27 -?5 81.24 /5.9 75.68 29.6 9/-9F 05.8 9457 127 88. /g <7.l 40.36 28 5-3.4 81.46 /7.5 75.89 3/.O 92.^- 067 94.90 14.3 88.39 18.$ 41. /8 29 -T4.3 Sl.(,7 /9./ 76.09 32.5 93.54 076 95*2 /59 98.60 20. C 42.00 30 /455.) /8/.S9 2S207 176.30 E734.0 694.3? /505 / 95.2 5 29/76 /S8.8Z 282/4 74?. 82 3f 5.6.0 82.ii Z24 7650 354 95.) 3 094 95.48 19.2 89.03 2Z9 43.64 3* 569 82.33 ( Z4> 76. 7/ 36.9 95.9J /0.3 95.70 20$ 89.24 243 44.46 33 578 82.55 ( 25.6 76.91 3?. 3 9672 11.2 59;? 224 39 45 25^ 45. Z8 34 57 82.77 27.Z 77.12 39.8 9752 IZ.I 96.16 240 89.67 27.2 46. /o 35 5-9.6 82.99 288 77.32 4/.3 9832 12.9 96.39 25.6 99.88 287 46.93 36 60S 83.e/ 30.4 77 427 99. // '3.9 %.6I 272 9009 3o.l 4-7. 7 f 37 11.4 93.42 ?2.l 77.7* 44.^ 99.9/ 14.7 96.94 28.g 90.30 Z/.6 4g.S7 ft 62.Z 83.64 3i7 7794 45.7 700.71 MX 97.07 30.5 90.52 3JP 4-9.40 39 63.1 83.*6 35.3 78.15 47/ 01.51 /65 97.30 ?2.l ft>.73 34.5 S0.2Z 4o /464.0 124.08 2836.9 178. 35 Z7486 70 2.3 / /5/74 197.53 2933.7 / 90.94 2835.9 757.05 4j 649 84.30 38.5 78.5(, 50 03JI /8.3 97.75 35.3 9/./6 374 J-/87 A2 65.8 84.52 40.1 78.77 5-/5 03.9) /9.2 9Z9? 36.9 9/-37 388 5170 43 66.7 84.74 41.7 78.97 53.0 04 7/ 20.) 9?.!' 38.5 9/.W 40.3 5351 44 67-6 84.96 434 79., 8 54.4 05.F/ 2)0 98.44 40.1 31.90 41.7 54.35 4? 65 85.18 45.0 7939 559 06.31 2)9 98.67 417 92.01 43.1 55.17 46 69.3 8540 46.6 79.59 574 07.11 22.8 9g.90 433 92.Z? 44.6" 5600 47 70.2 8563 A8.Z 79.80 58.8 07.91 23.6 99.13 4S.o 9244 460 56.83 48 7/J 05.R5 #)X 90.01 60.3 08.72 245 99.36 46 6 9265 47.5 J7.66 49 72p 86.07 5J.4 80.21 61.7 09.52 . 2x4 99.59 4F> 92>7 4&9 58.49 5-0 (472.9 186.29 285*0 / 80.42 2765.2 7/0.33 /S263 J99.82 2549.8 /9J-08 28504 759.32 5V 73.8 86.51 J4.7 80.63 64.7 //./3 272 20oo5 5/-4 93.30 5/.tf 60./4 52 74.7 86.73 563 So.g4 66 / 11.9) 28.1 00.28 53.0 9?.5) 53.3 60.97 53 7T6 8695 579 8/.05 67.6 '2.74 29.0 00.51 546 95.73 54.7 (,1.90 34 75 97.17 ^59.5 gt.25 69.0 /3S4- 29.9 0074 562 93.94 F6.2 62.64 5f 77.3 8740 61. 1 81.46 705 /4.3S 30.8 00.97 578 94/6 576 6j[47 56 791. 8762 62.7 8/67 72.0 /5./S 3/7 0/.20 59.4 94.37 590 64.30 57 79.1 87.84 643 81.38 7J.4. ^5.96 32.6 0/.43 61. / 9459 605 65J3 58 80.0 88.06 66.0 82.09 74.9 /677 33.5 0/.66 627 94.90' 6J.9 65.96 59 80.9 88.23 676 2.29 7.3 /7.5 3AA oi.89 64.3 95.02 614- 66.79 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE 30 3\ / r E c M X V T E C M X Y 1535 3 202.12 2965.9 (9523 2864.8 767.63 1589.0 Z/625 30624 208.38 295V. <3/838 O 36. / 02. 35 675 95.45 66.3 68.46 89.9 16.49 64.0 08.6,1 524 79.24 1 37.0 02-?? 69. / 9566 6Z7 69.30 908 /6.73 65.6 08.83 S3.8 2JD.IO 2. 379 02.8/ 70.7 95.88 69.? 70.13 9|.7 /6.97 672 09.05 55.3' 20.96 3 38.8 OJ.05 72.3 96/0 70.6 3296 92.6 /7.2I 68.8 09.28 567 ZI.8Z 4 39.7 03.29 7J.9 96.31 72 .0 7igo 935 /74F 70.4 09.50 58.1 226? S 406 0351 7S-.5 %5) 7.3.5 72. V 94> 17.69 72.0 09.72 59.6 23.54 6 41.5 0)74 77.2 96.75 74.9 73.47 95.3 (7.93 736 09.95 61.0 24.40 7 41.4 03.97 78 96.96 764- 74.31 362 I9.H 7S.Z 10.17 624 2?.26 8 43.3 04.21 80.4 97)ff 77.* 7/./^ 971 /8.4I 763 10.39 6A8 26./2 9 1544 Z 204.44 2.982P 19740 2S75.Z 775.9? 15-98.0 Zt$,66 30784 2/0.62 29653 926.99 /O 45: / 9 75-.Z 33.03 17 5/3 06.30 949 99.) 3 90.? 82.70 05. / 20.59 91.3 12.41 76.7 3*90 >8 SZ.z 06.54 96.5 99.35 92.2 83^4 06.0 20.83 923 12.64 78.1 54.77 J9 tr&.i 206.77 299S./ 199.57 2893.6 7g*.3g 1606.9 21.\JDZ 3094.5 2/2.86 29725 35:63 ZO S~4.0 07.01 99.7 99.79 95./ 95. 2 a 07.? 2/.31 96.1 13.09 80.9 36.50 2/ 5-4.9 07.24 ?00'. 3 zoo oi 96.5 86.06 087 21-56 97.7 /3.3I 814 37.37 22 55.8 07.4? 02.9 00. 22 9/> 86.90 09.6 21.80 99.3 13.54 8.3.8 3^23 23 56.7 07.71 045 00.44 99.4 07.75 lO.S 22.05 3/009 13.76 85.2. 3910 24 57.6 07.90- 06.1 0C.6(> Z90S8 5^.5"9 11.4 2229 025 1339 86.6 3297 25 585 08.18 077 OO.S2 02.3 ^94^ 12.3 22.53 04.1 14.21 88.0 46.&1 26 59.4 08.41 09.3 01. to 03.7 90. a 8 132 2?.7* 05.7 W.4A 89.5 41.71 27 60.3 08.65 109 0/.32 0y./ Jilt 14.1 Z\0l 073 /4.67 90.9 42.58 28 61.2 08.98 125 01.54 06.6 91.97 ISO 2i.27 08.9 /4.89 ~9t.3 43.45- 29 IJ62 1 209/2 30/4 Z 10/.76 2902.0 792.32 K>/s:9 223.5) 31105 2/5/2 2993.7 844.32 30 63.0 09.36 15.8 0/.98 095 93.66 16.8 23.75 IZJ /5.34 95.2 45" /9 3/ 63.9 09.5"9 17.4 OZ.\9 io!9 94.5' 17.7 24.00 13.7 /S57 96.6 46.06 32 64.8 09.83 19.0 024-1 /2.3 95J36 /8.6 24.24 15.3 15.80 \8P 46.93 33 65.7 10 Of, 206 02.63 .g %.2o 19.5 24.49 169 1602 %.4 47$l 34 66.6 10.30 22.2 02.85 /^.i 9705" 20.4 24.7^ 13.5 16.25 3000.9 4868 35 67.5 10.53 23.8 03.07 '6.6 979o 2/3 24.9? 20.1 16.42 02.3 4-9.5? 36 68.4 10.77 25.4 03.29 // 98.75 2Z2 25.22 21.7 16.70 03.7 S0.43 37 69.2 11.01 27.0 03.51 >25 9960 2?.l 25.47 23.3 16.93 OfJ S/.30 38 7*.' //.Z5 23.6" 03.73 20.9 800.45 24.o 2S.7/ 25.0 17.16 065 52/7 39 >57/.o Z//.4S 3030.2 203.95 29224 8o/.3o ;6Z4.9 2Z5.96 3/2.6.6 21739 3007.9 853.05 40 7/9 II.T2 31.8 04.17 23.8 02.15 25.8 26.21 282 '7.6 / 094 53.92 4-1 72.8 11-96 33.4 04.39 25.2 03 oo 267 26.45 29. 8 17.94 10.2 54.8o 42 73.7 IZ.I9 WJ 04.62 26.7 03.95 276 26.70 31.4 18.07 le.z 55.68 43 3*6 /2.43 36.7 9A4 20.7 60.94 49 ; 58.o i/3.86 3046.3 206 If, ?936.7 9o9.se /633.9 2Z9.42 3/4-2.6 2/9.67 3022 1 ?6/.2 SO ?0.9 I4.io 479 06.39 38./ /o67 34.8 2867 44.2 19.89 23.'? 62.70 51 8/.8 1434 49.5 06.61 ^9.6 H.S3 35.7 28.92 45.8 20.12 24.<) 63.f8 52 82. 7 14.57 51.1 06.83 4/0 /2.3g 36.6 29./7 474 20.35 26.4 6446 5J 8t.6 1431 52.7 0705 424- /3.24- 37.5 29.41 49.0 20. 59 27.? 65.34 54 va.s 15.05 543 0727 438 14.09 38.4 2966 50.6 20.81 29 Z 66.22 55 85.4 /5.29 55.9 0749 453 W.9f 39.3 29.91 52.2 21.04 30.6 67.10 5^ 96.3 /5.53 575 07.72 46.7 /S.8I 40 2 30.16 53.8 2/27 32.0 67.98 57 872 '5.77 59.a 07.94 4g. / 16.67 41.1 30.40 55.4 21 5o 33.4 6g$7 58 88.1 /6.0/ (,o.S OS. 16 A9.6 /7.52 42.0 30.65 57.0 21. 73 34.8 6975 W 28 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE / 3 3J T E c M X y T E C M X Y o 1643.0 23090 3158(3 221.96 30363 870.63 (697. 2 246.08 3254.6 23595 31206 924- 3 6 ( 439 31. If 60.2 2Z.I9 377 71. S? 98.7 4634 562 36./9 220 25.27 2 448 37.40 61.$ ^^.4z 39. / 72.40 99.0 46.60 57? 36-4? 23.4 26.18 3 45.7 37.65 63.4 22.65 405 73.28 99.9 46M f9.4 36.6k 14.8 27.09 4 466 37.90 6X0 Z2.S5 4/.9 74 17 1700.8 47 II 61.0 3690 26.2 28.00 5 47.5 32 J5 66.6 23.11 443 75.05 01.7 47.37 626 37'3 27.6 28.90 6 48.4 32.40 68.2 23.34 44.7 7f94 02.6 4763 64 .Z 3737 29.0 29 H/ 7 493 32.65 69.8 23.57 46.1 76.82 03.5 4789 658 3767 304 30.72 8 J-0.2 32.99 71.4- 23.20 476 77. 71 04.5 49.15 6J.4 3785 3 IS 31.64 9 5V./ 33.14 7J.O 24.03 49.0 78.60 05.4 48.41 ,69.0 ^8.08 33.Z 32.55 to /652o 23339 3174.6 224.26 3050.4 879.48 1706.3 Z48.U, 3270.6 23#.32 31346 93^.46 II 52/3 33.64 76,-i 24.49 S/.8 80.37 07.2 489? 722 39.56 36.0 34.37 /2 53.8 33.90 77.8 24.72 S3.z 87.26 08 1 49.18 738 38.80 37.3 35.28 /3 54.7 34.15 79.4 24.95" 546 82J5 O9.o 49.44 754 39.04 38.7 36.ZO 14 55:6 5440 8i.o 25. 18 56.0 W04 09.9 4970 77 466 3477 /3.6 H.?3 A7.2 6o47 4?> 49. (4 97. / 7490 5 93.6 45.05 4S.I 35.00 ISO' 20.73 48. 1 60.71 440 49.3g 984 7/83 57 945 453/ 49.3 35.24 16 4 Z/.6? 49.0 6-t.Oo 45.6 4V 6 J 99.8 76.76 59 95:4 45.57 51.4 &.48 17.8 2?.5f 49.9 61.27 47.Z 49.S7 3101.? 77.69 f9 %.3 45.8? 530 35.71 '9.2 2J.45T 508 a.si 488 50/7 02.6 78.62 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE 34 ' J5 f T E C M X Y T E C M y Y / 75"' .7 26/ SO 33S0.4 ^5O.36 3204.0 979.56 1806.6 2 7$O 5 34459 26519 32864 /036.2 52.6 62.06 520 SO 60 05.4 80.49 075 78.33 47-5 6544 37.2 1 53.G 62.33 fS.6 50.85 06.7 81.42 08 4 7g.6l 49. / 65.69 89. / 38.1 Z 54.5 62.60 55.2 57.09 og./ 82.35 09^3 78.9% 50.6 65.94 90.5 554 62.86 56.8 5/.33 09.5 loZ 79.16 66./9 9/.9 40.0 4 56.3 63.13 58.? 5/58 /O.9 84.22 ll.l 79.43 5J8 66.44 ?J.2 41.0 S 57.2 5?. 9 Sl.Qt '2.3 95.15 IZ.I 7971 S5.4 66.69 96.6 4/ 9 6 8.1 63.67 6/.5 S207 /3.6 86.09 I3.o 79.99 57.0 66.94 959 42.9 7 590 63.93 63.; 52.3) If.O 8702. /3 9 90.26 59.6 67J9 97.3 43.9 8 59.9 64.20 64.7 52.56 /6.4 8796 '4.8 80.54 60.2 6745 98.7 44.8 9 1760.8 2-64.47 33663 25280 3217.8 988.89 lf.7 280.82 346/.S 267.70 33000 (045.8 10 64.74- 67.9 5/05 19.7. 89.83 ;6.& Si. to 63.4 67.95 46.7 II 62.7 65.0 / 6A5 53.29 20.5 90.77 '7.6 81.37 64.9 68.20 02.8 47.7 >Z 636 65.27 71.1 53.54 21.9 71.70 /8.5 &.6S 665 6845 041 48.7 13 64.5 65.54- 72.7 23.3 9264 8/93 68.1 68. 71 05.5 496 14 65.4 65.81 74.3 54.03 24.7 9J.58 20.3 82*0 69.7 68.96 06 S 50.6 IS 66.3 75.9 54.27 26.1 94.52 2/.2 #2.48 71.3 6921 08Z 5A5 16 67.2 66.35 77. S 54.52 Z74- 82.76 72.9 69.46 096 SZ.S 17 66.62 791 54.76 28.8 96.40 23!' 83.04 745 697/ 10.9 53.5- '8 69.1 66.89 80.6 ff.OI 30.2 37.34 24.0 8i.3Z 76.' 69.97 12.3 J4.4 19 1770.0 267/6 3382Z ZSS.Z5 323J.6 998.28 /8249 83.60 3477.7 27022 3313. fe tOSS. 4 20 70.9 67.43 83.8 55.50 329 99.2Z 25.' 83.87 79.2 7o.47 ISO S64 zl 71*. 67.70 ?574 55.75 343 /000.2 26.7 84 15 80.8 70. 7 i 16.4 57.3 22 727 67.97 87.0 5599 35.7 01.' 27.6 84.43 824 70.98 17.7 8 3 23 736 68.24 88.6 5624 37.1 02.0 8471 84.0 7/Z3 19.1 f9 } 24 745 68.57 902 56.49 38.4 03 O 29.5 8499 85.6 7/49 204 60.Z 25 7SA 6876 91. S 5673 39.8 03.9 30.4 85.27 87Z 7/.74 2/.g 61.2 26 764 69.05 93.4 56.98 4V.Z 04.9 31.3 85.55 888 7A99 23.2 62.2 27 77.3 69.32 95.0 5723 426 05.8 32.2 8583 72.25 245 63. 1 28 7g.Z 69.59 96.6 57.47 43.9 06.8 33.2 91.9 72.50 E5.9 64.1 29 1779.1 269.86 339S>Z 257.72 32453 }007.7 J834.I 286.39 3493.5 272.76 3327.2 106$ 1 30 80.0 7(7. / 3 99.8 3~7 97 46.7 09.6 35.0 86.67 95. / 73.01 28.6 66.0 31 80.9 7<7.40 340/.3 58ZI 48' 09.6 359 86.95 967 73.26 299 67.0 32 BIJ 70.67 02.9 584.6 49.4 10. S 36.8 983 73.51 31.3 68.0 3? 82.8 70.94 04.5 58.71 508 11.5 378 97.SI 99.9 73.77 32.7 699 34 83.7 7/.2I 06.1 58.96 52 t 12.4 97.79 350 1.5 74.03 ?4.0 69.9 ^5* 84.6 7X.49 07.7 S9ZO 53.5 396 8807 03.1 7AZ9 354 70.9 36 85.5 71.76 09.3 59.45 54.9 14.3 40.5 883? 046 74.54 367 7/:8 37 86.4 72.03 109 59.70 56) 15.3 4/.4 89.63 06.2 74.79 38. / 38 873 72.30 IZ.S J995 577 '6.2 42.3 88.92 07.8 7S.OS 39.4 7/8 39 '7F8 2 272.58 34/41 260.20 3259.0 \o\7.l /84J.3 289.20 3509.4 27530 3340.8 1074% 4o 89.7. 72.85 J5.7 60.44 604 18.1 44.2 //.o 7f.S6 42.1 7f.7 A! 9o.l 73. JS 173 60.69 61.8 45. 1 89.76 7f.Vl 4.3.5 76.7 42 9l o 73.39 tg.8 66.94 63.1 20.0 46.0 90.04 I4.Z, 76.07 44.8 77.7 4? 919 73.67 20.4 6/.I9 645 2/.0 46.9 90. H IS.7 76.32 46.2 78. 6 44 92.8 73.94 220 61.44 >5.9 2/9 47.3 9061 17.3 76.52 475 79.6 45 93.7 74.21 23.6 61.69 673 229 488 90.99 >8 9 48.9 So.6 46 946 74.49 25.2 61.94 68.6 23.8 497 91.17 205 77.09 50.3 8/6 47 9516 74.76 26.8 62.19 7oo 24.8 50.6 91.46 221 77.35 82.5 48 96.5 7S.03 28.4 62.44 714 2S.7 5/.5 91.74 23.7 77.60 53.0 49 17974 275. 3 / 3430.0 262.69 3272.7 /026.7 /852.S 29202 3525.3 27796 3354.3 /084.5 So 98.3 7f.58 31.6 62.93 74.1 276 534 92>0 268 78. It 55.7 5V 99. e 7586 33 Z 63.l# 75 S 28^ 54.3 92.59 28.4 78.37 570 86 '.4 5"2 tSoo.i 76. 13 34.7 63.43 768 29. f 55.2 92.87 30.0 7863 58.4 87.4 5? 01 .1 76.40 363 63.68 30.5 56 ) 93. 16 316 7S99 59.7 98.4 54 02.0 76 .68 379 63.93 796 57' 93.44 33.2 79.14 61.1 89.4- /y 02.9 76. 9J J9.5 64. IB 809 32.4 58.0 93.72 34.8 7940 62.4 j 90.4 56 7^3 41.1 64.43 92.3 ji 3 58.9 9401 364 79.66 63.8 I 9Y3 57 04.7 7*50 A27 64 6# 34.3 59.8 9429 379 79.91 65. / 92 3 5? 056 77.78 443 6490 #5.O 352 60.8 94.5? 39.5 9o.i7 66.5 93.3 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE / 36" 37 T E C M X Y T E C M Y Y o !&(>! 7 294.86 55"4/ / 280.43 3367.8 J094.3 1917.' 3/2.2Z 3636 1 29609 34481 1(537 1 62.6 9514 42.7 80.69 69.2. 95.2 I8.o X2.52 377 495 54 8 z 63.5 95.43 44.3 80.94 70.5 96.1 I9.o 12.91 39.3 9662 509 558 3 64.4 95.72 45.9 81.20 71.8 97.2 19.9 13. 10 40.8 9688 56.8 4 65.4- 96 oo 47.5 81.46 73.1 991 zog 13.40 424 97.15 53.5 578 5 66 3 96*9 49.0 8 1.7 -a 74. S 99.2 21. 7 13.69 440 97.41 54.8 58.8 6 67> 96.57 S0.6 81.98 75.9 lloo.z 22.7 '3.99 45.6 97.68 56.2 59.8 7 68. / 96.86 SZZ 82.23 77.2 01 1 23.6 14.18 47.2 9794 57.5 608 8 69.0 97.14 S3 % Sz.49 786 Oi.l 14.58 487 98.Z\ 58S 61.8 9 7O.O 97.43 SS.4 9175 79.9 03.1 2*5 14.97 503 98.47 60.2 6Z.8 /O 19709 297.72 35-57.* Z83.0I 33 g,3 1104 1 '9264 3\5.\7 36J~/9 298.74 346/5 1163.8 // 7/.g 98.oo 5"86 8327 826 05. \ 27.3 15.47 53. 5 99. 00 62.8 /Z 7i 7 98*9 60.1 83.53 84.0 06.1 28.2 1576 SS.I 99.27 641 65 8 /3 73.7 9857 61.7 83.79 853 07.0 29.2 566 99.53 655 66.8 /4 746 98.86 633 84.05 8G.7 08.0 30.1 /63S S8.2 99.80 66.8 67.8 /5 7,5"" 5" 99.15 64.9 8431 880 090 31.0 /6.65 300.07 68.1 688 /6 76.4 99.44 665 84.57 89.3 10,0 320 /6.95 61.4 694 69.8 17 77.4 99. 7j? 68.1 84.83 90.7 II.O 32.9 17. 24 629 00.60 70.8 70.9 18 783 300.OI 69.6 85.08 92.0 /2 ^ 33.8 J7.54 645 00.97 7Z\ 19 79. ^ 00.30 71.2. 85.34 93.4 13.0 34.7 17.84 01.13 73.4- 7Z.9 20 1880.1 300.S9 3572? 295.60 1594-7 11133 '935.7 3l8.\3 3667.7 301.40 3474.7 1173.9 Zl Bio 00.87 74.4 85.86 96.1 J4.9 36.6 1843 69.? OI.6J 76.1 74.9 ZZ 820 01.16 76.0 96.12 974 15.9 37.5 #.75 70.8 01.93 774 23 92.9 01.45 77.6 86.3g 98.7 /6.9 3g.S f9.o3 724 02.20 79.7 76.3 14 839 01.74 79.1 86.64 34001 '7.9 39.4 740 0247 80.1 77.9 25 847 0203 80.7 86.90 01.4 18.9 40.3 J962. 75.6 02.73 814 78.9 26 25.7 02.32 923 87.16 19.9 41.2 19% 772 03 OO 2.7 80.0 27 86.6 02 83.9 07.42 04.1 20.9 42.2 20. ZZ 787 Oi.Zl 840 91.0 28 875 02.89 85.5 87.69 05.4 2/.9 43.1 20.52 03.54 9S3 92.0 Z9 88.4 r O}.!8 S7.I 87.9? 06.9 2Z.g 44.0 Z0.8I 81.9 OJ.VO 867 Vi.o 30 19894 303.47 3588.6 Z.99.Z \ 3408.1 //23.8 1945.0 3Zl.ll 36g3.S 304.07 34880 1/84.0 3 1 9o.3 0),76 ** 88.47 09.5 24.9 459 21.41 850 0434 893 32 91.2 04.05 98.73 10.8 25.8 46.8 Zl 11 86.6 04.61 90.6 86.0 33 92.1 04.34 93.4 88.99 12.1 47.7 22.01 es.t 04m 92.0 87.' 34 93.1 04.63 89.15 '3.5 27.g 48.7 22.31 89.8 933 88.1 35 94.0 04.92 96.6 89.51 14.8 28^ 4-9.6 22.61 91-4 OS.4I 94(, 89.1 94.9 05.21 98.1 89.77 I6.Z 29.8 50.5 22.91 92.9 05.68 959 37 OS.So 99.7 90.04 17.5 Si. 5 23.21 94.5 05.95 97? 9/7 3# 9(..7 05.79 3601.3 90.30 18.8 3/'.8 524 23. Si 96./ 06.11 98.6 92.1 29 97.7 06.08 02.9 90.56 20.2 32.9 J3.3 23.8; 97.7 0649 99.9 93.2 40 '89? & 306.37 3604.5 290 .9Z 342/.5 ) 133.9 I9S4.3 324. )/ 3699.3 306.76 350/.Z /W.2 41 99.5 06.66 06.0 9/.08 228 348 55.2 &4I 37^.8 07.03 025 952 42 W00.4 06.95 07.6 91.35 Z4Z 35.8 56.1 24.71 02.4 07.23 03.8 96.2 43 01.4 07.25 09.2 15.5 36.8 570 2501 04.0 07.56 05.2 97.2 44 023 0754 10.8 91.97 37.7 58.0 2531 OS 6 07.83 06.5 98.3 45 03.2 07.83 12.4 91.13 Z8.Z 38.7 58.9 25.61 07.1 OB 10 078 99.3 46 04.1 09.12 13.9 92.40 29.5 39.7 59.8 25.9; 08.7 0837 09 / 1200. 3 47 05.1 09.4) /5 92.66 30.9 4o.7 60.8 26.2 103 08.64 104 01.3 48 06.0 "8.70 17.1 92.92 3Z.T. 41.7 61.7 26.52 11.9 OS. 91 /1. 7 013 49 06.9 09.00 187 93. '9 3J.5 42.7 ^62.6 26.82 13.4 09.18 '3.1 03.4 fo 190/9 309.29 3620.3 293.45 3*34.9 1143.7 ;963.6 327. IZ 37/5.0 309.45 3514.4 120 A. 4 ft 09.8 09 5g 21.9 93.71 36.T. 44.7 64.5 Z.7.4Z Id (, 09.72 15.7 05.4 52 09.7 09.97 234 93.98 ?7.5 457 64 Z7.7Z ft.Z 09.99 I7O 06.4 53 /o.6 250 94.24 38.9 46.7 66.4 29.03 '9.7 10. Ik '8.3 07.4 54 11.6 10.46 266 94.50 AO 2. 47.7 67.3 2933 21.3 10 5~3 19.6 08.5 IZ 5" 291 94.77 41.'$ 487 68.2 28.63 22.9 fo 80 2/0 09.5 5C /J.4 11.05 29.8 95.03 42 9 * 49.7 245 //. 07 223 10.5 57 14.3 11.34 313 95.29 44Z S0.7 70 1 29.24 11.35 23.6 11.5 S8 ff.3 11.63 32.9 95.56 45.5 51.7 7/.0 2954 276 II. & 249 /.(> /6.Z 11.93 34.5 95.82 46.9 52.7 7/.9 29.S4 29.2 n. 89 26.2 //,6 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE 29 38* 59 / T F c M X Y T E C M X Y 19729 530/5 J730S 312.16 35Z7.S IZ/4.6 2029 O 348.64 30252 3286"4 3605.8 \Z76.9 73.9 30.45" 31.4 /2.43 ^9S /57 29.9 48.95 26.8 28.92 07.1 77.9 1 74.7 30.75 33.9 IZ.70 30.2 /6.7 30.9 49.27 2?.3 29.20 09.4 790 2 75.7 31. of, 35.5 11.97 3 IS ^7.7 31.8 49.5? 29.9 29.4g 09.7 80.0 3 76.6 31.36, 37.1 13.25 32.8 >8.7 327 49.89 31.5 2976 H.O 1 4 77.5 31.67 39.7 /3.S2 34. 1 /9.g 33.7 fazi 33.0 3oM /*.? 1 5 78.5 31.97 402 X3.79 35A 20.8 346 SO.SZ 34.6 30.32 13.6 2 6 79A 32.27 41.8 /4.06 3B.7 2/.8 35.5 &.84 36.Z 30.59 14.9 84* 7 903 32.58 43.4 14.33 38.0 22.8 36.S S/.tS 37.8 30.87 16.1 85.3 8 913 J2.88 45.o I4.

    />?24.9 2039.4 3f/.7g 3840.9 331.43 36/8.7 1297.4 10 93.1 33.49 48. / 15.15 4to 259 39.? 52.10 42.5 31.71 zo o 884 II 84 / 33 go 49.7 15.41 43.3 27.0 40.2 52.4 1 44.0 31.99 il.3 89 f ft 95.o 34. M 5J.3 IS. 70 446. 280 4f.z 5Z.K 45.6 32.27 226 90.5 /) 85.9 34.41 528 15.97 4-59 29.0 42.1 53.04 472 #55 23.9 9/.6 14 86.9 34-72 544 I6.Z4 472 3o. 1 43.1 5-3.36 48.7 3283 25.2 92.7 15 878 3S.OZ. 56.0 16. 57 485 31.1 44o 53.67 50.3 33.'// 26.5 937 16 88.7 3533 576 '6.79 49.S 32.' 44'9 53.99 5A9 33.39 27.8 949 n 897 J563 5?/ /7.06 51.1 J3.2 459 S4.30 53.5 33.67 29.1 9f.8 /8 9o.6 35.94 60.7 X7.34 52.4 34.Z 4t S4.6Z 55.0 33.95 3o.3 969 19 19915 356.25 37623 3/76/ 35 S3 7 23S.2 2047.8 354M 3856.6 334.23 3631.6 Z97.9 "20 9*5 36.55 63.9 /7.W 550 363 55.25 S8.Z 34.51 32.9 99.0 21 93.4 36.86 65.4 /8./6 S6.3 373 f6 5557 59.7 34.79 341 I3oo. a 22 94.3 37. /7 670 /8.43 57.7 383 ^ 5T09 61.3 35.07 35. 5 01. 1 23 95.3 37 4? 68.6 19.70 59.0 39.4 57.5 56.20 62.9 35.35 36.8 02 2. 24 96.2 37.7* 70. Z /8.9B 60.3 40.4 szs 5652 64.4 35.63 39.1 03.2 25 97. / 38.W 7/7 /9.25 6/6 41.4 53.4 56.94 66.0 3S.9Z 39.4 043 26 981 38.40 7?. 3 19 S3 629 4Z.5 543 57/5 676 36.20 40.6 05.3 27 99.0 ^9.71 74.9 I9$0 64> 43. S 55.3 5747 69/2 36.48 41.9 06.4 28 99.9 39.01 76$ 20.08 65:5 44.5 5*. 2 5779 70.7 36.76 43.2 07.4 29 Z0009 339.32 37780 320.35 3566.8 l&f.f. 20572 358.11 3872.3, 33704 3644.5 1308.5 30 0/.8 39.63 79.6 20.63 69. 1 466 S8.I S8AZ 73.9 37.32 4f.8 09.6 31 ozs 39.94 m 20.90 69.4- 47.7 59.0 58.74 7S.4 37.60 47.1 /o.6 32 037 40.25 82.7 2/./9 70.7 4^.7 60.0 59jCX> 77.0 37.89 48.4 11.7 33 04.6 40.56 843 Z/.45 72P 49.7 60.9 59.38 78.6 38.17 49.6 12.9 34 05-.6 4087 85.9 2A73 7J.3 50.9 6/.9 59.70 80. / 38.45 50.9 13.3 35~ 06? 41.17 875 22.> 746 S/.2 62.? 6002. 91.7 38.73 52 $ 14.9 36 07.4 4-1.48 89.0 22.tg 759 52.9 63.7 60.34 83.3 39.01 53.5 IS. 9 37 084 4/.79 90.6 Z2.55 77? 53.9 64.7 60.65 84.8 39.30 548 )7-0 38 09.1 42./0 92.2 22.93 78.5 54.9 65.6 60.97 .* 39. SB 56.1 /d.t 39 2010.2 J42.4I 3793? 323./0 3S79.8 IZS6.0 2066.6 361.29 3898.0 339.86 3657.4 1319 1 4-0 \IZ 42.72 95.3 23.38 31.1 510 675 fel.6/ 89.5 4o. is 58f> 20 Z 41 12. 1 4303 96.9 23.66 K4. 58.1 68.5 6J.93 91.1 A043 S9.9 21.3 42 /30 43.34 98.5 23.93 83.7 59. / 9.4 6Z.Z5 92.7 40.71 61.2 22.3 43 M.O 43.6? 3800.0 24 21 950 60.1 70.3 62.57 94.2 46.99 62.5 29.4 44 '49 43.96 01.6 24.4? 863 6 (.2 7/.3 62.89 95-8 41.19 63.9 24.5 45 /*9 4427 03.2 2476 926 622 7.2 63.21 97.4 4V.56 65.0 25.5 46 16.8 44.59 048 2504 88.3 63.3 73.2 63.53 98.9 4/.*4 663 26.6 47 17.7 449o 063 2S.3I 9. Z fe43 74. 1 63.85 3900.5 42.13 676 277 4S /ft 7 45\2I 07.9 25.59 9/.5 65.4 75.0 64./8 02.1 42.41 689 28.7 49 zo/9.6 345.52 3*09.5 325.87 3592.9 \2A64 2.076.O 364.50 3903.6 34Z.70 3670.2 13298 50 zo.s 4fg3 1 l.o 26. >5 94. / 675 76.9 64 8Z 052 42.9* 7/4 30.9 SI 2f.5 46.14 I2f, 26.4? 95.4 685 77.9 6514 06.8 4326 727 31.9 Si 2Z.4 46.45 /4.2 26.70 96.7 69.5 7*. 8 65.46 08.3 43.55 74.0 33.0 53 234 46.77 158 26.9ff 9*0 70.6 79.8 65.78 49.9 43.83 753 34 / ?4 24.3 47 08 17.3 2725 993 7/6 80.7 66. 10 II.S 44.1Z 76.6 35. / 55 25. 1 47.39 189 27.53 36006 72.7 S/.6 66.43 13.0 44.4o 778 36.2 56 26. 2 47.70 eo.s 27.91 01.9 73.7 9Z.6 66.75 146 44.69 79.) 37.3 57 27/ 48.02 2Z.I 209 OJ.t 74. f 8S.S 67.07 16.7. 44.97 804 38.3 58 28.0 48.33 23,6 2.37 045 758 84.5 67.3? 17.7 45-26 8i.7 39.4- 59 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE / 40 41 T E c M X V T E C M X Y 208S-.4- 367.72 3919.3 345.54 3692.9 1340.5 EI42.-Z. 39738 40/3.1 362.85 3759.0 1405.4 1 864 68.04 20.9 45.83 #4.2 4>.6 43. Z 87.7 / '4.7 63. 14 60.2 Ob. 5 1 873 6836 22.4 46.li 855 426 44.1 88.04 /6.2 63.43 6/.5 07.6 3 883 68.69 24'.0 46.40 86Z 437 45.1 88.38 17.8 63.72 62.8 08.7 4 892 69.o| Z5.(, 46.68 88.1 .44.8 46.0 88.71 19.4 64.01 64.0 09.8 5 90.1 69.33 27. / 4697 893 45.8 47.0 89.04 209 64.31 65.3 10.9 6 91.1 69.66 28.7 4725 90.6 46.9 479 89.38 ZZ.5 64.60 66.5 lip 7 92.0 69.98 30.3 47.54 91.9 48o 48.9 89.71 24. f 64.89 678 13.1 8 3io 70.30 31.8 47. 8Z 932. 49.1 49.9 90.04 256 65.18 69.0 14.1 9 93.9 70. 6 3 33.4 48.11 94.4 fo.l So.8 90.38 27.2 65.48 70.3 '5.3 10 0949 370.95 393f.o 349.40 36*5\7 /3S-/.2 2IS-I.7 390.71 40287 365.77 3771.5 I4l(,4 II 9f.8 7/.Z8 36.5 49.68 97.0 52.3 52.7 91.05 3o.3 66.06 72.8 '7.5 11 96.9 7/.60 38.1 4V.97 98 Z 53.4 S3. 6 91.38 31.9 66.36 74./ /8.6 1) 97.7 7/93 39.7 49.26 99.5 54.4 546 97.72 33.4 66.65 7^.3 19.7 14 98.6 72.2? 4/.Z 49.54 3700.8 55.5 Sf.5 9205 35.0 66.94 76.6 248 IS 99.6 72.58 42 S 49.83 C2J 56.6 WS 92.39 36.5 67.24 77.8 Z/.9 16 Z 100.5 72.90 44.4 50.11 033 57.7 57.4 92.71 38.1 67.53 79.1 230 17 OI.S 73Z3 453 SO*0 04 (, 5-0.7 584 93.06 39.7 67.82 80.3 24.1 18 02.4 73.55 47.5 S0.69 Os.9 59.8 59.3 93.39 41.2. 68. IZ 81.6 25. a 11 03.4 73.98 49.1 S0.9* 07.2 60.9 60.3 93.73 42.8 68.41 82.8 26.3 20 2/043 374.20 33*0.6 357.26 3708.4 I36Z.O 2I61.Z 394.06 4044.3 368.71 3704. f 1427.4 2/ 0513 74. S3 52.Z SI.S5 09.1 63.1 62* 94.40 459 69.00 85.3 285 2Z 06.2 #.86 53.7 51.84 11.0 64.1 63.1 94.74 475 69.29 86.6 29.6 23 072 7S./8 SS.3 5-2.13 tzz 65.Z 641 95.07 49.0 6959 87.g 30.7 24 08.1 75.51 56.9 S2.4t (3.5 66.3 65.1 95.41 SO.b 69.88 9.1 31.8 25 09.0 7S.84 584 5170 I4. 2113.9 377.47 3966.3 354.14 3721. 1 1372,8 2/70.8 357.43 40599 371.65 37966 /43.4 3/ 14.7 77.80 67.8 54.43 224 73.9 7/7 9777 61.5 7/.9S 97> 39.5 3Z IS 7 78.13 69.4 ,54.72 23.6 75.0 7/.7 98.11 63.0 72.24 99.1 40.6 33 lit 78.46 71.0 55.OI 24.9 760 7*6 98.45 64.6 72.54 38003 4-1.7 74- 176 78.79 72.5 55.30 262 77.1 746 9878 66.2 72.83 01. (, 42.8 35 IB.S 79.11 74./ 55.5$ 27.4 78.Z 7X5 99.lt 677 73.13 02.8 43.9 36 19. S 79.44 7f.6 55.87 28.7 79.3 76. 5 99.46 69.3 73.43 0&I 4-5.0 37 Z0.4 79.77 77.Z 56.16 30.0 80.4- 774 99.90 70.8 7*72 053 46.1 38 2/.4 80.10 TBS 56.4J 3/Z 81 S 78.4 4oo.(4 724 74 .OZ 06fr 47.2 39 22.3 80.43 80.3 S6.74- 32.5 82.5 79.4 00.48 74.0 74,3' 07.8 4-8A 40 2/23.3 380.76 3981.3 357.03 3733.8 1383.6 zieo.3 400.82 407S.S 374.61 3809.0 7449.5 4-1 24-.Z 81.09 93.5 57.32 35.0 84.7 81.3 01.16 77.1 749' '0.3 So. 6 42. 25.1 81.44. 8*0 57.61 36.3 8F. 8 02.2 0/.49 7g6 7S.V> 11.5 57.7 43 261 8l.7f 866 57.90 37.6 86.9 *3.2 01.83 8oZ 7S.SO 12.8 52.8 44 27.0 82.08 88.1 58.19 38.8 08.0 04.1 OZ.I7 8/.7 7S.SO lH-.o 53.9 45 28.0 82.41 89.7 58.48 40.1 89. 1 8S.I 0252 83.3 71. 09 15.3 55.0 46 28.9 82.14 91.3 S8.77 413 90.2 810 02.86 849 76.39 16.5 S6.I 47 29.9 91.07 92fi 59.06 426 91. z 87.0 03.ZO 864 *.69 17.8 57.2 49 30.8 83.40 94,4 59.35 43.9 92.3 87.9 03.54 88.0 76.91 19.0 5-ft3 49 31.8 83.73 96o 59.64 45.1 93.4 88.9 01.88 89.5 77.28 2 60.51 49.9 96.7 31.8 04.90 94.7 78.18 24.0 62.8 S3 35.6 95.05 02.2 60.81 50.Z 97.8 92.7 05.24 9.58 78.47 W 63.9 54 365 85.39 03.8 6\\0 fl.4 98.9 93.7 05.58 973 7877 26.4 65.0 SS 37.5 8572 05.3 61.39 52.7 I4ooo 94.6 05.92 98.9 79.07 277 66.1 56 38.4 86.05 063 61.68 54.0 01. 1 95.6 06.27 4100.4 79.37 28.9 672- 57 39.4 86.39 094 61.97 55.2. OZ 1 JM 06.61 02.0 79.67 30.1. 68.3 SS 40.3 8f.7/ fO.O 62.26 S6.5 03.2 97.5 06.95 03.5 79.96 31.4 69.5 S9 4/.3 87.05 11.6 62.55 S7.7 04.3 OS. S 07.29 0511 90.26 32.6 70.6 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE 81 42 45 / T E c M X V T E C M X y 2199.4 40764 4(06.6 380.56 39*?9 J47/.T 22570 4zp.ro 4-199.8 399.68 3907.6 1539.2 22004 0798 08. 2 80.86 35.1 728 579 z$.g$ 4ZOI.4 98.99 08.8 4-0.4 1 01.3 08. 32 09.8 8I.[(, 36.4 7^.9 59.9 29.21 02.9 99.Z9 IO.O 415 Z 02? 08.66 /A* 81.46 376 75.0 59.9 29.56 04.5 99. 60 11.3 427 3 03.2 O90/ /2.9 91.76 3S.8 76.Z 60. B 29. 9) 06.0 99.91 /2.5 43.3 4 04.2 09.35 M.4- ff?.06 4<7./ 77.) 61.8 30.27 07.6 400.2 f /3-7 4 4.9 O5.| 03.69 /6~.o 82.35 4 /.3 784 (& 7 30.6Z 09.2 00.52 14.9 46. f 06. | 10.04 /7.S- 82.65 425 79.5 63.7 30.97 IO.7 00.82 16.1 47.2 7 07. 1 /0.38 19.1 82.35 4J.S 80.6 64-7 3133 t.3 01. 1.3 '7.4 48.4 8 09P 10.73 Zo.C 93.25 45.0 8l.7 65.6 31.68 13.9 01.40. /8.6 49.5 9 22090 41107 4/222 383.55 39463 S48Z3 2266.6 432.04 42IS.4- 401.74 39/9.8 1550.6 10 09.9 II.4Z 2J.8 83.9S 475 84.0 676 32.39 /6.9 02.05 ZI.O 51.8 It 10.9 11.76 25.3 84 15 487 85.1 695 32.74 /84 02.36 222 52.9 12 11.8 12. to 26.9 84.45 50.0 86* 69.5 33.10 too 02.66 234 541 13 iz.8 IZ-A5 ES4 84.75 51.2. 873 705 3346 Z.I.S 02.97 2^4 55.Z 14- 13. e 12.79 3 P6.26 57.4- 92.9 7S.3 35.23 2.9.3 04. 51 30.7 60.9 19 22is.fe 4/4.52 4/37.7 36.5~6 3tt8.(> 1434.1 2.276.Z 43559 4Z308 40A$I 393X.9 1562.1 20 )9.5 14.97 39.3 86.86 59.9 95.2 77. Z 35.55 3e.4- 05.12 33.1 632 Zl 205 IS. 21 449 87/6 61.1 963 78.2 3610 33.9 05.43 34.3 64.3 22 21.4 IS 56 42.4 9*46 62.3 97.4 79. 1 36.66 35.5 05.74 35.6 65.5 23 22.4 15.91 44.0 *77 6i5 98.G 90.1 37.02 37.0 06.05 368 66.6 24 23.3 16.25 455 88.06 647 99.7 81.1 37.37 38.6 06.35 3*0 67.8 25" 243 16.60 47./ 88 36 660 ;5oo.8 8Z.O 37.73 4o. 1 06.66 39.2 69.9 26 25.3 16.95 48.6 88*7 (,7.Z 01.9 83.o 38.09 41.7 0697 464 70.1 27 26.2 17.30 50.2 88.97 68.4 03.1 84.0 38.44 43.2 07.2? 41.6 7/2 28 27.2 17.64 5/.7 89.27 69.7 04.2 84.1 38.90 44.? 07. 59 42.8 724 29 222ff./ 4/7.99 4/53.3 189.57 33709 /505-.3 2285.9 439. / 6 4246.3 407.90 3944.0 I57J.5 30 29. f '8.34 S48 99.97 72. 1 06.4 86.9 39.52 479 08.il 45.Z 74.7 31 30. / 18. V) 564 90.18 73.4. 07.6 87.8 39.88 49.4 og.si 464 75.9 32 3/.0 19 03 57.9 90.48 746 08.7 88.8 40.24 5l.o 08.32 47.6 77.0 33 32.0 19.38 59.5 9o. 7g 7S.8 09. 8 89.8 40.5J 52.5 09.13 48.9 78.1 34 3Z9 19.73 61.1 91.09 77.0 10.9 9o7 40.95 S4.I 09.44 So.l 79.3 35 33.9 20.03 62.6 91.38 7SJ> /Z 1 91.7 41.31 SS.6 09.7f 5/.3 8o.4 36 34.9 2o.43 6*.? 91.65 79.5 13.2 917 41.67 S7.2 /0.06 525 SIS 37 35.8 2078 65.7 9/.99 90.7 (4.3 93.6 42.03 587 1037 S3.7 82.7 38 J6.8 21.13 67.3 92.29 91.9 If.S 94. & 42.39 60.3 io.es 549 83.8 39 2237.7 4H.48 4/68.8 392.60 3933 ^ 1516.6 22956 442.75 4261.3 4J0.99 3956./ /595-.0 40 3?. 7 21.32 704 92.90 84.4 17.7 96.5 43.lt 61.4 11.30 573 86.1 41 59.7 22.17 71.9 93.20 95.6 '8.8 97.5 A34.7 649 /'.(,! 58.5 87.3 42 45.6 2252 73. 5 9} 51 96.8 20.0 9.5 43.83 66.4 //.92 59.7 98.4 4-) 41.6 2z.8 750 9).3I 88.1 21.1 99.4 44.19 69.0 /Z.23 60.9 896 44 42.5 23.23 76t 94.11 89.3 21.1 2300.4 44.55 69.S /2..S4 621 90.8 45 43.5 23.SJ 78.1 34.42 90.5 2.34- OJ.4 44.9 / 7'.l /2.8S 633 91.9 46 44.5 23.93 79.7 94.72 3'7 14 S OZ3 45.27 72.6 /3.I6 645 93.1 47 45.4 2428 81.2 95.03 no 25.6 03.3 4563 74.2 I3A7 65.7 94.* 48 46.4 24.63 82 95.33 94. T. 26.8 04.3 4599 757 /3.7g 66.9 95.4 4-9 22.47. 3 424.98 4(94.3 395". 6 3 3?95-4 15279 2305.2 446.3S 42773 414.10 3968.1 /5P65 50 48.3 25.33 859 95.94 9f6 290 06 2 4672 78.3 14.41 69.3 977 51 49.3 25.68 87.4 96.24 979 301 07.2 47.08 80.4 14.11 70. 5 98.8 52 5-0.2 2603 89.0 96.55 99.1 31.3 08.1 47.44 61.9 15.03 71-7 1600. 53 51. z 26. 305 96.85 39003 324 09 1 47. go 83.5 15.34 72.9 01.1 S4 S2.Z 26.74 92.1 97/6 0/.5 336 10. I 4B./6 85o 15.65 74 1 023 55 53.1 2709 93.6 97.46 02.7 34.7 II. 1 48. 5J 865 1596 75.3 035 56 5*1 2744 952 97.77 O40 358 I2.O 48.89 98.1 16.29 76.5 046 57 55.0 27.79 967 98.07 Of 2 370 I3.o 49.25 89.6 I6.S9 77.7 05.8 f8 56.0 *.* 98.3 98.39 06,4 38.1 14.0 49.6 9.2 16.90 79.9 06.9 .59 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE / 44 45 T E c M X Y T E C M X Y 23/4.9 449.9? A2.92.7 4/7E/ J980.I )b08.l 237:7.3 472.08 4-3853 436J4 405/.5 167&.Z 1 If. 9 J&.34- 94.3 17.52 81.3 09.2 /#.? 72.45 6.8 36.46 5E7 79.4 2 /6.9 SO. 70 55.8 /7.8) 82.5 /0.4 7513 72.83 98.4 -76.7* J3.8 80.5 3 2* 51.07 97.4- 19 15 83.7 //. 6 7^.Z 73 Zo 89.9 ^7/0 550 917 4 j 51.43 98.9 Hi.*, 849 12.7 77.2 73.57 91.4 37.42 561 829 5 /9> SI. 79 4300.5 18.77 ?6./ 13.9 72 73.95- 93.0 37.74 57.4 841 6 20.7 52. Ik 02.0 19.09 873 IS 79 Z 74.-3Z 945 JR06 585 S5.3 7 21.7 52.52 035 /9.4o sg.s tb.Z 80. ; 74.70 961 38.38 59.7 96.4 1 22.7 52.09 03: / 13.71 89.7 17.4 fttl 75.07 97.6 38.7* 60.9 87.6 9 23.7 5J2S 06.6 20.03 90.9 /8.S P2./ 7S.4-S 99. / 39.02 6Z./ 88.8 /.W 79. / 34.87 46.8 73.5 2R2 93.28 71.4- 541? 16.9 4-4.7 57 704 /&.9fc 807 35J9 47.9 74.6 29.1 93.66 72.9 54.50 /e.' 453 59 7/.3 7X.33 82/2 35.51 49 / 758 3o.i 94-05 744 54.23 I9.Z 47-' 59 72.3 7/.7(J^ 837 35 ?2 503 77.o 31.1 9443 76.0 55.15 20.4 48.3 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE 46 47 / T E c M X Y T E C IM X Y 2432.1 494.02 4-4775 4554-g 4I2/.6 17495 249X.3 5IV.-UD 4-569.4 475:22 4-190.4 / 822.0 33.J 95! 20 79.0 55. BO 22.7 50.7 92 .5 1859 70.9 7f.ff 91.5 23.3 / 34-.I 95.58 90.b S6.I3 23.9 57.9 937 >8.99 72.4- 7V3 927 Z4.5 2 35.0 95197 82.1 56.46 250 53.; 94.3 /9.38 740 76. Zl 93.8 25.7 3 36.0 96.35 83.6 5678 262 54.3 95.3 19.78 75". 5 76.55 94.9 26.9 4 37.0 96.74 $5.2 57.11 273 555 96.3 20.17 77.0 76.88 96.1 28. 5 38.0 97.12 86.7 57.43 8.5 56.7 973 20.57 78.6 77.21 972. 29.4 6 39.0 97.51 88.2 5776 9.7 57.9 9*3 2037 80.1 77.SS 98.3 30.6 7 40.0 97.89 898 509 ?0.g 59.1 99.3 21.36 81.6 7788 99.5 31.8 3 41.9 98.28 91.3 5&4| 3?.0 60.3 2500.2 21.76 83.1 78.21 4200.6 33.0 9 Z4-4/.9 498.67 44928 458.74 4/33.1 1 761.5 2SOI.2. 522.>6 4584.7 478S5 4-^01.7 tB34.z 10 4? 9 99.05 94.4 59.07 3A3 627 OZ. 1 22.55 86.2 7B.88 o^.<> J5!5 II 43.9 99.44 953 5^.39 35> 63.9 03.2. 32.95 877 79.21 04.0 36.7 It 44.9 99.83 974 59.72 36.6 65./ 04. i 23.35 39.Z 79. f 5 or.i 37.9 /) 45.9 500. 2 / 99.0 60.05 37.7 663 05.2 23.75 90.8 79.88 06.3 39./ 14 46.9 00.60 4-500.5 6039 JS9 67f 06. Z 24.14 923 80 zi 07.4 40.4 IS 479 0099 02.0 60.70 40.0 63.7 07.2 24-54 913 80 & OSS 41.6 76 48% 01. 37 03 6 61.63 41.?- 69.9 08. Z 24.94 95.4 80.98 09J 42.8 17 498 01 76 OS./ 6/.36 42.3 71.1 09.2 25.34 96.9 gf.22 to.s 44.0 /? 50.9 02. IS 06.6 61.69 4J.5 72.3 10.2 25.74 98.4 8/.S5 H.9 45.3 /9 2451.8 50Z.54 4508.2 462 O/ 4M46 17735 25V/.2 526. /? 45-99.9 481.8? 4213.1 /846.5 20 5Z.8 02. 92 09.7 62'. 34 45-.S 74.8 IZ.Z. 2653 460/.5 ?2.22 l+z 4-77 2/ 53.9 03.31 II 2 62.67 46.9 76.0 '3.2. 26.9J 03.0 SZ.5S /) 48.9 22 54.7 0370 12$ 63.00 49.1 77.2 141 27.33 04.5 82. W K.S 50.2 23 55.7 04.09 143 63.33 49.Z 784 15.1 27.73 060 93.Z2 176 5/.4- 24 56.7 0448 15.8 63.65 50.4 79. 6 '6.1 2813 07.6 W.56 /8.7 K.6 25 57.7 04.97 17.4- 63. 98 5/.5 go.8 17.1 **.n 09.1 83.99 '9.8 5^.8 26 58.7 05.26 S8.9 64.31 52.7 82-0 /8.1 28.95 10.6 94.23 21.0 55:/ 27 59.7 Of. 65 204 64.64 55.8 83.2 19.1 29.3? IZ.\ 84.56 ^^.( 56.3 28 60.7 06.03 zip 64.97 55.0 B4.4 20. 1 23.73 13.7 84.90 Z 3.Z S7.5 29 24617 50k. 42 45235 465.3o 4/56. / 17556 Z52H f30.il 46/5.Z 495.2.4 42143 /8S8.8 30 6Z.6 06.91 25.0 656? 577 86.3 22. 1 10.S1 167 ?f.S7 25.5 60.0 31 63.6 0720 26.6 65.96 584 88P 23.1 3033 182 8f.9l 26.C, 6I.Z 32 f&6 07.59 28.1 66.29 59. (, 89.2 24.1 3/.3) 19. 8 86.24 27.7 624 33 G5.6 0798 Z9.6 66.62 60.7 50.S 25.1 31.74 21.3 86. SB 28.8 63> 14- 66.6 08.17 3A / 66.94 61.9 91-7 26.1 ^2.14 zz.8 86.91 3o.o 64.9 35 676 08.76 32.7 67.27 63.0 92.9 27.f 3 Z.5-4 24.3 87.25 3U 66.) 36 68.6 09.\6 34.2 67.60 64? 94. / 2l 32.94 259 87.59 3Z.2 674 ?7 69.6 09.55 75.7 67. 93 6S-.3 95:3 29. 1 33.34 2.7.4 87.92 33.3 68.6 38 7O.S 09.34 37.3 62.26 6.5 96.5 J0.I 33.74 28.9 83.26 34.5 69.8 39 2471.5 5/0.33 45388 468.59 4-167.6 /797.7 2531.1 JM./5 4^,304 4-88.60 42356 X87/. / 40 72. S IO.7Z 40.3 68.92 68.7 98. 9 32. \ 34.55 32.: 88.93 36.7 723 41 7*5 11.11 4/.9 6925 69.9 1200.2. 33.1 34.95 33.5 89.2? 37.8 73.5 4Z 745 //.SI 4-3.4 69.58 7 l.o 014 34. | 35.36 350 89. 61 39.0 74-S 43 75.5 11.90 4-4.9 69.<)l 72.2 026 J5.0 35.76 J6.5 89.94 40.1 76.0 44 76.5 IZ.29 46.4 70 24 7*3 03. S 36.0 36. 16 38.1 90.2$ 41.2 77.2. 45 77.5 /2.68 4g.o 79/ 75.6 06.2 39.0 J6.97 4-/.I 90.% 43.4 79.7 47 79 A 11.47 51.0 71.24. 76.7 07.4- 39.0 37.37 42.6 9/.Z9 44.6 80.9 48 80.4 '3.86 52.6 7I.S7 779 086 40.0 3778 44.Z 9/. 45.7 82.2 49 2481 4- 514.23 45f4.l 4-7/.90 41790 ;?09.9 Z54/.0 538/8 4645.7 49/,97 4246.8 /88J4 SO 82.4 14 65 556 72.23 to'.z ll.l 42.0 38.58 47.Z 92.31 479 84.6 51 93.4 15.04 57.2 ^.?6 $1.3 12.3 43.0 38.99 497 92.65 4-9.0 859 52 844 IS 43 58.7 7289 22.4- 13.5 440 39.39 50.3 92. 95> 50./ 87/ 53 85.4 /5.M 60.2 7J.Z3 93.6 14.7 45.0 39.80 51.8 93.3i 5.3 88.3 54 86.4 16.21 61.7 73.56 84.7 15.9 460 40.2D 53.3 93.6k 524 896 55 87.4 /6.6Z 63.3 7^-S9 859 17.2 47.0 40.61 54.8 94-.00 5*5 90.8 56 88.4. 17.01 64.8 74^ 870 fg.4 48.0 41.02 56.3 94.34 54.6 92.1 57 89.3 17.41 66.3 74.55 89.1 >9.. 49. O 41.4-2 579 94.feg 55.7 93.3 58 90.3 17.80 679 74 M 89.3 20.8 50.0 41. g) 59.4 95o2 568 94.5 59 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE / 4-8 49 T E C IY\ X Y T E C M X Y 255AO 542.23 4660.9 495.35 42580 J895.fi? 261 /.Z 566.94 4 73-2. / 5/5.89 4324.Z /970.7 1 52-0 4264 6Z.4 95^9 59. / 97/0 12.2 6735 53.6 16.24 25.3 7/9 z s*.o 4305 64.0 96.o? 60 2. 98.2 /3.2 67-77 55.7 16.58 264 73.Z 3 54.0 43.45 65.5 96.37 6 (.3 99.5 /4.z 68.19 566 /6-9J 275 74.4 4 55.0 43.86 670 96.7/ 6Z.4 /900.7 If.l 68 A 1 5RZ 17.27 2g6 757 5 560 44 27 685 9705 63.5 020 16. z 69.03 597 I7.G>2 297 77.0 6 57.0 44.67 70.1 9739 646 03.2 17.2 69.44 6/.2 17.97 30.8 78.Z 7 S8.0 45.08 71.6 97.73 658 044 19.2 69.86 62.7 /8.3/ 3).9 79.5 S S9.0 45.49 73.1 98.07 669 05.7 I9.Z 70.28 64.2 18.66 33.0 80.7 9 60.O 45.90 74.6 98.41 68.0 06.9 20.2 70.70 65.7 19.01 34.0 82.0 /> 2561.0 546.30 46 76 1 4-98.75 4269./ /90S.2 2611.2 571 IZ 4767J 5/9.35 4-3 * / ; 9831 3 n 62.0 4671 77.7 99.09 70.2 09.4 22. -i. 71.94 68.8 19.70 36.2 845 12 63.0 47. IZ 79.1 99.43 7/.3 10.7 23.2 71.96 70.3 2o. OS 373 85^8 /3 64.0 47.53 80.7 99-77 724 11.9 24.Z 72.3g 7/.g 20.39 3R4 87.0 /4 65.0 47.94 8*.Z 500.11 73.5 13.1 253 72.80 73.3 20.74 395 883 'f 66.0 4835 837 00.45 74.6 14.4 26.3 7*22 74.^ 21.09 40.6 89.6 If, 670 49. 75 85.3 00.79 7f8 15.6 273 7J.64 7^.3 21.43 4/.7 90.8 17 (,8.0 49.16 86.8 01.13 76.9 16.9 23. 3 74.06 779 21.78 428 92./ /8 69.0 4957 88.3 01.47 79.0 ISA 29.5 74-48 794 Z2 13 4-3.8 934 19 7O.O 49.98 89.8 01.81 79.1 19.4 30.3 74.90 0C9 22.48 4-4.9 94.6 io Z57I.O 550.39 4691.3 502J6 4Z00.Z 1920.6 2.631.3 57^.32 47824 522.82 4346.0 19959 11 72.0 50.80 92.9 02. SO 81.3 21.8 32.3 75.74 W> 23.17 47/ 97.1 22 73.0 5V. 2 / 94.4 02.84 82.4 23.1 33.3 76.16 9f.4 23.52 48.2 984 23 740 57.62 95.9 03. /8 93.5 24.3 54.3 76.59 S7.o 2J.87 49.3 99.7 24 7S.O 52.03 97.7.4 39 89.0 -5780 19.7 08.31 4-300.1 43.1 49.5 8Z.13 09.7 29. /O 655 19.7 V 90 .0 5B.2/ 20* 08.66 01.2 44.3 50.5 3.36 //.Z 29.45 66.6 20.0 4o 25T9/J 55S63 4721.7 509.0O 43023 /9456 26? J. 5 563.78 4FI27 529.80 4J677 2 02 1.2 4| 91.1 59.04 Z33 09.34 03.4 46.8 52.5 4.2/ (4.2 30.1 5 6S.7 225 42 93 .1 59.45 24'g 09.69 04.5 48.1 53. 5 94.63 15.7 30.50 69.8 2^8 43 94.1 59.97 163 /O 03 oJ6 49.3 54.6 8T06 172 30.85 70.9 25.0 44 9S-.I 60.28 278 10.37 06.7 5o.6 55.6 85:48 18.7 3120 72.0 263 45 96.1 60. To 29.3 10.72 07.8 51.8 56.6 85.91 20.2 31.55 73.1 276 46 97./ 61.11 30.9 11.06 o3./3 /5.5 60.6 63.7 88.90 30.8 54.01 80.6 36.5 S3 O4.t 64-.OZ 4>.5 /3.47 /6.6 6A9 64.7 P9.32 32-3 34.36 W.7 37? 54 05. f 6444 43.o A3.82 '77 63.1 65.7 89.75 33.8 34.71 82.7 390 fS~ 06 J 64 85 445 14.16 #.8 64.4 66.7 90/8 354 35.06 ?3.8 403 Ft, 07.1 65.'27 46P 1451 /9.8 656 677 90.6 / 369 3542 84.9 4/.6 57 08.1 65.69 A-7.S 14.85 20.9 669 68.7 91.03 38> 35J77 86.0 42-9 58 09.1 66.10 A9.I AS". 20 22.0 68.1 69.8 91-46 39.9 36.lt 870 44.1 59 /O.I 66 52 SOB /i~54 Z?.l 69.4 7o.8 9/.89 4/.4 36.47 88 / 45.4 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE 50 51 5 / T E C M T E C M T E C M 2671.8 59,2.32 4842.9 536.8Z Z73Z9 6/R39 49^4- 55915 Z794.5 6451/7 S0234 f 79.97 o 7Z.8 92. 7 T 444 J7./8 33.9 18.8) 34.9 58 SI 95.6 4562 24-9 so. m 1 73.9 93.19 4f.9 37.5) 34.9 19.27 36.4 58.87 96.6 46.09 26.4- 80 61 3 7*9 9J.6I 47.4 37.88 3b.o /9.72 J79 59.23 97 (, 46.53 27.9 80.97 3 7*8 94.04- 49o 38.23 37.o 20.16 39.4 59.59 987 46.98 2-94 8l.i4 A 769 94^7 50.5 JR59 38.o 20.60 40? 59. 95 99.7 474? 3o. 9 81.70 5 77.9 94-90 52.0 38. 5 >4 39.0 21.04 42.4 60.31 2*00.7 47.89 324 82.07 78.9 9533 53.S 39.29 4-01 21.4-8 43.9 60.67 01.8 45.34 33.9 82.4) 7 79.9 95.76 SS.O 39.64 41.1 21.92 45.4 61.03 02.8 48.79 35.4 82.80 8 80. 9 96.19 S6.S 40.00 M..\ 22.3fc 469 61.39 03.8 4-9.25 36.9 83. 17 9 268 /. 9 59k. 62 48S80 5-403S 2743 / 622 .g / 49484 5LI.7S 2804.9 649-70 5032.4 583.53 10 *2.9 9705 S9.S A0.70 44-2 23.ZS 4-9.9 62.11 059 50. !(, 39.9 8/P0 n 84.0 97.48 6/.O 41.06 45. Z 23.69 5V. 4- 62.47 06.9 S0.6I 4/.4 84.27 12 8*.0 97.91 625 4-1.4-1 46.2 24..I3 52.9 62.8? 080 51.07 42.9 84.6? 13 86.0 98.34 640 4-176 47-2 H.S8 54.4 63/9 09.0 51.52 44.4- 5.00 14- 7.0 38.77 65.6 42. |Z *g.3 25.02 559 63X5 loo J7.98 45.9 83:37 15 880 99.20 67.1 42.47 49.3 25.46 574- 63.91 in 52.43 47.4 a7> ft. 99.0 99.64 696 42.83 SO. 3 2f.9/ /9 64.27 /2.I -T2.89 4-8.9 86.10 17 9o.l 600.07 70.1 43.18 51.3 Z6.?5 604 64.63 /3.' 5J.34 50.4 86.47 '8 91.1 00.50 7/.6 43.53 52.4 26.80 6/.9 64.99 /4.2 53-80 5/.9 86.84 /9 2692' 600.93 4873.1 543.89 27S3.4 6273* 496*4 565.35 28/5.2. 654. as 5053.4 S87.20 zo 93 ( 01.37 74.6 44.24- S4.4 27.68 64.9 65. 71 16 i 54.7 1 549 87.57 21 94.1 01.90 76.1 44.60 55. 4 29 13 66.4 66.07 17.3 55. H 5M 87.94 22 951 02.23 77.6 44.95 Sfe.5 28.57 67.9 66.43 *3 5J.62 f7.9 89.30 23 96 .i 02.67 79.1 45. 3 / 57.? 29.02. 69.4 66.79 * 56. 08 59.3 98.67 24 972 0310 806 45.66 58.5 Z9.46 709 67/6 2o.4 56.54 60.8 89.04 25 98.2 03 S) 8ZI 46. OZ 595 29.91 724 67.52 2/.4 56.99 62.3 89 At 26 99.2. 0*97 837 46 37 60.6 30.35 73.9 6788 22.4- S7.45 63.8 89.78 27 2.700 i 04.40 85.2 4673 61.6 30.80 7f 8.24- 235 57. 91 653 9o.l5 28 0/.3 04.93 86.7 47.08 62.6 3/.2S 76.9 60-60 24.5 f8.37 66.8 90.51 29 2702. 3 (,05.27 4888.?. 547.44- Z7637 63A69 44~794- 56?-% -zgzs.6 6SRW 50683 594*8 30 03.3 Of. 70 89.7 47.79 64.7 32. 14 79.9 69.33 266 59.29 69.8 9/.2S 31 04.3 Ok 14 91. Z 48. 15 tf.7 32.59 81.4 69.69 27.6 S9.14 7;. 3 9/.62 32 OS. 3 06. 57 92.7 48. 5V 667 33.03 82.9 70.05 28.7 bO.W 72.8 91.99 33 064 07.01 94.2 4S.&6 67. 8 &?.4 84.4 70.4-1 29.7 60.6(> 743 92.36 34 07.4- 07.44. 9ST.7 49.22 68.S 3J.9J 8F.9 70.78 30.7 61.12 7J-8 92.73 95 08.4 07.88 972 49.57 69.8 34.37 87.4- 71.14 31.8 61. SB 77.3 97.10 36 09.4. 08.32. 38.7 49.93 70.9 34.82 899 71.50 32.8 62.04 79.8 93.47 37 10.4 Og.7f 4900.2 50. Z9 71.9 35.27 90.4 7/86 33.8 62.50 80.3 9*84- 38 11.5 09.19 01-7 50.64 7Z.9 35.72 91.9 72.23 34.9 62.96 */.g 94.20 39 27/2.5 605.62 4-903.Z 551.00 277*9 636.17 4393.4 572.59 283S.9 663.42 50833 594." 40 I3.S /o.ot, 04.8 57.36 75.0 36.61 94.9 72.95 37.0 63.88 84.8 ^4.94 41 I4.S /O.SO 06 3 S-/.7I 76.o 37.06 96.4 73.3Z 38.0 64.34 86.2 95.3/ 42 IS.S #.93 07.8 52.07 770 37.SI 979 73.6% 39.0 64.80 87.7 95" 68 43 te.6 //.37 093 52.43 78.1 97.9fe 994 7404 4o.i 65.26 89.1 96.05 44 /7k It. SI 108 52.78 79.1 *4I 5000> 74-.4-I 4-1.1 65.72 9o.7 96.42 45 /86 X2.2S 12.3 S3. 14 801 3g.8t 024- 74.77 4-2.1 66 18 92 Z 36.79 46 '9.6 /2.6g 13.8 53.50 81.1 39. 3 / 03.9 7S.I3 43.2 66.64 93.7 97. Ho 47 20.6 13. IZ IS. 3 J3.S5 ffi.2 39.76 05.4 75.50 44.2 67. // 95.Z. 97.53 48 2/.7 13.56 16.9 54.21 83.1 40.21 06.9 75.86 45.3 6757 96.7 9^9' 49 2722.7 614.00 49/8.3 554 JT7 Z784Z 640.66 50084 576.23 2846.3 66R03 S0982 598.Z? 50 23.7 /4 40- 19.* 54.93 853 41.11 09.9 76.59 473 68.49 99.7 98.65 5"* 24.7 14. ft 11.3 55.29 86.3 4/.SC H.4 76.96 48.4 68.96 5101.2 99.02 52 25.7 iji 22.8 55.64 87.3 42. 0/ 12.9 77.32 49.4 69.42 Oil 9939 53 26.8 IS. 7 5 24? 56.00 98.4 42.46 144 77.68 50.5 69.818 04,2 9976 54- 27.8 16.19 25.8 56.36 89.4 4291 1*9 7805 51.5 7434 057 600./3 53- 28.8 /663 27.3 5fe.72 904 4J.36 t7.4 78.4\ 525 70.81 07. / 00. 59 56 29.8 17.07 Z*8 57.09 9/.4 4J.S/ /8.9 70.78 53.fe 7/.Z7 08.6 00.87 57 3o.<) 17.51 30.3 57 A3 92.5 44.27 204 79.14 54.6 7X.74 'O.I 0/.25 58 31-9 17.95 31.8 S7.79 93.5 4472 21.9 7951 55.7 72. ZO tl-6 0/.62 59 30 TABLE IT. FUNCTIONS OF A ONE-DEGREE CURVE / 53 5-^0 JJ' T E c M T | C M T E C M o 2W6.7 672.66 SI 13.1 60/99 Z9/9.4 7> ?3.i7 77 %.72 82? 24.54 64.3 20.8' 6 54.0 63./0 90.1 7).4\ /R5 9*69 7g.2 97/Z 83.6 2507 &.8 ZI.ZZ 7 55. 1 63.60 9/.6 7J.30 /?6 94z/ 79.& 97.5t 97 3/ gg.4 99.9; 9A3 28.79 7^.0 24.05 74 62.6 67. /3 01.9 76.55 27Z 97F^ ?9.9 700.31 924 29.32 774 2446 75" 63.6 6^.64 03.) 7694 28.Z WJ5 9/,3 00.71 93.5 9.85 79 24.06 76 64.7 68/4 04.8 77.34 29.3 9*.^ 92.8 01.11 94.5 ^).38 00.3 25.27 /7 te.8 6065 06? 7773 3o/ 99. JF 94.3 0151 95:6 30.91 81.9 2567 / 6.8 69.15 07.* 79 M 31.5 99.90 95.7 0>3I 96.7 3/44 S3. 3 26.08 79 30673 769.66 5409.2 678.52 Wtf> QOOA2 54972 70Z.3I 3I97& 83/.9g 5584.7 7/6.49 2O 69.0 70. l(, 10.7 79.91 3J6 caw 98.6 01.71 9P.9 72.51 S6Z 26.89 2/ 70. \ 7o^7 122 7* *> 347 0/.44 5500.1 03.11 3200.O 33.04 ez& 27.30 az 7/.I 71.18 13.6 79.70 35.8 01-98 Ol6 03.51 01. 1 33.58 99.1 277/ 23 TZ.Z 7/69 I?./ 90.09 J6.9 OZ.50 030 03.97 02 JL 3411 90.5 zs.n 24 74.3 72. '9 16.6 80.4g 39.0 03.02. 045 ^.3/ C) 3 34.64 9ZO 28. S 25 744 72.70 /8.o 80.88 39. / 03.54 059 04.77 04.4 351? 93.4 28.93 26 7f.4 73.ZI '9.5 8/.Z7 40. / 04.06 07.4 05.11 os.s 35. 71 9A.9 29.33 27 76.5 73.72 2/.0 9/.67 4/.Z 04.5^ 09 05.51 06.6 36.Z4 96.3 29.74 2ff 776 74:2-1 22.4 82.<* 42.3 os. to 10.* 05 9/ 077 36.7^? 97^ 30/5 29 3075.7 774.73 423.9 6^46 3/43.4 9t>5-63 S5ns 706 31 92088 S373I 5599.3 730.55 30 797 7S.24 4S.4 gz.5 44.5 06./5 /A? 06. -71 099 37.85 56007 30.96 Jl 80.3 7S.7S Zfe.8 83.24 4T.6 06.67 147 07.H )0<* 38.38 oi.t 31.37 32 811 7626 2?. 3 83.64 466 0719 16.2 O7.S2 12.0 3892 03.6 31.76 33 82 ? 7^77 298 84.03 477 O7.7I /7.6 0792 >3.l 39.46 05. / 3Z.I8 34 84.o 77.28 31.3 8443 408 08.Z3 /9./ 08.32 14.2 79.99 065 32.59 35 Sf.l 77.79 327 84:?2 499 "8.76 20.6 0872 15.3 40.53 08.0 33.00 36 86.2 70.90 34.1 85.2? 57.0 09 Zff 220 09J2 /6.4 41.06 094- 33.41 37 97.2 7ff.9l 357 85.61 52.; 09.90 23.5 09. '7.5 4-1.60 10.9 33.8 ' 38 98.3 79.3Z 37. / 86.01 53.Z 10.13 Z4.9 09.9? 6 4Z.I4 12.3 341* 39 3089.4 779.33 54396 686.40 3/54.2 V/oSf 55264- 7/0.33 32 9. 7 842.67 ft f 3.8 734.63 4o 90S 8o.34 40.1 96.80 55.? n.i7 Z7.9 /0.73 20.8 43.ZI /s-.z 35.04 4) 9/. 80. *$ 4/.S 8720 564 I/.90 29.3 ///3 Zl.9 43.73- /6.7 35.45 42 926 ?i.76 430 8759 575 /2fc ?o.g //.53 23.0 4429 18.2 35-86 43 917 8/.g7 44l 5 8799 59 6 I2.<)S 3TZ.Z //.93 24. j 44.83 /9.6 36.26 44 9*0 8238 459 88.18 59.7 H.47 33.7 72.34 252 45.36 21.1 36.67 45 95.9 2.89 4-74- 88.7g 60.9 I4oo J5.2 A?. 74 26.3 45.90 225 3709 44 96.9 83.40 49.9 89.19 bl.S 4.5^ 766 /*./# 27.4 46.44 24.0 37.49 47 98.0 8392 So.3 89.57 6Z.9 15.05 58 / 73.J2 2S.5 46.95 25.4 3790 48 99.1 #7.43 Sl.g 89.97 64P W.57 39.5 73.95 Z9.6 4752 26.9 38.31 49 3/oo * 7^494 545-3 3 69036 3/65. / SI6./0 5541.0 7/4.35 32J0.7 34S06 56283 738K 50 0/.2 8T45 5-4.7 9o.76 66.z /6.6Z 4?.5 /4.7J 31.9 4860 29.g 39.13 51 02.3 8X97 ^6-2 9/./6 67? 17/5 43.9 /5./5 32.9 49. M ?/.t 39.54 52 03.4 8648 577 9/.S5 684 17. 6g 45.4 75.56 34-0 4*. 68 32.7 39.95 S3 045 97.00 59.1 9/95" 69.5 /?.2C 448 75.96 35.1 50.22 ?*./ 40.36 54 0T6 67. SI 606 92.35 70.6 8.73 48.3 76.37 36.2 5o.76 55.6 40.77 55 06.6 8?.o? 620 92.7r 7/6 19 7 51.2 77/7 38.4 5A*4 7S5 41.59 57 0*$ 89.0? 650 93 S4 73.? 20.31 52.7 77.58 79.5 52. Jg 39.9 42.00 *8 09.9 89.57 6(4 9394 7* 9 20 BA 54 1 /7.98 406 5292 474 42 4/ 59 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE / 59 GO 61 T E c M T E- C M r E C M 3241.7 953.46 5642-2 74-2 8Z 3308.0 g'^.Sg' 5729.7 7^76^ 3375-.0 920. J 4 J9/6.0 75>2.?? / 42.8 54.01 443 43 - Z3 09.1 W.9A 31.1 68.04 76.1 20 71 17.5 93. 24 z 43.9 54.55 45> 4-3.64 /O* 97.4? 32.5 68.44 77.3 21.18 18.9 9A 3 4S. 55.09 47/Z 44 0? H.3 8.05 ?40 68.88 79.4 2/.8S Z0.3 94.09 4 46.1 J5J-.63 48$ 44.4fe /2.5 88.60 354 69.30 79.5 22.42 Zl.g 94.51 s 4 7 .z 5618 50.1 4^.87 /^.6 89. /6 369 69.7 / 80.6 Zl.99 23.2 94.93 6 48.3 56.72 n.r 4-J.Z8 /4-7 89.72 3ff.3 70.13 81* 23.56 24.6 95.36 7 494 .5726 Sl.O 45.69 /5.F 90.27 39.8 70S? 8Z.9 2.4/3 26. 9578 9 SOS S7.80 S4A 46/0 /69 90.33 4|.2 70.96 ^4.0 24.70 275 96.20 9 5/6 58.35 55.9 46.51 /RO 91.39 4Z.6 7/.3* m Z5Z7 ^.C' 96.63 /o 3252.7 858.89 5657.3 74693 33/9. / 8W.9S 57441 77/.ff0 3386? 9M.84 5830.4 797.05 // 51. 6 59.4.4 S83 4734 30. "Z 32.50 4J.5 72.1 $7.4 2642 313 97.47 /t S4-.9 S9.98 6o.1 4775 2A4- 93.06 4-70 72.63 98.5 2699 33.3 97-90 /) S(,o 60.52 61.7 48.16 2Z.5 93 6^ 48.4 73.05 99.6 27.56 34.7 98.32 /4 57.1 6V. 07 63.1 4S.57 23.6 94.18 498 73.47 90.8 28. '3 36.1 98.75 /S 59 z. 61.61 646 42.98 ^?7 9474 51.3 73.29 91.9 2&.7I ?7.6 99.17 Id 593 61.16 66.0 49.40 25^ 95.30 52.7 74.31 93.0 29-28 39.0 99.60 17 60.4 6Z.7I 67.5 49.QI ^6.9 95.86 54.2. 7*73 94.1 29.86 40.4 gOO.OZ '8 61.5 63.25" 68.9 So. 22. 7.V.O 96.4? 55.6 7J./5 95-3 30.43 4/9 00.45 t9 6Z.6 63.90 70.4 50.63 29. Z 96.98 57.1 7S.S6 96.4 31.00 43.3 00.87 20 3263.7 364.34 567 f. 8 757.05 3330.3 S97.& S7S&5 77/98 3397? 93/58 584Q..7 SO/. 30 Zl 64.9 64.89 73.3 5IA6 3A4 98 Jo S9.9 76.40 99.6 32. / 5 461 01.72 22 6S-.9 65.44' 74.7 51.87 32.5" 98M 61.4 76%i. 99.9 32.73 476 02.15 Z3 67o 65.98 76 Z SZ.tf 33.6 99.27 6?.8 77.24 34oo.9 33.30 49.0 02.5? 24 68.1 66.5) 77.6 52.70 34.7 59.75 64.3 77.66 ,020 33.88 50.5 03.00 Z5 W.I 67.08 79.1 53. // 3fr.9 900.34 65.7 70g 0*.\ 34.45 5V.0 03.42 26 703 67.62 go.5 51.SZ ?7.o 00.90 67. / 75o 043 35.03 53.3 03.35 27 7/.4 68.17 gz.o 5/94 38.1 0/.47 62.6 70.9Z PSA 3S.6/ 548 04-. 27 2? 72.6 68 72 834 ^J5 39.2 02. 03 7O o 7^33 065 36.18 56.2 04.70 29 73.7 69!a7 84.9 54.76 40.3 02.59 7i.S 79:7/ 07.7 36.76 576 05.13 .70 32748 869.92 5696.3 7SS.I7 334 1.4- 903 J5 57729 7^./7 3408.8 937.34 S 8 S9.i 905.55 ?/ 7S.9 70.37 977 SS.59 42.6 03.72 743 00S9 09.9 37.9' 60.5 05. 9g 72 77.0 70.9 Z- g9.t 5600 4-3.7 04.29 758 S/.OI 11.0 38.49 61.9 0640 *.? ^8.1 7X.46 90.6 J6.42 44* 04.84 772 0/43 tz z 39.07 63.4 06.83 ?4 79.2 72.01 92.1 56.83 4W 05,41 787 a/ 55 /3.3 3965* 64.8 0726 35 80.3 72.56 93.5 57.Z4 4-7O OS. 97 80.1 8ZZ8 144 4 43.70 74.8 10.24 42 88P 76.42 03.6 60.14 S4-.8 09.92 90* 5.Z2 223 44.28 76.2 10.61 4J 89.2 76.97 05.1 60.56 56.0 /0.49 91.6 8f.64 23> 44.86 77.7 ll.io 44 90.3 77.fi 06.5 6097 57/ II 05 93.o $6.06 24.6 45.44 73.1 11.53 4 91.4- 78.07 08.0 61.39 58> II. 62- 945 86.4$ 2F.7 46.0Z go. 5 11-96 46 92.S 78.62 09.4 61.80 59.3 /Z.tS 9S.9 86.90 26.9 46.60 S2.0 /2.38 47 9^.6 79.18 10.9 62 Zi 60.4- 11.75" 97.4 8733 28-0 47.19 83.4 /z.8 45 94.7 79.73 123 62'.64 tf.6 /3.3Z 9gg 97.75 29.1 4176 84.8 /5.24 49 95.? 80. 28 13.8 6j.o5 .7 13.89 5*00.2 S8./7 30.3 4tW 86.3 13.67 50 32969 980.84 57/5Z 763.47 3363.5 9/4.45 58017 78859 3431.4 94-8.92 5887.7 814.09 5V 9*0 8J.39 16.7 6^.8g 64.9 IS OZ. 03. / 89.01 S3L.5 4950 89.1 /452 52 99. / 1.94 /8.I 64.30 660 I5S9 04.? 89.44 33. 7 5^.09 90. S /495 53 3300.2 8Z.50 19.5 64.71 672- 16.15 06.0 09.86 34.? SC.67 92.0 15.38 5V 01.4 83.0? 2lo 65". |3 68.3 X6.72 074 9o.2% 35.9 J/.2S 934 15.81 55 02.5 81.61 224 65.55 69.4 /7.29 0.9 90.70 37. / SI.83 948 16.14 ^6 03.6 $4/6 239 65.96 ro.5- /7.8t iO.3 9'JZ 38.2 52.42. 96.3 '6.67 f7 04.7 8471 Z53 66.3g 71.7 /8.*3 tl.7 91.55 39.3 53.00 977 17.09 59 05.8 8f.Z7 26.1 66.79 72.9 I9.oo /3.1 91.97 40.5 S3.5S 991 /7.52 59 Ob.9 8*92- 29Z 67. z/ 739 ft 57 /4.C 92,39 4/6 54. )7 59 oo. 5 '795 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE 62 63 64 , T E C M T E C M T E C M 3442.7 35475 590Z.O 8 '18.38 351 1. 1 990.24 59875 944.32 3S8O.3 /026.6 6072.5 3fO b 3 O 43.9 SS33 OJ.4 I8.8\ 12.3 9084 88.9 44.76 81.4 272 7J.9 7/07 1 45.0 5X92 04.8 I9.Z4 13.4 91.44 90.3 45. 19 8^6 279 7/52 I 46./ 56.50 06.3 19.67 14.6 92.04 9l.7 45.63 83.8 285 76.7 7/96 3 473 5703 07.7 ZO.IO 15.7 92.64- 93. Z 46.06 849 29. 1 78.Z 72.40 4 4UM 5767 09.1 to 5 3 16.9 93 Z4 946 4650 861 29.7 79.6 72.84 5 495 59.26 10.5 2096 I9.O 93.84 96.0 46!93 g7Z 30.3 8i.o 7J& 6 50.7 58.85 12.0 ZI.39 /9.Z 9444 974 47.37 88.4 30.9 7J.1Z 7 5i8 59.4) 13.4 ZI.92 95.01 98.8 478/ 896 31. 5 83.9 74.17 52.9 6O.02 14-8 22.25 2/5 95.64 6000.3 48.24 90.7 32.2 8f.2 74.61 9 3454. / 960.61 59/63 822.68 3522.6 9924 6001.7 848.68 359/9 /OJ2j8 &7S05 10 55.2 61.19 17.7 23. // 23.8 96 8$ 03.1 4& 12. 9*0 33.4 2.3 O 55.24 09.3 '42..I 07.8 81.70 25 72.3 To.OZ 39. / 41.0 059 244 55.68 /O.S 92.15 26 73.4 70.61 40.5 30.01 06.5 56. M 11.6 43.3 IO6> 8259 27 74-h 7/20 4/.9 30.44 4*3 07. / 272 56.55 43.9 I2JO 83.04 7S.7 7/.79 4-J.4 30.87 44.5 077 26 56.99 l4.o 44.5 13.4 83.48 29 3476.9 972.39 J-944.8 83/.30 3545fe J00A3 603O.O 95743 36I5-.I /0452 (,114.8 883.93 30 78.O 72.98 46.2 31.74 46.8 08.9 31.5 5787 16.3 458 /6.3 84.37 31 79.1 7*57 47.6 32.17 479 09.5 3Z.9 58.31 17.5 464 17.7 84.91 32 ^73 74. 16 49.1 J2.60 49 / 10 J 34-3 59.74 78.6 470 /9.I 95.26 33 9i+ 74.7S 50.5 3*03 50.2 10.8 357 59.18 /9.8 477 20.5 8570 34 F2.5" 7S.35 5/.9 ?3.47 S/.4 11.4- 37/ 59.62 2/0 48.3 2 1.9 *6./5 15 S3. 7 75:94 53.3 3190 52.5 I2.P J85 60.06 22. / A-8.9 233 96.59 36 84.8 76.53 547 34.33 53.7 IZ6 400 60.50 23.3 4-9.5 24.7 704 37 86.0 77/2 56.2 34.77 54 /3.Z 4-A4 60.94 245 50.1 2.6.1 8749 38 87. / 7772 1 576 35.20 56.0 n.8 4Z.8 6/.3S 25!6 508 27.5 87.W 39 34 882 973/ 5959.0 g963 35572 1014.4 6044 Z 86I.SZ 3626 8 /os/. 4 6/289 40 39.4 7991 60.4 36.07 58.3 15.0 45.6 62.Z6 29.0 52.0 30.3 88.92 4/ 905 79.50 61.9 36.50 59.5 15.6 47.0 62.70 29.1 52.6 31.8 09.27 42 9 2 7 80.10 633 36.93 60.6 I6.Z 48.5 63/4 70.3 33.2 89.72 0-3 00.63 64.7 3737 61. ff 16.8 49.9 63.58 3/.5 53.9 34.6 94/6 44 94.0 fl.Z9 66.1 3780 629 17.4- 51.3 64.02 32.6 54? 360 90.61 45 9X1 1.08 676 3F.23 64 / 19.1 52.7 64.46 55.1 374 91.05 46 96/2. 82.4% 69.0 .78.67 65.2 /8.7 54 / 64.90 35.0 F5" S 388 91.50 47 974. 93.07 70.4 39./0 66.4 '9.3 555 65. 34 56.4 402 97.95 4-8 9&S- 83.67 71.8 39.54 67-5" 56.9 6S.78 373 57 O 4-1.6 92.39 49 3495? 7 984.2.7 5973.3 839.97 3568.7 lozo.s 6058.4- 866.22 363 5" 1057.7 6I4-3.O 892.84 50 5500.8 54.86 74.7 4040 69.9 21.1 59.8 6666 39.7 50.3 44.4- 93.29 51 02.0 55.46 76.1 40.84 ZI.7 6/.2 67/0 4-0.8 5P.9 45-8 93.73 52 03.1 86.05 77. S 4/.27 72.2 22.3 626 6754 42..0 59.5 47-2 94.18 53 04.3 S6.65 79.9 4/.7/ 73.3 22.9 64.0 67.98 43.2 60 Z 54.63 54 054 872? 80.4 42.14 74.5 23.6 65.4 68.42 44.3 60.8 500 9507 55 066 $7%5 8/8 42.58 7.5.6 24^ 668 68.87 455 61.4- 51.5 9552 56 077 88.45 83.2 AJ.OI 76.8 24.8 68.3 69. 31 46.7 62.0 529 95.97 57 oag S3. oA 84.6 AJ.45 780 69.7 6975 478 627 543 96.42 58 IO.O 89.64 86.0 43.88 79 / ff.O 71.1 70.19 4?0 63.3 5S.7 96.86 59 Ill TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE , 65 66 69.6 69.7 01.35 53.8 28.45 O3.2 473 373 55.92 /7 08.O 50.0 429 57.76 14- 66.6 72.8 03.57 37.5 tl.2 60.7 30.72 09.2 5d7 443 58.23 jf 67. 9 73.4 "7$ 1 04.04 38.7 //9 62. / 3/ /$ /0.4 5/.3 45.6 5?.69 /6 69.0 74.0 79.6 04.49 39.9 12.5 63.5 31.64 n.6 52.0 470 59. IS X7 70. / 74-7 81.0 04.94 13.2 6A.9 32.09 12$ 52.7 4-8.4 59.61 J9 71.3 75.3 05.39 4-E 2 13.$ 66.3 32.55 14.0 53.3 49.8 6007 f9 72.5 75.9 93.3 05.84 43.'4 14.5 67.7 33.00 IS.2 54.0 57? 60.53 20 367? 7 1076.6 6185.2 906.29 3744.6 IH5.I 6269.1 93*46 3316.4 1154.7 6352.6 960.99 tt 74\? 772 86.6 4-5.8 15.8 70.5 33.9; 17.6 55.3 540 61.46 22 2-3 76.0 77.2 778 78.5 88.0 89.4 07. 13 07.64 4-7.0 48.2 16.4 17 / 71.9 73.3 34.37 34.93 18.9 2O.O 56.0 56.7 55:4 56.7 6 1.32 6238 2.4- 78.4 79. 1 Og.09 49.4 17.7 747 ?52S 21 2 573 58. / 62.84 25 79-i 79.8 922. 73,2 86.3 17.6 82. 83 465 27.6 6500. 2 11.0 20.6 70.0 82.3 39.5 7 74.4 Z7.0 19.0 83.29 47.7 Z8.3 01.6 US z.9 70.7 83.7 40.0 9 7S.(, 87.7 20.4 3.75 48.9 29.0 O3.0 11.9 23.1 7/4 857 40.5 9 387$ 8 //884 642 1.9 904.22 39502 229.7 6504.3 0/24 4-024.4 272 1 6586.4 O4/O to 78.0 89.0 23.2 84.69 SI. 4 304 05.7 IZ.9 Z5.6 72 87. 8 US' II 79.3 89.7 245 gfl5 52.6 3/.I 07.1 13.4- 26.9 735 89.2. 41.9 /z 30.5 90 A 25.9 85.62 5*9 319 085 13.8 WJ 74.2 90.5 42.4 /3 817 91. / 273 86.09 55. 1 32. 5 09-8 t4-.3 29.4- 750 9/9 42.9 14 829 91.8 287 3656 56.3 33.Z 11.1 14.8 J0.6 75.7 93.2. 43.4 IS 84-1 924- 300 8702 575 33.9 /2.6 15.3 J/.8 76.4 94.6 4-3.9 16 853 93.1 3/.4 749 58.8 34.6 /40 15.7 33. / 77.1 96.0 44.3 17 866 938 32 g 796 60.0 353 15.3 te.z 34-.3 77.8 97.3 44.8 18 078 94.5 342 S&4-3 6J.2 56.0 16.7 /6.7 ?5.6 785 987 4-5.3 /9 3889.0 1195.2 64356 90F.89 3962.5 1236.7 65/9.1 /0/72 40J6.? IZ79.3 6600. / 1045.9 20 10.1 95.9 369 09.36 63.7 37.4 194- 17.6 3ft / So.o 0/.4 46.3 Zl 9 /.4 96.5 383 89.83 64-9 38.1 20.8 >8.t 39.3 80.7 O28 46.7 22 926 972 397 90.30 66.2 38.8 222 )8.6 40.6 81 A 04 f 47.2 23 93.9 97.9 41.1 90.77 674 39.5 23.5 19.1 41.8 82.1 05.5 47.7 24 95". / 90.6 425 91 & 69.6 46.2 24.9 f9.5 43.1 32.9 069 4S.2. 25 96.3 99.3 4/.? 91.70 69.9 40.9 26.3 20.0 44.3 83.6 08.2 4-8.7 Z6 975 Izooo 45.2 92/7 71.1 4-1.6 277 20.5 45.6 843 09.6 49.i 27 38.7 00.7 466 9264 7?. 3 42.3 29.0 Z/.O 46.5 85.0 11.0 49.6 28 390 o.o OL3 4-8.0 9J.II 73.6 43.0 30.4 2/4 48.1 85.7 /2.3 So.l Z9 390 1.Z / 2 02.0 64494 9)3.59 3974.9 /24*7 653/.S )02/.9 4449.3 IZ86.S 66/3.7 10566 30 02.4 02.7 50.7 94.05 76.0 44.4 33. 1 22.4 50.6 872. 15-0 57. / 31 03.6 03.4 52.1 94.52 77.3 4^.1 34.5 Pz.9 5/.8 879 16.4 5X5- 32 O4 8 04 I 535 9499 78.5 45? 35.9 23.3 53.1 896 17.8 52.0 33 06.1 04.? 54.9 95.46 79.7 46.5 372 23.? 54.3 89> /9.I 52.5 7 i 07.3 05.5 542 95.93 81.0 47? 38. 6 24.3 55.6 90.1 20.5 53-0 35 08 S 06. / 57.6 96.40 82.2 4-7.9 4O.O 24-. 8 56.8 90.8 2/.g 53.5 36 09.7 06.9 59.0 96.87 03.4 4*7 4-1.3 25.2 58. / - 91.5 23.? 53.? 37 io.9 07.5 60.4 97.34 84.7 49.4 42.7 Z5.7 59.3 92.Z 24.6 S4.4 38 12.2 08.2 61.7 97.81 85.9 SO.I 4-4. / 26.2 60.6 93.0 25.9 54.9 39 3313.4 1208V 6463.1 998.18 39*72 1250.8 654^5 /026.7 4461.8 1293.7 6627? I055-.4- 4O 14.6 09.6 64.5 98.75 884 51.5 46.8 27. / 63.9 94.4 2g6 55:9 41 IS.8 '0.3 65.9 99.22 89.6 S2^ 4$Z 27.6 64.3 95.1 30.0 56.4 42 17-1 //.o 672 99.69 90.9 SZ9 4-9.6- Z8.I 656 959 3/.4 56.8 43 18.3 11.7 60.6 /000.2 92.1 53.6 50.9 2-86 66.8 96.6 32.7 57.3 44 J9S 12.4 70.0 00.6 93.3 54.3 52.3 2.9.0 68.1 973 34.1 57.9 45 20.7 1)0 7 1.4- 01.1 94.6 550 53.7 ^9.S 69.3 98.0 35.4 58.3 4-6 2/.9 13. -r 72.8 01.6 958 5 <>. 7 55.0 3 O.O 70.6 98.? 36.8 58.8 47 23.2 I4-.4 74-. 1 02.0 97.1 56 A 564 30.5 71-9 99.5 332 59.3 48 244 /s-.i 75.S 02.5 983 571 578 10.9 73.1 I3O0.2 39.5 59.7 49 3925.6 1215.9 64-769 1003.0 3999.5 IZ57.9 6559.1 10 3 1.4- 44744 13009 6640.9 I060.-i 50 268 16 5 783 035 4000.8 58.6 60.5 3>.9 7JT6 01.7 42.2 6o.7 51 291 172 79(, 03.9 02.0 59.3 619 32.4 76.9 014 43.6 6/z 52 29.3 17.9 81.0 044 03.3 60.0 632 329 78.1 03.1 449 6/7 53 305 18^ 924 049 045 60.7 64.6 333 79.4 03.9 463 62.2 ?4 31.7 193 937 05J 05.7 61.4 66.0 33.8 80.6 O46 477 62.6 55 33.0 20.0 95.1 058 07O 6Z.I 67? 343 81.9 OS: 3 4-9.0 63. 56 34.2 2o7 86 S 063 o8.r 62.8 6*7 348 83.1 06.0 504- 63.6 57 75.4 2/.4 879 06.8 095 63.5 70-1 352 4.4 06.8 51.7 64 / 58 36.7 22o 892 072- iO 7 64.3 7_/.4 35.7 S5.7 07. S3. 1 64,6 59 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE , w 72 7? T E C M T E C M T E C M o 1 40*6.9 88.i L3O8.2 09.0 55.8 1065.1 65". 5* 4/62.8 647 53.3 ?&.(> 37.0 1094-3 94.8 4Z397 4l'.0 1398.0 99.8 69/6.3 /7.6 IIZ3.3 24.3 2 89.4 09.7 572 G6i0 65.4 547 38.3 423 996 &9-$ 3 9o.7 /0.4 58.5 665 66.7 54.8 39.7 9517 43.6 14004 20^3 25/3 4 92.0 //.2 670 67* 4/o 449 o/7 2/.6 25.8 f 93.2 6J.2 675 69.Z 5<3 42.3 96.7 4,6.2 0/.9 2J.O 26.3 6 94.5 62 6 68.0 705 577 43.7 972 47.5 02.7 24.3 26.8 7 95.7 13.4 63.9 71.8 578 45.0 977 48.8 03.4 25.6 273 8 9 *70 98.2 14. 1 14.8 ss 69.9 69.4 74.1 586 59.3 47.7 9*2 987 50.0 51.3 04.2 05.0 270 2g.3 3? 10 4099.5 f5 66690 /069.9 4l7Sf> /3607 6749.1 [099.1- 4252.6 14-057 6829.6 //28.8 If 4/008 "2 94 70.4 76.9 60.8 504 997 5/9 06.5 31.0 -2?3 OZ.O 17.0 70.7 70.9 78.1 616 S/.8 I/OO. 2 55.2 07.3 32.3 29.8 ff 03.3 178 72.1 7/-4 79.4 623 53. / 00 6 08.0 337 30.? (4- 04.5 '8.5 73.4 90.7 63. 1 545 O'.'/ 578 48.8 35.0 3^ ^ 15 05.3 I9.Z 74*. 72.3 820 63.8 558 01.6 59.1 09.6 36.3 3/!s /6 077 20.0 83.2 64.6 572 OZ.I 604 fo.4 37.7 ?/ 8 /7 08.3 20.7 775 73.3 845 65.4 58.5 01 6 6/.7 // / 39.0 323 /8 19 09.6 22.2 78.9 80.2 7?. 8 7*3 85.8 877 66.1 66.9 59.9 6I.Z 03" / 03.6 63.0 64.3 li.9 12.7 40.3 4.1.7 32.8 33.3 20 4//2./ / 322.9 6681.6 1074.8 4/89.4 /3676 6762.5 H04.I 42656 14-135 6843.0 X/^.8 21 23.6 82.9 89.6 6g.4 63! 9 016 669 I4Z 44.4 34.3 22 14.6 24.4 84.3 757 90.9 69. / 05.1 682 /5.0 45.7 $4 & 23 76.* 92.2 69.9 6.6 Of. 6 69.5 /5.8 470 35.3 n.z 258 970 767 93.5 70.6 679 06.1 7 90.2 28.2 68.4 43.2 40 4/374 /33/7 670&6 1084.5 42/4.0 I38ZB 67894 11/3* 429/5 I4Z9.0 6869.7 11437 4-1 *8.7 3 $4- /o.o 90.8 f& Q 92.8 29.8 71.1 44. 42 40.0 3*2 l>3 ss's ix*r 84.3 921 14- 9 94 / 30.5 724 44-7 43 41Z 42.5 39.9 40.7 /2.T 14.0 86.0 86.4 17.8 19.1 85.1 85.8 lil 15.4- /5.9 954 967 3/.3 32- ?/, 45.2 457 45 46 43.8 45:0 4/.4 42. / 86.9 874 20.4 2/7 86.6 873 96.1 975 /6'.9 98.0 99.1 32.9 33.7 76.4 77.7 462 46.7 47 4-8 46.3 42.9 4-3.6 /fi 87.9 88.4 230 24'.3 88.1 88.9 98.8 6800.2 17.4- 17.9 4300.6 01.9 HI 79.1 804 47.2 477 49 48 B 44.4 88.9 25.5 89.6 0/.5 /84 03.2 36.0 81.7 48.2 5~O 41 f O.I /3451/ 6722 . /089.4 4226? 1390.4- 6802.8 ft/99 43045 14368 68837 11487 5 / ffc 4-5.9 23.5 oq ^ 281 91 1 04.2 19.4 059 376 4.4 49. Z fz 52.7 46.6 24.8 9o 4 294 91.9 055 19.9 072 39.4 85.7 49.7 53 53.9 474 26Z 9o'.8 307 92.7 06.9 20.4 085 39.2 87 / 542 B5.2 32.0 93.5 08.2 20.9 09.8 399 Z8.4 BO. 7 55 565 48.8 28.9 9r8 33.3 94.2 09.6 21.4 407 89.7 5/2 577 496 30.2 346 950 ZI.9 /2.4 4/5 91.1 5/7 57 5-9.0 50.3 92 o 35.9 95.7 IZ'.2 22 3 13.7 42.3 9E4 52.2 60.3 5/./ 329 9*3 37 / 96.5 I3.G 22.8 (ffi 437 937 5 2 470 69004 55? 4400.5 948 79.9 85 5 80.5 43.9 S9.0 16 Z. 3 22.8 0/.7 55> 01-8 95.6 81.3 86. 91.9 44.7 60.3 '6.7 4 /LO g 030 O3.I 96.4 &2 G 86 6 83.2 455 6/6 172 s 254 4*4 O4.4 56? 04.5 973 83'.9 87.1 84.6 46.3 62.9 17.7 6 265 50.2 OS.7 573 85.2 87.6 85.9 4-7? 642 18.2 7 28./ J0.9 07.0 57.8 07./ II.9 96.6 V8. 1 872 4F.O 65.6 187 8 29.4 S/-7 084 S9.3 08.4 99.7 879 89.S> 88.6 48.8 66.9 I9.Z 9 4330.7 /452.5 6909.7 11589 4409.8 /500.S 6989.Z 1189.1 4489.9 /5497 7069V2 1219.9 to 320 533 //.O 93 / / / 0/.3 90.5 89.6 91.3 So. 5 69.5 20.3 // 33.3 SO-.I IZ 3 59* 124 02 A 90.1 92.6 51.3 70.8 20.8 34.6 54.9 13.7 60.3 13.8 02.9 932 90.6 54.0 52.1 72.1 /3 557 60. g 15.1 03.7 94.5 91. 1 95.3 53.0 734 Z\.9 14 372 56.5 /6.3 04.5 9S.9 91.6 96.7 53.9 74.7 223 If 35 573 17.7 l!:l 17.7 05.4 971 92. / 98.0 54.6 76.0 229 39.9 58. 1 t9O 19. 1 06.2 98.4 92.7 95.4 55.5 21.4 .~ 41.2 42.5 S9.6 20.3 2/.G 63> 20.4 ZI.7 070 078 95.8 7<70V./ 93.2 93.7 4*00.7 O2.O W, 80.0 23.9 24.4- '8 '9 4343.8 14604- 69230 1/63.0 4423.1 /500.6 7002.4 //94.Z 4503.4 \5580 7081.3 I2Z4.9 20 45.1 61.2 243 64.3 24.4 09.4 03.7 947 04.7 58.8 9& 25.4 21 464 620 256 64.9 25.7 /O.Z 05.O 952 06.1 59.6 93.9 25.9 22 477 628 27.0 //.O 06.4 95.7 074 60.5 85.2 26.4 23 49.0 636 283 65> 11.9 077 96.2 08.8 6f.3 86.5 2.7.0 24 504 64.4 29.6 66.3 29.7 12.7 09.0 96.7 /O.I 62 / 878 27.5 517 652 668 31.0 13.5 '0.3 972 n.5 63.0 29.0 26 53.0 66.0 32.3 673 32.4 14.3 //.6 977 )% $ 63.8 905 28.5 27 54.3 55.6 66.g 676 33.6 34.9 67.8 68.3 33.7 35.0 /5J 15.9 /2.9 9*. 3 98.8 /4.2 15.5 655 9/.'8 93. / 29.0 29.5 Z8 29 4356.9 /468.4 69362 1/698 4436.4 1 5/6.7 70/5.6 /I99.3 4-5/6.9 1566.3 70944 /230.I 30 58.2 69.2 376 693 377 176 /6 9 99.8 18.2 67-2 95"' 7 30.6 31 7O.O 38.9 69.8 39.0 182. /200.3 19.6 68.0 970 32 60.9 7o 8 40? 70 A 40.4 /9 *2~ 19.5 00.8 20.9 68.B 98.3 3l!6 33 62.2 7/6 4/.6 70.9 41.7 200 2o.9 01.3 22.3 69.7 99.6 32.1 34- 63.5 724 429 43.0 2.6.8 22.2 018 23.7 70.5 32.6 35- 648 73.2 44.2 7/.9 4-4.4 2J.6 2.3 5 02.3 25.0 7/? 02.'2 33.2 36 66.1 74.0 455 72.4 45.7 22.5 248 02.8 26.4 72.2 03.5 33.7 37 675 74.8 469 72.9 47.0 23.3 26J 03.4 277 73.0 O4.8 342 75.6 48.2 73.4 24. / 274- 03.9 29.1 73.9 O6.2 34.7 39 4*70.1 1476.4 6949.5 //7*9 4449.7 /524.9 70Z8.S 1204+ 4-5304 1574.7 7/075 1235.2 46 -71.4 77.2 50.8 74.4 5"^ 1 25.7 30. / 04:9 3I.'8 75.5 08.8 35.7 72.1 52.2 74.9 52.4 26.6 3/.4 05.4 33.1 76.4 10. 1 36.3 A? 74.0 78.8 53.5 75.4. 53.7 27.4 32.7 05.9 34.5 772 11.4- 36.8 43 7S.4 79.6 54.8 75.9 55.) 28.2 34.0 06.4 12-7 37.3 44 76.7 90.4 56./ 764- 56.4 Z9.0 35.3 06.9 372 Tf'9 140 378 45 81.2 575 76.9 577 29 8 36.6 074 3S6 79.7 /5.3 38.3 46 79.3 82.0 5? 8 77.4 59. 1 30.7 30.0 O8.O 39.9 80.6 38.8 47 80.6 82.8 60.1 77.9 604 31.5 39.3 08-5 AI.3 91.4 179 39.4 48 82.0 816 6/.4 78.4 61.7 32.3 40.6 09.O 42.6 82.3 19.2 39.9 49 43833 1494.4 6962.8 1/78.9 4463.1 /533.I 7O4-I9 /2<725 45440 1583.1 7/20.5" 1240.4- 50 8*6 95.1 64. f 79.4 6*4 34.0 43.2 /o.o 4-5.3 840 2/.8 40.9 SI 8*9 86.0 654 80 O 58 348 445 /0.5 4-67 848 231 41.4- 52 973 869 66.7 go 5 67 'l 35.6 45.8 //.o 48'l 85.7 24.4 41.9 53 88.6 876 680 8l.o 684 36.4 47.Z 11.5 49.4 865 -2.5.8 42.5 54 9.9 884 69.4 81.5 698 773 48.5 IZ.\ So 8 873 27.1 43.0 ss 9;.2 89.2 82.0 71.1 38.} 12.6 S2.I 882 284- 43.5 56 92.5 90.O 72 O 82.5 72.5 38.9 si.i 13 1 53.5 890 29.7 440 5-7 73.3 830 73.9 39.7 524 /3. 6 54.8 89.9 31.0 4-45 59 95:2 91.6 74.7 83,5 7S,Z /4.I 562 90,7 32.3 4-5.1 59 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE , 77 76 79 T E C M T E C M T E C M o 45576 J59/.6 7/33.6 (24? 6 4639.8 1643.0 7211.6 \2769 4723.2 \69S.8 72890 1308.5 ; 5*9 92.4 J4-.9 46.1 4).2 43.9 12.9 77.4 246 96.7 90.3 09.0 2 Bo 3 93.3 362 /!,> 425 44-g 142 779 26.0 976 9/6 09.6 3 6/.7 94.1 37.5 47.' 439 45.6 '5.5 78.4 274 985 929 /O./ 4 63.0 950 388 477 453 46? 161 79.0 28.8 994 94.Z 10.6 S 64.4 95.9 40.1 48 2 46.7 474 /8.0 79.5 30.2 /700.Z 95.4 11.2 65.7 96.7 4|.4 48> 48.1 48.2 t93 90.0 3/.6 96.7 It. 7 7 67. / 975 42.7 49.2 49.4 49. / 20.6 80.5 33.0 O2 O 9SO '22 9 68.5 99.4 44.0 49.7 50. 8 50.O 2/9 81.1 54.4 02.9 993 9 698 99.2 45.3 50.3 52.2 50.9 23.2 91. 6 35.8 03.5 7300.6 13.3 JO 457A-2 \60o \ 7/466 >250. 46536 1651.7 72245 /22.f 4737.2 1704.7 7301.3 1313.8 II 72.6 00.9 4-7 "9 51 3 55.0 52.6 Z5> 82.6 38.6 O56 031 143 /Z 73.9 01.8 49.2 5 (.8 56.4 535 27. / 83.2 40.0 06.5 04.4 149 /3 7*3 02.6 50.5 52.3 577 54.3 28.4- 83.7 4/.4 07.4- 05.7 154 14 76.6 03.5 5/.8 52.9 59. / 55.2 29.7 84.2 42.8 08.3 O7O 159 IS 780 043 53. / .53.4 605 56.1 31.0 4.8 44.2 09.2 OS.3 16 S /6 744 05.2 54.4 6/9 57.0 323 85.3 4-56 10. 1 03.6 170 /7 ffO.7 06.0 55.7 54 4 63.3 57.8 336 85.8 47.0 11.0 /0.9 175 J& 06.9 57.O 54.9 64.7 58.7 349 86.3 484 11-9 >2.\ '81 19 83.5 077 ^5!5 66.1 59-6 362 86.9 49. S 12.8 18.6 20 45848 1608.6 7/5*6 / 256.0 46674- /6605 7237.4 /2874 47572 17/3.7 7314-7 13 1 9.1 2 86.2 09.4 60.9 56.5 68.8 6/-3 38.7 879 52".6 14.6 16.0 197 22 87.6 10.3 62.2 70.2 62.2 4o.o 88.4 54.O 15.5 17.3 20 2 Z3 11:1 63.5 575 71.6 63.1 4-1.3 89.0 55.4 164- 18.6 207 24 90.3 I2.O 648 73.0 64.0 42.6 895 56.8 17.3 /9.S 2i3 25 91.7 12 *) 66. 1 58.6 74.4 649 43.9 900 50.3 18.2 2/.S 93.1 13.7 674 59.1 75.8 65.7 45.2 90.5 59.7 19.1 22.4 22.3 27 94.4 14.6 68.7 596 772 66.6 46.5 91.1 6/.I 200 237 229 28 958 15.4 70.O 60. ( 78.5 675 47.8 91.6 62.5 209 25.0 Z3.4 29 97.2 16.3 7/3 60.7 79.9 63.4 49.1 92.1 63.9 26.2 23.9 90 459*5 1617.1 7/726 1261.2 46913 /669.Z 7250.4 /292.7 47653 '7227 73275 / 324.5 31 9*9 18 73.9 61.7 '82.7 70. f 51-7 93.2 667 236 28.9 25.0 32 460 A3 /89 75.2 62.2 71.0 529 93.7 68.1 245 30. / 25.5 33 026 /9.7 76.5 62.8 85.5 7/9 54.2 942 69.5 25.4 31.4 26 / 34 04.0 20.6 77.9 63.3 86.9 55.5 94.8 70.9 26.3 32.6 26".6 35 05.4 2/4 79.1 63.8 883 736 568 953 72.4 27.2 33.9 27 / 06.8 22.3 80.4 64.3 89.7 74.5 58. 1 9S.8 73.8 352 27.7 37 08. 1 23.2 8 1.7 64.8 91.1 59.4- 96.3 7-5T2 29.0 365 28 i 38" 09.5 24.0 83.0 65.4 92.4 763 60.7 96.9 76.6 29.9 379 28.7 39 /0.9 249 84.3 65.9 93.8 772 62.0 974 78.0 308 39. 1 29.3 40 46/2.2 ;&z57 7/3*6 J266.4 4695.2 16781 7263.3 12979 4-779.4 1731.7 7-3403 329.8 47 13.6 26.6 869 66.9 96.6 79.9 64.5 98.5 80.8 32.6 A 16 Jo. 3 4Z 150 275 92.2 675 98.0 79.8 658 99.0 82.2 335 429 30.9 43 164 28.3 89.5 68.0 99.4- 80.7 67/ 99.5 837 344 442 31.4- 44 17.7 29.2 908 68.5 4700.3 81.6 68.4 1300.0 85.1 35.3 454 31.9 45 30.O 92 1 69.0 02.2 92.5 69.7 00.6 86.5 36.Z 467 32.5 46 20.5 30.9 934 69.5 03.6 $3.4 71.0 01.1 879 37J 48.0 330 47 2/9 31.8 947 70.1 O5.0 f4.2 72.3 01.6 89.3 38.0 493 33. 5 48 23.2 32.6 96.0 70.6 O64 5.1 73.6 02.2 9o.7 38.9 50.6 34. 1 49 246 33.5 973 7 /.I 07* 860 74.9 02.7 92. / 39.9 5I.S 34.6 50 46260 1634.4- 7/98.6 127/6 47092 1 686.9 7276. / / 303.2 47936 174-0.9 7353. \ 1335 \ 51 27.4 35.2 99.9 72.2 87.8 774 03.7 95.0 41.7 54.4 35.7 52 28.8 36.1 7201-2 72.7 /20 887 73. 7 043 964 42.6 55.7 36.2 5*3 37.0 025 ~73 ? 13.4 89.6 80.0 978 43.5 570 36.7 54 3/5 378 03.8 73.7 '48 9O.S 8i.3 05 3 99.2 582 373 55 32.9 387 05.1 745 '6.2 91 3 82.6 05.9 4800.7 453 59.5 37 g S"6 343 396 06.4 74.$ 922 83.9 064 02. l 608 383 57 35.6 4o4 077 '9.0 93 / 85.2 069 035 47.1 62.1 38.9 370 41.3 090 75.8 20.4 94-.0 864- 07.4- 04.9 48.1 633 394 .59 384 422 /0.3 76.4- 949 87.7 O6.3 64.6 39.9 TABLE H. FUNCTIONS OF A ONE-DEGREE CURVE 45 80 81 3Z / r E c M T E C M T H C M 4.907.7 1749.9 7i6ry I34OS 48936 /0O5"3 744 Z.Z 37^# 49807 1962.2 75/80 /4054 o O3.Z SOS 672 4-1.0 95.0 063 435 75:3 8z.Z 63.2 19 Z 06 O f 106 51.7 685 4-7.6 965 07.2 44.? 7J.9 83.6 64. / ao.s 065 2 IZ.O 52.6 69.7 4-21 979 08 / 460 74.4 85- / 65. / 2/.g 07.1 3 /34 535 71.0 426 954 09. / 473 75.0 ?66 66 f 2)0 07.6 4 /4.9 54> 723 43 Z 4900. lo.o 4F.6 7JT5 880 670 241 08.2 5 16.3 SS4- 736 437 02 Z no A98 76.0 89^ 6ffO 255 08.7 6 17.7 563 74 8 442 03.7 II 9 Sl.l 766 91.0 6g.9 268 09.3 7 19.1 572 76.' 448 051 '2.8 524 771 9Z4 699 29.0 09.9 9 20.5 S8.I 77.4 453 06.6 /3.^ 53.6 777 93.9 749 29.3 /04 9 4222.0 I7S90 73787 345.g 49000 /F/4.7 7454.9 13782 4-99S4 187/8 7S30.5 /4/0.9 /O 234 S9.9 799 464 095 '5 7 S6.Z 78.7 9(,.8 72 S 318 UA // 248 60.3 8/.2 469 109 /6.6 574 79.3 90.1 73.3 33.1 12. It 2fe.2 6/8 82.5 47.5 IZ4- /7.5 587 7*8 99.8 T4-7 343 /2 5 i) 277 e.2.7 fc?.S 43.0 13.8 18 5 600 9^4 5OOI. ^ 75.7 3yfe /}./ 14- 39.1 63.6 85.0 45 IS?. /9.4 61.2 50.9 O2 7 76.7 36.9 I3.(> ts 30.5 64,5 ?6.3 49.1 '67 204- 625 9/.S Oi? 776 38.1 142 )(, 3I.<) 65.4 76 49.6 181 2/3 63.7 W.O O5.6 7^6 39} 14 7 17 334 664 98.9 50. i /96 223 65.0 F2.5 07/ 79 6 406 15.3 18 34.8 67> 90.1 50.7 210 23. 2 66.3 ?3. Off.6 80.5 4/.8 15.8 19 4W6.2 /7fc?2 73914- 35/. 2 4-9225 I8Z4. 1 74675 /^836 5O/0.0 1881.5 7ST43.I )4/(>.4 TO 376 69. / 927 51.8 Z3.9 Z-S.I 68.8 ^4.7 //. 5 82.5 44.4 /6.9 Tl 391 70. f 9J9 S2.3 ?5".4 26o 70.1 S47 13.0 gS.4 45.6 17-5 22 40.5 7A0 93"2 51.8 268 270 71.3 i?5.3 145 9*.4 469 19.0 23 41.9 7X9 96.5 5J Z8J 27.9 726 85.9 159 85.4 48. / /S6 24 43.4 72.9 97* 539 297 287 739 86.3 17.4 86.3 494 >9'l 25 44.8 73.7 990 54.4 31.2 298 7f.l 069 19.9 5^6 19.7 26 462 74,7 7400.3 55.0 32.6 30.3 76.4 874 Z0.3 88 3 5/-9 20.2 27 476 7*6 or 6 55.5 34. / 31.7 77.6 vito zi.S 89 2 53.1 20.8 28 49.1 76.5 023 56. / 755 32.6 78.9 98.5 2*3 90.2 54.4 21 3 29 4-S505 /7774 7*04. 1 /356.6 4-9J7^ 1333. 6 7490Z 1389.1 524. 1891.2 755J6 14219 30 51.9 74 054 57' 384 ?4.5 Vl'.4- 89.6 Z62 9 Z.Z 56.9 22.4 31 53.4 79.3 06.7 577 39.9 3*. 5 82.7 90.2 277 93.1 58.1 23.0 32 54.8 8*0. Z 07.9 55.2 411 36.4 8A.O 90.7 29.2 94.1 594 23.5 33 56? 81. I 09 Z 5*7 42.9 37.4 5.2 9/.2 307 9S.\ 60.7 24. / 34 577 #2. 1 /05 59.? 44.a 39.3 86.5 9< 9 32.1 96.1 61.9 246 35 59.1 2*0 //.8 59. 9 45.7 393 97.7 92.3 33(, 970 632 25.2 36 60S &39 13.0 60.4 472 40 a 89.0 92.9 35.1 98.0 64.4 25.7 37 620 #4-8 14-3 60.9 4*6 412 90.3 9^.4 366 99.0 65.7 26 3 38 63.4 85.8 /5.6 G.4 50.1 42.1 91.5 54.0 3&.I 1900.0 669 26.8 39 AS64.8 1786.7 74/6.5 136? P 495/5 1843.1 7492 9 /J945 50395 I90Q.3 7S682 1427 A 4o 66.3 976 /8.f 62.5 53.0 44P 94.1 95.1 41.0 ol.9 69.4 27.9 4-1 677 88. > 19.4 63.1 54.4 45.0 95.? 95.6 425 02.9 70.7 22 5 42 69.1 895 20.7 6*6 55.9 46.0 966 9(, 1 44.0 03.9 T-9 29.0 4-3 706 90.4 21.9 C4./ 575 469 97g> 999 51.4 OF. 7 78.2 3/.8 48 778 9*1 29.3 66. S 64 51. 7 04-.I 99.4 5?.g 09.7 79.4- 32. 3 49 4879.2 17960 7*295 13674 49661 /#r2& 7505.4 400.0 5054.3 19/0.7 7S80.7 14329 50 8o.G 36.9 30.8 67.9 676 5/6 066 O0.5 55.8 // 7 81.9 33.4 s-/ 221 979 32. 68. 5 69.0 5-4.5 079 Ol.l 57.3 /2.7 93.2 J4.O 52 S3 5 98.8 33.3 69.0 705 55.5 O9 2 01.$ 5ff.8 > 814 34.5 53 84-9 99.7 34.6 69.5 7/9 56.5 /0.4 02,1 60.3 >4.6 gS.7 35. 1 54 #64i /gOO. 7 359 70.1 7*4 574 11.7 02.7 6/-7 /S.6 969 356 55 B7S 0/.6 57 / 70.6 74.9 50.4 12.9 0^2 C3.3 /6*6 88.2 36. z 56 83.3 02.ST 384 rt.z 76.3 593 142 03.9 647 /7. 994 36.7 57 90.7 0.J.5 39.7 71.7 778 60.3 155 04-3 &'i )8S> 907 373 5g> 92,1 , 04,4 4 to 72.2 79Z 6/3 /e',7 04.9 677 /ae 9i'.9 J7 *? TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE / S3* 84 85 T E c M T E C M T E C i M o 5069.2 '920.5 7 f 93.1 /43S-4 5IS9.0 19^.4 766/.g 1471.7 5250.3 Z04I.7 77^/.9 5053 1 70.7 21.5 94.4 389 60.5 81.4 69.0 7^3. 5/.8 411 43.0 Of9 2 72.' 225 95.7 39.5 62.0 Sz4 702 72.8 S3. 3 438 44Z Of.4 3 7?.6 23.S 96.9 40.1 63.5 83.4 7/:s 7/4 549 44 g 455 070 4 75. / 245 98.2 40.6 65.0 9A4 72.7 7/9 564 459 467 076 5 766 25.5 99.4 41.2 66.6 8S.4 74.0 745 S7<) 46.9 479 08.1 6 78.1 26.4 7600.6 4/.7 68.1 864 75.2 75.0 595 479 4-9.2 087 7 79 6 274 01.9 42.3 69.6 874 764 75.6 61.0 49o 504 09.3 3 8/.' 2*4- 03.1 42.? 71.1 88.4 77.7 7t,Z 625 5oo 51.* 09. g 9 92.6 29.4 OA.4 43.4 72.6 99.5 7B9 76.7 64.1 5(.| 52.8 10.4 IO 5084-.0 '930.4 7605.6 /44-J.9 5/74./ 1990S 7680.1 /4773 5265.6 2052.1 77S4J 15/09 II 95.5 3/.4 069 445 7f.6 9/.S 91 A 77.8 67. / 53. / 55.3 ll'.S IZ 870 32.4 08.1 ASO 77 / 92.5 . 826 754 68.7 54.2 ,565 12 1 /3 88.5 334 09 A 456 79.7 93.5 83.9 78.9 702 SS.-L 57.8 /2.6 14 90.0 34.4 /o.6 46. / 90.?. 94.5 85.1 79.5 71.8 563 590 I3Z 15 9/.S 35.4 11.9 4fe7 81.7 95.5 86.3 80.1 73.3 57.3 60.2 13.8 l(> 93.0 36.? /3 / 472 83.2 966 87.6 $0.6 748 58.3 614 >43 17 94-5 37? /4.4 47 g 84.7 976 88.8 8/.Z 764 59.4 62.7 74-9 18 96.0 38 3 /5.6 4g.4 86Z 986 9o.o 81.7 779 604 639 >55" f9 975 39.? /6.9 48.9 977 99.6 V/.3 823 79.5 6I.'5 65.) '6.0 20 S099.0 /940.3 76/0./ /449.5 51 89. 3 2000.6 7692.5 14829 52810 2062.5 77663 15/66 2/ 5/OO.4 41.3 / 845 85.6 65.7 700 >S.3 24 04.9 44.3 23. f 5/.7 95.3 04.7 974 8S.I 872 66.7 71.2 19.8 2? 06.4 45.? 24.3 52.2 96.8 05.7 98.7 85.7 83.7 677 7Z5 19.4 26 079 46.? 256 52.? 984- U.8 999 ^.2- 90.3 68.9 73.7 20.0 27 09 A 47? 26.5 J3.3 999 07.9 7701. 2 86.8 91.8 69.8 749 20.5 29 10.9 483 28.' J3.9 520/. 4 08. 472 39.6 393 04.2 39.9 02.5 IZ.8 38.1 f? 575 79.3 $6? 71.1 48,7 40.7 406 04.7 414 03.6 I4.o .32.7 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE 47 6 BT #0* / T E c M T E C M T E C M JJ43.0 2/047 78/S-2 /S-39.2 54372 2/69.2 7888.1 IS 73 5 5533.1 22355 7960.$ 76081 44.S 057 /6.4 39.8 388 70.3 89.3 74-. 1 ?4.r 36.6 61. 5 087 1 i4fe./ 068 17.7 40.4- 40.4 7/.4 90.5 74.7 363 377 627 092 2 47.7 07'g ri.i 4*0 42.0 725 91.7 75.2 3/9 389 63.9 09? 3 49.2 00.9 20 1 4/ 5 43.6 73^6 92.9 75.? 39.5 40.0 65" / 104 4 SO 8 100 2/.3 42. 1 45.2 74.7 94- J 764 4/./ 4-J. / 663 /I.O J- St. 3 1 1.0 ZZ5 427 46.7 7S8 95.3 77.0 427 422 675 11.6 6 539 It.t 23? 4*2 483 76.9 96.5 775 443 43.3 8.7 /Z.I 7 555 131 250 43. g 4^.9 79 O 97.7 7^. / 46.0 445 69.9 12.7 8 57.0 U.2. 26.2 44.4 5/.S 79.1 98.9 7.7 476 45.6 7L) /3.1 9 5358.6 ill 5. 3 7274 /5449 5453.1 ZI80.Z 7900.1 /579.1 5-5492 2246.7 7972.1 y&/9 /o 60.1 164 296 455 54.7 813 OI.4- 79.? ^.8 47.5 735 /4-5 // 61.7 17.4 29.8 46. / 563 824- OZ 6 80.4 ^?4 49 74.7 /5JO /2 633 /8.5 31.1 466 579 S3A 03.8 8J.O 54.0 Sd.l 7*9 IS. 6 /3 6A8 /9. 6 323 4-72 595 84.5 050 81.5 55.7 n2 771 /6.-Z- )4 '664 20.6 33.5 47.8 6/.0 85.6 06.2 BZ.t 574 52.3 78.3 /6.8 )S 63.0 21.7 34.7 4? 4 62.6 6.7 07.4- 82.7 5"8.9 5i5 79.5 /74 16 695 228 359 48 9 64.2 878 08.6 83.3 605 5*6 80.7 /7.9 17 71.1 23.9 37.1 49.' 5 65.8 89.9 09.9 83.8 62.1 55.7 8/.9 ts.s 18 72.7 24.9 38.4 50. 1 674 9o.o It.o 34.4 63.7 %.B 83.0 &.) /9 5374.2 Z/260 72396 1 550.6 5469.0 2/9/./ 79/Z.Z /5-85.0 5565.4 2ZS8P 79fo Z 16/9.7 20 7S.8 277 40.8 5/.Z 70.6 92.Z /3.4 8^6 67O S9J 85.4 20.3 Zl 774 28.1 420 St. 8 72.2 93.3 /4.6 86. 1 68.6 60.2 86.6 Zo.8 22 783 292 43 2 52.3 73.8 94.4 /r.# 86.7 7ft Z 6/.4 878 2/4 23 go.5 30.3 44 4 52.9 754 95.5 17.0 87.3 7/.ff 62.5 89.0 22.0 24- gz.i 3/.4 456 535 77.0 96.6 1ST. 879 73.5 63.6 90.? 22.6 25 836 32.4 469 54 / 78.<> 97.7 /9.* 88.4 7S.I 64-.B 9/4 23.2 ^6 852 33.5 48J 546 80.2 98.8 20.6 89.0 76.7 65.9 92.6 Z37 27 968 346 49.3 55.Z 81.8 99.9 2/.g 896 78.3 67.0 93.8 24.3 ^8 89.3 35.7 50.5 55? 83.4 220 I.I 23.1 9o.Z 80.0 68.1 95.0 24.9 29 53*9.9 2/36.7 75/.7 /556.J 54#4.5> 22022 7924.3 1590.8 55F/.6 2269.3 7996.2 ;625.r 30 9/-5 378 529 56.9 86.5 03.3 25.5 9t.3 83.2 70.4 97.4 16.\ 31 93.; 383 54-1 575 8S.I 04.4 26.7 9/.9 843 7/5 98.6 26.7 32. 946 4oo 55T4 58.1 39.7 05.5" 27.9 925 865 72.7 99.8 27.2 33 962 41.0 56.6 50.6 9A? 06.6 29. / 93! 1 88.1 73.* 800 i.o 278 34 97? 42.1 57.8 59.2 92.9 077 30.3 936 83.7 75.0 02.2 294 3sr 99.3 4-?. 2 590 59.8 94.5 08.8 J/.5 942 91.3 76. / 034- 29.0 36 5400.9 44.3 602 60.3 96.1 09.9 32.7 94.8 930 77.2 045 29.C 37 025 4r.4 61.4 60.9 977 // O ?^.9 95.4- 94 fc 784- 05.7 30. / 38 Q*J 46.4 62.6 61.5 99.3 /-' 3J:/ 95.9 96.Z 79.5 06.9 30.7 79 5405.6 2/475 75-658 1562.1 55*009 22/J2 79J63 > 59 6.? 5597.8 2280.6 80081 1631.3 40 072 4*6 65.1 62.C 025 /4.3 375 97. / 99.5 818 093 3/9 4-1 08 49 7 663 63.2 04.1 /5.4 38.7 977 560 /. 829 /as* 32.5 42 /0.4 50.8 675 6J.g 05.7 /6.5 39.9 983 02.7 84. \ 117 33.\ 43 /2.0 S/.9 67 64-J 073 177 41. J 98> 04.4 85.1 /2.9 336 44 /3.5 52.9 69.9 649 O90 123 423 99.4 06.0 86.* I4-.I 342 45 IS.I 54.0 7'.l 655 10.6 /9.9 4-3.5 /6OO.O 076 875 /5.3 34.8 46 16.7 55. / 72.J 66.' IZ.Z 21.0 447 00.6 09.3 . 88.6 16.5 3S.4. 4-7 18.3 56.2 7*5 66 /3.8 22.1 4JT9 01. { /0.9 89.8 17.7 36.0 48 19.9 57? 74.8 67.2 /54 23.2 47/ 01.7 12.5 90.9 19.8 36.6 4-9 5A2I.4 2/58.4 7*76P /567S 55/7.^ 2224-3 79483 /60Z.3 5-614.2 2292.0 9020.0 '637. 1 5-0 ^3.o 55.4 77.Z- 68.3 19.6 25 5 495 02.9 IS.8 932 21.2 37.7 5/ 24 1, 605 78.4- 6F9 20 2 2fc6 50.7 OJ.5 17.4 94-3 22* 38.3 52 26^ 61.6 79G 69.5 2;.? 27.7 5/.9 O4P /9.I 955 23.6 38.9 53 27.7 62.7 SOS 70.1 23.4 28.8 53. / 04.6 20.7 96.6 24.8 395 54 29.3 638 820 70.6 2S.O *9.9 54.3 05.2 223 97.8 260 40. / 55 309 649 83.2 7I.Z 26.6 3/.0 555 058 24.0 98.9 272 4o.6 56 32? 66.0 944 71 B 28.2 32.1 56.7 063 25.6 2300.1 28.4 4-/.2 57 *4.f 67.1 ?5.6 72.4 298 33.3 579 06.9 272 0/2 Z96 418 58 35.7 69.1 96.9 7?,<) 3/4 34.4 59. / 07.5 2g9 024 30.7 4-24- 59 48 TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE , $9 90 91 r E C M T E C M T E C M 5630.5 2303.5 8031.9 /643.0 8/02.9 /6/^2 5830.5 2444-.9 8I7J.4 /7/3. 7 32.2 04.7 33.1 43.6 31.3 74.5 CU f "70 S 32.2 46.2 74.5 14. 3 z 338 05.8 44./ 33.0 757 05J 79.4 339 474 7f.7 I4-.9 3 4 354 06.9 08.' 35.'5 36.7 447 4f.3 34.7 36.3 76.8 78.0 06.5 077 79.9 80.5- 356 373 49.6 49.8 76.9 78.0 /5.5 16. 1 5 ^O "T 09,2 379 459 30 79.Z. 088 39.0 s/.o 79. Z 16.7 6 40.3 (0.4 39.1 46.5 39.7 80.4- lo.o 81-7 40.7 52.2 00.4 17.3 7 42.0 fl.6 40.2 47.' 4-1-3 81.6 11.2 82.3 42.4 534 8/5 17.8 8 436 12.7 41.4 47.7 43.0 827 124 82.9 44.1 54.6 827 /84 9 45.3 13.9 447 53.9 13.5 83.5 45.8 55.9 83.9 /9io 10 5646.9 23/5.0 80438 /648 5746.3 2385 / 81147 !684-.l 5847.5 2457/ 9195.0 17/9.6 n )6.2 45.0 49.4 48.0 86.3 15.9 847 49.2 583 86.2 20.2 / 502 /7.3 46.2 50.0 49.7 875 17.1 953 50.9 535 87.4 20.8 /3 5J-8 18.5 474 88.7 18.3 85.8 52.6 60.7 895 21.4 /4- 53.5 19.6 48.6 5I.Z 53.0 99.8 X9.4 86.4 543 6'.9 89.7 22.0 If 55.1 20.8 49.7 51.7 -54.7 91.0 20.6 87.0 56.0 63.2 9o'9 22.6 '6 568 2/.9 50.9 52.3 56.4 9t.Z 21.8 87.6 577 644 92.0 23.2 /7 584 23.f 52.9 58.1 93.4 23.0 88.2 59.4 65.6 9.22 23.8 > 60.1 24.3 533 53.5" 597 94.6 24.1 98.8 61.1 66.8 94.3 24.4 /9 61.7 25.4 545 54./ 61.4 95.8 253 89.4 62.9 68.0 955 25.0 2.0 5663.4- 2326.6 8055.7 /6547 5763.' 23970 81 26.5 1690.0 J264.6 24693 8/96.7 /T256 Zt 65.0 277 56.9 55> 648 98.Z 27.7 9o & 66? 70.5 978 26.2 ZZ 667 28.9 580 664 99.4 28.8 9/z 680 71.7 99.0 26.8 23 68.3 30 O 59.2 56.4 681 2400.5 30.0 91.8 69> 72.9 8200.2 274 24 3/.2 60.4 570 69.8 0/7 3/.Z 923 74-./ 0/.3 28; 25 7/-6 324 6/6 57.6 029 324 92.9 73. / 75T4 02.5 28.6 26 73.3 33.5 62$, S8.Z 73. / 04./ 33.5 93.5 74.8 76.6 29.2 27 74.9 34.7 64.0 74.8 05.3 94.1 76.5 77.8 048 29.8 28 766 65 / 59.4 . 765 065 35"Q 94.7 7F.2 79.0 06.0 304 29 7R2 37.0 66.3 59.9 78.2 07.7 37.1 9S.3 79.9 80.3 072 3}'.0 30 56799 2338.2 20675 /660.5 5779.3 240R9 9/38.2 '695:9 58%l.7 Z.481.5 82083 /T3/6 31 815 39.3 687 61.1 81-6 10. 1 39.4- 96.5 834 82.7 09.5 32.2 32 83.2 4o.5 69.9 617 83.2 11.3 40.6 97-1 85.' 83.9 /0.6 32.9 33 848 41.7 623 54.9 12.5 41-7 97-7 868 85.2 33.4 34 86.5 ' 428 72 Z '629 86.6 13.7 44? 98.3 885 86.4 13.0 34.0 44.0 734 635 883 14.9 983 90.2 976 14.1 34.6 36 898 45.2 74\6 64.1 90.0 )6.\ 45~ 3 99.4 9'.9 888 351 37 9/-'4 463 75.? 64.6 91.7 173 46.4* /7oao 9*6 90.1 /6.5 35.7 475 77.0 93.3 /8.5 4-76 00.6 95T4 91-3 17-6 36.3 39 948 48.7 7g.Z 65:8 950 19.7 48.8 Cl.2 971 92.5 18.8 36.9 >*0 5696.4 2349.8 8079.3 '666.4 5796.7 2420.9 91500 I70/.8 5#98 24938 92/99 /7375 4-f 98.1 510 805 67O 984 22.1 Sl.l O4- 5$OO 5 95.0 2 ). | 38.1 42. 99.7 52.2 81.7 676 5800.1 23.3 52.3 030 02> 96.2 2*Z3 387 4-3 570 /. 4 5J.3 68.2 0/.8 245 53.5 03.6 03.9 975 234 39.3 44 03.0 545 84.1 03.5 257 54.6 042 05.7 937 2.46 J9.9 45 85.3 69.3 "05. 1 269 558 048 074 99^9 257 40.5 46 064 56 "9 86.4. 69.9 06.8 28.1 570 or.4 09.; 2 50'. 2 269 41.' 47 00.0 58.0 ?7.(> 70.5 085 29.3 06. /o 8 O2 4 28. 1 41.7 4-8 097 59. z S3 8 71.1 10 Z 30.5 59^3 06.6 /2 5" 036 29. z 42.3 4-9 J/.3 60.4 90.0 71.7 113 3A7 60.5" 072 14.3 04.9 30.4 42.9 So 57/3.0 236/5 809) Z I67Z3 S8I3.6 2432.9 8161.7 /7 U 272 290 30'.8 32.5 ?0.0 2S8./.3 82.6 8/9 857 877 88.9 90.2. 91.5 92$ Kf SI 9JT/ III 95 9*7 W00.8 0/.9 O3f 04.2 065 /0 /7* 79 0403.S 046 058 069 08.0 09.2 70.3 72.6 I3J 94/4.8 /6.o 20. S Zt.6 227 239 25.0 1822.0 22.6 23.3 239 245 25.' I 25.7 26.3 269 275 18*8.1 1 II 3/8 32.4 33.0 336 155 62/6.4 2724.5 426.1 Si UJ 64.9 660 67. / 68.3 9369.4 70.6 7/7 72.? 7S: 7 7S.3 774 78.5 79.7 11.7 /4.I (47 '5.3 /8.2 2o.o 2/.9 1!? 2 7^ 32.8 85 I?I 32.5 33.9 35.2 36.5 ntl 778 20. "i. 20.8 21.4 78.2 40.0 4/.9 473 fi f 4^7.6 4/-9 43.2 273 284 ^9.5 30.6 31.3 32.9 ?4o in 84374 jfr 40.8 4>9 1^ 453 464 476 /3 367 37.3 379 ?9.rl27 39.' 7 29 5/.4 5^.0 49 4J.O 4/.6 422 42.8 43.4 440 446 45.3 4f.9 47.; ft 7 . a? 538 545 55. / IB If, TABLE II. FUNCTIONS OF A ONE-DEGREE CURVE , 9 5 36 37 T E c M T E C M T E C. M o 6252.8 2757. 3 8448.7 IS588 63634 2833.2 #575-9 18959 6476.2 29/73 85825 1933.1 / $> 52.7 4*8 59.4 653 *?4 6 17.0 964 78.1 /8.7 836 337 2. 56.5 509 60.0 67 / 3S.9 /8,-i 970 90.0 20.2 847 343 3 58.3 fS") 52.1 606 37.3 J9.3 976 21.6 34.9 4 60 1 567 53.2 61.2 709 387 20.4 98.2 93.9 23.0 S6.9 35.6 5 62.0 58.0 54.3 61.8 727 40. / Z1.S 989 8S7 2.4.4 880 362 6 63.8 554 74.6 4'. 5 22.6 99.5 97.6 2.58 89.1 36.8 7 65.6 60> S6.(, 63 j 765 429 2-37 /9oo/ 995 27.3 902 374 8 67.4 62./ 57.7 63.7 44.3 24/8 00.7 9/4 287 9/3 3B \ 9 69.3 63.4 58.8 64.3 842 45-J 25.9 0A3 93.3 30. / 9Z.4 397 /o 6277. / 2764.* 845-9.9 /S64.9 63 82.1 28470 9527.1 /9020 6495.2 293'. 6 8593.5 19393 // 729 66. / S/ / 6-5^5" 839 48.4 2g 2 02 G 97 / 33.0 946 39.9 /2. 74% 67.5 62 Z 66! / 858 49.8 29.3 03. Z 99.0 34.4 957 406 /3 76.6 689 63.3 66.7 97.7 s\ t. 30.4 65O09 358 96.9 4l'.2 14. 70.2 644 674 89.5 526 3/.5 04.4 028 373 990 4-1.8 /f 80.3 60 91.4 32.6 05. / 04.7 39.7 99.1 424 )6 8Z.\ 72.9 i&7 68"6 93.3 554 33.7 05.7 06.6 40.1 8600.2 43. / 17 83.9 743 67.8 692 95-.I S6'.8 34.9 06.3 08.5 4/-6 01.3 43.7 IB $fj8 639 69.8 97.0 5S.2 36.0 06.9 10.5 43.0 02.4, 443 19 87.6 77.0 7o.o 70.4 98.9 59.6 37 / 12.4 44.4 03.5 449 20 6299.4- 27784 847/.Z 197 IJ 6400.8 286 l.o 8?3g2 /90^.2. 6514.3 2945.9 8604.6 J945-6 21 9/3 79.7 72.3 717 02.6 624 39.3 o$ 8 16. Z 473 057 46.2 2.2 93. / 73.4 72.3 04.5 63'.8 40.4 O94- /8.I 4*7 06.S 23 24 74.5 729 064 65.2 4/ 5 /d.o 20.0 50.2 07.9 474 24 96 /y 7 73'5 08.3 66.6 ^?2 6 /O 7 516 09.0 48.1 25 98.6 85V 76> 74/ /O.I 68.0 43> //.3 23 <8 53.1 10., 2& 63005 86S 779 748 12.0 69.4 44-9 11$ 258 545 If. 2 49.3 27 02:3 879 79.0 75.4 13.9 70.8 46.0 12 5 27.7 55:9 /2.3 50.0 28 04/2 89.2 90.1 76.0 lf.8 47. / 29.6 574 13.4 50.(> 29 06.0 90.6 8 'A3 76.6 17.7 73.6 48.2 f3.S 3A5 58.8 51.2 30 63079 2792.0 84824 '8772 64/9.5 287570 8549.3 IS/44- 65334 2960.2 8615.6 I9SI.8 31 09.7 93.3 835 779 21.4 76.4 50.4 /f.O 35 3 61 7 16.7 525 32 /A5 947 785 233 77? 5/ 5 1 5 & 37- Z 63.1 I7.S 53.1. 33 96'.' 857 79. t Z5.2 79.2 tg IG.2 39.2. 64.6 S3.7 34 / 97.4 86.9 79.7 80.6 7 /6.9 4-1-1 66.0 20.0 54-3 35 17.1 98.8 803 28.9 82.0 4-3.0 675 Zt.l 55.0 36 18.9 2900.2 89 1 80.9 30 S 83.4 560 /g 1 44.9 68.9 22. 1 55.6 37 20.8 01.5 90.2 8/.5 3Z.7 848 57' f$ 7 468 7<7.4 23.2 56.2 38 22.1 029 9/.J 346 86.2 58.2 IQ A 488 71-8 24.3 568 39 245 04.3 92.5 82.8 36.5 87.6 S9.3 20.0 50.7 735 575 4? 63263 28> 2805.6 07.0 493.6 1883.4 840 64394 40 2 Z989.0 90.4 8S60.4- 61 5 /920.6 6552.6 54.5 2974.7 76. / 9626.5 276 S87 42 30.0 084- 958 846 42.1 91.9 62.6 2/ S 56.5 776 2#.7 59.4 4-3 31.9 09 S 969 853 44JO 93 Z 6^ 7 2Z.S 5$ 4 79.0 29.8 60.0 -44 33.7 //./ 9/ 859 459 94.6 64.8 60.3 80.5 309 60.6 45 356 12 5 99.2 86.5 47? 961 659 137 62.2 8A9 32.0 6/2 46 37* 13.9 87.1 49.7 97.5 67.0 243 64.2. 834 33.1 6}.9 47 39.3 /53 0/4 #77 98.9 68.1 250 66. ' 84 S 34.2 625 48 41. / '6.6 02.5 88.3 535 2900.3 69.?- 256 68.0 S63 35.3 3.1 49 4-3.0 /8.o 89.0 55/4 o/.7 70.3 26.Z 70.0 87f 36.4 63.7 5"0 S~l 6344.? 467 22/9.4 20.8 8504:8 1889.6 90.2 64572 59. / 290JJ 045 72.6 19268 27.5 657/9 73.8 Z989.Z 90.7 &375 38.6 1964.4 65.0 52 48.6 22.1 07.0 90.8 6/0 06.0 73.7 7S.7 39.7 65.6 5-4 |f 2-35 08.' 09.1 9/4- 629 64.8 0/4- 088 74.8 28.7 29.3 77.7 79.6 93.6 95.0 40.8 4-1.9 III 55 26? 927 /0.'2 77.0 29.9 0/.5 96.5 4B.O 67.5 56 ito 277 //.S 93.3 68.6 H.6 78.1 30.6 93.5 979 441 68.1 57 57# 29.0 /2.fe 93.9 70.5 13.0 79.2. 3A2. ,5~4' 99.4 452 8.8 55 304 137 945 7Z4 80.3 31.8 #7:3 3000.9 463 69.4 5? 6;. is 3/.8 I4S 95-. / AT.9 8J.4 32.4 89. 3 023 4-7.3 70.0 T.UiLE IT. FUNCTIONS OF A ONE-DEGREE CURVE A T E C M ggo. & 6591.2 30O38 86494 19707 IO 66/0.6 18.4 59.4 77.0 2.0 30.1 33.1 70.3 33.3 30 49.6 47.9 81.2 89.6 A/\ 69.2 6Z.8 920 95.9 SO 88.8 77.7 9702.9 2002.2 99- 67og.6 92.7 13.7 08.5 10 28.4 3107.7 24.5 14.9 ZO 48. 2 229 35.3 30 68.1 381 46 1 27.6 4O 88.1 S3 3 56.9 33.9 SO 6808.2 68.7 676 40.3 tocP- o 6828.3 3184.1 877F.3 20467 10 48.5 99.6 99.0 53.' / zo 68.8 3Z 15. / 99.7 &.S 30 40 89.2 6909.6 30.9 465 99104 Zl.o 65.9 72 3 . 50 30. \ 2.3 31.7 787 101- 50.6 78. / 42.3 10 71.3 941 9l'.6 ZO 9Z.O 33 to'.l 6J.4- 98.0 30 70IZ.7 Z6.I 74.0 21045 40 33.6 4*3 84.5 10. 9 50 54.5 95.0 17.4- 102* 7075.5 33 74.9 890S5 2123 9 10 96.6 91.2 ]6.O 30.3 20 7/178 34077 26.5 36.8 30 39.0 24,3 433 40 60.3 40.9 47.4 49.8 50 8/.7 57.6 57.8 56.3 /03- 7203.2 74.4 681 62.9 10 24.7 31.3 78.5 ZO 463 3S08.Z 88.9 7T9 30 68.0 25.2 99.* 825 40 89.8 424 9009.5 89.0 SO 73 1/. 7 59.6 19.8 9S.6 (04*- O 10 7333.6 55.6 3576.9 94 -z- 9030.1 40.3 2202.1 08.7 20 778 36 / / .7 so.s IS. 3 30 99.9 292 6O7 219 40 50 7422.2 44.6 46.8 64.5 70.3 811 Z8S 35.1 /oyQ- o 67.0 823 91.3 4-17 /o 89.6 3700.1 9/0/4 48.3 zo 7//2. 2 18.2 II.S 54.9 30 349 36.2 2/.6 61.5 40 57-7 54.4- 31.7 50 80.5 72.6 41.8 74.8 /06- to 7603.ST 26.6 3791.0 3809. 4 9/S/.8 61.8 2Z9I.S 88.1 zo 49.7 27.9 7/.8 94.8 30 72.9 46.5 91.9 230/4 40 96.3 9/8 O8 1 SO 7719.7 840 920/7 148 /O/-P O 43.2 39029 116 21.5 10 66.8 21.9 21.5 29.1 Zo 90.5 40.9 3/4 349 30 78/4.3 6O ( 4i.3 41.7 40 38.1 79.4 Sf.l 484 SO 6Z.I 98.7 6/0 SS.l A T E C M toe*- o 1 70861 40181 9270.8 236/.S /o 79/0.4 37.9 80.6 68.6 20 34.6 S7.4 90.3 7S.3 3o 59.0 772 9300 1 82.1 834 97.1 09.8 889 50 109- #708.0 32.7 4117.0 37.1 /9.5 29.2 95.8 2402.4 /o 574 573 389 09.2 Zo 82.3 775 48.5 /6.0 30 8(073 979 58.1 iZ.8 32.3 42/84 67.8 29.6 so S75 39.0 77.3 364 /A? 9 O 91828 4259.7 9387.0 2443.3 /O 8Z08.2 80.5 96.5 SO.I 33.7 43O/.4 9406.0 S6.9 30 59.3 22.4- 15.5 63.8 40 85.O 43.6 ZS.O 70.6 so 93/0.3 64% 34.5 77.S ///* 36.7 96.1 43.9 84.3 to 6Z7 4407-6 3*3 3 91.2 899 29.2 62.8 98. > 3O 84-15-1 50.9 72.; 25049 40 4-1.5 72.7 8/.5 11.9 68.0 94.6 90.9 18.8 ^/^ - o 94946 4576.6 35-00.2 2S25.7 10 8521.3 38 & 09.5 32.6 20 48.1 61'. 1 78.8 ?9.5 3O 40 7S.O 860Z.I 93.4 4606.0 28. 1 37.3 US 50 29.3 28.6 46.5 60.3 113- 56.6 S/.3 55.7 672 10 84.0 74.2 ,64.9 74-3. 20 87//.S 97.Z 74- / 91.2 30 39.2 4-720.3 S3.'3 88.1 6TO 43.6 24 95.1 SO 94.9 66.9 960/.S 602.1 II4&- o 8822.9 4790.4 96/0.6 2609-1 to SI.O 4914.1 19.6 16.1 2.0 79.3 378 287 23.1 30 8907.7 61.7 37.7 30.1 4O 363 95.7 46.7 37.1 so 64.9 4909.9 55.7 441 /A? 9 - /O 93.8 90ZZ.7 34-.I 64.7 73.6 \ zo 51.7 8s'. 1 82.5 65.2 3O 5007.9 722. 40 91/0.3 32.6 9700.3 79.3 SO 39.8 57.6 09.2 86.3 116**- 9169.4 5082.7 97/8.0 2693.4- 99.1 S/O7. 9 6.9 2700.5" 20 9229.O 33 3 3S7 07.5 30 59.0 S8.8 44.4 / A f^ 40 09.2- 94.5 S3. 2 2/7 Q so 93/9.5 61.9 )I7- 49.9 36.2 70.7 3579 10 805 62.3 79.4 43.O zo 9411.3 886 880 50. / 3O 42.2 53I5O 367 57.3 40 73.2 4-1.5 9805:3 64.4 so 9 f 04.4 68.2 13.9 7/5 52 TABLE III. CORRECTIONS' (TO BE ADDED) VALUE FDR A PCVME DCGRFF OF CURVE VALUE FOR A tcwvi 2 3 4 5 <0 7 8 9 10 11 /2 o 13 100 .00 .00 .00 .01 .01 .01 .01 .01 .01 Ol .01 .02 too ZOO -00 .01 .01 .01 .01 .02 .02 .01 0) 03 03 .03 200 3OO .01 .01 .01 .02 .02 .03 .03 .03 .04 .04 .05 05 300 400 .01 .01 .02 02 .03 .03 .04 .05 .05 .06 .06 07 400 500 .01 .02 .02 .03 .04 .04- .05 .06 .06 .07 .OB .08 500 600 .01 .02 .03 O4 .04- .05 .06 .07 .08 .08 .09 lo 600 700 .01 .02 .'04 05 .06 .07 .08 .09 JO Jl JZ 700 800 .02 .03 '04- .05 06 .07 .08 .09 10 Jl IZ .13 Boo 9OO .02 .03 .04 .05 .07 .08 .09 .10 Jl JZ J4 .15 900 /OOO .02, .03 .Of .06 .07 .09 JO Jl .14 .16 /OOO 1100 .02. .04 .05 .07 .08 JO Jl JZ .14. .15 .17 J8 I/OO /ZOO .02 .04 .06 .07 09 JO JZ .14- .15" .17 JS ZO /Zoo 13 OO .02 .04 .06 .08 JO Jl J3 .15 J6 J8 .20 .21 /300 lAOO .03 .05 .07 .09 JO JZ .14 .16 .19 .19 .Z/ .23 1400 1500 .03 .Of .07 .09 Jl J3 iS J7 J9 .Zl .23 .25 1500 /600 .03 .05 .08 JO JZ .14- 16 JS .20 .22 .24 .26 /6OO /700 .03 .06 .08 JO .13 15 '.17 .zl .23 .26 .Z9 1700 I90O .03 .06 .09 Jl .13 '.16 J8 .20 23 .25 .27 .30 /goo 1900 .04 .06 .09 JZ .14 .17 .19 .21 '24 .26 Z9 .31 /9oo 2000 .04 .07 .10 IZ .If J7 .20 .23 .25 .29 .30 .3-3 zooo 2/00 .04 .07 JO .13 16 .18 .-21 .24 .26 .2.9 .32 .35 ZIOO zzoo .04 .07 JO J3 '.16 19 .Zi .25 .23 .30 .33 .36 2200 2.300 .04- .08 Jl .14 .17 '.20 .23 .26 .29 .32 35 .32 3oo 2400 .05 .08 Jl JS J8 .21 24 .27 .30 .33 ".36 .39 24.00 2500 J0f .09 JZ .15 .19 .22 .25 .28 3\ .35 .39 .41 2500 2600 rfS O9 .IZ .16 J9 .23 .26 .29 '33 .36 .39 .43 2600 2700 .05 '.09 .13 .16 .20 .24 .27 .30 .34 .37 41 44 2.700 2800 .05 JO .13 .17 .21 .24 .28 .3Z .35 39 42 '46 2900 Z900 .06 .10 .14 .18 .21 .25 .29 .33 .36 .40 44 '.49 Z9oo 30OO .06 JO .14 J8 .22 .26 .30 .34- .38 .42 '.45 .49 3000 -3 too .06 II J5 .19 .23 .27 .31 .35 '.39 43 47 .51 3/00 3200 .06 II 15 24 .28 .32 .36 .40 .44 .48 53 3200 3300 .06 .11 .16 '.20 .24 .2.9 .33 .37 .42 .46 50 .54 3300 3400 .06 JZ .16 .21 .25 3o .34 .38 .43 .47 52 .56 3400 350O .07 ' IZ .17 .Zl .26 30 35 .40 44 .49 53 .58 3500 3600 .07 JZ 17 .22 27 yt .36 .41 .'45 .50 .55 59 3600 3700 .07 .13 .23 '27 ~32 37 42 47 56 .61 3700 3800 3900 .07 .07 './3 : !f '.24 .28 .29 '% '.38 .39 43 '.44 >8 49 '1 .58 .62 64 3800 390O 4000 .08 .14 ' .24 .30 .35 4o .45 .50 .55 '.61 .66 44 OO 4100 .08 14 20 .25 30 36 41 46 .52 57 .62 67 4/OO 42 OO .08 '.14 .20 .26 '31 .42 '47 .53 '.58 64 -69 4200 4300 .08 .1? .20 .26 .3Z '37 43 .49 54 60 65 .71 43OO -4400 .08 .15 .27 .33 '.39 44 50 .55 .61 67 .72 44-OO 4-50-0 09 .15 2>| .27 .33 .39 '45 51 .62 68 74 4500 4600 .16 .22 .28 .34 .40 '46 .52 '55? 6-4 7O 76 4600 4700 .09 .16 .22 .29 .35 .4-1 '47 .5) '.59 65 7t 77 4700 4800 .09 .16 23. .29 36 .42. '4? .54- 60 67 '73 '.79 4800 4900 .09 17 .23 .30 .36 .43 49 .55 .62 .68 '74 .81 4300 SOOO .10 .17 .30 .37 '.so .56 .63 .69 '76 .82 5OOO 5/00 .10 .17 .24 31 .38 .44 5.; .5? 64 7t 77 .84 5700 52OO .10 .25 .32 .52 59 .65 '72 79 .85 520O 5300 JO IS 25" .32 '.39 '.46 53 .60 .67 .73 So .97 5300 5400 JO 18 .26 .33 .40 .47 54 61 .68 7_5~ '82 .89 5400 5500 .10 .19 .26 .34 4f .4 .55 '.62 .69 '.76 .83 .90 5500 5600 Jl .19 .27 .34 '4| .49 .56 63 70 .78 B5 .92 5600 5700 J9 .27 35 .42 .57 .64 7Z 96 .94 5700 1 1 .20 .28 .35 43 51 .SB 65- 73 'Jo .88 .95 58OO 5900 'if .20 28 .36 .44 '.51 59 '67 74 9Z .97 5900 6000 11 .20 .29 37 .44 ,52 .60 ',6? .76 9? .91 .99 6000 TABLE III. CORRECTIONS (TO BE ADDED) VALUE DEGRE e o " Cul 7VE VALUF FOR A lCWJVE 3 4 5 6* 7 # 9 }4 '54 64 73 .8i 92 l.ll i zo 73OO 7400 14 .25 .35 .45 55 .64 '.74 .84 .93 1 03 A/2 A 22 7400 7500 '.14 .26 .36 .46 .56 .65 75 95 .94 f.o4- / 14 A 23 7500 76OO I A- .26 .36 46 .66 .76 '.86 .96 A 05 A/5 / ^5* 7600 7700 '.15 .26 .37 >7 >7 67 77 .87 97 A 07 1-17 A 26 77OO 7800 15 .27 .37 .58 .68 .78 .88 '.98 1.08 7800 7SOO .'5 .27 .38 '.48 .58 .69 .79 .99 .99 1.09 A 20 1.30 7900 8000 .15 .27 .38 .4-9 .59 .70 .go .90 /.// /.2I 132 8000 8ZOO .16 .28 .39 .50 61 7f .82 .93 103 /.I4- IZ4 /.35 5200 8400 .16 .29 .40 51 .62 '.73 .95 /.06 / J (> i 27 1.39 840O 8600 .16 29 4; .52 .64 86 .97 /.og I./ 9 A 30 1.41 8600 8800 .17 .'30 '.4Z .54 .65 '.77 88 .99 I.H A 22 1.45 9800 9000 .17 .3/ .4-3 .55 .67 .78 '.90 /.oz 1.13 A25 1.36 1.48 9000 9ZOO .IS .31 .44 .56 .6* .80 .92 I.o4 1.16 I.2S /.39 1.51 9200 9400 19 32 .45 .57 70 .82 .94 JO& 1.30 A 42 /.55 9400 9<00 '.IS !33 .46 .58 .71 .84 .96 i.08 1 2 1 /33 /.45 A 58 9600 9800 .19 .33 .47 .60 .73 .95 .98 l.u A23 A 36 A4 A6/ 9800 14 IS \<0 Itf to 22 24 26 28 30" 35"' 40' /OO O2 oz .oz .oz .03 .03 .03 .03 .04 04 04. .OS 100 200 .04 .04 .04 05 .05 .06 .06 o7 .07 .08 >9 .10 ZOO 30O .05 .Ofe .06 >7 .08 .08 .09 I/O .11 ,/2 .13 .IS 200 400 .07 og oS JO tZ 13 .14 ./5 . /n* 2.1 400 500 .09 09 .10 '/ / .13 '.14- .If '.17 .18 19 .zz .26 soo 600 / / 'II .'/* .ts .n .IB 2.O .21 ,23 .27 .31 600 700 'iz .13 '.14 /6 .'8 .20 .21 .23 .25 27 .31 34> 700 ?00 '14 .15 .16 */o .20 .22 Z4 .27 .29 .31 .36 '41 800 900 .ik .18 !2I .23 25 .28 .35 .40 .46 9oo IOOO .IS 19 .20 .23 .25 .28 .31 .33 36 .38 AS $1 /ooo IIOO .19 *2i 22 .25 .34 .36 '39 '49 '.57 //oo IZOO .21 "2,3 '2.4. .-27 ~30 '34 .37 .4-0 '.43 A4> ..'54 .62 /zoo 13 OO ;4oo .23 .25 .'25 27 >8 !?2 1 ill 4O '.43 43 47 46 '.50 SO 54 .58 .63 .67 72 1300 1400 /500 27 .2? .30 .34 .4-Z. .46 So .54 .58 .67 .77 ISOO 1600 3O 32 *4/ 45 .49 53 .57 .61 .72 .82 /6OO 1700 .3o .32 34 .'39 .43 AS .52 '.56 61 65 .76 .97 I7OO ISOO 32. .34 '.37 46 .50 55 .60 .64 .69 fl .93 1900 1900 .34 36 !43 .4-8 .58 .63 .68 .73 s .98 1900 2000 .35 3? 4/ .46 .5; .56 .6; .6C 7 I .77 .9o /.O) 2.OOO ZJOO .37 .'40 43 AS .53 .59 .64 .70 '.75 .81 .94 l.oS 2100 azoo .39 4Z .'45 .56 .62 .67 .73 .79 .99 1.13 22.00 2300 41 .44 47 '.53 .58 .64 .70 76 .82 *$8 1.0) 1.19 2300 2400 .41 46 .49 .6/ .67 80 .96 *02 IZ4 2500 .47 .51 !57 .64 70 '.76 .S3 .89 '.96 i.iz. 1.29 2-5OO 2600 .'46 49 .53 .59 .66 73 .So 93 /oo 1.17 1.34 2600 2700 .48 '51 .55 62 .69 '.76 .83 '.90 .97 io4 i.z\ / 39 2700 2800 .50 .53 .57 .64 71 .78 .8G 93 /.OO /or 1.26 1.44- 2900 .51 .55 .59 .66 '.74 .gl .89 .96 1.04 i.n A 30 1.49 2.900 .vi TABLE III. CORRECTIONS (TO BE ADDED) VALUE" FOR A lcuve DEGREE Of CURVF V/J-or FOR A ICURVE 14 \5 16 18 20 22 24 26 28 C 30 55 40 300O .53 .57 .61 69 .76 .64 92. .99 1.07 1.15 1.35 '.54 3000 3/oo .55 .59 .63 '.71 .79 .87 .95 103 l.ll 1.19 /.39 I 60 31 OO 3200 .57 61 65 73 .81 .90 .98 1.06 1.14 '23 A44 1.65 3200 3300 .58 .63 67 '75 84 .92 1.01 /09 1.18 '27 1-48 I.7O 3300 3400 60 .65 69 '78 .86 .95 104 1.13 l.il 1.30 1 53 1.75 3400 BSoo 62 .66 71 '.90 .89 .98 1-07 !.!(, I.Zf 1.34 1.57 !.8o 35OO 36 oo 64 .68 .73 .82 .91 l.ol I.IO 1.19 1.29 1.38 1.62 1-85' 3600 3700 6f 7O .7S 85 .94 1.04 1.13 1.23 /.3i: 1.42. 1.66 1-90 370O 3800 '.67 72 .77 .87 .97 I.Of, A/6 1.^6 '.36 146 1-71 /.% 3goo 3900 .69 '.74 .79 .99 .99 1.09 A/9 /29 /.39 1.50 I.7S 2.01 3900 4000 .71 .76 .81 91 1.02. m /2^ 133 /43 \53 ISO 2.0k 4OOO 4-JOO .7} .78 .93 '94 1.04 1. IS /.ZS /.3h /47 157 /.B4 2.11 4/oo 4-2.00 .74 .80 .95 '.96 1.07 I.I'd 1.28. 1.39 /.5o 1.61 W9 2.16 4200 4-300 .76 .82 .87 .98 1.09 1.20 1.31 14) /.54 AG5 1.93 2.2\ 4-300 4-400 .78 84 89 1.01 /./2 I.Z3 1.15 A46 I.f7 A69 1.98 2.26 4400 4-500 .Bo .85 .9' 1.03 1.14 1.26 1.3$ /.49 1.61 /.73 202 2 32 4500 4$00 .81 .87 .93 UDS 1.17 129 141 153 '.64 /-76 2.06 2.37 46oo 4700 .83 .89 95 1.07 1.19 1.32 1.44 1.56 1.68 1.90 2.11 2.42 4700 4300 .95 91 .97 I.IO 1.22 '.34 1.47 1.59 1.72 1.84 2.)5 247 4gOO A$OO .37 .93 99 \.\Z I.ZS 1.37 1.50 t.62 1.7* 1.88 2.20 2.52- 4900 5000 .9B 95 1.0 1 M4 1.17 140 1.53 '.66 179 I.9Z 2.24 257 5OOO 5/00 .90 .97 1.03 1-17 1.30 143 1.56 1.69 1.92 1.96 2.29 262 5100 5200 92 .99 1.05 1.19 1.32 1.46 1.59 1.72 '.86 1.99 2.33 268 52 OO S300 '94 1.0 1 1.07 1.21 I.3S I.4-9, I.6Z 1.76 1.89 203 2.38 273 5300 5400 .'96 1.03 I.IO 1.23 137 /.SI 165 '.79 '93 207 2.42 2.78 5400 5500 .97 1.04 l.ll IZ6 1.40 154 1.69 ISZ 1-97 2JI 2.47 283 5500 5600 .99 1.06 1.14 *.z% 141 1.57 171 /.86 2.00 2.15 2.5-1 288 5600 5700 l.oi t.o8 1.16 |.3o 145 1.60 1.74 1.89 2.04 2.19 2.56 23? 5700 5900 103 I./O U8 1.33 147 1.62 /77 1.9*- 2.07 2.ZZ 2.60 2.99 5800 5900 104 f.12 I.IO 35 1.50 I.6S A8P 1.96 2.// 2.Z6 2.65 3.04 5900 6OOO 1.06 f/4 I.Zt 1.37 \5i 1.68 1.93 199 214 2.30 2.69 309 60OO 6/00 1.09 IJ6 1-2.4- 139 I.SS 1.71 1.87 2.02 2J8 2.34 2.74 3.14 6/OO 6200 I.IO 1.19 '.26 /.42 1.58 1.74 1-90 2.06 2.22 2.3g 2.7F 7/9 62-00 6300 l.ll I.ZO 1.18 144 1.60 1.76 /.93 209 2.25 2.42 2.83 3.24 6300 6400 1.13 I.ZZ 1.30 146 1.63 1.79 1.96 2.12 229 2.4J 2.87 3.29 64oo 6500 1.15 /.Z3 1.32 1.48 1.65 1.82 1.99 2./6 232 2.49 2.92 ?.35" 65-00 6600 U7 /.25 134 1.51 1.68 1.85- 202 2./9 2.36 2.53 2.96 3.40 6600 6/00 U9 1 2-7 /.3G I.S3 1.70 /.88 2.05 2 22 2.39 2.57 3.0 / 3.45 6700 6800 /.2.0 /.29 1. 38 155 1.73 i.9o 2.08 2>r 2.43 2.61 3. Of J.50 6800 6900 LIZ /.3I 1.40 1.58 1.75 193 2-11 2.29 2.47 2.65 3 JO 3.55 6900 700O 1.24 )3* 1.42 1.60 178 1.96 2.14 2.32 2.50 a.68 ?.I4 3.60 7OOO 7IOO I.Z6 /.35 1.44 1.62 A 80 1.99 2.17 2.35 2.54 2.7? 3.19 3.65 7100 72OO A 27 /.37 146 1.64 1.83 202 2.20 2.39 2.57 2.76 3.23 3.7/ 72-00 7300 1.29 1.39 1.49 1.6-7 /.8(, 204 2.23 2.42 2.6/ 2. SO 3.28 3.76 7300 7400 '.31 /4l 1.50 1.69 1.8V 2.07 2.2C 2.45 2.6* 2.84 3.32 3.81 74OO 7fOO A33 /42 1.5 1 1-71 1.91 2/0 2.29 2.49 2.68 238 337 3.86 7fOO 7600 A 34 A44 1.54 1.74 1.93 2.13 2.32 252 272 2.91 3.41 3.91 7600 77OO /36 /.*6 1.56 1.76 1.96 "216 2..3S 255 275 Z.9J 3.46 3.96 7700 7900 /.38 1.48 1.58 178 '.98 2.18 2.39 2.59 2.79 2.99 3.50 4.01 7800 7900 1.40 1.50 160 1.80 2.01 2.21 242 2.62 2.82 3.03 3.55 4,07 7900 8000 142 152 I.6Z 1.83 2.03 Z.24 245- 2.65 Z$6 3.97 3.59 4.IZ 8000 8200 1.45 1.56 1.66 1.97 2.08 2.30 2.SI 272 2.93 3.14 3.68 4.22 82OO 84oo 1-49 1.60 1.70 1.92 2.13 2.35 2.57 2.79 3.oo $21. 3.77 4.32 34.OO 8600 1.52 f.63 1.74 1.96 2.19 2.41 2.63 2.85- 3.07 3.30 3.86 4.43 9600 8800 1.56 1.67 1.79 2.01 2.24 2.44 2.69 2.92 3. IS 3.37 3.95 4.53 88OO 9ooo 1.59 171 AgJ 2.06 2.21 2.52 275 2.9g 3.22 ?45 4-04 4.63 9ooo 9200 '.63 I.7S '.87 2.10 2.3A 2.5g 2.81 3.05 3.29 3.53 4.13 4.74 9200 9400 /.66 1-78 1.91 2.15 2.39 2.63 2..S7 3.12 3.36 3.60 4.Z1 4.84 9400 9600 170 1.82 I9S 2.19 2.44 2.69 2.94 3.18 3.43 3.68 4-31 494 9600 9800 1.73 '.96 1.99 2.24 2.43 2.74 3.00 3.25 3.50 3.76 4.40 5.O4 9oo TABLE IV. CURVES DESIGNATED BY RADIUS r,r> RADIUS MULTIPLY IC. FUNCTIONS 8Y DEGREE OF- CURVE 5 .000975 10 .00/74-5" 15 .0026/8 20 .003491 25 .004-363 30 .005-236 35 .006/09 40 .00698 1 45 .007854- 50 .008727 55 .009539 60 .0/O472 65 .01 1344 70 .01 22.17 75 .O/3O90 80 .0/3962 85 .0/4835 90 .015708 95 .016580 /oo .O/ 74 y 3 /05 .019326 ItO .0/9/58 115 ,O20O7/ 120 O0944 125 Q2. \ 3/> 130 .022689 135 140 '.024434 145 .025307 ISO .026/80 155 .02 7O52 37^38.3' 160 .027^25 36-25.2 165 .02 875? 7 35- /6.8 170 .02967O 34- 12 6 175 .0305-4-3 33- l?.i 180 .031415 32- /53 185 .032288 31-21.6 30 30.9 '. 03 4-03 3 29-429 ZOO .034-306 28-573 205 2/0 .035779 .03665/ 28-/4.0 27-32.9 2/5 .03757.4 26-53.7 220 .038397 26- 16.4 25- .039269 25- -40.8 Z3O .04OI42 25 -06.7 235 .04/O/5 Z4-34./ 2AO 04/887 24 - O3.O 245 .042760 23-33J 250 .04 363 3 23-04.4 255 044505 22 -369 260 ! 04 53 78 22 - /0.'5 265 046250 2/ -45M 270 .047/23 21 - 20.6 27T .047996 20-57.1 z $o 0A886 8 20-344 285 04974 / 2O- 12.5 290 '.05-06 14 19-51.4 295 05/486 '9-3/0 3OO .052355 >9 - 11.3 RADIUS MULTIPLY IC. FUNCTIONS BY DEGREE OF CURVE 305 .053232 18^ 52.2 3/0 .054/04- 18-33.9 315 054977 18-16.0 320 !o55850 I7-S8 7 325 .056722 /7-4-2.0 330 .0575-95 17-2.5.8 335 .0584-68 17- IO.O 340 .0*9340 16-549 345 .0602/3 16 - 40.0 35-0 .06/086 355" .06/958 16' 116 360 .06283/ 15-58.0 365 370 .063703 .064576 15- 32.0 375 .065449 IS- /95 390 .06632J 1 5- 07.3 J&5- 390 .067/94 .068067 14-55.4 395- .068939 J4'3ZJ 400 .0698/2 14-21.7 405 O7OG8S W-II.O A-IO '.071*5 '7 14 - 00.6 4-15 .072430 / 3 -50.4 420 425 .073303 .074-I7S /3-40.5 4-30 .0750 4-8 /3~2/ 3 435 .075921 /3-I2.0 440 .076793 /3 *O3 O 445 .077666 /2 -54.1- 4-50 .0785-39 455- .0794-1 1 /Z- 37.1 46O .080284 X2-28.8 465 .08I/S6 I2.-20.7 4-70 .082029 12-12.8 475 .082902 /2 -05. / //-575 485 '.08464-7 !/-5o.\ 4-90 495 .085520 .086392 50 O s .087265 H-W.7 SOS .088138 // - 2 1 9 5/0 .0890/O // - 5.2 5/5 .0$883 // - 08.6 520 .090 7,56 // ~ 02.1 525 09/628 530 .09250/ A3 -496 535 .093374 xo-43.5 545 .094-246 095//9 /0 - 375 /0-3/.7 550 '. 0959 9 2 555- .096864- /O -2O3 560 - 565 .097737 098609 10-147 IO-09.2. 57O 573- .099482 .1003 55 /0-03? 9-58.6 580 ./0/227 9-535 585 ./02,/cO 9-48.4 590 ./02973 9-434 595 9 - 385 6OO '.104718 9-33.6 TABLE V. RADII , DEGREE OF CURVE 1 2 5 4 5 G 7 r3 9 Infinite S729.65 2864.93 /9/G08 143269 1/46.28 95537 819.02 71678 63727 3437747 5635.72 2841.26 /899.S3 1426.74" /1 4-2 .47 952.72 81708 7/5.23 636.10 2 7/887.3 5544.83 2817.97 / 8 89. 09 /420.85 f / 3^ 69 8/5.14 7/381 634.93 3 / I4S9I.6 5456 82 2795.06 187877 /1 34.94 94748 8/3.22 712 33 633.76 4 85943.7 5371.56 2772.53 /409.2I M3A2/ 94488 3//.30 7/087 632.60 5 68754.9 5288-92 2-750. )5 185847 140)46 1127.50 94-229 709.40 6)1.44 6 572958 5^08.79 272852 '848.48 '397.76 /I 3.82 939.72 80750 707.94 630.29 7 49//07 5131.05 2707o4 /83S.59 1392.10 H20./6 937/6 805.61 70649 629.14 8 4297/.S 505X59 2685.89 7 20222.1 446470 2509.47 1 745.29 '33796 108495 9/233 787 20 692.30 617.87 19098.6 4407.46 2491.29 J332.77 108144 909.92 78540 69091 61676 '9 18093.4 4351.67 2473.37 1727.75 1)27.63 107805 907.52 783% 689. 5 3 615.66 20 17/58.8 429728 245570 17/9.12 X32253 1074.69 905)3 78/84 688.16 6/456 21 / 63 70.2 4244.23 2438.29 f 7IO.57 1)17.46 I07lf.34 902.76 780.07 686.78 613.47 22 /5626 / 4192.47 2421.12 1702 10 /JI243 IO68.0I 900.40 779. )l 68542 6/2.J8 23 /4946.S 414196 2404.19 169172 1)07.45 I06A7I 898.05 776.55 GftA OL 611.30 24 '4324.0 4092.66 238750 /6S5.42. /302.50 I06i43 895. 7 7 77481 682.70 6/021 25 / 37570 4044.51 Z37/.04 K.77.2Q '058.IC 893.39 773.07 81.) 5 609.14 26 /3222./ 2354.80 I6C906 1232.71 IO5492 891.08 77/.34 &80.0I 608.06 27 /27324 3951.54 Z3 38.78 f 66 1.00 'Z87.87 I05/.70 76961 678.67 (,06.99 28 /2 2 7 7/7 390664 2322.98 /653.0I I2Z3.07 /04849 886.49 767.^0 677.34 605.93 29 118543 3862.74 2-307.39 /645.H '278.30 884. Zl 766.19 676.01 60486 J 11459.2 38198) 229201 X637.28 /273.S7 /O42 14 881.95 76449 67469 603.80 31 1 loS95 377785 Z 2 76.84 1629.52 / 268.87 1039.00 879.69 762.80 673.37 602.75 32 I0743.O 3736.79 261-86 X62/.84 /264.2I 103587 877.45 67206 601.70 33 10417.5 369661 224708 1614.21 '259.58 103276 875" 2.2. 75943 670.7S (,00.65 34 IOIII.I 365729 "2,232. 4Q 1606.68 X254.98 1029.67 873.00 757.76 669.45 599.61 35 9822.18 36/8.80 221809 /S99.2I '25042 1026.60 870.79 7 56. to 668. /5 598.57 36 9549.34 3581.10 2203.87 '$91-81 /2 45.89 1023 55 86860 754.44 666.86 597.53 37 929/.2S 3*44 19 2-189.84 f 584 48 / 24 1.40 1020.51 86641 75-2.80 6557 596.50 38 9046.75" 3S00.02 2175:98 1577.2] 10/7.49 864.24 757. 16 664.29 59547 39 88/4.78 3472.59 2162.30 /57O.OI /2325I 1014-50 862.07 74952 663.01 594.44 40 41 8594.42 8394.80 343787 3403.83 214-8.79 13544 156288 ' 5~5 5. 81 /228.II /Z23.74 loii.fi I008.5S 859.92 857J8 74627 661.74 66047 F93.42 592.40 42 8'85. 16 3370.46 2/22'.26 /54S.80 1219.40 /005.60 744.66 659.21 591. 38 43 7994.81 3)37.74 2/09.24 /54'- 86 12.15.09 IO0267 85353 743.06 657.95 44 78/3.11 3305.65 2.096.39 /5J4.9* I2.1O.92 999.76 851.' 41 74/46 656.69 589.36 45 7639.43 3274.17 I20f>57 996.87 84932 739.86 65545 58836 46 747/42 3243.29 207A/3 /52j 4.9 I20i 36 99*99 84723 738.28 654.20 597:36 47 73/4.4; 3212.98 /5I470 1198.17 991.13 845.15 73670 652.96 586.36" 48 7/62.03 3 '3.23 2046.48 I$O80(> //940I 988Z% 843.08 735.13 65'. 73 585.36 49 70/5.87 3/54.03 2034.37 ISOIA8 1/89.88 985.45 841.02 733.56 650.50 5^4.37 5o 6875.55 3/25.36 2.022.41 1 494.9 S 1185.78 98264 838.97 73201 649.27 58338 5-1 6740.74 309720 2O JO 5 1 ? JI8/.7/ 979.84 83693 730.45 64805 582.40 52 6611.12 3063.55 '998.90 1177.66 977.06 834.90 728.9 / 646.84 581.42 53 64-86.38 3042 39 198735 I475.7/ 1 173.65 974.29 727.37 64563 580 4 i 54 6366.26 3015.71 '97S.93 (44941 1169.66 97/.S4 830.88 725.84 644.42 579.47 55 6250.5* 298948 '96464 /463J6 1165.70 969.81 823.88 724.31 643.22 57843 56 6138.90 2963.72 / 953 48 /456.96 1161.76 966.09 826.89 722.79 642.02 577.5} 57 603/.20 2938.39 / 942.44 (450. 8 / IIS785 963.39 34.9/ 721.28 640.83 ?76 56 $& 592 7 2 29/3.49 /93/.S3 (44472 1153.97 96070 7/9.77 639.64 57Ji6o 59 5826.76 289901 /920 75 143868 1150.11 958.02 82Q97 7/8-27 63845 57^.64 TABLE V. RADII 57 DEGREE OF CURVE: / 10 n 12 )3 14- IS 16 1 7 /S 19 57^.69 52/.67 479.34 441.68 410.28 333.06 759.26 338.27 5/9.62 J02.94 Z. 577.75 520./0 47702 440.56 382 22. 358.52 337.62. 3/9.04 302.42 4 569.90 5/8.54 4-757' 439.44 409 34 38l'.38 357 7 336.96 3/8.45 301.89 6 568.02 5/6.99 47440 43833 40738 380.54 35" "7 OS' 336.31 31787 30/37 8 5/5.44 473. 10 43722 40642 379.71 35632 335166 317.29 300.85 /O 564 3 1 5/3.91 436 12 40547 378.95' 3S5.59 335:c?/ 316.71 300.3.7 12. 562 >7 5/2 38 470.53 43502 404.53 379.05 354.86 33437 3/6.74 299. 82 /4 5/0.87 469.25 433.93 A03.5? 37/23 3S4.I3 3^3.73 3/557 299.30 16 55*9*82 509.36 46799 432.84 402.65 376.41 3/5.00 2.98. 79 J8 557 02 50786 466.72 43/.76 401.71 375T60 3*2.70 332.45" 3/443 29 28 20 555!23 506.30 465.46 430.69 44078 37479 351.98 33/.F2 313 86 29777 22 553.45 504.90 464.2 1 429.62 399 86 373.98 351.27 33 IJ 8 31? 29 197.26 24 551.68 462.97 -4Z0.56 398! 94 373.17 350.56 33055 312. 7* 296.75 26 549.92 50/96 427.50 398.02 372.37 349.85 32^.93 312.17 296.25 28 548. ' 7 50O.5/ 46Q5O 426.44 397.77 371.57 349/5 329.30 31 1.61 295 75 30 32 546.44 499.06 49762 459.28 458.06 425.4HO 424.35 J96.20 395:30 370.78 369.99 34845 34775- 111 310.50 295.25 29475 54- 54 3.00 496. / 9 423.32 394.40 369.20 30995 29425 36 541.30 494.77 455.65 422.28 33 3. SO 346.37 326 83 30940 293.^5 3? 539.6/ 49.3.36 454.45 39Z.6/ 367.64 34-5.68 326. Zl JOS! 95 29?. 26 40 *3792 49/.96 453-26 42023 39/72 36696 34^.99 325.60 3Off3o 292.77 42- 536.25 49056 419.22 390.84 366.09 344.31 32500 3O7.76 2-92.28 44- 534.59 489.17 45o 89 418.20 389.96 343.6Z 32439 307.22 48 532.94 S3 /. 30 48779 486.42 449.72 44-R56 417/9 416.13 388. Zl -364.55 363.78 342.95- 34-227 323.79 32 3. /9 306.68 30614 297/30 290. #2 50 52 J4 56 529.67 528.0? 526.44 524.04 425.05 483.69 482.34 447.40 446.24 445.09 44J.95 4/5.79 414.26 4/3 21 41223 387.34 386.48 385.6-2. 384.77 363.02 .762.26 360.76 341.60 340.93 340.26 33960 32259 32 /. 99 321.39 320.80 305.60 30506 304.53 30 A. 00 290.33 289.85 289. 37 5{? 523.25 479.67 44 2.. 81 4I/.25 383.91 J6O.O' 320.21 3O147 228 41 DEGREE MINUTE'S DEGKfE CURVE 0' i3I 58 131.12. 44 45 '30.66 130.20 129.75 12930 '885 1 2g.4l 45 46 X2797 127.53 127.09 726.66 '2624 46 47 t2S. 39 /24.97 /24.56 '24. '5 123.74 /23 33 47 41 '22.93 '20.57 122.53 120.19 122.13 I2/.74* 119.43 /2I.35 "9.05 /20.96 7/g-6g 48 49 58 TA15LE VI. NATURAL SINES AND COSINES SINB5 DEGRFE5 MINUTES 0' 10' 20' ^ 4-0' 50' 60' O / 2 3 4 .0000000 0/74-524 034.8995" 0523360 06975S5 0029089 0203608 0378065 0552406 07^6580 .OO58 1 77 .O232690 040//3I 058/448 .07555B9 OO87265 0261769 0436/94 06/0485 075-4591 O/I6353 O290847 0465253 06395/7 05/3587 14 543 9 0319922 O49A-308 0668544 0542576" 0/74-524 0348995 0523360 069756F OB7I5S7 89 88 87 86 85 5 6 7 8 9 087/53"7 /04528S 12/8693 J39/73/ 0900532 1 074-110 1 24-75-6 o /42053/ 1593069 .05294-99 .1103(26 .12.764-16 .144-9319 J62/779 0955458 //3203E .1305262 1478094 .1650476 0987408 //60929 /334096 1506 57 1679/5-9 IOJ635I //898I6 /3629/9 /535607 1707829 /04S285 /2<8693 1391 731 /56"4-345 /7J6482 84 83 2 a/ 80 10 II 12. 13 14 .17364-82 .1308090 2079/17 .2JL495// 24/9219 I765-/2/ /936636 2/07561 .2177844 244-7433 .1793746 .1965/66 .2135988 .2306/59 .2475627 (822355 1993679 .2164-396 .23344-54 .2503800 /850949 E022I76 ZJ92786 2362729 2531952 1879528 2050655 222M58 2 3 90984 256008Z /908090 2079/17 22495/1 24192/9 2588190 79 70 77 76 7f 15 /6 :i /9 2 5*88 190 2756374- 29237/7 3090/70 3255682 Z6I6277 27^43 a4- Z95I5E2 3II70Z .3283172 .Z644-34-2 .Z8I225I .2979303 .3J4-544-8 .33/0634 2672384 2840153 .3007058 .3173047 .3338069 27004-03 668032 3034788 32006/9 .3365475 2728400 2895887 3062492 3228/64- 3392852 2756374 Z9237/7 309O/7O 3255682 3420201 74- 73 72 71 70 20 XI zz 23 24 .342020 / 3583679 '.3746066 .39073 // .4067366 544752J 36I082/ 3773021 3934071 4093923 .34-74812 .3637932 .3799944 .3960798 4-120445 3502074 3665012 3826834 .3987491 .4I4.693E 3529306 3692061 3853693 .<*OJ4-I50 4-173385 3556508 37/9079 388O5/8 4O4O775 41 99 80 / 3583679 3746066 39073// 4067366 4226183 fl 67 66 65 a? ae 2.7 28 29 4-226 133 '.43B37// ^539905~ 4694-7/6 4848096 4252528 .44^9538 456J804 A720380 '.4S735-/7 4279838 44-35927 459/665 .4746004 .4898897 4305/ / / '44-61978 4417486 .477/588 .4924236 433 /J48 4487992 4643269 479 7/3/ 4949532 4357548 4513967 46690/Z 4g22634 4974787 43837// 4539905 .46947/6 .4848096 5OOOOOO 64 63 62 61 60 30 3/ 3Z 33 34 .ffoooooo .5/5038/ .5299/93 .5446390 .55-9/929 .502SI7O .5/75293 .5323839 .5470763 .56/602 / .5050298 52OO/&I 5348440 .5495090 .5640066 5075384 'S2249S6 5372996 55/937O 5664062 5/00426 5249766 53975-07 5543603 .5688011 5/25425 52745O2 54ai97/ .5567790 S7//9/2 5(50381 5299193 .5446390 559/929 .57J5764 59 ?7 56 5-5 35 36 37 98 39 .57J5764- .5P7755-3 6O/8/5"C> .'6/566/5" .62932O4 .5759568 590/36/ .604/356 .(>l79sr/i .61/5784 .57^3323 ,59248/9 .606 4-5 // .6202355 .63383/0 5*907^30 5948228 .60876/4- 6225/46 .6360782 .5S30687 597/586 .6//O666 .6247885 .638320 / 5954294 '.5994893 6133666 '.62.70571 .6405566 .5877553 .60/8/50 .6/566/5 .6293204 .6427876 54 53 52 5/ >5O 4-0 41 42 A3 44 6427876 !6560590 669/Jo6 .(,819980- .694-6584 .64501 3 Z .65825/6 .67/2895 .6841229 .6967479 .6472334 .6604386 .67J44Z7 .6624-/6 .69833/5 6494480 .66^6200 .6755^02 6883546 7OO9O93 .65/6572 .6647959 .6777320 .69046/7 702981 1 6538609 666966/ .67^8681 .6925630 .705"C>469 656O5-9O .669/306 .68/9984 .6946584 -707/068 49 48 4-7 8 60' 5(9' 40' 50' 20' 10' O' DEGREES MINUTES COSINE5 TABLE VI. NATURAL SINES AND COSINES S/ME5 MINUTES DEGREES 0" 10' 20' 3 92^896 5 99/06/0 9932384 99/4449 99357/9 99/8204 9938969 .992/874 9942'36 .9 92 546Z .99452/9 7 6 94 .99452/9 .9948I7 995//32 9953962 .9956708 .9959370 .996/947 S 85 996/947 9964440 9966849 9969 f 75 997/4-13 .9973569 .9975641 4 86 '99T564/ 9977627 9979530 999/348 $983082 .9 9 8473 / .9986295 3 87 9986295 998777J- 9989/77 9990482 .9991709 .99925-/ .9993908 2 88 9993908 9 99488 / 9995770 9996573 9997292 .9997927 9998477 I 89 9998477 ;9995942 9999323 99996/9 .999983 / .9999958 /.oooooo O GO' 50' 40' ?0' 20' /0' 0' DEGREES MINUTES COSINE'S r,o TABLE VII. NATURAL TANGENTS AND COTANGENTS TANGE-NTS MINUTES DEGffEPS O' 10' 20' 30' 40' 50' 60' .0000000 .O029O89 .0058178 0O 872 6 9 .OM636I .0 14-5454 .0/7455/ 89 .0/7455/ .020365O .0232753 .0261 855> O29097O .0320086 O 349208 88 2 .03492O8 0378335 .0407469 .0436609 0465757 .04949/3 052407? 87 3 .0524070 0553 2 5/ .0582434 .0611626 .0640829 067004-3 86 4 .0659268 .0728505 .0757753" .O7S7OI7 .0816293 .0845583 0874887 85 5 .0874-887 .09O42O6 .09J3540 .09628 90 .0952257 .IO2/G4I ./05/O42 84 6 ;|O5VO42 .1090462 .1109899 ./) 39356 .1/68832 .1/98329 (227846 83 7 .1227546 .1286943 .13/6525 J346/29 . (375-757 / 405408 82 8 .1405408 \ 1435084. . 1464-784 .14945/0 .(52 4262 .1554040 .1585844 8/ 9 .1583844 .16/3677 .164-3537 .I67J4-Z6 .1733292 .1763270 80 to .1763270 .\793279 ./823J/9 .1853390 ./ 883495 .1913632 J943803 79 II .1943803 .1974008 .2004248 2034-523 2064834 .2095/81 .2125566 73 /Z .2125566 .Z 155988 .Z/ 8644 8 22/6947 .2247485 .2278063 .2308682 77 /3 .7.308682 .Z33934Z .2370044 2400728 .243/575- .2462405 2493280 76 14 .2493280 .1 524200 .2555/65 .25-86/76 .26/7234 .2648339 .2679492 75 15 .2679492 .27/O694 .274/945 .2773245 .2804597 2835999 2867454 74 f 6 .28674-54 2898961 .293052 1 .2962/35 2.9938O3 3025527 3057307 1* 17 .30573(77 .3089/43 .3/2/036 .3/52988 3 / 84998 .3217067 3249/97 72 /8 .3249/97 .328/387 33/3639 .3345353 3378330 34-I077/ 3443276 71 /9 .3443276 .3475846 3508483 354//S6 3573956 |3 606795 3639702 70 2o .3639702 367-2680 3705728 37J884-7 .3772038 3805302 3838640 69 a .3838640 '.3872053 3 90554 / .3939/05 3972746 '4006465 4O40262 >8 22 .404O262. .4074/39 4/08097 .4/42136 /f/76257 '.42/0460 4244748 67 23 .424474-8 4279 121 .43/3579 4348/24 4382756 .4417477 4452287 66 24 .4452287 4427/87 .4522/79 .4557263 4592439 .46277/0 '.4663077 65 25 46?077 4698539 4734098 4769755 480F.T/2 .4941368 .4877326 64 26 .4877J26 .49/3386 4949549 49858/6 5022/89 .5058668 5095254- 63 27 28 .5095254 .53/7094 .5/3/950 5354465 '5"I68755 539/952 .52 056 7 / .5429557 5242698 546728 1 5279839 .5505/25 5? / 709 4 .554309 / 62 61 29 .554309 / 55g//79 56/9391 .5657728 5696/91 .5734783 .5773503 60 3a .577350? .58/2353 585/335 5890450 5929699 5969084 60086O6 59 .6008606 6048266 .6088067 .6/2go08 .6168092 .6208320 6248694 58 32. .6248694 .62892/4 6329883 6370703 .6452797 .6494076 57 33 .6494076 .6577/03 .66/8856 '.6660769 .670284-5" .6745085 56 34 .6745085 '.6787492 6830066 G8728/O .69/5725 .6958813 .7002075 55 JS .7OO2 O75 .70455/5 7089/33 .7/32931 .7/769 // .722/075 .7265425 5-4 36 .7265425 .7309963 735469 1 73996 If 7444724 .7490033 .753554 / 53 37 .7581248 7627/57 7673270 77/9589 77661 18 7g/2856 52 [78/2856 .7859808 .790697-5 .7954359 800/S63 .8049790 .8097840 51 39 .8097840 .8/46M8 8/94625 .8243364 8292337 .834/547 .8390996 50 4o 41 4Z .8390996 .9692867 .9004040 .8440688? 8744067 .90S"6 85 / 8490624 8795528 9/09540 8540807 8847253 9/673/2 859/240 8899244 .92/6965 .864/926 895/506 .92709/4 .8692867 9O04-040 ".9^25/51 49 48 47 4-3 .932515/ 9379683 94345/3 .9489646 .9545083 .960082.9 .9656888 46 44 96 56JJS SL 97/3262 9769956 982697J 98843/6 .9941991 /.OOOOOO 45 GO' JO' 40' 30' ao' 10' 0' DFGREFS I MINUTES COTANGENT5 TABLE VIII. FROGS AND SWITCHES 61 FROG NO. FROG ANGLE TURNOUT CURVE Theoretic.1 Lead AB CHORD AC FROG NO. RADIUS DEGREE 4 l4-/5' I5O.67 ^0-46' 37.67 37.38 4 4% (2-4f 190.69 30-24 42.37 4Z.IZ 4^ s I/-25 2354-2 24- 3 / 4-7.08 46.85 5 7 5k /0-23 284.85 20-13 51.79 5/.58 1* c 9-32 339.00 16-58 56.50 J6.3/ 6 8-4* 39785 /4--Z6 61. Zl 6/.03 6> 2 7 8-/O 46/.4Z IZ.-27 65.92 65". 75" 7, Tfc 7-38 529.69 10-50 70-62 70.47 7792 .9844 .9896 92421 "/* 0:2 TRIGONOMETRICAL FORMULAS SOLUTION OF RIGHT v TRIANGLES. I. sin A = %r ~ cos B . c.osA = 4. = s "'8 -3. faa A - T~~ 4. jj= fe/5 5. sec A = - = cosecf? 6. cosecA = -| -^ = ^ 8. exsecA=-| SOLUT/O/M OP OBLIQUE TRIANGLES. sin A _ g sinB _ fc IO ' sin C "" "c" 5/n C ~ c = sec B 12.. .4. 15. 17. area = 18. Let s 19. GENERAL FORMULAS. 2e longer piece on the. outer rail and Me shorter piece, on Me inner rail. 5". Expansion of o S/ee/ Roil. Steel expane/s .O/ oer /00' for eocA /J"/T r/se /V? temperature.. Thus if #>e temperature, changes from O to 90 a 30 roil w/7/ ex/W (o/X^Jf G. To determine tne Decree of Curve of a TracK wiPiouf a First ^fetfcoc/. 0,o standard quaqe frock the degree of curve = f-p-j, in w/?cJi C = /OA)^ chord of outer yuo^e /ne Tangent fo inner li'ne, the middle, ore/mate being "Hie gua^e of $e TracK. Second Method. /f f/)e |on^ chord of outer quaqe line = 62. middle ordinafe i'n inclies = degree of curve. 64 MISCELLANEOUS FORMULAS AND THEIR APPLICATION 7 Compensation for Curvature. To maKe. resistance on a curve eooo/ to resistance on o tanqent c/ecrease 1he grade, on ffre curve .05" x( degree of curve). 8. 7b/7S of Rail per Mile of TracK. The number of tons of H240 Its. in ,a m/'/e of track- xfve'iqhi / * per yard). Thus for a 56 /ts. ra/7 tons per /ft/Ye =~xS6 = 88, 9. Formula giving the. Radius of o Reversed Curve fce/Vrefl Parol/el Taogents. Let p =perpenount when c.namtnq on inner rail and lengthened bj "/fee so/we amount when chawing on outer roil. MISCELLANEOUS FORMULAS AND THEIR APPLICATION 65 12.. Correct/on "for Grode. in chaining TracK. In cboi'ning on Q grocfe each loo' station should he lengthened by an amount equal t> the 5Qjor& of the grade ' >n w ^ /c ^ ^ r= me base of a right triangle and h ihe altitude-, h be//y small in comparison w/'w D . A* - Me amount "the hupothenvse is longer than the. base. . Thus in laying off a riqht~- angled distance, of 66' suppose an obstacle is encountered but a point" f0i/ be set 2.l' off of 1he right-angled lioe The distance on me. hypolhe- Vvse w/'// fee 66+^ i. = 66.04 /J. Afc^oy Offsets w/tijot/f a TranSn. Aoproxim^tc offset f com tangent" ~o('j^o) O /^ which L- lenqth of ccrve onof D dcarcf of curvG- Given a a"-3o' curve . Station of RC,= /76/32. ffeauired to set po/nts ot each Po.'nf a = PC. of corve. Extend ffre tangent fro/r a to d rnakma aa = 68 ' c e voting c.e = too'. ef = ^ (;|fjx2.5 =Z.O9 loo' from c and 2.09' fro/7? e /oco/es station 178 of f. Extend chord cf to h maKinj fh~'Oo'. ZX 2.09 = 4.18'- 6g. asuring loo' from f are P.C . set the ZnJ station from original tangent. APPENDIX. FIELD ENGINEERING WITHOUT A FIELD BOOK Let & -any onqle exyoresse^ in degrees one/ decimals of a c/eqree. ran - natural tangent of A. /?- radius of a curve wAose c/eoree = D. A may le. exyoressec/ in terms of ton by $e tollow/ncj formulas*. fl) r\~S7.}\Tan- l &>] for values of tar, fro, f2) A ' [60- ^(ton-^ton -.6 4 tan for WWK of ^ from .25 to.50 (3) >U fcqfa-jfo-%1f*? for valves of ton from. 50 1o. 7 !> (4) A = fa- ^{ton-^ton -.O/ for values of to* from .75 to (oo For approximate, results t/>e <7^?/e formulas mou lye simplified follows: (5) A - S7.3 fen -for values of tfff from O to.25 (.6) A */60~"g- (fon-. IJjfOn for values of &/> fre>/n .25 to 1.00 R way be expressed in terms of D as follows: ERF?O/? IN U5NG FORMULAS 5 AND 6. Tangent HZ Angle by Form. 6 fjroct Angle. Error in Minutes Tangent Angle, by BOB II-/2.6 14-02.2. 16 -42.0 2I-40./ -fo.i + 1.2. 49.0 420.3 4/8.0 4//. 9 O.5 0.6 0.7 0.9 0.9 l.o 26 -40' J/- JT- 39-40 4-1- 4-5- O 2G-33.3' 30-578 34-59.5 38-39.6 A 1 -59.2 45- O + 6.1 42.2 40.5- 4-0.4 4-0.8 0.0 IN USING FORMULA 7. D Radius bi/ Form. 7 fxoct Error D I RotHo-i bf Form. 7 xocf Radius Error o*-/^' 229/S.34 229/^.75 +.ot II" 521.67 S2/. 67 O o-?o //459.20 11459. !9 + .01 IZ 4-78.34 4 78 34- .0-45 7639.4-9 7639.49 13 441.69 44//6S 4.0 / /- O 5729.65 5729.65 14 4-/0.28 4/O.28 O 1-30 38)9.83 o 15 333.07 3F^. 06 4.01 2 2g64.94 2 86 4. 9 J 4. Of /6 359.27 J59. 26 4.0f 3 /9/O.O8 19/0.08 o 17 330.28 338. Z7 4.0/ 4 /432.69 J432.69 o 18 3/9.62 3/9.62 5" 1 146.2,8 19 3O2.94 302.94 6 955. 3 7 955.37 o 20 29794 2S7.94- O 7 8/9.02 8/9.02 o 25 23A O/ 31.01 O 9 7/^ 70 7/6. 7# o 30 193. /g I93./9 -01 9 63728 4. Of 35 I6f>. 26 /&? 2 8 -.02 to 373.69 573. 9 o 40 //Z6 . /6 146.19 -.03 APPENDIX. FIELD ENGINEERING WITHOUT A FIELD BOOK 67 EF?f?OR IN USING FORMULAS I, Z, 3 AHD 4-. Tangent Formula 1 Fxoct Ang/e Error M^'Cfev Tory** Angle by rormvla 2 *"?' Angte Error ggfc .005 O-/72' 0"-/7.2' 0.0 .25 I4-OI.S' I4-02.2' -0.7 .Ol .02 0-34.4 1-08.8 0-34.4 1-08.8 0.0 o.o .26 .27 14 - 34.0 (5- 06.3 14 -34.5 15-06.6 -o.S -0.3 .03 1-4-3.1 1-43.1 0.0 .28 /S-3R4 J5-3B.5 -O.I .04 2-174 Z-17.4. o.o .29 I6-/0.-3 I6-/0.3 o.o .05 2- 51.8 2-5V.8 o.o .30 76-420 16-42.0 0.0 .06 3- 26.G 3-26.0 0.0 .?/ /7- /3.5 17- 13.4- + O.I .07 .08 4- - 00.3 4-34.5 4--OO.2, 4-- 34.4 -fO.f +0.1 i! 77-44.8 /8-/S.V / 7 -4-4.7 /8-/S.8 + 0.1 +o.\ .09 5-03.6 5-08.6 o.o .34- 18 -46.8 /ff-46.7 + 0.1 ./O 5- 42 .7 5-42.6 +0.1 .35 19-17.5 I9-/74- + 0.1 .// 6-/6.7 6- /6.6 + 0.1 .36 19-42.0 /9-479 +0.1 ./2 6-50.6 6-50.6 0.0 .37 2.0-19.3 20-18.3 o.o .13 7- 24. 4 7-24.4 0.0 .38 20-48.4 20 -48-4- o.o .14 7-59.2 7-5-0.2 o,.o .39 2/-/8.B ZI-/8.3 0.0 .AT ./6 8-31.8 9 - 05.4 f-3/.ff -05.4 o.o 0.0 .40 4' g-.'SW 2/- 48./ 22-/76 -o.i -O.I J7 9-7*8 9-38.9 -O.I .42 22 -46.8 22-46.9 -O.f J8 /0-/2.2 10-12.2. 0.0 .43 23-/5:9 23-16.1 -0.2 .19 /0-45.4 IO-4S.S -O.I .4-4 23-44.8 23-45.0 -0.2 .20 1 1 - / ff.4 II-/8.G -0.2 ."4-5 24-73.5 S4-/3.7 -0.2 .21 II- 51.4 H~5I. 6 -0.2 .4-6 24 -42.0 24 -42.1 -O.I .21 /2-24.2 /2-24.5 -0.3 .47 25- f 0.3 25 - /0.4- -O.I .23 J2-56.8 12-572 -0.4 .4-8 25- 38.4 25 - 38.5 -o.l .24 /3-29.3 l3-^9.7 -0.4 .49 26 -06.3 26-06.3 o.o .25 /4-0/. 6 14-02.2 -0.6 .<5o 26-J4.0 26 - 33.9 + 0.1 loojenf Artf/e fey rormulo 3 Angle Error Mtite* To^ent Aoyle by Formvlo 4 Exact Angle Error Miftfes .50 .51 26- 33.8' 27-0/./ 26- 33.9' 27- O/.3 -O.I -0.2 .75- .76 36*57.9' 37- /3. 8 36-52.2' 37- /4.I -0.3 -0.3 .52 27-28.3 27-28.5 -0.2 .77 37-35.5 37-3S-.8 -0.3 .53 27-55:3 27-55.4 -O.I .78 v?7-^70 37-57.3 -0.3 .54 28-22.0 28-22.f -o. .79 38 -IB. 3 38-/8.S -0.2 .55 .56 28-48.5" 29-/4.S 2g-49.6 29- 14.9 -O.I -o.l .80 .91 38-39.4 39-00.3 33-39.6 39-00.4 -0.2 -o.t .57 29-40.9 29-4I.O -O.t .82 39 - 21.0 39-21.1 O 1 .58 30-06.7 30 - 06 g -o.t .83 39-4-1.5 39-41. 6 -o.i .59 3O-32.3 30 -32 '.4 -O.I .84 4-0-01.8 40- 01.8 0.0 .60 70-578 30-57.8' o.o .85 40-Z/.9 40-21.9 o.o .61 3/- 22.9 3/ -23.0 -O.I .96 40-4/8 40-41.7 + 0.1 .62 3) -47.9 3/-479 o.o 7 4/-0/.ST 41 -OI.4 + 0.1 .63 32 - /2 .7 5T2 - /2.7 o.o g 4-I-2I.O 41-2.0.9 f O.I .64 32-37.2 32-372 o.o .39 4-1-40.3 41-40.1 w .65 33-01.5" 33-01.4- +0.1 .90 4-1- 59.4- 41- 59.2 +O.Z .66 33-25.6 33-25.5 + 0.1 .91 42 - 18. 3 42 - /8. 1 + O.2 .67 33-49.5 33-49.3 +0.2 .92. 4-2-37.0 42-368 +0.2 .68 34-/3.I 34-13.0 + 0.1 .93 42-5-5:5 42-55:4 +0.1 .69 34 - 36.5 34-36.3 + 0.2. .94 43-XJ.g' 43-13.7 +0.1 .70 .71 34-59.7 35-22.7 34-59.5 35-22.5 +O.Z +O.2. .95 .96 4?-3/.9 43-49.8 43 - 3/.9 43-439 0.0 -O.I .72 35-45.5" 35-45.2 -fO.3 .97 44-075" 44-O7.6 -O.I .73 36-08.1 36-07# +0.3 .98 44-25.0 44-25.3 -0.3 .74 36 - 30.4 36-30.1 +O.3 .99 44-423 44-42.7 -0.4 7f 36 - 52.5 36-522 +0.3 1.00 44-59.4 4-5-00.0 -0,6 IS -52. 7 *~ APPENDIX. FIELD ENGINEERING WITHOUT A FIELD BOOK l/se of Formulas. Given a 4-" curve. A = 37-44'. Tb f/>?c/ 7T 2;A = /8-5". /5y /v<7/ ton ^_A is found 1b be between .3 one/. 4 5//7C6 //" &/7 = .4 !rj form U/O (6) A = 22- O' o/? = .66= appro x/tfff/e tan 3?-i7 2-/7' 4" rr Tan 3^-17' //'e5 be.tyYeen.S0 cwc/ .7f Therefore use formda (3) If to. ft = .66 in formula (3) A ~ 33-25.6' If tan - .65 in formula (3) A~ 3d- O/.S of .01 in tan changes A by 0-24-.\ 33*17' 33^01^ *-(.oi) -.0064-3 &5-h0Wto =.65643 = tan 33-i7 tan S6- 43 = 1.52332 , Frror .00007 OF THE UNIVERSITY OF THE LAST T 53599 20410 . . //r 2 / l*^*f *^X_r 04109