CORNELL UNIVERSITY LIBRARY MATHEMATICS Cornell University Library QA 342.V27 bles of the exponential function a Ml thu iit math NATIONAL MEMOIRS OF THE sof arrest 7 vee re yas ACADEMY OF SCIENCES Volume XIV FIFTH MEMOIR WASHINGTON GOVERNMENT PRINTING OREICE 1921 MEMOIRS NATIONAL ACADEMY OF SCIENCES Volume XIV FIFTH MEMOIR GOVERNMENT PRINTING OFFICE NATIONAL ACADEMY OF SCIENCES. Volume XIV. FIFTH MEMOIR. TABLES OF THE EXPONENTIAL FUNCTION AND OF THE CIRCULAR SINE AND COSINE TO RADIAN ARGUMENT. BY C. E. VAN ORSTRAND. a TABLES OF THE EXPONENTIAL FUNCTION AND OF THE CIRCULAR SINE AND COSINE TO RADIAN ARGUMENT.’ By ©. E. Van Onstranp. The tables accompanying this paper have been prepared with the expectation of meeting a twofold requirement. The first was to obtain a few high place values at sufficiently small intervals of argument for general use in the evaluation of integrals and other functions; the other object was to obtain a basis for subsequent interpolation to small intervals of argument for use in the construction of complete 10-place tables which are applicable in the various fields of pure and applied mathematics. The need of tables-meeting these and other require- ments has been emphasized by various authors. The most important tables of extended values of the exponential function in which the exponents are integers or fractions have been constructed by Schulze, Bretschneider, Newman, Gram, Glaisher, and Burgess. Bretschneider included a few high place values of the circular sine and cosine to radian argument, but with the exception of these and a few values computed by Gudermann, there appears to be no extended values of these important functions. Schulze ? gives values of the ascending exponential at intervals of unity between the limits 1 and 24, inclusive, to 28 or 29 significant figures, and for the special arguments 25, 30, and 60 his values include 32 or 38 figures. In so far as I have been able to ascertain, Schulze gives no information regarding methods of computation or accuracy of results. Glaisher* verified the first 15 figures of Schulze’s value of e'* by direct substitution in the series; the first 13 powers of e were verified to 22 places of decimals; and the values of e™, e'®, ... e to 15 places of decimals by means of the relation en — é— Bretschneider ‘ evaluated e, e—', sin 1 and cos 1 each to 105 places of decimals; also values of the same functions at intervals of unity between the limits 1 and 10, inclusive, to 20 places of decimals. He corrected the erroneous value of e given in Callet’s tables and Vega’s Thesaurus and the slightly erroneous values of sin 1 and cos 1 ae to the twenty-fifth decimal by Gudermann.® Bretschneider obtained his values by direct sitsiinnion in the exponential series in con- nection with the evaluation of the three transcendants, 1 1 Ser tten? |. +e+]. 1 Published by permission of the Director of the U. 8. Geological Survey. 21. 8, Schulze, Sammlung logarithmischer Trigonometrischer-Tafeln (Berlin, 1778). 83. W. L. Glaisher, Tables of the exponential function. Camb. Phil. Trans., vol. 13 (1883), pp. 243-272. (In Salomon’s Tafeln (1827) the values of en, enn €0-0n, ,,, ¢0-000000n where 7 has the values 1, 2, ... 9 are given to 12 places. 4C.A. Bretschneider. Berechnung der Grundzahl der natiirlichen Logarithmen, so wie mehrerer anderer mit ihr zusammenhingender Zah]- werthe. Grunert’s Archiv der Math. und Phys., Bd. 3 (1843), pp. 27-34. 5C. Gudermann. Potenzial oder cykisch-byperbolische Functionen. Jour. fiir die reine und angewandte Math., Bd. VI (1830), pp. 1-89. me 6 MEMOIRS NATIONAL ACADEMY OF SCIENCES. [Vou, XIV, sin x 123 125 12’ sie. dame—s ate a7 7t 1 2! 4! 6! ] =~ ¢os x = 2 z eo a 1 gi, si-rl, 2 _ asin al 5- a5 - ae ac | Ri cos @ to Go. fe da=y + Logete!) — pare e a _ 2! 4! —S+ od =sin a] = “ v ze “t 3Y 5! ut ea | tg =) Ora x 9 3 ' Bis~ [Sac da=ytz joe. @+et+sgqtgat ct 1 2t 4) => tatbt at st - | known, respectively, as the sine nie the cosine tabeerel anil the exponential anieerel: The quantity y is the Eulerian constant 0.5772156 .... . i Newman’s* contribution to the subject consists of the following: ' 18-place values ‘of e* from =0.0 to 7=37.0 at intervals of 0.1. “ 12-place values of e~* from z=0.000 to = 15.349 at intervals of 0.001. '14-place values of e~* from «= 15.350 to e=17.298 at intervals of 0.002. 14-place values of e~* from 2= 17.300 to «= 27.635 at intervals of 0.005. 16-place values of e* from 7=0.1 to =3.0 at intervals of 0.1. 12-place values of e* from 4=0.001 to z=2.000 at intervals of 0.001. ’ The 18-place table is hardly the ogpivaiecn of a Us-plaes table, as the original came y included only 18 decimals. All of Newman's computations: are based on formulas of the a 2 3 usvarnefishs Rahs] 8 7 NI tof a, Ole Oo wherein fh assumes the constant ahs 1, 0.1, 0.01, Apes upon the interval of inter- polation. Having given e~* and e~* ibe value of eek is sormpnted. ron the formula by putting — We ah ee and N= me es, m! n! m being an even and 7 an odd integer. The values of the separate terms in these expressions may be computed by successive divisions. Then the appropriate summations give M+ N=e-h a known quantity, and M-—N=e->% 1F, W. Newman. Tables of the descending exponential function to 12 or 14 places of decimals. Trans. Camb. Phil. Soc., vol. XIII (1883), PP. 146-241; table of the exponential function ez to 12 places of decimals. Trans. Camb. Phil. Soc., vol. XIV (1889), pp. 237-249, No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. 7 the quantity to be determined. The equation for M+N provides a check on the values of Mand N, but the sum or difference which is the quantity sought is not verified by this method until another interpolation is made. Gram! gives values of the ascending exponential to 24 places of decimals at intervals of unity between the limits s=0 and 2=20, inclusive; also values of the same function from 2=5.00 to s=20.00, inclusive, at intervals of 0.02, the number of tabular decimals ranging from 4 to 15; and from z=0.1 to z=15.0, the values are given to one decimal only at inter- vals of 0.1. Some of the values were obtained by either repeated multiplication or logarith- mic computation, and the remainder were borrowed from Schulze, Bretschneider, and Opper- mann. Glaisher? gives 10-place logarithmic values and 9 significant figures of the natural values of both the ascending and descending function for the following ranges of argument: From z=0.001 to x=0.100 at intervals of 0.001. From z=0.01 to z=2.00 at intervals of 0.01. From 2=0.1 to x=10.0 at intervals of 0.1. From x=1 to x=500 at intervals of unity. . - Since: the’ natural values were computed from the logarithmic values, the maximum tabular error is one unit in the ninth significant figure with the exception of values of e~* con- tained in Newman’s tables. Tho remaining values of Glaisher’s tables were checked either by differences or by duplicate computation. Glaisher gives also the reciprocals of the factorials from 1 to 50, inclusive, to 28 significant figures, and verifies his values by forming the summa- tions for e and e. A further verification is obtained by evaluating e~ to 32 decimal places by means of the formula yth. 10” et= og oT Eg Ss ta } ie The quantity y X 10-* is here an approximate value of e~*. The equation gives log. (y +h) =n log.10—z a known quantity. Since logy is also known, we may evaluate the expressions [log.(y +h) —log,y] and y[log.(y +h) —log.yl. . - The expansion of the first by Taylor’s series gives 2 8 = logely +8) —logal+5 = G+. nid from which an approximate value of hy may be computed by neglecting terms in h beginning with the square. Finally the substitution of - 2 2.1? —— a by mand—$h in the preceding equation gives a corrected value of h. | oe Burgess * gives 30-place values of e~* for x=0.5, 1, 2, ... 10; and 14 values of e-*? at irregular intervals between the limits 1.0 and 3.0, ranging in extent from, 23 to 27 decimals. These values were used in his evaluation of the probability integral, but no information seems to have been given with regard to either method or accuracy of computation. | In his “Rectification of the Circle” (1853), Shanks evaluates the Naperian base by direct substitution in the series to 137 places of decimals. His second computation 4 was carried to 1J. P, Gram, Undersogelser angaaende Maengden af Primtal under en given Graense. Copenhagen Academy, 6 vol. IT (1884), pp. 183-306. 13. W. L. Glaisher. Tables of the exponential function, Trans. Camb. Phil. Soc., vol. 13 (1883), pp. 244-272. a be On the definite integral = Pa, with extended tables of values. Trans. Roy. Soc. Edinburgh, vol. 39 (1900), pp. . TJO : ‘ 4 William Shanks. On the extension of the value of the base of Napier’s logarithms; of the Naperian logarithms of 2, 3, 5, and 10, and of the Modulus of Brigg’s, or the Common system of logarithms; all to 205 places of decimals. Proc. Roy. Soc. Vol., VI (1850-1854), p. 397, 8 MEMOIRS NATIONAL ACADEMY OF SCIENCES. [Von. XIV, the two hundred and fifth decimal by a method given in J. R. Young’s. Elementary essay on the computation of logarithms (pp. 13-14). Glaisher} verified the first result, auane the con- tinued fraction e—1 Pete 1 Pig "eee sa? i 6 but the second result was shown by Boorman? to be incorrect after the one hundred and eighty- seventh decimal. Boorman’s formula is readily deduced. Since we have identically ; m' mn n mn we obtain 1 1 #1, 2 m mn nt mn by the substitution m=n—1 in the numerator of the right-hand member. The series for the Naperian base may thus be transformed into the series 1, 2 e=(145) +4 at ie +7 ad ata.) Tn kf el +o mn mn, atan)in wherein m=2, n=3; m,=4, n,=5; m,=6, n,=7; Tichaének * and Minks verified Boorman’ 8 salu oh e as far as the two hundred and ee third decimal, making use of Euler’s continued fraction 1 1 1 F=aqta3ta5t sey in connection with the relations ent th 1— gl i i. i 1 1 2 “i 1777.71” 71.1001 * 1001.18089 ~ Gauss ‘ gives values of e**ranging from 15 to 57 decimals for 13 values of n at eeeules intervals between the limits 1/2 and —16. He used the formula en™ = Nels a+10 log >—log c—log 5... —n The quantity NV is an approximate value of e multiplied by ax 10°, and the quantities c,d,... are the factors of N so selected that their natural logarithms may. be | taken from Wolfram’s 5 tables. The present contribution consists of the following tables: Table I: Values of the reciprocal of n! to 108 places of decimals at intervals of unity from 1 to 74. Table II: Values of ¢* to 42 significant figures at intervals of unity from 0 to 100. Table III: Values of ¢? to 33 significant figures at intervals of 0.1 from 0.0 to 50.0." 1J. W.L. Glaisher. On the calculation of ¢ from @ continued fraction. Brit. Assoc. Rep. (1871), pp. 16-18. 2J. Marcus Boorman. Computation of the Naperian base. Math. Mag. vol. I (1882-1884), pp. 204-205; see also L’Intermediaire des mathe- maticiens, vol. 7 (1900), p. 53; G. Peano, Formelaire de mathematiques. Tome II, No. 3, p. 125. 8 F, J. Studni¢ka. Veber’ “die Berechnung die transcendenten Zahle. Jahr. iiber die Fort. der Math. Bd. 23 (1891), p. 440: Vortriige fiber mono- periodische Functionen. Jahr. tiber die Fort. der Math. Bd. 25 (1893-1894), p. 736. 4 Lemniscatische Functionen. Werke 3, pp. 413-432. 5 Logarithmorum Naturalium. (48 decimals). See Vega’s Thesaurus, pp. 641-684. No.5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. 9 Table IV: Values of e* to 62 places of decimals at decimal intervals from 1 xX 10-” to 9 x 107. Table V:. Values of e~” ranging from 52 to 62. places of decimals at intervals of unity from 0 to 100. Table VI: Values of e~* ranging from 33 to 48 places of decimals at intervals of 0.1 from 0.0 to 50.0. Table VII: Values of e-* to 62 places of decimals at decimal intervals from 1 x 10-* to 9 x 107. Table VIII: Values of e+!) to 23 places of decimals or significant figures at intervals of unity from n=0 to n=360. Table IX: Values of e+"" to 25 places of decimals or significant figures for various values of n. Table X: Values of sin z and cos x to 23 places of decimals at intervals of unity from 0 to 100. Table XI: Values of sin z and cos z to 23 places of decimals at intervals of 0.1 from 0.0 to 10.0. Table XII: Values of sin x and cos z to 23 places of decimals at intervals of 0.001 from 0.000 to 1.600. Table XIII: Values of sin z and cos z to 25 places of decimals at decimal intervals from 1 xX 10° to9x10-, Table XIV: Miscellaneous values of ¢”, e~*, sin x and cos « to a great number of decimals, including Boorman’s value of e. The tabular error of the preceding tables may in some cases slightly exceed 5 units in the next succeeding tabular digit as two digits only were dropped from most of the values. In my preliminary computations, Glaisher’s' table of the reciprocals of the factorials was used. It contains all of the recurring decimals from n=1 to n=12, inclusive, and from n=13 to n=50, inclusive, the values are given to 28 significant figures. This table frequently failed to give the requisite number of decimals in the vicinity of n=13 and upwards, so it was afterwards extended roughly to 110 decimals, and the range of the argument extended from 50 to 74, the results being verified by forming the summations for e and e~, and then computing the product of these two quantities, in addition to making a direct comparison with the well known value of e. A further check on the value of ¢~ consisted in reciprocating e, ea in the form (a+})-. With the table of reciprocal factorials as a basis, it was easy to compute the value of et from the series: and afterwards by repeated multiplications by this factor, in accordance with the formula, e=th? — et. gA® (2), the values of ¢°?, e&*, ... e were obtained and verified by comparing the last computed value with the well known value of ¢. Similarly the value of ¢° was computed from e and the value of ¢ was computed from ¢. Values of the descending exponential for the same inter- vals of argument were determined in the same manner, and the evaluation of both functions was verified at frequent intervals by means of the product relation, e*e-*. Another check con- sisted in substituting values of x and Az in (2). Subsequent interpolations to one-tenth the previous interval of interpolation provided a further complete check on the entire computation. The maximum difference between any value and the corresponding value obtained by 10 interpolations did not exceed 15 units in the last decimal or significant figure. , Practically all of the computations were made with a 10-groove computing machine of the millionaire type. 13. W. L. Glaisher, Tables of the exponential function. Trans. Camb. Phil. Soc., vol. 13 (1883), pp. 244-272. 3C, F. Degen, Tabularum Enneas (Copenhagen 1824) gives 18-place values of loess (n!) from n=1 to n=1200. De Morgan reprinted the same to 6 places in his article on ‘‘ Probabilities” in Encyclopedia Metropolitana. J. W. L. Glaisher gives 20-place values of n X n! and 10-place valueg of—log (n Xn!) to n=71in Phil. Trans. Roy. Soc., vol.’ 160, 1870, p. 370. Shortrede, Tables (1849, Vol. I) contains 5-place values of log (n!) to n=1000 and 8-place values for arguments ending in 0. 10 MEMOIRS NATIONAL ACADEMY OF SCIENCES, — [Vou. XIV, The values of e+" contained in Tables VIII and IX were computed in the manner just described from the values, e#7/3. The latter function was evaluated for the first 10 decimals of the exponent by successive multiplication of the appropriate factors taken from Tables IV and VII. The values for the remaining decimals of the exponents were obtained by sub- stitution in the exponential series. The product of the two factors thus obtained is the re- quired result. Checks were applied in the usual manner, also by ‘ecmiperizou met the values given by Gauss.! — Values of the exponential function previously obtained provided an eaeslloit ‘chieck on the fundamental values needed‘in the computation of sin z and cos z. These values were com- puted at intervals of 0.1 from 0.0 to 1.6, os by direct Seuiaule in the series and verified by means of the relation =sin:~+cos 1+2 [Stet .|+2[ F+a+- ]-@ Interpolations were made by means of the formulas 2 us sin(# + Az) =sin ath cos 7— eas sin z+... ; ; 2 cos (¢-+Az) =cos oF sin 7— oe) cos &+... in which Az assumes the values 0.1, 0.01, ... according to the interval of interpolation. It will be noted that the two equations topotlior goutain terms of the form “i De og (Az)® sin ant and (Az) cos 2/n! wherein n assumes. successive values of the natural numbers beginning with unity. There are thus two series of. terms, : oe AD Dae Sn ot OS 5i Sin z, sy sin 2, 77 sing, ... [ew aT COS 2, ar cos 2, iv COS @, ... which may a scakiatosl By dividiine ‘the sine or cosine, as the case may be, iret by.2, die quo- tient by 3, the last by 4, and so on, thus avoiding the use of large factors. The computation of both functions is. made at the same time, and a complete check is obtained on the tenth inter- polation. Themaximum difference between the interpolated values is 10 units, and as there were two interpolations, the maximum error of interpolation is of the order of magnitude of 20 units in the twenty-fifth decimal.. Table X was computed with the assistance of a com- puting machine by substitution i in the trigonometric expansions for sin («+ Ax) and cos (4+ Az), and verified by. assigning various values to z and Az; also by forming the sum of the squares of the sine and cosine for several values of the argument. The values of sin z and cos x con- tained in Tables XIII and XIV were computed by substitution i in the: respective series and verified by means of equation (3). ‘Writers on interpolation emphasize the importance of interpolation by differences while not much attention is given to interpolation by means of derivatives. This procedure does not seem justifiable as the time lost in retabulating and differencing the quantities is some- times much greater than the loss of time due to the possible increased labor and difficulty of ‘computation by the derivative formula. Furthermore the check provided by the derivative formula is much more reliable than that of the difference formula when both the interval of interpolation and the interpolated values are large. Neither method provides an absolute check, for experience proves that positive and negative errors of equal or approximately equal magnitudes very frequently escape detection. The same is true of the various methods of mechanical quadratures which could be used for the same purpose. 1 Loc. cit. No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. 11 A comparison of the present values with those mentioned in the first part of this paper shows some interesting results. The values given by Schulze are generally incorrect in the last or the next to the last decimal. Newman’s 18-place table of the descending exponential is correct to 16 decimals when the last two decimals are taken into account. His values for a= —3.5, —26.1, —26.4, and —26.9 contain misprints. The values of e~°*® by Burgess is in error by approximately one unit in the thirtieth decimal. Glaisher’s value of e—° computed from formula (1) is correct. His table of the reciprocals of the factorials contain errors slightly in excess of 5 units in the next succeeding decimal for n=20, 27, 41, and 50. All of Bret- schneider’s values are correct and the values of e* given by Gram to 24 decimals are correct. The value of e"/? given by Gauss is incorrect in the twenty-third and following decimals. The present paper was completed before the 1916 report! of the British Association for the Advancement of Science was received. The report of the committee on the calculation of mathematical tables (pp. 59-126) contains the following tables of sin x and cos « to radian argument: Table I: Values of sin x and cos z to 11 places of decimals at intervals of 0.001 from 0.000 to 1.600. Table II: Values of x—sin x and 1—cos x to 11 places of points at intervals of 0.00001 from 0.00001 to 0.00100. . Table III: . Values of sin z and cos z to 15 places of decimals at intervals of 0.1 from 0.1 to 10.0. id In one value only, does the tabular error of Tables I and III exceed 10 units in the next succeeding decimal; the value of sin 9.1 should read 52 instead of 53 in the last two tabular digits. Nearly all of the numerical computations were made by A. G. Sofia piece work computer, and R. Weinstein and A. T. Harris, aids in the physical laboratory of the Geological Survey. I am indebted to F. A. Wolff, of the United States Bureau of Standards, Washington, D. C., for valuable suggestions in regard to the contents of Table IX, and to E. B. Escott, who kindly called my attention to the omission of several important references which had been overlooked in my preliminary publications in the Journal of the Washington Academy of Sciences (1912-13). The values given by Gram and Bretschneider were especially useful as a partial check on certain values which I had previously carried to a slightly greater number of decimals. ‘No errors were discovered in my computations, 1 The same report, pp. 123-126, contains the following: 10 place values of the logarithmic gamma function at intervals of 0.005 from 0.005 to 1.000. - 10 place values of the integral of the logarithmic gamma function at intervals of 0.01 from 0. ‘on to 1.00. 13 place. values of the logarithmic derivate of the gamma function at intervals of ney from 1 to 101, and from 0.5 to 100.5, 12 TasBie I.— Values of the reciprocal of ni to 108 places of decimals at intervals of unity from 1 to 74. MEMOIRS NATIONAL ACADEMY OF SCIENCES, [Von XIV, i mt nt 1] o4 2] 0.5, 3 16. 4 . 0416 : 5 | 0.0083 6 . 00138 7] 00019 84126 8 00002 48015 878 9| .(5) 27557 31922 39858 90652 10| 0.5) 02785 73192 23985 89065 2 11 .(5) 00250 52108 38544 17187 7 12] .(5) 00020 87675' 69878 68098 97921 00903 21201 43231 25434 23654 53476 5645 13 | .(5) 00001 60590 43886 82161 45993 92377 17015 49479 32725 71050 34882 8126 14 (10) 11470 74559 77297 24713 85169 79786 82105 66623 26503 59634 48661 86136 02740 58686 75709 94555 12153 92485 23375 508 15 | 0. (10) 00764 71637 31819 81647 59011 31985 78807 04441 55100 23975 63244 12409 06849 37245 78380 66303 67476 92832 34891 701 16 (10) 00047 79477 33238 73852 97438 20749 ° 11175 44027 59693 76498 47702 75775 56678 08577 86148 79143 97967 30802 02180 731 17 (10) 00002 81145 72543 45520 76319 89455 83010 32001 62334 92735 20453 10339 73922 24033 99185 22302 58703 95929 53069 455 18 . (15) 15619 20696 85862 26462 21636 43500 57333 42351 94040 84469 61685 54106 79112 99954 73461 25483 55329 41837 192 19 (15) 00822 06352 46624 32971 69559 81236 87228 07492 20738 99182 61141 34426 67321 73681 82813 75025 45017 33780 905 20} 0.(15) 00041 10317 62331 21648 58477 99061 84361 40374 61086 94959 13057 06721 33366 08684 09140 68751 27250 86689 045 21 (15) 00001 95729 41063 39126 12308 47574 37350 54803 55287 47379 00621 76510 53969 81365 90911 46131 01297 66032 812 22 (20) 08896 79139 24505 73286 74889 74425 02468 34331 24880 86391 _ 89841 38816 80971 17768 70278 68240 80274 219 23 . (20) 00386 81701 70630 68403 77169 11931 52281 23231 79342 64625 73471 36470 29607 44250 81316 46445 25229 314 24 . (20) 00016 11737 57109 61183 49048 71330 48011 71801 32472 61026 07227 97352 92900 31010 45054 85268 55217 888 25 | 0. (25) 64469 50284 38447 33961 94853 21920 46872 05298 90441 04289 11894 11716 01240 41802 19410 74208 716 26 . (25) 02479 59626 32247 97460 07494 35458 47956 61742 26555 42472 65842 08142 92355 40069 31515 79777 258 27 . (25) 00091 83689 86379 55461 48425 71683 64739 13397 86168 71943 43179 33634 92309 45928 49315 39991 750 28 . (25) 00008 27988 92370 69837 91015 20417 27312 11192 78077 45426 55113 54772 67582 48068 87475 54999 705 29 . (30) 11309 96288 64477 16931 55876 45769 38316 99244 05014 70865 98440 43709 74071 34050 88103 438 30 | 0. (30) 00376 99876 28815 90564 38529 21525 64610 56641 46833 82362 19948 01456 99135 71135 02936 781 31 (30) 00012 16125 04155 35179 49629 97468 56922 92149 72478 51043 94191 87143 77391 47455 96868 928 32 (35) 38003 90754 80474 35925 93670 89278 84129 67889 95345 12318 49598 24293 48357 99902 154 33 (85) 01151 63356 20771 95028 05868 81493 29822 11148 18040 76130 86351 46190 71162 36360 671 34 (85) 00033 87157 53552 11618 47231 43573 33230 06210 24060 02239 14304 45476 19740 06951 784 35 | 0.(40) 96775 92958 63189 09920 89816 38092 28748 86401 71492 54694 41299 31992 57341 480 36 (40) 02688 22026 62866 36386 69161 56613 67465 24622 26985 90408 17813 86999 79370 597 point. The numbers in the parentheses represent the number of zeros between the first tabular figure and the decimal No. 5.] Taste I.— Values of the reciprocal of nf to 108 places of decimals at intervals of unity from 1 to 74—Continued. TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. 13 i n ni 37 0. (40) 00072 65460 17915 30713 15382 74503 07228 79043 84513 13254 27508 48297 29172 178 38 (40) 00001 91196 32050 40281 92510 07223 76506 02080 10118 76664 58618 64428 87609 794 39 (45) 04902 46975 65135 43397 69415 99397 59027 69490 22478 57913 29857 15066 918 40 0. (45) 00122 56174 39128 38584 94235 39984 93975 69237 25561 96447 83246 42876 673 41 . (45) 00002 98931 08271 42404 51078 91219 14487 21200 90867 36498 72762 10801 870 42 . (50) 07117 re 12914 39311 40267 12249 69552 40258 74678 54113 ' 38352 425 43 . (50) 00165 ozs 67742 19518 86982 95633 71384 98959 50573 91956 12519 8 44 . (50) 00003 76184 28812 32261 79249 61264 40258 74862 71603 95271 73011 814 45 | 0. (55) ae 65084 71828 03983 32472 54227 97219 17146 75450 48289 a 151 46 . (55) 00181 73154 01561 47912 68097 22917 99939 54720 58161 96701 938 47 . (55) 00003 86662 85139 60593 88682 91976 97871 05419 58684 29717 ‘ 063 ; 48 : a 08055 47607 07512 37264 22749 52038 98029 57472 58952 439 49. . (60) 00164 39747 08316 57903. 35158 15347 73429 17499 44060 254 50 0. (60) 00003 28794 94166 33158 06703 16306 95468 58349 98881 205 51 - (65) 06446 95964 04571 72680 45417 78342 52124 50958 455 52 . (65) 00123 97999 30857 14859 23950 34198 89463 93287 663 53 . (65) 00002 33924 51525 60657 72150 00645 26216 30062 031 54 - (70) 043381 93546 77049 21706 48160 09744 74630 778 55 0. (70) 00078 76246 30491 80394 66330 18358 99538 741 56 . (70) 00001 40647 25544 49649 90470 18184 98206 049 57 . (75) 02467 49570 95607 89306 49441 84179 053 58 - (75) 00042 54302 94751 86022 52576 58347 915 59 . (80) 72106 82961 89593 60213 16243 185 60 0. (80) 01201 78049 36493 22670 21937 386 61 . (80) 00019 70131 95680 21683 11835 039 62 . (85) 31776 32188 39059 40513 468 63 . (85) 00504 38606 16493 00643 071 64 . (85) 00007 88103 22132 70322 548 65 | 0.(90) 12124 66494 34928 039 66 . (90) 00183 70704 45983 758 67 - (90) 00002 74189 61880 355 68 - (95) 04032 20027 652 69 - (95) 00058 43768 517 70 0. (100)83482 407 71 . (100)01175 809 72 - (100)00016 331 73 . (105 )224 ‘ 74 - (105)003 The numbers in the parentheses represent the number of zeros between the first tabular figure and the decimal point. 14 MEMOIRS NATIONAL ACADEMY OF SCIENCES. [Vou. XIV, TaBLe II.— Values of et to 42 signijicant figures at intervals of unity from 0 to 100. x ex 0 1.00000 00000 00000 00000 00000 00000 00000 00000 0 1 2.71828 18284 59045 23536 02874 71352 66249 77572 5 2 7.38905 60989 30650 22723 04274 60575 00781 31803 2 3 20. 08553 69231 87667 74092 85296 54581 71789 69879 4 '64.59815 00331 44239 07811 02612 02860 87840 27907 5 148. 41315 91025 76603 42111 55800 40552 27962 3488 6 403. 42879 34927 35122 60838 71805 48388 27960 5900 7 1096. 63315 84284 58599 26372 02382 88121 43244 222 8 2980. 95798 70417 28274 74359 20994 52888 67375 597 9 _ 8108. 08392 75753 84007 70999 66894 32759 96501 148 10 22026. 46579 48067 16516 95790 06452 84244 36635 35 i 59874. 14171 51978 18455 32648 57922 57781 61426 11 12 1 62754. 79141 90039 20808 00520 48984 86783 17020 9 13 4 42413. 39200 89205 03326 10277 59490 88281 78439 1 14 12 02604.28416 47767 77749 23677 07678 59449 41249 15 82 69017. 37247 21106 39301 85504 60917 21815 50574 16 88 86110. 52050 78726 36763 02374 07814 50350 80272 17 241 54952.'75357 52982 14775 43518 03858 23879 8676 18 . 656 59969. 13733 05111 38786 50325 90600 33569 2164 19 1784 82300. 96318 72608 44910 03378 87227 03883 620 20 4851 65195. 40979 02779 69106 83054 15405 58684 639 21 13188 15734. 48321 46972 09998 88374 53027 85091 44 22 35849 12846.13159 15616 81159 94597 84206 89222 69 23 97448 08446, 24890 26000 34632 68482 29752 77649 39 24 2 64891 22129.84347 22941 39162 15281 18828 40870 2 25 7 20048 99837.38587 25241 61351 46612 61579 15223 5 26 19 57296 (09428. 83876 42697 76397 87609 53427 92036 27 53 20482 40601. 79861 66837 47304 34117 74416 59256 28 144 62570 64291.47517 36770 47422 99692 88569 0206 29 393 13342 97144.04207 43886 20580 84352 76857 9694 30 1068 64745 81524. 46214 69904 68650 74140 16500 245 31 2904 88496 65247. 42523 10856 82111 67982 56667 647 32 7896 29601 82680. 69516 09780 22635 10822 42199 562 33 21464 35797 85916. 06462 42977 61531 26088 03692 26 34 58346 17425 27454. 88140 29027 34610 39101 90036 59 35 1 58601 34523. 13430, 72812 96446 25774 66012 51762 0 36 4 31123 15471 15195.22711 34222 92856 92539 07888 6 37 11 71914 23728 02611.30877 29397 91190 19452 16754 38 . 81 85593 17571 13756. 22032 86717 01298 64599 95422 39 86 59340 04239 93746.95360 69327 19264 93424 97019 40 235 38526 68370 19985.40789 99107 49034 80450 8872 41 639 84349 35300 54949.22266 34035 15570 81887 9337 42 1739 27494 15205 01047. 39468 13036 11235 22614 798 43 4727 83946 82293 46561.47445 75627 44280 37081 975 44 12851 60011 43593 08275. 80929 96321 43099 25780 11 45 34934 27105 74850 95348.03479 72334 06099 53341 17 46 94961 19420 60244 88745.13364 91171 18323 10181 72 47 2 58131 28861 90067 39623.28580 02152 73380 43163 7 48 7 01673 59120 97631 73865.47159 98861 17405 45593 8 49 19 07346 57249 50996 90525.09984 09538 48447 38819 50 51 84705 52858 70724 64087. 45332 29334 85384 82747 51 140 93490 82426 93879 64492.14331 23701 68788 6848 52 883 10080 00716 57684 93035. 69548 78619 93898 7056 53 1041 37594 33029 08779 71834. 72933 49379 64398 047 54 2830 75330 32746 93900 44206. 35480 14074 54085 083 55 7694 78526 51420 17138 18274.55901 29393 99207 077 56 20916 59496 01299 61539 07071.15721 46737 78152 97 57 56857 19999 33593 22226 40348. 82063 32533 03372 16 58 54553 89355 90103 93035 30766.91117 46200 68363 7 59 20121 04037 90514 25495 65934.30719 16176 84111 1 No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. Taste II.— Values of et to 42 significant figures at intervals of unity from 0 to 100—Continued. x ex 60 11 42007 38981 56842 83662 95718.31447 65630 19805 61 81 04297 93570 19199 08707 3421411071 00372 06295 62 84 38356 66874 14544 89073 32948.03731 17960 08069 63 229 37831 59469 60987 90993 52840. 26861 36004 6328 64 623 51490 80811 61688 29092 38708.92846 97448 3139 65 1694 88924 44103 33714 14178 36114.37197 49489 262 66 4607 18663 43312 91542 67731 84428.06008 68933 490 67 12523 63170 84221 37805 13521 96074. 43657 67534 89 68 34042 76049 . 93174 05213 76907 18700. 43505 95373 88 69 92537 81725 58778 76002: 42397 91668. 73458 73476 60 70 2 51543 86709 19167 00626 57811 74252.11296 14074 1 71 : 6 83767 12297 62743 86675 58928 26677.71095 59458 4 72 18. 58671 74528 41279 80340 37018 12545. 41194’ 69464 73 560 52393 63027 61041 94557 03833 21857.64648 53672 74 137 33829 79540 17618 77841 88529 80853. 89315 7998 75 373 32419 96799 00164 02549 08317 26470.01434 2778 76 1014 80038 81138 88727 83246 17841 31716.97577 666 77 2758 51345 45231 70206 28646 98199 02661. 94334 152 78 7498 41699 69901 20434 67563 05912 24060.45470 466 79 20382 81066 51266 87668 32313 75371 72632. 37469 74 80 55406 22384 39351 00525 71173 39583 16612.92485 67 81 1 50609 73145 85030 54835 25941 30167 67498.18994 0 82 4. 09399 69621 27454 69666-09142 29327 82904.32005 4 83 «ll 12863. 75479 17594 12087 07147 81839 40805. 73408 84 30 25077 32220 11423 38266 56639 64434 28742. 46903 85 82 23012 71462 29135 10304 382801 64077 74695. 48629 86 223° 52466 03734 71504 74430 65732 33271 47398. 7754 87 607 60302 25056 87214 95223 28938 13027 60752. 6138 88 1651 63625 49940 01855 52832 97962 64858 76706. 963 89 4489 61281 91743 45246 28424 55796 45316 27776. 598 90 12204 03294 31784 08020 02710 03513 63697 53970. 75 91 33174 00098 33574 26257- 55516 10785 25919 09603. 01 92 90176 28405 03429 89314 00995 98217 09052 59128. 75 93 2 45124 55429 20085 78555 27729 43110 91534 23487.6 94 6 66317 62164 10895 83424 48140 50240 87326 26873.9 95 18 11239 08288 90232 82193 79875 80988 15925 04790. 96 49 23458 28601 20583 99754 86205 91133 04494 83780. 97 133 83347 19204 26950 04617. 36408 70611. 50290 7672 98 363 79709. 47608 80457. 92877, 43826 76018 57298 9310 99 988 90303 19346 94677. 05600 30967. 13803 ,71014 0508 100 | 2688 41262 58736 111 11714 15 35448 55515 80013 15 16 MEMOIRS NATIONAL ACADEMY OF SCIENCES. TaBie III.— Values of e& to 88 significant figures at intervals of 0.1 from 0.0 to 50.0. ex ees el DUS gl ee BE ae Re ee I a ee BO oe we ele Pp aa ee EO Oe eg Se oe COIAT PONE OS OWONADTH PWNHO OWONAT PWN RO CONAN PONHO OWONATMN PWNHNHOS OCWNAMPM RWNHO aoe 1. 00000 1.10517 1. 22140 1. 34985 1, 49182 1. 64872 ~ 1.82211: 2. 01375 2. 22554 2. 45960 2.71828 3. 00416 3, 32011 3, 66929 4. 05519 4, 48168 4. 95303 5. 47394 6. 04964 6. 68589 7. 38905 8. 16616 9. 02501 9. 97418 11. 02317 12, 18249 13. 46373 14. 87973 16. 44464 18. 17414 20. 08553 22. 19795 24. 53253 27. 11263 29. 96410 33. 11545 36. 59823 40. 44730 44. 70118 49, 40244 54. 59815 60. 34028 66. 68633 73. 69979 81. 45086 90. 01713 99. 48431 109. 94717 121. 51041 134, 28977 148. 41315 164. 02190 181. 27224 200. 33680 221. 40641 244. 69193 270. 42640 298. 86740 330. 29955 365. 03746 00000 ° 09180 27581 88075 46976 12707 88003 27074 09284 31111 18284 60239 69227 66676 99668 90703 24243 73917 74644 44422 60989 99125 34994 24548 63806 39607 80350 17248 - 67710 53694 69231 12814 01971 89206 00473 19586 44436 43600 44933 91055 00331 75973 10409 36995 86649 13005 56419 24521 75187 96849 91025 72999 18751 99747 62041 22642 74261 09670 99096 78653 00000 75647 60169 76003 41270 00128 90508 70476 92467 56949 59045 46433 36547 19244 44674 38064 95114 27199 12946 79269 30650 67650 34120 14720 41601 03473 01690 72834 97049 43060 87667 41633 09348 57887 97013 92313 77987 67390 00823 30173 44239 61969 25141 95796 68117 21813 33808 23498 34880 35484 76603 01743 51179 91684 87087 20387 52628 60232 48654 28777 00000 62481 83392 10398 31782 14684 97487 52162 60457 66380 23536 11205 48953 22045 58722 82260 80365 76079 08373 41607 22723 07344 92647 73995 65223 43807 39775 11186 87149 94267 74092 40482 64356 42681 34816 75065 75259 52889 03755 87976 07811 49748 64502 91176 44440 55011 73545 87972 75704 84005 42111 94514 36998 83525 02509 91518 15292 67202 12024 31505 00000 17078 10719 37443 48529 86507 53676 45493 95375 01265 02874 84079 07674 74899 41088 20554 42863 08626 10239 25307 04274 97274 17771 76151 79397 01759 08253 89930 80160 62565 85296 79743, 02637 83721 27530 32493 47658 41892 78287 14865 02612 72197 17346 19511 08117 54567 40534 87004 81162 86277 55800 82613 41338 66156 46801 89495 10465 80305 52287 32150 00000 26490 94639 13328 52837 87814 68162 88583 31395 63602 71352 53588 29601 16011 95228 60119 56423 63009 53027 27692 60575 10478 66888 56908 69667 51168 32584 19468 10925 74128 54581 81257 27964 10231 33730 50388 99183 39039 29065 41220 02860 08124 53992 70652 26181 45574 87566 55366 97884 74352 40552 02021 23353 38620 14279 11839 31487 55296 64816 83072 NP FPOORD WORN NNNNANT HFPORRSO (Vou. XIV, No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. Tanpie TII.—Values of et to $3 significant figures at intervals of 0.1 from 0.0 to 50.0—Continued. ex an 3 a > oo go ee oe so e S - S ~ = . . so - ee w oe oe eo ee w e bed bet pet et 403. 42879 445, 85777 492. 74904 544. 57191 601. 84503 665. 14163 735. 09518 812. 40582 897. 84729 992. 27471 1096. 63315 1211. 96707 1339. 43076 1480, 29992 1635. 98442 1808. 04241 1998. 19589 2208. 34799 2440. 60197 2697. 28232 2980. 95798 3294. 46807 3640. 95030 4023. 87239 4447. 06674 4914. 76884 5431. 65959 6002. 91221 6634. 24400 7331. 97353 8103. 08392 8955. 29270 9897. 12905 10938. 01920 12088. 38073 13359. 72682 14764. 78156 16317. 60719 18033. 74492 19930. 37043 22026. 46579 24343. 00942 26903. 18607 29732. 61885 32859. 62567 36315. 50267 40134. 83743 44355. 85513 49020. 80113 54176. 36379 59874. 14171 66171. 16016 73130. 44183 80821. 63754 89321. 72336 98715. 77101 09097. 79927 20571. 71498 33252. 35294 47266. 62524 34927 00825 10932 01259 78720 30443 92419 51675 16504 56050 84284 44925 43944 75845 99959 44560 51041 18872 76244 82685 70417 52838 73323 38223 76998 02991 13629 72610 62778 91559 75753 34825 87439 81651 02169 96618 55772 80154 78285 82302 48067 44083 42975 28914 44433 42466 08757 02978 63817 66987 51978 83766 34154 . 03135 08055 07604 65075 64506 55309 05526 35122 16931 56254 29033 82056 61840 72894 43113 17697 25876 58599 76721 17829 45222 26540 63206 17959 08523 99077 08847 28274 41333 54721 09841 56085 34375 80321 21980 85158 92905 84007 11710 15886 83753 84397 72275 72615 32232 11245 89490 16516 88345 60998 13820 12762 37738 93109 66938 18305. 33990 18455 04182 97311 52465 55699 97428 80429 07884 39735 56665 60838 79233 57006 05938 60929 69396 90710 47226 57784 97253 26372 19815 68735 83730 06633 90380 25232 98030 24871 21116 74359 08812 56857 54472 59847 43137 56806 07565 52737 24450 70999 77437 85434 33850 55833 90175 55426 76797 99526 56032 95790 98557 95889 76842 26957 91202 47683 62836 10499 00463 32648 26482 60903 42612 37363 11026 18173 32987 38206 65566 71805 21972 20910 86677 82761 14942 17107 72512 39706 10085 02382 40043 15152 58693 38342 14827 48348 94345 55411 61148 20994 83565 18339 32070 50173 36763 91897 92099 29275 31452 66894 . 86428 02479 61222 57238 59729 11148 34500 53348 14677 06452 99428 84543 75016 08978 69013 09703 34286 68773 83753 57922 33834 28180 50238 40540 81147 80085 03867 60578 98194 43388 16812 66389 33165 16979 42634 60161 95340 81908 94319 8812 4583 9872 3122 5709 7881 4882 1393 2634 7690 5289 2825 5742 1925 2566 4783 0967 0448 5448 0296 3276 2849 7437 010 533 146 697 972 081 875 842 153 248 320 804 166 197 021 316 492 578 845 212 593 407 200 19 70 27 62 115394°—21——2 17 18 MEMOIRS NATIONAL ACADEMY OF SCIENCES. Taste III.—Values of et to 88 significant figures at intervals of 0.1 Jrom 0.0 to 50.0—Continued. er ro) bo i) ow w nr e or e or) i] a> H I roy QI ry a an ee > 2 ro) a e opoon BD OUOCTH He G9 G2 bo bo NNREHE 218 241 266 295 326 360 398 486 537 594 62754. 79141 79871. 86225 98789. 15114 19695. 98867 42801. 61749 68337. 28652 96558. 56029 27747. 90187 62217. 44961 00312. 19132 42413. 39200 88942. 41461 40364. 93724 97195. 61379 60003. 22476 29416. 36984 06129. 75912 90911. 16597 84609. 11122 88161. 35540 02604. 28416 29083. 28081 68864. 18965 23345. 98500 94074. 77260 82759. 26353 91287. 87560 21747. 63325 76445. 05518 57929. 23882 69017. 37247 12822. 93074 92786. 83521 12711. 89235 76800. 85327 89698. 47628 56538. 01318 82992. 58458 75331. 95838 40485. 29975 86110. 52050 20670. 92207 53519. 89906 94994. 55120 56519. 14046 50719. 42895 91549. 04176 94429. 11955 76402. 65849 56305. 08232 54952. 75357 95351. 31074 02925. 91644 05775. 72099 34955. 08814 24784. 39757 13193. 53483 42101. 50633 57835. 97888 11596. 94254 90039 37510 29545 21377 83235 08744 82029 38118 12478 98824 89205 54600 66919 28162 61566 77013 39902 91609 90349 26400 47767 20933 40950 84583 62144 75687 68098 24135 90966 23613 21106 02438 09471 04420 22664 30123 46158 37360 95879 85202 78726 13565 44180 13332 35683 35169 52861 46139 77754 56648 52982 27049 54583 58447 16391 62250 40439 36988 36562 29315 20808 99202 30399 34715 41021 56956 28131 24915 85014 57935 03326 59140 42887 51018 27675 31861 17000 45513 84647 42869 77749 72415 11264 73176 46062 67141 30730 50747 65944 37256 39301 44330 82558 61860 04847 67815 94525 04428 21060 66729 36763 82889 45529 33724 00166 10097 05552 61390 96058 14775 13394 71110 95506 55271 21870 30710 59843 28073 75595 00520 55498 15171 78951 99665 47967 06698 27613 64554 63962 10277 29689 77702 72789 08247 08259 49212 21710 14285 04190 23677 65547 71279 94920 26766 76278 21834 88825 60323 83192 85504 52318 38605 72912 12229 21079 78083, 51377 75789 31241 02374 22079 12596 02003, 44194 65773 22585 62473 92622 58443 43518 12187 68906 06223 54298 67634 38742 73758 19655 99097 48984 70958 71829 40139 43832 37871 18068 20512 45272 48069 59490 39772 08966 72271 66901 40363 27173 16782 05695 82607 07678 31032 19631 55661 69215 73256 00372 38372 31294 42565 60917 26886 78417. 49413 15576 20761 82516 35395 28904 77682 07814 08745 65383 53020 17466 23551 06037 92240 74676 63455 03858 57749 11219 13988 50110 98518 44398 07283 81474 66876° wan NTH OO NOONN AWTOHh NARNWO [Vou. XIV, No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. Taste III.— Values of e® to 38 significant figures at intervals of 0.1 Jrom 0.0 to 50.0—Continued. er wo e ne = be at Hee hs a a seo oe ae i eae! i 8 we Oe ee ee it Wo SO ee OS he ee IO ee ee CHONM PWONHO CONRAN PWNHO OWNRATM PWNHO CHONARAMT PRWNHO ONMYSHM PWNWHO OWONDM PWNHHO yo 2» TS) « no nw bw nw _ no tw ee bo _ NESE See 656 725 801 886 979 1082 1196 1322 1461 1614 1784 1972 2179 2409 2662 2942 3252 3504 3972 4389 4851 5361 5925 6549 7237 7999 9770 10797 11933 13188 14575 16108 17802 19674 21743 24030 26557 29350 32437 35849 39619 43786 48391 53480 59105 65321 72191 79783 88174 97448 07696 19023 31541 45375 60664 77561 96236 16874 _ 39683 59969. 13733 65488. 37232 97267. 40504 31687. 64519 53163. 60543 54987. 75023 40264. 19819 22940. 62272 28948. 67868 97464. 36864 82300. 96318 53448. 41573 98774. 67921 25905. 95158 64304. 66872 67566. 04150 15956. 12198 19216. 80017 19665. 80508 95622. 73550 65195. 40979 90464. 42938 82107. 83683 04512. 15323 81420. 94827 02177. 47550 28623. 85131 02725. 82690 54999. 46453 13824. 05498 15734. 48321 16796. 05142 05175. 60282 15034. 76198 41884. 33997 59553. 57648 38944. 05268 68755. 97023 78394, 23224 63283. 57765 12846. 13159 41421. 38043 22438. 02895 26179. 74308 61522. 75056 22063. 02329 37094. 69782 27949. 94318 70264. 14427 62789. 57177 03446. 24890 73371. 15763 29806. 97713 08760. 01606 38454. 77387 64720. 62247 89565. 52034 24323. 65135 58909. 74138 48874. 00676 05111 22497 71134 41289 32304 07572 05133 72454 13129 74215 72608 97114 04573 92662 50454 88065 05562 87860 38215 64203 02779 89023 56144 80392 82113 54067 39326 79801 41371 96018 46972 39203 86330 29093 16024 85454 31647 86819 92632 25326 15616 39369 04595 56773 74038 06142 08990 43117 69362 77864. 26000 45779 79397 93214 81109 86090 81110 78359 08217 57400 38786 75110 14452 61081 45541 48748 97759 49131 20356 13410 44910 12668 69563 02664 28992 66680 88545 03058 53744 80154 69106 64651 86124 40495 22801 04598 49420 12264 25566 57459 09998 84629 43100 45688 55721 85310 45191 92208 94732 80093 81159 91055 53310 45193 45957 72278 20985 28947 61695 45437 34632 38536 34848 92804 95934 61991 48593 05185 35308 68251 50325 99891 49662 78952 27301 04460 51385 49731 77145 14609 03378 18600 01720 76985 02822 80045 56147 99120 05532 45375 83054 69867 27127 98782 67333 83728 01192 26784 62697 21390 88374 61823 62026 56781 30300 20243 75991 74387 06188 80230 94597 46827 41691 39107 13828 94443 63179 05249 53886 68482 25530 01024 01732 22322 59775 83852 09236 44175 23095 90600 90593 99965 16349 00064 1217 3688 9827 8982 5743 8723 1486 4717 1347 0165 3345 9971 6792 4200 0896 1541 1124 3255 8846 7645 3990 2695 8714 510 201 530 210 135 729 926 562 160 373 19 20 MEMOIRS NATIONAL ACADEMY OF SCIENCES. Taste III.—Values of et to 83 significant figures at intervals of 0.1 from 0.0 to 50.0.— Continued. ex bo bo iw) bn bo Lote as hd oe od hig nae a IO gy ate ge aa: ag eM a gcd ea ES Ae ri 0 | oe i Ege oe ae TO oO RWDeH oO woraa PRONE OS CoOnan PWNEH S © oostooan RWNH OS woonon POwNH S CO CONT OD Or RPwONWHE © bo s 2 bo a: 8O a SCOONN OOTP wOcDD 215 238 263 291 321 355 393 480 530 586 648 716 791 874 966 64891 92750 23538 57565 95171 36731 82663 33425 89526 51527 20048 95777 79469 71964 74186 87160 12014 50000 02498 71034 57296 63146 90646 42073 19942 27035 66426 41510 56042 14171 20482 80042 98451 81900 37227 71992 94551 14135 40951 86275 62570 83612 64623 22428 75620 44747 52621 24040 87042 72183 13342 47963 17425 67462 48615 16744 - 33581 67350 93453 95220 22129. 84347 07423. 25706 86830. 63240 74811. 92562 26612. 13642 79097. 64641 27438. 62807 41407. 48840 25459. 80221 27202. 37940 99337. 38587 20706. 64333 82651. 72848 47559. 19382 87182. 68578 09132. 16965 80802. 87690 60991. 79992 50527. 33242 74428. 77727 09428. 83876 72147. 05767 84809. 99645 37190. 92910 65405. 62132 70371. 15483 01133. 37854 30919. 46297 56701. 72586 56296. 70645 40601. 79861 42526. 42283 88545. 30248 03631. 65428 05666. 34806 51318. 76492 01915. 23018 85016. 77547 35391. 71069 07869. 76518 64291. 47517 47516. 40054 67334. 23784 36252. 86153 07648. 18119 84797. 67787 87043. 08195 78915. 26116 89702. 04007 74864. 02890 97144. 04207 34436. 96185 53781. 40567 26525. 50089 99163. 66652 77934. 32021 33446. 16669 84845. 35758 81880. 23393 68253. 50589 22941 46440 94606 51762 04797 45304 18527 78591 23469 92103 25241 60674 99796 99044 47334 09652 06069 16792 01261 54108 42697 28406 04520 83050 14147 07849 36755 12378 52960 41109 66837 53382 85133 08266 33381 83096 62951 89905 44133 22787 36770 90476 68124 64001 79284 68074 72729 09982 25720 79644 43886 95024 43880 96447 71853 79214 80045 16856 20218 75038 39162 91249 10181 98574 38119 17828 03687 38870 39592 46415 61351 37733 19698 89837 69615 01023 24450 65970 84906 41351 76397 29286 70140 91670 79370 19455 39770 08766 40096 23997 47304 81240 02409 99454 19699 93392 00965 47059 88465 42513 47422 75464 17444 24396 16722 52711 35918 34926 34279 36208 20580 47682 77859 48663 60117 42218 98003 01647 01897 08871, 15281 77678 71913 72157 69976 87281 39155 16973 04239 77990 46612 94535 43300 30276 59214 04023 49061 81555 43941 39504 87609 74083 43285 72539 61947 52377 00888 28766 29323 81144 34117 46422 44687 22658 12653 27847 77092 90553 01118 40126 99693 54890 60541 78170 73105 03802 88625 73407 28499 11659 84353 30942 92347 05030 55890 51631 56392 30249 03542 22088 No BDOoORWN MANWNWH BONOCOM HOMOW [Vou. XIV, No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. TaBLE III.— Values of e% to 38 significant figures at intervals of 0.1 from 0.0 to 50.0.—Continued ex w oo oo oo oo ie g on Ba te ee an es stan eh ees 8 pl ae SOE, cee Se ees Ga ROR iairedee nde aa star Lar ate alba o a Sak ate tee thes dene ca he SO: rat 2 Salsa See WOOIM]S HM RONEH OS OO TAH CH PONE OS OCONMN BHRWNHO OO Wma RON O OONTIDH BONES OOr~Imr LONE OS oo bs oo bo oo eo ow a = = $8 wo » wjCOWNdD NDOEHEHR HREH 1068 1181 1305 1442 1594 1761 1947 2151 2378 2628 2904 3210 3548 3921 4333 4789 5293 5849 6464 7144 7896 8726 9644 10658 11779 13018 14387 15901 17573 19421 21464 23721 26216 28973 32021 35388 39110 43223 47769 52793 58346 64482 71264 78759 87042 96196 06313 17494 29851 43508 58601 75281 93716 14089 36605 61489 88990 19383 52973 90096 64745 03809 24895 52318 23467 90179 20262 99171 31865 44861 88496 39438 03451 18455 57913 34563 04551 71996 94038 86410 29601 75671 55773 88472 88941 79120 98942 18748 52997 75425 35797 78421 62603 85266 05935 74356 61021 90899 80718 80166 17425 49496 17816 09720 26376 57855 66103 76637 79882 - 43171 34523 59431 12051 42275 40389 41144 49291 88836 78512 36216 81524. 46214 24255. 46209 28882. 52476 35807. 87724 11433, 85149 51355. 63141 44891. 01937 21859. 31322 62477. 10567 28017. 22881 65247. 42523 53582. 96612 02513. 33135 70585. 46635 68684. 45663 32463. 72707 04764. 87666 62294. 84813 55632. 86150 12173. 08287 82680. 69516 99064. 03195 59617. 86912 74864. 77539 99387. 29527 50632. 93871 83349. 67368 57756. 68324 21476. 94368 31483. 77619 85916. 06462 31044. 37760 71890. 35741 63661. 34260 14764, 11460 12259. 87392 11037. 88087 35043. 72041 51694. 68936 31304. 10421 27454, 88140 51084. 44647 03972. 25326 34327. 18570 31269. 08969 44776. 41048 67882. 10250 20104. 34037 04385. 00894 61583, 15354 13430. 72812 73561. 61212 34757. 28303 39307. 66424 52471. 09566 45696. 60738 32558. 10962 80768. 63352 63176. 61523 46888. 64411 69904 01487 97252 46546 18434 21609 17824 47658 98775 21183 10856 04636 61277 65946 26741 54403 92400 15789 88365 18592 09780 78574 13519 68973 90142 26745 39501 09867 79223 09187 42977 36693 51580 27596 39540 92482 97251 86857 96145 90549 29027 43293 59900 84270 92798 71247 93915 07747 18446 06356 96446 33756 31243 27337 20224 41656 41749 22189 70828 37401 68650 22090 90255 87919 29655 84760 87753 79141 07647 58524 82111 67150 07371 87032 42381 58901 05063 57425 43609 40090 22635 92376 98498 56901 63008 74701 94593 00264 01141 05800 61531 34787 61740 09521 04425 12571 60053 86658 39196 88835 34610 22486 26513 17314 21172 85963 64891 33623 81468 61404 25774 44114 64910 78435 56329 44430 67431 34573 13371 49460 7414 7004 6973 4322 0257 9319 5604 9410 3359 8783 6798 6906 6175 8266 5711 8061 9297 7372 9270 3405 1082 1833 2802 625 392 261 909 261 219 413 264 132 573 907 642 174 133 391 21 22 MEMOIRS NATIONAL ACADEMY OF SCIENCES. TaBLE III.— Values of et to 33 significant figures at intervals of 0.1 Jrom 0.0 to 50.0—Continued. er eo oe wo wo & Pe) N a a oe oo 8 s wo eo CONAA PONS OONOTN PONE OD CONRAT RPWONHO CBONAT PONE O OONAT PWONHO OWHNOT PwWNHO ..- a oe CONT BOP 10 212 235 260 287 317 351 388 474 523 578 639 707 781 863 954 1054 1165 1288 1423 1573 31123 76464 26575 81955 43160 10801 85557 68175 59482 60391 71914 95165 31379 81918 48290 32159 35366 59945 08143 82443 85593 20624 90892 00101 52346 52155 04529 14996 89667 35294 59340 70050 76541 88886 18217 76838 78346 37769 71715 98539 38526 14095 50021 73687 15355 08469 89992 00771 85954 95433 84349 13642 50660 69837 53432 92357 87085 48656 99788 76104 15471 77269 01027 38753 16992 91546 60548 42005 22603 85262 23728 53352 28174 75491 60269 93044 96419 46824 09975 90402 17571 93461 29119 00558 57616 22859 21585 88248 99407 88586 04239 78458 81163 42402 34052 11812 29023 45528 67809 70885 68370 14517 41450 56135 45283 62436 00386 83917 53099 46328 35300 11693 77884. 52117 62732 77020 88686 74535 26807 73400 15195. 22711 61994. 98745 13635. 63500 72964. 47397 36632, 16821 42244, 06486 35257. 60090 35355. 65163 12769. 18144 02523, 59786 02611. 30877 09485. 45824 12826. 72968 64744, 53050 21254. 81056 02836. 20844 36677. 02922 63243. 03968 02543. 50501 36540. 01941 13756. 22032 64588. 56603 00887. 26618 80104. 30725 37170, 45041 25158. 15729 94036. 20184 82561. 06182 19634. 02423 00468. 95973 93746. 95360 77343. 61342 33982. 46846 83560. 86698 53920. 49038 91985. 91758 02477. 43715 92517. 50602 35081. 54052 14544, 13549 19985. 40789 50670. 00948 03765. 77508 79105. 26803 47072. 98994 20324. 02317 70710. 64074 09565. 01140 08701. 59178 43124, 57201 54949, 22266 40529. 35962 47896. 96629 44030. 73926 08325. 47163 81418. 45053 56114. 75075 16481. 07600 42680. 14854 54746, 30325 34222 07283 14974 44109 94211 15833, 79367 79156 67304 47544 29397 65306 64500 66757 07962 22759 94101 93611 04825 88916 86717 83582 70087 30475 48507 58254 79777 08507 10740 47814 69327 17376 15693 34176 85620 33666 59460 13224 84561 39399 99107 59692 14124 06064 83315 21875 96477 65056 65130 85917 34035 83009 84417 44719 27987 91711 60769 60987 81712 05193 92856 67350 59058 37106 47485 68420 46411 01753 04477 17130 91190 72850 92801 27100 69122 20919 03254 44775 61149 28577 01298 49016 82885 49330 32909 60641 28230 97636 15188 57630 19264 38971 64994 84070 11921 53263, 30821 60008 81318 97850 49035 83355 91637 59178 42259 72699 64288 82629 82966 65939 15571 93650 00348 24967 89991 6615 2286 0147 4332 6633 RO WOMDOODN AWOOhD ANOWIT NWOWODND [Vou. XIV, No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. TasLE III.— Values of et to 83 significant figures at intervals of 0.1 Jrom 0.0 to 50.0—Continued. ez » os rs RT OT ee eT LY ae eee er Ce ee eee ee ee eee eee eer CANAAN PONS OONBMW PONE S OWONBM PWONHO DOHNRATN PWONHO CONRAD PWNHHO CHONSRA RwWNHS 8 Onanrr WWWOND NNR HE Bee 1739 1922 2124 2347 2594 2867 3169 3502 3870 4277 4727 5225 5774 6381 7053 7794 8614 9520 10522 11628 12851 14203 15696 17347 19172 21188 23417 25879 28601 31609 34934 38608 42668 47156 52115 57596 63654 70348 77747 85924 94961 04948 15985 28184 41665 56564 73030 91228 11340 33566 68131 85279 15282 48440 85086 25586 70345 19812 74481 34900 27494 19608 35521 77559 69331 57959 16556 46962 82756 92605 83946 07068 59616 91574 10768 88949 68518 69952 00023 60866 60011 21469 97982 84560 33445 70647 14218 94452 76205 83562 27105 34041 81502 33347 80835 87576 39207 98292 65004 44177 19420 35018 86452 20437 45483 54077 57727 36193 02432 84870 28861 19322 26788 79345 63159 54617 87396 58133 T4774 52057 15205 39061 07720 86076 37488 16805 99926 25224 82552 73211 82293 56173 66338 69948 51877 57253 02889 96326 98864 51075 43593 71275 64500 58126 48105 10763 34749 56189 11251 46231 74850 69043 39272 31937 76508 88795 17816 55181 54829 89905 60244 22319 14218 69374 40564 85583 03314 70115 40292 83171 90067 71176 66936 33095 58012 93903 17208 93678 61013 42614 01047. 39468 80476. 58968 08071. 35617 86074. 87538 59588. 85140 71559. 56393 08018. 31712 63704. 82268 18196. 19954 46063. 77834 46561. 47445 08600. 14746 34529. 15450 30360. 69842 09178, 99594 06399. 59362 58825. 49151 24602. 82213 74241. 01297 19279. 13929 08275. 80929 74732. 70231 13186. 98266 80995. 55797 90107. 58191 90948. 92010 10750. 51432 42730. 17190 17788. 91534 64724. 23096 95348. 03479 28227. 13228 88395. 41377 07791. 30039 83053. 61114 35865. 26851 19332. 12347 17701. 87293 17232. 44579 22451. 73279 88745. 13364 54147. 90908 49473. 77180 71210. 96429 33686. 31382 41656. 97621 92805. 23175 42258. 16763 75711. 22343 34964, 40927 39623. 28580 49551. 26703 88624. 40776 38552. 71985 11272, 71553 18634. 74249 02496. 15995 24359. 56886 95112. 69333 89472, 44726 13036 93786 33172 89370 73151 30187 57371 16568 73844 40083 75627 75513 27874 21728 13708 37456 03780 30778 41703 36648 96321 52164 35129 31144 10264 98100 14409 82453 78007 09490 72334 24629 10669 79777 98817 87821 80923 63572 79926 26071 91171 66367 46271 62509 49717 59025 74257 34724 53462 95531 02152 03268 84037 37705 28309 65238 73329 42328 79245 63512 1124 0494 1242 8665 4199 8547 5547 0900 1926 1416 4428 6950 7849 8812 6927 5717 4263 8026 5134 7541 4310 8956 2425 1650 4550 2595 6533 0870 8747 4714 061 23 MEMOIRS NATIONAL ACADEMY OF SCIENCES. [Vou. XIV, TaBLEe III.—Values of et to $3 significant figures at intervals of 0.1 from 0.0 to 50.0—Continued. x ex » @ 01673 59120 97631 73865.47159 98861 17 75469 24698 67306 37991.61667 18811 74 57026 05963 17562 39656.99046 28407 19 47160 27713 79827 71146. 82358 95213 41 10 46773 99304 93692 57138.00626 58991 2 11 56864 17491 60830 07521.04037 92992 12 78532 64228 08340 57448. 38688 41765 14 12997 09405 91929 46708. 68045 97513 15 61603 29567 96204 89284. 58072 41039 17 25838 54795 62031 90250. 54761 43153 07346 57249 50996 90525. 09984 09538 21 07943 96261 28491 13381.14667 72236 23 29638 36441 28610 87238. 76943 67133 25 74648 56998 24118 27728. 21369 31403 28 45426 72380 96153 72548.47735 30218 31 44682 86466 96548 51738. 26948 84493 34 75412 04860 37200 08737.07381 37971 38 40924 32444 65405 26989. 78298 37803 42 44877 86190 76698 38363. 39647 78017 46 91315 56376 34916 3437410241 66244 51 84705 52858 70724 64087. 45332 29334 So CONANT PWONRFO CONOO RWNEOS ra oO oO POW ONADon HOCH on = No. 5.) TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. 25 TaBLe IV.— Values of e% to 62 places of decimals at decimal intervals from 1X10 to 9X10. x ex 1.00000 00001 00000 00000 50000 00000 16666 66666 70833 33333 34166 66666 67 1.00000 00002 00000 00002 00000 00001 33333 33334 00000 00000 26666 66666 76 1.00000 00003 00000 00004 50000 00004 50000 00003 37500 00002 02500 00001 O01 1.00000 00004 00000 00008 00000 00010 66666 66677 33333 33341 86666 66672 36 1.00000 00005 00000 00012 50000 00020 83333 33359 37500 00026 04166 66688 37 1.00000 00006 00000 00018 00000 00036 00000 00054 00000 00064 80000 00064 80 1.00000 00007 00000 00024 50000 00057 16666 66766 70833 33473 39166 66830 07 1.00000 00008 00000 00032 00000 00085 33333 33504 00000 00273 06666 67030 76 1.00000 00009 00000 00040. 50000 00121 50000 00273 37500 00492 07500 00738 11 1.00000 00010 00000 00050 00000 00166 66666 67083 33333 34166 66666 68055 56 1.00000 00020 00000 00200 00000 01333 33333 40000 00000 26666 66667 55555 56 1.00000 00030 00000 00450 00000 04500 00000 33750 00002 02500 00010 12500 00 1.00000 00040 00000 00800 00000 10666 66667 73333 33341 86666 66723 55555 56 Dette es sccciceiiee 1.00000 00050 00000 01250 00000 20833 33335 93750 00026 04166 66883 68055 57 Osetiieisin caress 1.00000 00060 00000 01800 00000 36000 00005 40000 00064 80000 00648 00000 06 Wesisistagrcve niejociieee 1.00000 00070 00000 02450 00000 57166 66676 67083 33473 39166 68300 68055 72 Seiciiascta sett aac 1.00000 00080 00000 03200 00000 85333 33350 40000 00273 06666 70307 55555. 98 Deetcrad sa eens 1.00000 00090 00000 04050 00001 21500 00027 33750 00492 07500 07381 12500 95 TIO So cscs 1.00000 00100 00000 05000 00001 66666 66708 33333 34166 66666 80555 55557 54 Dis ean Brent | 1.00000 00200 00000 20000 00013 33333 34000 00000 26666 66675 55555 55809 52 Duk oel ee rouse 1.00000 00300 00000 45000 00045 00000 03375 00002 02500 00101 25000 043839 29 BS sc iatetens 1.00000 00400 00000 80000 00106 66666 77333 33341 86666 67235 55555 88063 49 Dsecutes asec . 00000 00500 00001 25000 00208 33333 59375 00026 04166 68836 80557 10565 48 1 1.00000 00600 00001 80000 00360 00000 54000 00064 80000 06480 00005 55428 58 haat anwitea tween 1.00000 00700 00002 45000 00571 66667 66708 33473 39166 83006 80571 89569 46 1.00000 00800 00003 20000 00853 33335 04000 00273 06667 03075 55597 16571 47 1.00000 00900 00004 05000 01215 00002 73375 00492 07500 73811 25094 90017 96 01000 00005 00000 01666 66670 83333 34166 66668 05555 55753 96825 64 02000 00020 00000 13333 33400 00000 26666 66755 55555 80952 38158 73 03000 00045 00000 45000 00337 50002 02500 01012 50004 33928 58770 09 04000 00080 00001 06666 67733 33341 86666 72355 55588 06349 36888 89 05000 00125 00002 08333 35937 50026 04166 88368 05710 56548 58785 97 Gicececeuccain 1.00000 06000 00180 00003 60000 05400 00064 80000 64800 00555 42861 30857 17 Tos pee 1.00000 07000 00245 00005 71666 76670 83473 39168 30068 07189 56958 74206 71 Bee iesen ds a 1.00000 08000 00320 00008 53333 50400 00273 06670 30755 59716 57184 46730 53 Co 1.00000 09000 00405 00012 15000 27337 50492 07507 38112 59490 01892 47699 73 1 Ponce asc 1.00000 10000 00500 00016 66667 08333 34166 66680 55555 75396 82787 69844 03 crcl aecy 1.00000 20000 02000 00133 33340 00000 26666 67555 55580 95238 73015 88712 52 o gcneeeneetiaen 1.00000 30000 04500 00450 00033 75002 02500 10125 00433 92873 41518 39955 37 Dees ee 1.00000 40000 08000 01066 66773 33341 86667 23555 58806 35083 17467 54144 91 Oras sesecies 1.00000 50000 12500 02083 33593 75026 04168 83680 71056 55730 71730 41021 76 Ce 1.00000 60000 18000 03600 00540 00064 80006 48000 55542 89880 00277 71445 23 eee 1.00000 70000 24500 05716 67667 08473 39183 00682 18957 08742 07709 26023 06 Cece 1.00000 80000 32000 08533 35040 00273 06703 07559 71657 55895 91000 27103 65 Oo cee 1.00000 90000 40500 12150 02733 75492 07573 81134 49002 85334 23622 70826 94 TSS cceacue 1.00001 00000 50000 16666 70833 34166 66805 55575 39685 01984 40255 75947 97 eee ee 1.00002 00002 00001 33334 00000 26666 75555 58095 24444 44585 53820 10587 14 Be aca. 1.00003 00004 50004 50003 37502 02501 01250 43393 01986 66138 40912 95086 65 oe 1.00004 00008 00010 66677 33341 86672 35558 80636 54603 89700 46532 73294 25 Be aad 1.00005 00012 50020 83359 37526 04188 36821 05664 45007 86247 45526 60354 36 oe 1.00006 00018 00036 00054 00064 80064 80055 54327 37170 62873 80580 51744 80 Wadoeees wae 1.00007 00024 50057 16766 70973 39330 06968 95837 42177 17672 36470 63988 79 Bee as 1.00008 00032 00085 33504 00273 07030 75971 66130 39100 02976 67262 81645 47 Ooo ae 1.00009 00040 50121 50273 37992 08238 12199 01246 20911 38661 76502 68546 00 1X10-4..0 00.22. 1.00010 00050 00166 67083 34166 68055 57539 70734 15454 17217 83810 34635 39 Bee ae 1.00020 00200 01333 40000 26667 55558 09530 15887 12550 26506 33402 81249 62 ee 1.00030 00450 04500 33752 02510 12543 39448 44292 42698 70509 44536 57909 05 Meri srasisiveis ara 1.00040 00800 10667 73341 86723 55880 65117 53256 02089 28421 81273 13638 99 26 MEMOIRS NATIONAL ACADEMY OF SCIENCES. (Vou. XIV, Taste IV.—Values of et to 62 places of decimals at decimal intervals from 1X10~ to 9X10~'—Continued. zx ex 51074... 1.00050 01250 20835 93776 04383 69605 75164 84877 16767 77200 56676 54052 3 Gest ovrancccecn 1.00060 01800 36005 40064 80648 05554 70231 34873 80662 32142 77422 18779 ee Uesicinisaisiaiseieiats 1.00070 02450 57176 67223 40800 84397 12431 78087 29972 04988 70829 20697 5 Soccanerianiccens 1, 00080 03200 85350 40273 10307 97169 87567 14849 70787 02383 19576 98136 83 Deca tremens. 1.00090 04051 21527 34242 14882 07410 85590 92409 60364 43887 07063 86170 96 1X1073... 22... | 1.00100 05001 66708 34166 80557 53993 05831 15630 76200 58070 14602 28514 67 Ds Bora 1.00200 20013 34000 26675 55809 58731 56994 71412 62360 35588 16507 84254 33 Sac neietlape Ses 1.00300 45045 03377 02601 29340 91348 90020 53318 72719 56193 06400 58163 87 Ae icnistiget cud 1.00400 80106 77341 87235 88079 75325 86225 67866 79584 56844 65158 24520 10 Distdeeeces -...| 1.00501 25208 59401 06388 35662 41124 06858 07348 75538 59395 63607 58053 70 1.00601 80360 54064 86485 55845 42073 81480 76633 97023 13120 72381 28209 31 1.00702 45572 66848 55523 16000 31941 33738 72606 26958 32484 35735 15364 69 1.00803 20855 04273 43117 20736 14608 63184 74612 48193 62989 84773 19670 85 1.00904 06217 73867 81406 25704 81311 87427 40577 45096 80755 75335 36793 79 1.01005 01670 84168 05754 21654 56902 36003 38073 62201 52429 25151 64404 03 1.02020 13400 26755 81016 01439 20483 15143 53035 08991 19392 55772 74241 06 - 1.03045 45339 53516 85561 24399 53831 19818 29050 25142 98822 33256 69945 48 1.04081 07741 92388 22675 70447 57916 85474 40829 77050 31281 20352 33957 19 Biosviecs es damiisers 1.05127 10963 76024 03969 75176 36335 64522 01748 21296 05506 25287 83938 48 Gsiaica wa cannes 1.06183 65465 45359 62222 46848 77168 37232 84282 60420 33007 90597 72946 22 Paice tava nares 1.07250 81812 54216 47905 31039 49889 11460 55749 58973 09301 36313 68582 00 Bo ocean tate 1.08328 70676 74958 55443 59877 58674 88850 01987 13572 83659 39689 77149 14 Ovo cashes 1.09417 42837 05210 35787 28976 23544 88601 18465 19908 74708 51134 95537 27 1X1071.... 2. 1.10517 09180 75647 62481 17078 26490 24666 82245 47194 73751 87187 92863 29 Decora ake ees 1.22140 27581 60169 83392 10719 94639 67417 03075 80941 52050 36412 73425 10 eee eeeraerone 1.34985 88075 76003 10398 37443 13328 00733 03782 99697 35936 58030 49917 99 cs a ae erates 1.49182 46976 41270 31782 48529 52837 22228 06432 82773 93742 52815 95633 15 Boceeisaaedees 1. 64872 12707 00128 14684 86507 87814 16357 16537 76100 71014 980115 75079 31 Gio accmaasaces 1. 82211 88003 90508 97487 53676 68162 86451 33822 38808 54643 53863 20547 48 Tec sssieestvaye eetacd 2.01375 27074 70476 52162 45493 88583 06527 00175 42394 14586 73115 68989 30 Boaters 2.22554 09284 92467 60457 95375 31395 07675 70536 34135 04848 45961 18583 96 DQ eccisideisidisndericis 2.45960 31111 56949 66380 01265 63602 47069 54217 72306 44008 30207 48545 74 No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. Taste V.— Values of e~2 ranging from 52 to 62 places of decimals at intervals of unity from 0 to 100. x er 0 1.00000 00000 00000 00000 00000 00000 00000 00000 00000 00000 00 1 0.36787 94411 71442 32159 55237 70161 46086 74458 11131 03176 78 2 . 18583 52832 36612 69189 39994 94972 48440 34076 31545 90957 59 3 .04978 70683 67863 94297 93424 15650 06177 66316 99592 18842 32 4 .01831 56388 88734 18029 37180 21273 24124 22119 12067 55347 56 5 0.00673 79469 99085 46709 66360 48423 14842 42488 49585 02735 51 6 .00247 87521 76666 35842 30451 67430 81666 78915 06479 58553 39 7 .00091 18819 65554 51620 80031 36084 . 40928 26264 73724 52743 61 8 .00033 54626 27902 51183 88213 89125 78086 10193 10900 13372 03 9 .00012 34098 04086 67954 94976 36690 73003 38260 72152 83228 89 10 0.00004 53999 29762 48485 15355 91515 56055 06102 37918 08886 66 il .00001 67017 00790 24565 93126 35517 36058 08790 77938 04695 93 12 -00000 61442 12353 32820 97586 82308 17880 55323 11223 98931 49 13 .00000 22603 29406 98105 43257 85277 29053 86894 69353 14242 27 14 .00000 08315 28719 10356 78840 63985 14256 52622 94607 65836 50 15 0.00000 03059 02320 50182 57883 71479 49770 22896 39370 82078 08 16 .00000 01125 35174 71925 91145 13775 17906 01271 91637 94080 07 17 00000 00413 99377 18785 16665 96510 27718 95528 06229 36694 37 18 00000 00152 29979 74471 26284 36136 62923 35174 31862 17484 33 19 -00000 00056 02796 48753 72675 40012 98281 62064 63079 78387 37 20 0.00000 00020 61153 62243 85578 27965 94038 01558 20976 37580 73 21 00000 00007 58256 04279 11906 72794 17432 41268 12644 29803 62 22 -00000 00002 78946 80928 68924 80771 89130 30644 29320 76931 73 23 .00000 00001 02618 79631 70189 03039 27527 84061 24977 59833 84 24 .00000 00000 37751 34544 27909 77516 44969 54752 34067 79168 61 25 0.00000 00000 13887 94886 49640 20594 66176 37460 86856 91039 98 26 -00000 00000 05109 08902 80633 24719 87440 01934 79215 76659 41 27 -00000 00000 01879 52881 65390 83294 75827 04184 22192 62122 87 28 .00000 00000 00691 44001 06940 20300 94125 84658 74140 92711 82 29 .00000 00000 00254 36656 47376 92291 03033 85614 85768 16666 03 30 0.00000 00000 00093 57622 96884 01746 04915 83222 33787 06744 96 31 -00000 00000 00034 42477 10846 99764 58392 38933 28515 57284 62 32 .00000 00000 00012 66416 55490 94175 72312 09041 55965 09638 21 33 -00000 00000 00004 65888 61451 03397 36418 42455 43610 16841 14 34 - 00000 00000 00001 71390 84315 42012 96630 27203 42576 04924 12 35 0.00000 00000 00000 63051 16760 14698 93856 39021 19224 65427 61 36 .00000 00000 00000 23195 22830 24356 93883 12263 60973 80800 41 37 .00000 00000 00000 08533 04762 57440 65794 27804 98229 41244 17 38 .00000 00000 00000 03139 13279 20480 29628 70896 46522 31919 65 39 .00000 00000 00000 01154 82241 73015 78598 62624 42063 32386 87 40 0.00000 00000 00000 00424 83542 55291 58899 53292 34782 85865 80 41 .00000 00000 00000 00156 28821 89334 98876 80908 82995 10583 41 42 .00000 00000 00000 00057 49522 26429 35598 06664 38088 05734 23 43 . 00000 00000 00000 00021 15131 03759 10804 86631 40100 70226 51 44 .00000 00000 00000 00007 78113 22411 33796 51571 33167 29279 90 45 . 00000 00000 00000 00002 86251 85805 49393 64447 01216 29183 94 46 - 00000 00000 00000 00001 05306 17357 55381 23787 63324 44942 81 47 .00000 00000 00000 00000 38739 97628 68718 71129 31477 49726 91 48 . 00000 00000 00000 00000 14251 64082 74093 51062 85321 02803 41 49 - 00000 00000 00000 00000 05242 88566 33634 63937 17180 53028 32 50 0.00000 00000 00000 00000 01928 74984 79639 17783 01734 28165 27 27 28 MEMOIRS NATIONAL ACADEMY OF SCIENCES. TaBLE V.— Values of e~* ranging from 52 to 62 places of decimals at intervals of unity from 0 to 100—Continued. x e-% X10? 50 0.01928 74984 79639 17783 01734 28165 27012 57475 28 51 .00709 54741 62284 70413 89832 69387 80807 34876 89 52 .00261 02790 69667 70480 47026 95315 33186 48093 16 53 .00096 02680 05450 86760 30230 76967 00074 90907 63 54 . 000385 32628 57220 08070 29735 39281 01772 08837 39 55 0.00012 99581 42500 75030 73600 71340 60714 85530 28 56. .00004 78089 28838 85469 08127 71770 42317 96289 39 57 .00001 75879 22024 24811 64895 58751 28803 43631 78 58 .00000 64702 34925 64546 03261 54039 55292 64893 76 59 - 00000 23802 66408 69440 06058 94824 58880 24963 31 60 0.00000 08756 51076 26965 20338 48873 28007 39166 04 61 . 00000 03221 34028 59925 16089 00124 77758 48943 75 62 00000 01185 06486 42339 81006 28503 07390 97280 99 63 .00000 00435 96100 00063 08097 36231 24815 88845 96 64 . 00000 00160 38108 90548 63785 29760 87034 14233 54 65 0.00000 00059 00090 54159 70613 91401 26029 55584 23 66 .00600 00021 70522 01130 36394 11986 56925 95727 06 67 .00000 00007 98490 42456 86978 80839 26942 66474 24 68 .00000 00002 93748 21117 10802 94660 88806 42392 87 69 -00000 00001 08063 92777 07278 49453 66496 16247 34 70 0.00000 00000 39754 49735 90864 68077 89099 75379 48 71 00000 00000 14624 86227 25123 09468 26378 73083 16 72 -00000 00000 05380 18616 00211 38413 81818 72704 54 73 00000 00000 01979 25987 79469 04553 74919 15336 02 74 .00000 00000 00728 12901 78321 64883 42969 73716 88 75 0.00000 00000 00267 86369 61808 07794 43444 15201 08 76 -00000 00000 00098 54154 68611 12580 28938 09797 36 77 00000 00000 00036 25140 91914 35592 24240 83319 73 78 .00000 00000 00013 33614 81550 22613 41453 01407 91 79 -00000 00000 00004 90609 47306 49280 56613 53873 52 80 0.00000 00000 00001 80485 18878 45415 17231 21283 57 81 -00000 00000 00000 66396 77199 58073 44007 02255 27 82 -00000 00000 00000 24426 00737 74052 76794 40802 61 83 -00000 00000 00000 08985 82594 40493 80669 66884 82 84 .00000 00000 00000 03305 70062 67607 34298 45509 64 85 0.00000 00000 00000 01216 09929 92528 25564 41682 63 86 -00000 00000 00000 00447 37793 06181 12073 46276 56 87 -00000 00000 00000 00164 58114 31082 27365 11660 34 88 . 00000 00000 00000 00060 54601 89540 11858 84531 86 89 .00000 00000 00000 00022 27363 56179 57487 39222 91 90 0.00000 00000 00000 00008 19401 26239 90515 48086 11 91 -00000 00000 00000 00003 01440 87850 65374 55326 31 92 .00000 00000 00000 00001 10893 90193 12136 37945 96 93 .00000 00000 00000 00000 40795 58667 17756 01577 01 94 -00000 00000 00000 00000 15007 85762 70739 48875 45 95 0.00000 00000 00000 00000 05521 08227 70285 32731 72 96 00000 00000 00000 00000 02031 09266 27348 10925 69 97 . 00000 00000 00000 00000 00747 197283 .37342 99016 06 98 .00000 00000 00000 00000 00274 87850 07910 21493 00 99 .00000 00000 00000 00000 00101 12214 92610 44852 99 100 0.00000 00000 00000 00000 00037 20075 97602 08359 63 i [Vou. XIV, No. 6.) TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. TaBLe VI.— Values of e~* ranging from 38 to 48 places of decimals at intervals of 0.1 from 0.0 to 50.0. ez q wo CO IDM PONE OS WOo1H 01 PONE OS OO TD oH LONE S Oorriacn PODH OS WOooO-~ T1091 RON OS OMe RONE OS 1. 00000 0. 90483 . 81873 . 74081 - 67032 0. 60653 . 54881 - 49658 . 44932 - 40656 0. 36787 . 33287 . 30119 . 27253 . 24659 0. 22313 - 20189 . 18268 . 16529 . 14956 0. 13533 » 12245 - 11080 10025 09071 0. 08208 . 07427 - 06720 . 06081 . 05502 0. 04978 . 04504 . 04076 - 03688 . 03337 0. 03019 . 02732 . 02472 . 02237 . 02024 0. 01831 . 01657 . 01499 . 01356 . 01227 0. 01110 - 01005 . 00909 - 00822 . 00744 0. 00673 - 00609 . 00551 . 00499 . 00451 0. 00408 . 00369 . 00334 . 00302 . 00273 00000 74180 07530 82206 00460 06597 16360 53037 89641 96597 94411 10836 42119 17930 69639 01601 65179 35240 88882 86192 52832 64282 31583 88437 79532 49986 35782 55127 00626 32200 70683 92023 22039 31674 32699 73834 37224 35264 07718 19114 56388 26754 55768 85590 73399 89965 18357 52771 97470 65830 79469 67465 65644 15939 65809 67714 78637 59654 75547 94448 00000 35959 77981 81717 35639 12633 94026 91409 17221 40599 71442 98079 12202 34012 41606 48429 94655 52734 21586 22635 36612 52981 62333 22803 89412 23898 14333 39749 25217 56407 67863 93557 78366 01240 60326 22318 47292 70339 56165 45804 88734 01761 20477 12200 03068 38242 44633 01695 49020 70924 99085 65515 20760 06910 42612 38464 16482 57471 45375 - 18768 00000 57316 85866 86606 30074 42360 43262 51470 59143 11188 32159 55328 09664 60312 47693 82893, 40848 65022 53829 05264 69189 91021 88333 73372 50337 79516 88042 76512 96499 22902 94297 80606 21516 00544 07948 50073 56080 39120 59577 38847 18029 24754 70621 93175 44117 30649 58164 81709 02884 34051 46709 63610 77241 21621 66798 06699 93082 27276 81474 36923 00000 42490 99355 68737 44329 37995 84589 48000 01023 34542 55237 88469 49776 23331 98612 32804 51792 39008 68047 10120 39994. 86473 41444 99406 51722 95286 82105 65517 56213 99465 93424 83350 60792 56037 24001 97862 15630 27573 85833 20275 37180 19836 19843 72305 89393 61431 21330 20540 13620 82360 66360 71345 79937 22867 16490 34647 06926 57324 81920 27755 00000 59446 08619 79317 25147 34991 ° 17232 93397 85015 39645 70161 06431 07083 67563 39833 70764 67643 37758 20432 69103 94972 76072 25849 93797 20079 74467 70169 00855 88183 30834 15650 92178 62144 04741 31470 92363 62435 82983 22540 43743, 21273 98083 60228 74525 86236 34286 94331 74291 26766 46420 48423 64785 54667 25942 18705 02684 36441 36020 44595 20842 000 437 039 817 826 180 568 529 563 626 461 316 222 350 768 013 350 940 214 735 484 626 939 987 691 160 975 966 941 175 062 425 515 948 620 553 403 823 654 241 451 729 767 542 931 550 388 074 128 148 425 303 075 780 721 249 607 488 145 29 30 MEMOIRS NATIONAL ACADEMY OF SCIENCES. Taste VI.— Values of e~2 ranging from 88 to 48 places of decimals at intervals of 0.1 from 0.0 to 50.0—Continued. 6.0 6 7. 7 8. 1 2 3 4 5 -6 wh 8 9 0 al 2 3 A 5 6 7 8 9 0 1 2 3 4 8.5 -6 yi -8 a) 9.0 sel: 2 3 4 9.5 -6 7 8 9 10.0 ook 2 3 4 10.5 6 7 -8 a) 11.0 1 12 3 4 11.5 6 7 8 9 Eer-z 0. 00247 - 00224 - 00202 - 00183 - 00166 0. 00150 - 00136 - 00123 - 00111 - 00100 0. 00091 - 00082 . 00074 - 00067 - 00061 0. 00055 - 00050 - 00045 - 00040 - 00037 0. 00033 - 00030 - 00027 . 00024 - 00022 0. 00020 - 00018 - 00016 - 00015 . 00013 0. 00012 - 00011 . 00010 - 00009 - 00008 0. 00007 - 00006 - 00006 - 00005 - 00005 0. 00004 . 00004 . 00003 . 00003 - 00003 0. 00002 - 00002 - 00002 . 00002 . 00001 0. 00001 . 00001 - 00001 - 00001 - 00001 0. 00001 - 00000 - 00000 - 00000 - 00000 87521 28677 94306 63047 15572 34391 03680 09119 37751 77854 18819 51049 65858 55387 12527 30843 04514 28271 97349 07435 54626 35391 46535 85168 48673 34683 41057 65858 07330 63889 34098 16658 10394 14242 27240 48518 77287 12834 54515 01746 53999 10795 71703 36330 04324 75364 49160 25449 03995 84582 67017 51123 36741 23729 11954 01300 91660 82938 75045 67904 76666 35842 19485 80247 36295 73436 77028 90682 73173 93449 92977 57244 37547 89341 02673 48118 47844 80307 29048 51076 65554 51620 23265 90427 08376 67936 75193 84423 61129 57255 70147 83358 33440 61069 82886 79705 78979 78670 40459 08837 27902 51183 38078 86666 69972 14232 27107 95202 24178 84827 69010 64417 93667 57912 10987 63341 75095 47660 26482 01144 04086 67954 08490 11473 01837 09335 31478 17333 65556 63226 29887 70059 36490 85387 95053 22209 99432 17698 82056 17530 29762 48485 55225 30070 18684 12670 95185 71899 83008 40363 49349 74715 09731 50319 37913 21219 03411 17193 33995 78056 00790 24565 23819 85502 96065 68095 24261 78823 84842 59094 93598 63071 87736 24761 19160 75736 57915 07686 04807 37947 30451 32236 33862 52279 90832 73829 68557 46234 87892 14475 80031 01462 80906 78367 56702 31020 55020 79972 84619 44300 88213 08655 76277 08034 27986 43689 49547 14921 06434 78477 94976 56400 07306 78629 27291 14711 29971 55132 18088 21858 15355 84235 45551 37288 65062 78574 62336 44136 64237 47431 93126 79896 33745 05171 36391 07289 44734 50913 33506 30051 67430 16521 58459 36299 54173 03332 63685 76276 19640 35575 36084 25456 47515 24317 29776 00088 35820 07264 67840 21422 89125 09532 89393 74470 33560 33430 76189 30507 06463 65082 36690 85376 72733 43248 71823 89319 88458 40931 77544 33726 91515 23804 91140 28297 22204 11097 14140 71874 54489 58551 35517 87011 88026 26757 53266 41355 00846 52973 65463 67517 817 454 782 895 641 168 588 674 468 166 409 749 335 781 745 530 856 598 934 977 781 761 637 122 487 858 125 915 136 730 178 712 947 338 355 992 438 465 590 561 485 292 935 232 102 627 562 295 471 361 424 747 815 479 749 298 571 934 816 [Vou XIV, No. 5.) TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. TaBLe VI.— Values of e-* ranging from 88 to 48 places of decimals at intervals of 0.1 from 0.0 to 50.0—Continued. eX 10° HK e i - Br ber G er anaes pad tees aR Merry eae a gee i oer Girt: kins LR a casks RwONeE © © CONT SD Ot RwONDeH © © CONT OD Or RONKH OS woorIaca hRWwWNH © ocn~aIrdc hRwWNH © CO 0 ~10) er hRODe- OS ron a 0. 61442 “55595 - 50304 . 45517 - 41185 0. 37266 . 33720 - 30511 . 27607 . 24980 0. 22603 . 20452 . 18506 . 16744 . 15151 0. 18709 . 12404 . 11224 . 10156 . 09189 0. 08315 - 07523 . 06807 . 06160 . 05573 0. 05043 - 04563 . 04129 . 03736 . 03380 0. 03059 . 02767 . 02504 . 02266 . 02050 0. 01855 . 01678 . 01519 . 01374 . 01243 0. 01125 . 01018 . 00921 . 00833 . 00754 0. 00682 . 00617 . 00558 . 00505 . 00457 0. 00413 . 00374 . 00338 . 00306 . 00277 12353 13241 55607 44463 88707 53172 15234 25558 72572 50325 29406 30624 01197 93209 44112 59086 95079 46365 31471 81357 ‘28719 98299 98134 11626 90369 47662 52636 24941 29937 74348 02320 91865 51637 18012 52457 39136 82752 06596 50772 70602 35174 26036 36008 68107 34583 56033 60613 83313 65313 53387 99377 59705 94943 69412 50832 32820 65014 11144 08323 53570 07867 13918 03642 03720 86663 98105 52348 58190 43426 14324 38408 95671 23434 00249 89795 10356 21642 39763 13205 26945 56788 79039 58732 98852 39047 50182 85408 23276 77657 56119 26159 99956 75689 79213 36028 71925 93120 34566 89962 49844 76334 35580 92518 48335 69445 18785 56295 26196 94563 42240 97586 42782 43312 47633 92504. 09929 32115 02182 07929 59687 43257 88517 67532 71792 96163 43645 29562 33766 09180 74280 78840 10566 37737 31394 98049 80758 92229 68861 62858 38111 57883 06275 19971 11644 27503 78240 62558 62781 96984 70065 91145 00088 12805 77760 24816 86975 37163 26353 52410 80493 16665 25069 92178 55723 75246 82308 64691 43226 86288 35497 24851 08762 53527 85038 66158 85277 46920 46783 86875 05769 02599 42723 81407 75395 69218 63985 16958 59450 82053 07658 92222 75634 37841 23297 80934 71479 11062 12378 48865 43940 71710 32695 87087 28825 42338 13775 98479 18330 99947 62940 53833 68288 28123 44488 73240 96510 03124 25752 45060 48379 179 467 772 946 759 476 687 096 819 817 291 038 110 852 581 613 616 425 895 720 143 717 189 038 331 233 380 627 360 638 49770 90303 74692 71008 88106 86473 60836 19027 38479 53941 17906 40768 14487 21871 02631 89689 57083 48887 14372 17735 27718 10250 20721 05384 49380 229 601 052 072 805 493 212 273 717 588 013 981 091 855 941 872 203 751 545 568 955 558 809 994 576 31 32 MEMOIRS NATIONAL ACADEMY OF SCIENCES — Taste VI.— Values of e~* ranging from 33 to 48 places of decimals at intervals of 0.1 from 0.0 to 50.0—Continued. e-=X105 ran NI tb p 1) ra e be = be a ae Es <4 ® & eg 8 sea at @ Ghee ek & Be oan atk ee pa be ee ae te BO ae a eR ee eee BONES OONRDA PBWODHS OBNATMN BPWNHS OORT PWWHO ONWONSOTM AWNHHO CHONATMN PWHHO CHONIHSUHM 3 if i) 2° 22. 22. 23. 0. 00056 . 00050 . 00045 . 00041 . 00037 0. 00033 . 00030 . 00027 - 00025 . 00022 0. 00020 - 00018 . 00016 . 00015 . 00013 0. 00012 - 00011 - 00010 . 00009 - 00008 0. 00007 . 00006 . 00006 . 00005 . 00005 0. 00004 - 00004 . 00003 . 00003 . 00003 0. 00002 . 00002 . 00002 . 00002 . 00001 0. 00001 . 00001 . 00001 - 00001 - 00001 0. 00001 - 00000 . 00000 . 00000 . 00000 09991 . 20459 58322 01939 31730 29979 80655 69252 82646 08960 37449 58390 62984 43271 92047 02796 69619 87181 50653 55666 98267 74879 82266 17498 77927 61153 65008 87529 26940 81632 50152 31185 23538 26136 38002 58256 86098 20807 61729 08274 59905 16139 76538 40706 08283 78946 52401 28382 06648 86983 69189 53089 38520 25338 13411 02618 92853 84017 76021 68787 55743 92773 29760 26691 69673 74471 54894 78575 49549 72359 66197 10137 11826 02221 68266 43753 86232 74664 68769 76593 81949 87958 37101 71943 04120 62243 92190 85750 15912 59107 86638 09177 59775 02205 52694 04279 43996 54094 89244 22551 53786 73942 80736 40224 90131 80928 51068 33123 87892 63804 79226 25478 88603 88086 30933 79631 32670 16438 87409 43627 98180 85882 44687 55236 75730° 26284 57374 09801 66131 76231 05948 46206 51341 79922 40298 72675 22936 75209 82261 82970 60712 66105 58709 82798 53677 85578 27697 85307 66097 95387 67426 16341 94154 67760 79477 11906 93450 03619 17303 05926 52316 24154 11354 29893 38675 68924 45210 61576 07581 26844 15130 79478 13758 06835 74976 70189 14494 85889 60735 13460 35473 20171 85201 15658 08575 36136 37067 76125 01387 78545 97883 26295 18612 76049 69210 40012 08100 98545 54061 51383 25140 71369 84770 60011 29238 27965 33189 37206 18605 89246 28987 53263 25949 50298 46801 72794 45164 76867 97323 15332 77907 70246 32827 53380 51913 80771 21742 64470 80510 64135 36130 29098 75438 66073 68297 03039 21797 17671 66299 03812 43740 05083 69381 41796 95356 62923 27046 51553 32549 44852 17038 28090 28066 65053 94237 98281 57441 73639 18520 03756 73787 28807 56340 88884 72891 94038 22598 62805 61466 35435 55311 71739 62818 19435 25352 17432 74732 91816 90528 48072 05925 73925 62725 54451 32631 89130 73861 64849 04029 94383, 19439 85778 72331 58263 68776 27527 43920 85250 49779 13048 193 212 462 203 349 352 561 128 077 002 460 620 415 096 034 621 536 897 217 200 681 703 891 527 016 761 645 414 639 923 791 845 554 979 413 749 079 550 717 361 373 700 820 879 306 281 105 230 017 206 291 863 954 038 841 867 385 464 694 [Vot. XIV, No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. 115394°—21——3 Taste VI.— Values of e~* ranging from 38 to 48 places of decimals ot intervals of 0.1 from 0.0 to 50.0—Continued. e-=X 10" db bp bo bo iw) bo bp so . @ SS eo 0. 62241 . 56318 - 50958 - 46109 - 41721 0. 37751 . 34158 . 30908 . 27966 . 25305 0. 22897 . 20718 . 18746 - 16962 . 15348 0. 13887 - 12566 . 11370 . 10288 . 09309 0. 08423 . 07621 . 06896 - 06240 . 05646 0. 05109 . 04622 - 04182 . 03784 . 03424 0. 03098 - 02803 . 02537 - 02295 . 02077 0. 01879 . 01700 . 01538 . 01392 . 01259 0. 01139 - 01031 - 00933 - 00844 - 00764 0. 00691 - 00625 . 00566 - 00512 - 00463 0. 00419 . 00379 . 00343 . 00310 . 00281 44622 38950 98614 59744 68910 34544 82993 18748 88455 48361 34845 37765 76334 77294 55167 94386 33126 48673 44186 36717 46375 86519 54882 25543 41661 08902 89492 96830 90624 72479 81913 92750 09852 66168 20058 52881 66800 82804 38919 88584 99185 50728 34638 52673 15939 44001 64079 10320 23135 48609 37956 47032 35894 68402 11852 90778 07427 37956 80822 16002 27909 78385 40832 92692 51189 64555 72088 52428 18406 14253 49640 86023 92667 29702 09030 44686 45129 32212 05624 16749 80633 46686 74887 30743 24915 87218 84414 70981 05623 77241 65390 14814 33968 35884 28277 30443 48906 83457 61639 14129 06940 40031 06637 84304 97992 58379 35298 77640 37543 98789 32321 98158 07815 57885 20720 77516 77078 95528 90452 69970 28940 85115 00712 63987 44644 20594 89591 30575 25556 56681 47405 01041 00165 06152 62792 24719 68940 40238 59536 87477 25441 72566 83277 56169 34158 83294 06878 11670 98620 88967 55345 83550 69077 73721 46027 20300 33604 63070 92092 98618 54442 56414 25514 44761 04044 36689 22576 32879 97649 16549 44969 17927 56856 20914 95413 85224 75223 00483 44513 47610 66176 28573, 06855 66047 48387 87646 86087 51703 61704 72023 87440 73403 10483 01635 54037 64178 40350 48943 40441 48280 75827 50865 38458 87677 69065 31786 57811 84065 35688 61067 94125 79651 77960 59075 53973 52680 35892 74190 24890 93344 302 375 224 739 798 548 744 901 954 063 694 970 363 620 507 37460 24497 57781 29002 57235 52628 42569 34317 36655 10934 01934 07967 40957 97079 63906 60818 61367 37439 23976 41113 04184 79529 16312 77862 98718 95696 58485 71852 85617 13778 84658 20550 29403 13264 63255 72672 66116 24136 39628 23703 869 477 lil 133 814 816 880 985 883 402 792 410 393 765 063 385 907 574 976 052 222 609 667 518 199 403 712 384 335 082 741 275 337 538 792 186 403 674 848 026 33 MEMOIRS NATIONAL ACADEMY OF SCIENCES. [Vou. XIV, Taste VI.— Values of e~2 ranging from 88 to 48 places of decimals at intervals of 0.1 from 0.0 to 50.0—Continued. x e-zX<10!° bo © 0.00254 36656 47376 92291 03033 85614 858 .00230 16038 56719 30252 98961 98444 442 . 00208 25772 91055 50034 41929 59577 002 .00188 43938 58898 98201 66055 82710 392 .00170 50700 73848 97320 95731 68146 459 0.00154 28112 03191 88783 29721 02046 747 .00139 59933 05613 09997 76718 93894 576 -00126 31469 78246 44161 41824 90288 582 -00114 29426 50396 43462 40460 89725 866 .00103 41772 76747 88631 14871 35865 680 0.00093 57622 96884 01746 04915 83222 338 . 00084 67127 40607 93341 71972 67749 165 .00076 61373 70029 83365 22776 85364 170 . 00069 32297 59758 65528 77079 03801 763 . 00062 72602 25925 71015 47054 72075 602 0.00056 75685 23263 27224 61872 78872 381 .00051 35572 387148 02171 53091 68192 004 - 00046 46858 04474 69695 17315 32710 431 - 00042 04651 03518 84753 93216 26484 901 - 00088 04525 58642 21646 74684 33532 907 0.00084 42477 10846 99764 58392 38933 285 . 00081 14882 09847 58694 36580 83265 878 . 00028 18461 87547 13372 67019 06804 197 - 00025 50249 76623 42730 31718 36825 785 . 00023 07561 41382 62290 86183 09083 925 0.00020 87967 91164 59335 50509 88967 622 -00018 89271 49411 56410 78926 37742 140 . 00017 09483 54070 45362 63790 25908 984 00015 46804 67314 60627 92270 38923 531 . 00018 99606 74665 54398 29638 60755 089 0.00012 66416 55490 94175 72312 09041 560 .00011 45901 08570 22324 18777 38161 942 -00010 36854 17971 14108 12572 72255 979 - 00009 38184 45884 98657 78521 57413 808 - 00008 48904 40338 71765 13373 59415 985 0.00007 68120 46852 02094 90674 25977 989 - 00006 95024 14147 63979 20547 50203 795 -00006 28883 84964 61633 73835 11081 070 - 00005 69037 63875 83490 75590 29624 051 - 00005 14886 54781 93836 54103 95285 602 0.00004 65888 61451 03397 36418 42455 436 . 00004 21553 45104 58862 97123 52302 914 . 00003 81487 33620 85080 38776 35563 724 .00003 45138 77443 74206 47237 60762 601 .00003 12294 47752 60511 44037 56739 759 0.00002 82575 72871 15611 21020 28754 875 .00002 55685 09276 69987 34084 22688 697 - 00002 31353 43916 95759 36958 40314 990 .00002 09337 24855 19385 25874 99128 963 . 00001 89416 17547 84879 72752 75933 317 0.00001 71390 84315 42012 96630 27203 426 . 00001 55080 84799 46536 18659 27328 468 . 00001 40322 95408 63094 99211 85099 450 .00001 26969 45946 66347 89949 81449 683 . 00001 14886 71787 32112 48054 47810 798 0.00001 03953 80116 70221 94395 13367 453 - 00000 94061 28904 29918 83443 95415 969 .00000 85110 17391 47948 70615 64947 459 -00000 77010 87001 36544 68253 41936 893 - 00000 69682 31678 38580 11813 28543 327 0.00000 63051 16760 14698 93856 39021 192 oo oo oe ny r -2 S 2 oo fay (oe) oo ww oo oo DS GCOTMAMN PWONH OSD OWONAMN PWNWH OS DHONBAMA PWNHOS OWONATM PWONH SO OCHONBA ROONEY SO OCHONAN PWNS eo » wo oO No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. TaBLe VI.— Values of e~* ranging from 88 to 48 places of decimals at intervals of 0.1 from 0.0 to 50.0—Continued. e~z X10" i wo cw ow oo ow wo wo wo wo ee ee hrc eh chek NEES fac. aeRO Ch caute GEE oly ae ee Wa Gets TE ae A a ea hie Se eS Poe eoggigel oonou PwnNH © oOo PON eH © won mc RwWONEH © woonrImca RwWNH © oom can RwONH © CO CONT SD Or PRwONHS . oO 0. 00156 - 00141 - 00127 - 00115 - 00104 0. 00094 - 00085 - 00077 - 00070 - 00063 0. 00057 - 00052 - 00047 - 00042 - 00038 0. 00034 - 00031 . 00028 - 00025 - 00023 0. 00021 - 00019 - 00017 - 00015 . 00014 0. 00012 - 00011 . 00010 - 00009 . 00008 0. 00007 . 00007 - 00006 - 00005 - 00005 0. 00004 . 00004 - 00003 - 00003 - 00003 0. 00002 - 00002 - 00002 . 00002 - 00001 0. 00001 - 00001 . 00001 - 00001 - 00001 0. 00001 . 00000 - 00000 - 00000 - 00000 0. 00000 - 00000 - 00000 - 00000 . 00000 89334 84892 11846 02638 61103 65350 31351 26781 35171 79932 26429 88056 69328 85360 02888 53199 72062 26026 88318 31066 03759 70686 82726 61177 73448 82360 52529 98886 63809 10626 22411 96064 22595 45417 89220 52715 59159 59178 80895 22876 85805 39215 19931 59215 35866 52831 35055 46589 25085 32052 17357 96620 40279 73213 83911 42293 25341 49819 11388 29515 98876 25895 40038 29407 31040 47559 14917 09860 14588 56898 35598 36486 36896 38765 41921 44467 59800 96901 39275 48315 10804 16334 55584 68999 94625 87848 36166 08059 29842 01859 33796 63864 82837 65886 86203 26123 20617 04557 67763 74373 49393, 04273 52920 10958 91742 00294 40862 30674 64558 95109 55381 13365 52610 50302 89917 05842 07926 61195 78448 91910 80908 04128 13520 39244 88099 45429 47393 09063 95695 16115 06664 16013 66194 82354 20220 34281 09588 02510 69583, 69181 86631 16651 82545 51381 92151 92767 06882 21548 77008 42848 51571 02594 94977 78362 68464 41636 46712 49710 67822 05000 64447 31305 73161 48008 41361 72541 91529 99007 58060 72519 23787 08941 01613 88340 38002 23502 11131 00313 78157 04355 82995 48638 71489 53079 91446 56113 06788 86820 22686 01639 38088 12077 65095 83665 99004 84859 74554 06254 84336 60051 40100 97089 15506 41226 05608 77284 27545 25900 33343 36603 33167 11819 89144 28242 15609 05846 38215 54130 60571 03529 01216 92431 89041 45775 20466 72775 13892 15384 81817 37515 63324 90311 69548 07777 38406 28846 32265 96943 94017 72624 106 316 987 409 531 551 324 825 530 407 057 002 023 338 186 880 002 767 693 823 702 136 796 635 824 128 051 989 029 861 293 481 024 312 422 918 253 889 334 236 292 185 858 273 612 788 163 638 263 872 449 942 955 956 937 869 356 218 572 796 [Vou. XIV, No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. 37 TasLe VI.— Values of e~2 ranging from 88 to 48 places of decimals at intervals of 0.1 from 0.0 to 50.0—Continued. x e-2< 1079 a q 0.38739 97628 68718 71129 31477 497 we . 35053 38011 81874 44181 14696 776 sgarwrenen .31717 60995 95737 66419 90234 132 error acaane . 28699 28030 20923 62903 85594 584 cnnekt UNI . 25968 18268 80355 27517 22837 845 > < 0.23496 98337 45281 70976 26987 584 - 21260 94976 82419 38687 22606 325 - 19237 70289 32882 68879 79646 073 - 17406 99341 49058 66327 58806 721 - 15750 49897 73123 74854 18083 799 0.14251 64082 74093 51062 85321 028 - 12895 41788 90489 43765 81148 006 - 11668 25662 72217 70475 74887 795 - 10557 87519 95563 20838 55106 156 -09553 16053 55124 32778 83159 356 0.08644 05711 30360 94557 72312 023 - 07821 46631 95149 50544 60620 901 -07077 15538 98051 27453 54748 366 - 06403 67500 99505 46535 26327 711 -05794 28476 19450 50254 69685 961 abs oO Oona c PRONE © WOOnNao RWNHO woorsxIaoo RWONE OS ~ 2 0.05242 88566 33634 63937 17180 530 - 04743 95912 66955 45835 05016 148 -04292 61172 74673 23310 79205 757 . 03884 02522 83706 09393 43055 524 . 03514 41135 92253 90440 00963 185 0.03179 97090 01977 49498 18153 259 -02877 35665 87644 17741 59121 756 . 02603 53996 98849 71336 86526 680 - 02355 78038 41041 37407 48630 165 -02131 59824 02125 48791 98821 454 0.01928 74984 79639 17783 01734 282 a © Ss 38 MEMOIRS NATIONAL ACADEMY OF SCIENCES. [Vou. XIV, Tasie VII.— Values of e~* to 63 places of decimals at decimal intervals from 1X10-*° to 9X107. x er 110-9. .| 0.99999 99999 00000 00000 49999 99999 83333 33333 37499 99999 99166 66666 668 Be acwiesiess 99999 99998 00000 00001 99999 99998 66666 66667 33333 33333 06666 66666 756 Bice sicine ote 99999 99997 00000 00004 49999 99995 50000 00003 37499 99997 97500 00001 012 FecveieSes's -99999 99996 00000 00007 99999 99989 33333 33343 99999 99991 46666 66672 356 Bicsscceas 0.99999 99995 00000 00012 49999 99979 16666 66692 70833 33307 29166 66688 368 Cesiacesinicisre 99999 99994 00000 00017 99999 99964 00000 00053 99999 99935 20000 00064 800 Tcalsibiercaeis -99999 99993 00000 00024 49999 99942 83333 33433 37499 99859 94166 66830 068 Siceccnsce 99999 99992 00000 00031 99999 99914 66666 66837 33333 33060 26666 67030 755 Dasara Siossratins -99999 99991 00000 00040 49999 99878 50000 00273 37499 99507 92500 00737 112 1X10-...} 0.99999 99990 00000 00049 99999 99833 33333 33749 99999 99166 66666 68055 556 Jabmsicecisis -99999 99980 00000 00199 99999 98666 66666 73333 33333 06666 66667 55555 9556 Seeaaees ss -99999 99970 00000 00449 99999 95500 00000 33749 99997 97500 00010 12500 000 fe saccionraee .99999 99960 ° 00000 00799 99999 89333 33334 39999 99991 46666 66723 55555 552 Dscsceeeee 0.99999 99950 00000 01249 99999 79166 66669 27083 33307 29166 66883 68055 540 Ci saci recta .99999 99940 00000 01799 99999 64000 00005 39999 99935 20000 00647 99999 944 Tse cisis' eins .99999 99930 00000 02449 99999 42833 33343 33749 99859 94166 68300 68055 392 Ssesioes ane .99999 99920 00000 03199 99999 14666 66683 73333 33060 26666 70307 55555 139 Oe easeises .99999 99910 00000 04049 99998 78500 00027 33749 99507 92500 07381 12499 051 1X10-%.. .| 0.99999 99900 00000 04999 99998 33333 33374 99999 99166 66666 80555 55553 571 Qeasis ecisin’ .99999 99800 00000 19999 99986 66666 67333 33333 06666 66675 55555 55301 587 Oeeceacciss .99999 99700 00000 44999 99955 00000 03374 99997 97500 00101 24999 95660 714 Bes cisciecs . 99999 99600 00000 79999 99893 33333 43999 99991 46666 67235 55555 23047 619 Bus ceiceees 0.99999 99500 00001 24999 99791 66666 92708 33307 29166 68836 80554 00545 636 Gosmescses . 99999 99400 00001 79999 99640 00000 53999 99935 20000 06479 99994 44571 433 Veasensicss .99999 99300 00002 44999 99428 33334 33374 99859 94166 83006 80539 21541 681 Sasccwases . 99999 99200 00003 19999 99146 66668 37333 33060 26667 03075 55513 94539 724 Qo csseuwss .99999 99100 00004 04999 98785 00002 73374 99507 92500 73811 24905 09982 250 1X10-7.. .| 0.99999 99000: 00004 99999 98333 33337 49999 99166 66668 05555 55357 14285 962 Deiniwieisis 0s .99999 98000 00019 99999 86666 66733 33333 06666 66755 55555 30158 73079 365 Dewecscws .99999 97000 00044 99999 55000 00337 49997 :97500 01012 49995 66071 44484 375 Ar ciseinintss 2 .99999 96000 00079 99998 93333 34399 99991 46666 72355 55523 04762 06730 158 Deweecies'es 0.99999 95000 00124 99997 91666 69270 83307 29166 88368 05400 54564 46087 544 ee . 99999 94000 00179 99996 40000 05399 99935 20000 64799 99444 57147 02285 686 W scelsiss 232 . 99999 93000 00244 99994 28333 43337 49859 94168 30068 03921 54180 96428 708 Si scecetee . 99999 92000 00319 99991 46666 83733 33060 26670 30755 51394 54009 86412 329 Dec ccmiasie . 99999 91000 00404 99987 85000 27337 49507 92507 38112 40509 98321 04840 450 1X10-*.. .| 0.99999 90000 00499 99983 33333 74999 99166 66680 55555 35714 28819 44441 689 . 99999 80000 01999 99866 66673 33333 06666 67555 55530 15873 65079 35097 002 . 99999 70000 04499 99550 00033 74997 97500 10124 99566 07159 12945 88616 088 . 99999 60000 07999 98933 33439 99991 46667 23555 52304 76353 01580 07760 430 De ciesem arate 0.99999 50000 12499 97916 66927 08307 29168 83680 40054 57318 01781 49459 812 Gicmestees .99999 40000 17999 96400 00539 99935 20006 47999 44457 18451 42579 42873 806 Cxeiaieisietecels . 99999 30000 24499 94283 34333 74859 94183 00678 92154 30964 27707 40799 293 Besecinnanre . 99999 20000 31999 91466 68373 33060 26703 07551 39454 38435 51856 87773 848 Oo ckes ware .99999 10000 40499 87850 02733 74507 92573 81115 50999 28191 16555 88237 649 1X1078. ..| 0.99999 00000 49999 83333 37499 99166 66805 55535 71431 05158 45458 58134 918 Desc c:cervnd . 99998 00001 99998 66667 33333 06666 75555 53015 87936 50652 55760 14104 217 DO ctectae sees . 99997 00004 49995 50003 37497 97501 01249 56607 30557 98147 33770 08484 782 Bios ccc . 99996 00007 99989 33343 99991 46672 35552 30477 81586 57919 16021 05894 536 0.99995 00012 49979 16692 70807 29188 36790 05466 03727 25662 68892 76375 056 . 99994 00017 99964 00053 99935 20064 79944 45755 94257 94302 37705 19692 856 . 99993 00024 49942 83433 37359 94330 06642 15559 64176 99149 98717 24649 249 . 99992 00031 99914 66837 33060 27030 75139 45812 92328 54757 97343 88835 463 . 99991 00040 49878 50273 37007 93238 10301 00889 04490 41831 39216 07633 246 1X10-4...| 0.99990 00049 99833 33749 99166 68055 53571 45337 27403 02579 34002 74654 599 Dcarrete eric . 99980 00199 98666 73333 06667 55553 01593 65065 25601 41042 16856 39331 863 Saccwieisies = . 99970 00449 95500 33747 97510 12456 60877 00350 46270 04490 77652 95014 129 Seca os . 99960 00799 89334 39991 46723 55230 49244 37220 74750 27202 47629 64868 422 No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. Taste VII.—Values of e~* to 68 places of decimals at decimal intervals from 1X 10- to 9X 10~'—Continued. 39 er 0. 99950 . 99940 . 99930 - 99920 . 99910 0. 99900 - 99800 . 99700 . 99600 0. 99501 . 99401 . 99302 . 99203 . 99104 0. 99004. - 98019 . 97044 . 96078 0. 95122 . 94176 . 93239 - 92311 . 91393 0. 90483 . 81873 . 74081 . 67032 0. 60653 - 54881 - 49658 - 44932 - 40656 01249 01799 02449 03199 04048 04998 19986 44955 79893 24791 79640 44429 19148 03787 98337 86733 55335 94391 94245 45335 38199 63463 11852 74180 07530 82206 00460 06597 16360 53037 89641 96597 79169 64005 42843 14683 78527 33374 67333 03372 43991 92682 53935 33235 37060 72883 49168 06755 48508 52323 00714 84248 05948 86635 71228 35959 77981 81717 35639 12633 94026 91409 17221 40599 27057 39935 33609 73060 33257 99166 06675 97601 47235 31335 26474 10490 63033 66216 05357 30222 17693 20943 00909 70953 22885 78291 18674 57316 85866 86606 30074 42360 43262 51470 59143 11188 29383 20647 95800 30307 99880 80553 55301 20662 23063 25642 44987 47970 98697 45647 39059 08141 25283 92106 14253 71527 79726 07598 73535 42490 99355 68737 44329 37995 84589 48000 01023 34542 66505 94446 51716 13949 17610 57167 65077 34097 86579 46232 72245 31756 00268 74627 77180 04225 51959 91323 19779 83271 32484 49572 46499 59446 08619 79317 25147 34991 17232 93397 85015 39645 55322 13082 84631 55747 49663 65597 95442 56091 47756 50418 22520 01454 87164 71266 03655 30886 19433 24588 65216 14970 96785 38881 52061 43662 03942 81687 82607 18045 56787 52896 56279 62598 50247 93730 76235 14313 11297 47023 67564 07417 69165 53859 14254 93896 93433 41139 77720 62997 34867 60279 06570 60946 43600 00435 02105 11947 43585 21822 19369 34419 53323 17076 59342 78337 26223 94766 05215 50962 83926 55902 61972 74804 28160 08435 35943 51151 59144 11021 79081 12400 36815 72093 87449 88662 68377 83063 85194 05360 91256 51231 80925 18135 11956 67165 14941 03376 02486 25908 89370 82217 91894 36008 92438 89844 35315 97232 49101 39821 20431 68667 25383 46914 52894 71791 34037 54183 74845 14608 82680 98040 26901 99900 21081 48718 69062 71181 27218 17037 90844 96603 76242 88989 32872 20590 30580 71559 78639 32954 19096 82973 49248 32984 74668 40777 36205 65716 31345 92213 73976 64993 97766 09520 56724 63482 21998 69556 80669 62620 44908 81677 35858 96600 29612 57251 95547 52028 58147 07658 52494 07758 12949 32899 41054 92224 83878 25203 32113 23439 30249 74047 05493 87892 63588 56257 - 78028 95310 88910 82892 80712 54711 97989 46288 478 982 618 938 511 637 983 899 993 836 764 925 745 931 634 566 235 459 996 265 317 40 nt TaBLE VIII.— Values of e *360 to 28 places of decimals omsigmipeantfigures- at intervals of unity MEMOIRS NATIONAL ACADEMY OF SCIENCES. ‘rom n=0 to n=860. nT nT n 360 €& 360 0 1.00000 00000 00000 00000 000 1.00000 00000 00000 00000 000 1 -00876 48344 41532 05452 851 0.99131 13203 96706 33089 086 2 -01760 64912 05851 57557 922 . 98269 81339 46661 35321 293 3 .02652 56436 27899 209238 149 .97415 97847 14044 24673 777 4 - 03552 29709 44284 88002 636 . 96569 56224 62250 37866 736 5 1.04459 91583 45014 94512 101 0.95730 50026 04372 64019 161 6 -05375 48970 25672 72888 534 .94898 72861 54113 03484 687 7 - 06299 08842 40056 40824 120 .94074 18396 77120 78035 553 8 .07230 78233 53278 26787 366 .93256 80352 42753 21810 750 9 -08170 64238 95329 35157 955 .92446 52503 76255 85664 364 10 1.09118 74016 15113 60646 067 0.91643 28680 11357 90742 001 11 -10075 14785 34955 62442 319 . 90847 02764 43279 70277 354 12 -11039 93830 05586 13551 147 - 90057 68692 82148 41737 686 13 - 12013 18497 61609 43998 758 . 89275 20454 06818 54556 387 14 . 12994 96199 77457 00326 997 . 88499 52089 19093 61773 205 15 1.13985 34413 23831 47486 813 0.87730 57690 98345 66958 381 16 - 14984 40680 24645 42979 844 . 86968 31403 56529 00825 980 17 . 15992 22609 14459 16864 183 . 86212 67421 93584 84944 480 18 - 17008 87874 96421 95040 967 . 85463 59991 53233 42929 363 19 - 18034 44220 00721 07072 304 . 84721 03407 79150 22453 252 20 1.19068 99454 43543 23648 548 0. 83984 92015 71522 94334 292 21 -20112 61456 86552 72724 323 . 83255 20209 43985 97863 261 22 -21165 38174 96890 87278 267 . 82531 82431 80929 04404 425 23 . 22227 37626 07701 41621 544 .81814 73173 95176 74154 744 24 . 23298 67897 79186 37185 061 . 81103 86974 86035 83770 873 25 1.24379 37148 60197 02755 267 0.80399 18420 97707 05373 653 26 - 25469 53608 50364 78203 834 .79700 62145 78058 20215 764 27 . 26569 25579 62776 54867 601 . 79008 12829 87755 538050 019 28 . 27678 61436 87199 49882 300 - 78321 65198 09750 15963 722 29 . 28797 69628 53859 95957 082 . 77641 14024 09116 53148 702 30 1.29926 58676 97781 32296 996 0.76966 54124 93239 80757 377 31 -31065 37179 23685 86637 747 . 76297 80363 22349 18652 629 32 .82214 13807 71465 42651 469 . 75634 87646 20394 13493 606 33 . 33372 97310 82225 91314 403 .74977 70925 36260 55211 O11 34 . 34541 96513 64910 69197 373 . 74326 25196 05323 91514 228 35 1.35721 20318 63507 91048 389 0.73680 45497 11336 47638 859 36 . 36910 77706 24846 88483 649 . 73040 26910 48645 61087 260 37 - 38110 77735 66988 71089 244 -72405 64560 84740 43636 504 38 . 39321 29545 48216 30761 162 -71776 53615 23123 85388 162 39 - 40542 42354 36629 14676 135 .71152 89282 66507 18112 526 40 1.41774 25461 80347 96890 877 0.70534 66813 80324 57596 608 41 -43016 88248 78334 83212 599 .69921 81500 56564 47140 580 42 -44270 40178 51833 88669 716 . 69314 28675 77915 26761 562 43 . 45534 90797 16438 31638 830 - 68712 03712 82222 55056 820 44 .46810 49734 54788 93452 606 - 68115 02025 27255 13050 927 45 1.48097 26704 89909 97123 524 0.67523 19066 55777 21708 207 46 .49395 31507 59187 63671 005 - 66936 50329 60924 07083 184 47 .50704 74027 88997 09434 472 -66354 91346 51878 49532 865 48 .52025 64237 69983 52692 842 -65778 37688 19845 55425 741 49 .53358 12196 33003 02892 202 65206 84964 04322 92403 513 50 1.54702 28051 25729 10808 292 | 0.64640 28821 59664 31222 960 51 56058 22038 89930 63039 387 .64078 64946 21933 39577 206 52 .57426 04485 30427 09338 494 63521 89060 76045 75468 076 53 68805 85807 38727 16452 016 . 62969 96925 23196 29899 492 54 .60197 76512 82356 47335 368 62422 84336 48569 70885 975 55 1.61601 87201 74880 69865 091 0.61880 47127 89331 42525 659 56 . 63018 28567 11630 04461 975 -61342 81169 02896 76423 722 57 64447 11395 60131 25381 130 .60809 82365 35475 72070 156 58 . 65888 46568 42253 35813 200 .60281 46657 90891 08375 381 59 . 67342 45062 17073 42376 336 .59757 70022 99667 47848 532 {Vou. XIV, No. 5.) TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. ta : TaBLe VIII.—Values of e °° to 23 places of decimals or significant figures at intervals of unity nT from n=0 to n=360—Continued. um, _ tr a ¢ 360 e360 60 1.68809 17949 64468 60061 685 | 0.59238 48471 88388 98366 542 61 . 70288 76400 69440 84226 286 -58723 78050 49322 99127 427 62 .71781 31683 07180 71806 918 . 58213 54839 10307 99458 797 63 . 73286 95163 28876 79556 987 .57707 74952 04903 01162 498 64 - 74805 78307 48277 12786 401 .57206 34537 42796 37068 836 65 1.76337 92682 29009 43812 068 | 0.56709 29776 80471 60448 935 66 . 77883 49955 72666 65104 439 -56216 56884 92128 21891 844 67 . 79442 61898 07664 47944 055 .55728 12109 40855 12193 974 68 .81015 40382 78877 83281 609 .55243 91730 50054 51732 561 69 . 82601 97387 38062 87426 137 .54763 92060 75114 08702 308 70 1.84202 44994 35071 61169 047 0.54288 09444 75325 30485 148 71 . 85816 95392 09865 96987 248 . 53816 40258 86045 74297 510 72 . 87445 60875 85338 35057 029 - 53348 80910 91103 25117 573 73 .89088 53848 60945 74952 191 - 52885 27839 95439 90737 003 74 -90745 86822 07164 56095 507 .52425 77515 97993 65607 591 75 1.92417 72417 60773 26282 571 0.51970 26439 64815 56963 376 76 - 94104 23367 20970 23901 766 .51518 71142 02420 68493 176 77 - 95805 52514 46334 05834 083 -51071 08184 31370 38617 250 78 .97521 72815 52633 59432 218 .50627 34157 60084 32185 175 79 -99252 97340 11495 43450 340 .50187 45682 58879 86159 993 80 2.00999 39272 49936 09324 583 | 0.49751 39409 34237 11586 546 81 -02761 11912 50766 60790 224 -49319 12017 03287 55859 665 82 .04538 28676 53877 16465 121 -48890 60213 68524 31010 739 83 .06331 03098 58409 46730 841 -48465 80735 92732 15419 220 84 - 08139 48831 25824 63003 504 . 48044 70348 74135 38029 032 85 2.09963 79646 83874 44306 209 0.47627 25845 21761 55808 661 86 . 11804 09438 31483 92934 532 .47213 44046 31019 36838 163 87 . 13660 52220 44553 17946 512 - 46803 21800 59488 63036 447 88 . 15533 22130 82686 52209 299 -46396 55984 02920 68158 185 89 . 17422 33430 96857 15796 707 .45993 43499 71447 28291 620 90 2.19328 00507 38015 45655 977 | 0.45593 81277 65996 23676 592 91 . 21250 37872 66649 18648 471 .45197 66274 64911 92236 275 92 . 23189 60166 63304 02318 445 - 44804 95473 50778 96776 722 93 . 25145 82157 40072 75057 055 -44415 65883 87447 29355 240 94 .27119 18742 53061 64705 804 . 44029 74540 97256 77852 204 95 2.29109 84950 15842 62085 369 | 0.43647 18505 88459 81301 115 96 .81117 95940 13899 73442 713 . 43267 94865 22840 02038 712 97 . 33143 67005 20078 83382 137 - 42892 00730 93525 44230 900 98 . 35187 13572 11049 07485 054 -42519 33240 02994 49811 129 99 . 37248 51202 84785 21529 362 .42149 89554 41273 04335 996 100 2.39327 95595 79079 61992 899 | 0.41783 66860 64320 86718 102 101 . 41425 62586 91093 00367 250 - 41420 62369 72605 98238 893 102 . 43541 68150 97953 01718 646 - 41060 73316 89865 07674 338 103 . 45676 28402 78409 85912 539 - 40703 96961 42048 50783 996 104 . 47829 59598 35558 17968 202 - 40350 30586 36448 23819 430 105 2.50001 78136 20634 62130 019 | 0.39999 71498 41007 12101 097 106 .52193 00558 57900 42433 634 | .39652 17027 63807 96093 901 107 . 54403 43552 70618 60808 433 . 39307 64527 32740 78780 699 108 . 56633 23952 08135 32093 526 . 38966 11373 75346 79490 198 109 . 58882 58737 74075 03753 213 . 38627 54965 98837 40681 099 110 2.61151 65039 55659 36560 368 | 0.38291 92725 70286 95517 995 111 . 63440 60137 54159 31073 041 . 37959 22096 96997 45396 697 112 .65749 61463 16490 93361 367 . 37629 40546 07033 97887 229 113 . 68078 86600 67964 42149 403 . 37302 45561 29929 16861 994 114 . 70428 53288 46196 68320 288 . 36978 34652 77555 37864 663 115 2.72798 79420 36197 66593 929 | 0.36657 05352 25163 03051 267 116 .75189 83047 06640 68124 869 . 36338 55212 92583 71303 459 117 . 77601 82377 47327 11784 814 . 36022 81809 25596 60362 966 118 . 80084 95780 07856 00990 098 . 35709 82736 77456 79087 012 119 . 82489 41784 37509 02109 953 . 35399 55611 90584 09151 846 41 42 nT TaBLE VIII.— Values of e380 to 23 places of decimals or significant figures at intervals of unity from n=0 to n=860—Continued. MEMOIRS NATIONAL ACADEMY OF SCIENCES. nT UT n ¢ 300 e360 120 2.84965 39082 26361 49747 413 0.35091 98071 78410 96756 574 121 - 87463 06529 47630 33521 788 34787 07774 07388 16090 274 122 . 89982 63147 01269 50400 604 . 34484 82396 79146 67526 631 123 - 92524 28122 58824 16130 382 .34185 19638 12814 74700 914 124 - 95088 20812 09554 38900 424 . 33888 17216 27488 45804 511 125 2.97674 60741 07839 68042 567 0. 33593 72869 24854 65602 228 126 3.00283 67606 21875 40323 374 . 33301 84354 71964 85837 499 127 -02915 61276 83672 56224 289 .33012 49449 84158 82840 442 128 .05570 61796 40372 28530 512 32725 65951 08136 52293 545 129 . 08248 89384 06886 55561 611 .32441 31674 05177 12239 654 130 3.10950 64436 19876 81476 913 0.32159 44453 34503 86537 070 131 . 13676 07527 93082 16277 217 . 81880 02142 36793 42076 927 132 . 16425 39414 74008 98402 237 .31603 02613 17828 54178 719 133 . 19198 81034 01993 93191 080 . 81328 43756 32292 75671 061 134 . 21996 53506 67652 30931 867 . 31056 23480 67705 86246 376 135 3.24818 78138 73723 98777 048 0.30786 39713 28498 99750 548 136 - 27665 76422 97329 11443 926 . 30518 90399 20228 08131 505 137 . 30537 70040 53645 96356 078 . 80253 73501 33924 41824 435 138 . 334384 80862 61023 39711 728 . 29990 87000 30581 27395 911 139 . 36357 30952 07540 50890 318 . 29730 28894 25775 24304 706 140 3.39305 42565 19026 13629 581 0.29471 97198 74421 23663 566 141 - 42279 38153 28551 03522 967 . 29215 89946 55659 92903 789 142 - 45279 40364 47405 62602 350 . 28962 05187 57876 51253 226 143 . 48305 72045 37576 33084 269 . 28710 40988 63849 61938 250 144 . 51358 56242 85733 63770 467 . 28460 95433 36029 28011 557 145 3.54438 16205 78745 14106 010 0.28213 66622 01942 79690 337 146 . 57544 75386 80726 92511 704 .27968 52671 39727 42063 470 147 . 60678 57444 11646 77322 765 . 27725 61714 63788 72992 081 148 » .63839 86243 27492 80483 585 . 27484 61901 10583 61985 084 149 - 67028 85859 02021 26069 947 . 27245 81396 24526 81780 282 150 3.70245 80577 10097 27735 985 0.27009 08381 44019 85302 330 151 73490 94896 12642 61314 616 . 26774 41053 87601 41601 409 152 . 76764 53529 43204 41037 843 . 26541 77626 40218 05300 877 153 . 80066 81406 96159 20188 329 . 26311 16327 39614 14998 621 154 . 83398 03677 16566 49446 801 . 26082 55400 62840 16975 235 155 3. 86758 45708 91686 38762 187 0.25855 93105 12878 11462 718 156 . 90148 33093 44175 81243 803 . 25631 27715 05383 19620 141 157 . 93567 91646 26978 10358 430 . 25408 57519 55540 70247 661 158 . 97017 47409 19920 74610 667 . 25187 80822 65037 06147 574 159 4.00497 26652 28036 26893 504 24968 95943 09144 10910 763 160 4.04007 55875 81621 38818 691 0.24752 01214 23915 57768 972 161 . 07548 61812 38049 63574 063 . 24536 94983 93494 83007 990 162 * .11120 71428 85352 84208 626 . 24323 75614 37532 87283 989 163 . 14724 11928 47586 97716 905 . 24112 41481 98715 69025 103 164 . 18359 10752 91997 98882 778 . 23902 90977 30399 94932 856 165 4.22025 95584 38003 41550 903 0. 23695 22504 84356 13423 360 166 . 25724 94347 68005 68821 813 . 23489 34482 98618 17666 319 167 - 29456 35212 40053 17615 989 . 23285 25343 85438 65690 883 168 . 33220 46595 02365 17123 644 - 23082 93533 19348 65831 400 169 - 37017 57161 09737 14851 779 . 22882 37510 25321 36583 071 170 4.40847 95827 41842 78299 274 0. 22683 55747 67038 50727 579 171 -44711 91764 23449 34735 479 - 22486 46731 35258 74371 974 172 . 48609 74397 46563 26129 116 . 22291 08960 36287 12320 482 173 . 52541 73410 94522 70973 329 . 22097 40946 80544 71968 532 174 . 56508 18748 68054 39580 576 . 21905 41215 71237 58671 293 175 4.60509 40617 13311 64878 935 0.21715 08304 93124 16295 306 176 . 64545 69487 51911 21830 277 . 21526 40765 01380 27411 572 177 . 68617 36098 12986 37812 013 . 21339 37159 10560 88331 709 178 . 72724 71456 67273 83658 665 . 21153 96062 83657 74925 548 179 - 76868 06842 63252 45548 740 . 20970 16064 21252 15888 956 [Vou. XIV, No. 6.) : TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. nT TaBLe VIII.— Value of e360 to 28 places of decimals or significant figures at intervals of unity Jrom n=o to n=360—Continued. am: im n e 360 e 360 180 4, 81047 73809 65351 65547 304 0.20787 95763 50761 90854 696 181 . 85264 04187 94247 68376 546 - 20607 33773 15781 71456 866 182 . 89517 30086 69266 03886 689 . 20428 28717 65516 24171 015 183 - 93807 83896 52908 51238 967 . 20250 79233 44304 94457 308 184 . 98135 98291 97523 46992 426 - 20074 83968 81237 92433 351 185 5.02502 06233 94138 15608 064 0.19900 41583 79862 00996 409 186 .06906 40972 23471 97348 712 . 19727 50750 07976 28001 825 187 . 11349 36048 09149 85162 220 . 19556 10150 87516 24785 622 188 . 15831 25296 73134 98890 260 . 19386 18480 84525 93994 446 189 . 20352 42849 93400 42046 668 .19217 74445 99217 10355 391 190 5.24913 23138 63859 03458 976 0.19050 76763 56114 78681 754 191 . 29514 00895 56571 83265 967 . 18885 24161 94288 54068 539° 192 . 84155 11157 86254 40114 022 . 18721 15380 57668 49883 602 193 . 38836 89269 77101 73897 017 . 18558 49169 85445 59806 685 194 . 43559 70885 31951 76039 916 . 18397 24291 02555 20809 382 195 |. 5.48323 91971 03807 97136 379 0.18237 39516 10243 44604 271 196 - 53129 88808 69741 99716 920 - 18078 93627 76715 45721 131 197 .57977, 97998 07196 82047 891 . 17921 85419 27864 94992 380 198 . 62868 56459 72711 77144 131 . 17766 13694 38084 27848 651 199 . 67802 01437 83090 49620 933 - 17611 77267 21154 37438 854 200 5.72778 70502 99033 31615 443 0.17458 74962 21213 83197 126 201 - 77799 01555 11255. 57775 134 . 17307 05614 03806 46081 903 202 . 82863 32826 29113 78243 032 -17156 68067 47006 62309 877 203 . 87972 02883 71761 47667 295 .17007 61177 32621 68000 005 204 . 93125 50632 61857 07528 136 - 16859 83808 37470 87729 933 205 5.98324 15319 21845 98509 259 0.16713 34835 24740 00589 333 206 6.03568 36533 72839 59245 528 - 16568 13142 35411 17891 704 207 . 08858 54213 36113 87554 966 . 16424 17623 79767 07278 251 208 . 14195 08645 37250 60212 885 . 16281 47183 28968 98514 529 209 .19578 40470 12944 27450 523 . 16140 00734 06708 06842 675 210 6.25008 90684 20498 18661 514 0.15999 77198 80929 10309 347 211. .. 80487 00643 50033 16278 404 . 15860 75509 55626 18041 887 212 - 36013 12066 39432 75439 813 . 15722 94607 62709 66992 878 213 . 41587 67036 92048 87908 302 - 15586 33443 53943 85216 098 214 - 47211. 08007 97192 09721 086 - 15450 90976 92954 60275 062 215 6. 52883 77804 53430 93262 120 0.15316 66176 47306 51918 782 216 . 58606 19626 94724 85836 308 . 15183 58019 80648 88688 251 217 . 64878. 77054 19415 78406 301 . 15051 65493 44929 88641 365 218 . 70201 94047 22103 09921 242 . 14920 87592 72678 44903 714 219 . 76076 14952 28427 54626 483 . 14791 23321 69353 17267 840 220 6.82001 84504 32789 41895 435 0.14662 71693 05757 71574 243 221 . 87979 47830 39026 80471 041 . 14535 31728 10522 09113 701 222 .94009 50453 04079 81546 502 - 14409 02456 62649 28792 320 223 7.00092 38293 84666 97854 660 - 14283 82916 84126 65298 220 224 .06228 57676 87000 18874 469 . 14159 72155 32601 47001 970 225 7.12418 55332 19564 85403 134 0.14036 69226 94120 17811 747 226 . 18662 78399 48992 10085 391 . 13914 73194 75930 67688 869 227 . 24961 74431 59050 14038 971 . 13793 83129 99347 17009 761 228 .81315 91398 12782 13469 168 . 13673 98111 92677 00436 697 229 .37725 77689 17818 14127 594 . 13555 17227 84208 96431 763 230 7.44191 82118 94888 95642 314 0.13437 39572 95262 49016 520 231 .50714 53929 49569 92130 574 . 13320 64250 33297 28843 804 232 . 57294 42794 47283 00103 068 . 13204 90370 85082 81107 998 233 . 63931 98822 91585 69482 006 . 13090 17053 09927 08276 070 234 . 70627 72563 05775 58586 066 . 12976 43423 32964 36073 612 235 7.773882 15006 17839 59185 504 0.12863 68615 38501 11608 165 236 .84195 77590 48777 23202 201 . 12751 91770 63419 82956 263 237 - 91069 12205 04327 48324 230 . 12641 12037 90640 09980 896 238 . 98002 71193 70129 06724 452 . 12531 28573 42636 56582 583 239 8.04997 07359 10344 19219 860 . 12422 40540 75013 15019 892 20m 5s Tasre VITI.— Values of e *© to 28 places of decimals or significant figures at intervals of unity from n=0 to n=$60—Continued. MEMOIRS NATIONAL ACADEMY OF SCIENCES. nT nT Te nm ¢ 300 ¢ 300 240 8.12052 73966 69776 31584 700 0.12314 47110 70183 13364 153 241 -19170 24748 79512 20337 923 . 12207 47461 30804 57578 317 242 . 26350 13908 66119 52166 269 .12101 40777 74020 60131 364 243 . 33592 96124 64430 92220 258 .11996 26252 24754 07477 529 244 - 40899 26554 33946 11833 666 . 11892 03084 09806 19143 782 245 8.48269 60838 78883 65769 776 0.11788 70479 51708 51579 606 246 - 55704 55106 71914 37891 883 .11686 27651 62678 00330 151 247 - 63204 65978 81608 82193 324 . 11584 73820 38624 54497 323 248 .70770 50572 03631 14405 896 . 11484 08212 53210 57853 367 349 . 78402 66503 95712 37936 932 . 11384 30061 51962 31368 003 250 8.86101 71897 16436 16666 869 0.11285 38607 46432 12303 254 251 . 93868 25383 67870 36172 912 .11187 33097 08411 65419 737 252 9.01702 86109 42078 24232 692 -11090 12783 64195 22224 482 253 -09606 13738 71543 31006 758 . 10993 76926 88893 04573 217 254 . 17578 68458 83541 99102 710 . 10898 24793 00793 89319 680 255 9.25621 10984 58498 83788 916 0.10803 55654 55776 71080 766 256 . 33734 02562 92359 13954 448 . 10709 68790 41770 80559 368 257 -41918 04977 63014 15006 354 .10616 63485 73264 16236 506 258 .50173 80554 00814 45758 072 . 10524 39031 85859 47610 938 259 . 58501 92163 63207 32495 911 . 10432 94726 30877 48527 800 260 9.66903 03229 13534 14816 610 0.10342 29872 70007 19498 038 261 - 75377 77729 04024 49510 263 . 10252 43780 70002 58267 516 262 - 83926 80202 63023 50721 902 10163 35765 97425 38248 614 263 .92550 75754 86489 76864 133 -10075 05150 134383 54778 112 264 10.01250 30061 33801 07274 906 .09987 51260 68614 99512 953 265 10. 10026 09373 27905 84421 191 0.09900 734380 97866 23620 359 266 . 18878 80522 59858 30543 655 .09814 71000 15315 50760 602 267 - 27809 10926 97775 81021 711 .09729 438313 09290 01199 605 268 . 36817 68595 00257 10415 295 . 09644 89720 37326 88724 480 269 - 45905 22131 34300 61111 832 09561 09578 21227 52368 126 270 10.55072 40741 97762 18776 707 0.09478 02248 42154 85279 102 271 - 64319 94239 46392 13375 833 .09395 67098 35773 23400 282 272 . 73648 53048 25491 59412 138 - 09314 03500 87480 56944 153 273 . 83058 88210 06228 84196 705 . 092383 10834 27382 27974 251 274 .92551 71889 26656 28462 535 .09152 88482 26056 77720 981 275 11.02127 74878 37469 39427 194 0.09073 35833 89362 07576 123 276 11787 71603 52549 12522 656 - 08994 52283 54033 18023 577 277 . 21532 35130 04329 74439 212 - 08916 37230 83019 90074 479 278 - 31362 39668 04034 36878 174 . 08838 90080 60914 74082 642 279 . 41278 60078 06820 87478 044 - 08762 10242 89420 51121 503 280 11, 51281 71876 81881 21773 686 0.08685 97132 82857 32406 240 281 . 613872 51242 87537 57770 642 . 08610 50170 63708 62544 664 282 .71551 75022 51379 12769 988 . 08535 68781 58205 92697 753 283 - 81820 20735 55483 60465 906 . 08461 52395 91951 90025 436 284 .92178 66581 26768 25061 373 . 08388 00448 85581 50085 363 285 12.02627 91444 32515 08210 017 0.08315 12380 50460 79142 032 286 . 18168 74900 81115 83997 199 - 08242 87635 84423 13630 715 287 . 23801 97224 28082 36923 751 -08171 25664 67542 44305 263 288 . 34528 39391 87368 57954 636 -08100 25921 57943 12880 954 289 . 45348 83090 48050 54145 018 . 08029 87865 87646 49263 274 290 12. 56264 10722 96411 68161 042 0.07960 10961 58453 17730 730 291 .67275 05414 43480 45175 074 -07890 94677 37861 40714 661 292 . 78382 51018 58068 26138 346 . 07822 38486 55020 69091 440 293 . 89587 32124 05355 88321 175 .07754 41866 96720 68172 576 294 18.00890 34060 91076 96265 160 .07687 04301 03414 88845 924 295 13.12292 42907 11347 68916 485 0.07620 25275 65278 93586 651 296 . 23794 45495 08192 11707 660 . 07554 04282 18303 07319 705 297 . 35397 29418 30813 05730 179 .07488 40816 40418 63376 343 298 - 47101 83038 02658 89895 883 . 07423 34378 47658 15045 833 299 . 58908 95489 94337 16123 604 .07358 84472 90348 83479 756 (Vou. XIV, No. 5.) TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. Taste VIII.— Value of e+36 to 23 places of decimals or significant figures at intervals of unity nT from n=0 to n=860—Continued. nT nT n 360 e300 300 | 13.70819 56691 02426 02113 374 | 0.07294 90608 49339 12960 414 301 . 82834 57346 34235 51186 394 .07231 52298 32258 04796 701 302 94954 88955 98570 53978 601 -07168 69059 69807 01360 509 303 | 14.07181 43822 02548 32482 414 07106 40414 12083 92024 232 304 .19515 15055 54523 33038 599 -07044 65887 24939 13005 305 305 | 14.31956 96583 73173 21391 698 | 0.06983 45008 86363 13366 939 306 44507 83157 02799 79841 590 06922 77312 82905 59665 336 307 57168 70356 34899 53854 180 06862 62337 06125 51972 697 308 . 69940 54600 36058 43239 420 06802 99623 49072 24242 264 309 82824 33152 82226 81168 582 06743 88718 02797 02216 549 310 | 14.95821 04129 99429 92888 587 | 0.06685 29170 52894 92312 725 311 | 15.08931 66508 10970 75002 865 06627 20534 76076 75149 998 312 22157 20130 91181 85629 540 06569 62368 36770 77612 585 313 35498 65717 25783 85622 353 06512 54232 83753 97568 760 314 .48957 04868 78908 21351 505 06455 95693 46812 55591 273 315 | 15.62533 40077 66842 90294 364 | 0.06399 86319 33431 48247 389 316 | .76228 74734 38559 81883 558 06344 25683 25512 77747 710 317 90044 13135 63083 37706 315 - 06289 13361 76122 32962 040 318 | 16.03980 60492 23760 27247 885 | 06234 48935 06264 97027 672 319 - 18039 22937 19490 87927 558 -06180 31987 01687 56990 743 320 | 16.32221 07533 72983 31192 026 | 0.06126 62105 09709 91134 679 321 -46527 22283 46091 69911 820 06073 38880 36083 09861 317 322 60958 76134 62300 76276 270 06020 61907 41875 26199 944 323 75516 78990 36419 33804 977 05968 30784 40384 32297 413 324 90202 41717 11546 01993 393 (05916 45112 94077 57888 523 325 | 17.05016 76153 03370 67490 843 | 0.05865 04498 11557 88910 155 326 19960 95116 51876 11575 491 (05814 08548 44556 20705 151 327 - 35036 12414 80504 30046 591 .05763 56875 84950 25362 667 328 (50243 42852 62855 98504 099 :05713 49095 61809 09020 719 329 | 65584 02240 96979 33333 821 (05663 84826 38463 37113 933 330 | 17.81059 07405 87331 56566 908 | 0.05614 63690 09601 05185 051 331 96669 76197 34463 31140 320 05565 85311 98388 33142 596 332 | 18.12417 27498 32503 91954 067 -05517 49320 53615 61039 295 333 | 28302 81233 74512 57506 306 105469. 55347 46868 24636 339 334 | 44327 58379 65764 66793 056 05422 03027 69721 89207 412 335 | 1860492 80972 45042 96590 118 | 0.05374 91999 30962 20223 646 336 "76799 72118 14003 75195 206 05328 21903 53828 69746 206 337 “93249 56001 74688 70203 097 - 05281 92384 73282 57537 209 338 | 19.09843 57896 75253 89920 315 05236 03090 33298 26082 030 339 | 26583 04174 63988 00603 375 05190 53670 84178 48896 838 340 | 19.43469 22314 51692 24830 545 | 0.05145 43779 79892 71674 436 341 ‘60503 40912 82495 49996 317 05100 73073 75438 65999 091 342 -77686 89693 13178 40155 162 05056 41212 24226 75537 216 343 | 95020 99516 01081 09241 569 05012 47857 75487 34785 287 344 | 20.12507 02389 00669 79061 689 04968 92675 71700 40629 501 345 | 20.30146 31476 68838 11393 295 | 0.04925 75334 46047 57143 187 346 : 47940 21110 79019 70049 959 . 04882 95505 19886 34218 104 347 "65890 06800 44189 35867 752 . 04840 52862 00246 20794 325 348 - 83997 25242 48830 65263 134 04798 47081 77346 53620 544 349 | 21.02263 14331 89948 51294 515 04756 77844 22136 02642 314 350 | 21.20689 13172 27206 15042 175 | 0.04715 44831 83853 54279 980 351 | 39276 62086 42266 24607 222 04674 47729 87610 14020 846 352 58027 02627 07417 09125 285 . 04633 86226 31992 09911 568 353 76941 77587 63565 05900 027 04593 60011 86684 78696 681 354 : 96022 31013 07675 50090 701 04553 68779 90117 16507 855 355 | 22.15270 08210 89744 88342 326 | 0.04514 12226 47126 76165 636 356 "34686 55762 19387 70332 009 04474 90050 26644 93311 316 357 "54273 21532 82122 45426 202 04436 01952 59402 23741 086 358 "74031 54684 65441 65506 596 04397 47637 35653 74467 767 359 | 93963 05686 94751 69532 741 04359 26811 02924 11187 273 360 | 23.14069 26327 79269 00572 909 | 0.04321 39182 63772 24977 442 45 46 MEMOIRS NATIONAL ACADEMY OF SCIENCES. [Vou. XIV, Tasie IX.—Values of e*"™ to 25 places of decimals or significant figures for various values of n. n ett en nt 7/6 39. 06861 33631 89410 86273 103 | 0.02559 92703 67096 25596 73767 13/6 903. 95906 99632 95008 11733 87 .00110 62447 77255 90464 07938 19/6 20918. 23899 06336 20474 74990 .00004 78051 71384 06160 18611 5/4 50. 75401 95117 34935 60233 883 | 0.01970 28729 86617 11028 26839 9/4 1174, 48316 53991 39896 15170 1 .00085 14383 42805 15803 58525 13/4 27178. 35393 28751 52262 56105 . 00003 67939 86952 62379 65643 4/3 65. 94296 52000 64414 66050 359 | 0.01516 46198 64546 56995 25407 7/3 1525. 96588 89887 50315 18599 0 00065 53226 43327 69247 97556 10/3 35311. 90760 51944 42270 60088 .00002 83190 59145 16207 79080 3/2 111. 31777 84898 56226 02684 10 0.00898 32910 21129 42788 96650 5/2 2575.97049 65975 70550 92240 7 . 00038 82032 03926 76624 72325 7/2 59609. 74149 28721 55884 50138 .00001 67757 81524 22578 70825 5/8 187.91462 85023 98509 43960 74 0.00532 15654 78800 58297 30579 8/3 4348. 47465 93769 06427 43192 0 . 00022 99656 95636 20042 96150 11/3 1 00626.71551 40705 19800 4780 .00000 99377 18774 69429 21058 7/4 244.15106 28542 75029 02837 17 0.00409 58248 89350 83589 25536 11/4 5649. 82470 14771 50409 93657 8 .00017 69966 41991 13104 12384 15/4 1 30740. 85684 59666 27285 2389 . 00000 76487 18419 96689 60038 11/6 317. 21714 25286 95191 88997 58 0.00815 24147 52962 28940 00659 17/6 7340. 62439 31050 68162 80074 8 .00013 62281 93468 02216 28376 23/6 1 69867. 13281 35262 43509 0267 . 00000 58869 54017 74846 24408 2 535. 49165 55247 64736 50304 93 0.00186 74427 31707 98881 44302 3 12391. 64780 79166 97481 50654 00008 06995 17570 30459 92392 4 2 86751. 31313 66532 99746 6916 . 00000 34873 42356 20899 54918 5 66 35623. 99934 11342 33266 264 0.00000 01507 01727 53900 64611 6 1535 52935. 39544 66939 22626 2 00000 00065 12412 13607 99007 7 35533 21280. 84704 43596 96468 . 00000 00002 81426 84574 85553 8 8 22263 15585.59499 52749 6691 0.00000 00000 12161 55670 94093 9 190 27738 95292.16129 16866 54 . 00000 00000 00525 54851 76006 10 | 4403 15058 60632.02901 14005 4 . 00000 00000 00022 71101 06832 No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. TasLe X.— Values of sin x and cos x to 28 places of decimals at intervals of unity from 0 to 100. x sin x C08 x 0 0.00000 00000 00000 00000 000 1.00000 00000 00000 00000 000 1 + .84147 09848 07896 50665 250 +0. 54030 23058 68139 71740 094 2 + .90929 74268 25681 69539 602 — .41614 68365 47142 38699 757 3 + .14112 00080 59867 22210 074 — .98999 24966 00445 45727 157 4 — .75680 24953 07928 25137 264 — .65364 36208 63611 91463 917 5 —0.95892 42746 63138 46889 315 +0. 28366 21854 63226 26446 664 6 — .27941 54981 98925 87281 156 + .96017 02866 50366 02054 565 7 + .65698 65987 18789 09039 700 + .75390 22543 48304 63814 120 8 + .98935 82466 23381 77780 812 — .14550 00338 08613 52586 884 9 + .41211 84852 41756 56975 627 — .91113 02618 84676 98836 829 10 —0.54402 11108 89369 81340 475 —0. 83907 15290 76452 45225 886 11 — .99999 02065 50703 45705 156 + .00442 56979 88050 78574 836 12 — .53657 29180 00434 97166 537 + .84885 39587 32492 10465 396 13 + .42016 70368 26640 92186 896 + .90744 67814 50196 21385 269 14 + .99060 73556 94870 30787 535 + .18673 72182 07833 59424 893 15 +0. 65028 78401 57116 86582 974 —0.75968 79128 58821 27384 815 16 — .28790 33166 65065 29478 446 — .95765 94803 23384 64189 964 17 — .96139 74918 79556 85726 164 — .27516 33380 51596 92222 034 18 — .75098 72467 71676 10375 016 + .66031 67082 44080 14481 610 19 + .14987 72096 62952 32975 424 + .98870 46181 86669 25289 835 20 +0.91294 52507 27627 65437 610 +0. 40808 20618 13391 98606 227 21 + .83665 56385 36056 03186 648 — .54772 92602 24268 421388 427 22 — .00885 13092 90403 87592 169 — .99996 08263 94637 12645 417 23 — .84622 04041 75170 63524 133 — .53283 30203 33397 55521 576 24 — .90557 83620 06623 84513 579 + .42417 90073 36996 97593 705 25 —0. 13235 17500 97773 02890 201 +0.99120 28118 63473 59808 329 26 + .76255 84504 79602 73751 582 + .64691 93223 28640 34272 138 27 + .95637 59284 04503 01343 234 — .29213 88087 33836 19337 140 28 + .27090 57883 07869 01998 634 — .96260 58663 13566 60197 545 29 — .66363 38842 12967 50215 117 — .74805 75296 89000 35176 519 30 —0. 98803 16240 92861 78998 775 +0.15425 14498 87584 05071 866 31 — .40403 76453 23065 00604 877 + .91474 23578 04531 27896 244 82 + .55142 66812 41690 55066 156 + .83422 33605 06510 27221. 553 33 + .99991 18601 07267 14572 808 — .01327 67472 23059 47891 522 34 + .52908 26861 20023 82083 249 — .84857 02747 84605 18659 997 35 —0.42818 26694 96151 00440 675 —0. 90369 22050 91506 75984 730 36 — .99177 88534 43115 73683 529 — .12796 36896 27404 68102 833 37 — .64353 81333 56999 46068 567 + .76541 40519 45343 35649 108 38 + .29636 85787 09385 31739 230 + .95507 36440 47294 85758 654 39 -+ .96379 53862 84087 75326 066 + °.26664 29323 59937 25152 683 40 +0. 74511 31604 79348 78698 771 —0. 66693 80616 52261 84438 409 41 — .15862 26688 04708 98710 332 — .98733 92775 23826 45822 883 42 — .91652 15479 15633 78589 899 — .39998 53149 88351 29395 471 43 — .83177 47426 28598 28820 958 + .55511 33015 20625 67704 483 44 -+ .01770 19251 05413 57780 795 + .99984 33086 47691 22006 901 45 +0. 85090 35245 34118 42486 238 +0. 52532 19888 17729 69604 746 46 + .90178 83476 48809 18503 329 — .43217 79448 84778 29495 278 47 + .12357 31227 45224 00406 153 — .99233 54691 50928 71827 975 48 — .76825 46613 23666 79904 497 — .64014 43394 69199 73131 294 49 — .95375 26527 59471 81836 042 + .30059 25437 43637 08368 703 50 —0. 26237 48537 03928 78591 439 +0. 96496 60284 92113 27406 896 51 + .67022 91758 43374 73449 435 + .74215 41968 13782 58946 738 52 + .98662 75920 40485 29658 757 — .16299 07807 95705 48100 333 53 + .39592 51501 81834 18150 339 — .91828 27862 12118 89119: 973 54 — .55878 90488 51616 24581 787 — .82930 98328 63150 14772 785 &5 —0.99975 51733 58619 83659 863 +0.02212 67562 61955 73456 356 56 — .52155 10020 86911 88018 741 + .85322 01077 22584 11396 968 57 + .48616 47552 47824 95908 053 + .89986 68269 69193 78650 300 58 -++ .99287 26480 84537 11816 509 + .11918 01854 48819 28543 584 59 -+- .63673 80071 39137 88077 123 — .77108 02229 75845 229388 744 47 48 TaBle X.—Values of sin x and cos x to 28 é MEMOIRS NATIONAL ACADEMY OF SCIENCES. laces of decimals at intervals of unity from 0 to 100— ontinued. x sin x cos x 60 —0. 30481 06211 02216 70562 565 —0, 95241 29804 15156 29269 382 61 — .96611 77700 08392 94701 829 — .25810 16359 38267 44570 121 62 — .73918 06966 49222 86727 602 + .67350 71623 23586 25288 783 63 + .16735 57003 02806 92152 784 + .98589 65815 82549 69743 864 64 -+ .92002 60381 96790 68335 154 + 39185 72304 29550 00516 171 65 +0. 82682 86794 90103 46771 021 —0.56245 38512 38172 03106 212 66 — .02655 11540 23966 79446 384 — .99964 74559 66349 96483 045 67 — . 85551 99789 75322 25899 683 — .51776 97997 89505 06565 339 68 — .89792 76806 89291 26040 073 + .44014 30224 96040 70593 105 69 — .11478 48137 83187 22054 507 + .99339 03797 22271 63756 155 70 +0. 77389 06815 57889 09778 733 +0. 63331 92030 86299 83233 201 71 + .95105 46532 54374 63665 657 — .30902 27281 66070 70291 749 72 -+ .25382 33627 62036 27306 903 — .96725 05882 73882 48729 171 73 — .67677 19568 87307 62215 498 — .73619 27182 27315 96016 815 74 — .98514 62604 68247 37085 189 + .17171 73418 30777 55609 845 75 —0.38778 16354 09430 438773 094 +0.92175 12697 24749 31639 230 76 + .56610 76368 98180 32361 028 + .82433 13311 07557 75991 501 77 + .99952 01585 80731 24386 610 — .03097 50317 31216 45752 196 78 + .51897 84559 87535 21169 609 — .85780 30932 44987 85540 835 79 — .44411 26687 07508 36850 760 — .89597 09467 90963 14833 703 80 —0. 99388 86539 23375 18973 081 —0.11038 72438 39047 55811 787 81 — .62988 79942 74453 87856 521 + .77668 59820 21631 15768 342 82 + .31322 87824 33085 15263 353 + .94967 76978 82543 20471 326 83 -+- .96836 44611 00185 404385 015 + .24954 01179 73338 12487 735 84 + .73319 03200 73292 16636 321 — .68002 34955 87338 79542 720 85 —0.17607 56199 48587 07696 212 —0. 98437 66433 94041 89491 821 86 — .92345 84470 04059 80260 163 — .38369 84449 49741 84477 893 87 — .8218]1 78366 30822 54487 211 + .56975 03342 65311 92000 851 88 + .03539 83027 33660 68362 543 + .99937 32836 95124 65698 442 89 -+ .86006 94058 12453 22683 685 + .51017 70449 41668 89902 379 90 +0. 89399 66636 00557 89051 827 —0. 44807 36161 29170 15236 548 91 + .10598 75117 51156 85002 021 — .99486 74609 28201 52610 672 92 — .77946 60696 15804 68855 400 — .62644 44479 10339 06880 027 93 — .94828 21412 69947 23213 104 + .31742 87015 19701 64974 551 94 — .24525 19854 67654 32522 044 + .96945 93666 69987 60380 439 95 +0. 68326 17147 36120 98369 958 +0. 73017 35609 94819 66479 352 96 + .98358 77454 34344 85760 773 — .18043 04492 91083 95011 850 97 + .37960 77390 27521 69648 192 — .92514 75365 96413 89170 475 98 — .57338 18719 90422 88494 922 — .81928 82452 91459 25267 566 99 — .99920 68341 86353 69443 272 + .03982 08803 93138 89816 180 100 —0. 50636 56411 09758 79365 656 +0. 86231 88722 87683 93410 194 [Vou. XIV, No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. TaBLe XI.—Values of sin x and cos x to 23 places of decimals at intervals of 0.1 from 0.0 to 10.0. x sin x cos £ 0.0 +0. 00000 00000 00000 00000 000 +1.00000 00000 00000 00000 000 ahs . 09983 34166 46828 15230 681 0.99500 41652 78025 76609 556 2 . 19866 93307 95061 21545 941 . 98006 65778 41241 63112 420 3 . 29552 02066 61339 57510 532 . 95533 64891 25606 01964 231 4 . 38941 83423 08650 49166 631 . 92106 09940 02885 08279 853 0.5 +0. 47942 55386 04203 00027 329 +0. 87758 25618 90372 71611 628 .6 . 56464 24733 95035 35720 095 . 82533 56149 09678 29724 095 it . 64421 76872 37691 05367 261 . 76484 21872 84488 42625 586 .8 - 71735 60908 99522 76162 717 . 69670 67093 47165 42092 075 9 . 78332 69096 27483 38846 138 . 62160 99682 70664 45648 472 1.0 +0. 84147 09848 07896 50665 250 +0. 54030 23058 68139 71740 094 aL . 89120 73600 61435 33995 180 .45359 61214 25577 38777 137 2 . 93203 90859 67226 34967 013 . 36235 77544 76673 57763 837 3 . 96355 81854 17192 96470 135 . 26749 88286 24587 40699 798 4 . 98544 97299 88460 18065 947 .16996 71429 00240 93861 675 1.5 +0.99749 49866 04054 43094 172 +0. 07073 : 72016 67702 91008 819 .6 . 99957 36030 41505 16434 211 — .02919 95223 01288 72620 577 st .99166 48104 52468 61534 613 . 12884 44942 95524 68408 764 .8 . 97384 76308 78195 18653 237 . 22720 20946 93087 05531 667 9 . 94630 00876 87414 48848 971 . 32328 95668 63503 42227 883 2.0 +0. 90929 74268 25681 69539 602 —0.41614 68365 47142 38699 757 -l . 86320 93666 48873 77068 076 . 50484 61045 99857 45162 094 tt . 80849 64038 19590 18430 404 68850 11172 55345 70852 414 .3 . 74570 52121 76720 17738 541 . 66627 60212 79824 19331 788 4 . 67546 31805 51150 92656 577 . 73739 37155 41245 49960 882 2.5 +0. 59847 21441 03956 49405 185 —0. 80114 36155 46933 71483 350 .6 .51550 18718 21464 23525 773 . 85688 87533 68947 23379 770 at .42787 98802 33829 93455 605 . 90407 21420 17061 14798 253 .8 . 33498 81501 55904 91954 385 . 94222 23406 68658 15258 679 .9 . 23924 93292 13982 32818 426 .97095 81651 49590 52178 111 3.0 +0.14112 00080 59867 22210 074 —0. 98999 24966 00445 45727 157 Ll + .04158 06624 33290 57919 470 . 99913 51502 73279 46449 238 -2 — .05837 41434 27579 90913 722 . 99829 47757 94753 08466 166 3 .15774 56941 43248 38201 165 . 98747 97699 08864 88393 659 4 . 25554 11020 26831 31924 990 . 96679 81925 79461 01428 220 3.5 —0. 35078 32276 89619 84812 037 —0. 93645 66872 90796 33769 866 .6 . 44252 04482 94852 38426 673 . 89675 84163 34147 00587 029 .7 . 52983 61409 08493 21321 078 . 84810 00317 10408 15883 567 .8 .61185 78909 42719 07573 359 . 79096 77119 14416 69999 657 .9 .68776 61591 83973 81809 089 . 72593 23042 00140 12937 233 4.0 —0. 75680 24953 07928 25137 ‘264 —0. 65364 36208 63611 91463 917 wk 81827 71110 64410 50426 504 . 57482 39465 33268 91153 503 .2 . 87157 57724 13588 06001 858 . 49026 08213 40699 57765 554 3 .91616 59367 49454 98403 171 .40079 91720 79975 29690 676 4 .95160 207388 89515 95403 539 . 30733 28699 78419 68311 914 4.5 —0.97753 01176 65097 05538 914 —0.21079 57994 30779 70598 048 .6 .99369 10036 33464 45613 810 — .11215 25269 35054 51742 991 Pa .99992 32575 64100 88417 954 — .01238 86634 62890 73715 051 .8 .99616 46088 35840 67178 160 + .08749 89834 39446 56932 022 .9 , 98245 26126 24332 51227 638 . 18651 23694 22575 40449 433 5.0 —0. 95892 42746 63138 46889 315 -++0. 28366 21854 63226 26446 664 all .92581 46823 27732 29694 615 . 37797 77427 12980 56332 058 22 . 88345 46557 20153 26467 308 . 46851 66713 00376 95863 909 3 . 83226 74422 23901 16356 456 . 55437 43361 79160 92944 495 .4 .77276 44875 55987 36235 847 . 63469 28759 42634 36240 675 5.5 —0. 70554 03255 70391 90623 192 +0. 70866 97742 91260 00002 742 .6 .63126 66378 72321 31146 367 .77556 58785 10249 79765 581 wl 55068 55425 97637 76122 735 . 83471 27848 39159 68274 923 .8 46460 21794 13757 21141 823 . 88551 95169 41319 00416 466 .9 . 37387 66648 30236 35981 485 . 92747 84307 44035 74090 610 115394°—20——4 49 MEMOIRS NATIONAL ACADEMY OF SCIENCES. [Vou. XIV, Taste XI.— Values of sin x and cos x to 28 oe of decimals at intervals of 0.1 from 0.0 to 10.0— ontinued. z sin cos x 6. —0. 27941 54981 98925 87281 156 +0. 96017 02866 50366 02054 565 ‘ — .18216 25042 72095 54002 413 . 98326 84384 42584 59658 502 — .08308 94028 17496 57800 058 .99654 20970 28217 47513 940 + .01681 39004 84349 89031 097 . 99985 86363 83415 14228 667 - 11654 92048 50493 28948 042 .99318 49187 58192 65859 474 6. +0. 21511 99880 87815 52429 695 -+0.97658 76257 28023 49988 631 ‘ - 31154 13635 13378 17435 499 . 95023 25919 58529 46621 974 - 40484 99206 16598 16163 219 .91488 31482 35319 44113 790 -49411 33511 38608 32222 208 . 86939 74908 49825 17244 162 . 57843 97643 88199 87017 378 . 81572 51001 25357 07265 676 I: +0. 65698 65987 18789 09039 700 +0. 75390 22543 43304 63814 120 , . 72896 90401 25876 15207 599 . 68454 66664 42806 34062 180 . 79366 78638 49153 05246 445 . 60835 18145 32254 67100 485 . 85048 66206 28564 51751 737 .52607 75173 81105 18891 541 . 89870 80958 11626 75926 950 . 43854 73275 74890 64913 410 +0. 93799 99767 74738 85794 846 +0. 34663 58178 35025 81097 162 - 96791 96720 31486 42590 346 + 25125 98425 82255 38005 815 - 98816 82338 77000 36855 239 + .15337 38620 37864 52597 738 - 99854 33453 74604 96343 877 + .05395 54205 62649 57303 257 ea SF CONOTA PONE S OCONAT PWONH OS ODBNAPST PWNH OS OONON BRWNEOS . 99894 13418 39772 03630 491 — .04600 21256 39536 59449 775 +0. 98935 82466 23381 77780 812 —0. 14550 00338 08613 52586 884 - 96988 98108 45086 24322 432 . 24854 41537 35791 46446 505 . 94073 05566 79772 90115 365 . 33915 48609 83835 20740 049 . 90217 18337 56293 64000 050 . 438137 68449 70620 17370 933 . 85459 89080 88280 66283 324 .51928 86541 16685 29914 480 8. +0. 79848 71126 23490 28666 691 —0. 60201 19026 84823 61534 843 . . 73439 70978 74113 14871 716 . 67872 00473 20012 70086 447 . . 66296 92300 82182. 79220 235 . 74864 66455 97399 15731 879 . 58491 71928 91762 25353 093 . 81109 30140 61655 56288 909 . 50102 08564 57884 98201 617 . 86543 52092 41112 05963 983 9. +0.41211 84852 41756 56975 627 —0.91113 02618 84676 98836 829 i + .31909 83623 49351 77079 400 .94772 16021 31112 02471 907 + .22288 99141 00246 95752 807 . 97484 36214 04163 74194 145 + .12445 44235 07062 40798 941 . 99222 53254 52603 40775 691 + .02477 54254 53358 12107 977 . 99969 30420 35206 47217 795 9. —0.07515 11204 61809 30728 348 —0.99717 21561 96378 47289 160 : - 17432 67812 22979 98512 410 . 98468 78557 94126 91002 034 .27176 06264 10943 12433 774 . 96236 48798 31310 03407 036 . 36647 91292 51927 74816 925 . 93042 62721 04753 51854 938 -45753 58937 75321 04441 382 . 88919 11526 25361 05463 444 10. —0. 54402 11108 89369 81340 475 —0. 83907 15290 76452 45225 886 No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. TaBLe XII,— Values of sin x and cos x to 23 places of decimals at intervals of 0.001 from 0.000 to 1.600. x sin £ cos x 0. 000 0.60000 00000 00000 00000 000 1.00000 00000 00000 00000 000 . 001 . 00099 99998 33333 34166 667 0.99999 95000 00041 66666 528 . 002 .00199 99986 66666 93333 331 - 99999 80000 00666 66657 778 . 003 - 00299 99955 00002 02499 957 . 99999 55000 038374 99898 750 . 004 - 00399 99893 33341 86666 342 - 99999 20000 10666 66097 778 0. 005 0.00499 99791 66692 70831 783 0.99998 75000 26041 64496 529 - 006 - 00599 99640 00064 79994 446 - 99998 20000 53999 93520 004 . 007 - 00699 99428 33473 39150 327 - 99997 55001 00041 50326 542 . 008 . 00799 99146 66939 73291 723 - 99996 80001 70666 30257 819 . 009 - 00899 98785 00492 07405 100 . 99995 95002 73374 26188 857 0. 010 0.00999 98333 34166 66468 254 0.99995 00004 16665 27778 026 -O11 -01099 97781 68008 75446 684 - 99993 95006 10039 20617 059 . 012 -01199 97120 02073 59289 053 - 99992 80008 63995 85281 066 -013 01299 96338 36427 42921 659 .99991 55011 90034 96278 551 .014 -01399 95426 71148 51241 801 - 99990 20016 00656 20901 438 0. 015 0.01499 94375 06328 09109 944 0.99988 75021 09359 17975 106 . 016 -01599 93173 42071 41340 585 - 99987 20027 30643 36508 430 .017 .01699 91811 78498 72691 726 - 99985 55034 80008 14243 829 - 018 01799 90280 15746 27852 832 - 99983 80043 73952 76107 331 . 019 01899 88568 53967 31481 205 . 99981 95054 29976 32558 650 0. 020 0.01999 86666 93333 07936 649 0.99980 00066 66577 77841 270 . 021 02099 84565 34033 81764 335 . 99977 95081 03255 88182 556 . 022 -02199 82253 76279 77175 771 -99975 80097 60509 19593 878 . 023 .02299 79722 20302 18277 769 .99973 55116 59836 06320 750 . 024 . 02399 76960 66354 28999 311 .99971 20188 23734 58193 002 0. 025 0.02499 73959 14712 33066 217 0.99968 75162 75702 58624 967 . 026 .02599 70707 65676 53973 517 - 99966 20190 40237 62215 698 . 027 -02699 67196 19572 14955 411 - 99963 55221 42836 92299 214 . 028 .02799 63414 76750 38952 746 . 99960 80256 09997 38394 779 . 029 02899 59353 37589 48577 881 . 99957 95294 69215 58557 207 0. 030 0.02999 55002 02495 66076 853 0.99955 00337 48987 51627 216 . 031 . 08099 50350 71904 13288 752 - 99951 95384 78809 04381 810 . 032 .03199 45389 46280 11602 188 - 99948 80436 89175 38584 710 - 033 . 03299 40108 26119 81908 762 - 99945 55494 11581 32936 824 . 034 .038399 34497 11951, 44553 435 . 99942 20556 78521 14926 773 0. 035 0.03499 28546 04336 19281 702 0.99938 75625 23488 57581 460 . 036 08599 22245 03869 25183 461 - 99935 20699 80976 76116 700 . 037 .03699 15584 11180 806383 489 - 99931 55780 86478 24487 902 . 038 .03799 08553 26937 03228 414 - 99927 80868 76484 91840 819 . 039 .08899 01142 51841 09720 085 - 99923 95963 88487 98862 358 0. 040 0.03998 93341 86634 15945 255 0.99920 01066 60977 94031 457 . 041 . 04098 85141 32096 36751 449 -99915 96177 33444 49770 040 - 042 .04198 76530 89047 85918 946 -99911 81296 46376 58494 043 . 043 .04298 67500 58349 76078 755 .99907 56424 41262 28564 524 . 044 .04398 58040 40905 18626 492 . 99903 21561 60588 80138 853 0. 045 0.04498 48140 37660 23632 066 0.99898 76708 47842 40921 992 . 046 .04598 37790 49604 99745 054 - 99894 21865 47508 41817 869 . 047 .04698 26980 77774 54095 689 - 99889 57033 05071 12480 849 . 048 .04798 15701 23249 92191 340 . 99884 82211 67013 76767 299 . 049 .04898 03941 87159 17808 403 . 99879 97401 80818 48087 272 0. 050 0.04997 91692 70678 32879 487 0.99875 02603 94966 24656 287 . O51 .05097 78943 75032 37375 800 - 99869 97818 58936 84647 237 . 052 .05197 65685 01496 29184 649 . 99864 83046 23208 81242 407 . 053 05297 51906 51396 03981 925. . 99859 58287 39259 37585 623 . 054 .05397 37598 26109 55099 505 . 99854 23542 59564 41634 531 0. 055 0.05497 22750 27067 73387 446 0.99848 78812 37598 40913 005 . 056 .05597 07352 55755 47070 891 . 99843 24097 27834 37163 704 . 057 .05696 91895 13712 61601 567 . 99837 59397 85743 80900 770 . 058 .05796 74868 02534 99503 794 .9983L 84714 67796 65862 676 . 059 .05896 57761 23875 40214 896 . 99826 00048 31461 23365 235 51 52 Taste XII.—Values of sin x and cos x to 28 places of decimals at intervals of 0.001 from 0.000 MEMOIRS NATIONAL ACADEMY OF SCIENCES. to 1.600—Continued. x sine cos x 0. 060 0.05996 40064 79444 59919 909 0.99820 05399 35204 16554 766 . 061 .06096 21768 71012 31380 500 99814 00768 38490 34561 437 . 062 -06196 02863 00408 23757 982 -99807 86156 01782 86552 769 . 063 . 06295 83337 69523 02480 343 /99801 61562 86542 95687 334 . 064 . 06395 63182 80309 28803 166 -99795 26989 55229 92968 628 0. 065 0.06495 42388 34782 60114 361 0.99788 82436 71301 10999 144 . 066 06595 20944 35022 49232 601 .99782 27904 99211 77634 635 . 067 06694 98840 83173 44449 361 .99775 63395 04415 09538 592 . 068 . 06794 76067 81445 89264 458 .99768 88907 53362 05636 926 . 069 . 06894 52615 32117 22165 004 .99762 04443 13501 40472 866 0. 070 0.06994 28473 37532 76397 655 0.99755 10002 53279 57462 091 . O71 07094 038632 00106 79734 071 .99748 05586 42140 62048 084 . 072 .07193 78081 22323 54229 480 .99740 91195 50526 14757 726 . 073 .07293 51811 06738 15974 250 . 99733 66830 49875 24157 139 . 074 . 07393 24811 55977 74838 360 .99726 32492 12624 39707 777 0. 075 0.07492 97072 72742 34208 684 0.99718 88181 12207 44522 774 . 076 .07592 68584 59805 90718 980 .99711 33898 23055 48023 568 077 .07692 39337 20017 33972 485 .99703 69644 20596 78496 785 . 078 07792 09320 56301 46257 015 .99695 95419 81256 75551 417 079 .07891 78524 71660 02252 478° .99688 11225 82457 82476 279 0. 080 0.07991 46939 69172 68730 688 0.99680 17063 02619 38497 771 ', 081 08091 14555 51998 04247 389 . 99672 12932 21157 70937 933 . 082 08190 81362 23374 58826 394 .99663 98834 18485 87272 823 . 083 -08290 47349 86621 73635 718 .99655 74769 76013 67091 212 . 084 . 08390 12508 45140 80655 638 .99647 40739 76147 53953 598 0. 085 0.08489 76828 02416 02338 544 0.99638 96745 02290 47151 570 . 086 08589 40298 62015 51260 514 . 99630 42786 38841 93367 506 - 087 . 08689 02910 27592 29764 492 . 99621 78864 71197 78234 626 . 088 .08788 64653 02885 29594 973 .99613 04980 85750 17797 412 . 089 . 08888 25516 91720 31524 112 . 99604 211385 69887 49872 388 0. 090 0.08987 85491 98011 04969 125 0.99595 27330 11994 25309 284 . 091 .09087 44568 25760 07600 919 . 99586 23565 01450 99152 586 . 092 . 09187 02735 79059 84943 819 .99577 09841 28634 21703 483 . 093 09286 59984 62093 69966 323 . 99567 86159 84916 29482 217 . 094 -09386 16304 79136 82662 751 . 99558 52521 62665 36090 844 0. 095 0.09485 71686 34557 29625 724 0.99549 08927 55245 22976 426 . 096 .09585 26119 32817 03609 347 . 99539 55378 57015 30094 649 . 097 . 09684 79593 78472 83083 006 . 99529 91875 63330 46473 881 . 098 .09784 32099 76177 31775 683 . 99520 18419 70541 00679 686 . 099 . 09883 83627 30679 98210 683 .99510 35011 75992 51179 796 0.100 0.09983 34166 46828 15230 681 0.99500 41652 78025 76609 556 -101 -10082 83707 29567 99512 975 . 99490 38343 75976 65937 840 -102 10182 32239 83945 51074 864 . 99480 25085 70176 08533 469 - 103 .10281 79754 15107 52769 040 .99470 01879 61949 84132 117 - 104 - 10381 26240 28302 69768 897 . 99459 68726 53618 52703 737 0.105 0.10480 71688 28882 49043 655 0.99449 25627 48497 44220 501 . 106 -10580 16088 22302 18823 209 . 99438 72583 50896 48325 268 .107 . 10679 59430 14121 88052 588 - 99428 09595 66120 03900 596 . 108 -10779 01704 10007 45835 941 .99417 36665 00466 88538 307 .109 .10878 42900 15731 60869 939 . 99406 53792 61230 07909 607 0.110 0.10977 83008 37174 80866 495 0.99395 60979 56696 850385 784 .li1 -11077 22018 80326 31964 714 . 99384 58226 96148 49459 483 .112 -11176 59921 51285 18131 952 .99373 45535 89860 26316 578 -113 .11275 96706 56261 20553 909 . 99362 22907 49101 25308 652 114 .11375 32364 01575 97013 636 . 99350 90342 86134 29576 080 0.115 0.11474 66883 93663 81259 372 0.99339 47843 14215 84471 755 .116 .11574 00256 39072 82361 097 . 99327 95409 47595 86235 439 .117 .11673 32471 44465 84055 722 .99316 33043 01517 70568 768 -118 .11772 63519 16621 44080 790 . 99304 60744 92218 01110 921 .119 .11871 93389 62434 93496 613 .99292 78516 36926 57814 950 {Vou. XIV, No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. TaBLeE XII.— Values of sin x and cos x to 28 places of decimals at intervals of 0.001 from 0.000 to 1.600 —Continued. x sin & cos & 0.120 0.11971 22072 88919 35996 735 0.99280 86358 53866 25224 810 .121 -12070 49559 03206 47206 615 .99268 84272 62252 80653 067 . 122 .12169 75838 12547 73970 447 .99256 72259 82294 82259 329 - 123 . 12269 00900 24315 33626 003 . 99244 50321 35193 57029 382 .124 .12368 24735 46008 13267 407 . 99232 18458 48142 88655 070 0.125 0.12467 47333 85227 68995 744 0.99219 76672 29329 05314 910 .126 . 12566 68685 49729 25157 389 .99207 24964 17930 67355 462 .127 . 12665 88780 47372 73569 978 -99194 63335 34118 54873 474 . 128 -12765 07608 86148 72735 909 .99181 91787 04055 55198 803 . 129 . 12864 25160 74174 47043 273 -99169 10320 54896 50278 123 0.130 0.12963 41426 19694 85954 121 0.99156 18937 14788 03959 451 .1381 - 13062 56395 31083 43179 968 .99143 17638 12868 49177 481 . 132 - 13161 70058 16843 35844 483 - 99130 06424 79267 75039 751 .133 - 13260 82404 85608 43632 907 .99116 85298 45107 13813 659 . 134 . 13359 93425 46144 07929 171 .99103 54260 42499 27814 325 0.135 0.13459 03110 07348 30938 844 0.99090 138312 04547 96193 339 . 136 .18558 11448 78252 74799 575 .99076 62454 65348 01628 375 .137 .13657 18431 68023 60677 867 . 99063 01689 59985 16913 714 . 138 .18756 24048 85962 67852 453 .99049 31018 24535 91451 667 . 139 .18855 28290 41508 32784 107 .99035 50441 96067 37644 937 0. 140 0.13954 31146 44236 48171 799 0.99021 59962 12637 17189 895 .141 -14053 32607 03861 61995 092 -99007 59580 13293 27270 829 .142 -14152 32662 30237 76542 691 .98993 49297 38073 86655 145 .148 . 14251 313802 33359 47427 025 .98979 29115 28007 21689 546 .144 . 14850 28517 23362 82584 791 . 98964 99035 25111 52197 214 0.145 0.14449 24297 10526 41263 332 0.98950 59058 72394 77275 984 . 146 . 14548 18632 05272 32992 773 . 98936 09187 13854 60997 551 .147 .14647 11512 18167 16543 800 .98921 49421 94478 18007 704 . 148 .14746 02927 59922 98870 997 . 98906 79764 60241 99027 617 . 149 . 14844 92868 41398 34041 627 -98892 00216 58111 76256 193 0. 150 0.14943 81324 73599 22149 773 0.98877 10779 36042 28673 498 .151 .15042 68286 67680 08215 725 . 98862 11454 42977 27245 283 . 152 .15141 53744 34944 81070 5382 - 98847 02243 28849 20028 611 . 153 .15240 37687 86847 72225 604 . 98831 83147 44579 17178 614 . 154 .15339 20107 34994 54727 267 .98816 54168 42076 75856 382 0. 155 0.15438 00992 91143 41996 190 0.98801 15307 74239 85038 006 . 156 .15536 80334 67205 86651 555 -98785 66566 94954 50224 794 . 157 .15635 58122 75247 79319 902 .98770 07947 59094 78054 663 .158 .15734 34847 27490 47428 529 . 98754 39451 22522 60814 736 . 159 . 15833 08998 36311 53983 354 . 98788 61079 42087 60855 150 0.160 0.15931 82066 14245 96331 146 0.98722 72833 75626 94904 095 .161 .16030 53540 73987 04906 020 .98706 74715 81965 18284 099 . 162 .16129 23412 28387 41960 095 .98690 66727 20914 09029 574 . 163 .16227 91670 90460 00278 226 - 98674 48869 53272 51905 638 . 164 .16326 58306 73379 01876 705 .98658 21144 40826 22328 234 0.165 0.16425 23309 90480 96685 825 0.98641 83553 46347 70185 554 .166 .16523 86670 55265 61216 228 .98625 36098 33596 03560 791 . 167 .16622 48378 81396 97208 916 . 98608 78780 67316 72356 233 - 168 . 46721 08424 82704 30268 843 . 98592 11602 138241 51818 712 .169 .16819 66798 73183 08481 981 .98575 34564 38088 25966 434 0.170 0.16918 23490 66996 01015 762 0.98558 47669 09560 70917 193 171 .17016 78490 78473 96702 805 . 98541 50917 96348 38117 998 .172 .17115 31789 22117 02607 812 .98524 44312 68126 37476 124 173 .17213 83376 12595 42577 560 . 98507 27854 95555 20391 598 » 174 .17312 33241 64750 55773 865 . 98490 01546 50280 62691 158 0.175 0.17410 81375 93595 95189 433 0.98472 65389 04933 47463 670 .176 .17509 27769 14818 26146 505 . 98455 19384 33129 47797 052 -177 .17607 72411 42278 24778 176 . 98487 63534 09469 09416 699 -178 .17706 15292 93011 76492 317 . 98419 97840 09537 33225 448 .179 .17804 56403 82230 74417 975. . 98402 22304 09903 57745 046 53 MEMOIRS NATIONAL ACADEMY OF SCIENCES. [Vou. XIV, Tasie XII.— Values of sin x and cos x to 23 places of decimals at intervals of 0.001 from 0.000 to 1.600—Continued. x sin z cos x 0.180 0.17902 95734 25824 17834 180 0.98384 36927 88121 41459 272 181 .18001 33274 39859 10581 029 .98366 41713 22728 45058 522 182 .18099 69014 40581 59452 980 98348 36661 93246 13586 083 .183 .18198 02944 44417 72574 233 .98330 21775 80179 58485 974 . 184 .18296 35054 67974 57756 116 .98311 97056 65017 39552 448 0. 185 0.18394 65335 28041 20836 370 0.98293 62506 302381 46781 122 186 .18492 93776 41589 64000 231 .98275 18126 59276 82121 799 .187 . 18591 20368 25775 84083 224 .98256 63919 36591 41132 959 188 . 18689 45100 97940 70855 554 .98237 99886 47595 94537 971 189 .18787 67964 75611 05288 013 98219 26029 78693 69683 022 0. 190 0.18885 88949 76500 57799 285 0.98200 42351 17270 31896 788 191 . 18984 08046 18510 86484 571 .98181 48852 51693 6575] 875 .192 .19082 25244 19732 35325 424 .98162 45535 71313 56228 034 193 .19180 40533 98445 32380 691 .98143 32402 66461 69777 178 194 .19278 53905 73120 87958 485 98124 09455 28451 35290 214 0.195 0.19376 65349 62421 92769 058 0.98104 76695 49577 24965 723 196 .19474 74855 85204 16058 510 .98085 34125 283115 35080 479 197 .19572 82414 60517 03723 204 .98065 81746 48322 66661 867 .198 .19670 88016 07604 76404 820 .98046 19561 05437 06062 170 199 .19768 91650 45907 27565 917 98026 47571 05677 05434 796 0. 200 0.19866 93307 95061 21545 941 0.98006 65778 41241 63112 420 201 . 19964 92978 74900 91597 545 .97986 74185 10310 03887 090 . 202 . 20062 90653 05459 37903 151 .97966 72793 12041 59192 306 . 208 . 20160 86321 06969 25571 640 .97946 61604 46575 47187 084 . 204 . 20258 79972 99863 82615 083 .97926 40621 15030 52742 047 0. 205 0.20356 71599 04777 97905 397 0.97906 09845 19505 07327 536 . 206 .20454 61189 42549 19110 856 .97885 69278 63076 68803 784 . 207 . 20552 48734 34218 50612 330 .97865 18923 49802 01113 156 . 208 . 20650 34224 01031 51399 175 . 97844 58781 84716 53874 491 . 209 . 20748 17648 64439 32944 665 . 97823 88855 73834 41879 553 0. 210 0.20845 98998 46099 57060 871 0.97803 09147 24148 24491 614 271 . 20943 78263 67877 33732 895 . 97782 19658 43628 84946 201 212 .21041 55434 51846 18932 346 . 97761 20391 41225 09554 014 213 . 21139 30501 20289 12409 982 .97740 11348 26863 66806 -039 214 . 21237 03453 95699 55467 398 .97718 92531 11448 86380 882 0. 215 0.21334 74283 00782 28707 677 0.97697 63942 06862 38054 344 216 . 21432 42978 58454 49764 905 .97676 25583 25963 10511 247 217 . 21530 09530 91846 71012 439 . 97654 77456 82586 90059 555 218 . 21627 73930 24303 77249 851 . 97633 19564 91546 39246 782 219 .21725 36166 79385 83368 434 .97611 51909 68630 75378 786 0. 220 0.21822 96230 80869 31995 179 0.97589 74493 30605 48940 602 221 .21920 54112 52747 91115 124 .97567 87317 95212 21920 392 . 222 . 22018 09802 19233 51671 977 .97545 90385 81168 46034 788 . 223 .22115 63290 04757 25146 920 . 97523 83699 08167 40857 388 224 . 22218 14566 33970 41115 484 .97501 67259 96877 71849 392 0. 225 0.22310 63621 31745 44782 417 0.97479 41070 68943 28292 737 . 226 . 22408 10445 23176 94494 428 .97457 05133 46983 01125 708 227 . 22505 55028 33582 59230 720 . 97434 59450 54590 60681 052 . 228 . 22602 97360 88504 16071 214 .97412 04024 16334 34326 607 . 229 .22700 37433 13708 47642 363 . 97389 38856 57756 84008 477 0. 230 0.22797 75235 35188 39540 462 0.97366 63950 05374 83696 773 . 231 . 22895 10757 79163 77782 354 . 97343 79306 86678 96733 940 . 232 . 22992 43990 72082 45933 437 . 97320 84929 30133 53085 695 . 233 . 23089 74924 40621 22962 869 .97297 80819 65176 26494 602 . 234 . 23187 03549 11686 80075 884 .97274 66980 22218 11536 294 0. 235 0. 23284 29855 12416 78273 112 0.97251 48413 32643 00578 389 . 236 . 23381 53832 70180 65586 809 . 97228 10121 28807 60642 091 . 237 .23478 75472 12580 74343 904 . 97204 67106 44041 10166 529 . 238 .23575 94763 67453 18405 752 . 97181 14371 12644 95675 843 . 239 . 23673 11697 62868 90384 520 .97157 51917 69892 68349 034 No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. 5D TaBLe XII.— Values of sin x and cos x to 23 places of decimals at intervals of 0.001 from 0.000 to 1.600—Continued. x sin x cos x 0. 240 0.23770 26264 27134 58836 079 0.97133 79748 52029 60492 618 . 241 . 23867 38453 88793 65429 334 .97109 97865 96272 61916 095 . 242 - 23964 48256 76627 22091 869 .97086 06272 40809 96210 262 . 243 - 24061 55663 19655 08131 828 . 97062 04970 24800 96928 391 . 244 . 24158 60663 47136 67335 933 . 97087 93961 88375 83670 294 0. 245 0.24255 63247 88572 05043 522 0.97013 73249 72635 38069 313 . 246 . 24352 63406 78702 85196 546 . 96989 42836 19650 79682 233 . 247 . 24449 61130 32513 27365 389 . 96965 02723 72463 41782 166 . 248 . 24546 56408 95231 03750 445 . 96940 52914 75084 47054 425 . 249 . 24643 49232 92328 36159 337 96915 93411 72494 83195 397 0. 250 0.24740 39592 54522 92959 685 0.96891 24217 10644 78414 459 . 251 . 24837 27478 12778 86007 332 - 96866 45333 36453 76838 955 . 252 - 24934 12879 98307 67549 922 . 96841 56762 97810 13822 250 . 253 - 25030 95788 42569 27105 742 . 96816 58508 43570 91154 897 - 254 .25127 76193 77272 88317 722 . 96791 50572 23561 52178 941 0. 255 0.25224 54086 34878 05782 506 0.96766 32956 88575 56805 375 . 256 . 25321 29456 46095 61854 486 . 96741 05664 90374 56434 780 . 257 - 25418 02294 44888 63424 714 . 96715 68698 81687 68781 180 . 258 . 25514 72590 63473 38674 587 . 96690 22061 16211 52599 126 . 259 - 25611 40335 34820 33804 209 . 96664 65754 48609 82314 035 0. 260 0.25708 05518 92155 09735 339 0.96638 99781 34513 22555 824 . 261 . 25804 68131 68959 38788 820 96613 24144 30519 02595 835 . 262 - 25901 28163 98972 01336 401 . 96587 38845 94190 90687 131 - 263 . 25997 85606 16189 82426 844 . 96561 43888 84058 68308 107 . 264 . 26094 40448 54868 68386 239 . 96535 39275 59618 04309 520 0. 265 0.26190 92681 49524 43392 399 0.96509 25008 81330 28964 923 . 266 . 26287 42295 34933 86023 278 . 96483 01091 10622 07924 537 . 267 . 26383 89280 46135 65779 278 . 96456 67525 09885 16072 584 . 268 . 26480 33627 18431 39579 372 . 96430 24313 42476 11288 118 . 269 . 26576 75325 87386 48230 942 . 96403 71458 72716 08109 368 0. 270 0.26673 14366 88831 12873 229 0.96377 08963 65890 51301 623 .271 . 26769 50740 58861 31394 301 . 96350 36830 88248 89328 696 . 272 .- 26865 84437 33839 74821 451 . 96323 55063 07004 47727 972 . 273 . 26962 15447 50396 83684 915 . 96296 63662 90334 02389 084 . 274 .27058 48761 45431 64354 828 . 96269 62633 07377 52736 246 0. 275 0.27154 69369 56112 85351 302 0.96242 51976 28237 94814 248 . 276 . 27250 92262 19879 73627 557 . 96215 31695 23980 94278 169 .277 . 27347 12429 74443 10825 981 . 96188 01792 66634 59286 807 . 278 . 27443 29862 57786 29507 043 . 96160 62271 29189 13299 879 . 279 . 27539 44551 08166 09350 952 - 96133 18133 85596 67778 997 0. 280 0.27635 56485 64113 73331 967 0.96105 54383 10770 94792 459 . 281 .27731 65656 644385 83865 270 . 96077 86021 80586 99523 878 . 282 . 27827 72054 48215 38926 293 - 96050 08052 71880 92684 682 . 283 . 27923 75669 54812 68142 411 . 96022 20478 62449 62830 504 . 284 . 28019 76492 23866 28856 909 . 95994 23302 31050 48581 495 0. 285 0.28115 74512 95294 02165 110 0.95966 16526 57401 10746 590 . 286 .28211 69722 09293 88922 591 - 95938 00154 22179 04351 746 . 287 . 28307 62110 06345 05725 374 . 95909 74188 07021 50572 193 . 288 . 28403 51667 27208 80861 997 . 95881 38630 94525 08568 713 . 289 . 28499 38384 12929 50237 384 - 95852 93485 68245 47227 984 0. 290 0.28595 22251 04835 53268 394 0.95824 38755 12697 16807 013 . 291 . 28691 03258 44540 28750 981 .95795 74442 13353 20481 688 . 292 . 28786 81396 73943 10698 841 . 95767 00549 56644 85799 478 . 293 . 28882 56656 35230 24153 475 . 95738 17080 29961 36036 308 . 294 . 28978 29027 70875 80965 551 .95709 24037 21649 61457 636 0. 295 0.29073 98501 23642 75547 489 0.95680 21423 21013 90483 768 . 296 . 29169 65067 36583 80597 155 - 95651 09241 18315 60759 429 . 297 .29265 28716 53042 42792 582 . 95621 87494 04772 90127 632 . 298 . 29360 89489 16653 78457 616 . 95592 56184 72560 47507 858 . 299 .29456 47225 71345 69198 389 . 95563 15316 14809 23678 590 56 TaBLE XII.— Values of sin x and cos x to 23 places of decimals at tntervals of 0.001 from 0.000 MEMOIRS NATIONAL ACADEMY OF SCIENCES. to 1.600—Continued. x sin x cos & 0. 300 0.29552 02066 61339 57510 532 0.95533 64891 25606 01964 231 . 301 . 29647 53952 31151 42357 025 .95504 04912 99993 28826 414 . 302 . 29743 02873 25592 74716 586 .95474 35384 33968 84359 763 - 303 . 29888 48819 89771 53102 518 . 95444 56308 24485 52692 116 . 304 . 29933 91782 69093 19051 897 .95414 67687 69450 92289 242 0. 305 0.30029 31752 09261 52585 026 0.95384 69525 67727 06164 084 . 306 . 30124 68718 56279 676385 045 .95354 61825 19130 11990 559 . 307 . 30220 02672 56451 07447 613 .95324 44589 24430 12121 945 . 308 . 303815 33604 56380 39950 549 . 95294 17820 85350 63513 878 . 309 . 30410 61505 02974 53093 365 . 95263 81523 04568 47552 001 0. 310 0.30505 86364 43443 50156 564 0. 95233 35698 85713 39784 281 .3ll . 30601 08173 25301 45030 632 .95202 80351 33367 79558 038 . 312 . 30696 26921 96367 57464 615 .95172 15483 53066 39561 711 - 313 .30791 42601 04767 08284 189 .95141 41098 51295 95271 383 .314 . 30886 55200 98932 14579 138 .95110 57199 35494 94302 111 0. 315 0.30981 64712 27602 84860 120 0.95079 63789 14053 25664 080 . 316 - 31076 71125 39828 14184 658 . 95048 60870 96311 88923 617 317 31171 744380 84966 79252 234 .95017 48447 92562 63269 094 - 318 . 31266 74619 12688 33468 402 .94986 26523 14047 76481 749 - 319 . 31861 71680 72974 01977 833 . 94954 95099 72959 73811 467 0. 320 0.31456 65606 16117 76666 176 0.94923 54180 82440 86757 531 . 321 31551 56385 92727 11130 659 . 94892 03769 56583 01754 395 - 322 - 31646 44010 53724 15619 332 .94860 43869 10427 28762 501 . 323 .81741 28470 50346 51938 844 . 94828 74482 59963 69764 173 - 324 . 31836 09756 34148 28330 674 .94796 95613 22130 87164 613 0. 325 0.31930 87858 57000 94315 718 0.94765 07264 14815 72098 048 . 326 . 32025 62767 71094 35507 128 . 94733 09438 56853 12639 034 327 . 82120 34474 28937 68391 319 .94701 02139 68025 61918 976 . 328 . 82215 02968 83360 35077 048 . 94668 85370 69063 06147 877 . 329 . 32309 68241 87512 98012 460 . 94636 59134 81642 32541 351 0. 330 0. 32404 30283 94868 34670 020 0.94604 234385 28386 97152 941 . 331 . 82498 89085 59222 32199 224 . 94571 78275 32866 92611 768 . 332 32593 44637 34694 82047 O11 . 94539 23658 19598 15765 535 . 333 . 382687 96929 75730 74545 756 .94506 59587 14042 35228 939 . 834 . 32782 45953 37100 93468 777 . 94473 86065 42606 58837 502 0. 335 0.32876 91698 73903 10553 241 0.94441 03096 32643 01006 864 . 336 .32971 34156 41562 79990 386 - 94408 10683 12448 49997 577 . 337 . 33065 73316 95834 32882 957 . 94375 08829 11264 35085 413 - 338 . 33160 09170 92801 71669 766 . 94341 97537 59275 93637 243 . 339 . 33254 41708 88879 64517 288 . 94308 76811 87612 38092 499 0. 340 0.33348 70921 40814 39678 177 0.94275 46655 28346 22850 264 . 841 . 33442 96799 05684 79816 635 .- 94242 07071 14493 11062 025 - 342 . 33537 19332 40903 16300 519 - 94208 58062 80011 41330 105 . 343 . 33631 38512 04216 23460 104 . 94174 99633 59801 94311 834 . 344 . 33725 54328 53706 12813 399 . 94141 31786 89707 59229 468 0. 345 0.33819 66772 47791 27257 928 0.94107 54526 06513 00285 905 . 346 . 33913 75834 45227 35228 880 - 94073 67854 47944 22986 218 . 347 . 34007 81505 05108 24823 531 . 94039 71775 52668 40365 059 «348 . 34101 83774 86866 97891 850 - 94005 66292 60293 39119 944 . 349 .34195 82634 50276 64093 188 . 93971 51409 11367 45650 473 0. 350 0.34289 78074 55451 34918 963 0.93937 27128 47378 92003 503 . 351 . 34383 70085 62847 17681 237 . 93902 93454 10755 81724 321 . 352 . 34477 58658 33263 09467 102 .93868 50389 44865 55613 841 . 353 .34571 43783 27841 91058 778 . 93833 97937 94014 57391 869 . 854 .34665 25451 08071 20819 319 . 93799 36103 03447 99266 461 0. 355 0.34759 03652 35784 28548 852 0.93764 64888 19349 27409 412 . 356 . 34852 78377 73161 09276 237 . 93729 84296 88839 87337 915 . 357 .34946 49617 82729 17091 064 . 93694 94332 59978 89202 418 . 358 . 35040 17363 27364 58840 891 . 93659 94998 81762 72980 716 . 359 . 35133 81604 70292 87868 632 . 93624 86299 04124 73578 312 [Vou. XIV, No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. TaBLe XII.— Values of sin x and cos x to 28 places of decimals at intervals of 0.001 from 0.000 to 1.600—Continued. x sine c08 0. 360 0.35227 42332 75089 97684 991 ' 0.93589 68236 77934 85835 091 - 361 - 35320 99538 05683 15610 866 . 93554 40815 54999 29438 322 - 362 . 30414 53211 26351 96384 608 . 93519 04038 88060 13742 042 . 363 - 35508 03343 01729 15734 065 . 93483 57910 30795 02492 855 . 364 . 385601 49923 96801 63913 294 . 93448 02433 37816 78462 165 0. 365 0.35694 92944 76911 39203 863 0.93412 37611 64673 07984 897 - 366 . 35788 32396 07756 41380 647 . 93376 63448 67846 05404 739 . 367 . 385881 68268 55391 65142 021 . 93340 79948 04751 97425 922 . 368 . 35975 00552 86229 93504 354 . 93304 87113 33740 87371 606 . 369 . 36068 29239 67042 91160 721 . 93268 84948 14096 19348 871 0. 370 0.36161 54319 64961 97803 729 0.93232 73456 06034 42320 381 . 371 . 36254 75783 47479 21412 373 - 93196 52640 70704 74082 737 - 372 - 36347 93621 82448 31502 813 . 93160 22505 70188 65151 560 . 373 . 36441 07825 38085 52343 006 - 93123 83054 67499 62553 347 . 374 . 36534 18384 82970 56131 067 - 93087 34291 26582 73524 125 0. 375 0.36627 25290 86047 56137 291 0.93050 76219 12314 29114 948 . 376 . 36720 28534 16625 99809 733 . 93014 08841 90501 47704 265 377 - 36813 28105 44381 61843 251 . 92977 32163 27881 98417 211 . 378 . 36906 23995 39357 37211 926 . 92940 46186 92123 64451 836 . 379 . 36999 16194 71964 34164 758 . 92903 50916 51824 06312 328 0. 380 0.37092 04694 12982 67184 6549 0.92866 46355 76510 24949 253 . 381 . 37184 89484 33562 49909 881 . 92829 32508 36638 24806 858 . 382 .37277 70556 05224 88020 096 . 92792 09378 03592 76777 471 . 383 . 37370 47899 99862 72083 184 92754 76968 49686 81063 030 . 384 . 37463 21506 89741 70366 479 .92717 35283 48161 29943 792 0. 385 0.37555 91367 47501 21610 089 0.92679 84826 73184 70454 235 . 386 . 37648 57472 46155 27762 945 . 92642 24101 99852 66966 223 . 887 .37741 19812 59093 46681 397 .- 92604 54613 04187 63679 438 . 388 . 37833 78378 60081 84790 240 . 92566 75863 63138 47019 143 . 389 . 37926 33161 23263 89706 110 . 92528 87857 54580 07941 297 0. 390 0.38018 84151 23161 42823 118 0.92490 90598 57313 04145 068 . 391 . 38111 31339 34675 51860 671 . 92452 84090 51063 22192 776 . 392 . 38203 74716 33087 43373 349 . 92414 68337 16481 39537 ° 314 . 393 . 38296 14272 94059 55222 774 . 92376 43342 35142 86457: 070 . 394 . 38388 49999 93636 29011 366 . 92338 09109 89547 07898 401 0. 395 0.38480 81888 08245 02477 888 0.92299 65643 63117 25225 693 . 396 . 38573 09928 14697 01854 707 . 92261 12947 40199 97879 040 . 397 . 38665 34110 90188 34186 658 . 92222 51025 06064 84939 589 . 398 . 38757 54427 12300 79611 426 . 92183 79880 46904 06602 584 . 399 . 38849 70867 59002 83601 363 . 92144 99517 49832 05558 150 0. 400 0.38941 83423 08650 49166 631 0.92106 09940 02885 08279 853 .401 .39033 92084 39988 29019 595 -92067 11151 95020 86221 075 - 402 .39125 96842 32150 17700 358 -92028 03157 16118 16919 248 - 403 .39217 97687 64660 43663 363 .91988 85959 56976 45007 979 - 404 .39309 94611 174384 61324 955 91949 59563 09315 43137 110 0.405 0.39401 87603 70780 438071 820 0.91910 23971 65774 72800 745 - 406 .39493 76656 05398 71230 202 .91870 79189 19913 45073 295 .407 .39585 61759 02384 29995 816 . 91831 25219 66209 81253 568 . 408 .39677 42903 48226 97324 356 ~ .91791 62067 00060 73416 956 -409 .39769 20080 09812 36782 508 .91751 89735 17781 44875 737 0.410 0.39860 93279 84422 89359 380 0.91712 08228 16605 10547 564 -411 39952 62493 49738 65238 251 .91672 17549 94682 37232 150 412 .40044 27711 88838 35528 558 .91682 17704 51081 03796 202 413 .40135 88925 85200 23958 010 .91592 08695 85785 61266 649 .414 .40227 46126 22702 98524 766 .91551 90527 99696 92832 194 0.415 0.40818 99303 85626 63109 550 0.91511 63204 94631 73753 232 . 416 .40410 48449 58653 49047 645 .91471 26730 73322 31180 180 417 40501 93554 26869 06660 654 -91430 81109 39416 03880 251 .418 .40593 34608 75762 96747 939 -913890 26344 97475 01872: 722 .419 .40684 71603 91229 82037 655 .913849 62441 52975 65972 725 57 MEMOIRS NATIONAL ACADEMY OF SCIENCES. [Vou. XIV, TaBLE XII.— Values of sin x and cos x to 28 places of decimals at intervals of 0.001 from 0.000 to 1.600—Continued. x sin & cos £ 0. 420 0.40776 04530 59570 18597 279 0.91308 89403 12308 27243 609 -421 .40867 33379 67491 47203 546 .91268 07233 82776 66357 915 -422 40958 58142 02108 84671 703 .91227 15937 72597 72866 996 - 423 41049 78808 50946 15143 980 .91186 15518 90901 04379 332 -424 -41140 95370 01986 813837 201 .91145 05981 47728 45647 576 0.425 0.41232 07817 43424 75749 4385 0.91108 87329 540383 67564 373 -426 -41323 16141 64165 31825 593 .91062 59567 21681 86066 990 .427 .41414 20383 53326 15081 889 .91021 22698 63449 20950 808 - 428 41505 20384 00488 14189 067 .90979 76727 93022 54591 701 -429 -41596 16283 95646 32014 301 .90988 21659 24998 90577 360 0.430 0.41687 08024 29210 76621 692 0.90896 57496 74885 12247 591 431 -41777 95595 92007 52231 243 .90854 84244 59097 41143 638 - 432 -41868 78989 75279 50136 257 .90813 01906 94960 95366 563 - 433 .41959 58196 70687 39579 028 .90771 10488 00709 47844 729 434 .42050 33207 70310 58584 774 .90729 09991 95484 84510 435 0. 435 0.42141 04013 66648 04753 684 0.90687 00422 99336 62385 731 - 436 -42231 70605 52619 26011 018 .90644 81785 33221 67577 465 - 437 .42322 32974 21565 11315 146 .90602 54083 19003 73181 601 - 438 .42412 91110 67248 81323 456 .90560 17320 79452 97096 848 - 439 .42503 45005 83856 79016 027 .90517 71502 38245 59747 647 0. 440 0.42593 94650 65999 60276 972 0.90475 16632 19963 41716 554 441 42684 40036 08712 84483 381 .90432 52714 50093 41286 061 -442 .42774 81153 07458 04751 750 . 90389 79753 55027 31889 904 - 433 .42865 17992 58123 58891 823 .90346 97753 62061 19473 892 444 .42955 50545 57025 59317 745 . 90304 06718 99394 99766 305 0.445 0.43045 78803 00908 83666 443 0.90261 06653 96132 15457 899 . 446 .43136 02755 86947 65073 141 .90217 97562 82279 13291 573 -447 -43226 22395 12746 82453 917 .90174 79449 88745 01061 718 «448 -43316 37711 76342 50745 219 .90131 52319 47341 04523 319 -449 - 43406 48696 76203 11100 244 .90088 16175 90780 24210 832 0.450 0.43496 55341 11230 21042 084 0.90044 71023 52676 92166 884 -451 43586 57635 80759 44573 567 90001 16866 67546 28580 847 -452 -48676 55571 84561 42243 681 . 89957 53709 70803 98337 319 . 453 .43766 49140 22842 61170 507 .89913 81556 98765 67474 569 454 . 43856 38331 96246 25020 568 - 89870 00412 88646 59552 965 0. 455 0.43946 23138 05853 23944 492 0.89826 10281 78561 11933 463 .456 - 44036 03549 53183 04468 918 .89782 11168 07522 31966 167 .457 .44125 79557 40194 59344 542 .89738 03076 15441 53089 030 - 458 .44215 51152 69287 17350 215 . 89693 86010 43127 90836 721 459 . 44305 18326 43301 33053 008 . 89649 59975, 32287 (98759 714 0. 460 0.44394 81069 65519 76524 151 0.89605 24975 25525 24253 639 -461 44484 39373 39668 23010 752 . 89560 81014 66339 64298 937 .462 44573 93228 69916 42563 218 .89516 28097 99127 21110 867 .463 .44663 42626 60878 89618 275 -89471 66229 69179 57699 918 464 .44752 87558 17615 92537 506 . 89426 95414 22683 53342 602 0.465 0.44842 28014 45634 43101 319 0.89382 15656 06720 58962 873 - 466 .44931 63986 50888 85958 244 . 89337 26959 69266 52423 883 -467 . 45020 95465 39782 08029 479 . 89292 29329 59190 93730 459 - 468 45110 22442 19166 27868 603 -89247 22770 26256 80142 134 469 -45199 44907 96343 84976 342 - 89202 07286 21120 01196 857 0.470 0.45288 62853 79068 29070 327 0.89156 82881 95328 93645 402 471 .45377 76270 75545 09309 736 -89111 49562 01323 96296 541 -472 45466 85149 94432 63474 735 - 89066 07330 92437 04773 005 473 .45555 89482 44843 07100 635 - 89020 56193 22891 26178 292 474 .45644 89259 36343 22566 671 .88974 96153 47800 33674 367 0.475 0.45733 84471 78955 48139 307 0.88929 27216 23168 20970 288 -476 . 45822 75110 838158 66969 994 - 88883 49386 05888 56721 822 «477 .45911 61167 59888 96047 279 .88837 62667 53744 38842 074 -478 .46000 42633 20540 75103 180 . 88791 67065 25407 48723 197 «479 .46089 19498 76967 55473 739 .88745 62583 80438 05369 212 No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. 59 Tasue XII.— Values of sin x and cos x to 28 places of decimals at intervals of 0.001 from 0.000 to 1.600—Continued. x sin & cos & 0. 480 0.46177 91755 41482 88913 664 0.88699 49227 79284 19439 995 .481 - 46266 59394 26861 16364 968 .88653 27001 83281 47206 469 - 482 - 46355 22406 46338 56679 522 . 88606 95910 54652 44417 0651 - 483, . 46443 80783 13613 95295 430 .88560 55958 56506 20075 401 «484 - 46532 34515 42849 72867 132 .88514 07150 52837 90129 517 0.485 0.46620 83594 48672 73849 162 0.88467 49491 08528 31072 223 - 486 -46709 28011 46175 15033 451 . 88420 82984 89343 33453 094 - 487 -46797 67757 50915 34040 104 . 88374 07636 61933 55301 874 - 488 -46886 02823 78918 77761 558 . 88327 23450 93833 75463 416 489 . 46974 33201 46678 90760 024 . 88280 30482 53462 46844 214 0. 490 0.47062 58881 71158 03618 136 0.88283 28586 10121 49570 547 - 491 -47150 79855 69788 21242 715 -88186 17916 33995 44058 307 - 492 . 47238 96114 60472 11121 556 . 88138 98427 96151 23994 541 . 493 - 47327 07649 61583 91533 149 .-88091 70125 68537 69230 763 . 494 .47415 14451 91970 19709 261 . 88044 33014 23984 98588 075 0.495 0.47503 16512 70950 79950 264 0.87996 87098 36204 22574 157 - 496 .47591 13823 18319 71693 150 . 87949 32382 79786 96012 154 - 497 -47679 06374 54345 97532 118 .87901 68872 30204 70581 529 - 498 .47766 94157 99774 51191 668 . 87853 96571 63808 47270 917 - 499 .47854 77164 75827 05452 099 .87806 15485 57828 28743 023 0. 500 0. 47942 55386 04203 00027 329 0.87758 25618 90372 71611 628 - 501 . 48030 28813 07080 29394 947 .87710 26976 40428 38630 733 . 502 .48117 97437 07116 30578 414 . 87662 19562 87859 50795 903 - 503 .48205 61249 27448 70881 314 . 87614 03383 13407 39357 847 . 004 . 48293 20240 91696 35573 583 .87565 78441 98689 97748 295 0. 505 0.48380 74403 23960 15529 617 0.87517 44744 26201 33418 203 . 506 .48468 23727 48823 94818 170 . 87469 02294 79311 19588 355 . 507 .48555 68204 91355 38243 967 . 87420 51098 42264 46912 391 . 508 . 48643 07826 77106 78840 928 .87371 91160 00180 75052 318 . 509 .48730 42584 32116 05316 931 . 87323 22484 39053 84166 561 0. 510 0.48817 72468 82907 49450 013 0.87274 45076 45751 26310 581 .511 .48904 97471 56492 73435 934 . 87225 58941 08013 76750 129 .512 .48992 17583 80371 57187 006 87176 64083 14454 85187 176 .513 .49079 32796 82532 85582 104 . 87127 60507 54560 26898 565 .514 .49166 43101 91455 35667 778 .87078 48219 18687 53787 441 0. 515 0.49253 48490 36108 63810 364 0.87029 27222 98065 45347 504 . 516 49340 48953 45953 92799 025 .86979 97523 84793 59540 132 .517 .49427 44482 50944 98899 617 . 86930 59126 71841 83584 429 . 518 49514 35068 81528 98859 309 . 86881 12036 53049 84660 240 519 .49601 20703 68647 36861 855 86831 56258 23126 60524 189 0. 520 0.49688 01878 43736 71483 446 0.86781 91796 77649 90038 785 .521 .49774 77084 38729 62299 043 . 86732 18657 13065 83614 647 . 522 .49861 47812 86055 57189 109 . 86682 36844 26688 33565 898 . 523 .49948 18555 18641 78596 658 . 86632 46363 16698 64378 779 . 524 .50034 74302 69914 10484 518 . 86582 47218 82144 82893 524 0. 525 0.50121 30046 73797 84942 748 0.86532 39416 22941 28399 561 . 526 .50207 80778 64718 68796 092 . 86482 22960 39868 22644 077 527 .50294 26489 77603 50161 411 . 86431 97856 34571 19753 996 . 528 .60380 67171 47881 24954 981 . 86381 64109 09560 56071 436 . 529 . 50467 02815 11483 83349 596 . 86331 21723 68210 99902 671 0. 530 0.50553 33412 04846 96181 366 0.86280 70705 14761 01180 670 . 531 .50639 58953 64911 01306 143 . 86230 11058 54312 41041 248 . 532 .50725 79481 29121 89905 473 .86179 42788 92829 81312 894 - 533 50811 94836 35431 92741 999 86128 65901 37140 13920 311 . 534 50898 05160 22300 66364 220 .86077 80400 94932 10201 726 0. 535 0.50984 10394 28695 79260 534 0.86026 86292 74755 70140 025 . 536 .51070 10529 94093 97962 456 .85975 83581 86021 71507 760 . 537 51156 05558 58481 73096 946 . 85924 72273 39001 18926 068 . 538 .51241 95471 62356 25387 754 . 85873 52372 44824 92837 581 . 539 .51327 80260 46726 31605 686 . 85822 23884 15482 98393 339 MEMOIRS NATIONAL ACADEMY OF SCIENCES. [Vou, XIV, TasLe XII.— Values of sin x and cos x to 28 places of decimals at intervals of 0.001 from 0.000 to 1.600—Continued. x sin £ cos £ 0. 540 0.51413 59916 53113 10467 728 0.85770 86813 63824 14253 797 541 -51499 34431 23551 08484 914 .85719 41166 08555 41303 947 - 542 -51585 03796 00588 85758 874 .85667 86946 49241 51282 623 - 543 -51670 68002 27290 01726 969 .85616 24160 16304 35326 032 544 -51756 27041 47234 00855 920 . 85564 52812 21022 52425 567 0. 545 0.51841 80905 04516 98283 861 0.85512 72907 80530 77799 957 . 546 .51927 29584 48752 65410 714 85460 84452 12819 51181 787 . 547 .52012 73071 10073 15436 812 . 85408 87450 36734 25018 472 . 548 .52098 11856 49129 88849 675 . 85356 81907 71975 12587 703 . 049 -52183 44432 07094 38858 868 . 85304 67829 39096 36027 442 0. 550 0.52268 72289 30659 16778 838 0.85252 45220 59505 74280 498 . 551 .52353 94919 67038 57359 653 . 85200 14086 55464 10953 761 . 552 .52439 12314 63969 64065 565 .85147 74482 50084 82092 114 . 053 52524 24465 69712 94301 297 .85095 26263 67333 23867 110 . 054 - 52609 31364 33053 44585 976 . 85042 69585 32026 20180 431 0. 555 0.52694 33002 03301 35674 635 0.84990 04402 69831 50182 218 . 556 .52779 29370 30292 97627 180 . 84937 30721 07267 35704 287 . 057 . 52864 20460 64391 54824 757 84884 48545 71701 88608 318 . 508 .52949 06264 56488 10933 415 . 84831 57881 91352 58049 047 . 559 . 5380383 86773 58002 33815 002 .84778 58734 95285 77652 517 0. 560 0.53118 61979 20883 40385 187 0.84725 51110 13416 12609 452 -o61 . 53203 31872 97610 81418 533 . 84672 35012 76506 06683 799 . 562 .53287 96446 41195 26300 543 . 84619 10448 16165 29136 481 . 563 .58372 55691 05179 47726 585 .84565 77421 64850 21564 438 . 564 . 53457 09598 43639 06347 607 84512 35938 55863 44654 991 0. 565 0.53541 58160 11183 35362 572 0.84458 86004 23353 24855 579 . 566 . 53626 01367 62956 25057 521 . 84405 27624 02313 00958 945 . 567 53710 39212 54637 07291 168 . 84351 60803 28580 70603 796 . 568 53794 71686 42441 39926 969 84297 85547 38838 36691 O11 . 569 .53878 98780 83121 91211 553 . 84244 01861 70611 53715 445 0. 570 0.53963 20487 33969 24099 446 0.84190 09751 62268 74013 376 571 54047 36797 52812 80524 005 . 84136 09222 53020 93925 658 . 572 .54131 47702 98021 65614 465 . 84082 00279 82920 99876 632 . 573 .54215 53195 28505 31859 028 . 84027 82928 92863 14868 839 . 574 . 54299 53266 03714 63213 905 . 83973 57175 24582 41898 605 0. 575 0.54383 47906 83642 59158 222 0.83919 23024 20654 14757 5438 . 576 . 54467 37109 28825 18694 718 . 83864 80481 24493 38825 019 .577 54551 20865 00342 24296 136 . 83810 29551 80354 39176 658 - 578 54634 99165 59818 25797 231 . 83755 70241 33330 05683 918 579 .54718 72002 69423 24232 321 . 83701 02555 29351 38499 807 0. 580 0.54802 39367 91873 55618 270 0.83646 26499 15186 93465 789 . 081 .54886 01252 90432 74682 851 - 83591 42078 38442 27434 927 . 582 54969 57649 28912 38538 382 - 83536 49298 47559 43511 337 . 583 .55053 08548 71672 90300 563 . 83481 48164 91816 36205 988 . 584 .551386 53942 83624 42652 424 . 83426 38683 21326 36508 907 0. 585 0.55219 93823 30227 61353 309 0.83371 20858 87037 56877 861 . 586 . 55303 28181 77494 48692 799 - 83315 94697 40732 36143 543 . 587 .55386 57009 91989 26889 504 . 83260 60204 35026 84331 337 . 588 .55469 80299 40829 21434 637 . 83205 17385 23370 27399 720 . 589 .55552 98041 91685 44380 278 - 83149 66245 60044 51895 332 0. 590 0.55636 10229 12783 77572 254 0.83094 06791 00163 49524 800 - 591 .55719 16852 72905 55827 556 - 83038 39026 99672 61643 346 . 592 .55802 17904 41388 50056 192 . 82982 62959 15348 23660 255 . 593 .55885 13375 88127 50327 409 . 82926 78593 04797 09361 243 . 594 .55968 03258 83575 48880 201 . 82870 85934 26455 75147 786 0. 595 0.56050 87544 98744 23078 004 0.82814 84988 39590 04193 468 . 596 .56133 66226 05205 18307 516 .82758 75761 04294 50517 407 . . 597 . 56216 39293 75090 30821 541 . 82702 58257 81491 82974 799 . 598 .56299 06739 81092 90525 792 . 82646 32484 32932 29164 660 . 599 . 56381 68555 96468 43709 545 . 82589 98446 21193 19254 799 No. 5.) TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. 61 TABLE XII.— Values of sin x and cos x to 28 places of decimals at intervals of 0.001 from 0.000 to 1.600—Continued. x sin x cos & 0. 600 0.56464 24733 95035 35720 095 0.82533 56149 09678 29724 095 . 601 . 56546 75265 51175 93580 897 . 82477 05598 62617 27022 123 . 602 . 56629 20142 39837 08553 336 . 82420 46800 45065 11146 193 . 603 . 56711 59356 36531 18642 028 . 82363 79760 22901 59135 858 . 604 . 56793 92899 17336 91043 574 . 82307 04483 62830 68484 934 0. 605 0.56876 20762 58900 04538 687 0. 82250 20976 32380 00471 116 . 606 - 56958 42938 38434 31827 607 . 82193 29243 99900 23403 216 . 607 .57040 59418 33722 21808 719 . 82136 29292 34564 55786 102 . 608 .57122 70194 23115 81800 299 . 82079 21127 06368 09403 380 . 609 .57204 75257 85587 59705 300 . 82022 04753 86127 32317 893 0. 610 0.57286 74601 00481 26119 098 0.81964 80178 45479 51790 075 .611 - 57368 68215 48012 56380 111 . 81907 47406 56882 17114 225 . 612 - 57450 56093 08770 12563 221 . 81850 06443 93612 42372 770 . 613 . 57532 38225 63966 25415 904 . 81792 57296 29766 49108 549 . 614 .57614 14604 95387 76236 989 . 81734 99969 40259 08915 198 0. 615 0.57695 85222 85396 78697 975 0.81677 34469 00822 85945 685 . 616 .57777 50071 16931 60606 809 . 81619 60800 88007 79339 051 . 617 .57859 09141 73507 45614 047 . 81561 78970 79180 65565 411 . 618 . 57940 62426 39217 34861 330 - 81503 88984 52524 40689 288 . 619 . 58022 09916 98732 88572 073 . 81445 90847 87037 62551 318 0. 620 0.58103 51605 37305 07584 296 0.81387 84566 62533 92868 400 . 621 . 58184 87483 40765 14825 522 . 81329 70146 59641 39252 335 . 622 . 58266 17542 95525 36729 641 . 81271 47593 59801 97147 027 . 623 . 58347 41775 88579 84595 681 . 81218 16913 45270 91684 290 . 624 . 58428 60174 07505 35888 387 . 81154 78111 99116 19458 331 0. 625 0.58509 72729 40462 15480 540 0.81096 31195 05217 90218 953 . 626 . 58590 79433 76194 76836 923 . 81037 76168 48267 68483 556 . 627 . 58671 80279 04032 83139 861 . 80979 13038 13768 15067 973 . 628 .58752 75257 13891 88356 252 . 80920 41809 88032 28536 214 . 629 . 58833 64359 96274 18246 006 . 80861 62489 58182 86569 178 0. 630 0.58914 47579 42269 51311 811 0.80802 75083 12151 87252 371 . 631 .58995 24907 438555 99690 151 . 80743 79596 38679 90282 722 . 632 .59075 96335 92400 89983 484 . 80684 76035 27315 58094 522 - 633 .59156 61856 81661 44033 509 . 80625 64405 68414 96904 569 . 634 . 59237 21462 04785 59635 440 . 80566 44713 53140 97676 566 0. 635 0.59317 75143 55812 91193 198 0.80507 16964 73462 77004 837 . 636 .59398 22893 29375 30315 454 . 80447 81165 22155 17917 411 . 637 .59478 64703 20697 86352 425 . 80388 37320 92798 10598 548 - 638 .59559 00565 25599 66873 364 . 80328 85437 79775 93030 752 . 639 .59639 30471 40494 58084 641 . 80269 25521 78276 91556 338 0. 640 0.59719 54413 62392 05188 355 0.80209 57578 84292 61358 611 . 641 .59799 72383 88897 92681 375 . 80149 81614 94617 26862 715 . 642 .59879 84374 18215 24594 757 . 80089 97636 06847 22056 216 - 643 .59959 90376 49145 04673 426 . 80030 05648 19380 30729 469 . 644 . 60039 90382 81087 16496 070 .79970 05657 31415 266385 842 0. 645 0.60119 84385 14041 03535 151 0.79909 97669 42951 13571 848 . 646 .60199 72375 48606 49156 949 . 79849 81690 54786 65377 243 . 647 .60279 54345 85984 56561 576 . 79789 57726 68519 65855 159 . 648 , 60359 30288 27978 28662 868 . 79729 25783 86546 48612 327 . 649 , 60439 00194 76993 47908 070 . 79668 85868 12061 36819 444 0. 650 0.60518 64057 36039 56087 252 0.79608 37985 49055 82891 760 . 651 60598 21868 08730 33782 358 . 79547 82142 02318 08089 927 . 652 .60677 73618 99284 80505 818 . 79487 18343 77432 42041 183 . 653 . 60757 19302 12527 93778 646 . 79426 46596 80778 62180 929 . 654 . 60836 58909 53891 48897 929 . 79365 66907 19531 33114 757 0.655 | 0.60915 92433 29414 78343 652 0.79304 79281 01659 45900 987 . 656 60995 19865 45745 51174 755 . 79243 83724 35925 57253 785 . 657 .61074 41198 10140 52364 359 . 79182 80243 31885 28666 909 - 658 .61153 56423 30466 62074 073 . 79121 68843 99886 65458 154 " 659 "1232 65533 15201 34867 307 "79060 49532 51069 55734 550 MEMOIRS NATIONAL ACADEMY OF SCIENCES. [Vou XIV, Taste XII.—Values of sin x and cos x to 28 places of decimals at intervals of 0.001 from 0.000 to 1.600—Continued. x sin & cos x 0. 660 0.61311 68519 73433 78861 515 0.78999 22314 97365 09278 382 . 661 . 61390 65375 14865 34819 272 . 78937 87197 51494 96354 080 . 662 . 61469 56091 49810 55178 137 . 78876 44186 26970 86436 061 . 663 . 61548 40660 89197 83019 186 .78814 93287 38093 86857 558 . 664 . 61627 19075 44570 30974 165 78753 34506 99953 81380 523 0. 665 0.61705 913827 28086 60071 171 0.78691 67851 28428 68686 643 . 666 . 61784 57408 52521 58518 785 . 78629 93326 40184 00789 551 . 667 - 61863 17311 31267 20428 576 . 78568 10938 52672 21368 279 . 668 . 61941 71027 78333 24475 901 . 78506 20693 841382 04022 017 . 669 . 62020 18550 08348 12498 919 . 78444 22598 53587 90446 244 0. 670 0.62098 59870 36559 68035 744 0. 78382 16658 80849 28530 294 . 671 .62176 94980 78835 94799 654 . 78320 02880 86510 10376 414 . 672 . 62255 23873 51665 95092 281 . 78257 81270 91948 10240 374 . 673 . 62333 46540 72160 48154 700 . 78195 51835 19324 22393 698 . 674 . 62411 62974 58052 88456 349 . 781383 14579 91581 98907 578 0. 675 0.62489 73167 27699 83921 682 0.78070 69511 32446 87358 526 . 676 . 62567 77111 00082 14094 496 . 78008 16635 66425 68455 830 . 677 . 62645 74797 94805 48239 849 . 77945 55959 18805 93590 877 . 678 . 62723 66220 32101 23383 477 . 77882 87488 15655 22308 414 . 679 . 62801 513870 32827 22288 658 . 77820 11228 83820 59699 786 0. 680 0.62879 30240 18468 51370 418 0.77757 27187 50927 93718 239 - 681 .62957 02822 11138 18547 018 . 77694 35370 45381 32416 339 . 682 . 63034 69108 33578 11028 644 .77631 35783 96362 41105 566 . 683 . 63112 29091 09159 73043 207 . 77568 28434 33829 79488 156 . 684 . 63189 82762 61884 83499 207 . 77505 18327 88518 38411 247 0. 685 0.63267 30115 16386 33585 507 0.77441 90470 91938 77293 390 . 686 . 63344 71140 97929 04308 094 . 77378 59869 76376 60473 500 . 687 . 63422 058382 32410 43963 552 .77315 215380 74891 94232 293 . 688 . 63499 34181 46361 45549 316 . 77251 75460 21318 63436 286 . 689 .63576 56180 66947 24110 576 .77188 21664 50263 68154 418 0. 690 0. 63653 71822 21967 94023 743 0.77124 60149 97106 60197 354 - 691 . 63730 81098 39859 46216 467 . 77060 90922 97998 79579 541 . 692 . 63807 84001 49694 25323 984 . 76997 138989 89862 90904 069 . 693 . 63884 80523 81182 06781 899 . 76933 29357 10392 19670 418 . 694 . 63961 70657 64670 73855 200 . 76869 37030 98049 88505 182 0. 695 0.64038 54395 31146 94603 464 0.76805 37017 92068 53315 502 . 696 .64115 31729 12236 98782 185 . 76741 29324 32449 39366 321 . 697 . 64192 02651 40207 54680 136 . 76677 18956 59961 77279 757 . 698 . 64268 67154 47966 45892 698 . 76612 90921 16142 38958 434 . 699 . 64345 25230 69063 48031 063 . 76548 60224 43294 73431 759 0. 700 0.64421 76872 37691 05367 261 0.76484 21872 84488 42625 586 . 701 . 64498 22071 88685 07414 902 . 76419 75872 83558 57055 252 . 702 . 64574 60821 57525 65445 583 . 76355 22230 85105 11442 075 . 703 . 64650 93118 80337 88940 870 . 76290 60953 34492 20253 368 . 704 . 64727 18940 93892 61979 783 . 76225 92046 77847 53166 023 0. 705 0. 64803 38295 35607 19561 705 0.76161 15517 62061 70453 752 . 706 . 64879 51169 43546 23864 641 . 76096 31372 34787 58298 030 . 707 . 64955 57555 56422 40438 747 . 76031 39617 44439 64022 815 - 708 .65031 57446 13597 143835 062 . 75966 40259 40193 31253 107 . 709 . 65107 50833 55081 46169 354 . 75901 33304 71984 34997 406 0. 710 0.65183 37710 21536 68121 013 0.75836 18759 90508 16654 146 711 . 65259 18068 54275 19866 915 .75770 96631 47219 18942 159 . 712 . 65334 91900 95261 24450 173 . 75705 66925 94330 20755 235 . 713 .65410 59199 87111 64083 709 . 75640 29649 84811 71940 852 . 714 . 65486 19957 73096 55888 565 . 75574 84809 72391 28003 128 0. 715 0.65561 74166 97140 27566 883 0.75509 32412 11552 84730 074 . 716 . 65637 21820 03821 93009 463 . 75443 72463 57536 12745 203 717 .65712 62909 38376 27837 851 . 75378 04970 66335 91983 563 . 718 . 65787 97427 46694 44880 853 . 75312 29939 94701 46092 263 .719 . 65863 25366 75324 69585 417 . 75246 47378 00185 76755 558 No. 5.) TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. Taste XII.— Values of sin x and cos x to 23 places of decimals at intervals of 0.001 from 0.000 to 1.600—Continued. x sin & cos & 0. 720 0.65938 46719 71473 15361 800 0.75180 57291 40894 97944 549 721 .66013 61478 83004 58862 952 .75114 59686 75987 70091 576 . 722 . 66088 69636 58443 15198 027 -75048 54570 65174 34189 363 . 723 .66163 71185 46973 13079 967 .74982 41949 68966 45814 983 . 724 . 66238 66117 98439 69907 065 .74916 21830 48626 09078 707 0. 725 0.66313 54426 63349 66778 441 0.74849 94219 66165 10497 806 . 726 . 66388 36103 92872 23448 354 74783 59123 84344 52795 369 727 . 66463 11142 38839 73184 280 .74717 16549 66673 88624 209 . 728 . 66537 79534 53748 37633 666 .74650 66503 77410 54215 910 . 729 .66612 41272 90759 01524 309 -74584 08992 81559 02955 103 0. 730 0.66686 96350 03697 87373 259 0.74517 44023 44870 38879 013 . 731 66761 44758 47057 30099 195 74450 71602 33841 50102 364 . 732 . 66835 86490 75996 51573 181 74383 91736 15714 42167 693 . 733 .66910 21539 46342 35102 739 74317 04431 58475 71821 153 . 734 . 66984 49897 14589 99849 159 . 74250 09695 30855 77713 862 0. 735 0.67058 71556 37903 75177 973 0. 74183 07534 02328 18528 866 . 736 . 67132 86509 74117 74942 523 74115 97954 43109 01033 791 . 137 . 67206 94749 81736 71700 537 74048 80963 24156 15559 237 . 738 . 67280 96269 19936 70863 650 .73981 56567 17168 68402 998 . 739 . 67354 91060 48565 84779 796 .73914 24772 94586 14660 158 0. 740 0. 67428 79116 28145 06748 388 0.73846 85587 29587 90979 142 741 . 67502 60429 19868 84968 216 . 73779 39016 96092 48243 787 . 742 . 67576 34991 85605 96417 996 . 73711 85068 68756 84181 492 . 743 .67650 02796 87900 20669 485 73644 23749 22975 75897 5382 . 744 . 67723 63836 89971 13633 096 . 73576 55065 34881 12335 582 0. 745 0.67797 18104 55714 81235 936 0.73508 79023 81341 26664 537 . 746 . 67870 65592 49704 53032 193 . 73440 95631 39960 28591 681 TAT . 67944 06293 37191 55745 803 . 73373 04894 89077 36602 285 . 748 68017 40199 84105 86745 313 . 73305 06821 07766 10125 695 . 749 . 68090 67304 57056 87450 880 . 73237 01416 75833 81627 975 0. 750 0.68163 87600 23334 16673 324 0.73168 88688 73820 88631 184 751 . 68237 01079 50908 23885 163 .73100 68643 83000 05659 342 ~ 752 .68310 07735 08431 22423 554 .73032 41288 85375 76111 160 . 153 . 68383 07559 65237 62625 080 . 72964 06630 63683 44059 608 . 154 . 68456 00545 91345 04892 285 .72895 64676 01388 85978 367 0. 755 0.68528 86686 57454 92691 917 0.72827 15431 82687 42395 268 . 756 -68601 65974 34953 25484 772 . 72758 58904 92503 49472 750 . 757 68674 38401 95911 31587 089 . 72689 95102 16489 70515 436 758 68747 03962 13086 40963 419 72621 24030 41026 27404 867 . 759 “68819 62647 59922 57950 885 . 72552 45696 53220 31961 494 0. 760 0.68892 14451 10551, 33914 776 0.72483 60107 40905 17233 969 . 761 68964 59365 39792 39835 383 . 72414 67269 92639 68715 814 . 762 . 69036 97383 23154 38826 030 . 72345 67190 97707 55489 548 . 763 - 69109 28497 36835 58582 200 . 72276 59877 46116 61298 318 . 764 .69181 52700 57724 63761 700 . 72207 45336 28598 15545 123 0. 765 0. 69253 69985 63401 28295 794 0.72138 23574 36606 24219 693 . 766 69325 80345 32137 07631 223 . 72068 94598 62317 00753 084 . 767 69397 83772 42896 10903 039 .71999 58415 98627 96800 072 . 768 . 69469 80259 75335 73038 195 . 71930 15033 39157 32949 410 . 769 69541 69800 09807 26789 802 . 71860 64457 78243 29362 010 0. 770 0. 69613 52386 27356 74701 988 0.71791 06696 10943 36337 129 771 69685 28011 09725 61005 296 . 71721 41755 33033 64806 626 .772 . 69756 96667 39351 43442 524 .71651 69642 41008 16757 355 773 69828 58347 99368 65024 972 . 71581 90364 32078 15581 770 774 . 69900 13045 73609 25718 983 . 71512 03928 04171 36356 807 0.775 0.69971 60753 46603 54062 TAT 0.71442 10340 65931 36051 117 .776 . 70043 01464 03580 78713 256 . 71372 09608 86716 83660 709 117 .70114 35170 30469 99923 379 . 71302 01739 96600 90273 093 .778 “70185 61865 13900 60948 949 . 71231 86740 86370 39059 972 .779 .70256 81541 41203 19385 818 . 71161 64618 57525 15198 564 MEMOIRS NATIONAL ACADEMY OF SCIENCES. [Vou. XIV, TaBLe XII.— Values of sin x and cos x to 28 places of decimals at intervals of 0.001 from 0.000 to 1.600—Continued. x sin & cos x 0.780 | 0.70327 94192 00410 18436 790 0.71091 35380 12277 35721 626 781° . 70398 99809 80256 58108 374 . 71020 99032 53550 79296 239 . 782 . 70469 98387 70180 66337 280 .70950 55582 84980 15931 435 . 783 - 70540 89918 60324 70046 581 . 70880 050388 10910 36614 737 . 784 . 70611 74395 41535 66131 480 .70809 47405 36395 82877 671 0. 785 0.70682 51811 05365 92374 614 0.70738 82691 67199 76290 330 . 786 - 70753 22158 44073 98290 801 . 70668 10904 09793 47885 059 . 787 . 70823 85430 50625 15901 193 .70597 32049 71355 67509 330 . 788 . 70894 41620 18692 304386 730 .70526 46135 59771 73107 880 «789 - 70964 90720 42656 50970 857 .70455 53168 83632 99934 173 0. 790 0.71035 32724 17607 80981 403 0.70384 53156 52236 09691 278 . 791 71105 67624 39345 88841 574 .70313 46105 75582 19602 208 792 -71175 95414 04380 78239 979 . 70242 32023 64376 31409 812 793 . 71246 16086 09933 58529 620 .70171 10917 30026 60306 275 - 794 . 71816 296383 53937 15005. 776 . 70099 82793 84643 63792 314 0.795 - 0.713886 36049 35036 79112 713 0.70028 47660 41039 70466 123 796 71456 35326 52590 98579 148 69957 05524 12728 08742 151 797 71526 27458 06672 07482 391 . 69885 56392 13922 35499 779 «798 71596 12436 98066 96241 109 . 69814 00271 595385 64661 971 . 799 - 71665 90256 28277 81536 630 . 69742 37169 65179 95703 964 0. 800 0.71735 60908 99522 76162 718 0.69670 67093 47165 42092 075 - 801 - 71805 24388 147386 58803 753 . 69598 90050 22499 59652 695 - 802 . 71874 80686 77571 43741 255 . 69527 06047 08886 74871 538 . 803 . 71944 29797 92397 50488 651 . 69455 15091 24727 13123 218 . 804 72013 71714 643803 73354 263 . 693883 17189 89116 26831 236 0. 805 0.72083 06429 99098 50932 396 0.69311 12350 21844 23558 425 . 806 . 72152 33937 03310 35522 503 . 69239 00579 43394 94027 956 . 807 . 72221 54228 84188 62476 322 . 69166 81884 74945 40074 951 - 808 . 72290 67298 49704 19472 935 . 69094 56273 38365 02528 784 - 809 . 72359 731389 08550 15721 677 . 69022 23752 56214 89026 151 0. 810 0. 72428 71743 -70142 51092 818 0.68949 84329 51747 01754 964 811 . 72497 63105 44620 85175 959 68877 38011 48903 65129 158 . 812 . 72566 47217 42849 06266 069 - 68804 84805 72316 53394 472 - 813 . 72635 24072 76416 00277 085 . 68732 24719 47306 18165 280 - 814 . 72703 93664 57636 19583 027 .68659 57759 99881 15892 545 0. 815 0.72772 55985 99550 51786 534 0.68586 83934 56737 35262 969 . 816 . 72841 11080 15926 88414 775 -68514 03250 45257 24529 414 . 817 . 72909 58790 21260 93542 651 . 68441 15714 93509 18772 652 . 818 . 72977 99259 30776 72343 223 . 68368 21335 30246 67094 544 . 819 . 73046 324380 60427 39565 302 .68295 20118 84907 59742 692 0. 820 0.73114 58297 26895 87938 131 0.68222 12072 87613 55166 656 . 821 . 73182 76852 47595 56503 084 "68148 97204 69169 07005 802 . 822 . 73250 88089 40670 98872 320 - 68075 75521 61060 91008 857 . 823 . 73318 92001 24998 51414 329 . 68002 47030 95457 31885 232 . 824 . 73386 88581 20187 01366 283 . 67929 11740 05207 30088 213 0. 825 0. 738454 77822 46578 54873 150 0. 67855 69656 23839 88530 058 . 826 . 73522 59718 25249 04953 477 . 67782 20786 85563 39229 106 . 827 . 73590 34261 78008 99391 793 . 67708 65189 25264 69888 949 - 828 . 73658 01446 27404 08557 557 . 67635 02720 78508 50409 750 - 829 73725 61264 96715 93150 579 . 67561 33538 81536 59331 781 0. 830 0. 73793 13711 09962 71872 858 0. 67487 57600 71267 10211 246 - 831 . 738860 58777 91899 89026 752 - 67413 74913 85293 77928 481 - 832 . 73927 96458 68020 820389 434 . 67339 85485 61885 24928 580 . 833 73995 26746 64557 48913 544 . 67265 89323 39984 27394 537 . 834 . 74062 49635 08481 15603 989 - 67191 86434 59207 01352 983 0. 835 0.74129 65117 27503 03320 808 0.67117 76826 59842 28712 570 . 836 .- 74196 73186 50074 95758 049 - 67043 60506 82850 83235 098 . 837 | . 74263 73836 05390 06248 576 -66969 37482 69864 56439 445 . 838 . 74330 67059 23383 44844 755 -66895 07761 63185 83438 385 . 839 . 74397 52849 34732 85324 932 - 66820 71351 05786 68708 357 No. 5. TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. 65 TaBLe XII.— Values of sin x and cos x to 28 places of decimals at intervals of 0.001 from 0.000 to 1.600—Continued. x sin £ : cost 0. 840 0. 74464 31199 70859 32125 657 0. 66746 28258 41308 11792 267 . 841 - 74531 02103 63927 87199 577 . 66671 78491 14059 32935 396 - 842 . 74597 65554 46848 16798 923 . 66597 22056 69016 98654 482 - 843 . 74664 21545 53275 18184 539 . 66522 58962 51824 47240 065 . 844 - 74730 70070 17609 86260 385 . 66447 89216 08791 14192 152 0. 845 0.74797 11121 74999 80133 429 0.66373 12824 86891 57589 286 . 846 . 74863 44693 61339 89598 886 . 66298 29796 33764 83391 100 . 847 . 74929 70779 138273 01550 724 . 66223 40137 97713 70674 409 . 848 - 74995 89371 68190 66317 368 . 66148 43857 27703 96802 946 . 849 . 75062 00464 64233 63922 547 . 66073 40961 73363 62530 783 0. 850 0.75128 04051 40292 70271 207 0.65998 31458 84982 17039 542 . 851 . 75194 00125 36009 23260 432 . 65923 15356 13509 82909 449 - 852 . 75259 88679 91775 88815 295 . 65847 92661 10556 81024 321 - 853 . 75325 69708 487387 26849 594 .65772 63381 28392 55410 547 . 854 . 75391 43204 48790 57151 380 . 65697 27524 19944 98010 152 0. 855 0.75457 09161 34586 25193 237 0. 65621 85097 38799 73388 013 . 856 . 75522 67572 49528 67867 227 . 65546 36108 39199 433873 300 . 857 . 75588 184381 37776 79144 450 - 65470 80564 76042 91635 218 . 858 . 75653 61731 44244 75659 143 . 65395 18474 04884 48193 134 . 859 - 75718 97466 14602 62217 260 - 65319 49843 81933 13861 148 0. 860 0.75784 25628 95276 97229 459 0.65243 74681 64051 84627 203 - 861 - 75849 46213 33451 58068 441 . 65167 92995 08756 75966 794 . 862 . 75914 59212 77068 06350 566 - 65092 04791 74216 47091 357 . 863 . 75979 64620 74826 53141 684 -65016 10079 19251 25131 418 - 864 . 76044 62430 76186 24087 122 . 64940 08865 03332 29254 574 0. 865 0.76109 52636 31366 24465 750 0. 64864 01156 86580 94718 373 . 866 . 76174 35230 91346 04168 073 . 64787 86962 29767 96858 196 - 867 . 76239 10208 07866 22598 272 .64711 66288 94312 75010 . 176 . 868 . 76303 77561 33429 13500 144 - 64635 39144 42282 56369 276 . 869 . 76368 37284 21299 49706 858 . 64559 05536 36391 79782 561 0. 870 0. 76432 89370 25505 07814 480 0. 64482 65472 40001 19477 766 . 871 . 76497 33813 00837 32779 191 . 64406 18960 17117 08727 234 . 872 . 76561 70606 02852 024388 134 . 64329 66007 32390 63447 280 - 873 . 76625 99742 87869 91953 834 . 64253 06621 51117 05733 O91 . 874 .76690 21217 12977 38182 114 . 64176 40810 39234 87329 202 0. 875 0. 76754 35022 36027 03963 458 0.64099 68581 63325 138035 656 . 876 .76818 41152 15638 42337 736 . 64022 89942 90610 64049 903 . 877 . 76882 39600 11198 60682 252 . 63946 04901 88955 21244 528 . 878 . 76946 30359 82862 84773 027 - 63869 13466 26862 88380 872 . 879 . 77010 13424 91555 22769 271 . 63792 15643 73477 15258 639 0. 880 0.77073 88788 98969 29120 965 0.63715 11441 98580 20801 550 . 881 . 77187 56445 67568 68399 506 . 63638 00868 72592 16079 181 . 882 .77201 16388 60587 79051 337 . 63560 83931 66570 27264 -710 - 883, . 77264 68611 42032 37074 497 . 63483 60638 52208 18529 695 - 884 . 77328 13107 76680 19618 049 .63406 30997 01835 14874 218 0. 885 0.77391 49871 30081 68504 290 0.63328 95014 88415 24894 213 . 886 .77454 78895 68560 538673 706 - 63251 52699 85546 63485 020 . 887 .77518 00174 59214 36552 600 . 63174 04059 67460 74481 571 - 888 77581 13701 69915 83343 321 . 63096 49102 09021 53235 256 . 889 .77644 19470 69310 78237 045 . 63018 87834 85724 69127 530 0. 890 0.77707 17475 26823 86549 033 0.62941 20265 73696 88020 355 . 891 .77770 07709 12654 17776 316 . 62863 46402 49694 94643 540 892 "77832 90165 97778 38577 722 162785 66252 91105 14919 057 . 893 77895 64839 53950 85676 211 . 62707 79824 75942 38222 428 . 894 77958 31723 53704 28683 432 . 62629 87125 82849 39581 242 0. 895 0.78020 90811 70350 32846 443 0.62551 88163 91096 01810 880 . 896 . 78083 42097 77980 21716 548 . 62473 82946 80578 37587 545 . 897 78145 85575 51465 39740 163 . 62395 71482 31818 11458 656 . 898 . 78208 21238 66458 14771 667 . 62317 53778 25961 61790 683 . 899 . 78270 49080 99392 20508 171 . 62239 29842 44779 22654 524 115394°—21—_5 66 Taste XII.— Values of sin x and cos x to 28 places of decimals at intervals of 0.001 from 9.000 MEMOIRS NATIONAL ACADEMY OF SCIENCES. to 1.600—Continued. x sin x cos x 0. 900 0. 78332 69096 27483 38846 138 0. 62160 99682 70664 45648 472 . 901 . 78394 81278 28730 22159 796 . 62082 63306 86633 21658 870 — . 902 . 78456 85620 81914 55501 279 . 62004 20722 76323 02558 530 . 903 . 78518 82117 66602 18722 439 . 61925 71938 23992 22842 983 - 904 . 78580 70762 63143 48518 260 .61847 16961 14519 21204 658 0. 905 0. 78642 51549 52674 00391 817 0.61768 55799 33401 62045 040 - 906 - 78704 24472 17115 10540 713 .61689 88460 66755 56924 921 . - 907 . 78765 89524 39174 57664 940 .61611 14953 01314 85952 792 © . 908 . 78827 46700 02347 24696 094 . 61532 35284 24430 19111 466 - 909 . 78888 95992 90915 60447 888 .61453 49462 24068 37523 020 0. 910 0.78950 37396 89950 41187 896 0.61374 57494 88811 54652 118 - 911 . 79011 70905 85311 32130 474 . 61295 59390 07856 37447 803 . 912 . 79072 96513 63647 48850 789 .61216 55155 71013 27423 839 - 913 . 79134 14214 12398 18619 897 .61137 44799 68705 61677 674 . 914 .79195 24001 19793 41660 812 .61058 28329 91968 93848 110 0. 915 0.79256 25868 74854 52325 499 0.60979 05754 32450 15011 758 . 916 . 79317 19810 67394 80192 738 . 60899 77080 82406 74518 350 . 917 . 79378 05820 88020 11086 785 . 60820 42317 34706 00764 999 . . 918 . 79438 83893 28129 48016 785 .60741 01471 82824 21909 476 . . 919 . 79499 54021 79915 72036 860 60661 54552 20845 86522 589 — 0. 920 0.79560 16200 36366 03026 828 0.60582 01566 48462 84179 741 . 921 . 79620 70422 91262 60393 471 .60502 42522 45973 65991 745 . 922 . 79681 16683 39183 23692 319 . 60422 77428 24282 65074 984 - 923 .79741 54975 75501 93169 858 . 60343 06291 74899 16960 980 . 924 . 79801 85293 96389 50226 129 . 60263 29120 94936 79945 468 0. 925 0.79862 07631 98814 17797 639 0.60183 45923 82112 55377 043 . 926 . 79922 21983 80542 20660 537 .60103 56708 34746 07885 466 . 927 . 79982 28343 401388 45653 978 — . 60023 61482 51758 85549 703 . 928 . 80042 26704 76967 01823 638 .59943 60254 32673 40005 791 . 929 . 80102 17061 91191 80485 294 . 59863 53031 77612 46494 584 0. 930 0.80161 99408 83777 15208 432 0.59783 39822 87298 23849 491 - 931 . 80221 73739 56488 41719 806 .59703 20635 63051 54424 260 . 932 . 80281 40048 11892 57726 899 . 59622 95478 06791 03960 905 «933 . 80840 98328 53358 82661 218 59542 64358 21082 41397 846 . 934 . 80400 48574 85059 17341 371 . 59462 27284 08887 58618 345 0. 935 0.80459 90781 11969 03555 863 0.59381 84263 74063 90139 324 . 936 . 80519 24941 39867 83565 545 - 59301 35305 20863 32740 634 - 937 . 80578 51049 75339 59525 671 . 59220 80416 54181 65034 867 . 938 . 80637 69100 25773 52827 488 .59140 19605 79507 66977 785 . 939 . 80696 79086 99364 63359 313 . 59059 52881 02922 39319 443 0. 940 0.80755 81004 05114 28687 022 0.58978 80250 31098 22996 099 . 941 .80814 74845 52830 83153 915 .58898 01721 71298 18462 976 . 942 . 80873 60605 53130 16899 872 . 58817 17303 31375 04967 973 . 943 . 80932 38278 174386 34799 758 . 58736 27003 19770 59766 388 - 944 . 80991 07857 57982 15321 017 . 58655 30829 45514 77276 748 0. 945 0. 81049 69337 87809 69300 383 0.58574 28790 18224 88177 827 . 946 .81108 22713 20770 98639 669 . 58493 20893 48104 78446 913 . 947 . 81166 67977 71528 54920 560 - 58412 07147 45944 08339 436 . 948 . 81225 05125 55555 97938 351 - 58330 87560 23117 31810 012 . 949 . 81283 34150 89138 54154 591 - 58249 621389 91583 12874 994 0. 950 0. 81341 55047 89373 75068 542 0.58168 30894 63883 49416 618 . 951 . 81399 67810 74171 95507 433 - 58086 93832 53142 86928 810 . 952 . 81457 72433 62256 918385 411 - 58005 50961 73067 39704 748 . . 953 .81515 68910 73166 40081 165 - 57924 02290 37944 08966 253 © . 954 . 81573 57236 27252 73984 145 .57842 47826 62640 01435 096 0. 955 0.81631 37404 45683 42959 322 0.57760 87578 62601 47846 300 . 956 . 81689 09409 50441 69980 433 .57679 21554 53853 21403 511 ~ 957 . 81746 73245 64327 09381 654 .57597 49762 52997 56176 536 . 958 . 81804 28907 10956 04577 644 .57515 72210 77213 65441 113 - 959 81861 76388 14762 45701 891 . 574383 88907 44256 59961 007 | (Vou. XTV, No. 5.1 TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. 67 TABLE XII.— Values of sin x and cos x to 28 places of decimals at intervals of 0.001 from 0.000 to 1.600—Continued. x sin x C08 0. 960 0.81919 15683 00998 27163 322 0.57351 99860 72456 66212 505 - 961 .81976 46785 95734 05121 101 .57270 05078 80718 44551 395 - 962 - 82033 69691 25859 54877 569 .57188 04569 88520 07322 513 - 963 - 82090 84393 19084 28189 263 .57105 98342 15912 36911 940 - 964 - 82147 90886 03938 10495 962 . 57023 86403 83518 03741 923 0. 965 0.82204 89164 09771 78067 694 0.56941 68763 12530 84208 614 - 966 . 82261 79221 66757 55069 656 .56859 45428 24714 78562 699 - 967 - 82318 61053 05889 70544 986 .56777 16407 42403 28733 004 - 968 . 82375 34652 58985 15315 328 . 56694 81708 88498 36093 162 - 969 - 82432 00014 58683 98799 136 . 56612 41340 86469 79171 417 0.970 0. 82488 57133 38450 05747 662 0.56529 95311 60354 31303 653 - 971 . 82545 06003 32571 52898 564 . 56447 43629 34754 78229 727 - 972 . 82601 46618 76161 45547 087 . 56364 86302 34839 35633 190 - 973 - 82657 78974 05158 34034 750 . 56282 23338 86340 66624 480 . 974 . 82714 03063 56326 70155 495 .56199 54747 15554 99167 663 0. 975 0.82770 18881 67257 63479 226 0.56116 80535 49341 43450 813 . 976 . 82826 26422 76369 37592 699 . 56034 00712 15121 09200 110 -977 - 82882 25681 22907 86257 689 . 55951 15285 40876 22937 736 - 978 . 829388 16651 46947 29486 397 . 55868 24263 55149 45183 654 . 979 . 82993 99327 89390 69534 022 .55785 27654 87042 87601 358 0. 980 0.83049 73704 91970 46808 453 0.55702 25467 66217 30087 666 - 981 - 83105 39776 97248 95697 028 .55619 17710 22891 37806 645 - 982 . 83160 97538 48619 00310 290 . 55536 04390 87840 78167 757 - 983 . 83216 46983 90304 50142 703 . 55452 85517 92397 37748 295 . 984 . 83271 88107 67360 95650 254 . 55369 61099 68448 39160 207 0. 985 0. 83327 20904 25676 03744 902 0.55286 31144 48485 57861 376 . 986 . 83382 45368 11970 13205 801 . 55202 95660 65354 38911 453 . 987 - 83437 61493 73796 90007 262 .55119 54656 52753 13672 322 - 988 . 83492 69275 59543 82563 379 - 55036 08140 44732 16453 272 - 989 . 83547 68708 184382 76889 279 . 54952 56120 75943 01100 969 0. 990 0. 83602 59786 00520 51678 926 0.54868 98605 81587 57534 313 . 991 - 83657 42503 56699 33299 444 .54785 35603 97417 28224 252 . 992 . 83712 16855 38697 50701 883 .54701, 67123 59732 24618 647 . 993 . 83766 82835 99079 90248 385 .54617 93173 05380 43512 268 . 994 . 83821 40439 91248 50455 694 . 54534 13760 71756 83362 006 0. 995 0.83875 89661 69442 96654 953 0.54450 28894 96802 60547 3875 - 996 . 83930 30495 88741 15567 733 . 54366 38584 19004 25576 412 997 . 83984 62937 05059 69798 245 . 54282 42836 77392 79237 026 . 998 . 84038 86979 75154 52241 668 -54198 41661 11542 88693 907 . 999 . 84093 02618 56621 40408 555 .54114 35065 61572 03531 067 1.000 0. 84147 09848 07896 50665 250 ,0.54030 23058 68139 71740 094 - 001 . 84201 08662 88256 92390 268 . 58946 05648 72446 55654 214 . 002 . 84254 99057 57821 22046 578 58861 82844 16233 47828 237 . 003 . 84308 81026 77549 97169 747 .53777 54653 41780 86864 465 . 004 . 84362 54565 09246 30271 873 . 53693 21084 91907 73184 669 1.005 0.84416 19667 15556 42661 273 0.53608 82147 09970 84748 188 . 006 .84469 76327 59970 18177 851 .93024 37848 39863 92716 262 . 007 84523 24541 06821 56844 116 . 53439 88197 26016 77062 668 . 008 . 84576 64302 21289 28431 774 . 53355 33202 13394 42130 747 . 009 . 84629 95605 €9397 25943 853 .53270 72871 47496 32136 904 1,010 0.84683 18446 18015 19012 310 0.53186 07213 74355 46620 673 -011 . 84736 32818 34859 07211 051 538101 36237 40537 55841 426 .012 . 84789 38716 88491 73284 331 .53016 59950 98140 16121 808 .013 . 84842 36136 48323 36290 466 .52931 78362 79791 851387 984 . 014 . 84895 25071 84612 04660 810 .52846 91481 48651 37156 798 1.015 0.84948 05517 68464 29173 940 0.52761 99315 48406 78219 896 .016 -85000 77468 71835 55845 003 .52677 01873 28274 61274 932 .017 - 85053 40919 67530 78780 164 .52591 99163 37999 01253 921 .018 -85105 95865 29204 92646 111 .52506 91194 27850 90098 832 .019 . 85158 42300 31363 45804 549 .62421 77974 48627 11734 503 MEMOIRS NATIONAL ACADEMY OF SCIENCES. [Vou, XIV, TaBLe XII.— Values of sin x and cos x to 28 places of decimals at intervals of 0.001 from 0.000 to 1.600—Continued. x sin & cos & 1.020 0.85210 80219 49362 92361 655 0.52336 59512 51649 56988 961 . 021 .85263 09617 59411 44882 415 .52251 35816 88764 38461 245 . 022 . 85315 30489 38569 26719 808 .52166 06896 12341 05336 792 . 023 . 85367 42829 64749 24308 778 .52080 72758 75271 58150 502 . 024 .85419 46633 16717 39374 945 .51995 33413 30969 63497 542 1.025 0.85471 41894 74093 41057 997 0.51909 88868 33369 68691. 985 . 026 . 85523 28609 173851 17949 715 .51824 39132 36926 16373 373 027 . 85575 06771 27819 30046 586 .51738 84218 96612 59061 276 - 028 .85626 76375 87681 60616 931 .51653 24121 67920 73657 956 . 029 . 85678 37417 79977 67982 525 .51567 58864 06859 75899 186 1. 030 0.85729 89891 88603 37214 627 0.51481 88449 69955 34753 350 - 031 . 85781 33792 98311 31744 398 .51896 12887 14248 86768 878 . 032 . 85832 69115 94711 44887 626 .51310 32184 97296 50370 116 . 033 . 85883 95855 64271 51283 734 .51224 46351 77168 40101 715 . 034 85935 14006 94317 58248 998 .51138 55396 12447 80821 625 1. 035 0.85986 23564. 73034 57043 938 0.51052 59326 62230 21842 776 . 036 . 86037 24523 89466 74054 819 .50966 58151 86122 51023 5385 . 037 . 86088 16879 383518 21889 224 .50880 51880 44242 08807 028 . 038 . 86139 00625 95953 50385 634 .50794 40520 97216 02209 404 . 039 .86189 75758 68397 97536 975 .50708 24082 06180 18757 138 1.040 0.86240 42272 43338 40328 079 0.50622 02572 32778 40373 447 . 041 86291 00162 14123 45486 997 .50535 76000 39161 57213 919 . 042 . 86341 49422 74964 20150 1381 .50449 443874 87986 81451 427 . 043 . 86391 90049 20984 62441 124 . 50363 07704 42416 61010 426 . 044 . 86442 22036 47972 11963 456 .50276 65997 66117 93250 711 1.045 0.86492 45379 52878 00206 699 0.50190 19263 23261 38600 728 . 046 . 86542 60073 33318 00866 385 .50103 67509 78520 34140 520 . 047 .86592 66112 87822 80077 424 .50017 10745 97070 07184 396 . 048 . 86642 63493 15788 46561 037 -49930 48980 44586 88513 415 . 049 .86692 52209 17477 01685 140 . 49843 82221 87247 26307 756 1,050 0.86742 32255 94016 89438 141 0.49757 10478 91726 99029 085 051 .86792 03628 47403 46316 092 .49670 33760 25200 29002 975 052 . 86841 66321 80499 51123 146 49583 52074 55338 95651 499 . 053 . 86891 20330 97035 74685 276 49496 65430 50311 48726 051 . 054 . 86940 65651 01611 29477 198 .49409 73836 78782 21490 510 1.055 0.86990 02276 99694 19162 460 0.49322 77302 09910 43854 806 . 056 . 87039 30203 97621 88046 624 -49235 758385 13349 55459 008 . 057 .87088 49427 02601 70443 529 -49148 69444 59246 18707 979 . 058 .87137 59941 22711 39954 543 .49061 58139 18239 31756 732 . 059 . 87186 61741 66899 58660 794 .48974 41927 61459 41446 534 1.060 0.87235 54823 44986 926228 295 0.48887 20818 60527 56191 864 . 061 . 87284 39181 67663 28925 947 . 48799 94820 87554 58818 317 . 062 . 87333 14811 46494 88556 345 - 48712 63943 15140 19351 528 . 063 . 87381 81707 93918 11299 356 . 48625 28194 16372 07757 202 064 . 87430 39866 23243 36468 402 . 48537 87582 64825 06632 362 1.065 0.87478 89281 48654 85179 424 0.48450 42117 34560 23847 867 . 066 . 87527 29948 85211 08932 453 . 48362 91807 00124 05142 811 . 067 .87575 61863 48845 38105 753 .48275 36660 386547 46667 387 . 068 . 87623 85020 56366 30362 492 .48187 76686 19345 07484 800 . 069 .87671 99415 25458 18969 874 -48100 11893 24514 22014 811 1.070 0.87720 05042 74681 61030 706 0.48012 42290 28534 12436 509 .071 . 87768 01898 23473 85627 336 .47924 67886 08365 01039 904 .072 . 87815 89976 92149 41877 919 . 47836 88689 41447 22529 904 .073 . 87863 69274 01900 46904 963 .47749 04709 05700 36282 289 .074 .87911 39784 74797 33716 111 .47661 15953 79522 38551 762 1.075 0.87959 01504 33788 98997 101 0.47573 22432 41788 74632 160 .076 .88006 54428 02703 50816 869 47485 24153 71851 50968 911 .077 . 88053 98551 06248 56244 731 .47397 21126 495388 47223 840 .078 .88101 33868 70011 88879 619 - 47309 13359 55152 28292 396 .079 .88148 60376 20461 76291 297 . 47221 00861 69469 56273 392 No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. Tasie XII.— Values of sin x and cos x to 23 places of decimals at intervals of 0.001 from 0.000 to 1.600—Continued. 1.080 081 . 082 . 083 - 084 1. 085 - 086 . 087 . 088 . 089 1.090 091 - 092 . 093 094 1.095 . 096 . 097 . 098 . 099 1. 100 101 102 - 103 . 104 1.105 . 106 . 107 . 108 . 109 1.110 .111 .112 . 118 .114 1.115 .116 .117 -118 -119 1.120 .121 122 . 123 -124 1, 125 . 126 . 127 - 128 129 1.130 131 . 182 . 133 . 184 1.135 "136 : 138 +139 sin x cos x 0.88195 78068 84947 47373 533 0.47132 83641 73740 02391 353 - 88242 86941 91699 79609 169 .47044 61708 49685 58871 547 - 88289 86990 69831 46247 031 .46956 35070 79499 50767 810 - 88336 78210 49337 63390 660 . 46868 03737 45845 47743 217 - 88383 60596 61096 36998 790 .46779 67717 31856 75803 727 0.88430 34144 36869 09797 534 0.46691 27019 21135 28984 862 - 88476 98849 09301 08104 243 -46602 81651 97750 80991 522 - 88523 54706 11921 88562 972 .46514 31624 46239 96791 014 - 88570 01710 79145 84791 522 .46425 76945 51605 44159 401 - 88616 39858 46272 53940 000 . 46337 17623 99315 05181 235 0. 88662 69144 49487 23160 860 0.46248 53668 75300 87702 790 - 88708 89564 25861 35990 371 .46159 85088 65958 36738 852 - 88755 01113 13352 98641 470 -46071 11892 58145 45833 190 - 88801 03786 50807 26207 951 - 45982 34089 39181 68372 764 . 88846 97579 77956 88779 948 . 45893 51687 96847 28855 783 0.88892 82488 35422 57470 660 0.45804 64697 19382 34113 686 - 88938 58507 64713 50354 274 -45715 73125 95485 84487 142 - 88984 25633 08227 78315 047 . 45626 76983 14314 84956 158 - 89029 83860 09252 90807 488 . 45537 76277 65483 56224 382 -89075 33184 11966 21527 609 .45448 71018 39062 45757 688 0.89120 73600 61435 33995 180 0.45359 61214 25577 38777 137 -89166 05105 03618 67046 971 . 45270 46874 16008 69206 400 -89211 27692 85365 80240 901 -45181 28007 01790 30573 730 - 89256 41359 54417 99171 080 - 45092 04621 74808 86868 576 - 89301 46100 59408 60693 678 .45002 76727 27402 83352 928 0.89346 41911 49863 58063 585 0.44913 44332 52361 57327 478 . 89391 28787 76201 85981 812 .44824 07446 42924 48852 689 - 89436 06724 89735 85553 594 - 44734 66077 92780 11424 866 - 89480 75718 42671 89157 146 -44645 20235 96065 22607 305 - 89525 35763 88110 65223 027 - 44555 69929 47363 94616 628 0.89569 86856 80047 62924 063 0.44466 15167 41706 84864 374 - 89614 28992 73373 56775 801 -44376 55958 74570 06453 951 - 89658 62167 23874 91147 427 - 44286 92312 41874 38633 030 . 89702 86375 88234 24683 120 -44197 24237 39984 37201 474 .89747 01614 24030 74633 785 .44107 51742 65707 44874 890 0.89791 07877 89740 61099 138 0.44017 74837 16293 01603 891 . 89835 05162 44737 51180 079 - 43927 93529 89431 54849 166 . 89878 93463 49293 03041 321 . 43838 07829 83253 69812 438 . 89922 72776 64577 09884 230 -43748 17745 96329 39623 410 . 89966 43097 52658 43829 826 -43658 23287 27666 95482 777 0.90010 04421 76504 99711 910 0.43568 24462 76712 16761 399 .90053 56744 99984 38780 263 -43478 21281 43347 41055 736 - 90097 00062 87864 32313 880 . 43388 13752 27890 74199 612 -90140 34371 05813 05144 201 . 43298 01884 31095 00232 420 . 90183 59665 20399 79088 276 .43207 85686 54146 91323 845 0.90226 75940 99095 16291 842 0.43117 65167 98666 17655 197 .90269 83194 10271 62482 258 .43027 40337 66704 57257 452 . 90312 81420 23203 90131 256 .42937 11204 60745 05806 078 .90355 70615 08069 41527 464 .42846 77777 83700 86372 749 .90398 50774 35948 71758 658 .42756 40066 38914 59134 030 0.90441 21893 78825 91603 708 0.42665 98079 30157 31037 122 . 90483 83969 09589 10334 160 .42575 51825 61627 65422 763 .90526 36996 02030 78425 425 -42485 01314 37950 91605 376 . 90568 80970 30848 30177 523 .42394 46554 64178 14410 540 .90611 15887 71644 26245 348 . 42303 87555 45785 23669 902 0.90653 41744 00926 96078 401 0.42213 24325 88672 03673 585 -90695 58534 96110 80269 960 .42122 56874 99161 42580 219 -90737 66256 35516 72815 632 .42031 85211 83998 41784 656 -90779 64903 98372 63281 260 -41941 09345 50349 25243 478 -90821 54473 64813 78880 126 .41850 29285 05800 48758 379 69 70 Tasie XII.— Values of sin x and cos x to 28 places of decimals at intervals of 0.001 from 0.000 MEMOIRS NATIONAL ACADEMY OF SCIENCES. to 1.600—Continued. x sin x cos £ 1.140 0.90863 34961 15883 26459 422 0.41759 45039 58358 09217 519 .141 - 90905 06362 33532 34895 940 .41668 56618 16446 53794 933 . 142 . 90946 68673 00620 94400 939 .41577 64029 88907 89108 094 143 . 90988 21889 00918 03234 153 .41486 67283 85000 90333 707 . 144 -91029 66006 19102 04826 885 .41395 66389 14400 10281 852 1,145 0.91071 01020 40761 29314 164 0.41304 61354 87194 88428 529 - 146 91112 26927 52394 39475 912 .41213 52190 13888 59906 732 . 147 .91153 43723 41410 67087 073 .41122 38904 05397 64456 120 . 148 -91194 51403 96130 56676 684 .41031 21505 73050 55331 381 . 149 91235 49965 05786 06195 821 .40940 00004 28587 08169 395 1.150 0.91276 39402 60521 08094 403 0.40848 74408 84157 29815 258 - 151 -91317 19712 51391 90306 792 .40757 44728 52320 67107 284 . 152 .91357 90890 70367 57146 165 .40666 10972 46045 15621 071 . 153 -91398 52933 10330 30107 602 .40574 73149 78706 28372 706 . 154 . 91439 05835 65075 88579 865 .40483 31269 64086 24481 224 1.155 0.91479 49594 29314 10465 816 0.40391 85341 16372 97790 397 . 156 .91519 84204 98669 12711 431 .40300 353738 50159 25449 945 . 157 .91560 09663 69679 91743 383 .40208 81375 80441 76456 266 . 158 .91600 25966 39800 63815 143 .40117 23357 22620 20152 779 . 159 91640 33109 07401 05261 556 40025 61326 92496 34689 958 1.160 0.91680 31087 71766 92661 866 0.39933 95294 06273 15445 164 . 161 -91720 19898 33100 42911 136 . 89842 25267 80553 83402 355 . 162 -91759 99536 92520 53200 023 . 39750 51257 32340 93491 775 - 163 .91799 69999 52063 40902 883 . 89658 73271 79035 42889 706 164 .91839 31282 14682 83374 147 . 39566 91320 38435 79278 377 1.165 0.91878 83380 84250 57652 941 0.39475 05412 28737 09066 125 . 166 91918 26291 65556 80075 906 . 39383 15556 68530 05567 898 . 167 91957 60010 64310 45798 178 . 39291 21762 76800 17146 187 . 168 .91996 84533 87139 68222 492 . 39199 24039 72926 75312 486 . 169 .92035 99857 41592 18336 360 .39107 22396 76682 02789 366 1.170 0.92075 05977 36135 63957 301 0.39015 16843 08230 21533 266 mayb .92114 02889 80158 08886 071 . 38923 07387 88126 60718 072 172 .92152 90590 83968 31967 851 . 38830 94040 37316 64679 599 173 .92191 69076 58796 26061 369 . 38738 76809 77135 00821 054 174 . 92230 38343 16793 36915 902 . 38646 55705 29304 67479 575 1.175 0.92268 98386 71033 01956 127 0.38554 307386 15936 01753 942 176 .92307 49203 35510 88974 783 . 38462 01911 59525 87293 547 177 .92345 90789 25145 34733 097 . 38369 69240 82956 62048 718 .178 . 92384 23140 55777 83468 944 . 88277 32733 09495 25982 487 .179 .92422 46253 44173 25312 701 . 38184 92397 62792 48743 902 1,180 0.92460 60124 08020 34610 754 0.38092 48243 66881 77302 960 . 181 .92498 64748 65932 08156 619 . 38000 00280 46178 438547 271 . 182 . 92536 60123 37446 03329 642 .37907 48517 25478 71840 534 . 183 .92574 46244 43024 76141 242 . 387814 92963 29958 86542 917 . 184 .92612 23108 04056 19188 645 .37722 33627 85174 19493 444 1.185 0.92649 90710 42853 99516 095 0.37629 70520 17058 17454 471 . 186 .92687 49047 82657 96383 480 . 37537 03649 51921 49518 342 . 187 .92724 98116 47634 38942 352 . 37444 33025 16451 14476 334 . 188 .92762 37912 62876 43819 290 . 37351 58656 37709 48149 962 . 189 .92799 68432 54404 52606 588 . 37258 80552 43133 30684 752 1,190 0.92836 89672 49166 69260 202 0.37165 98722 60532 93806 568 . 191 .92874 01628 75038 97404 950 . 37073 18176 18091 28040 589 . 192 .92911 04297 60825 77546 899 . 36980 23922 44362 89893 026 . 193 .92947 97675 36260 24192 928 . 36887 30970 68273 08995 672 . 194 . 92984 81758 32004 62877 403 . 36794 34330 19116 95213 382 1.195 0.93021 56542 79650 67095 956 0.36701 34010 26558 45714 570 . 196 . 93058 22025 11719 95146 303 . 36608 30020 20629 52004 819 . 197 .93094 78201 61664 26876 083 . 36515 22369 31729 06923 698 - 198 .93131 25068 63866 00337 679 . 36422 11066 90622 11604 876 . 199 .93167 62622 53638 48349 974 . 36328 96122 28438 82399 631 [Vou, XIV, No. 5.1 TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. TaBLe XII.— Values of sin x and cos x to 28 places of decimals at intervals of 0.001 from 0.000; to 1.600—Continued. 1. 200 - 201 - 202 - 203 . 204 1. 205 - 206 . 207 - 208 . 209 1, 210 -211 - 212 - 213 214 1. 215 . 216 217 - 218 -219 1. 220 - 221 . 222 - 223 . 224 1, 225 226 227 . 228 . 229 1. 230 . 231 . 232 233 234 1. 235 . 236 . 237 . 238 . 239 1. 240 241 «242 . 243 . 244 1. 245 - 246 - 248 249 1. 250 - 251 - 252 - 253 - 254 1. 255 - 256 257 1259 sin £ cos 0. 93203 90859 67226 34967 013 0.36235 77544 76673 57763 837 - 93240 09776 41805 91853 542 . 86142 55343 67184 05108 539 - 93276 19369 15485 54567 367 . 36049 29528 32190 27614 189 - 93312 19684 27305 98748 519 . 35956 00108 04273 71008 651 - 93348 10568 17240 76215 175 . 35862 67092 16376 30309 065 0.93383 92167 26196 50966 302 0.35769 30490 01799 56527 660 - 93419 64427 96013 35090 992 . 85675 90310 94208 63341 607 . 93455 27346 69465 24584 444 . 35582 46564 27606 33727 018 - 93490 80919 90260 35070 567 . 35488 99259 36382 26557 166 . 93526 25144 03041 37431 162 . 35395 48405 55261 83165 039 0.93561 60015 53385 93341 646 0.35301 94012 19330 33870 301 - 93596 85530 87806 90713 291 . 35208 36088 64027 04470 775 - 93632 01686 53752 79041 926 .385114 74644 25144 22698 521 - 93667 08478 99608 04663 095 . 35021 09688 38826 24640 616 . 93702 05904 74693 45913 598 . 84927 41230 41568 61124 730 0.93736 93960 29266 48199 416 0.34833 69279 70217 04069 578 .93771 72642 14521 58969 959 . 34739 93845 61966 52800 358 - 93806 41946 82590 62598 617 . 34646 14937 54860 40329 260 - 93841 01870 86543 15169 574 . 34552 32564 85289 39601 140 . 93875 52410 80386 79170 848 . 34458 46736 92990 69704 455 0.93909 93563 19067 58093 524 0.34364 57463 16047 02047 552 . 93944 25324 58470 30937 151 . 34270 64752 93385 66500 405 . 93978 47691 55418 86621 257 .34176 68615 64277 57501 890 .94012 60660 67676 58302 957 . 84082 69060 68336 40132 702 - 94046 64228 53946 57600 622 . 33988 66097 45517 56153 996 0.94080 58391 73872 08723 559 0.33894 59735 36117 30011 855 .94114 438146 88036 82507 685 . 33800 49983 80771 74807 668 -94148 18490 57965 30357 157 . 33706 36852 20455 98234 533 94181 84419 46123 18091 912 . 33612 20349 96483 08479 750 94215 40930 15917 59701 104 . 33518 00486 50503 20093 523 0.94248 88019 31697 51002 382 0.33423 77271 24502 59823 955 . 94282 25683 58754 03206 998 . 33329 50713 60802 72418 427 . 94315 53919 63320 76390 684 . 83235 20823 02059 26391 462 . 94348 72724 12574 12870 299 33140 87608 91261 19759 164 . 94381 82093 74633 70486 175 . 83046 51080 71729 85740 328 0.94414 82025 18562 55790 164 0.32952 11247 87117 98424 316 .94447 72515 143867 57139 322 . 32857 68119 81408 78405 786 . 94480 58560 32999 77695 223 . 32763 21705 98914 98386 387 .94513 25157 46354 68328 851 . 32668 72015 84277 88743 487 . 94545 87303 27272 60431 046 . 32574 19058 82466 438066 054 0.94578 39994 49538 98628 471 0.32479 62844 38776 23657 769 .94610 83227 87884 73405 063 . 32385 03381 98828 67007 475 . 94643 17000 17986 53628 942 . 32290 40681 08569 89227 042 .94675 41308 16467 18984 738 .32195 74751 14269 91456 764 .94707 56148 60895 92311 309 . 32101 05601 62521 65238 364 0.94739 61518 29788 71844 815 0.32006 33242 00239 97855 712 .94771 57414 02608 63367 118 .31911 57681 74660 77643 341 . 94803 43832 59766 12259 472 .31816 78930 33339 99262 871 . 94835 20770 82619 35461 479 . 31721 96997 24152 68947 423 .94866 88225 53474 53335 262 . 31627 11891 95292 09714 116 0.94898 46193 55586 21434 849 0.31532 23623 95268 66544 754 .94929 94671 73157 62180 713 . 31487 32202 72909 11534 791 .94961 33656 91340 96439 444 . 31342 37637 77355 49010 665 .94992 63145 96237 75008 528 . 31247 39938 58064 20615 601 . 95023 83135 74899 10006 196 .31152 39114 64805 10363 979 0.95054 93623 15326 06166 303 0.31057 35175 47660 49664 355 .95085 94605 06469 92038 225 . 30962 28130 57024 22311 242 .95116 86078 38232 51091 729 . 30867 17989 48600 69445 729 .95147 68040 01466 52726 783 .30772 04761 58403 94485 052 .95178 40486 87975 83188 287 . 30676 88456 52756 68021 196 rai 72 Tasie XIT.— Values of sin x and cos x to 28 places of decimals at intervals of 0.001 from 0.000 MEMOIRS NATIONAL ACADEMY OF SCIENCES. to 1.600—Continued. x sin © cos & 1. 260 0.95209 03415 90515 76385 682 0. 30581 69083 78289 32688 634 . 261 - 95239 56824 02793 44617 416 . 30486 46652 86939 08001 291 . 262 . 95270 00708 19468 09200 227 . 30391 21173 30948 95158 833 . 263 . 95300 ee 36151 31003 222 . 30295 92654 62866 81822 373 . 264 - 95330 59892 49407 40886 709 . 30200 61106 35544 46859 693 1. 265 0.95360 75186 56753 70045 767 0.30105 26538 02136 65060 070 . 266 - 95390 80944 56660 80258 512 .30009 88959 16100 11818 814 . 267 - 95420 77163 48552 94039 032 .29914 48379 31192 67791 595 - 268 . 95450 63840 32808 24694 963 . 29819 04808 01472 23518 675 - 269 - 95480 40972 10759 06289 671 . 29723 58254 81295 84019 121 1. 270 0.95510 08555 84692 23509 018 0.29628 08729 25318 73355 114 271 . 95539 66588 57849 41432 673 . 29532 56240 88493 39166 425 272 - 95569 15067 34427 35209 944 . 29437 00799 26068 57175 182 . 273 . 95598 53989 19578 19640 104 . 29341 42413 93588 35661 000 274 - 95627 83351 19409 78657 170 . 29245 81094 46891 19906 579 1, 275 0.95657 03150 40985 94719 118 0.29150 16850 42108 96613 869 - 276 . 95686 13383 92326 78101 497 . 29054 49691 35665 98290 890 277 95715 14048 82408 96095 419 . 28958 79626 84278 07609 308 . 278 - 95744 05142 21166 02109 886 . 28863 06666 44951 61732 860 .279 - 95772 86661 19488 64678 437 . 28767 30819 74982 56616 726 1. 280 0.95801 58602 89224 96370 075 0.28671 52096 31955 51277 939 . 281 . 95830 20964 43180 82604 453 . 28575 70505 73742 72036 934 - 282 - 95858 73742 95120 10371 286 . 28479 86057 58503 16730 332 . 283 . 95887 16935 59764 96853 962 . 28383 98761 44681 58895 050 . 284 . 95915 50539 52796 17957 320 . 28288 08626 91007 51923 831 1, 285 0.95943 74551 90853 36739 577 0.28192 15663 56494 33192 303 . 286 . 95971 88969 91535 31748 357 . 28096 19881 00438 28157 651 . 287 - 95999 93790 73400 25260 814 . 28000 21288 82417 54428 993 . 288 - 96027 89011 55966 11427 805 . 27904 19896 62291 25809 577 . 289 - 96055 74629 59710 84322 094 . 27808 15714 00198 56310 871 1. 290 0.96083 50642 06072 65890 556 0.27712 08750 56557 64138 661 - 291 -96111 17046 17450 33810 354 . 27615 99015 92064 75651 234 . 292 . 96138 73839 17203 49249 056 . 27519 86519 67693 29289 769 . 293 - 96166 21018 29652 84528 675 . 27423 71271 44692 79480 997 . 294 - 96193 58580 80080 50693 590 . 27327 53280 84588 00512 263 1. 295 0.96220 86523 94730 24982 339 0.27231 32557 49177 90379 053 . 296 . 96248 04845 00807 78203 231 .27135 09111 00534 74605 108 . 297 . 96275 13541 26481 02013 782 . 27038 82951 01003 10035 206 - 298 . 96302 12610 00880 36103 915 . 26942 54087 13198 88600 711 - 299 - 96329 02048 54098 95282 920 . 26846 22529 00008 41057 992 1. 300 0.96355 81854 17192 96470 135 0.26749 88286 24587 40699 798 . 301 . 96382 52024 22181 85589 331 . 26653 51368 50360 07039 695 . 302 - 96409 12556 02048 64366 761 . 26557 11785 41018 09469 650 . 303 .- 96435 63446 90740 17032 855 . 26460 69546 60519 70890 877 - 304 . 96462 04694 23167 36927 537 . 26364 24661 73088 71318 016 1. 305 0.96488 36295 35205 53009 126 0.26267 77140 48213 51456 761 . 306 - 96514 58247 63694 56266 806 - 26171 26992 35646 16255 031 . 307 . 96540 70548 46439 26036 635 . 26074 ' 74227 15401 38427 774 - 308 . 96566 73195 22209 56221 061 . 25978 18854 47755 61955 494 - 309 . 96592 66185 30740 81411 924 . 25881 60883 98246 05556 626 1. 310 0.96618 49516 12734 02916 926 0.25785 00325 32669 66133 818 . 311 . 96644 23185 09856 14689 520 . 25688 37188 17082 22194 242 . 312 .- 96669 87189 64740 29162 218 25591 71482 17797 37244 030 .313 - 96695 41527 20986 02983 276 . 25495 03217 01385 63156 911 314 . 96720 86195 23159 62656 736 - 25398 32402 34673 43517 173 1.315 0.96746 21191 16794 30085 794 0.25301 59047 84742 16937 022 . 316 .96771 46512 48390 48019 478 . 20204 83163 18927 20348 457 .317 . 96796 62156 65416 05402 607 - 25108 04758 04816 92269 738 .318 . 96821 68121 16306 62628 991 . 25011 23842 10251 76046 556 . 319 . 96846 64403 50465 76697 879 . 24914 40425 03323 23067 996 [Vor. XIV, No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. TasLy XII.— Values of sin x and cos x to 23 places of decimals at intervals of 0.001 from 0.000 to 1.600—Continued. x sin & cos x 1,320 0.96871 51001 18265 26273 590 0.24817 54516 52372 95957 398 . 321 - 96896 27911 71045 36648 340 . 24720 66126 25991 71738 199 - 322 - 96920 951382 61115 04608 211 . 24623 75263 93018 44974 865 «323 . 96945 52661 41752 23202 252 . 24526 81939 22539 30889 004 324 . 96970 00495 67204 06414 685 . 24429 86161 83886 68450 760 1,325 0.96994 38632 92687 13740 188 0. 24832 87941 46638 23445 582 - 326 - 97018 67070 74387 74662 236 . 24235 87287 80615 91516 463 . 327 - 97042 85806 69462 13034 465 . 24138 84210 55885 O1181 759 - 328 -97066 94838 36036 71365 051 . 24041 78719 42753 16828 662 329 - 97090 94163 33208 35004 060 . 23944 70824 11769 41682 448 1. 330 0.97114 83779 21044 56233 768 0. 23847 60534 33723 20751 578 . 331 . 97188 63683 60583 78261 900 . 23750 47859 79643 43748 768 - 332 . 97162 33874 13835 59117 786 . 23653 32810 20797 47988 097 . 333 . 97185 94348 48780 95451 405 . 23556 15395 28690 21258 288 . 334 . 97209 45104 14372 46235 282 . 23458 95624 75063 04672 221 1. 335 0.97232 86138 90534 56369 230 0. 23361 73508 31892 95492 805 . 336 . 97256 17450 38163 80187 900 . 23264 49055 71391 49935 286 - 337 . 97279 39036 24129 04871 129 . 23167 22276 66003 85946 099 - 338 . 97302 50894 16271 73757 046 . 23069 93180 88407 85958 358 . 339 - 97325 53021 83406 09557 931 . 22972 61778 11512 99624 085 1. 340 0.97348 45416 95319 37478 787 0.22875 28078 08459 46523 264 . 34) . 97371 28077 22772 08238 616 . 22777 92090 52617 18849 831 - 342 - 97394 01000 37498 20994 365 . 22680 53825 17584 84074 691 - 343 - 97416 64184 12205 46167 522 . 22583 13291 77188 87585 859 . 344 . 97439 17626 20575 48173 349 . 22485 70500 05482 55305 819 1. 345 0.97461 61324 37264 08052 713 0.22388 25459 76744 96286 212 . 846 . 97483 95276 37901 46006 501 . 22290 78180 65480 05279 929 . 347 - 97506 19479 99092 43832 603 . 22193 28672 46415 65290 729 . 348 . 97528 33932 98416 67265 423 . 22095 76944 94502 50100 463 . 349 . 97550 38633 14428 88217 916 21998 23007 84913 26774 007 1. 350 0.97572 33578 26659 06926 111 0.21900 66870 93041 58142 002 . 851 . 97594 18766 15612 73996 110 - 21803 08543 94501 05261 504 « 352 - 97615 94194 62771 12353 536 -21705 48036 65124 29854 627 . 353 . 976387 59861 50591 39095 407 . 21607 85358 80961 96725 291 . 854 . 97659 15764 62506 87244 418 -21510 20520 18281 76154 163 1, 355 0.97680 61901 82927 27405 609 0.21412 53530 53567 46271 899 . 306 .97701 98270 97238 89325 386 . 21314 84399 63517 95410 772 . 357 . 97723 24869 91804 83352 894 21217 18137 25046 24484 790 . 358 . 97744 41696 53965 21803 706 .21119 39753 15278 49048 406 . 359 .97765 48748 72037 40225 805 .21021 64257 11553 02083 908 1. 360 0.97786 46024 35316 18567 849 0.20923 86658 91419 35767 598 . 361 .97807 33521 34074 02249 690 - 20826 06968 32637 23964 842 . 362 . 97828 11237 59561 23135 125 . 20728 25195 13175 64404 112 . 363 .97848 79171 04006 20406 864 - 206380 41349 11211 80880 089 . 364 . 97869 37319 60615 61343 685 . 205382 55440 05130 254385 952 1.365 0.97889 85681 23574 61999 774 0.20434 67477 73521 80524 932 . 366 . 97910 24253 88047 07786 196 . 20336 77471 95182 61151 240 . 367 . 97930 53035 50175 73954 516 . 20288 854382 49113 16990 457 . 368 . 97950 72024 07082 45982 521 . 20140 91869 14517 34489 495° . 369 .97970 81217 56868 39862 027 . 20042 95291 70801 38946 217 1.370 0.97990 80613 98614 22288 769 0.19944 97209 97572 96568 820 371 - 98010 70211 32380 30754 328 . 19846 97133 74640 16515 079 . 372 - 98030 50007 59206 93540 094 19748 95072 82010 52911 545 373 - 98050 20000 81114 49613 233 . 19650 91036 99890 06852 798 . 374 - 98069 80189 01103 68424 652 .19552 85036 08682 28380 853 1.375 0.98089 30570 23155 69608 920 0.19454 77079 88987 18444 9822 376 -98108 71142 52232 42586 155 .19356 67178 21600 30840 918 .377 - 98128 01903 94276 66065 826 . 19258 55340 87511 74132 912 . 378 - 98147 22852 56212 27452 479 .19160 41577 67905 138553 129 379 - 98166 33986 45944 42153 343 . 19062 25898 44156 72884 094 MEMOIRS NATIONAL ACADEMY OF SCIENCES. [Vou XLV, TaBLE XII.— Values of sin x and cos x to.28 places of decimals at intervals of 0.001 from 0.000 to 1.600—Continued. x sin x cos x 1. 380 0.98185 35303 72359 72787 813 0.18964 08312 97834 36320 915 . 381 . 98204 26802 45326 48298 791 . 18865 88831 10696 50314 508 . 382 . 98223 08480 75694 82965 850 .18767 67462 64691 25395 757 . 383 . 98241 80336 75296 95320 221 .18669 44217 41955 37980 715 . 384 . 98260 42368 56947 26961 571 .18571 19105 24813 32156 930 1. 385 0.98278 94574 34442 61276 561 0.18472 921385 95776 21451 016 . 386 . 98297 36952 22562 42059 162 |. . 18374 63319 37540 90577 542 . 387 - 98315 69500 37068 92032 708 .18276 32665 32988 97169 360 - 388 . 98333 92216 94707 31273 673 .18178 00183 65185 73489 451 . 389 . 98352 05100 13205 95537 148 .18079 65884 17379 28124 404 1.390 0.98370 08148 11276 54484 004 0.17981 29776 72999 47659 616 391 - 98388 01359 08614 29809 722 .17882 91871 15656 98336 311 . 392 - 98405 84731 25898 13274 870 .17784 52177 29142 27690 484 3893 | .98423 58262 84790 84637 207 .17686 10704 97424 66173 860 - 394 . 98441 21952 07989 29485 405 .17587 67464 04651 28756 976 1.395 0.98458 75797 18974 56974 360 0.17489 22464 35146 16514 467 . 396 . 98476 19796 42512 17462 083 .17390 75715 73409 18192 681 . 397 . 98493 53948 04152 20048 145 .17292 27228 04115 11759 690 - 398 . 98510 78250 30479 50013 670 .17193 77011 12112 65937 830 . 399 .98527 92701 49063 86162 846 .17095 25074 82423 41718 833 1. 400 0.98544 97299 88460 18065 947 0.16996 71429 00240 93861 675 -401 . 98561 92043 78208 63203 840 .16898 16083 50929 72373 233 . 402 . 98578 76931 48834 84013 966 . 16799 59048 20024 23971 842 . 403 . 98595 51961 31850 04837 776 . 16701 00332 93227 93533 854 - 404 . 98612 17131 59751 28769 609 .16602 39947 56412 25523 303 1. 405 0.98628 72440 66021 54406 982 0.16503 77901 95615 65404 770 - 406 . 98645 17886 85129 92502 294 . 16405 14205 97042 61039 544 -407 98661 53468 52531 82515 912 . 16306 48869 47062 64065 184 - 408 . 98677 79184 04669 09070 631 . 16207 81902 32209 31258 571 409 . 98693 95031 78970 18307 486 .16109 13314 39179 25882 568 1.410 0.98710 01010 13850 34142 909 0.16010 43115 54831 19016 356 411 .98725 97117 48711 74427 198 .15911 71315 66184 90869 577 . 412 .98741 83352 23943 67004 304 . 15812 97924 60420 32080 359 413 .98757 59712 80922 65672 895 .15714 22952 24876 44997 336 414 .98773 26197 62012 66048 706 . 15615 46408 47050 44945 751 1.415 0.98788 82805 10565 21328 142 0.15516 68303 14596 61477 752 . 416 . 98804 29533 70919 57953 120 . 15417 88646 15325 39606 967 .417 .98819 66381 88402 91177 144 15319 07447 37202 41027 471 - 418 . 98834 93348 09330 40532 586 . 15220 24716 68347 45317 231 .419 . 98850 10430 81005 45199 170 .15121 40463 97033 51126 135 1. 420 0.98865 17628 51719 79273 627 0.15022 54699 11685 77348 698 -421 .98880 149389 70753 66940 521 . 14923 67432 00880 64281 559 422 .98895 02362 88375 97544 222 . 14824 78672 53344 74765 840 423 .98909 79896 55844 40562 021 . 14725 88430 57953 95314 499 424 .98924 47539 25405 60478 351 . 14626 96716 03732 387224 747 1. 425 0.98939 05289 50295 31560 129 0.14528 035388 79851 37675 648 - 426 .98953 53145 84738 52533 174 . 14429 08908 75628 60810 986 ) ,427 .98967 91106 83949 61159 714 . 14330 12835 80526 98807 514 - 428 .98982 19171 04132 48716 941 . 14231 15329 84153 72928 666 429 .98996 37337 02480 74876 619 . 141382 16400 76259 34563 848 1. 430 0.99010 45603 37177 79485 729 0.14033 16058 46736 66253 390 . 481 .99024 43968 67397 01748 121 . 18934 14812 85619 82699 275 , 482 . 99088 32431 53301 89307 176 . 13835 11173 83083 31761 733 » , 433 . 99052 10990 56046 14729 460 . 13736 06651 29440 95441 799 - 434 .99065 79644 37773 88889 346 . 13637 00755 15144 90849 940 | 1.485 0.99079 38391 61619 74754 605 0.13537 93495 30784 71160 849 486 .99092 87230 91709 01072 941 . 13488 84881 67086 26554 495 . 4387 .99106 26160 93157 75959 459 . 13339 74924 14910 85143 546 - 438 .99119 55180 32073 00385 060 . 13240 636382 65254 13887 244 . 439 .99182 74287 75552 81565 735 . 138141 51017 09245 19491 852 No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. TaBLe XII.— Values of sin x and cos x to 28 places of decimals at intervals of 0.001 from 0.000 to 1.600—Continued. x sin & cos £ 1. 440 0.99145 83481 91686 46252 760 0.13042 37087 38145 49297 752 . 441 .99158 82761 49554 53923 766 . 12948 21853 43347 92153 306 - 442 .99171 72125 19229 09874 676 . 12844 05325 16375 79275 576 - 443 . 99184 51571 71773 78212 505 . 12744 87512 48881 85098 002 . 444 -99197 21099 79243 94748 990 . 12645 68425 32647 28105 135 1. 445 0.99209 80708 14686 79795 055 0.12546 48073 59580 71654 525 - 446 99222 30395 52141 50856 088 . 12447 26467 21717 24785 871 447 . 99234 70160 66689 35228 024 . 12348 08616 11217 438017 513 . 448 . 99247 00002 34203 82494 216 . 12248 79530 20366 29130 391 . 449 . 99259 19919 31850 76923 086 .12149 54219 41572 33939 548 1. 450 0.99271 29910 37588 49766 535 0.12050 27693 67366 57053 287 - 451 . 99283 29974 30417 91459 118 . 11950 99962 90401 47620 080 - 452 - 99295 20109 90332 63717 946 .11851 71037 03450 05063 327 - 453 . 99307 00315 98319 11543 325 .11752 40925 99404 79804 068 . 454 .99318 70591 36356 75120 114 .11653 09639 71276 73971 735 1, 455 0.99330 30934 87418 01619 777 0.11553 77188 12194 42103 061 - 456 . 99341 81345 35468 56903 143 . 11454 43581 15402 91829 237 . 457 . 99353 21821 65467 37123 830 . 11355 08828 74262 84551 407 . 458 . 99364 52362 63366 80232 355 . 11255 72940 82249 36104 618 . 459 . 99375 72967 16112 77380 893 11156 35927 32951 17410 313 1. 460 0.99386 83634 11644 84228 683 0.11056 97798 20069 55117 465 . 461 . 99397 84362 38896 32148 075 . 10957 58568 37417 32232 463 . 462 .99408 75150 87794 39331 194 . 10858 18232 78917 88737 835 . 463 . 99419 55998 49260 21797 223 . 10758 76816 38604 22199 915 . 464 . 99430 26904 15209 04300 286 . 10659 34324 10617 88365 556 1. 465 0.99440 87866 78550 31137 923 0.10559 90765 89208 01747 983 - 466 . 99451 38885 33187 76860 141 . 10460 46151 68730 36201 884 - 467 . 99461 79958 74019 56879 043 . 10361 00491 43646 25487 846 - 468 - 99472 11085 96938 37979 012 . 10261 53795 08521 63826 230 - 469 . 99482 32265 98831 48727 437 .10162 06072 58026 06440 584 1. 470 0.99492 43497 77580 89785 993 0.10062 57333 86931 70090 698 -471 . 99502 44780 32063 44122 430 .09963 07588 90112 33595 391 472 99512 36112 62150 87122 898 .09863 56847 62542 38345 147 473 . 99522 17493 68709 96604 762 .09764 05119 99295 88804 678 .474 . 99531 88922 53602 62729 932 . 09664 52415 95545 53005 525 1. 475 0.99541 50398 19685 97818 664 0.09564 98745 46561 63028 806 - 476 .99551 01919 70812 46063 854 .09465 44118 47711 15478 186 .477 .99560 48486 11829 93145 787 .09365 88544 94456 71943 189 . 478 .99569 75096 48581 75747 356 .09266 32034 82355 59452 948 .479 .99578 96749 87906 90969 720 .09166 74598 07058 70920 484 1. 480 0.99588 08445 37640 05648 408 0.09067 16244 64309 65577 623 481 .99597 10182 06611 65569 851 . 08967 56984 49943 69400 641 . 482 .99606 01959 04648 04588 337 .08867 96827 59886 75526 752 . 483 .99614 83775 42571 53643 374 .08768 35783 90154 44661 519 . 484 . 99623 55630 32200 49677 461 . 08668 73863 36851 05477 303 1. 485 0.99632 17522 86349 44454 246 0.08569 11075 96168 55002 845 - 486 . 99640 69452 18829 13277 079 08469 47431 64385 59004 070 . 487 . 99649 11417 44446 63607 933 .08369 82940 37866 52356 240 . 488 .99657 43417 79005 43586 693 .08270 17612 13060 39407 518 . 489 .99665 65452 39305 50450 815 .08170 51456 86499 94334 076 1. 490 0.99673 77520 43143 38855 320 0.08070 84484 54800 61486 832 491 . 99681 79621 09312 29093 143 .07971 16705 14659 55729 907 492 . 99689 71753 57602 15215 811 .07871 48128 62854 62770 926 - 493 .99697 53917 08799 73054 448 .07771 78764 96243 39483 234 494 .99705 26110 84688 68141 099 .07672 08624 11762 14220 152 1. 495 0.99712 88334 08049 63530 364 0.07572 37716 06424 87121 354 496 -99720 40586 02660 27521 334 .07472 66050 77322 30411 478 497 -99727 82865 93295 41279 821 .07372 93638 21620 88691 060 . 498. -99735 15173 05727 06360 877 .07273 20488 36561 79219 898 . 499 -99742 37506 66724 52131 595 .07173 46611 19459 92192 943 75 DEPARTMENT OF BATWEMAT TOR CORMELL URFYERSITY 76 TABLE XII.— Values of sin x and cos x to 28 places of decimals at intervals of 0.001 from 0.000 MEMOIRS NATIONAL ACADEMY OF SCIENCES. to 1.600—Continued. x sin £ COs % 1.500 0.99749 49866 04054 43094 172 0.07073 72016 67702 91008 819 . 501 99756 52250 46480 86109 251 .06973 96714 78750 12531 065 - 502 99763 44659 23765 37519 509 . 06874 20715 50131 67342 208 . 503 .99770 2709) 66667 10173 501 .06774 44028 79447 39990 761 . 504 .99776 99547 06942 80349 750 .06674 66664 64365 89231 245 1. 505 0.99783 62024 77346 94581 063 0.06574 88633 02623 48257 343 . 506 . 99790 14524 11631 76379 092 . 06475 09943 92023 24928 268 . 507 - 99796 57044 44547 32859 104 . 06375 30607 30434 01988 470 . 508 .- 99802 89585 11841 61264 976 .06275 50633 15789 37280 758 . 509 . 99809 12145 50260 55394 397 .06175 70031 46086 63952 953 1.510 0.99815 24724 97548 11924 274 0.06075 88812 19385 90658 160 - 511 99821 27322 92446 36636 332 .05976 06985 33809 01748 769 - 512 .- 99827 19988 74695 50542 912 . 05876 24560 87538 57464 281 . 513 . 99833 02571 85033 95912 947 .05776 41548 78816 94113 053 . 514 - 99838 75221 65198 42198 118 .05676 57959 05945 24248 072 1. 515 0.99844 37887 57923 91859 188 0.05576 73801 67282 36886 851 - 516 - 99849 90569 06943 86092 495 . 05476 89086 61243 97425 545 517 -99855 33265 56990 10456 612 . 05377 03823 86301 48297 399 . 518 - 99860 65976 53793 00399 163 . 05277 18023 40981 08625 609 .519 - 99865 88701 44081 46683 784 .05177 31695 23862 74620 716 1. 520 0.99871 01439 75583 00717 231 0.05077 44849 33579 19672 613 . 521 - 99876 04190 97023 79776 634 .04977 57495 68814 94487 284 - 522 - 99880 96954 58128 72136 872 . 04877 69644 28305 27218 360 - 623 . 99885 79730 09621 42098 089 .04777 81305 10835 23593 598 . 524 99890 52517 03224 34913 328 . 04677 92488 15238 67036 388 1. 525 0.99895 15314 91658 81616 285 0.04578 03203 40397 18782 371 . 526 - 99899 68123 28645 03749 180 . 04478 13460 85239 17991 291 .527 - 99904 10941 68902 17990 729 . 04378 23270 48738 81854 166 528 - 99908 43769 68148 40684 234 04278 32642 29915 05695 871 . 529 -99912 66606 83100 92265 762 .04178 41586 27830 63073 262 1. 530 0.99916 79452 71476 01592 427 0.04078 50112 41591 05868 899 . 531 . 99920 82305 91989 10170 755 . 08978 58230 70343 64880 513 . 532 . 99924 75169 04354 76285 152 . 03878 65951 13276 47406 277 - 533 . 99928 58038 69286 79026 436 . 03778 73283 69617 42326 008 - 534 - 99932 30915 48498 22220 463 . 03678 80238 38633 15178 390 1,535 0.99985 93799 04701 38256 819 0.03578 86825 19628 10734 312 - 536 - 99939 46689 01607 91817 592 . 03478 93054 11943 52566 435 . 537 . 99942 89585 03928 83506 202 . 03378 98935 14956 43115 073 - 538 99946 22486 77374 53376 306 . 03279 04478 28078 63750 505 - 539 . 99949 45393 88654 84360 752 .03179 09693 50755 74831 796 1. 540 0.99952 58306 05479 05600 596 0.03079 14590. 82466 15762 248 . 541 99955 61222 96555 95674 180 .02979 19180 22720 05041 568 . 542 .99958 54144 31593 85726 242 . 02879 23471 71058 40314 858 . 043 .99961 37069 81300 62497 095 .02779 27475 27051 98418 526 . 544 . 99964 09999 17383 71251 832 . 02679 31200 90300 35423 217 1. 545 0.99966 72932 12550 18609 586 0.02579 34658 60430 86673 867 546 . 99969 25868 40506 75272 821 .02479 37858 37097 66826 971 . 547 .99971 68807 75959 78656 660 . 02379 40810 19980 69885 184 . 548 . 99974 01749 94615 35418 249 . 02279 43524 08784 69229 328 . 549 .99976 24694 73179 23886 150 .02179 46010 03238 17647 934 1. 550 0.99978 37641 89356 96389 761 0.02079 48278 03092 47364 391 . 551 . 99980 40591 21853 81488 767 .01979 50338 08120 70061 827 . 552 .99982 33542 50374 86102 606 . 01879 52200 18116 76905 802 . 553 .99984 16495 55624 97539 966 .01779 53874 32894 38564 929 . 554 .99985 89450 19308 85428 298 . 01679 55370 52286 05229 507 1.555 0.99987 52406 24131 03543 342 0.01579 56698 76142 06628 284 . 556 . 99989 05363 53795 91538 676 .01479 57869 04329 52043 433 . 557 . 99990 48321 93007 76575 277 . 01379 58891 36781 30323 849 . 558 .99991 81281 27470 74851 093 .01279 59775 73245 09896 874 .. 559 . 99993 04241 43888 93030 623 .01179 60532 13782 38778 533 [Vou. XIV, No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. Taste XII.— Values of sin x and cos x to 28 places of decimals at intervals of 0.001 from 0.000 to 1.600—Continued. x sine cos x 1.560 0.99994 17202 29966 29574 517 0.01079 61170 58267 44582 392 . 561 - 99995 20163 74406 75969 172 . 00979 61701 06636 34527 146 - 562 - 99996 13125 66914 17856 344 . 00879 62133 58835 95443 014 - 563 - 99996 96087 98192 36062 758 .00779 62478 14822 93777 062 . 564 . 99997 69050 59945 07529 731 .00679 62744 74562 75597 546 1. 565 0.99998 32013 44876 06142 794 0.00579 62943 38028 66597 372 - 566 - 99998 84976 46689 03461 318 . 00479 63084 05200 72096 784 - 567 - 99999 27939 60087 69348 142 . 00379 63176 76064 77045 359 - 568 - 99999 60902 80775 72499 201 00279 63231 50611 46023 436 . 569 . 99999 83866 05456 80873 162 -00179 63258 28835 232438 059 1.570 0.99999 96829 31834 62021 053 +0. 00079 63267 10783 32548 541 .571 - 99999 99792 58612 83315 895 —0. 00020 367382 03695 22583 254 - 572 - 99999 92755 85495 12082 337 -00120 36729 14450 59042 804 - 573 - 99999 75719 13185 15626 285 00220 36714 215383 14087 901 . 574 - 99999 48682 43386 61164 539 . 00320 36677 24944 45343 613 1.575 0.99999 11645 78803 15654 423 —0. 00420 36608 24688 30802 109 - 576 - 99998 64609 23138 45523 419 00520 36497 20771 68822 280 .577 - 99998 07572 81096 16298 798 - 00620 36334 13205 78129 029 - 578 . 99997 40536 58379 92137 261 .00720 36109 02006 97812 142 . 579 . 99996 63500 61693 35254 568 .00820 35811 87197 87324 647 1. 580 0.99995 76464 98740 05255 179 —0. 00920 35432 68808 26480 539 - 581 - 99994 79429 78223 58361 895 01020 34961 46876 15451 796 . 582 - 99993 72395 09847 46545 499 01120 34388 21448 74764 568 . 583 . 99992 55361 04315 16554 408 -01220 33702 92583 45294 454 . 584 .99991 28327 73330 08844 324 . 013820 32895 60348 88260 743 1. 585 0.99989 91295 29595 56407 893 —0. 01420 31956 24825 85219 553 . 586 - 99988 44263 86814 83504 374 -01520 30874 86108 38055 737 . 587 - 99986 87233 59691 04289 313 .01620 29641 44304 68973 475 - 588 - 99985 20204 63927 21344 232 -01720 28245 99538 20485 440 . 589 . 99983 43177 16226 24106 322 .01820 26678 51948 55400 452 1.590 0.99981 56151 34290 87198 158 —0.01920 24929 01692 56809 503 . 591 .99979 59127 36823 68657 422 . 02020 22987 48945 28070 065 . 592 .99977 52105 43527 08066 646 . 02120 20843 93900 92788 583 . 593 .99975 35085 75103 24582 972 . 02220 18488 36773 94801 039 . 594 99973 08068 53254 14867 933 . 02320 15910 77799 98151 502 1,595 0.99970 71054 00681 50917 259 —0. 02420 13101 17236 87068 552 - 596 - 99968 24042 41086 77790 702 |- . 02520 10049 55365 65939 492 . 597 99965 67033 99171 11241 891 - 02620 06745 92491 59282 234 . 598 . 99963 00029 00635 35248 219 .02720 03180 28945 11714 764 . 599 . 99960 23027 72179 99440 759 . 02819 99342 65082 87922 093 1. 600 0.99957 36030 41505 164384 211 —0. 02919 95223 01288 72620 577 7 18 MEMOIRS NATIONAL ACADEMY OF SCIENCES. Tape XIII.— Values of sin x and cos x to 25 places of decimals at decimal intervals from 1X10—" to 9X10-*, (Vou. XIV, x sin x cos X& 1X10-19_ 2... 0.00000 00001 00000 00000 00000 0.99999 99999 99999 99999 50000 ID eSeeccatowias -00000 00002 00000 00000 00000 . 99999 99999 99999 99998 00000 De cestaeisibenialcts -00000 00003 00000 00000 90000 .99999 99999 99999 99995 50000 As somes tatestae .00000 00004 00000 00000 00000 .99999 99999 99999 99992 00000 Sswsnciws osc -00000 00005 00000 00000 00000 . 99999 99999 99999 99987 50000 Ghisssceinsiess -00000 00006 00000 00000 00000 . 99999 99999 99999 99982 00000 ieee es .00000 00007 00000 00000 00000 .99999 99999 99999 99975 50000 Bisa iinsiecicn -00000 00008 00000 00000 00000 .99999 99999 99999 99968 00000 OF aeorstajcvcdorepeet -00000 00009 00000 00000 00000 . 99999 99999 99999 99959 50000 1x10- 0.00000 00010 00000 00000 00000 0.99999 99999 99999 99950 00000 Dinca se. se ey -00000 00020 00000 00000 00000 .99999 99999 99999 99800 00000 O sicivacsieecuarees - 00000 00030 00000 00000 00000 .99999 99999 99999 99550 00000 Bi ees savers aioe .00000 00040 00000 00000 00000 . 99999 99999 99999 99200 00000 Diciwaaaraiaaen -00000 00050 00000 00000 00000 . 99999 99999 99999 98750 00000 GC rcizcssqecctern -00000 00060 00000 00000 00000 .99999 99999 99999 98200 00000 Wis ciasstehzpeve oe -00000 00069 99999 99999 99999 - 99999 99999 99999 97550 00000 Bi cotte nye .00000 00079 99999 99999 99999 . 99999 99999 99999 96800 00000 Dieretiteah aden -00000 00089 99999 99999 99999 .99999 99999 99999 95950 00000 1X08... 0.00000 00099 99999 99999 99998 0.99999 99999 99999 95000 00000 Diapiek oanvayneind .00000 00199 99999 99999 99987 . 99999 99999 99999 80000 00000 Be cus 2 -00000 00299 99999 99999 99955 . 99999 99999 99999 55000 00000 Bi via miarrsvatecoiess -00000 00399 99999 99999 99893 . 99999 99999 99999 20000 00000 Coes ced -00000 00499 99999 99999 -99792 . 99999 99999 99998 75000 00000 Genscan -00000 00599 99999 99999 99640 .99999 99999 99998 20000 00000 coca ais .00000 00699 99999 99999 99428 .99999 99999 99997 55000 00000 B elercicahicie sine .00000 00799 99999 99999 99147 .99999 99999 99996 80000 00000 Oeciaee ak -00000 00899 99999 99999 98785 . 99999 99999 99995 95000 00000 1X1077. 2... 0.00000 00999 99999 99999 98333 0.99989 99999 99995 00000 00000 Deca. -00000 01999 99999 99999 86667 | .99999 99999 99980 00000 00000 9 any taescas .00000 02999 99999 99999 55000 . 99999 99999 99955 00000 00000 We cea siete .00000 03999 99999 99998 93333 . 99999 99999 99920 00000 00000 Dae tines .00000 04999 99999 99997 91667 . 99999 99999 99875 00000 00000 (a .00000 05999 99999 99996 40000 . 99999 99999 99820 00000 00000 Wis ciciantatnle xe .00000 06999 99999 99994 28333 .99999 99999 99755 00000 00000 Ba. ndusecad .00000 07999 99999 99991 46667 . 99999 99999 99680 00000 00000 GD se cejeavasntsiae .00000 08999 99999 99987 85000 .99999 99999 99595 00000 00000 1X10. .... 0.00000 09999 99999 99983 33333 0.99999 99999 99500 00000 00000 Doshi aetece .00000 19999 99999 99866 66667 . 99999 99999 98000 00000 00007 Bass maec ceeds .00000 29999 99999 99550 00000 . 99999 99999 95500 00000 00034 fh raechsei ee EN -00000 39999 99999 98933 33333 . 99999 99999 92000 00000 00107 Be oso e .00000 49999 99999 97916 66667 . 99999 99999 87500 00000 00260 Gea sjaceaee .00000 59999 99999 96400 00000 . 99999 99999 82000 00000 00540 Tes dey besa cs -00000 69999 99999 94283 33333 .99999 99999 75500 00000 01000 Bicnmacnaest .00000 79999 99999 91466 66667 .99999 99999 68000 00000 01707 Dyce rea seta .00000 89999 99999 87850 00000 . 99999 99999 59500 00000 02784 110-5 0.00000 99999 99999 83333 33333 0.99999 99999 50000 00000 04167 .00001 99999 99998 66666 66667 . 99999 99998 00000 00000 66667 .00002 99999 99995 50000 00002 .99999 99995 50000 00003 37500 .00003 99999 99989 33333 33342 . 99999 99992 00000 00010 66667 .00004 99999 99979 16666 66693 . 99999 99987 50000 00026 04167 .00005 99999 99964 00000 00065 . 99999 99982 00000 00054 00000 .00006 99999 99942 83333 33473 . 99999 99975 50000 00100 04167 .00007 99999 99914 66666 66940 .99999 99968 00000 00170 66667 .00008 99999 99878 50000 00492 . 99999 99959 50000 00273 387500 1X10... ... 0.00009 99999 99833 33333 34167 0.99999 99950 00000 00416 66667 Dhaest .00019 99999 98666 66666 93333 . 99999 99800 00000 06666 66666 Die orate haicea ke .00029 99999 95500 00002 02500 .99999 99550 00000 33749 99990 Besser ase .00039 99999 89333 33341 86667 . 99999 99200 00001 06666 66610 Doeecancenres .00049 99999 79166 66692 70833 .99999 98750 00002 60416 66450 Gees cnsmieisesais .00059 99999 64000 00064 80000 .99999 98200 00005 39999 99352 IT cesiereeciapesiaads .00069 99999 428383 33473 39167 .99999 97550 00010 00416 65033 Bia hin memes .00079 99999 14666 66939 73333 .99999 96800 00017 06666 63026 Days eesetes .00089 99998 78500 00492 07499 .99999 95950 00027 33749 92619 No. 5.] TABLES OF EXPONENTIAL FUNCTION—VAN ORSTRAND. including Boorman’s value of e. TaBLE XIV.— Miscellaneous values of et, e-2, sin x and cos x to a great number of decimals, e+0.1-=1, 10517 87187 32917 e.1=0, 90483 09520 38478 sin 0.1=0. 09983 22599 67832 cos 0.1=0. 99500 40359 10723 et1.0—2. 71828 95749 27466 59563 15738 90567 92906 e71.0—(, 36787 78345 46627 sin 1.0=0. 84147 10656 54349 cos 1.0=0. 54030 22276 43572 09180 92863 12048 74180 56257 74531 34166 92766 50318 41652 59352 68588 18284 66967 39193 07381 34187 36251 45748 94411 07836 09848 72751 23058 70097 75647 28944 54012 35959 31705 46483 46828 86156 09359 78025 74468 08368 59045 62772 20030 32328 93070 50082 86005 71442 80169 07896 70999 68139 25538 62481 09679 44536 57316 57799 18498 15230 16517 89035 76609 52659 71860 23536 40766 59921 62794 21540 37715 84299 32159 74614 50665 19104 71740 11003 17078 66747 42490 65344 68141 44283 55619 10218 02874 30353 81741 34907 89126 27509 93465 55237 95744 25023 04391 09366 94774 26490 65430 59446 24836 98410 29242 87803 24046 71352 54759 35966 63233 94937 03586 94757 70161 89980 21630 23966 07442 47176 24666 29891 43662 10125 62202 76096 87029 65296 ofos9 713 29043 82988 99405 67692 59371 46086 33571 29899 89486 97660 45179 82245 43318 11947 03446 69899 62443 48385 63618 77572 82178 57290 07531 34631 05047 00435 74458 47274 96225 39743 373238 51856 47194 97074 05360 03609 15388 80406 76225 52826 47093 52516 03342 95251 93819 15575 26480 11131 34591 63060 54305 10420 08718 73751 86536 98040 04572 01798 30362 41508 29279 69995 64274 95260 01901 87250 85094 0 03176 96437 79837 26958 61792 30893 79 a ea is