QB 
 
 371 
 
 W5 
 
 UC-NRLF 
 
QB 
 
 371 
 
 TABLES 
 
 OF 
 
 MERCURY 
 
University of California. 
 
 < il KT OK 
 
 f- 
 
TABLES 
 
 OF 
 
 MEEOUE Y, 
 
 FOE THE USE OF 
 
 THE AMERICAN EPHEMERIS AND NAUTICAL ALMANAC. 
 
 BY 
 
 JOSEPHWINLOCK, 
 
 PROF. MATH. U. S. HAVT. 
 
 TIIK 
 
 UNIVERSIT7 
 
 BUREAU OF NAVIGATION, 
 
 WASHINGTON. 
 
 1864. 
 
tlsiVEKSlTY PRESS: 
 
 WELCH, BIGELOW, AND COMPANY, 
 
 CAMBRIDGE. 
 
 a_d <jf 
 
PREFACE. 
 
 THE preparation of these Tables was begun in the year 1852, by order of the 
 Superintendent of The American Ephemeris and Nautical Almanac, now the Chief of the 
 Bureau of Navigation, ADMIRAL C. H. DAVIS. They have been several years in type, 
 and have been used in computing the ephemeris of Mercury which is published in 
 the American Ephemeris for the years 1855 - 1865 inclusive. It is hoped that they 
 will be found especially convenient for computing an ephemeris, and as much so 
 as the ordinary Tables for isolated places, and that the test of actual use for a 
 number of years has rendered them unusually free from typographical errors. I 
 am indebted to MR. CHAUNCEY WRIGHT and MR. ISAAC BRADFORD for valuable assiet- 
 
 ance in completing their publication. 
 
 JOSEPH WINLOCK, 
 
 Prof. Math. U. S. N. 
 
 CAMBRIDGE, Feb. 16, 1864. 
 
RSIT 
 
 INTRODUCTION, 
 
 CONSTRUCTION AND USE OF THE TABLES. 
 
 1. THESE Tables are based on the Theory of Mercury by U. J. LE VERRIER, Additions to the Connais- 
 sance des Temps, 1848. The following elements are given for the epoch 1799, Dec. 31, Paris Mean Midnight, 
 from which the time t is reckoned in Julian years, or in units of 365.25 days : 
 
 L = 110 13 17.84 
 TT = 74 20 41.60 -j- 55.589 t 
 Q = 45 57 37.70 + 42.511 1 
 i = 70 4.60 + 0.071 U 
 e = 0.2056003 + 0".0434 t 
 n = 5381016".218 
 a = 0.3870984 
 
 The coefficients of t include the constant of precession and the motion of the mean ecliptic ; so that by sub- 
 stituting the value of t, corresponding to any date, and adding the secular inequality of precession to it and Q, 
 the value of the element obtained is referred to the mean equinox or the mean ecliptic of the date. 
 
 The value of the precession used is 
 
 50".223< + 0.000122 f 
 
 The following increments of the elements are derived from their mean motions : 
 
 L w Q 
 
 In 100 Julian years 74 4 4".100 1 32 38.900 1 10 5 LI 00 
 
 In a common year 1493 43 3.302 55.551 42.482 
 
 In a leap year 1497 48 35.859 55.703 42.599 
 
 In a mean day 4 5 32.557 0.152 0.117 
 
 From these numbers are deduced the values of L, Q, and JT in Table V., for the mean noon of Washington 
 at the beginning of each year of the nineteenth century. These, as well as all the constants and arguments in 
 the following Tables, are given for the mean noon of Jan. O d of each year, without excepting the leap-years, the 
 beginnings of which, according to the general usage of astronomical tables, are assumed to be the mean noon 
 of Jan. l d . 
 
 A corresponding modification is made in the Table VII. of the changes of L, IT, and & for fractional parts of a 
 year; so that the changes for months in Table VII. are, for common years, the changes between the mean noon 
 of Jan. O d and that of the 1st day of all the months but February. 
 
 1 
 
INTRODUCTION. 
 
 The values of the secular inequality of precession, 
 
 p = 0".000122 e, 
 
 by which the preceding elements are reduced to the mean equinox of the date, are also given in Table V. 
 
 2. Table VI. contains for the same dates the constants dependent on the positions of the celestial equator, the 
 equinoxes, and the plane of the orbit of Mercury ; from which the computation of heliocentric rectangular coor- 
 dinates can easily be effected, when the radius vector r and the true anomaly v are known, by the following 
 formulas : 
 
 x = rk^ sin (K* -f v), y = rk y sin (K^ = v), ' z = rk x sin (K z -\- v). 
 
 The values of & K v &c. were computed by the method of GAUSS'S Theoria Motus (Articles 55, 56) from the 
 elements & and TT of Table V., the inclination i, and the obliquity of the ecliptic given in HANSEN'S Tables of 
 the Sun. They were corrected for the secular inequality of precession by differential formulas, the coefficients 
 of which, computed for 1850, were found not to vary sensibly during the century. In the same manner, the 
 changes arising from the lunar nutation of the obliquity of the ecliptic, and of longitude, given in Table XLIV. 
 of HANSEN'S Tables of the Sun, were applied to log log k f , and log z . From the values so computed the 
 following constants were subtracted : 
 
 From It* 20.0 from log x units of 7th decimal place 
 
 Kj 22.0 " log k y 6 " " 
 
 " K z 20.0 log k z 20 " 
 
 These constants are added in Table VIII. to the perturbations of the above quantities, so as to render them 
 positive. The arguments H^ and H* with which Table VIII. is entered, are given in Table V. They are the 
 arguments XI. and I. of HANSEN'S Tables of the Sun, interpolated to Washington time, and have respectively 
 the periods of 6798.3 days and 365.24 days, on which depend the lunar and solar nutations. 
 
 Since the perturbations dependent on the lunar nutations are applied to the values of log k a log k r and log k z 
 given in Table VI., Table VIII. contains for these quantities only the perturbations dependent on the solar nuta- 
 tion, which sensibly affects only log k y and log k z . 
 
 3. The elliptic values of the true anomaly and of the logarithm of the radius vector, given in Tables XIV. 
 and XV., were derived from a table of the eccentric anomaly computed by the indirect method. They were 
 computed for every unit of the argument A (12 hours), and interpolated to every tenth of the unit. The con- 
 stant 20".8 was subtracted from the true anomaly, and the constant 0.0000111 from the log radius vector. 
 These constants are added in the Tables X. -XIII. of the planetary perturbations, so as to render their values 
 positive.* 
 
 Table IX. contains the logarithms of the differences of v and log r for a unit of the 5th decimal place in 
 the argument. The characteristics of these logarithms are therefore such that, if the 5th decimal place of the 
 argument be taken as that of the unit, the proportional part will be obtained in seconds for the anomaly, and 
 in units of the 7th decimal place for the log radius vector. 
 
 Since logarithms given to only four places of decimals may be insufficient for the largest differences of v and 
 log r in the most accurate computations, another Table is added, Table XVIII., with logarithms to five places, 
 for those portions of Tables XIV. and XV. which have the largest differences. 
 
 The argument A of the elliptic Tables, given in Table V., is equal to twice the number of days elapsed from 
 the preceding mean perihelion passage of Mercury, and its period is the anomalistic year of Mercury, namely, 
 
 87.969345 days, or 175.938690 half-days. 
 
 * Tables XIV. and XV. were computed in connection with a set of perturbation Tables in which two terms of long period were applied 
 to the mean anomaly. In the present Tables, however, all the planetary perturbations are applied to the true anomaly ; and the sums of 
 the constants added to render the values of the perturbations positive are 30".8 for r.and 0.0000121 for log r. Consequently 10".0 should 
 be subtracted from the sum of the perturbations of , and 10 units of the seventh decimal place should be subtracted from those of log r, 
 in applying them to the values of the Tables XIV. and XV. 
 
 2 
 
INTKODUCTION. 
 
 Table IX. contains also the logarithms of the variations of the true anomaly, and of the log radius vector for 
 one anomalistic year of Mercury. These were computed from the variations of v and r in 100 years, given 
 in the following formulas, in which z denotes the mean anomaly : 
 
 8v = 8".54 sin z -f 2".16 sin 2 z + 0".57 sin 3z 
 + 0".16 sin 4z 4- 0".04 sin 5z + 0".01 sin 6z. 
 
 8 r = 0.0000017 0.0000078 cos z 
 
 0.0000016 cos 2z 
 
 
 
 0.0000002 cos 3z. 
 
 The number m of the anomalistic years of Mercury elapsed from the epoch 1800 are given for the beginning 
 of each year in Table V. 
 
 4. The perturbations of the true anomaly are given by the following formulas, in which I, I', I", I", F denote 
 the mean longitudes of the planets Mercury, Venus, Earth, Jupiter, and Saturn respectively, referred to the 
 mean equinox of 1799, Dec. 31.5 Paris Mean Time. The perturbations produced by Mars are insignificant, on 
 account of the small mass of Mars ; and the action of Uranus is insensible, in consequence of its great distance 
 from Mercury. 
 
 Perturbations of the true anomaly produced by 
 
 VENUS. 
 
 &v = 4- 0.31 sin (V 76 25') 
 
 4- 0.75 sin (f I) 
 
 - 0.09 sin (*' 4- f 4- 32 1') 
 
 4- 0.19 sin (V 2 I 4- 77 28') 
 
 0.06 sin (/' 3 I 38 39') 
 
 4- 0.78 sin (2 I' -\- 31 36') 
 
 3.96 sin (2 V I 74 27') 
 4- 0.20 sin (2 ? 4- J 42 53') 
 
 2.22 sin (2 V 2 /) 
 
 0.58 sin (2 /' 3 I -\- 75 27') 
 4- 0.14 sin (21' 4J 30 16') 
 4- 0.06 sin (2 I' 5 I + 38 31') 
 
 0.11 sin (31' 37 53') 
 
 0.60 sin (3 t I 4- 32 19') 
 
 1.45 sin (3 I' 2 I 73 53') 
 
 0.48 sin (3 I' 3 I) 
 
 0.15 sin (3 I' 4 1 4- 74 3') 
 
 = O'.IO sin (4? I 45 0') 
 
 - 0.54 sin (4^ 2/4- 30 57') 
 
 4- 0.33 sin (4 V 3 I 73 49') 
 
 4- 0.05 sin (4 /' 4 I) 
 
 4- 0.39 sin (5 I' 4- 178 30') 
 
 4- 1.55 sin (5 V I 4- 252 54') 
 
 4- 0.09 sin (51' 4- I 4- 108 26') 
 
 4- 7.72 sin (5 P 2 / 32 54') 
 
 4- 3.03 sin (5 l> 3 I 4- 37 32') 
 
 4- 0.75 sin (5/' 4/ 4- 111 40') 
 
 4- 0.21 sin (5 /' 5 I 4- 188 32') 
 
 4- 0.06 sin (5 I' 6 I 4- 270 0') 
 
 4- 0.08 sin (6? 31 50 11') 
 
 0.09 sin (8 I' 3 I 6 44') 
 
 4- 0.09 sin (10 /' 4Z 69 14') 
 
 THE EARTH. 
 
 8 v 4- 0.21 sin (I" I) 
 
 0.24 sin (2 I" 21) 
 
 0.41 sin (2 I" I 74 21') 
 
 4- 0.02 sin (3 V ' 3 I) 
 
 = 4-0.14 sin (41" 94*33') 
 4- 0.67 sin (4Z" Z 20 12') 
 4- 0.03 sin (4/" 4- / 168 54') 
 4- 0.35 sin (4/"" 2; 4- 48 17') 
 4- 0.03 sin (41" 31 4- 128 30') 
 
INTKODUCTION. 
 
 JUPITER. 
 
 tv = + 0.57 sin (F* + 201 44') = + 0.50 sin (2P + 30 53') 
 
 + 0.65 sin (^ - + 3 ' 29 sin (2^ - J + 104 43') 
 
 + 0.94 sin (21" 21 + 180 0') 
 
 SATURN. 
 8t> = 6.40 sin (2 r I 74 21') 
 
 These expressions are put in a convenient form for computing tables of double entry by the following trans- 
 formations : Let t denote the mean longitude of Mercury at any epoch referred to the mean equinox of 1800 
 O d .5 Paris Mean Time ; let T be the number of days from that epoch, and n the daily sidereal motion in mean 
 longitude. We then have 
 
 I n T + , 
 
 and in the same way for the other planets, 
 
 t n' T 1 + *' 
 /" = n" T" + t" 
 f = n" T" + t' T 
 V n" T" + T 
 
 Instead of double-entry tables, with two continuously variable arguments, we may, by a simple change in the 
 formulas, construct tables for which one of the arguments shall remain constant during a period of the other. 
 Thus, from the general form of the preceding terms of the perturbations produced by Venus, 
 
 k sin (' t il + y) = t sin (f n' T 1 in T -f f' c' t c + 7), 
 
 we may, by subtracting and adding the angle f' n' T, and putting the constant ' ' t e -f- y = a, obtain 
 the form, 
 
 k sin [I'M' (T 1 T) -f (' n 1 i n) T + a], 
 
 in which the angle n' (T 1 T) is constant during a period of the argument T, and is increased for every 
 change of period in T by the addition of the angle n' 87.969 ; but for a change of period in T, it is dimin- 
 ished by a circle, or 360. 
 
 The epochs or the origins of the times T, T, &c., with the corresponding values of e, ', &c., may be taken 
 arbitrarily and independently for the different planets. If, therefore, we take the following values of the mean 
 longitudes and epochs and the daily sidereal motions, 
 
 f = 354 6.3 1844 0.5 Paris Time n 4 5 32.42 
 
 *' = 145 8.8 1800 0.0 " n 1 = 1 36 7.67 
 
 e" = 98 19.3 1800 1.545 " n" 59 8.15 
 
 1T = 81 52.3 1800 0.5 " n" = 4 59.13 
 
 we have for 1800 O d .O Washington Mean Time. 
 
 T = 28.11 Sidereal Period = 87.969 
 
 7" = 224.92 = 224.701 
 
 T" = 367.02 = 365.256 
 
 7" v = 4332.31 " = 4332.585 
 
 From these values the tables of arguments were constructed ; and the assumed values of *, e', &c., were substi- 
 tuted in the expressions of the perturbations. 
 
 4 
 
INTRODUCTION. 
 
 By developing the preceding general form, we have 
 k cos [(i'n' in) T -}- a] sin [i'n' (T T)~\ -\- k sin [(i'n' in) T -\- a] cos [i'n' (T 
 
 and if we put 
 
 &i, cos ^ = 2i (k cos [(i'n' in) T -\- a]) 
 
 and 
 
 ky sin <i, = 2i (k sin ((?' in) T -\- aj j 
 
 the expressions for the perturbations become 
 
 8v = S i( (/lv cos &, sin ['n' (7 1 T 7 )] 4~ k v sin ^ cos [' n' (7" 4- T 7 )] ) 
 = 2 ir ( Jt v sin [' n' ( 7" T) -\- fo] j 
 
 Substituting the values of k, i, and a, we have for the perturbations produced by 
 
 VENUS. 
 
 cos 
 
 cos 
 
 k s cos 
 
 = 0.31 cos [( n' ) T + 68 43] 
 
 4- 0.75 cos [( ' ) T 7 4- 151 2] 
 
 4- 0.09 cos [( n' 4- n) T 7 + 351 16] 
 
 4- 0.19 cos [( n' 2 ) 7 + 234 24] 
 
 4- 0.06 cos [( n> 3n) 7 1 + 304 11] 
 
 = 0.78 cos [(2 ' ) T 7 + 321 53] 
 
 4- 3.96 cos [(2 n' n) T -f 41 23] 
 
 4- 0.20 cos [(2 n 1 + n) T + 241 31] 
 
 4- 2.22 cos [(2n' 2 n) 7 1 + 122 5] 
 
 + 0.58 cos [(2 ' 3 n) T 7 + 203 26] 
 
 -f 0.14 cos [(2w' 4n) T + 283 36] 
 
 -}- 0.06 cos [(2' 5n) T 7 + 358 17] 
 
 = 0.11 cos [_(3 n 1 ) T 7 + 217 34] 
 
 + 0.60 cos [(3 n' n) T + 293 39] 
 
 -f 1.45 cos [(3 n' 2 n) T + 193 21] 
 
 cos 
 
 cos 
 
 + o!'48 cos [(3 n> 3n) T + 273 7] 
 
 -f 0.15 cos [(3 ' 4 ) 7* -(- 353 4] 
 
 = 0.10 cos [(4 w' n) T 7 + 1 29] 
 
 + 0.54 cos [(4rc' 2n) T + 83 19] 
 
 + 0.33 cos [(4' 3n) T 7 + 164 27] 
 
 + 0.05 cos [(4w' 4w) T + 244 10] 
 
 = 0.39 cos [(5 n< ) 7" + 184 20] 
 
 -f 1.55 cos [(5 n' n) T + 264 32] 
 
 + 0.09 cos [(5n' + n) T -f 108 16] 
 
 + 7.72 cos [(5 n' 'in) T + 344 37] 
 
 + 3.03 cos [(5 ' 3 n) 7* + 60 57] 
 
 + 0.75 cos [(on' 4??.) T -f 140 58] 
 
 + 0.21 cos [(5 n' 5 n) 7 1 4- 223 44] 
 
 4- 0.06 cos [(5' 6n) T 4- 311 6] 
 
 THE EARTH. 
 
 k!\ cos $\ = 0.21 cos [( n" n) 7 1 4- 104 13] " 4 cos 
 
 i" 2 cos ^>" 2 = 0.41 cos 1(2 n" n) T + 308 11] 
 
 4- 0.24 cos 1(2 n" 2 n) T 7 4- 28 26] 
 
 A", cos <" 3 = 0.02 cos [(3 n" 3 n) T 7 4- 312 39] 
 
 JUPITER. 
 
 = 0.14 cos [(4'" ) T 4- 298 44] 
 
 4- 0.67 cos [(4 n" n) T + 18 59] 
 
 4- 0.03 cos [(4 n" 4- ) T 4- 218 29] 
 
 4- 0.35 cos [(4 n" 2 n) T -\- 93 22] 
 
 4- 0.03 cos [(4 n" 3 n) T + 179 28] 
 
 ,k'\ cos <j>'\ = 0.57 cos [( n" n) T + 283 36] Tf\ cos <?\ = 0.50 cos [(2 n" ) T 7 4- 194 38] 
 
 4- 0.65 cos [( n" n) T + 87 46] + 3.29 cos [(2 n' T - n) T + 274 22] 
 
 4- 0.94 cos [(2w IT 2n) T 7 4- 355 32] 
 
 By changing cos into sin in these expressions, we obtain the values of t sin fa i^ sin fa &c. 
 
 5 
 
INTRODUCTION. 
 
 The expressions for the perturbations produced by Venus, the Earth, and Jupiter become 
 
 Sv = t, sin [ n' (T -- T) + <,] 
 
 + k, sin [ 2' (7 -- T) + fc] 
 
 + *, sin [ 3n' (7* -- 7") + fc] 
 
 + i, sin [ 4n' (7 T 7 ) + < 4 ] 
 
 + *, sin [ 5n' (7 T) + &] 
 
 + 0.08 sin [ 6n' (2 -- T) + ( 6 n' 8 n) T 7 + 118 23] 
 
 + 0.09 sin [ 8w' (7* T 7 ) -f ( 8 ' 3 n) 7 7 + 272 7] 
 
 + 0.09 sin [10 n' (7* T) + (10 ra' 4w) T + 325 49] 
 
 + 0".21 sin [ n" (7"' T 7 ) + (" ) T 7 -+- 104 13'] 
 
 + V' t sin [2n" (7" T 7 ) + </>" 2 ] 
 
 + 0".02 sin [3rc" (7"' T 7 ) + (3 n" 3 n) 7 1 + 312 39'] 
 
 + " 4 sin [4n" (7"" T 7 ) + <" 4 ] 
 
 + ** l8 in [ n* (7" T -- T) + <r,] 
 + #*, sin [2n" (7"' -- T 7 ) + $'%] 
 
 The single term of perturbation produced by Saturn is given in a table of single entry. 
 
 Tables giving the values of k, sin $, ^ cos fa 2 sin fa k 2 cos < 2 , or of k, <f>, &c., for values of the argu- 
 ment T at suitable intervals, for the complete period of T, the computation of which is the first step in prepar- 
 ing double-entry tables, would, with the aid of a table of natural sines and cosines, constitute a very compact 
 set of perturbation tables, which would be useful when a few places of a planet were to be computed, or when 
 double-entry tables would be of inconvenient size. 
 
 Table X. contains the perturbations produced by Venus, computed for values of the angle n' (T T) at 
 intervals of 3 from to 360. Tables XI. and XII. contain the perturbations produced by Jupiter and the 
 Earth, computed for values of the angles n iv (7" v T) and n" (T' 1 T) at intervals of 6 from to 360. 
 The intervals 3 and 6 are made the units of the vertical arguments of the tables, thus: F= ^ n' (T T), 
 J = n iT (7" T y), and E = % n " (^" ^) > n '> W ' T > an< ^ n " being expressed in degrees and decimals 
 of a degree. The period of V is therefore 120 units, and the periods of E and J are each 60 units. 
 
 The horizontal argument T of these tables has a period of 87.969 days ; and for every change of period in 
 T the arguments V, J, and E are increased by the quantities n' 87.969, n 87.969, and n" 87.969 
 respectively. These, reduced to numbers, are for V 46-98, for / 1.22, and for E 14.45. 
 
 Table XIII. contains the term of perturbation produced by Saturn, and its argument S is given in days with 
 a period of 89.432 days. 
 
 The arguments T 7 , V, J, E, and S are given in Table V. for Jan. O d Washington Mean Noon for each year 
 of the nineteenth century. J ' 
 
 5. The perturbations of the logarithm of the radius vector, denoted by r, were computed in the same man- 
 ner as those of the true anomaly, with the same intervals and arguments, and are placed in the same tables. 
 
 They are given in units of the seventh decimal place of the log radius vector, and are derived from the 
 following formula: 
 
 d r = 4.00 cos ( t I) 
 
 + 20.50 cos (21' 21 + 180) 
 
 + 11.50 cos (31' 21 + 105 16') 
 
 + 4.00 cos (31' 31 + 180) 
 
 + 3.06 cos (5 '' 1 36') 
 
 + 14.65 cos (5 '' I + 72 45') 
 
 4- 27.09 cos (5 '' 3 I + 35 32') 
 
 + 3.06 cos (5f 4Z + 115 48') 
 
 + 30.00 cos (2 p I + 105 39') 
 6 
 
INTRODUCTION. 
 
 The coefficients are in units of the seventh decimal place of the radius vector. 
 
 Terms of perturbation are included in this formula dependent on the inequality of long period in the mean 
 
 longitude, 
 
 7".49 sin (5 I' 2 1 32 54'), 
 
 which LE VERRIER proposed to apply to the argument of the elliptic tables. 
 
 The terms dependent on the action of Venus are multiplied by 1.031, in order to reduce them to the new 
 mass of Venus. 
 
 From this formula are derived the following perturbations of the logarithm of the radius vector. 
 
 8 log r = 0.46 cos ( F 74 21') 
 4- 4.49 cos ( F I) 
 4- 0.09 cos ( F 4- I 148 42') 
 4- 0.46 cos ( F 2 I 4- 74 21') 
 
 4- 0.09 cos ( 'I' 3 I 4- 148 42') 
 4- 0.48 cos (2 F 4- 31 18') 
 4- 2.35 cos (2? I 4- 105 39') 
 
 4- 22.99 cos (2 F 2 I + 180) 
 + 2.35 cos (2F 31 + 254 21') 
 + 0.48 cos (2 F 4 1 + 328 42') 
 4- 0.27 cos (3 F - - 43 26') 
 + 1.52 cos (31' I + 30 55') 
 
 4- 13.36 cos (3 I' 21 4- 105 20') 
 4- 5.81 cos (3F 31 + 180 
 4- 0.73 cos (3 F 4 1 4- 254 15') 
 4- 0.20 cos (3 /' 5 I 4- 328 42') 
 4- 5.11 cos (51' 1 36') 
 
 4- 16.15 cos (5? I 4- 72 58') 
 4- 0.69 cos (5 F 4- I 75 57') 
 4- 1.44 cos (5 l> 2 / 45 44') 
 
 4- 30.39 cos (5 /' 3 I -\- 35 32') 
 4- 6.53 cos (5? 4J 4- 112 54') 
 
 4- 0.97 cos (51' 51 + 185 53') 
 
 4- 3.44 cos (2?' 4-31 18') 
 
 4- 33.66 cos (2 F I -\- 105 39') 
 4- 0.70 cos (2 Z* 4- I 43 3') 
 4- 3.44 cos (2Z* -- 21 + 180) 
 4- 0.70 cos (2^ 3*4- 254 21') 
 
 By the same transformations as were made in the perturbations of the true anomaly we obtain the following 
 formula : 
 
 8 log r = ^ cos [ n' (T> T) + fr ] 
 
 4- *t -cos [2n' (T' - - T) + $, ] 
 
 4- *, cos [8n' (7" T) + <fe ] 
 
 + * 5 cos [5n' (T' T) + fc ] 
 
 4-.# T s cos [2 iT (T 7 " -- T) 4- ('",] 
 
 6. The reduction of the true orbit longitude to the ecliptic is given in Table XVI., and the latitude in Table 
 XVII. If we denote the true anomaly affected by the planetary perturbations by 
 
 v = v -\- &v 
 
 7 
 
INTRODUCTION. 
 
 and the true argument of the latitude by 
 
 <> = v -(- n- Q 
 we obtain from the value of the inclination 
 
 7 Q' 4".60 + 
 
 a. 
 
 the following expression for the reduction to the ecliptic : 
 
 (771".8914 + 0.0043 t) sin 2 a> -f- 1'.44 sin 4 
 
 The term dependent on t is given in the column of variation for 100 years. 
 The following are the formulas from which Table XVII. was computed : 
 
 sin Lat = sin t sin <o = [9.0859733] sin 
 variation in 100 years = 57".90 tan lat. 
 
 The interval of one degree in the argument <> for which Tables XVI. and XVII. are constructed is such 
 that the neglect of second differences in interpolation cannot cause an error in the reduction to the ecliptic of 
 more than 0".12, but in the latitude it may cause, near the higher latitudes, an error of nearly 1". In both 
 tables, however, second differences may be neglected without sensible error for those values of a near the nodes, 
 for which a transit of Mercury can occur. 
 
 At the heads of the columns of the argument in Table XVI. are placed the signs which belong to the 
 reduction to the ecliptic. Thus, the reductions are negative for values of to in the first and third quadrants, 
 and positive for a> in the second and fourth quadrants. The latitude is positive for values of <a less than 180, 
 and negative for greater values, for which the table should be entered with the argument <a 180. 
 
 7. The true ecliptic longitude is referred to the true equinox by the addition of the nutation and the secular 
 inequality of the precession p. Hence 
 
 True ecliptic longitude = v -\- n -\- p -\- Red. to Eel. -(- nutation. 
 
 The value of the nutation may be obtained from Table VIII., with an error of less than 0".01 by the 
 
 formula : 
 
 Nutation = rf> K^ + d Q K^ 20".0 
 
 RECAPITULATION. 
 
 The order of the tables is adapted to the work of computing ephemerides, an example of which will be given 
 at the end of the following summary : 
 
 Table I. contains the longitudes from Washington of the principal observatories ; western longitude being con- 
 sidered positive. 
 
 Tables II., III., and IV. are tables of Astronomical Dates in mean solar days, from which any date given in 
 the usual form of reference to the Christian era may be reduced to its value in days and decimals of a day 
 of the Julian period. They are taken from PEIKCE'S Lunar Tables. By adding the days given for the current 
 year of the century to the days of the previous centennial date we obtain the number of days elapsed of the 
 Julian Period for Jan. O d Mean Noon in common years and for Jan. 1* in leap years. To this should be added 
 the days and decimals of a day for fractional parts of the year given in Tables III. and IV. 
 
 Table V. contains for Jan. O d Washington Mean Noon of each year in the present century the elements L, 
 Q, and TT, and p the secular inequality of the precession by which these are referred to the mean equinox of 
 date : the arguments H and ff 2 defined in 2. Also, the arguments 
 
 A of Tables XL, XIV., XV., and XVIII. defined in 3. 
 T the horizontal argument of Tables X., XL, and XII. defined in 4. 
 
 F, J, E and S, the arguments of Tables X., XL, XII., and XIII. defined in 4 ; and m the num- 
 ber of anomalistic years of Mercury completed since 1800. 
 
 8 
 
INTKODUCTION. 
 
 Tables VI. and VIII. contain the quantities defined in 2. 
 
 Table VII. is described in 1. 
 
 Table IX. contains the logarithms of the differences of Tables XIV. and XV., and the log secular varia- 
 tions defined in 3. 
 
 Tables X., XI., XII., and XIII. contain the perturbations produced by Venus, Jupiter, the Earth, and 
 Saturn respectively, as described in 4. 
 
 To the perturbations 8 v are added constants which in the aggregate amount to 30".8. To the perturbations 
 r are added in the aggregate the constant 121. 
 
 Table XIV. contains the values of the true anomaly, diminished by the constant 20".8, at intervals of tenth 
 of units of argument A. 
 
 Table XV. contains the values of the logarithm of the radius vector, diminished by 0.0000111, for the same 
 intervals and arguments. (See note 3.) 
 
 Tables XVI. and XVII. are described in 6, and Table XVIII. in 3. 
 
 Example. 
 
 The perturbations are conveniently computed at intervals of four days, and if the dates of the computation 
 be so assumed that the argument I. is at the beginning nearly a multiple of four, its value will be for a long 
 period nearly the same as those for which the tables are constructed. The interpolations for decimals of T 
 may be performed upon the sums of the perturbations. 
 
 For January O d , 1865, the value of T is 17.38. For the previous day it is therefore 16.38. Assuming 
 this as the origin of the dates, we have the following table of arguments for the year. 
 
 Dav of the 
 Year. 
 
 T 
 
 V 
 
 J 
 
 E 
 
 Day of the 
 Year. 
 
 S 
 
 Day of the 
 Year. 
 
 A 
 
 m 
 
 1 
 
 16.38 
 
 69.55 
 
 28.56 
 
 57.31 
 
 1 
 
 25.0 
 
 1 
 
 169.467064 
 
 269 
 
 +71 
 159 
 
 0.41 
 0.44 
 
 116.53 
 43.51 
 
 29.78 
 31.00 
 
 11.76 
 26.21 
 
 +67 
 155 
 
 3.57 
 2.14 
 
 +3 
 91 
 
 1.528374 
 1.589684 
 
 270 
 271 
 
 247 
 
 0.47 
 
 90.49 
 
 32.22 
 
 40.66 
 
 243 
 
 0.71 
 
 179 
 
 1.650994 
 
 272 
 
 335 
 
 0.50 
 
 17.47 
 
 33.44 
 
 55.11 
 
 335 
 
 3.28 
 
 267 
 
 1.712304 
 
 273 
 
 3G7 
 
 32.50 
 
 17.47 
 
 33.44 
 
 55.11 
 
 367 
 
 35.28 
 
 355 
 
 1.773614 
 
 274 
 
 The dates preceding arguments T and S are of the assumed dates, the ones at which these arguments are 
 changed by their respective periods. For all such changes in T the arguments V, J, and E are increased 
 by the constants 46.98, 1.22, and 44.55 respectively, and have periods of 120.00, 60.00, and 60.00. 
 
 Argument A increases by two units each day until it exceeds its period 176.938690 which is then sub- 
 tracted from it, and m is increased by a unit. 
 
 Entering the tables of perturbations for the assumed dates with the argument T successively equal to 16, 20, 
 24, &c., and with the constant arguments V= 69.55, J= 28.56, and .#=57.31 ; adding together the values 
 
 Day of the 
 Year. 
 
 X. 
 
 XI. 
 
 XII. 
 
 Sum. 
 
 Diff. 
 
 Corr. 
 
 XIII. 
 
 Sum. 
 
 IX. 
 
 log sec var. 
 
 sec var. 
 
 Pert. 
 
 Diff. 
 
 1 
 
 19^99 
 
 II 
 
 4.76 
 
 0*60 
 
 25'.35 
 
 +d!33 
 
 +o'!o3 
 
 0.79 
 
 26J7 
 
 7.9487 
 
 0.3785n 
 
 M 
 
 2.4 
 
 +13"8 
 
 +3.4 
 
 +3 
 
 18.76 
 
 6.31 
 
 0.61 
 
 25.68 
 
 0.47 
 
 0.04 
 
 0.76 
 
 26.48 
 
 7.4231+! 9.85454 
 
 +0.7 
 
 17.2 
 
 3.0 
 
 7 
 
 17.65 
 
 7.86! 0.64 
 
 26.15 
 
 0.65 
 
 0.06 0.69 
 
 26.90 
 
 8.0884 
 
 0.5198 
 
 3.3 
 
 20.2 
 
 2.4 
 
 11 
 
 16.85 
 
 9.17 
 
 0.78 
 
 26.80 
 
 0.75 
 
 0.07 
 
 0.61 
 
 27.48 
 
 8.2738 
 
 0.7052 
 
 5.1 
 
 22.6 
 
 1.3 
 
 15 
 
 16.54 
 
 10.07 
 
 0.94 
 
 27.55 
 
 0.62 
 
 0.06J 0.50 
 
 28.11 
 
 8.3345 
 
 0.7659 
 
 5.8 
 
 23.9 
 
 +0.5 
 
 19 
 
 16.61 
 
 10.42 
 
 1.14 
 
 28.17 
 
 +0.29 
 
 +0.03 
 
 0.39 
 
 28.59 
 
 8.3355 
 
 0.7669 
 
 5.8 
 
 24.4 
 
 0.3 
 
 23 
 
 16.82 
 
 10.32 
 
 1.32 
 
 28.46 
 
 0.13 
 
 0.01 
 
 0.28 
 
 28.73 
 
 8.2992 
 
 0.7306 
 
 5.4 
 
 +24.1 
 
 
 1 
 
 115 
 
 2 
 
 
 117 
 
 6 
 
 1 
 
 
 116 
 
 9.3957n 
 
 1.8255ra 
 
 67 
 
 + 39 
 
 11 
 
 +3 
 
 111 
 
 
 
 
 111 
 
 6 
 
 1 
 
 
 110 
 
 9.4266 
 
 1.8580 
 
 72 
 
 28 
 
 + 5 
 
 7 
 
 103 
 
 2 
 
 
 105 
 
 4 
 
 
 
 
 105 
 
 9.3603 
 
 1.7917 
 
 62 
 
 33 
 
 16 
 
 11 
 
 93 
 
 8 
 
 
 101 
 
 2 
 
 
 
 
 101 
 
 9.1926 
 
 1.6240 
 
 42 
 
 49 
 
 21 
 
 15 
 
 82 
 
 17 
 
 
 99 
 
 
 
 
 
 
 99 
 
 8.839 6re 
 
 1.2710 
 
 19 
 
 70 
 
 22 
 
 19 
 
 73 
 
 26 
 
 
 99 
 
 +3 
 
 o 
 
 
 99 
 
 8.0152+ 
 
 0.4466+ 
 
 + 3 
 
 92 
 
 20 
 
 23 
 
 66 
 
 36 
 
 
 102 
 
 5\ 
 
 
 102 
 
 8.8646 
 
 1.2960 
 
 20 
 
 +112 
 
 
INTRODUCTION. 
 
 thus obtained for each date, and correcting the sums by the proportional parts of their differences for the 
 decimal of the argument T (0.38 or 0.095 for the interval of four days), and adding the perturbations from 
 Table XIII. ; we obtain the sums given in the ninth columns of the above example. These are further cor- 
 rected by the secular variations, and diminished by the constants 10".0 for 8v and 10 units for f. The loga- 
 rithms of the secular variations are obtained by adding log m to the values of log sec. var. in Table IX. 
 
 The values of the perturbations should be interpolated to intervals of a day, and added to the values of v 
 and log r given in Tables XVI. and XV. These tables are entered with the nearest values in tenths of units 
 of argument A, for every day, and interpolated to the true values of the argument by means of Table IX., 
 according to the precept of 3. Thus for 1865 we have 
 
 
 
 I 
 
 X. 
 
 XIV. 
 
 
 
 
 XV. 
 
 
 
 
 Day 
 of the 
 Year. 
 
 A 
 
 log! 
 v 
 
 . p. 
 
 log r 
 
 
 P.P. 
 
 Pert. 
 
 V 
 
 
 P.P. 
 
 Pert. 
 
 log r 
 
 
 1 
 
 2 
 3 
 4 
 5 
 
 171.5 
 173.5 
 175.5 
 1.5 
 3.5 
 5.5 
 
 2.57lOn 
 2.5740 
 2.5753n 
 2.5102+ 
 2.5079 
 2.5038 
 
 2.5134 
 2.2585 
 1.5155 
 1.9844 
 2.3483 
 2.5373 
 
 345 57 28.0 
 352 15 50.5 
 358 36 8.1 
 4 45 7.2 
 11 4 35.4 
 17 21 19.6 
 
 372.4 
 375.0 
 376.1 
 +323.7 
 322.0 
 +319.0 
 
 +14.7 
 15.6 
 16.4 
 17.2 
 
 18.0 
 +18.8 
 
 345 51 30.3 
 352 9 51.1 
 358 30 8.4 
 4 50 48.1 
 11 10 15.4 
 17 26 57.4 
 
 9.4900665 
 9.4885231 
 9.4878713 
 9.4881048 
 9.4892328 
 9.4912368 
 
 +326 
 181 
 33 
 96 
 223 
 +345 
 
 +34 
 31 
 29 
 
 28 
 28 
 
 +29 
 
 9.4901025 
 9.4885443 
 9.4878775 
 9.4881172 
 9.4892579 
 9.4912742 
 
 The true values of K^, log x , &c. are conveniently computed from Tables VI. and VIII., at intervals of ten 
 days, and interpolated to intervals of one day. This being done, we have, for 1865, 
 
 Day of the 
 Year. 
 
 Kk 
 
 K, 
 
 A- z 
 
 log k* 
 
 log lc y 
 
 log t, 
 
 
 
 O ( (( 
 
 165 8 15.1 
 
 77 52 13.2 
 
 65 4o 40.6 
 
 9.9982821 
 
 9.9453473 
 
 9.6812330 
 
 10 
 
 165 8 16.9 
 
 77 52 15.0 
 
 65 45 48.1 
 
 9.9982821 
 
 9.9453474 
 
 9.6812328 
 
 20 
 
 165 8 18.6 
 
 77 52 16.7 
 
 65 45 49.6 
 
 9.9982821 
 
 9.9453474 
 
 9.6812328 
 
 
 Day of the 
 Year. 
 
 t> + K* 
 
 v + K 7 
 
 + A' z 
 
 log fct sin (v + K x ) 
 
 log ky sin (v + Ky) 
 
 log k z sin (v + K z ) 
 
 
 
 150 59 45.4 
 
 O 1 II 
 
 63 43 43.5 
 
 51 37 16.9 
 
 9.6839088 
 
 9.8979986 
 
 9.5755075 
 
 1 
 
 157 18 G.4 
 
 70 2 4.5 
 
 57 55 37.9 
 
 9.5847315 
 
 9.9184284 
 
 9.6093082 
 
 2 
 
 163 38 23.9 
 
 76 22 22.0 
 
 64 15 55.3 ! 9.4480260 
 
 9.9329462 
 
 9.6358685 
 
 3 
 
 169 59 3.7 
 
 82 43 1.8 
 
 70 36 35.2 
 
 9.2386241 
 
 9.9418294 
 
 9.6558733 
 
 4 
 
 176 18 31.2 
 
 89 2 29.3 
 
 76 56 2.6 
 
 8.8070423 
 
 9.9452865 
 
 9.6698412 
 
 5 
 
 182 35 13.4 
 
 95 19 11.5 
 
 83 12 44.8 
 
 8.6528176re 
 
 9.9434726 
 
 9.6781784 
 
 
 Day of the 
 Year. 
 
 log* 
 
 'gy 
 
 log z 
 
 a; 
 
 y 
 
 Z 
 
 
 1 
 
 9.1740113 
 9.0732758 
 
 9.3881011 
 9.4069727 
 
 9.0656100 
 9.0978525 
 
 +0.1492833 
 0.1183793 
 
 +0.2444000 
 0.2552541 
 
 +0.1163081 
 0.1252715 
 
 2 
 
 8.9359035 
 
 9.4208237 
 
 9.1237460 
 
 0.0862787 
 
 0.2635261 
 
 0.1329677 
 
 3 
 
 8.7267413 
 
 9.4299466 
 
 9.1439905 
 
 0.0533017 
 
 0.2691204 
 
 0.1393126 
 
 4 
 5 
 
 8.2963002 
 8.1 4409 18re 
 
 9.4345444 
 
 9.4347468 
 
 9.1590991 
 9.1694526 
 
 +0.0197834 
 0.0139345 
 
 0.2719846 
 +0.2721114 
 
 0.1442445 
 +0.1477245 
 
 The computation of an ephemeris may be completed by the following formulas, in which X, T, and Z denote 
 the sun's coordinates, a, 8, and A the right ascension, declination, and geocentric distance of the planet. 
 
 x + X = A cos 8 cos a. 
 y + Y = A cos 8 sin a. 
 2 + Z = A sin 8. 
 
 Aberration 
 Semidiameter 
 
 = 8.22 X A X minute motion in A. R. or Dec. 
 3".34 
 
 Horizontal Parallax = 
 
 10 
 
TABLES OF MERCURY, 
 
TABLE I. 
 
 
 
 
 Place. 
 
 Longitude 
 from Washington 
 in Time. 
 
 Decimal of a 
 Day. 
 
 Place. 
 
 Longitude 
 from Washington 
 in Time. 
 
 Decimal of a 
 Day. 
 
 Abo, 
 
 h. m. 8. 
 
 6 37 20.0 
 
 0.275926 
 
 Kremsmunster, 
 
 h. m. s. 
 6 4 44.6 
 
 d. 
 
 0.253294 
 
 
 Albany, 
 
 13 12.6 
 
 0.009174 
 
 Leipsic, 
 
 5 57 39.7 
 
 0.248376 
 
 
 
 Altona, 
 
 5 47 57.4 
 
 0.241637 
 
 Leyden, 
 
 5 26 8.6 
 
 0.226488 
 
 
 
 Ann Arbor, 
 
 +0 27 12.0 
 
 +0.018889 
 
 Liverpool, 
 
 4 56 11.1 
 
 0.205684 
 
 
 
 Athens, 
 
 6 43 6.4 
 
 0.279935 
 
 London, 
 
 5 7 34.1 
 
 0.213589 
 
 
 
 Berlin, 
 
 6 1 46.1 
 
 0.251228 
 
 Madras, 
 
 10 29 8.2 
 
 0.436900 
 
 
 
 Bilk, 
 
 5 35 16.1 
 
 0.232825 
 
 Mannheim, 
 
 5 42 2.7 
 
 0.237531 
 
 
 
 Bonn, . 
 
 5 36 35.7 
 
 0.233747 
 
 Markree, 
 
 4 34 22.8 
 
 0.190542 
 
 
 
 Breslau, 
 
 6 16 21.2 
 
 0.261356 
 
 Marseilles, 
 
 5 29 40.2 
 
 0.228937 
 
 
 
 Brussels, 
 
 5 25 38.8 
 
 0.226144 
 
 Milan, 
 
 5 44 57.8 
 
 0.239558 
 
 
 
 Cambridge (Mass.), 
 
 23 41.5 
 
 0.016453 
 
 Modena, 
 
 5 51 55.2 
 
 0.244389 
 
 
 
 Cambridge (Eng.), 
 
 5 8 34.7 
 
 0.214291 
 
 Moscow, 
 
 7 38 28.5 
 
 0.318385 
 
 
 
 Cape of Good Hope, 
 
 6 22 7.2' 
 
 0.265361 
 
 Munich, 
 
 5 54 37.0 
 
 0.246269 
 
 
 
 Christiania, 
 
 5 51 6.0 
 
 0.243819 
 
 Naples, 
 
 6 5 12.1 
 
 0.253612 
 
 
 
 Cincinnati, 
 
 +0 29 46.9 
 
 +0.020682 
 
 Olmutz, 
 
 6 17 11.3 
 
 0.261809 
 
 
 
 Copenhagen, 
 
 5 58 30.5 
 
 0.248964 
 
 Oxford, 
 
 5 3 8.6 
 
 0.210516 
 
 
 
 Cracow, 
 
 6 28 2.4 
 
 0.269472 
 
 Padua, 
 
 5 55 40.2 
 
 0.246993 
 
 
 
 Dorpat, 
 
 6 55 5.8 
 
 0.288262 
 
 Palermo, 
 
 6 1 36.7 
 
 0.251119 
 
 
 
 Dublin, 
 
 4 4249.2 
 
 0.196403 
 
 Paramatta, 
 
 4-8 47 42.6 
 
 4-0.366465 
 
 
 
 Durham, 
 
 5 1 53.2 
 
 0.209644 
 
 Paris, 
 
 5 17 32.7 
 
 0.220517 
 
 
 
 Edinburgh, 
 
 4 55 28.2 
 
 0.205187 
 
 St. Petersburg, 
 
 7 9 24.7 
 
 0.298203 
 
 
 
 Florence, 
 
 5 53 12.9 
 
 0.245288 
 
 Philadelphia, 
 
 7 33.6 
 
 0.005250 
 
 
 
 Geneva, 
 
 5 32 48.9 
 
 0.231122 
 
 Prague, 
 
 6 5 53.2 
 
 0.254088 
 
 
 
 Georgetown, 
 
 +0 6.2 
 
 4-0.000072 
 
 Pulkowa, 
 
 7 9 29.9 
 
 0.298263 
 
 
 
 Gottingen, 
 
 5 47 57.3 
 
 0.241635 
 
 Rome, 
 
 5 58 .5.9 
 
 0.248679 
 
 
 
 Gotha, 
 
 5 51 6.9 
 
 0.243830 
 
 San Fernando, 
 
 4 43 22.1 
 
 0.196784 
 
 
 
 Greenwich, 
 
 5 8 11.2 
 
 0.214019 
 
 Santiago, 
 
 25 37.4 
 
 0.017966 
 
 
 
 Hamburg, 
 
 5 48 4.8 
 
 0.241722 
 
 Senftenberg, 
 
 6 14 1.1 
 
 0.259735 
 
 
 
 Hudson, 
 
 +0 17 32.1 
 
 4-0.012177 
 
 Vienna, 
 
 6 13 43.7 
 
 0.259534 
 
 
 
 Kasan, 
 
 8 24 43.1 
 
 0.350499 
 
 Washington, 
 
 0.0 
 
 0.000000 
 
 
 
 Konigsberg, 
 
 | 
 
 6 30 11.6 
 
 0.270968 
 
 Wilna, 
 
 6 49 23.0 
 
 0.284294 
 
 
 
TABLE IL 
 
 
 
 
 Year. 
 
 Date in Mean 
 Solar Days. 
 
 Year. 
 
 Date in Mean 
 Solar Days, 
 
 YEAR IN 
 THE CENTURY. 
 
 Days from 
 previous 
 Ctemennlal 
 Date. 
 
 YEAR IN 
 THE CENTURY. 
 
 Days from 
 previous Cen- 
 tennial Date. 
 
 If Negative. 
 
 IfPositiTB. 
 
 If Negative. 
 
 IfPositire. 
 
 
 47135. 
 
 
 
 1000 
 
 1356173 
 
 100 
 
 1 
 
 
 
 50 
 
 51 
 
 18262 
 
 
 
 -4712 
 
 365 
 
 900 
 
 1392698 
 
 99 
 
 2 
 
 365 
 
 495. 
 
 525. 
 
 18628 
 
 
 
 4711 
 
 730 
 
 800 
 
 1429223 
 
 98 
 
 3 
 
 730 
 
 48 
 
 53 
 
 18993 
 
 
 
 4710 
 
 1095 
 
 700 
 
 1465748 
 
 975. 
 
 45. 
 
 1096 
 
 47 
 
 54 
 
 19358 
 
 
 
 47095. 
 
 1461 
 
 600 
 
 1502273 
 
 96 
 
 5 
 
 1461 
 
 46 
 
 55 
 
 19723 
 
 
 
 4708 
 
 1826 
 
 500 
 
 1538798* 
 
 95 
 
 6 
 
 1826 
 
 455. 
 
 565. 
 
 20089 
 
 
 
 4707 
 
 2191 
 
 400 
 
 1575323 
 
 94 
 
 7 
 
 2191 
 
 44 
 
 57 
 
 20454 
 
 
 
 4706 
 
 2556 
 
 300 
 
 1611848 
 
 935. 
 
 85. 
 
 2557 
 
 43 
 
 58 
 
 20819 
 
 
 
 47055. 
 
 2922 
 
 200 
 
 1648373 
 
 92 
 
 9 
 
 2922 
 
 42 
 
 59 
 
 21184 
 
 
 
 4704 
 
 3287 
 
 100 
 
 1684898 
 
 91 
 
 10 
 
 3287 
 
 415. 
 
 605. 
 
 21550 
 
 
 
 4703 
 
 3652 
 
 1 
 
 1721423 
 
 90 
 
 11 
 
 3652 
 
 40 
 
 61 
 
 21915 
 
 
 
 4702 
 
 4017 
 
 101 
 
 1757948 
 
 895. 
 
 125. 
 
 4018 
 
 39 
 
 62 
 
 22280 
 
 
 
 47015. 
 
 4383 
 
 201 
 
 1794473 
 
 88 
 
 13 
 
 4383 
 
 38 
 
 63 
 
 22645 
 
 
 
 4700 
 
 4748 
 
 301 
 
 1830998 
 
 87 
 
 14 
 
 4748 
 
 375. 
 
 645. 
 
 23011 
 
 
 
 4600 
 
 41273 
 
 401 
 
 1867523 
 
 86 
 
 15 
 
 5113 
 
 36 
 
 65 
 
 23376 
 
 
 
 4500 
 
 77798 
 
 501 
 
 1904048 
 
 855. 
 
 165. 
 
 5479 
 
 35 
 
 66 
 
 23741 
 
 
 
 4400 
 
 114323 
 
 601 
 
 1940573 
 
 84 
 
 17 
 
 5844 
 
 34 
 
 67 
 
 24106 
 
 
 
 4300 
 
 150848 
 
 701 
 
 1977098 
 
 83 
 
 18 
 
 6209 
 
 335. 
 
 685. 
 
 24472 
 
 
 
 4200 
 
 187373 
 
 801 
 
 2013623 
 
 82 
 
 19 
 
 6574 
 
 32 
 
 69 
 
 24837 
 
 
 
 4100 
 
 223898 
 
 901 
 
 2050 14S 
 
 815. 
 
 205. 
 
 6940 
 
 31 
 
 70 
 
 25202 
 
 
 
 4000 
 
 260423 
 
 1001 
 
 2086673 
 
 80 
 
 21 
 
 7305 
 
 30 
 
 71 
 
 25567 
 
 
 
 3900 
 
 296948 
 
 1101 
 
 2123198 
 
 79 
 
 22 
 
 7670 
 
 295. 
 
 725. 
 
 25933 
 
 
 
 3800 
 
 333473 
 
 1201 
 
 2159723 
 
 78 
 
 23 
 
 8035 
 
 28 
 
 73 
 
 26298 
 
 
 
 3700 
 
 369998 
 
 1301 
 
 2196248 
 
 775. 
 
 245. 
 
 8401 
 
 27 
 
 74 
 
 26663 
 
 
 
 3600 
 
 406523 
 
 1401 
 
 2232773 
 
 76 
 
 25 
 
 8766 
 
 26 
 
 75 
 
 27028 
 
 
 
 3500 
 
 443048 
 
 1501 
 
 2269298 
 
 75 
 
 26 
 
 9131 
 
 255. 
 
 765. 
 
 27394 
 
 
 
 3400 
 
 479573 
 
 1583 
 
 2299238 
 
 74 
 
 27 
 
 9496 
 
 24 
 
 77 
 
 27759 
 
 
 
 3300 
 
 516098 
 
 15845. 
 
 2299604 
 
 735. 
 
 285. 
 
 9862 
 
 23 
 
 78 
 
 28124 
 
 
 
 3200 
 
 552623 
 
 1585 
 
 2299969 
 
 72 
 
 29 
 
 10227 
 
 22 
 
 79 
 
 28489 
 
 
 
 3100 
 
 589148 
 
 1586 
 
 2300334 
 
 71 
 
 30 
 
 10592 
 
 215. 
 
 805. 
 
 28855 
 
 
 
 3000 
 
 625673 
 
 1587 
 
 2300699 
 
 70 
 
 31 
 
 10957 
 
 20 
 
 81 
 
 29220 
 
 
 
 2900 
 
 662198 
 
 15885. 
 
 2301065 
 
 695. 
 
 325. 
 
 11323 
 
 19 
 
 82 
 
 29585 
 
 
 
 2800 
 
 698723 
 
 1589 
 
 2301430 
 
 68 
 
 33 
 
 11688 
 
 . 18 
 
 83 
 
 29950 
 
 
 
 2700 
 
 735248 
 
 1590 
 
 2301795 
 
 67 
 
 34 
 
 12053 
 
 175. 
 
 845. 
 
 30316 
 
 
 
 2600 
 
 771773 
 
 1591 
 
 2302160 
 
 66 
 
 35 
 
 12418 
 
 16 
 
 85 
 
 30681 
 
 
 
 2500 
 
 808298 
 
 15925. 
 
 2302526 
 
 655. 
 
 365. 
 
 12784 
 
 15 
 
 86 
 
 31046 
 
 
 
 2400 
 
 844823 
 
 1593 
 
 2302891 
 
 64 
 
 37 
 
 13149 
 
 14 
 
 87 
 
 31411 
 
 
 
 2300 
 
 881348 
 
 1594 
 
 2303256 
 
 63 
 
 38 
 
 13514 
 
 135. 
 
 885. 
 
 31777 
 
 
 
 2200 
 
 917873 
 
 1595 
 
 2303621 
 
 62 
 
 39 
 
 13879 
 
 12 
 
 89 
 
 32142 
 
 
 
 2100 
 
 954398 
 
 15965. 
 
 2303987 
 
 615. 
 
 405. 
 
 14245 
 
 11 
 
 90 
 
 32507 
 
 
 
 2000 
 
 1090923 
 
 1597 
 
 2304352 
 
 60 
 
 41 
 
 14610 
 
 10 
 
 91 
 
 32872 
 
 
 
 1900 
 
 1127448 
 
 1598 
 
 2304717 
 
 59 
 
 42 
 
 14975 
 
 95. 
 
 925. 
 
 33238 
 
 
 
 1800 
 
 1163973 
 
 1599 
 
 2305082 
 
 58 
 
 43 
 
 15340 
 
 8 
 
 93 
 
 33603 
 
 
 
 1700 
 
 1200498 
 
 16005. 
 
 2305448 
 
 575. 
 
 445. 
 
 15706 
 
 7 
 
 94 
 
 33968 
 
 
 
 1600 
 
 1237023 
 
 1601 
 
 2305813 
 
 56 
 
 45 
 
 16071 
 
 6 
 
 95 
 
 34333 
 
 
 
 1500 
 
 1273548 
 
 1701 
 
 2342337 
 
 55 
 
 46 
 
 16436 
 
 55. 
 
 965. 
 
 34699 
 
 
 
 1400 
 
 1210073 
 
 1801 
 
 2378861 
 
 54 
 
 47 
 
 16801 
 
 4 
 
 97 
 
 35064 
 
 
 
 1300 
 
 1246598 
 
 1901 
 
 2415385 
 
 535. 
 
 485. 
 
 17167 
 
 3 
 
 98 
 
 35429 
 
 
 
 1200 
 
 1283123 
 
 
 
 52 
 
 49 
 
 17532 
 
 2 
 
 99 
 
 35794 
 
 
 
 1100 
 
 1319648 
 
 
 
 51 
 
 50 
 
 17897 
 
 15. 
 
 1005. 
 
 36160 
 
 
 
 1000 
 
 1356173 
 
 
 
 50 
 
 51 
 
 18262 
 
 
 100 
 
 36159 
 
 
 
TABLE III. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1582. 
 
 
 
 JANUARY. 
 
 FEBRUARY. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 y 
 
 5MBER. 
 
 03 
 
 H 
 
 CQ 
 
 i 
 
 co 
 
 " 
 u 
 
 as 
 H 
 
 m 
 
 03 
 
 a 
 
 CO 
 
 1 
 
 
 
 
 
 
 
 Day 
 
 Com- 
 
 Bissex- 
 
 Com- 
 
 Bissex- 
 
 1 
 
 B 
 
 ti 
 
 W 
 2 
 
 >j 
 
 B 
 
 CD 
 
 F 
 
 i 
 
 w 
 
 W 
 
 
 
 M 
 
 1 
 
 
 
 of 
 
 mon 
 
 tile 
 
 mon 
 
 tile 
 
 <J 
 
 PH 
 
 < 
 
 3 
 
 p 
 
 s 
 
 &3 
 
 O 
 
 O 
 
 
 
 
 O 
 
 1 
 
 
 
 Month. 
 
 Year. 
 
 Year. 
 
 Year. 
 
 Year. 
 
 M 
 
 
 M 
 
 
 
 < 
 
 cc 
 
 O 
 
 
 Q 
 
 O 
 
 
 M 
 
 
 
 1 
 
 1 
 
 
 
 32 
 
 31 
 
 60 
 
 91 
 
 121 
 
 152 
 
 182 
 
 213 
 
 244 
 
 274 
 
 305 
 
 335 
 
 274 
 
 295 
 
 325 
 
 
 
 2 
 
 2 
 
 1 
 
 33 
 
 32 
 
 61 
 
 92 
 
 122 
 
 153 
 
 183 
 
 214 
 
 245 
 
 275 
 
 306 
 
 336 
 
 275 
 
 296 
 
 326 
 
 
 
 3 
 
 3 
 
 2 
 
 34 
 
 33 
 
 62 
 
 93 
 
 123 
 
 154 
 
 184 
 
 215 
 
 246 
 
 276 
 
 307 
 
 337 
 
 276 
 
 297 
 
 327 
 
 
 
 4 
 
 4 
 
 3 
 
 35 
 
 34 
 
 63 
 
 94 
 
 124 
 
 155 
 
 185 
 
 216 
 
 247 
 
 277 
 
 308 
 
 338 
 
 277 
 
 298 
 
 328 
 
 
 
 5 
 
 5 
 
 4 
 
 36 
 
 35 
 
 64 
 
 95 
 
 125 
 
 156 
 
 186 
 
 217 
 
 248 
 
 278 
 
 309 
 
 339 
 
 
 299 
 
 329 
 
 
 
 6 
 
 6 
 
 5 
 
 37 
 
 36 
 
 65 
 
 96 
 
 126 
 
 157 
 
 187 
 
 218 
 
 249 
 
 279 
 
 310 
 
 340 
 
 
 300 
 
 330 
 
 
 
 7 
 
 7 
 
 6 
 
 38 
 
 37 
 
 66 
 
 97 
 
 127 
 
 158 
 
 188 
 
 219 
 
 250 
 
 280 
 
 311 
 
 341 
 
 
 301 
 
 331 
 
 
 
 8 
 
 8 
 
 7 
 
 39 
 
 38 
 
 67 
 
 98 
 
 128 
 
 159 
 
 189 
 
 220 
 
 251 
 
 281 
 
 312 
 
 342 
 
 
 302 
 
 332 
 
 
 
 9 
 
 9 
 
 8 
 
 40 
 
 39 
 
 68 
 
 99 
 
 129 
 
 160 
 
 190 
 
 221 
 
 252 
 
 282 
 
 313 
 
 343 
 
 
 303 
 
 333 
 
 
 
 10 
 
 10 
 
 9 
 
 41 
 
 40 
 
 69 
 
 100 
 
 130 
 
 161 
 
 191 
 
 222 
 
 253 
 
 283 
 
 314 
 
 344 
 
 
 304 
 
 334 
 
 
 
 11 
 
 11 
 
 10 
 
 42 
 
 41 
 
 70 
 
 101 
 
 131 
 
 162- 
 
 192 
 
 223 
 
 254 
 
 284 
 
 315 
 
 345 
 
 
 305 
 
 335 
 
 
 
 12 
 
 12 
 
 11 
 
 43 
 
 42 
 
 71 
 
 102 
 
 132 
 
 163 
 
 193 
 
 224 
 
 255 
 
 285 
 
 316 
 
 346 
 
 
 306 
 
 336 
 
 
 
 13 
 
 13 
 
 12 
 
 44 
 
 43 
 
 72 
 
 103 
 
 133 
 
 164 
 
 194 
 
 225 
 
 256 
 
 286 
 
 317 
 
 347 
 
 
 307 
 
 337 
 
 
 
 14 
 
 14 
 
 13 
 
 45 
 
 44 
 
 73 
 
 104 
 
 134 
 
 165 
 
 195 
 
 226 
 
 257 
 
 287 
 
 318 
 
 348 
 
 
 308 
 
 338 
 
 
 
 15 
 
 15 
 
 14 
 
 46 
 
 45 
 
 74 
 
 105 
 
 135 
 
 166 
 
 196 
 
 227 
 
 258 
 
 288 
 
 319 
 
 349 
 
 278 
 
 309 
 
 339 
 
 
 
 16 
 
 16 
 
 15 
 
 47 
 
 46 
 
 75 
 
 106 
 
 136 
 
 167 
 
 197 
 
 228 
 
 259 
 
 289 
 
 320 
 
 350 
 
 279 
 
 310 
 
 340 
 
 
 
 17 
 
 17 
 
 16 
 
 48 
 
 47 
 
 76 
 
 107 
 
 137 
 
 168 
 
 198 
 
 229' 
 
 260 
 
 290 
 
 321 
 
 351 
 
 280 
 
 311 
 
 341 
 
 
 
 18 
 
 18 
 
 17 
 
 49 
 
 48 
 
 77 
 
 108 
 
 138 
 
 169 
 
 199 
 
 230 
 
 261 
 
 291 
 
 322 
 
 352 
 
 281 
 
 312 
 
 342 
 
 
 
 19 
 
 19 
 
 18 
 
 50 
 
 49 
 
 78 
 
 109 
 
 139 
 
 170 
 
 200 
 
 231 
 
 262 
 
 292 
 
 323 
 
 353 
 
 282 
 
 313 
 
 343 
 
 
 
 20 
 
 20 
 
 19 
 
 51 
 
 50 
 
 79 
 
 110 
 
 140 
 
 171 
 
 201 
 
 232 
 
 263 
 
 293 
 
 324 
 
 354 
 
 283 
 
 314 
 
 344 
 
 
 
 21 
 
 21 
 
 20 
 
 52 
 
 51 
 
 80 
 
 111 
 
 141 
 
 172 
 
 202 
 
 233 
 
 264 
 
 294 
 
 325 
 
 355 
 
 284 
 
 315 
 
 345 
 
 
 
 22 
 
 22 
 
 21 
 
 53 
 
 52 
 
 81 
 
 112 
 
 142 
 
 173 
 
 203 
 
 234 
 
 265 
 
 295 
 
 326 
 
 356 
 
 285 
 
 316 
 
 346 
 
 
 
 23 
 
 23 
 
 22 
 
 54 
 
 53 
 
 82 
 
 113 
 
 143 
 
 174 
 
 204 
 
 235 
 
 266 
 
 296 
 
 327 
 
 357 
 
 286 
 
 317 
 
 347 
 
 
 
 24 
 
 24 
 
 23 
 
 55 
 
 54 
 
 83 
 
 114 
 
 144 
 
 175 
 
 205 
 
 236 
 
 267 
 
 297 
 
 328 
 
 358 
 
 287 
 
 318 348 
 
 
 
 25 
 
 25 
 
 24 
 
 56 
 
 55 
 
 84 
 
 115 
 
 145 
 
 176 
 
 206 
 
 237 
 
 268 
 
 298 
 
 329 
 
 359 
 
 288 
 
 319 
 
 349 
 
 
 
 26 
 
 26 
 
 25 
 
 57 
 
 56 
 
 85 
 
 116 
 
 146 
 
 177 
 
 207 
 
 238 
 
 269 
 
 299 
 
 330 
 
 360 
 
 289 
 
 320 
 
 350 
 
 
 
 27 
 
 27 
 
 26 
 
 58 
 
 57 
 
 86 
 
 117 
 
 147 
 
 178 
 
 208 
 
 239 
 
 270 
 
 300 
 
 331 
 
 361 
 
 290 
 
 321 
 
 351 
 
 
 
 28 
 
 28 
 
 27 
 
 59 
 
 58 
 
 87 
 
 118 
 
 148 
 
 179 
 
 209 
 
 240 
 
 271 
 
 301 
 
 332 
 
 362 
 
 291 
 
 322 
 
 352 
 
 
 
 29 
 
 29 
 
 28 
 
 
 59 
 
 88 
 
 119 
 
 149 
 
 180 
 
 210 
 
 241 
 
 272 
 
 302 
 
 333 
 
 363 
 
 292 
 
 323 
 
 353 
 
 
 
 30 
 
 30 
 
 29 
 
 
 
 89 
 
 120 
 
 150 
 
 181 
 
 211 
 
 242 
 
 273 
 
 303 
 
 334 
 
 364 
 
 293 
 
 324 
 
 354 
 
 
 
 31 
 
 31 
 
 30 
 
 
 
 90 
 
 
 151 
 
 
 212 
 
 243 
 
 
 304 
 
 
 365 
 
 294 
 
 
 355 
 
 
 
TABLE IV. 
 
 5 
 
 
 
 
 Hours 
 and 
 Minutes. 
 
 Decimal of a Da}. 
 
 Minutes. 
 
 Decimal of a Day. 
 
 Minutes 
 and 
 Seconds. 
 
 Decimal of a Day. 
 
 Seconds. 
 
 Decimal of a Day. 
 
 
 h. 
 
 
 m. 
 
 
 m. 
 
 
 8. 
 
 
 
 
 1 
 
 .041666667 
 
 13 
 
 .009027778 
 
 50 
 
 .034722222 
 
 23 
 
 .000266204 
 
 
 
 2 
 
 .083333333 
 
 14 
 
 .009722222 
 
 51 
 
 .035416667 
 
 24 
 
 .000277778 
 
 
 
 3 
 
 .125000000 
 
 15 
 
 .010416667 
 
 52 
 
 .036111111 
 
 25 
 
 .000289352 
 
 
 
 4 
 
 .166666667 
 
 16 
 
 .011111111 
 
 53 
 
 .036805556 
 
 26 
 
 .000300926 
 
 
 
 5 
 
 .208333333 
 
 17 
 
 .011805556 
 
 54 
 
 .037500000 
 
 27 
 
 .000312500 
 
 
 
 6 
 
 .250000000 
 
 18 
 
 .012500000 
 
 55 
 
 .038494444 
 
 28 
 
 .000324074 
 
 
 
 7 
 
 .291666667 
 
 19 
 
 .013194444 
 
 56 
 
 .038888889 
 
 29 
 
 .000335648 
 
 
 
 8 
 
 .333333333 
 
 20 
 
 .013888889 
 
 57 
 
 .039583333 
 
 30 
 
 .000347222 
 
 
 
 9 
 
 .375000000 
 
 21 
 
 .014583333 
 
 58 
 
 .040277778 
 
 31 
 
 .000358796 
 
 
 
 10 
 
 .416666667 
 
 22 
 
 .015277778 
 
 59 
 
 .040972222 
 
 32 
 
 .000370310 
 
 
 
 11 
 
 .458333333 
 
 23 
 
 .015972222 
 
 60 
 
 .041666667 
 
 33 
 
 .000381944 
 
 
 
 12 
 
 .500000000 
 
 24 
 
 .016666667 
 
 
 
 34 
 
 .000393519 
 
 
 
 13 
 
 .541666667 
 
 25 
 
 .017361111 
 
 
 
 35 
 
 .000405093 
 
 
 
 14 
 
 .583333333 
 
 26 
 
 .018055556 
 
 
 
 36 
 
 .000416667 
 
 
 
 15 
 
 .625000000 
 
 27 
 
 .018750000 
 
 
 
 37 
 
 .000428241 
 
 
 
 
 
 
 
 8. 
 
 
 
 
 
 
 16 
 
 .666666667 
 
 28 
 
 .019444444 
 
 1 
 
 .000011574 
 
 38 
 
 .000439815 
 
 
 
 17 
 
 .708333333 
 
 29 
 
 .020138889 
 
 2 
 
 .000023148 
 
 39 
 
 .000451389 
 
 
 
 18 
 
 .750000000 
 
 30 
 
 .020833333 
 
 3 
 
 .000034722 
 
 40 
 
 .000462963 
 
 
 
 19 
 
 .791666667 
 
 31 
 
 .021827778 
 
 4 
 
 .000046296 
 
 41 
 
 .000474537 
 
 
 
 20 
 
 .833333333 
 
 32 
 
 .022222222 
 
 5 
 
 .000057870 
 
 42 
 
 .000486111 
 
 
 
 21 
 
 .875000000 
 
 33 
 
 .022916667 
 
 6 
 
 .000069444 
 
 43 
 
 .000497685 
 
 
 
 22 
 
 .916666666 
 
 34 
 
 .023611111 
 
 7 
 
 .000081019 
 
 44 
 
 .000509259 
 
 
 
 23 
 
 .958333333 
 
 35 
 
 .024305556 
 
 8 
 
 .000092593 
 
 45 
 
 .000520833 
 
 
 
 24 
 
 1.000000000 
 
 36 
 
 .025000000 
 
 9 
 
 .000104167 
 
 46 
 
 .000532407 
 
 
 
 
 
 37 
 
 .025694444 
 
 10 
 
 .000115741 
 
 47 
 
 .000543981 
 
 
 
 m. 
 
 
 
 
 
 
 
 
 
 
 1 
 
 .000694444 
 
 38 
 
 .026388889 
 
 11 
 
 .000127.315 
 
 48 
 
 .000555556 
 
 
 
 2 
 
 .001388889 
 
 39 
 
 .027083333 
 
 12 
 
 .000138889 
 
 49 
 
 .000567130 
 
 
 
 3 
 
 .002083333 
 
 40 
 
 .027777778 
 
 13 
 
 .000150463 
 
 50 
 
 .000578704 
 
 
 
 4 
 
 .002777778 
 
 41 
 
 .028472222 
 
 14 
 
 .000162037 
 
 51 
 
 .000590278 
 
 
 
 5 
 
 .003472222 
 
 42 
 
 .029166667 
 
 15 
 
 .000173611 
 
 52 
 
 .000601852 
 
 
 
 6 
 
 .004166667 
 
 43 
 
 .029861111 
 
 16 
 
 .000185185 
 
 53 
 
 .000613426 
 
 
 
 7 
 
 .004861111 
 
 44 
 
 .030555556 
 
 17 
 
 .000196759 
 
 54 
 
 .000625000 
 
 
 
 8 
 
 .005555556 
 
 45 
 
 .031230000 
 
 18 
 
 .000208333 
 
 55 
 
 .000636574 
 
 
 
 9 
 
 .006250000 
 
 46 
 
 .031944444 
 
 19 
 
 .000219907 
 
 56 
 
 .000648148 
 
 
 
 10 
 
 .006944444 
 
 47 
 
 .032638889 
 
 20 
 
 .000231481 
 
 57 
 
 .000659722 
 
 
 
 11 
 
 .007638889 
 
 48 
 
 .033333333 
 
 21 
 
 .000243056 
 
 58 
 
 .000671296 
 
 
 
 12 
 
 .008333333 
 
 49 
 
 .034027778 
 
 22 
 
 .000254630 
 
 59 
 
 .000682870 
 
 
 
 13 
 
 .009027778 
 
 50 
 
 .034722222 
 
 23 
 
 .000266204 
 
 60 
 
 .000694444 
 
 
 
6 
 
 TABLE V. 
 
 
 
 
 Year. 
 
 L 
 
 & 
 
 7T 
 
 P 
 
 H, 
 
 H, 
 
 
 1800 
 
 109 4 40.35 
 
 45 57 37.67 
 
 74 20 41.55 
 
 0.00 
 
 6170 
 
 1.7 
 
 
 
 1801 
 
 162 47 43.65 
 
 45 58 20.15 
 
 74 21 37.10 
 
 0.00 
 
 6535 
 
 1.5 
 
 
 
 1802 
 
 216 30 46.95 
 
 45 59 2.63 
 
 74 22 32.65 
 
 0.00 
 
 102 
 
 1.3 
 
 
 
 1803 
 
 270 13 50.26 
 
 45 59 45.11 
 
 74 23 28.20 
 
 0.00 
 
 468 
 
 1.0 
 
 
 
 1804 B 
 
 323 56 53.56 
 
 46 27.60 
 
 74 24 23.75 
 
 0.00 
 
 . 832 
 
 0.8 
 
 
 
 1805 
 
 21 45 29.42 
 
 46 1 10.19 
 
 74 25 19.46 
 
 0.00 
 
 1198 
 
 1.5 
 
 
 
 1806 
 
 75 28 32.72 
 
 46 1 52.68 
 
 74 26 15.01 
 
 0.00 
 
 1563 
 
 1.3 
 
 
 
 1807 
 
 129 11 36.02 
 
 46 2 35.16 
 
 74 27 10.56 
 
 0.00 
 
 1929 
 
 1.0 
 
 
 
 1808 B 
 
 182 54 39.32 
 
 46 3 17.64 
 
 74 28 6.11 
 
 0.00 
 
 2293 
 
 0.8 
 
 
 
 1809 
 
 240 43 15.18 
 
 46 4 0.24 
 
 74 29 1.81 
 
 0.00 
 
 2659 
 
 1.6 
 
 
 
 1810 
 
 294 26 18.48 
 
 46 4 42.72 
 
 74 29 57.36 
 
 0.01 
 
 3024 
 
 1.3 
 
 
 
 1811 
 
 348 9 21.79 
 
 46 5 25.20 
 
 74 30 52.91 
 
 0.01 
 
 3390 
 
 1.1 
 
 
 
 1812B 
 
 41 52 25.09 
 
 46 6 7.68 
 
 74 31 48.47 
 
 0.01 
 
 3754 
 
 0.8 
 
 
 
 1813 
 
 99 41 0.95 
 
 46 6 50.28 
 
 74 32 44.17 
 
 0.02 
 
 4120 
 
 1.6 
 
 
 
 1814 
 
 153 24 4.25 
 
 46 7 32.77 
 
 74 33 39.72 
 
 0.02 
 
 4485 
 
 1.3 
 
 
 
 1815 
 
 207 7 7.55 
 
 46 8 15.25 
 
 74 34 35.27 
 
 0.03 
 
 4851 
 
 1.1 
 
 
 
 18165 
 
 260 50 10.85 
 
 46 8 57.73 
 
 74 35 30.82 
 
 0.03 
 
 5215 
 
 0.9 
 
 
 
 1817 
 
 318 38 46.71 
 
 46 9 40.33 
 
 74 36 26.52 
 
 0.04 
 
 5581 
 
 1.6 
 
 
 
 1818 
 
 12 21 50.01 
 
 46 10 22.81 
 
 74 37 22.08 
 
 0.04 
 
 5946 
 
 1.4 
 
 
 
 1819 
 
 66 4 53.32 
 
 46 11 5.29 
 
 74 38 17.63 
 
 0.05 
 
 6312 
 
 1.1 
 
 
 
 1820 B 
 
 119 47 56.62 
 
 46 11 47.77 
 
 74 39 13.18 
 
 0.05 
 
 6676 
 
 0.9 
 
 
 
 1821 
 
 177 36 32.48 
 
 46 12 30.37 
 
 74 40 8.88 
 
 0.05 
 
 244 
 
 1.6 
 
 
 
 1822 
 
 231 19 35.78 
 
 46 13 12.86 
 
 74 41 4.43 
 
 0.06 
 
 609 
 
 1.4 
 
 
 
 1823 
 
 285 2 39.08 
 
 46 13 55.34 
 
 74 41 59.98 ' 
 
 0.06 
 
 974 
 
 1.2 
 
 
 
 1824 B 
 
 338 45 42.38 
 
 46 14 37.82 
 
 74 42 55.53 
 
 0.07 
 
 1339 
 
 0.9 
 
 
 
 1825 
 
 36 34 18.24 
 
 46 15 20.42 
 
 74 43 51.24 
 
 0.08 
 
 1705 
 
 1.7 
 
 
 
 1826 
 
 90 17 21.54 
 
 46 16 2.90 
 
 74 44 46.79 
 
 0.08 
 
 2070 
 
 1.4 
 
 
 
 1827 
 
 144 24.85 
 
 46 16 45.38 
 
 74 45 42.34 
 
 0.08 
 
 2435 
 
 1.2 
 
 
 
 1828 B 
 
 197 43 28.15 
 
 46 17 27.86 
 
 74 46 37.89 
 
 0.09 
 
 2800 
 
 0.9 
 
 
 
 1829 
 
 255 32 4.00 
 
 46 18 10.46 
 
 74 47 33.59 
 
 0.10 
 
 3166 
 
 1.7 
 
 
 
 1830 
 
 309 15 7.31 
 
 46 18 52.95 
 
 74 48 29.14 
 
 0.11 
 
 3531 
 
 1.5 
 
 
 
 1831 
 
 2 58 10.61 
 
 46 19 35.43 
 
 74 49 24.69 
 
 0.11 
 
 3897 
 
 1.2 
 
 
 
 1832 B 
 
 56 41 13.91 
 
 46 20 17.91 
 
 74 50 20.25 
 
 0.12 
 
 4261 
 
 1.0 
 
 
 
 1833 
 
 114 29 49.77 
 
 46 21 0.51 
 
 74 51 15.95 
 
 0.13 
 
 4627 
 
 1.7 
 
 
 
 1834 
 
 168 12 53.07 
 
 46 21 42.99 
 
 74 52 11.50 
 
 0.14 
 
 4992 
 
 1.5 
 
 
 
 1835 
 
 221 55 56.38 
 
 46 22 25.47 
 
 74 53 7.05 
 
 0.15 
 
 5358 
 
 1.2 
 
 
 
 1836 B 
 
 275 38 59.68 
 
 46 23 7.95 
 
 74 54 2.60 
 
 0.15 
 
 5722 
 
 1.0 
 
 
 
 1837 
 
 333 27 35.54 
 
 46 23 50.55 
 
 74 54 58.31 
 
 0.16 
 
 6088 
 
 1.8 
 
 
 
 1838 
 
 27 10 38.84 
 
 46 24 33.04 
 
 74 55 53.86 
 
 0.17 
 
 6453 
 
 1.5 
 
 
 
 1839 
 
 80 53 42.14 
 
 46 25 15.52 
 
 74 56 49.41 
 
 0.18 
 
 20 
 
 1.3 
 
 
 
 1840 B 
 
 134 36 45.44 
 
 46 25 58.00 
 
 74 57 44.96 
 
 0.19 
 
 385 
 
 1.0 
 
 
 
 1841 
 
 192 25 21.30 
 
 46 26 40.60 
 
 74 58 40.66 
 
 0.20 
 
 751 
 
 1.8 
 
 
 
 1842 
 
 246 8 24.60 
 
 46 27 23.08 
 
 74 59 36.21 
 
 0.21 
 
 1116 
 
 1.5 
 
 
 
 1843 
 
 299 51 27.91 
 
 46 28 5.56 
 
 75 31.76 
 
 0.22 
 
 1481 
 
 1.3 
 
 
 
 1844 B 
 
 353 34 31.21 
 
 46 28 48.04 
 
 75 1 27.31 
 
 0.23 
 
 1846 
 
 1.1 
 
 
 
 1845 
 
 51 23 7.07 
 
 46 29 30.64 
 
 75 2 23.02 
 
 0.24 
 
 2212 
 
 1.8 
 
 
 
 1846 
 
 105 6 10.37 
 
 46 30 13.13 
 
 75 3 18.57 
 
 0.25 
 
 2577 
 
 1.6 
 
 
 
 1847 
 
 158 49 13.67 
 
 46 30 55.61 
 
 75 4 14.12 
 
 0.26 
 
 2942 
 
 1.3 
 
 
 
 1848 B 
 
 212 32 16.97 
 
 46 31 38.09 
 
 75 5 9.67 
 
 0.28 
 
 3307 
 
 1.1 
 
 
 
 1849 
 
 270 20 52.83 
 
 46 32 20.69 
 
 75 6 5.37 
 
 0.29 
 
 3673 
 
 1.8 
 
 
 
 1850 
 
 324 3 56.13 
 
 46 33 3.17 
 
 75 7 0.92 
 
 0.30 
 
 4038 
 
 1.6 
 
 
 
TABLE V. 
 
 
 
 
 Year. 
 
 A 
 
 T 
 
 V 
 
 / 
 
 E 
 
 8 
 
 m 
 
 
 1800 
 
 16.974666 
 
 28.11 
 
 105.10 
 
 59.66 
 
 55.66 
 
 73.8 
 
 
 
 
 
 1801 
 
 43.219906 
 
 41.23 
 
 53.02 
 
 4.48 
 
 53.47 
 
 81.1 
 
 4 
 
 
 
 1802 
 
 69.465146 
 
 54.35 
 
 0.94 
 
 9.36 
 
 51.28 
 
 88.4 
 
 8 
 
 
 
 1803 
 
 95.710386 
 
 67.47 
 
 68.86 
 
 14.24 
 
 49.09 
 
 6.2 
 
 12 
 
 
 
 1804 B 
 
 121.955626 
 
 80.59 
 
 16.78 
 
 19.12 
 
 46.89 
 
 13.5 
 
 16 
 
 
 
 1805 
 
 150.200867 
 
 6.75 
 
 11.68 
 
 25.20 
 
 59.13 
 
 21.8 
 
 20 
 
 
 
 1806 
 
 0.507417 
 
 19.87 
 
 79.59 
 
 30.08 
 
 56.94 
 
 29.0 
 
 25 
 
 
 
 1807 
 
 26.752657 
 
 33.00 
 
 27.51 
 
 34.96 
 
 54.74 
 
 36.3 
 
 29 
 
 
 
 1808 B 
 
 52.997897 
 
 46.12 
 
 95.42 
 
 39.84 
 
 52.54 
 
 43.6 
 
 33 
 
 
 
 1809 
 
 81.243137 
 
 60.24 
 
 43.35 
 
 44.72 
 
 50.35 
 
 51.9 
 
 37 
 
 
 
 1810 
 
 107.488377 
 
 73.36 
 
 111.26 
 
 49.60 
 
 48.15 
 
 59.1 
 
 41 
 
 
 
 1811 
 
 133.733617 
 
 86.49 
 
 59.18 
 
 54.48 
 
 45.95 
 
 66.4 
 
 45 
 
 
 
 1812B 
 
 159.978857 
 
 11.64 
 
 54.08 
 
 0.52 
 
 58.18 
 
 73.7 
 
 49 
 
 
 
 1813 
 
 12.285407 
 
 25.76 
 
 2.00 
 
 5.40 
 
 56.00 
 
 82.0 
 
 54 
 
 
 
 1814 
 
 38.530648 
 
 38.88 
 
 69.92 
 
 10.27 
 
 53.81 
 
 89.2 
 
 58 
 
 
 
 1815 
 
 64.775888 
 
 52.01 
 
 17.83 
 
 15.16 
 
 51.61 
 
 7.0 
 
 62 
 
 
 
 1816B 
 
 91.021128 
 
 65.13 
 
 85.75 
 
 20.02 
 
 49.40 
 
 14.3 
 
 66 
 
 
 
 1817 
 
 119.266368 
 
 79.25 
 
 33.67 
 
 24.90 
 
 47.21 
 
 22.6 
 
 70 
 
 
 
 1818 
 
 145.511608 
 
 4.41 
 
 28.56 
 
 30.99 
 
 59.46 
 
 29.9 
 
 74 
 
 
 
 1819 
 
 171.756848 
 
 17.53 
 
 96.48 
 
 35.86 
 
 57.27 
 
 37.2 
 
 78 
 
 
 
 1820 B 
 
 22.063398 
 
 30.65 
 
 44.41 
 
 40.75 
 
 55.06 
 
 44.4 
 
 83 
 
 
 
 1821 
 
 50.308638 
 
 44.77 
 
 112.32 
 
 45.63 
 
 52.86 
 
 52.7 
 
 87 
 
 
 
 1822 
 
 76.553879. 
 
 57.90 
 
 60.24 
 
 50.52 
 
 50.66 
 
 60.0 
 
 91 
 
 
 
 1823 
 
 102.799119 ' 
 
 71.02 
 
 8.16 
 
 55.40 
 
 48.46 
 
 67.3 
 
 95 
 
 
 
 1824B 
 
 129.044359 
 
 84.14 
 
 76.08 
 
 0.21 
 
 * 46.27 
 
 74.5 
 
 99 
 
 
 
 1825 
 
 157.289599 
 
 10.29 
 
 70.97 
 
 6.31 
 
 58.53 
 
 82.8 
 
 103 
 
 
 
 1826 
 
 7.596148 
 
 23.42 
 
 18.88 
 
 11.18 
 
 56.34 
 
 0.6 
 
 108 
 
 
 
 1827 
 
 33.841389 
 
 36.54 
 
 86.80 
 
 16.07 
 
 54.12 
 
 7.9 
 
 112 
 
 
 
 1828 B 
 
 60.086629 
 
 49.66 
 
 34.72 
 
 20.94 
 
 51.93 
 
 15.2 
 
 116 
 
 
 
 1829 
 
 88.331869 
 
 63.78 
 
 102.64 
 
 25.81 
 
 49.73 
 
 23.5 
 
 120 
 
 
 
 1830 
 
 114.577110 
 
 76.91 
 
 50.56 
 
 30.69 
 
 47.55 
 
 30.7 
 
 124 
 
 
 
 1831 
 
 140.822350 
 
 2.06 
 
 45.46 
 
 36.78 
 
 59.80 
 
 38.0 
 
 128 
 
 
 
 1832B 
 
 167.067590 
 
 15.19 
 
 113.37 
 
 41.67 
 
 57.60 
 
 45.3 
 
 132 
 
 
 
 1833 
 
 19.374140 
 
 29.31 
 
 61.29 
 
 46.55 
 
 55.38 
 
 53.6 
 
 137 
 
 
 
 1834 
 
 45.619380 
 
 42.43 
 
 9.22 
 
 51.43 
 
 53.19 
 
 60.8 
 
 141 
 
 
 
 1835 
 
 71.864620 
 
 55.55 
 
 77.14 
 
 56.30 
 
 51.00 
 
 68.1 
 
 145 
 
 
 
 1836 B 
 
 98.109860 
 
 68.67 
 
 25.05 
 
 1.12 
 
 48.82 
 
 75.4 
 
 149 
 
 
 
 1837 
 
 126.355100 
 
 8280 
 
 92.97 
 
 6.00 
 
 46.61 
 
 83.7 
 
 153 
 
 
 
 1838 
 
 152.600341 
 
 7.95 
 
 87.87 
 
 12.11 
 
 58.85 
 
 1.5 
 
 157 
 
 
 
 1839 
 
 2.906891 
 
 21.07 
 
 35.79 
 
 16.97 
 
 56.67 
 
 8.8 
 
 162 
 
 
 
 1840B 
 
 29.152131 
 
 34.20 
 
 103.70 
 
 21.85 
 
 54.46 
 
 16.0 
 
 166 
 
 
 
 1841 
 
 57.397371 
 
 48.32 
 
 51.62 
 
 26.73 
 
 52.25 
 
 24.3 
 
 170 
 
 
 
 1842 
 
 83.642611 
 
 61.44 
 
 119.54 
 
 31.61 
 
 50.08 
 
 31.6 
 
 174 
 
 
 
 1843 
 
 109.887851 
 
 74.56 
 
 67.46 
 
 36.50 
 
 47.87 
 
 38.9 
 
 178 
 
 
 
 1844 B 
 
 136.133091 
 
 87.69 
 
 15.36 
 
 41.36 
 
 45.67 
 
 46.1 
 
 182 
 
 
 
 1845 
 
 164.378331 
 
 13.84 
 
 10.26 
 
 47.45 
 
 57.92 
 
 54.4 
 
 186 
 
 
 
 1846 
 
 14.684882 
 
 26.96 
 
 78.18 
 
 52.34 
 
 55.72 
 
 61.7 
 
 191 
 
 
 
 1847 
 
 40.930122 
 
 40.08 
 
 26.10 
 
 57.22 
 
 53.52 
 
 68.9 
 
 195 
 
 
 
 1848 B 
 
 67.175362 
 
 53.21 
 
 94.01 
 
 2.03 
 
 51.34 
 
 76.2 
 
 199 
 
 
 
 1849 
 
 95.420602 
 
 67.33 
 
 41.93 
 
 6.91 
 
 49.13 
 
 84.5 
 
 203 
 
 
 
 1850 
 
 121.665842 
 
 80.45 
 
 109.85 
 
 11.79 
 
 46.94 
 
 2.3 
 
 207 
 
 
 
8 
 
 TABLE V. 
 
 
 
 
 Year. 
 
 L 
 
 Q 
 
 7T 
 
 P 
 
 HI 
 
 H z 
 
 
 1850 
 
 324 3 56.13 
 
 4'6 33 3.17 
 
 o ; n 
 
 75 7 0.92 
 
 0.30 
 
 4038 
 
 1.6 
 
 
 
 1851 
 
 17 46 59.44 
 
 46 33 45.65 
 
 75 7 56.47 
 
 0.31 
 
 4403 
 
 1.4 
 
 
 
 1852 B 
 
 71 30 2.74 
 
 46 34 28.14 
 
 75 8 52.03 
 
 0.33 
 
 4768 
 
 . 1.1 
 
 
 
 1853 
 
 129 18 38.60 
 
 46 35 10.73 
 
 75 9 47.73 
 
 0.34 
 
 5134 
 
 1.9 
 
 
 
 1854 
 
 183 1 41.90 
 
 46 35 53.22 
 
 75 10 43.28 
 
 0.36 
 
 5499 
 
 1.6 
 
 
 
 1855 
 
 236 44 45.20 
 
 46 36 35.70 
 
 75 11 38.83 
 
 0.37 
 
 5864 
 
 1.4 
 
 
 
 18565 
 
 290 27 48.50 
 
 46 37 18.18 
 
 75 12 34.38 
 
 0.38 
 
 6229 
 
 1.1 
 
 
 
 1857 
 
 348 16 24.36 
 
 46 38 0.78 
 
 75 13 30.08 
 
 0.40 
 
 6595 
 
 1.9 
 
 
 
 1858 
 
 41 59 27.66 
 
 46 38 43.26 
 
 75 14 25.64 
 
 0.42 
 
 162 
 
 1.7 
 
 
 
 1859 
 
 95 42 30.97 
 
 46 39 25.74 
 
 75 15 21.19 
 
 0.43 
 
 527 
 
 1.4 
 
 
 
 1860 B 
 
 149 25 34.27 
 
 46 40 8.22 
 
 75 16 16.74 
 
 0.44 
 
 891 
 
 1.2 
 
 
 
 1861 
 
 207 14 10.13 
 
 46 40 50.82 
 
 75 17 12.44 
 
 0.46 
 
 1258 
 
 1.9 
 
 
 
 1862 
 
 260 57 13.43 
 
 46 41 33.31 
 
 75 18 7.99 
 
 0.47 
 
 1623 
 
 1.7 
 
 
 
 1863 
 
 314 40 16.73 
 
 46 42 15.79 
 
 75 19 3.54 
 
 0.48 
 
 1988 
 
 1.4 
 
 
 
 1864 B 
 
 8 23 20.03 
 
 46 42 58.27 
 
 75 19 59.09 
 
 0.49 
 
 2353 
 
 1.2 
 
 
 
 1865 
 
 66 11 55.89 
 
 46 43 40.87 
 
 75 20 54.80 
 
 0.51 
 
 2719 
 
 2.0 
 
 
 
 1866 
 
 119 54 59.19 
 
 46 44 23.35 
 
 75 21 50.35 
 
 0.53 
 
 3084 
 
 1.7 
 
 
 
 1867 
 
 173 38 2.50 
 
 46 45 5.83 
 
 75 22 45.90 
 
 0.55 
 
 3449 
 
 1.5 
 
 
 
 1868 B 
 
 227 21 5.80 
 
 46 45 48.31 
 
 75 23 41.45 
 
 0.56 
 
 3814 
 
 1.2 
 
 
 
 1869 
 
 285 9 41.66 
 
 46 46 30.91 
 
 75 24 37.15 
 
 0.58 
 
 4180 
 
 2.0 
 
 
 
 1870 
 
 338 52 44.96 
 
 46 47 13.40 
 
 75 25 32.70 
 
 0.60 
 
 4545 
 
 1.7 
 
 
 
 1871 
 
 32 35 48.26 
 
 46 47 55.88 
 
 75 26 28.25 
 
 0.62 
 
 4910 
 
 1.5 
 
 
 
 1872B 
 
 86 18 51.56 
 
 46 48 38.36 
 
 75 27 23.81 
 
 0.63 
 
 5275 
 
 1.3 
 
 
 
 1873 
 
 144 7 27.42 
 
 46 49 20.96 
 
 75 28 19.51 
 
 0.65 
 
 5641 
 
 2.0 
 
 
 
 1874 
 
 197 50 30.75 
 
 46 50 3.44 
 
 75 29 15.06 
 
 0.67 
 
 6006 
 
 1.8 
 
 
 
 1875 
 
 251 33 34:03 
 
 46 50 45.92 
 
 75 30 10.61 
 
 0.68 
 
 6371 
 
 1.5 
 
 
 
 1876 B 
 
 305 16 37.33 
 
 46 51 28.40 
 
 75 31 6.16 
 
 0.70 
 
 6736 
 
 1.3 
 
 
 
 1877 
 
 3 5 13.19 
 
 46 52 11.00 
 
 75 32 1.86 
 
 0.72 
 
 304 
 
 2.1 
 
 
 
 1878 
 
 56 48 16.49 
 
 46 52 53.49 
 
 75 32 57.42 
 
 0.74 
 
 669 
 
 1.8 
 
 
 
 1879 
 
 110 31 19.79 
 
 46 53 35.97 
 
 75 33 52.97 
 
 0.76 
 
 1034 
 
 1.6 
 
 
 
 1880 B 
 
 164 14 23.09 
 
 46 54 18.45 
 
 75 34 48.52 
 
 0.78 
 
 1398 
 
 1.3 
 
 
 
 1881 
 
 222 2 58.95 
 
 46 55 1.05 
 
 75 35 44.22 
 
 0.80 
 
 1765 
 
 2.1 
 
 
 
 1882 
 
 275 46 2.25 
 
 46 55 43.53 
 
 75 36 39.77 
 
 0.82 
 
 2130 
 
 1.8 
 
 
 
 1883 
 
 329 29 5.56 
 
 46 56 26.01 
 
 75 37 35.32 
 
 0.84 
 
 2495 
 
 1.6 
 
 
 
 1884 B 
 
 23 12 8.86 
 
 46 57 8.49 
 
 75 38 30.87 
 
 0.86 
 
 2859 
 
 1.4 
 
 
 
 1885 
 
 81 44.72 
 
 46 57 51.09 
 
 75 39 26.58 
 
 0.88 
 
 3226 
 
 2.1 
 
 
 
 1886 
 
 134 43 48.02 
 
 46 58 33.58 
 
 75 40 22.13 
 
 0.90 
 
 3591 
 
 1.9 
 
 
 
 1887 
 
 188 26 51.32 
 
 46 59 16.06 
 
 75 41 17.68 
 
 0.92 
 
 3956 
 
 1.6 
 
 
 
 1888 B 
 
 242 9 54.62 
 
 46 59 58.54 
 
 75 42 13.23 
 
 0.94 
 
 4321 
 
 1.4 
 
 
 
 1889 
 
 299 58 30.48 
 
 47 41.14 
 
 75 43 8.93 
 
 0.97 
 
 4687 
 
 2.1 
 
 
 
 1890 
 
 353 41 33.78 
 
 47 1 23.62 
 
 75 44 4.48 
 
 0.99 
 
 5052 
 
 1.9 
 
 
 
 1891 
 
 47 24 37.09 
 
 47 2 6.10 
 
 75 45 0.03 
 
 1.01 
 
 5417 
 
 1.7 
 
 
 
 1892 B 
 
 101 7 40.39 
 
 47 2 48.58 
 
 75 45 55.59 
 
 1.03 
 
 5782 
 
 1.4 
 
 
 
 1893 
 
 158 56 16.25 
 
 47 3 31.18 
 
 75 46 51.29 
 
 1.05 
 
 6148 
 
 2.2 
 
 
 
 1894 
 
 212 39 19.55 
 
 47 4 13.67 
 
 75 47 46.84 
 
 1.07 
 
 6513 
 
 1.9 
 
 
 
 1895 
 
 266 22 22.85 
 
 47 4 56.15 * 
 
 75 48 42.39 
 
 1.10 
 
 80 
 
 1.7 
 
 
 
 1896 B 
 
 320 5 26.15 
 
 47 5 38.63 
 
 75 49 37.94 
 
 1.12 
 
 444 
 
 1.4 
 
 
 
 1897 
 
 17 54 2.01 
 
 47 6 21.23 
 
 75 50 33.64 
 
 1.14 
 
 811 
 
 2.2 
 
 
 
 1898 
 
 71 37 5.31 
 
 47 7 3.71 
 
 75 51 29.20 
 
 1.17 
 
 1176 
 
 2.0 
 
 
 
 1899 
 
 125 20 8.62 
 
 47 7 46.19 
 
 75 52 24.75 
 
 1.19 
 
 1541 
 
 1.7 
 
 
 
 1900 
 
 179 3 11.92 
 
 47 8 28.67 
 
 75 53 20.30 
 
 1.22 
 
 1906 
 
 1.5 
 
 
 
TABLE V. 
 
 9 
 
 
 
 
 Year. 
 
 A 
 
 T 
 
 F 
 
 J 
 
 E 
 
 s 
 
 m 
 
 
 1850 
 
 121.665842 
 
 80.45 
 
 109.85 
 
 11.79 
 
 46.94 
 
 2.3 
 
 207 
 
 
 
 1851 
 
 147.911082 
 
 5.60 
 
 104.75 
 
 17.87 
 
 59.19 
 
 9.6 
 
 211 
 
 
 
 1852B 
 
 174.156322 
 
 18.73 
 
 52.66 
 
 22.76 
 
 56.98 
 
 16.9 
 
 215 
 
 
 
 1853 
 
 26.462873 
 
 32.85 
 
 0.58 
 
 27.65 
 
 54.78 
 
 25.2 
 
 220 
 
 
 
 1854 
 
 52.708113 
 
 45.97 
 
 68.50 
 
 32.52 
 
 52.60 
 
 32.4 
 
 224 
 
 
 
 1855 
 
 78.953353 
 
 59.10 
 
 16.41 
 
 37.40 
 
 50.39 
 
 39.7 
 
 228 
 
 
 
 1856 B 
 
 105.198593 
 
 72.22 
 
 84.33 
 
 42.28 
 
 48.20 
 
 47.0 
 
 232 
 
 
 
 1857 
 
 133.443833 
 
 86.34 
 
 32.25 
 
 47.17 
 
 45.99 
 
 55.3 
 
 236 
 
 
 
 1858 
 
 159.689073 
 
 11.49 
 
 27.15 
 
 53.24 
 
 58.25 
 
 62.5 
 
 240 
 
 
 
 1859 
 
 9.995623 
 
 24.62 
 
 95.07 
 
 58.12 
 
 56.05 
 
 69.8 
 
 245 
 
 
 
 1860 B 
 
 36.240863 
 
 37.74 
 
 42.98 
 
 2.95 
 
 53.86 
 
 77.1 
 
 249 
 
 
 
 1861 
 
 64.486104 
 
 51.86 
 
 110.90 
 
 7.83 
 
 51.67 
 
 85.3 
 
 253 
 
 
 
 1862 
 
 90.731344 
 
 64.99 
 
 58.81 
 
 12.71 
 
 49.47 
 
 3.2 
 
 257 
 
 
 
 1863 
 
 116.976584 
 
 78.11 
 
 6.73 
 
 17.57 
 
 47.26 
 
 10.5 
 
 261 
 
 
 
 1864 B 
 
 143.221824 
 
 3.26 
 
 1.63 
 
 23.67 
 
 59.52 
 
 17.7 
 
 265 
 
 
 
 1865 
 
 171.467064 
 
 17.38 
 
 69.55 
 
 28.56 
 
 57.31 
 
 26.0 
 
 269 
 
 
 
 1866 
 
 21.773614 
 
 30.51 
 
 17.46 
 
 33.43 
 
 55.10 
 
 33.3 
 
 274 
 
 
 
 1867 
 
 48.018854 
 
 43.63 
 
 85.39 
 
 38.31 
 
 52.92 
 
 40.6 
 
 278 
 
 
 
 1868B 
 
 74.264094 
 
 56.75 
 
 33.30 
 
 43.19 
 
 50.73 
 
 47.8 
 
 282 
 
 
 
 1869 
 
 102.509335 
 
 70.87 
 
 101.22 
 
 48.07 
 
 48.53 
 
 56.1 
 
 286 
 
 
 
 1870 
 
 128.754575 
 
 84.00 
 
 49.13 
 
 52.95 
 
 46.33 
 
 63.4 
 
 290 
 
 
 
 1871 
 
 154.999815 
 
 9.15 
 
 44.04 
 
 59.04 
 
 58.58 
 
 70.6 
 
 294 
 
 
 
 1872 B 
 
 5.306365 
 
 22.27 
 
 111.96 
 
 3.87 
 
 56.40 
 
 77.9 
 
 299 
 
 
 
 1873 
 
 33.551605 
 
 36.39 
 
 59.87 
 
 8.74 
 
 54.19 
 
 86.2 
 
 303 
 
 
 
 1874 
 
 59.796845 
 
 49.52 
 
 7.78 
 
 13.62 
 
 51.99 
 
 4.0 
 
 307 
 
 
 
 1875 
 
 86.042085 
 
 62.64 
 
 75.70 
 
 18.49 
 
 49.80 
 
 11.3 
 
 311 
 
 
 
 1876B 
 
 112.287325 
 
 75.76 
 
 23.62 
 
 23.37 
 
 47.60 
 
 18..6 
 
 315 
 
 
 
 1877 
 
 140.532566 
 
 1.92 
 
 18.52 
 
 29.47 
 
 59.84 
 
 26.9 
 
 319 
 
 
 
 1878 
 
 166.777806 
 
 15.04 
 
 86.44 
 
 34.36 
 
 57.64 
 
 34.1 
 
 323 
 
 
 
 1879 
 
 17.084356 
 
 28.16 
 
 34.36 
 
 39.23 
 
 55.45 
 
 41.4 
 
 328 
 
 
 
 1880B 
 
 43.329596 
 
 41.28 
 
 102.27 
 
 44.10 
 
 53.26 
 
 48.7 
 
 332 
 
 
 
 1881 
 
 71.574836 
 
 55.41 
 
 50.18 
 
 48.98 
 
 51.07 
 
 56.9 
 
 336 
 
 
 
 1882 
 
 97.820076 
 
 68.53 
 
 118.10 
 
 53.86 
 
 48.86 
 
 64.2 
 
 340 
 
 
 
 1883 
 
 124.065316 
 
 81.66 
 
 66.02 
 
 . 58.74 
 
 46.65 
 
 71.5 
 
 344 
 
 
 
 1884 B 
 
 150.310556 
 
 6.81 
 
 60.92 
 
 4.78 
 
 58.90 
 
 78.8 
 
 348 
 
 
 
 1885 
 
 2.617106 
 
 20.93 
 
 8.84 
 
 9.66 
 
 56.72 
 
 87.0 
 
 353 
 
 
 
 1886 
 
 28.862347 
 
 34.05 
 
 76.76 
 
 14.53 
 
 54.53 
 
 4.9 
 
 357 
 
 
 
 1887 
 
 55.107587 
 
 47.17 
 
 24.68 
 
 19.41 
 
 52.32 
 
 12.2 
 
 361 
 
 
 
 1888B 
 
 81.352827 
 
 60.29 
 
 92.60 
 
 24.29 
 
 50.12 
 
 19.4 
 
 365 
 
 
 
 1889 
 
 109.598067 
 
 74.42 
 
 40.51 
 
 29.16 
 
 47.93 
 
 27.7 
 
 369 
 
 
 
 1890 
 
 135.843307 
 
 87.54 
 
 108.42 
 
 34.05 
 
 45.73 
 
 35.0 
 
 373 
 
 
 
 1891 
 
 162.088547 
 
 12.69 
 
 103.33 
 
 40.13 
 
 58.00 
 
 42.2 
 
 377 
 
 
 
 1892B 
 
 12.395097 
 
 25.82 
 
 51.24 
 
 45.01 
 
 55.77 
 
 49.5 
 
 383 
 
 
 
 1893 
 
 40.640337 
 
 39.94 
 
 119.16 
 
 49.89 
 
 53.58 
 
 57.8 
 
 386 
 
 
 
 1894 
 
 66.885578 
 
 53.06 
 
 67.08 
 
 54.77 
 
 51.38 
 
 65.1 
 
 390 
 
 
 
 1895 
 
 93.130818 
 
 66.18 
 
 15.00 
 
 59.65 
 
 49.20 
 
 72.3 
 
 394 
 
 
 
 1896 B 
 
 119.376058 
 
 79.31 
 
 82.92 
 
 4.47 
 
 46.99 
 
 79.6 
 
 V 398 
 
 
 
 1897 
 
 147.621298 
 
 5.46 
 
 77.82 
 
 10.57 
 
 59.25 
 
 87.9 
 
 402 
 
 
 
 1898 
 
 173.866538 
 
 18.58 
 
 25.73 
 
 15.44 
 
 57.01 
 
 5.7 
 
 406 
 
 
 
 1899 
 
 24.173088 
 
 31.70 
 
 93.65 
 
 20.31 
 
 54.85 
 
 13.0 
 
 411 
 
 
 
 1900 
 
 50.418328 
 
 44.82 
 
 41.57 
 
 25.20 
 
 52.65 
 
 20.3 
 
 415 
 
 
 
10 
 
 TABLE VI. 
 
 
 
 
 Year. 
 
 K K 
 
 K 3 
 
 K* 
 
 \ogk x 
 
 log i' T 
 
 log k, 
 
 
 1800 
 
 O 1 II 
 
 161 7 30.0 
 
 7649'50'.'6 
 
 C f II 
 
 64 53 56.6 
 
 9.9983264 
 
 9.9450101 
 
 9.6821729 
 
 
 
 1801 
 
 164 8 25.5 
 
 76 50 47.6 
 
 64 54 44.0 
 
 .9983258 
 
 .9450140 
 
 .6821624 
 
 
 
 1802 
 
 164 9 21.1 
 
 76 51 44.7 
 
 64 55 31.4 
 
 .9983251 
 
 .9450191 
 
 .6821484 
 
 
 
 1803 
 
 164 10 16.7 
 
 76 52 41.7 
 
 64 56 18.8 
 
 .9983243 
 
 .9450255 
 
 .6821301 
 
 
 
 1804 B 
 
 164 11 12.2 
 
 76 53 38.8 
 
 64 57 6.2 
 
 .9983235 
 
 .9450327 
 
 .6821092 
 
 
 
 1805 
 
 164 12 7.9 
 
 76 54 36.0 
 
 64 57 53.7 
 
 .9983228 
 
 .9450407 
 
 .6820854 
 
 
 
 1806 
 
 164 13 3.5 
 
 76 55 33.0 
 
 64 58 41.1 
 
 .9983221 
 
 .9450489 
 
 .6820606 
 
 
 
 1807 
 
 164 13 59.1 
 
 76 56 30.1 
 
 64 59 28.5 
 
 .9983214 
 
 .9450574 
 
 .6820354 
 
 
 
 1808 B 
 
 164 14 54.6 
 
 76 57 27.1. 
 
 65 15.9 
 
 .9983208 
 
 .9450652 
 
 .6820118 
 
 
 
 1809 
 
 164 15 50.3 
 
 76 58 24.3 
 
 65 1 3.4 
 
 .9983202 
 
 .9450725 
 
 .6819901 
 
 
 
 1810 
 
 164 16 45.9 
 
 76 59 21.4 
 
 65 1 50.8 
 
 .9983195 
 
 .9450792 
 
 .6819721 
 
 
 
 1811 
 
 164 17 41.5 
 
 77 18.4 
 
 65 2 38.2 
 
 .9983190 
 
 .9450833 
 
 .6819583 
 
 
 
 1812B 
 
 164 18 37.0 
 
 77 1 15.5 
 
 65 3 25.6 
 
 .9983184 
 
 .9450871 
 
 .6819484 
 
 
 
 1813 
 
 164 19 32.7 
 
 77 2 12.7 
 
 65 4 13.2 
 
 .9983177 
 
 .9450898 
 
 .6819423 
 
 
 
 1814 
 
 164 20 28.3 
 
 77 3 9.7 
 
 65 5 0.6 
 
 .9983171 
 
 .9450921 
 
 .6819386 
 
 
 
 1815 
 
 164 21 23.8 
 
 77 4 6.8 
 
 65 5 48.0 
 
 .9983165 
 
 .9450931 
 
 .6819370 
 
 
 
 1816S 
 
 164 22 19.4 
 
 77 5 3.8 
 
 65 6 35.4 
 
 .9983158 
 
 .9450942 
 
 .6819356 
 
 
 
 1817 
 
 164 23 15.1 
 
 77 6 1.1 
 
 65 7 22.9 
 
 .9983151 
 
 .9450960 
 
 .6819326 
 
 
 
 1818 
 
 164 24 10.7 
 
 77 6 58.1 
 
 65 8 10.3 
 
 .9983144 
 
 .9450983 
 
 .6819278 
 
 
 
 1819 
 
 164 25 6.2 
 
 77 7 55.2 
 
 65 8 57.7 
 
 .9983136 
 
 .9451017 
 
 .6819197 
 
 
 
 1820 B 
 
 164 26 1.8 
 
 77 8 52.2 
 
 65 9 45.1 
 
 .9983128 
 
 .9451063 
 
 .6819078 
 
 
 
 1821 
 
 164 26 57.5 
 
 77 9 49.4 
 
 65 10 32.7 
 
 .9983121 
 
 .9451120 
 
 .6818921 
 
 
 
 1822 
 
 164 27 53.1 
 
 77 10 46.5 
 
 65 11 20.1 
 
 .9983113 
 
 .9451187 
 
 .6818728 
 
 
 
 1823 
 
 164 28 48.7 
 
 77 11 43.5 
 
 65 12 7.5 
 
 .9983105 
 
 .9451263 
 
 .6818506 
 
 
 
 1824 B 
 
 164 29 44.3 
 
 .77 12 40.5 
 
 65 12 54.9 
 
 .9983097 
 
 .9451345 
 
 .6818261 
 
 
 
 1825 
 
 164 30 40.0 
 
 77 13 37.8 
 
 65 13 42.5 
 
 .9983089 
 
 .9451430 
 
 .6818009 
 
 
 
 1826 
 
 164 31 35.5 
 
 77 14 34.8 
 
 65 14 29.9 
 
 .9983083 
 
 .9451510 
 
 .6817761 
 
 
 
 1827 
 
 164 32 31.0 
 
 77 15 31.9 
 
 65 15 17.3 
 
 .9983078 
 
 .9451588 
 
 .6817527 
 
 
 
 1828 B 
 
 164 33 26.7 
 
 77 16 28.9 
 
 65 16 4.7 
 
 .9983072 
 
 .9451656 
 
 .6817326 
 
 
 
 1829 
 
 164 34 22.4 
 
 77 17 26.1 
 
 65 16 52.3 
 
 .9983066 
 
 .9451710 
 
 .6817162 
 
 
 
 1830 
 
 164 35 18.0 
 
 77 18 23.2 
 
 65 17 39.7 
 
 .9983059 
 
 .9451759 
 
 .6817035 
 
 
 
 1831 
 
 164 36 13.6 
 
 77 19 20.2 
 
 65 18 27.1 
 
 .9983053 
 
 .9451789 
 
 .6816953 
 
 
 
 1832 B 
 
 164 37 9.1 
 
 77 20 17.3 
 
 65 19 14.5 
 
 .9983017 
 
 .9451811 
 
 .6816901 
 
 
 
 1833 
 
 164 38 4.8 
 
 77 21 14.5 
 
 65 20 2.1 
 
 .9983041 
 
 .9451827 
 
 .6816876 
 
 
 
 1834 
 
 164 39 0.4 
 
 77 22 11.5 
 
 65 20 49.5 
 
 .9983036 
 
 .9451840 
 
 .6816858 
 
 
 
 1835 
 
 164 39 56.0 
 
 77 23 8.5 
 
 65 21 36.9 
 
 .9983029 
 
 .9451855 
 
 .6816839 
 
 
 
 1836 B 
 
 164 40 51.6 
 
 77 24 5.6 
 
 65 22 24.4 
 
 .9983022 
 
 .9451875 
 
 .6816803 
 
 
 
 1837 
 
 164 41 47.3 
 
 77 25 2.8 
 
 65 23 11.9 
 
 .9983015 
 
 .9451903 
 
 .6816743 
 
 
 
 1838 
 
 164 42 42.8 
 
 77 25 59.8 
 
 65 23 59.3 
 
 .9983007 
 
 .9451939 
 
 .6616650 
 
 
 
 1839 
 
 164 43 38.4 
 
 77 26 56.8 
 
 65 24 46.8 
 
 .9982999 
 
 .9451990 
 
 .6816514 
 
 
 
 1840B 
 
 164 44 34.0 
 
 77 27 53.9 
 
 65 25 34.2 
 
 .9982991 
 
 .9452052 
 
 .6816338 
 
 
 
 1841 
 
 164 45 29.7 
 
 77 28 51.1 
 
 65 26 21.7 
 
 .9982983 
 
 .9152124 
 
 .6816132 
 
 
 
 1842 
 
 164 46 25.2 
 
 77 29 48.1 
 
 65 27 9.1 
 
 .9982977 
 
 .9452201 
 
 .6815901 
 
 
 
 1843 
 
 164 47 20.8 
 
 77 30 45.2 
 
 65 27 56.6 
 
 .9982969 
 
 .9452284 
 
 .6815650 
 
 
 
 18445 
 
 164 48 16.4 
 
 77 31 42.2 
 
 65 28 44.0 
 
 .9982962 
 
 .9452367 
 
 .6815396 
 
 
 
 1845 
 
 164 49 12.1 
 
 77 32 39.4 
 
 65 29 31.6 
 
 .9982955 
 
 .9452448 
 
 .6815154 
 
 
 
 1846 
 
 164 50 7.7 
 
 77 33 36.5 
 
 65 30 19.0 
 
 .9982949 
 
 .9452524 
 
 .6814835 
 
 
 
 1847 
 
 164 51 3.3 
 
 77 34 33.5 
 
 65 31 6.4 
 
 .9982944 
 
 .9452585 
 
 .6814743 
 
 
 
 1848 B 
 
 164 51 58.9 
 
 77 35 30.6 
 
 65 31 53.8 
 
 .9982938 
 
 .9452637 
 
 .6814593 
 
 
 
 1849 
 
 164 52 54.5 
 
 77 36 27.7 
 
 65 32 41.4 
 
 .9982932 
 
 .9452678 
 
 .6814484 
 
 
 
 1850 
 
 164 53 50.1 
 
 77 37 24.8 
 
 65 33 28.8 
 
 9.9982925 
 
 9.9452706 
 
 9.6814414 
 
 
 
TABLE VI. 
 
 11 
 
 
 
 
 Year. 
 
 z. 
 
 K Y 
 
 K t 
 
 logfc r 
 
 log kj 
 
 log*. 
 
 
 1850 
 
 164 53 50.1 
 
 O * II 
 
 77 37 24.8 
 
 65 33' 28'.8 
 
 9.9982925 
 
 9.9452706 
 
 9.6814414 
 
 
 
 1851 
 
 164 54 45.7 
 
 77 38 21.8 
 
 65 34 16.2 
 
 .9982919 
 
 .9452727 
 
 .6814372 
 
 
 
 1852 B 
 
 164 55 41.3 
 
 77 39 18.8 
 
 65 35 3.7 
 
 .9982914 
 
 .9452741 
 
 .6814352 
 
 
 
 1853 
 
 164 56 37.0 
 
 77 40 16.0 
 
 65 35 51.3 
 
 .9982907 
 
 .9452756 
 
 .6814334 
 
 
 
 1854 
 
 164 57 32.6 
 
 77 41 13.1 
 
 65 36 38.7 
 
 .9982900 
 
 .9452772 
 
 .6814310 
 
 
 
 1855 
 
 164 58 28.1 
 
 77 42 10.1 
 
 65 37 26.1 
 
 .9982892 
 
 .9452794 
 
 .6814263 
 
 
 
 1856 B 
 
 164 59 23.7 
 
 77 43 7.1 
 
 65 38 13.5 
 
 .9982884 
 
 .9452825 
 
 .6814191 
 
 
 
 1857 
 
 165 19.4 
 
 77 44 4.3 
 
 65 39 1.1 
 
 .9982877 
 
 .9452867 
 
 .6814079 
 
 
 
 1858 
 
 165 1 15.0 
 
 77 45 1.3 
 
 65 39 48.5 
 
 .9982870 
 
 .9452921 
 
 .6813931 
 
 
 
 1859 
 
 165 2 10.6 
 
 77 45 58.4 
 
 65 40 36.0 
 
 .9982862 
 
 .9452987 
 
 .6813744 
 
 
 
 1860 B 
 
 165 3 6.1 
 
 77 46 55.4 
 
 65 41 23.4 
 
 .9982854 
 
 .9453060 
 
 .6813526 
 
 
 
 1861 
 
 165 4 1.9 
 
 77 47 52.6 
 
 65 42 11.0 
 
 .9982846 
 
 .9453142 
 
 .6813285 
 
 
 
 1862 
 
 165 4 57.4 
 
 77 48 49.6 
 
 65 42 58.4 
 
 .9982840 
 
 .9453229 
 
 .6813032 
 
 
 
 1863 
 
 165 5 53.0 
 
 77 49 46.6 
 
 65 43 45.9 
 
 .9982833 
 
 .9453310 
 
 .6812778 
 
 
 
 1864 B 
 
 165 6 48.6 
 
 77 50 43.7 
 
 65 44 33.3 
 
 .9982827 
 
 .9453387 
 
 .6812543 
 
 
 
 1865 
 
 165 7 44.3 
 
 77 51 40.9 
 
 65 45 20.9 
 
 .9982821 
 
 .9453460 
 
 .6812330 
 
 
 
 1866 
 
 165 8 39.9 
 
 77 52 37.9 
 
 65 46 8.3 
 
 .9982815 
 
 .9453519 
 
 .6812156 
 
 
 
 1867 
 
 165 9 35.5 
 
 77 53 35.0 
 
 65 46 55.8 
 
 .9982809 
 
 .9453567 
 
 .6812022 
 
 
 
 1868 B 
 
 165 10 31.1 
 
 77 54 32.0 
 
 65 47 43.2 
 
 .9982803 
 
 .9453602 
 
 .6811927 
 
 
 
 1869 
 
 165 11 26.8 
 
 77 55 29.2 
 
 65 48 30.8 
 
 .9982797 
 
 .9453627 
 
 .6811868 
 
 
 
 1870 
 
 165 12 22.4 
 
 77 56 26.2 
 
 65 49 18.2 
 
 .9982791 
 
 .9453645 
 
 .6811832 
 
 
 
 1871 
 
 165 13 18.0 
 
 77 57 23.3 
 
 65 50 5.7 
 
 .9982785 
 
 .9453658 
 
 .6811817 
 
 
 
 1872 B 
 
 165 14 13.5 
 
 77 58 20.3 
 
 65 50 53.1 
 
 .9982778 
 
 .9453672 
 
 .6811798 
 
 
 
 1873 
 
 165 15 9.3 
 
 77 59 17.5 
 
 65 51 40.7 
 
 .9982771 
 
 .9453692 
 
 .6811765 
 
 
 
 1874 
 
 165 16 4.9 
 
 78 14.5 
 
 65 52 28.1 
 
 .9982763 
 
 .9453717 
 
 .6811709 
 
 
 
 1875 
 
 165 17 0.5 
 
 78 1 11.6 
 
 65 53 15.6 
 
 .9982756 
 
 .9453753 
 
 .6811620 
 
 
 
 1876S 
 
 165 17 56.0 
 
 78 2 8.6 
 
 65 54 3.0 
 
 .9982748 
 
 .9453799 
 
 .6811494 
 
 
 
 1877 
 
 165 18 51.8 
 
 78 3 5.8 
 
 65 54 50.6 
 
 .9982740 
 
 .9453858 
 
 .6811329 
 
 
 
 1878 
 
 165 19 47.4 
 
 78 4 2.8 
 
 65 55 38.1 
 
 .9982734 
 
 .9453927 
 
 .6811129 
 
 
 
 1879 
 
 165 20 43.0 
 
 78 4 59.9 
 
 65 56 25.5 
 
 .9982726 
 
 9454003 
 
 .6810902 
 
 
 
 1880B 
 
 165 21 38.6 
 
 78 5 56.9 
 
 65 57 13.0 
 
 .9982718 
 
 .9454087 
 
 .6810653 
 
 
 
 1881 
 
 165 22 34.3 
 
 78 6 54.1 
 
 65 58 0.6 
 
 .9982711 
 
 .9454171 
 
 .6810399 
 
 
 
 1882 
 
 165 23 29.9 
 
 78 7 51.1 
 
 65 58 48.1 
 
 .9982705 
 
 .9454253 
 
 .6810150 
 
 
 
 1883 
 
 165 24 25.5 
 
 78 8 48.1 
 
 65 59 35.5 
 
 .9982699 
 
 .9454329 
 
 .6809921 
 
 
 
 1884 B 
 
 165 25 21.1 
 
 78 9 45.2 
 
 66 23.0 
 
 .9982692 
 
 .9454396 
 
 .6809723 
 
 
 
 1885 
 
 165 26 16.8 
 
 78 10 42.4 
 
 66 1 10.6 
 
 .9982687 
 
 .9454451 
 
 .6809562 
 
 
 
 1886 
 
 165 27 12.4 
 
 78 11 39.4 
 
 66 1 58.0 
 
 .9982680 
 
 .9454494 
 
 .6809442 
 
 
 
 1887 
 
 165 28 8.0 
 
 78 12 36.4 
 
 66 2 45.5 
 
 .9982674 
 
 .9454525 
 
 .6809362 
 
 
 
 1888B 
 
 165 29 3.6 
 
 78 13 33.4 
 
 66 3 32.9 
 
 .9982668 
 
 .9454546 
 
 .6809313 
 
 
 
 1889 
 
 165 29 59.4 
 
 78 14 30.6 
 
 66 4 20.5 
 
 .9982662 
 
 .9454562 
 
 .6809289 
 
 
 
 1890 
 
 165 30 54.9 
 
 78 15 27.7 
 
 66 5 8.0 
 
 .9982656 
 
 .9454575 
 
 .6809270 
 
 
 
 1891 
 
 165 31 50.5 
 
 78 16 24.7 
 
 66 5 55.5 
 
 .9982649 
 
 .9454591 
 
 .6809248 
 
 
 
 1892 B 
 
 165 32 46.1 
 
 78 17 21.7 
 
 66 6 42.9 
 
 .9982641 
 
 .9454612 
 
 .6809207 
 
 
 
 1893 
 
 165 33 41.9 
 
 78 18 18.9 
 
 66 7 30.5 
 
 .9982633 
 
 .9454642 
 
 .6809139 
 
 
 
 1894 
 
 165 34 37.4 
 
 T8 19 15.9 
 
 66 8 18.0 
 
 .9982626 
 
 .9454683 
 
 .6809034 
 
 
 
 1895 
 
 165 35 33.0 
 
 78 20 .13.0 
 
 66 9 5.5 
 
 .9982619- 
 
 .9454733 
 
 .6808892 
 
 
 
 1896B 
 
 165 36 28.6 
 
 78 21 10.0 
 
 66 9 52.9 
 
 .9982611 
 
 .9454796 
 
 .6808713 
 
 
 
 1897 
 
 165 37 24.4 
 
 78 22 7.2 
 
 66 10 40.5 
 
 .9982603 
 
 .9454870 
 
 .6808499 
 
 
 
 1898 
 
 165 38 20.0 
 
 78 23 4.2 
 
 66 11 28.0 
 
 .9982595 
 
 .9454949 
 
 .6808262 
 
 
 
 1899 
 
 165 39 15.6 
 
 78 24 1.2 
 
 66 12 15.5 
 
 .9982588 
 
 .9455033 
 
 .6808012 
 
 
 
 1900 
 
 165 40 11.2 
 
 78 24 58.3 
 
 6.6 13 2.9 
 
 9.9982581 
 
 9.9455115 
 
 9.6807761 
 
 
 
12 
 
 TABLE VII. 
 
 
 
 
 
 Months. 
 
 C. B. 
 
 L n Q, 
 
 Hours. 
 
 L 
 
 Hours. 
 
 L 
 
 
 Jan. 
 
 
 
 o d o'.oo d'.oo d'.oo 
 
 1 
 
 6 10 13.86 
 
 13 
 
 O 1 II 
 
 2 13 0.13 
 
 
 
 Feb. 
 
 
 
 126 51 49.27 4.72 3.61 
 
 2 
 
 20 27.71 
 
 14 
 
 2 23 13.99 
 
 
 
 March 
 
 1 
 
 245 32 33.42 9.13 6.98 
 
 3 
 
 30 41.57 
 
 15 
 
 2 33 27.85 
 
 
 
 April 
 
 1 
 
 12 24 22.69 13.85 10.59 
 
 4 
 
 40 55.43 
 
 16 
 
 2 43 41.70 
 
 
 
 May 
 
 1 
 
 135 10 39.40 18.42 14.08 
 
 5 
 
 51 9.28 
 
 17 
 
 2 53 55.56 
 
 
 
 June 
 
 1 
 
 262 2 28.66 23.13 17.69 
 
 6 
 
 1 1 23.14 
 
 18 
 
 3 4 9.42 
 
 
 
 July 
 
 1 
 
 24 48 45.37 27.70 21.18 
 
 7 
 
 1 11 37.00 
 
 19 
 
 3 14 23.27 
 
 
 
 Aug. 
 
 1 
 
 151 40 34.64 32.42 24.79 
 
 8 
 
 1 21 50.85 
 
 20 
 
 3 24 37.13 
 
 
 
 Sept. 
 
 1 
 
 278 32 23.91 37.14 28.40 
 
 9 
 
 1 32 4.71 
 
 21 
 
 3 34 50.99 
 
 
 
 Oct. 
 
 1 
 
 41 18 40.62 41.70 31.89 
 
 10 
 
 1 42 18.56 
 
 22 
 
 3 45 4.84 
 
 
 
 Nov. 
 
 1 
 
 168 10 29.88 46.42 35.50 
 
 11 
 
 1 52 32.42 
 
 23 
 
 3 55 18.70 
 
 
 
 Dec. 
 
 1 
 
 290 56 46.59 50.99 38.99 
 
 12 
 
 2 2 46.28 
 
 24 
 
 4 5 32.56 
 
 
 
 Days. 
 
 L 
 
 7t 
 
 Q 
 
 Minutes, 
 
 L 
 
 L 
 
 Minutes, 
 
 L 
 
 L 
 
 
 
 
 
 
 Seconds. 
 
 
 
 Seconds. 
 
 
 
 
 
 i 
 
 O 1 (/ 
 
 4 5 32.56 
 
 0.15 
 
 ft 
 
 0.12 
 
 1 
 
 ld'.23 
 
 II 
 
 0.17 
 
 31 
 
 5 17.16 
 
 5'!29 
 
 
 
 2 
 
 8 11 5.11 
 
 0.30 
 
 0.23 
 
 2 
 
 20.46 
 
 0.34 
 
 32 
 
 5 27.39 
 
 5.46 
 
 
 
 3 
 
 12 
 
 16 37.67 
 
 0.46 
 
 0.35 
 
 3 
 
 30.69 
 
 0.51 
 
 33 
 
 5 37.62 
 
 5.63 
 
 
 
 4 
 
 16 
 
 22 10.23 
 
 0.61 
 
 0.47 
 
 4 
 
 40.92 
 
 0.68 
 
 34 
 
 5 47.85 
 
 5.80 
 
 
 
 5 
 
 20 
 
 27 42.78 
 
 0.76 
 
 0.58 
 
 5 
 
 51.15 
 
 0.85 
 
 35 
 
 5 58.08 
 
 5.97 
 
 
 
 6 
 
 24 
 
 33 15.34 
 
 0.91 
 
 0.70 
 
 6 
 
 1 1.39 
 
 1.02 
 
 36 
 
 6 8.31 
 
 6.14 
 
 
 
 7 
 
 28 
 
 38 47.90 
 
 1.07 
 
 0.81 
 
 7 
 
 1 11.62 
 
 1.19 
 
 37 
 
 6 18.54 
 
 6.31 
 
 
 
 8 
 
 32 
 
 44 20.46 
 
 1.22 
 
 0.93 
 
 8 
 
 1 21.85 
 
 1.36 
 
 38 
 
 6 28.78 
 
 6.48 
 
 
 
 9 
 
 36 
 
 49 53.01 
 
 1.37 
 
 1.05 
 
 9 
 
 1 32 08 
 
 1.53 
 
 39 
 
 6 39.01 
 
 6.65 
 
 
 
 10 
 
 40 55 25.57 
 
 1.52 
 
 1.16 
 
 10 
 
 1 42.31 
 
 1.70 
 
 40 
 
 6 49.24 
 
 6.82 
 
 
 
 11 
 
 45 
 
 58.^3 
 
 1.67 
 
 1.28 
 
 11 
 
 1 52.54 
 
 1.88 
 
 41 
 
 6 59.47 
 
 6.99 
 
 
 
 12 
 
 49 
 
 6 30.68 
 
 1.83 
 
 1.40 
 
 12 
 
 2 2.77 
 
 2.05 
 
 42 
 
 7 9.70 1 7.16 
 
 
 
 13 
 
 53 
 
 12 3.24 
 
 1.98 
 
 1.51 
 
 13 
 
 2 13.00 
 
 2.22 
 
 43 
 
 7 19.93 7.33 
 
 
 
 14 
 
 57 
 
 17 35.80 
 
 2.13 
 
 1.63 
 
 14 
 
 2 23.23 
 
 2.39 
 
 44 
 
 7 30.16 7.50 
 
 
 
 15 
 
 61 
 
 23 8.35 
 
 2.28 
 
 1.75 
 
 15 
 
 2 33.46 
 
 2.56 
 
 45 
 
 7 40.39 
 
 7.67 
 
 
 
 16 
 
 65 
 
 28 40.91 
 
 2.44 
 
 1.86 
 
 16 
 
 2 43.69 
 
 2.73 
 
 46 
 
 7 50.62 
 
 7.84 
 
 
 
 17 
 
 69 
 
 34 13.47 
 
 2.59 
 
 1.98 
 
 17 
 
 2 53.93 
 
 2.90 
 
 47 
 
 8 0.85 
 
 8.01 
 
 
 
 18 
 
 73 
 
 39 46.03 
 
 2.74 
 
 2.10 
 
 18 
 
 3 4.16 
 
 3.07 
 
 48 
 
 8 11.08 
 
 8.18 
 
 
 
 19 
 
 77 
 
 45 18.58 
 
 2.89 
 
 2.21 
 
 19 
 
 3 14.39 
 
 3.24 
 
 49 
 
 8 21.32 
 
 8.35 
 
 
 
 20 
 
 81 
 
 50 51.14 
 
 3.04 
 
 2.33 
 
 20 
 
 3 24.62 
 
 3.41 
 
 50 
 
 8 31.55 
 
 8.53 
 
 
 
 21 
 
 85 56 23.70 
 
 3.20 
 
 2.44 
 
 21 
 
 3 34.85 
 
 3.58 
 
 51 
 
 8 41.78 
 
 8.70 
 
 
 
 22 
 
 90 1 56.25 
 
 3.34 
 
 2.56 
 
 22 
 
 3 45.08 
 
 3.75 
 
 . 52 
 
 8 52.01 
 
 8.87 
 
 
 
 23 
 
 94 7 28.81 
 
 350 
 
 2.68 
 
 23 
 
 3 55.31 
 
 3.92 
 
 53 
 
 9 2.24 
 
 9.04 
 
 
 
 24 
 
 98 13 1.37 
 
 3.65 
 
 2.79 
 
 24 
 
 4 5.54 
 
 4.09 
 
 54 
 
 9 12.47 
 
 9.21 
 
 
 
 25 
 
 102 18 33.92 
 
 3.80 
 
 2.91 
 
 25 
 
 4 15.77 
 
 4.26 
 
 55 
 
 9 22.70 
 
 9.38 
 
 
 
 26 
 
 106 24 6.48 
 
 3.96 
 
 3.03 
 
 26 
 
 4 26.00 
 
 4.43 
 
 56 
 
 9 32.93 
 
 9.55 
 
 
 
 27 
 
 110 29 39.04 
 
 4.11 
 
 3.14 
 
 27 
 
 4 36.24 
 
 4.60 
 
 57 
 
 9 43.16 
 
 9.72 
 
 
 
 28 
 
 114 35 11.60 
 
 4.26 
 
 3.26 
 
 28 
 
 4 46.47 
 
 4.77 
 
 58 
 
 9 53.39 
 
 9.89 
 
 
 
 29 
 
 118 40 44.15 
 
 4.41 
 
 3.38 
 
 29 
 
 4 56.70 
 
 4.94 
 
 59 
 
 10 3.62 
 
 10.06 
 
 
 
 30 
 
 122 46 16.71 
 
 4.57 
 
 3.49 
 
 30 
 
 5 6.93 
 
 5.12 
 
 60 
 
 10 13.86 
 
 10.23 
 
 
 
 31 
 
 126 51 49.27 
 
 4.72 
 
 3.61 
 
 
 
 
 
 
 
 
 
 
TABLE VIII. 
 
 13 
 
 
 
 
 //! 
 
 d&K* 
 
 d^Ky 
 
 dq-Kz 
 
 H, 
 
 d<K* 
 
 rfjA'y 
 
 d^ 
 
 4 
 
 d^K^ 
 
 d^Ky 
 
 d^K,. 
 
 
 
 
 is'.oo 
 
 2l"03 
 
 2l".52 
 
 2400 
 
 32.02 
 
 33.88 
 
 21.28 
 
 4800 
 
 1.22 
 
 2.34 
 
 3.38 
 
 
 
 100 
 
 19.56 
 
 22.64 
 
 22.78 
 
 2500 
 
 31.00 
 
 32.75 
 
 26.19 
 
 4900 
 
 0.89 
 
 2.11 
 
 3.44 
 
 
 
 200 
 
 21.11 
 
 24.24 
 
 24.00 
 
 2600 
 
 29.87 
 
 31.53 
 
 25.03 
 
 5000 
 
 0.71 
 
 2.01 
 
 3.62 
 
 
 
 300 
 
 22.65 
 
 25.82 
 
 25.17 
 
 2700 
 
 28.63 
 
 30.17 
 
 23.82 
 
 5100 
 
 0.68 
 
 2.08 
 
 3.93 
 
 
 
 400 
 
 24.12 
 
 27.31 
 
 26.29 
 
 2800 
 
 27.29 
 
 28.72 
 
 22.53 
 
 5200 
 
 0.79 
 
 2.30 
 
 4.34 
 
 
 
 500 
 
 25.57 
 
 28.77 
 
 27.34 
 
 2900 
 
 25.87 
 
 27.20 
 
 21.20 
 
 5300 
 
 1.05 
 
 2.65 
 
 4.89 
 
 
 
 600 
 
 26.94 
 
 30.13 
 
 28.30 
 
 3000 
 
 24.38 
 
 25.61 
 
 19.86 
 
 5400 
 
 1.45 
 
 3.15 
 
 5.53 
 
 
 
 700 
 
 28.25 
 
 31.45 
 
 29.20 
 
 3100 
 
 22.83 
 
 23.98 
 
 18.49 
 
 5500 
 
 1.99 
 
 3.81 
 
 6.27 
 
 
 
 800 
 
 29.47 
 
 32.65 
 
 29.98 
 
 3200 
 
 21.24 
 
 22.31 
 
 17.12 
 
 5600 
 
 2.67 
 
 4.58 
 
 7.12 
 
 
 
 900 
 
 30.60 
 
 33.76 
 
 30.68 
 
 3300 
 
 19.62 
 
 20.62 
 
 15.75 
 
 5700 
 
 3.47 
 
 5.51 
 
 8.04 
 
 
 
 1000 
 
 31.63 
 
 34.74 
 
 31.26 
 
 3400 
 
 17.98 
 
 18.92 
 
 14.39 
 
 5800 
 
 4.39 
 
 6.54 
 
 9.07 
 
 
 
 1100 
 
 32.55 
 
 35.62 
 
 31.75 
 
 3500 
 
 16.35 
 
 17.23 
 
 13.09 
 
 5900 
 
 5.42 
 
 7.69 
 
 10.16 
 
 
 
 1200 
 
 33.35 
 
 36.37 
 
 32.12 
 
 3600 
 
 14.73 
 
 15.57 
 
 11.81 
 
 6000 
 
 6.56 
 
 8.93 
 
 11.30 
 
 
 
 1300 
 
 34.02 
 
 36.97 
 
 32.36 
 
 3700 
 
 13.14 
 
 13.95 
 
 10.59 
 
 6100 
 
 7.78 
 
 10.25 
 
 12.51 
 
 
 
 1400 
 
 34.56 
 
 37.44 
 
 32.50 
 
 3800 
 
 11.59 
 
 12.37 
 
 9.44 
 
 6200 
 
 9.09 
 
 11.65 
 
 1376 
 
 
 
 1500 
 
 34.96 
 
 37.76 
 
 32.52 
 
 3900 
 
 10.10 
 
 10.87 
 
 8.36 
 
 6300 
 
 10.47 
 
 13.13 
 
 15.03 
 
 
 
 1600 
 
 35.21 
 
 37.91 
 
 32.39 
 
 4000 
 
 8.68 
 
 9.45 
 
 7.36 
 
 6400 
 
 11.91 
 
 14.66 
 
 16.30 
 
 
 
 1700 
 
 35.32 
 
 37.94 
 
 32.15 
 
 4100 
 
 7.35 
 
 8.13 
 
 6.46 
 
 6500 
 
 13.40 
 
 16.24 
 
 17.64 
 
 
 
 1800 
 
 35.29 
 
 37.81 
 
 31.80 
 
 4200 
 
 6.11 
 
 6.93 
 
 5.69 
 
 6600 
 
 14.92 
 
 17.83 
 
 18.96 
 
 
 
 1900 
 
 35.10 
 
 37.52 
 
 31.32 
 
 4300 
 
 4.98 
 
 5.81 
 
 5.00 
 
 6700 
 
 16.47 
 
 19.45 
 
 20.26 
 
 
 
 2000 
 
 34.77 
 
 37.08 
 
 30.73 
 
 4400 
 
 3.96 
 
 4.84 
 
 4.43 
 
 6800 
 
 18.03 
 
 21.07 
 
 21.54 
 
 
 
 2100 
 
 34.29 
 
 36.50 
 
 30.01 
 
 4500 
 
 3.07 
 
 3.99 
 
 3.97 
 
 6900 
 
 19.59 
 
 22.68 
 
 22.81 
 
 
 
 2200 
 
 33.67 
 
 35.77 
 
 29.21 
 
 4600 
 
 2.32 
 
 3.30 
 
 3.67 
 
 7000 
 
 21.14 
 
 24.27 
 
 24.03 
 
 
 
 2300 
 
 32.91 
 
 34.89 
 
 28.29 
 
 4700 
 
 1.70 
 
 2.75 
 
 3.47 
 
 7100 
 
 22.66 
 
 25.82 
 
 25.19 
 
 
 
 2400 
 
 32.02 
 
 33.88 
 
 27.28 
 
 4800 
 
 1.22 
 
 2.34 
 
 3.38 
 
 7200 
 
 24.14 
 
 27.33 
 
 26.30 
 
 
 
 H, 
 
 d Q K f 
 
 d Q K y 
 
 dK z 
 
 d Q logk y 
 
 d Q logk z 
 
 H, 
 
 dQK^ 
 
 dQK,' 
 
 dQK, 
 
 (/QlOgfcy 
 
 </01ogfc z 
 
 
 
 
 
 2M 
 
 2.31 
 
 2.08 
 
 13 
 
 
 
 190 
 
 2.64 
 
 2.62 
 
 2.34 
 
 12 
 
 1 
 
 
 
 10 
 
 2.76 
 
 2.74 
 
 2.44 
 
 12 
 
 2 
 
 200 
 
 2.96 
 
 2.96 
 
 2.64 
 
 11 
 
 4 
 
 
 
 20 
 
 3.06 
 
 3.07 
 
 2.75 
 
 11 
 
 6 
 
 210 
 
 3.16 
 
 3.19 
 
 2.86 
 
 10 
 
 9 
 
 
 
 30 
 
 3.22 
 
 3.25 
 
 2.98 
 
 9 
 
 13 
 
 220 
 
 3.24 
 
 3.29 
 
 3.00 
 
 8 
 
 16 
 
 
 
 40 
 
 3.24 
 
 3.30 
 
 3.03 
 
 7 
 
 20 
 
 230 
 
 3.19 
 
 3.25 
 
 3.01 
 
 6 
 
 23 
 
 
 
 50 
 
 3.12 
 
 3.17 
 
 2.98 
 
 5 
 
 27 
 
 240 
 
 3.00 
 
 3.08 
 
 2.93 
 
 3 
 
 30 
 
 
 
 60 
 
 2.83 
 
 2.91 
 
 2.82 
 
 3 
 
 33 
 
 250 
 
 2.69 
 
 2.77 
 
 2.73 
 
 2 
 
 35 
 
 
 
 70 
 
 2.46 
 
 2.54 
 
 2.56 
 
 1 
 
 38 
 
 260 
 
 2.31 
 
 2.39 
 
 2.45 
 
 1 
 
 39 
 
 
 
 80 
 
 2.04 
 
 2.11 
 
 2.24 
 
 
 
 41 
 
 270 
 
 1.88 
 
 1.94 
 
 2.10 
 
 
 
 41 
 
 
 
 90 
 
 1.61 
 
 1.65 
 
 1.87 
 
 
 
 41 
 
 280 
 
 1.47 
 
 1.52 
 
 1.74 
 
 
 
 40 
 
 
 
 100 
 
 1.23 
 
 1.25 
 
 1.53 
 
 1 
 
 38 
 
 290 
 
 1.11 
 
 1.12 
 
 1.41 
 
 2 
 
 37 
 
 
 
 110 
 
 0.95 
 
 0.95 
 
 1,25 
 
 2 
 
 34 
 
 300 
 
 0.85 
 
 0.84 
 
 1.14 
 
 3 
 
 31 
 
 
 
 120 
 
 0.79 
 
 0.76 
 
 1.04 
 
 4 
 
 28 
 
 310 
 
 0.74 
 
 0.71 
 
 0.98 
 
 5 
 
 25 
 
 
 
 130 
 
 0.76 
 
 0.71 
 
 0.95 
 
 6 
 
 21 
 
 320 
 
 0.79 
 
 0.74 
 
 0.95 
 
 7 
 
 17 
 
 
 
 140 
 
 0.87 
 
 0.80 
 
 0.99 
 
 8 
 
 15 
 
 330 
 
 0.98 
 
 0.91 
 
 1.04 
 
 9 
 
 11 
 
 
 
 150 
 
 1.11 
 
 1.04 
 
 1.12 
 
 10 
 
 8 
 
 340 
 
 1.28 
 
 1.21 
 
 1.23 
 
 11 
 
 5 
 
 
 
 160 
 
 1.45 
 
 1.39 
 
 1.36 
 
 11 
 
 3 
 
 350 
 
 1.67 
 
 1.61 
 
 1.52 
 
 12 
 
 1 
 
 
 
 170 
 
 '.85 
 
 1.79 
 
 1.66 
 
 12 
 
 
 
 360 
 
 2.13 2.08 
 
 1.89 
 
 12 
 
 
 
 
 
 180 
 
 2.26 
 
 2.21 
 
 2.00 
 
 13 
 
 
 
 370 
 
 2.56 2.53 
 
 2.28 
 
 12 
 
 
 
 
 
14 
 
 TABLE IX. 
 
 
 
 
 A 
 
 .0 
 
 .1 
 
 .2 
 
 .3 
 
 .4 
 
 Log 
 SK. Tar. 
 
 LogDiff. 
 
 LogDiff. 
 
 Log 1 'ill . 
 
 Log Diff. 
 
 LogDiff. 
 
 V 
 
 Logr 
 
 V 
 
 i/ogr 
 
 V 
 
 Logr 
 
 V 
 
 Logr 
 
 V 
 
 Logr 
 
 V 
 
 
 o 
 
 9.0578 
 
 
 9.0578 
 
 7.3522 
 
 9.0578 
 
 7.6589 
 
 9.0578 
 
 7.8357 
 
 9.0578 
 
 7.9591 
 
 
 
 
 1 
 
 9.0576 
 
 8.3561 
 
 9.0575 
 
 8.3971 
 
 9.0575 
 
 8.4354 
 
 9.0574 
 
 8.4698 
 
 9.0574 
 
 8.5018 
 
 7.1299 
 
 
 
 2 
 
 9.0569 
 
 8.6556 
 
 9.0568 
 
 8.6767 
 
 9.0567 
 
 8.6968 
 
 9.0566 
 
 8.7160 
 
 9.0565 
 
 8.7340 
 
 7.4231 
 
 
 
 3 
 
 9.0558 
 
 8.8300 
 
 9.0556 
 
 8.8439 
 
 9.0555 
 
 8.8574 
 
 9.0553 
 
 8.8701 
 
 9.0552 
 
 8.8828 
 
 7.5965 
 
 
 
 4 
 
 9.0542 
 
 8.9518 
 
 9.0540 
 
 8.9622 
 
 9.0538 
 
 8.9725 
 
 9.0536 
 
 8.9823 
 
 9.0534 
 
 8.9917 
 
 7.7182 
 
 
 
 5 
 
 9.0522 
 
 9.0453 
 
 9.0519 
 
 9.0533 
 
 9.0517 
 
 9.0613 
 
 9.0514 
 
 9.0691 
 
 9.0512 
 
 9.0768 
 
 7.8131 
 
 
 
 6 
 
 9.0497 
 
 9.1198 
 
 9.0494 
 
 9.1266 
 
 9.0491 
 
 9.1331 
 
 9.0489 
 
 9.1394 
 
 9.0486 
 
 9.1460 
 
 7.8896 
 
 
 
 7 
 
 9.0469 
 
 9.1816 
 
 9.0466 
 
 9.1873 
 
 9.0463 
 
 9.1927 
 
 9.0459 
 
 9.1981 
 
 9.0456 
 
 9.2035 
 
 7.9522 
 
 
 
 8 
 
 9.0437 
 
 9.2337 
 
 9.0433 
 
 9.2384 
 
 9.0430 
 
 9.2429 
 
 9.0426 
 
 9.2475 
 
 9.0423 
 
 9.2521 
 
 8.0039 
 
 
 
 9 
 
 9.0401 
 
 9.2781 
 
 9.0397 
 
 9.2822 
 
 9.0393 
 
 9.2863 
 
 9.0389 
 
 9.2903 
 
 9.0385 
 
 9.2942 
 
 8.0491 
 
 
 
 10 
 
 9.0361 
 
 9.3166 
 
 9.0357 
 
 9.3201 
 
 9.0352 
 
 9.3236 
 
 9.0348 
 
 9.3270 
 
 9.0344 
 
 9.3303 
 
 8.0884 
 
 
 
 11 
 
 9.0318 
 
 9.3499 
 
 9.0313 
 
 9.3529 
 
 9.0309 
 
 9.3560 
 
 9.0304 
 
 9.3590 
 
 9.0299 
 
 9.3619 
 
 8.1236 
 
 
 
 12 
 
 9.0271 
 
 9.3789 
 
 9.0266 
 
 9.3816 
 
 9.0261 
 
 9.3843 
 
 9.0256 
 
 9.3870 
 
 9.0251 
 
 9.3897 
 
 8.1540 
 
 
 
 13 
 
 9.0222 
 
 9.4043 
 
 9.0217 
 
 9.4067 
 
 9.0212 
 
 9.4090 
 
 9.0206 
 
 9.4113 
 
 9.0201 
 
 9.4136 
 
 8.1810 
 
 
 
 14 
 
 9.0170 
 
 9.4266 
 
 9.0164 
 
 9.4286 
 
 9.0159 
 
 9.4307 
 
 9.0153 
 
 9.4327 
 
 9.0148 
 
 9.4347 
 
 8.2045 
 
 
 
 15 
 
 9.0115 
 
 9.4460 
 
 9.0109 
 
 9.4478 
 
 9.0104 
 
 9.4497 
 
 9.0098 
 
 9.4514 
 
 9.0092 
 
 9.4530 
 
 8.2256 
 
 
 
 16 
 
 9.0058 
 
 9.4630 
 
 9.0052 
 
 9.4646 
 
 9.0046 
 
 9.4662 
 
 9.0040 
 
 9.4676 
 
 9.0034 
 
 9.4692 
 
 8.2438 
 
 
 
 17 
 
 8.9999 
 
 9.4778 
 
 8.9993 
 
 9.4791 
 
 8.9987 
 
 9.4805 
 
 8.9981 
 
 9.4818 
 
 8.9975 
 
 9.4831 
 
 8.2596 
 
 
 
 18 
 
 8.9938 
 
 9.4905 
 
 8.9932 
 
 9.4917 
 
 8.9926 
 
 9.4928 
 
 8.9919 
 
 9.4940 
 
 8.9913 
 
 9.4951 
 
 8.2738 
 
 
 
 19 
 
 8.9876 
 
 9.5015 
 
 8.9869 
 
 9.5025 
 
 8.9863 
 
 9.5035 
 
 8.9856 
 
 9.5045 
 
 8.9850 
 
 9.5054 
 
 8.2864 
 
 
 
 20 
 
 8.9811 
 
 9.5108 
 
 8.9804 
 
 9.5116 
 
 8.9798 
 
 9.5125 
 
 8.9791 
 
 9.5133 
 
 8.9785 
 
 9.5141 
 
 8.2971 
 
 
 
 21 
 
 8.9746 
 
 9.5186 
 
 8.9739 
 
 9.5193 
 
 8.9733 
 
 9.5200 
 
 8.9726 
 
 9.5207 
 
 8.9720 
 
 9.5214 
 
 83065 
 
 
 
 22 
 
 8.9680 
 
 9.5251 
 
 8.9673 
 
 9.5257 
 
 8.9666 
 
 9.5262 
 
 8.9660 
 
 9.5268 
 
 8.9653 
 
 9.5273 
 
 8.3142 
 
 
 
 23 
 
 8.9612 
 
 9.5303 
 
 8.9605 
 
 9.5308 
 
 8.9598 
 
 9.5312 
 
 8.9592 
 
 9.5316 
 
 8.9585 
 
 9.5320 
 
 8.3207 
 
 
 
 24 
 
 8.9544 
 
 9.5343 
 
 8.9537 
 
 9.5346 
 
 8.9530 
 
 9.5350 
 
 8.9523 
 
 9.5353 
 
 8.9516 
 
 9.5356 
 
 8.3262 
 
 
 
 25 
 
 8.9475 
 
 9.5372 
 
 8.9468 
 
 9.5374 
 
 8.9461 
 
 9.5377 
 
 8.9454 
 
 9.5379 
 
 8.9447 
 
 9.5381 
 
 8.3311 
 
 
 
 26 
 
 8.9406 
 
 9.5392 
 
 8.9399 
 
 9.5398 
 
 8.9392 
 
 9.5395 
 
 8.9385 
 
 9.5396 
 
 8.9378 
 
 9.5397 
 
 8.3345 
 
 
 
 27 
 
 8.9337 
 
 9.5402 
 
 8.9830 
 
 9.5403 
 
 8.9323 
 
 9.5403 
 
 8.9316 
 
 9.5403 
 
 8.9309 
 
 9.5404 
 
 8.3374 
 
 
 
 28 
 
 8.9268 
 
 9.5404 
 
 8.9261 
 
 9.5404 
 
 8.9255 
 
 9.5403 
 
 8.9247 
 
 9.5403 
 
 8.9240 
 
 9.5402 
 
 8.3393 
 
 
 
 29 
 
 8.9198 
 
 9.5397 
 
 8.9191 
 
 9.5396 
 
 8.9184 
 
 9.5395 
 
 8.9177 
 
 9.5394 
 
 8.9170 
 
 9.5392 
 
 8.3403 
 
 
 
 30 
 
 8.9129 
 
 9.5384 
 
 8.9122 
 
 9.5382 
 
 8.9115 
 
 9.5380 
 
 8.9108 
 
 9.5379 
 
 8.9101 
 
 9.5377 
 
 8.3403 
 
 
 
 31 
 
 8.9060 
 
 9.5363 
 
 8.9053 
 
 9.5361 
 
 8.9046 
 
 9.5358 
 
 8.9039 
 
 9.5355 
 
 8.9032 
 
 9.5353 
 
 8.3408 
 
 
 
 32 
 
 8.8991 
 
 9.5335 
 
 8.8984 
 
 9.5332 
 
 8.8977 
 
 9.5328 
 
 8.8971 
 
 9.5325 
 
 8.8964 
 
 9.5322 
 
 8.3388 
 
 
 
 33 
 
 8.8923 
 
 9.5302 
 
 8.8916 
 
 9.5298 
 
 8.8910 
 
 9.5294 
 
 8.8903 
 
 9.5290 
 
 8.8896 
 
 9.5286 
 
 8.3374 
 
 
 
 34 
 
 8.8856 
 
 9.5262 
 
 8.8849 
 
 9.5257 
 
 8.8843 
 
 9.5253 
 
 8.8836 
 
 9.5248 
 
 8.8829 
 
 9.5244 
 
 8.3355 
 
 
 
 35 
 
 8.8789 
 
 9.5217 
 
 8.8782 
 
 9.5212 
 
 8.8776 
 
 9.5207 
 
 8.8769 
 
 9.5202 
 
 8.8763 
 
 9.5197 
 
 8.3325 
 
 
 
 36 
 
 8.8723 
 
 9.5167 
 
 8.8716 
 
 9.5161 
 
 8.8710 
 
 9.5156 
 
 8.8703 
 
 9.5150 
 
 8.8697 
 
 9.5145 
 
 8.3291 
 
 
 
 37 
 
 8.8658 
 
 9.5111 
 
 8.8651 
 
 9.5105 
 
 8.8645 
 
 9.5099 
 
 8.8638 
 
 9.5093 
 
 8.8632 
 
 9.5087 
 
 8.3252 
 
 
 
 38 
 
 8.8593 
 
 9.5051 
 
 8.8587 
 
 9.5044 
 
 8.8580 
 
 9.5038 
 
 8.8574 
 
 9.5031 
 
 8.8568 
 
 9.5025 
 
 8.3207 
 
 
 
 39 
 
 8.8530 
 
 9.4986 
 
 8.8524 
 
 9.4979 
 
 8.8517 
 
 9.4972 
 
 8.8511 
 
 9.4965 
 
 8.8505 
 
 9.4958 
 
 8.3162 
 
 
 
 40 
 
 8.8467 
 
 9.4916 
 
 8,8461 
 
 9.4909 
 
 8.8455 
 
 9.4901 
 
 8.8449 
 
 9.4894 
 
 8.8443 
 
 9.4886 
 
 8.3111 
 
 
 
 41 
 
 8.8406 
 
 9.4842 
 
 8.8400 
 
 9.4834 
 
 8.8394 
 
 9.4826 
 
 8.8388 
 
 9.4819 
 
 8.8382 
 
 9.4811 
 
 8.3055 
 
 
 
 42 
 
 8.8345 
 
 9.4764 
 
 8.8339 
 
 9.4756 
 
 8.8333 
 
 9.4748 
 
 8.8327 
 
 9.4739 
 
 8.8321 
 
 9.4732 
 
 8.2992 
 
 
 
 43 
 
 8.8286 
 
 9.4682 
 
 8.8280 
 
 9.4673 
 
 8.8274 
 
 9.4665 
 
 8.8269 
 
 9.4656 
 
 8.8263 
 
 9.4648 
 
 8.2923 
 
 
 
 44 
 
 8.8228 
 
 9.4596 
 
 8.8222 
 
 9.4587 
 
 8.8217 
 
 9.4578 
 
 8.8211 
 
 9.4569 
 
 8.8205 
 
 9.4560 
 
 8.2853 
 
 
 
 45 
 
 8.8171 
 
 9.4506 
 
 8.8165 
 
 9.4497 
 
 8.8160 
 
 9.4487 
 
 8.8154 
 
 9.4478 
 
 8.8149 
 
 9.4468 
 
 8.2777 
 
 
 
 46 
 
 8.8115 
 
 9.4412 
 
 8.8109 
 
 9.4402 
 
 8.8104 
 
 9.4392 
 
 8.8098 
 
 9.4383 
 
 8.8093 
 
 9.4373 
 
 8.2699 
 
 
 
 47 
 
 8.8060 
 
 9.4314 
 
 8.8055 
 
 9.4304 
 
 8.8049 
 
 9.4294 
 
 8.8044 
 
 9.4283 
 
 8.8039 
 
 9.4273 
 
 8.2619 
 
 
 
 48 
 
 8.8007 
 
 9.4212 
 
 8.8002 
 
 9.4201 
 
 8.7997 
 
 9.4191 
 
 8.7991 
 
 9.4180 
 
 8.7986 
 
 9.4170 
 
 8.2533 
 
 
 
 49 
 
 8.7955 
 
 9.4107 
 
 8.7950 
 
 9.4096 
 
 8.7945 
 
 9.4085 
 
 8.7940 
 
 9.4074 
 
 8.7935 
 
 9.4063 
 
 82444 
 
 
 
 50 
 
 8.7904 
 
 9.3997 
 
 8.7899 
 
 9.3986 
 
 8.7894 
 
 9.3974 
 
 8.7889 
 
 9.3963 
 
 8.7884 
 
 9.3951 
 
 8.2342 
 
 
 
 51 
 
 8.7854 
 
 9.3883 
 
 8.7849 
 
 9.3871 
 
 8.7844 
 
 9.3860 
 
 8.7840 
 
 9.3848 
 
 8.7835 
 
 9.3836 
 
 8.2237 
 
 
 
 52 
 
 8.7806 
 
 9.3766 
 
 8.7801 
 
 9.3753 
 
 8.7797 
 
 9.3742 
 
 8.7792 
 
 9.3729 
 
 8.7787 
 
 9.3717 
 
 8.2136 
 
 
 
 53 
 
 8.7759 
 
 9.3644 
 
 8.7754 
 
 9.3631 
 
 8.7750 
 
 9.3619 
 
 8.7745 
 
 9.3606 
 
 8.7741 
 
 9.3594 
 
 8.2032 
 
 
 
 54 
 
 8.7713 
 
 9.3518 
 
 8.7709 
 
 9.3505 
 
 8.7704 
 
 9.3492 
 
 8.7700 
 
 9.3479 
 
 8.7695 
 
 9.3466 
 
 8.1919 
 
 
 
 55 
 
 8.7669 
 
 9.3388 
 
 8.7665 
 
 9.3374 
 
 8.7660 
 
 9.3361 
 
 8.7656 
 
 9.3347 
 
 8.7652 
 
 9.3334 
 
 8.1803 
 
 
 
 56 
 
 8.7626 
 
 9.3253 
 
 8.7622 
 
 9.3239 
 
 8.7618 
 
 9.3225 
 
 8.7613 
 
 9.3211 
 
 8.7609 
 
 9.3198 
 
 8.1677 
 
 
 
 57 
 
 8.7584 
 
 9.3114 
 
 8.7580 
 
 9.3100 
 
 8.7576 
 
 9.3085 
 
 8.7572 
 
 9.3071 
 
 8.7568 
 
 9.3057 
 
 8.1540 
 
 
 
 58 
 
 8.7544 
 
 9.2969 
 
 8.7540 
 
 9.2954 
 
 8.7536 
 
 9.2939 
 
 8.7532 
 
 9.2924 
 
 8.7528 
 
 9.2909 
 
 8.1406 
 
 
 
 59 
 
 8.7505 
 
 9.2819 
 
 8.7501 
 
 9.2804 
 
 8.7498 
 
 9.2788 
 
 8.7494 
 
 9.2773 
 
 8.7490 
 
 9.2758 
 
 8.1268 
 
 
 
 60 
 
 8.7468 
 
 9.2664 
 
 8.7464 
 
 9.2648 
 
 8.7461 
 
 9.2632 
 
 8.7457 
 
 9.2616 
 
 8.7453 
 
 9.2600 
 
 8.1125 
 
 
 
TABLE IX. 
 
 15 
 
 
 
 
 A 
 
 .5 
 
 .6 
 
 .7 
 
 .8 
 
 .9 
 
 Log 
 Sec. Tar. 
 
 LogDiff. 
 
 LogDiff. 
 
 'Log Diff. 
 
 Log Diff. 
 
 LogDiff. 
 
 V 
 
 Logr 
 
 V 
 
 Logr 
 
 V 
 
 Logr 
 
 V 
 
 Logr 
 
 V 
 
 Logr 
 
 Log r 
 
 
 
 
 9.0577 
 
 8.0550 
 
 9.0577 
 
 8.1336 
 
 9.0577 
 
 8.2001 
 
 9.0577 
 
 8.2589 
 
 9.0576 
 
 8.3107 
 
 9.4294n 
 
 
 
 i 
 
 9.0573 
 
 8.5315 
 
 9.0572 
 
 8.5593 
 
 9.0572 
 
 8.5860 
 
 9.0571 
 
 8.6107 
 
 9.0570 
 
 8.6335 
 
 9.4286 
 
 
 
 2 
 
 9.0564 
 
 8.7555 
 
 9.0562 
 
 8.7687 
 
 9.0561 
 
 8.7847 
 
 9.0560 
 
 8.8001 
 
 9.0559 
 
 8.8153 
 
 9.4266 
 
 
 
 3 
 
 9.0550 
 
 8.8954 
 
 9.0548 
 
 8.9074 
 
 9.0547 
 
 8.9188 
 
 9.0545 
 
 8.9302 
 
 9.0543 
 
 8.9413 
 
 9.4235 
 
 
 
 4 
 
 9.0532 
 
 9.0012 
 
 9.0530 
 
 9.0105 
 
 9.0528 
 
 9.0193 
 
 9.0526 
 
 9.0280 
 
 9.0524 
 
 9.0367 
 
 9.4187 
 
 
 
 5 
 
 9.0509 
 
 9.0844 
 
 9.0507 
 
 9.0917 
 
 9.0504 
 
 9.0990 
 
 9.0502 
 
 9.1062 
 
 9.0499 
 
 9.1130 
 
 9.4123 
 
 
 
 6 
 
 9.0483 
 
 9.1522 
 
 9.0480 
 
 9.1582 
 
 9.0477 
 
 9.1642 
 
 9.0475 
 
 9.1701 
 
 9.0472 
 
 9.1760 
 
 9.4041 
 
 
 
 7 
 
 9.0453 
 
 9.2086 
 
 9.0450 
 
 9.2138 
 
 9.0447 
 
 9.2190 
 
 9.0443 
 
 9.2239 
 
 9.0440 
 
 9.2288 
 
 9.3950 
 
 
 
 8 
 
 9.0420 
 
 9.2567 
 
 9.0416 
 
 9.2612 
 
 9.0412 
 
 9.2656 
 
 9.0409 
 
 9.2698 
 
 9.0405 
 
 9.2740 
 
 9.3847 
 
 
 
 9 
 
 9.0381 
 
 9.2980 
 
 9.0377 
 
 9.3018 
 
 9.0373 
 
 9.3055 
 
 9.0369 
 
 9.3091 
 
 9.0365 
 
 9.3129 
 
 9.3734 
 
 
 
 10 
 
 9.0339 
 
 9.3338 
 
 9.0335 
 
 9.3371 
 
 9.0331 
 
 9.3404 
 
 9.0327 
 
 9.3434 
 
 9.0322 
 
 9.3467 
 
 9.3603 
 
 
 
 11 
 
 9.0294 
 
 9.3649 
 
 9.0290 
 
 9.3678 
 
 9.0285 
 
 9.3706 
 
 9.0280 
 
 9.3735 
 
 9.0276 
 
 9.3762 
 
 9.3455 
 
 
 
 12 
 
 9.0246 
 
 9.3922 
 
 9.0242 
 
 9.3946 
 
 9.0237 
 
 9.3970 
 
 9.0232 
 
 9.3994 
 
 9.0227 
 
 9.4019 
 
 9.8291 
 
 
 
 13 
 
 9.0196 
 
 9.4158 
 
 9.0191 
 
 9.4181 
 
 9.0186 
 
 9.4202 
 
 9.0180 
 
 9.4224 
 
 9.0175 
 
 9.4245 
 
 9.3111 
 
 
 
 14 
 
 9.0142 
 
 9.4367 
 
 9.0137 
 
 9.4386 
 
 9.0131 
 
 9.4405 
 
 9.0126 
 
 9.4423 
 
 9.0120 
 
 9.4442 
 
 9.2913 
 
 
 
 15 
 
 9.0086 
 
 9.4548 
 
 9.0081 
 
 9.4565 
 
 9.0075 
 
 9.4581 
 
 9.0069 
 
 9.4597 
 
 9.0064 
 
 9.4614 
 
 9.2699 
 
 
 
 16 
 
 9.0028 
 
 9.4707 
 
 9.0023 
 
 9.4720 
 
 9.0017 
 
 9.4735 
 
 9.0011 
 
 9.4750 
 
 9.0005 
 
 9.4764 
 
 ' 9.2462 
 
 
 
 17 
 
 8.9968 
 
 9.4843 
 
 8.9962 
 
 9.4856 
 
 8.9956 
 
 9.4869 
 
 8.9950 
 
 9.4881 
 
 8.9944 
 
 9.4893 
 
 9.2205 
 
 
 
 18 
 
 8.9907 
 
 9.4962 
 
 8.9901 
 
 9.4973 
 
 8.9895 
 
 9.4984 
 
 8.9888 
 
 9.4994 
 
 8.9882 
 
 9.5005 
 
 9.1926 
 
 
 
 19 
 
 8.9843 
 
 9.5064 
 
 8.9837 
 
 9.5073 
 
 8.9830 
 
 9.5082 
 
 8.9824 
 
 9.5091 
 
 8.9817 
 
 9.5099 
 
 9.1620 
 
 
 
 20 
 
 8.9778 
 
 9.5149 
 
 8.9772 
 
 9.5157 
 
 8.9765 
 
 9.5164 
 
 8.9759 
 
 9.5172 
 
 8.9752 
 
 9.5179 
 
 9.1291 
 
 
 
 21 
 
 8.9713 
 
 9.5220 
 
 8.9706 
 
 9.5227 
 
 8.9700 
 
 9.5233 
 
 8.9693 
 
 9.5239 
 
 8.9687 
 
 9.5245 
 
 9.0927 
 
 
 
 22 
 
 8.9646 
 
 9.5279 
 
 8.9639 
 
 9.5284 
 
 8.9632 
 
 9.5289 
 
 8.9626 
 
 9.5294 
 
 8.9619 
 
 9.5298 
 
 9.0519 
 
 
 
 23 
 
 8.9578 
 
 9.5324 
 
 8.9571 
 
 9.5328 
 
 8.9564 
 
 9.5332 
 
 8.9558 
 
 9.5336 
 
 8.9551 
 
 9.5340 
 
 9.0070 
 
 
 
 24 
 
 8.9510 
 
 9.5359 
 
 8.9503 
 
 9.5362 
 
 8.9496 
 
 9.5364 
 
 8.9489 
 
 9.5367 
 
 8.9482 
 
 9.5370 
 
 8.9569 
 
 
 
 25 
 
 8.9440 
 
 9.5383 
 
 8.9434 
 
 9.5385 
 
 8.9427 
 
 9.5387 
 
 8.9420 
 
 9.5389 
 
 8.9413 
 
 9.5390 
 
 8.9015 
 
 
 
 26 
 
 8.9372 
 
 9.5398 
 
 8.9365 
 
 9.5399 
 
 8.9358 
 
 9.5400 
 
 8.9351 
 
 9.5401 
 
 8.9344 
 
 9.5401 
 
 8.8396 
 
 
 
 27 
 
 8.9302 
 
 9.5404 
 
 8.9296 
 
 9.5404 
 
 8.9289 
 
 9.5404 
 
 8.9282 
 
 9.5404 
 
 8.9275 
 
 9.5404 
 
 8.7691 
 
 
 
 28 
 
 8.9233 
 
 9.5402 
 
 8.9226 
 
 9.5401 
 
 8.9219 
 
 9.5400 
 
 8.9212 
 
 9.5399 
 
 8.9205 
 
 9.5398 
 
 8.6849 
 
 
 
 29 
 
 8.9163 
 
 9.5391 
 
 8.9157 
 
 9.5390 
 
 8.9150 
 
 9.5388 
 
 8.9143 
 
 9.5387 
 
 8.9136 
 
 9.5385 
 
 8.5804 
 
 
 
 30 
 
 8.9094 
 
 9.5375 
 
 8.9088 
 
 9.5372 
 
 8.9081 
 
 9.5370 
 
 8.9074 
 
 9.5368 
 
 8.9067 
 
 9.5365 
 
 8.4462 
 
 
 
 31 
 
 8.9025. 
 
 9.5350 
 
 8.9019 
 
 9.5347 
 
 8.9012 
 
 9.5344 
 
 8.9005 
 
 9.5341 
 
 8.8998 
 
 9.5338 
 
 8.2568 
 
 
 
 32 
 
 8.8957 
 
 9.5318 
 
 8.8950 
 
 9.5315 
 
 8.8943 
 
 9.5312 
 
 8.8937 
 
 9.5309 
 
 8.8930 
 
 9.5305 
 
 7.9132n 
 
 
 
 33 
 
 8.8889 
 
 9.5282 
 
 8.8883 
 
 9.5278 
 
 8.8876 
 
 9.5274 
 
 8.8869 
 
 9.5270 
 
 8.8863 
 
 9.5266 
 
 7.0807+ 
 
 
 
 34 
 
 8.8823 
 
 9.5239 
 
 8.8816 
 
 9.5235 
 
 8.8809 
 
 9.5230 
 
 8.8802 
 
 9.5226 
 
 8.8796 
 
 9.5221 
 
 8.0152 
 
 
 
 35 
 
 8.8756 
 
 9.5192 
 
 8.8749 
 
 9.5187 
 
 8.8743 
 
 9.5182 
 
 8.8736 
 
 9.5177 
 
 8.8730 
 
 9.5172 
 
 8.2793 
 
 
 
 36 
 
 8.8690 
 
 9.5139 
 
 8.8684 
 
 9.5133 
 
 8.8677 
 
 9.5128 
 
 8.8671 
 
 9.5122 
 
 8.8664 
 
 9.5117 
 
 8.4386 
 
 
 
 37 
 
 8.8625 
 
 9.5081 
 
 8.8619 
 
 9.5075 
 
 8.8612 
 
 9.5069 
 
 8.8606 
 
 9.5063 
 
 8.8599 
 
 9.5057 
 
 8.5520 
 
 
 
 38 
 
 8.8561 
 
 9.5018 
 
 8.8555 
 
 9.5012 
 
 8.8549 
 
 9.5005 
 
 8.8543 
 
 9.4999 
 
 8.8536 
 
 9.4992 
 
 8.6394 
 
 
 
 39 
 
 8.8498 
 
 9.4951 
 
 8.8492 
 
 9.4944 
 
 8.8486 
 
 9.4937 
 
 8.8480 
 
 9.4930 
 
 8.8473 
 
 9.4923 
 
 8.7101 
 
 
 
 40 
 
 8.8436 
 
 9.4879 
 
 8.8430 
 
 9.4872 
 
 8.8424 
 
 9.4865 
 
 8.8418 
 
 9.4857 
 
 8.8412 
 
 9.4849 
 
 8.7709 
 
 
 
 41 
 
 8.8375 
 
 9.4803 
 
 8.8369 
 
 9.4795 
 
 8.8363 
 
 9.4787 
 
 8.8357 
 
 9.4780 
 
 8.8351 
 
 9.4772 
 
 8.8210 
 
 
 
 42 
 
 8.8315 
 
 9.4723 
 
 8.8310 
 
 9.4715 
 
 8.8304 
 
 9.4707 
 
 8.8298 
 
 9.4698 
 
 8.8292 
 
 9.4690 
 
 8.8646 
 
 
 
 43 
 
 8.8257 
 
 9.4639 
 
 8.8251 
 
 9.4630 
 
 8.8245 
 
 9.4622 
 
 8.8240 
 
 9.4613 
 
 8.8234 
 
 9.4605 
 
 8.9015 
 
 
 
 44 
 
 8.8199 
 
 9.4551 
 
 8.8194 
 
 9.4542 
 
 8.8188 
 
 9.4533 
 
 8.8182 
 
 9.4524 
 
 8.8177 
 
 9.4515 
 
 8.9331 
 
 
 
 45 
 
 8.8143 
 
 9.4459 
 
 8.8137 
 
 9.4450 
 
 8.8132 
 
 9.4440 
 
 8.8126 
 
 9.4431 
 
 8.8121 
 
 9.4421 
 
 8.9615 
 
 
 
 46 
 
 8.8087 
 
 9.4363 
 
 8.8082 
 
 9.4353 
 
 8.8076 
 
 9.4343 
 
 8.8071 
 
 9.4334 
 
 8.8065 
 
 9.4324 
 
 8.9870 
 
 
 
 47 
 
 8.8033 
 
 9.4263 
 
 8.8028 
 
 9.4253 
 
 8.8023 
 
 9.4243 
 
 8.8018 
 
 9.4232 
 
 8.8012 
 
 9.4222 
 
 9.0101 
 
 
 
 48 
 
 8.7981 
 
 9.4159 
 
 8.7976 
 
 9.4149 
 
 8.7971 
 
 9.4138 
 
 8.7965 
 
 9.4128 
 
 8.7960 
 
 9.4117 
 
 9.0320 
 
 
 
 49 
 
 8.7929 
 
 9.4052 
 
 8.7924 
 
 9.4041 
 
 8.7919 
 
 9.4030 
 
 8.7914 
 
 9.4019 
 
 8.7909 
 
 9.4008 
 
 9.0519 
 
 
 
 50 
 
 8.7879 
 
 9.3940 
 
 8.7874 
 
 9.3929 
 
 8.7869 
 
 9.3917 
 
 8.7864 
 
 9.3906 
 
 8.7859 
 
 9.3894 
 
 9.0692 
 
 
 
 51 
 
 8.7830 
 
 9.3824 
 
 8.7825 
 
 9.3813 
 
 8.7820 
 
 9.3801 
 
 8.7816 
 
 9.3789 
 
 8.7811 
 
 9.3778 
 
 9.0850 
 
 
 
 S2 
 
 8.7782 
 
 9.3705 
 
 8.7778 
 
 9.3693 
 
 8.7773 
 
 9.3681 
 
 8.7768 
 
 9.3668 
 
 8.7764 
 
 9.3656 
 
 9.0991 
 
 
 
 53 
 
 8.7736 
 
 9.3581 
 
 8.7731 
 
 9.3568 
 
 8.7727 
 
 9.3556 
 
 8.7722 
 
 9.3543 
 
 8.7718 
 
 9.3531 
 
 9.1125 
 
 
 
 54 
 
 8.7691 
 
 9.3453 
 
 8.7687 
 
 9.3440 
 
 8.7682 
 
 9.3427 
 
 8.7678 
 
 9.3414 
 
 8.7673 
 
 9.3401 
 
 9.1244 
 
 
 
 55 
 
 8.7647 
 
 9.3320 
 
 8.7643 
 
 9.3307 
 
 8.7639 
 
 9.3293 
 
 8.7635 
 
 9.3280 
 
 8.7630 
 
 9.3266 
 
 9.1360 
 
 
 
 56 
 
 8.7605 
 
 9.3184 
 
 8.7601 
 
 9.3170 
 
 8.7597 
 
 9.3156 
 
 8.7592 
 
 9.3142 
 
 8.7588 
 
 9.3128 
 
 9.1459 
 
 
 
 57 
 
 8.7564 
 
 9.3042 
 
 8.7560 
 
 9.3028 
 
 8.7556 
 
 9.3013 
 
 8.7552 
 
 9.2998 
 
 8.7548 
 
 9.2984 
 
 9.1555 
 
 
 
 58 
 
 8.7524 
 
 9.2894 
 
 8.7521 
 
 9.2879 
 
 8.7517 
 
 9.2864 
 
 8.7513 
 
 9.2849 
 
 8.7509 
 
 9.2834 
 
 9.1649 
 
 
 
 59 
 
 8.7486 
 
 9.2742 
 
 8.7483 
 
 9.2727 
 
 8.7479 
 
 9.2711 
 
 8.7475 
 
 9.2695 
 
 8.7472 
 
 9.2680 
 
 9.1734 
 
 
 
 60 
 
 8.7449 
 
 9.2584 
 
 8.7446 
 
 9.2568 
 
 8.7442 
 
 9.2552 
 
 8.7438 
 
 9.2536 
 
 8.7435 
 
 9.2520 
 
 9.1810+ 
 
 
 
16 
 
 TABLE IX. 
 
 
 
 
 
 .0 
 
 .1 
 
 .2 
 
 .3 
 
 .4 
 
 Log 
 
 
 A 
 
 LogDiff. 
 
 LogDiff. 
 
 LogDiff. 
 
 Log Dilf. 
 
 LogDiff. 
 
 Sec. TM. 
 
 
 
 
 V 
 
 L.gr 
 
 V 
 
 Logr 
 
 V 
 
 Logr 
 
 V 
 
 Logr 
 
 f 
 
 Log r 
 
 V 
 
 
 
 60 
 
 8.7468 
 
 9.2664 
 
 8.7464 
 
 9.2648 
 
 8.7461 
 
 9.2632 
 
 8.7457 
 
 9.2616 
 
 8.7453 
 
 9.2600 
 
 8.1125 
 
 
 
 61 
 
 8.7431 
 
 9.2503 
 
 8.7428 
 
 9.2486 
 
 8.7424 
 
 9.2470 
 
 8.7421 
 
 9.2453 
 
 8.7417 
 
 9.2437 
 
 8.0977 
 
 
 
 62 
 
 8.7396 
 
 9.2336 
 
 8.7393 
 
 9.2319 
 
 8.7389 
 
 9.2302 
 
 8.7386 
 
 9.2285 
 
 8.7383 
 
 9.2267 
 
 8.0824 
 
 
 
 63 
 
 8.7363 
 
 9.2162 
 
 8.7360 
 
 9.2144 
 
 8.7357 
 
 9.2126 
 
 8.7353 
 
 9.2108 
 
 8.7350 
 
 9.2090 
 
 8.0656 
 
 
 
 64 
 
 8.7331 
 
 9.1981 
 
 8.7328 
 
 9.1962 
 
 8.7325 
 
 9.1944 
 
 8.7322 
 
 9.1925 
 
 8.7318 
 
 9.1906 
 
 8.0482 
 
 
 
 65 
 
 8.7300 
 
 9.1793 
 
 8.7297 
 
 9.1774 
 
 8.7294 
 
 9.1754 
 
 8.7291 
 
 9.1735 
 
 8.7288 
 
 9.1715 
 
 8.0301 
 
 
 
 66 
 
 8.7270 
 
 9.1596 
 
 8.7267 
 
 9.1576 
 
 8.7264 
 
 9.1555 
 
 8.7262 
 
 9.1535 
 
 8.7259 
 
 9.1514 
 
 8.0111 
 
 
 
 67 
 
 8.7242 
 
 9.1390 
 
 8.7239 
 
 9.1369 
 
 8.7237 
 
 9.1348 
 
 8.7234 
 
 9.1327 
 
 8.7231 
 
 9.1305 
 
 7.9913 
 
 
 
 68 
 
 8.7215 
 
 9.1175 
 
 8.7212 
 
 9.1153 
 
 8.7210 
 
 9.1131 
 
 8.7207 
 
 9.1108 
 
 8.7205 
 
 9.1086 
 
 7.9705 
 
 
 
 69 
 
 8.7190 
 
 9.0948 
 
 8.7187 
 
 9.0925 
 
 8.7185 
 
 9.0901 
 
 8.7182 
 
 9.0878 
 
 8.7180 
 
 9.0854 
 
 7.9487 
 
 
 
 70 
 
 8.7165 
 
 9.0709 
 
 8.7163 
 
 9.0684 
 
 8.7160 
 
 9.0660 
 
 8.7158 
 
 9.0635 
 
 8.7156 
 
 9.0610 
 
 7.9258 
 
 
 
 71 
 
 8.7142 
 
 9.0457 
 
 8.7140 
 
 9.0431 
 
 8.7138 
 
 9.0405 
 
 8.7136 
 
 9.0378 
 
 8.7134 
 
 9.0352 
 
 7.9015 
 
 
 
 72 
 
 8.7121 
 
 9.0190 
 
 8.7119 
 
 9.0162 
 
 8.7117 
 
 9.0135 
 
 8.7115 
 
 9.0107 
 
 8.7113 
 
 9.0078 
 
 7.8738 
 
 
 
 73 
 
 8.7101 
 
 8.9906 
 
 8.7099 
 
 8.9877 
 
 8.7097 
 
 8.9847 
 
 8.7095 
 
 8.9817 
 
 8.7093 
 
 8.9787 
 
 7.8471 
 
 
 
 74 
 
 8.7082 
 
 8.9603 
 
 8.7080 
 
 8.9571 
 
 8.7078 
 
 8.9540 
 
 8.7077 
 
 8.9508 
 
 8.7075 
 
 8.9475 
 
 7.8163 
 
 
 
 75 
 
 8.7064 
 
 8.9277 
 
 8.7062 
 
 8.9243 
 
 8.7061 
 
 8.9209 
 
 8.7059 
 
 8.9174 
 
 8.7058 
 
 8.9139 
 
 7.7831 
 
 
 
 76 
 
 8.7048 
 
 8.8926 
 
 8.7046 
 
 8.8889 
 
 8.7045 
 
 8.8852 
 
 8.7043 
 
 8.8815 
 
 8.7042 
 
 8.8777 
 
 7.7491 
 
 
 
 77 
 
 8.7033 
 
 8.8545 
 
 8.7032 
 
 8.8504 
 
 8.7030 
 
 8.8464 
 
 8.7029 
 
 8.8426 
 
 8.7027 
 
 8.8382 
 
 7.7121 
 
 
 
 78 
 
 8.7019 
 
 8.8126 
 
 8.7018 
 
 8.8082 
 
 8.7017 
 
 8.8042 
 
 8.7015 
 
 8.7994 
 
 8.7014 
 
 8.7945 
 
 7.6695 
 
 
 
 79 
 
 8.7007 
 
 8.7664 
 
 8.7006 
 
 8.7616 
 
 8.7005 
 
 8.7567 
 
 8.7004 
 
 8.7517 
 
 8.7003 
 
 8.7467 
 
 7.6247 
 
 
 
 80 
 
 8.6996 
 
 8.7152 
 
 8.6995 
 
 8.7093 
 
 8.6994 
 
 8.7037 
 
 8.6993 
 
 8.6981 
 
 8.6992 
 
 8.6924 
 
 7.5720 
 
 
 
 81 
 
 8.6986 
 
 8.6564 
 
 8.6985 
 
 8.6507 
 
 8.6984 
 
 8.6440 
 
 8.6984 
 
 8.6375 
 
 8.6983 
 
 8.6310 
 
 7.5120 
 
 
 
 82 
 
 8.6978 
 
 8.5894 
 
 8.6977 
 
 8.5821 
 
 8.6977 
 
 8.5746 
 
 8.6976 
 
 8.5665 
 
 8.6975 
 
 8.5587 
 
 7.4462 
 
 
 
 83 
 
 8.6971 
 
 8.5092 
 
 8.6970 
 
 8.5004 
 
 8.6970 
 
 8.4914 
 
 8.6969 
 
 8.4829 
 
 8.6969 
 
 8.4735 
 
 7.3685 
 
 
 
 84 
 
 8.6965 
 
 8.4116 
 
 8.6964 ' 
 
 8.4006 
 
 8.6964 
 
 8.3892 
 
 8.6963 
 
 8.3775 
 
 8.6963 
 
 8.3655 
 
 7.2682 
 
 
 
 85 
 
 8.6960 
 
 8.2856 
 
 8.6960 
 
 8.2707 
 
 8.6959 
 
 8.2553 
 
 8.6959 
 
 8.2393 
 
 8.6959 
 
 82214 
 
 7.1451 
 
 
 
 86 
 
 8.6957 
 
 8.1072 
 
 8.6957 
 
 8.0846 
 
 8.6957 
 
 8.0607 
 
 8.6956 
 
 8.0355 
 
 8.6956 
 
 8.0086 
 
 6.9615 
 
 
 
 87 
 
 8.6955- 
 
 7.7094 
 
 8.6955 
 
 7.7521 
 
 8.6955 
 
 7.7404 
 
 8.6955 
 
 7.6858 
 
 8.6955 
 
 7.5682 
 
 6.6605 
 
 
 
 88 
 
 8.6955 
 
 6.301 In 
 
 8.6955 
 
 6.9294n 
 
 8.6955 
 
 7 1 7fi1n 
 
 8.6955 
 
 7.3325n 
 
 8.6955 
 
 7 4479n 
 
 
 
 
 89 
 
 8.6955 
 
 7.8261 
 
 8.6955 
 
 7.8663 
 
 8.6955 
 
 ( . l i \t i it 
 7.9031 
 
 8.6956 
 
 7.9370 
 
 8.6956 
 
 < ,t** 1 11 
 
 7.9685 
 
 6.6827n 
 
 
 
 90 
 
 8.6957 
 
 8.1206 
 
 86957 
 
 8.1415 
 
 8.6958 
 
 8.1614 
 
 8.6958 
 
 8.1804 
 
 8.6958 
 
 8.1987 
 
 6.9728 
 
 
 
 91 
 
 8.6960 
 
 8.2945 
 
 8.6961 
 
 8.3086 
 
 8.6961 
 
 8.3222 
 
 8.6962 
 
 8.3355 
 
 8.6962 
 
 8.3483 
 
 7.1526 
 
 
 
 92 
 
 8.6965 
 
 8.4183 
 
 8.6966 
 
 8.4290 
 
 8.6966 
 
 8.4402 
 
 8.6967 
 
 8.4503 
 
 8.6967 
 
 8.4594 
 
 7.2738 
 
 
 
 93 
 
 8.6971 
 
 8.5146 
 
 8.6972 
 
 8.5231 
 
 8.6972 
 
 8.5291 
 
 8.6973 
 
 8.5404 
 
 8.6974 
 
 8.5478 
 
 7.3729 
 
 
 
 94 
 
 8.6978 
 
 8.5927 
 
 8.6979 
 
 8.6010 
 
 8.6980 
 
 8.6075 
 
 8.6981 
 
 8.6149 
 
 8.6982 
 
 8.6217 
 
 7.4499 
 
 
 
 95 
 
 8.6987 
 
 8.6604 
 
 8.6988 
 
 8.6665 
 
 8.6989 
 
 8.6726 
 
 8.6990 
 
 8.6790 
 
 8.6991 
 
 8.6849 
 
 7.5152 
 
 
 
 96 
 
 8.6997 
 
 8.7181 
 
 8.6998 
 
 8.7239 
 
 8.6999 
 
 8.7292 
 
 8.7000 
 
 8.7340 
 
 8.7001 
 
 8.7400 
 
 7.5748 
 
 
 
 97 
 
 8.7008 
 
 8.7694 
 
 8.7009 
 
 8.7742 
 
 8.7010 
 
 8.7793 
 
 8.7012 
 
 8.7839 
 
 8.7013 
 
 8.7885 
 
 7.6272 
 
 
 
 98 
 
 8.7020 
 
 8.8153 
 
 8.7021 
 
 8.8199 
 
 8.7023 
 
 8.8242 
 
 8.7024 
 
 8.8284 
 
 8.7026 
 
 8.8325 
 
 7.6717 
 
 
 
 99 
 
 8.7034 
 
 8.8569 
 
 8.7035 
 
 8.8608 
 
 8.7037 
 
 8.8648 
 
 8.7038 
 
 8.8687 
 
 8.7040 
 
 8.8725 
 
 7.7141 
 
 
 
 100 
 
 8.7049 
 
 8.8948 
 
 8.7051 
 
 8.8984 
 
 8.7052 
 
 8.9020 
 
 8.7054 
 
 8.9056 
 
 8.7055 
 
 8.9091 
 
 7.7509 
 
 
 
 101 
 
 8.7065 
 
 8.9298 
 
 8.7067 
 
 8.9332 
 
 8.7069 
 
 8.9365 
 
 8.7070 
 
 8.9398 
 
 8.7072 
 
 8.9431 
 
 7.7848 
 
 
 
 102 
 
 8.7083 
 
 8.9622 
 
 8.7085 
 
 8.9653 
 
 8.7087 
 
 8.9684 
 
 8.7089 
 
 8.9715 
 
 8.7091 
 
 8.9745 
 
 7.8179 
 
 
 
 103 
 
 8.7102 
 
 8.9924 
 
 8.7104 
 
 8.9953 
 
 8.7106 
 
 8.9982 
 
 8.7108 
 
 9.0011 
 
 8.7110 
 
 9.0039 
 
 7.8486 
 
 
 
 104 
 
 8.7122 
 
 9.0206 
 
 8.7124 
 
 9.0233 
 
 8.7126 
 
 9.0261 
 
 8.7129 
 
 9.0288 
 
 8.7131 
 
 9.0315 
 
 7.8759 
 
 
 
 105 
 
 8.7144 
 
 9.0473 
 
 8.7146 
 
 9.0499 
 
 8.7149 
 
 9.0524 
 
 8.7151 
 
 9.0550 
 
 8.7153 
 
 9.0575 
 
 7.9028 
 
 
 
 106 
 
 8.7167 
 
 9.0724 
 
 8.7169 
 
 9.0748 
 
 8.7172 
 
 9.0772 
 
 8.7174 
 
 9.0797 
 
 8.7177 
 
 9.0821 
 
 7.9270 
 
 
 
 107 
 
 8.7191 
 
 9.0962 
 
 8.7194 
 
 9.0985 
 
 8.7196 
 
 9.1008 
 
 8.7199 
 
 9.1031 
 
 8.7201 
 
 9.1053 
 
 7.9499 
 
 
 
 108 
 
 8.7217 
 
 9.1188 
 
 8.7220 
 
 9.1210 
 
 8.7222 
 
 9.1232 
 
 8.7225 
 
 9.1254 
 
 8.7228 
 
 9.1275 
 
 7.9716 
 
 
 
 109 
 
 8.7244 
 
 9.1403 
 
 8.7247 
 
 9.1424 
 
 8.7250 
 
 9.1445 
 
 8.7252 
 
 9.1466 
 
 8.7255 
 
 9.1486 
 
 7.9924 
 
 
 
 110 
 
 8.7272 
 
 9.1608 
 
 8.7275 
 
 9.1628 
 
 8.7278 
 
 9.1648 
 
 8.7281 
 
 9.1668 
 
 8.7284 
 
 9.1688 
 
 8.0121 
 
 
 
 111 
 
 8.7301 
 
 9.1805 
 
 8.7304 
 
 9.1824 
 
 8.7307 
 
 9.1843 
 
 8.7310 
 
 9.1862 
 
 8.7313 
 
 9.1881 
 
 8.0310 
 
 
 
 112 
 
 8.7332 
 
 9.1993 
 
 8.7336 
 
 9.2011 
 
 8.7338 
 
 9.2030 
 
 8.7342 
 
 9.2048 
 
 8.7345 
 
 9.2066 
 
 8.0492 
 
 
 
 113 
 
 8.7365 
 
 9.2173 
 
 8.7368 
 
 9.2191 
 
 8.7372 
 
 9.2208 
 
 8.7375 
 
 9.2226 
 
 8.7378 
 
 9.2243 
 
 8.0665 
 
 
 
 114 
 
 8.7398 
 
 9.2346 
 
 8.7401 
 
 9.2363 
 
 8.7405 
 
 9.2379 
 
 8.7408 
 
 9.2396 
 
 8.7412 
 
 9.2413 
 
 8.0833 
 
 
 
 115 
 
 8.7433' 
 
 9.2513 
 
 8.7437 
 
 9.2529 
 
 8.7440 
 
 9.2545 
 
 8.7444 
 
 9.2561 
 
 8.7448 
 
 9.2577 
 
 8.0985 
 
 
 
 116 
 
 8.7470 
 
 9.2674 
 
 8.7474 
 
 9.2689 
 
 8.7477 
 
 9.2705 
 
 8.7481 
 
 9.2720 
 
 8.7485 
 
 9.2736 
 
 8.1133 
 
 
 
 117 
 
 8.7507 
 
 9.2829 
 
 8.7511 
 
 9.2844 
 
 8.7515 
 
 9.2859 
 
 8.7519 
 
 9.2874 
 
 8.7523 
 
 9.2889 
 
 8.1276 
 
 
 
 118 
 
 8.7547 
 
 9.2978 
 
 8.7551 
 
 9.2992 
 
 8.7555 
 
 9.3007 
 
 8.7559 
 
 9.3021 
 
 8.7563 
 
 9.3036 
 
 8.1414 
 
 
 
 119 
 
 8.7587 
 
 9.3122 
 
 8.7591 
 
 9.3136 
 
 8.7595 
 
 9.3150 
 
 8.7600 
 
 9.3164 
 
 8.7604 
 
 9.3178 
 
 8.1548 
 
 
 
 120 
 
 8.7629 
 
 9.3261 n 
 
 8.7633 
 
 9.3274n 
 
 8.7638 
 
 9.3288n 
 
 8.7642 
 
 9.3301n 
 
 8.7646 
 
 9.3315n 
 
 8.1685n 
 
 
 
TABLE IX. 
 
 17 
 
 
 
 
 
 .5 
 
 .6 
 
 .7 
 
 .8 
 
 .9 
 
 Log 
 
 
 A 
 
 Log Dig. 
 
 LogDiff. 
 
 LogDiff. 
 
 Log i iiir 
 
 LogDiff. 
 
 Sec. Tar. 
 
 
 
 
 V 
 
 Logr 
 
 t; 
 
 Logr 
 
 V 
 
 Logr 
 
 V 
 
 Logr 
 
 V 
 
 Log r 
 
 Log r 
 
 
 
 60 
 
 8.7449 
 
 9.2584 
 
 8.7446 
 
 9.2568 
 
 8.7442 
 
 9.2552 
 
 8.7438 
 
 9.2536 
 
 8.7435 
 
 9.2520 
 
 9.1810 
 
 
 
 61 
 
 8.7414 
 
 9.2420 
 
 8.7410 
 
 9.2404 
 
 8.7407 
 
 9.2387 
 
 8.7403 
 
 9.2370 
 
 8.7400 
 
 9.2353 
 
 9.1879 
 
 
 
 62 
 
 8.7379 
 
 9.2250 
 
 8.7376 
 
 9.2232 
 
 8.7373 
 
 9.2215 
 
 8.7370 
 
 9.2197 
 
 8.7366 
 
 9.2180 
 
 9.1939 
 
 
 
 63 
 
 8.7347 
 
 9.2072 
 
 8.7344 
 
 9.2054 
 
 8.7341 
 
 9.2036 
 
 8.7337 
 
 9.2018 
 
 8.7334 
 
 9.1999 
 
 9.1999 
 
 
 
 64 
 
 8.7315 
 
 9.1888 
 
 ' 8.7312 
 
 9:i869 
 
 8.7309 
 
 9.1850 
 
 8.7306 
 
 9.1831 
 
 8.7303 
 
 9.1812 
 
 9.2058 
 
 
 
 65 
 
 8.7285 
 
 9.1696 
 
 8.7282 
 
 9.1676 
 
 8.7279 
 
 9.1656 
 
 8.7276 
 
 9.1636 
 
 8.7273 ! 9.1616 
 
 9.2110 
 
 
 
 66 
 
 8.7256 
 
 9.1494 
 
 8.7253 
 
 9.1473 
 
 8.7250 
 
 9.1453 
 
 8.7248 
 
 9.1432 
 
 8.7245 
 
 9.1411 
 
 9.2155 
 
 
 
 67 
 
 8.7228 
 
 9.1284 
 
 8.7226 
 
 9.1263 
 
 8.7223 
 
 9.1241 
 
 8.7220 
 
 9.1219 
 
 8.7218 
 
 9.1197 
 
 9.2199 
 
 
 
 68 
 
 8.7202 
 
 9.1063 
 
 8.7200 
 
 9.1040 
 
 8.7197 
 
 9.1017 
 
 8.7195 
 
 9.0994 
 
 8.7192 
 
 9.0971 
 
 9.2237 
 
 
 
 69 
 
 8.7177 
 
 9.0830 
 
 8.7175 
 
 9.0806 
 
 8.7172 
 
 9.0782 
 
 8.7170 
 
 9.0758 
 
 8.7167 
 
 9.0734 
 
 9.2274 
 
 
 
 70 
 
 8.7153 
 
 9.0585 
 
 8.7151 
 
 9.0559 
 
 8.7149 
 
 9.0534 
 
 8.7147 
 
 9.0508 
 
 8.7144 
 
 9.0482 
 
 9.2317 
 
 
 
 71 
 
 8.7131 
 
 9.0325 
 
 8.7129 
 
 9.0299 
 
 8.7127 
 
 9.0272 
 
 8.7125 
 
 9.0245 
 
 8.7123 
 
 9.0217 
 
 9.2354 
 
 
 
 72 
 
 8.7111 
 
 9.0050 
 
 8.7109 
 
 9.0022 
 
 8.7107 
 
 8.9993 
 
 8.7105 
 
 8.9964 
 
 8.7103 
 
 8.9935 
 
 9.2384 
 
 
 
 73 
 
 8.7092 
 
 8.9757 
 
 8.7090 
 
 8.9727 
 
 8.7088 
 
 8.9696 
 
 8.7086 
 
 8.9665 
 
 8.7084 
 
 8.9634 
 
 9.2408 
 
 
 
 74 
 
 8.7073 
 
 8.9443 
 
 8.7071 
 
 8.9410 
 
 8.7069 
 
 8.9377 
 
 8.7068 
 
 8.9344 
 
 8.7066 
 
 8.9311 
 
 9.2432 
 
 
 
 75 
 
 8.7056 
 
 8.9105 
 
 8.7054 
 
 8.9069 
 
 8.7053 
 
 8.9034 
 
 8.7051 
 
 8.8998 
 
 8.7050 
 
 8.8962 
 
 9.2456 
 
 
 
 76 
 
 8.7040 
 
 8.8739 
 
 8.7039 
 
 8.8701 
 
 8.7037 
 
 8.8663 
 
 8.7036 
 
 8.8624 
 
 8.7034 
 
 8.8585 
 
 9.2474 
 
 
 
 77 
 
 8.7026 
 
 8.8341 
 
 8.7025 
 
 8.8300 
 
 8.7023 
 
 8.8255 
 
 8.7022 
 
 8.8215 
 
 8.7020 
 
 8.8173 
 
 9.2498 
 
 
 
 78 
 
 8.7013 
 
 8.7903 
 
 8.7012 
 
 8.7857 
 
 8.7011 
 
 8.7811 
 
 8.7009 
 
 8.7764 
 
 8.7008 
 
 8.7712 
 
 9.2509 
 
 
 
 79 
 
 8.7001 
 
 8.7416 
 
 8.7000 
 
 8.7364 
 
 8.6999 
 
 8.7312 
 
 8.6998 
 
 8.7255 
 
 8.6997 
 
 8.7206 
 
 9.2527 
 
 
 
 80 
 
 8.6991 
 
 8.6871 
 
 8.6990 
 
 8.6813 
 
 8.6989 
 
 8.6753 
 
 8.6988 
 
 8.6689 
 
 8.6987 
 
 8.6628 
 
 9.2539 
 
 
 
 81 
 
 8.6982 
 
 8.6243 
 
 8.6981 
 
 8.6176 
 
 8.6980 
 
 8.6107 
 
 8.6980 
 
 8.6037 
 
 8.6979 
 
 8.5966 
 
 9.2544 
 
 
 
 82 
 
 8.6974 
 
 8.5515 
 
 8.6974 
 
 8.5429 
 
 8.6973 
 
 8.5347 
 
 8.6972 
 
 8.5278 
 
 8.6972 
 
 8.5179 
 
 9.2556 
 
 
 
 83 
 
 8.6968 
 
 8.4632 
 
 8.6967 
 
 8.4541 
 
 8.6967 
 
 8.4441 
 
 8.6966 
 
 8.4338 
 
 8.6966 
 
 8.4225 
 
 9.2568 
 
 
 
 84 
 
 8.6962 
 
 8.3541 
 
 8.6962 
 
 8.3415 
 
 8.6961 
 
 8.3274 
 
 8.6961 
 
 8.3139 
 
 8.6960 
 
 8.3000 
 
 9.2579 
 
 
 
 85 
 
 8.6958 
 
 8.2055 
 
 8.6958 
 
 8.1876 
 
 8.6958 
 
 8.1673 
 
 8.6958 
 
 8.1492 
 
 8.6957 
 
 8.1288 
 
 9.2585 
 
 
 
 86 
 
 8.6956 
 
 7.9800 
 
 8.6956 
 
 7.9494 
 
 8.6956 
 
 7.9165 
 
 8.6955 
 
 7.8808 
 
 8.6955 
 
 7.8420 
 
 9.2591 
 
 
 
 87 
 
 8.6955 
 
 7.4914 
 
 8.6955 
 
 7.3802 
 
 8.6955 
 
 7.2553 
 
 8.6955 
 
 7.0792 
 
 8.6955 
 
 6.6532 
 
 9.2591 
 
 
 
 88 
 
 8.6955 
 
 7.5185n 
 
 8.6955 
 
 7.5966n 
 
 8.6955 
 
 7.6767n 
 
 8.6955 
 
 7.7324n 
 
 8.6955 
 
 7.7818 
 
 9.2591 
 
 
 
 89 
 
 8.6956 
 
 7.9979 
 
 8.6956 
 
 8.0253 
 
 8.6956 
 
 8.0512 
 
 8.6957 
 
 8.0756 
 
 8.6957 
 
 8.0987 
 
 9.2591 
 
 
 
 90 
 
 8.6958 
 
 8.2149 
 
 8.6958 
 
 8.2330 
 
 8.6959 
 
 8.2492 
 
 8.6959 
 
 8.2637 
 
 8.6960 
 
 8.2799 
 
 9.2591 
 
 
 
 91 
 
 8.6963 
 
 8.3608- 
 
 8.6963 
 
 8.3739 
 
 8.6964 
 
 8.3847 
 
 8.6964 
 
 8.3962 
 
 8.6965 
 
 8.4083 
 
 9.2585 
 
 
 
 92 
 
 8.6968 
 
 8.4691 
 
 8.6969 
 
 8.4786 
 
 8.6969 
 
 8.4879 
 
 8.6970 
 
 8.4977 
 
 8.6970 
 
 8.5065 
 
 9.2579 
 
 
 
 93 
 
 8.6975 
 
 8.5557 
 
 8.6975 
 
 8.5641 
 
 8.6976 
 
 8.5712 
 
 8.6977 
 
 8.5781 
 
 8.6977 
 
 8.5866 
 
 9.2568 
 
 
 
 94 
 
 8.6982 
 
 8.6284 
 
 8.6983 
 
 8.6350 
 
 8.6984 
 
 8.6415 
 
 8.6985 
 
 8.6484 
 
 8.6986 
 
 8.6542 
 
 9.2556 
 
 
 
 95 
 
 8.6992 
 
 8.6902 
 
 8.6993 
 
 8.6959 
 
 8.6994 
 
 8.7020 
 
 8.6995 
 
 8.7070 
 
 8.6996 
 
 8.7127 
 
 9.2544 
 
 
 
 96 
 
 8.7002 
 
 8.7447 
 
 8.7004 
 
 8.7494 
 
 8.7005 
 
 8.7548 
 
 8.7006 
 
 8.7597 
 
 8.7007 
 
 8.7646 
 
 9.2533 
 
 
 
 97 
 
 8.7014 
 
 8.7931 
 
 8.7015 
 
 8.7976 
 
 8.7016 
 
 8.8021 
 
 8.7018 
 
 8.8065 
 
 8.7019 
 
 8.8109 
 
 9.2521 
 
 
 
 98 
 
 8.7027 
 
 8.8367 
 
 8.7028 
 
 8.8408 
 
 8.7030 
 
 8.8448 
 
 8.7031 
 
 8.8488 
 
 8.7033 
 
 8.8528 
 
 9.2509 
 
 
 
 99 
 
 8.7041 
 
 8.8763 
 
 8.7043 
 
 8.8801 
 
 8.7044 
 
 8.8838 
 
 8.7046 
 
 8.8875 
 
 8.7047 
 
 8.8912 
 
 9.2492 
 
 
 
 100 
 
 8.7057 
 
 8.9127 
 
 8.7059 ' 
 
 8.9162 
 
 8.7060 
 
 8.9196 
 
 8.7062 
 
 8.9230 
 
 8.7063 
 
 8.9264 
 
 9.2474 
 
 
 
 101 
 
 8.7074 
 
 8.9463 
 
 8.7076 
 
 8.9496 
 
 8.7078 
 
 8.9528 
 
 8.7079 
 
 8.9559 
 
 8.7081 
 
 8.9591 
 
 9.2456 
 
 
 
 102 
 
 8.7092 
 
 8.9776 
 
 8.7094 
 
 8.9806 
 
 8.7096 
 
 8.9836 
 
 8.7098 
 
 8.9865 
 
 8.7100 
 
 8.9895 
 
 9.2432 
 
 
 
 103 
 
 8.7112 
 
 9.0067 
 
 8.7114 
 
 9.0096 
 
 8.7116 
 
 9.0123 
 
 8.7118 
 
 9.0151 
 
 8.7120 
 
 9.0179 
 
 9.2408 
 
 
 
 104 
 
 8.7133 
 
 9.0341 
 
 8.7135 
 
 9.0368 
 
 8.7137 
 
 9.0395 
 
 8.7140 
 
 9.0421 
 
 8.7142 
 
 9.0447 
 
 9.2384 
 
 
 
 105 
 
 8.7155 
 
 9.0600 
 
 8.7158 
 
 9.0626 
 
 8.7160 
 
 9.0650 
 
 8.7162 
 
 9.0675 
 
 8.7165 
 
 9.0700 
 
 9.2354 
 
 
 
 106 
 
 8.7179 
 
 9.0845 
 
 8.7181 
 
 9.0868 
 
 8.7184 
 
 9.0892 
 
 8.7186 
 
 9.0915 
 
 8.7189 
 
 9.0939 
 
 9.2317 
 
 
 
 107 
 
 8.7204 
 
 9.1076 
 
 8.7207 
 
 9.1098 
 
 8.7209 
 
 9.1121 
 
 8.7212 
 
 9.1144 
 
 8.7214 
 
 9.1166 
 
 9.2280 
 
 
 
 108 
 
 8.7230 
 
 9.1297 
 
 8.7233 
 
 9.1318 
 
 8.7236 
 
 9.1340 
 
 8.7239 
 
 9.1361 
 
 8.7241 
 
 9.1382 
 
 9.2243 
 
 
 
 109 
 
 8.7258 
 
 9.1507 
 
 8.7261 9.1527 
 
 8.7264 
 
 9.1548 
 
 8.7266 
 
 9.1568 
 
 8.7269 
 
 9.1588 
 
 9.2199 
 
 
 
 110 
 
 8.7286 
 
 9.1708 
 
 8.7289 
 
 9.1727 
 
 8.7292 
 
 9.1747 
 
 8.7295 
 
 9.1766 
 
 8.7298 
 
 9.1786 
 
 9.2155 
 
 
 
 111 
 
 8.7316 
 
 9.1900 
 
 8.7320 
 
 9.1919 
 
 8.7323 
 
 9.1938 
 
 8.7326 
 
 9.1956 
 
 8.7329 
 
 9.1975 
 
 9.2110 
 
 
 
 112 
 
 8.7349 
 
 9.2084 
 
 8.7352 
 
 9.2102 
 
 8.7355 
 
 9.2120 
 
 8.7359 
 
 9.2138 
 
 8.7362 
 
 9.2155 
 
 9.2058 
 
 
 
 113 
 
 8.7381 
 
 9.2261 
 
 8.7385 
 
 9.2278 
 
 8.7388 
 
 9.2295 
 
 8.7391 
 
 9.2312 
 
 8.7395 
 
 9.2329 
 
 9.1999 
 
 
 
 114 
 
 8.7415 
 
 9.2429 
 
 8.7419 
 
 9.2446 
 
 8.7422 
 
 9.2463 
 
 8.7426 
 
 9.2480 
 
 8.7429 
 
 9.2496 
 
 9.1939 
 
 
 
 115 
 
 8.7451 
 
 9.2593 
 
 8.7455 
 
 9.2610 
 
 8.7459 
 
 9.2626 
 
 8.7463 
 
 9.2642 
 
 8.7466 
 
 9.2658 
 
 9.1879 
 
 
 
 116 
 
 8.7488 
 
 9.2751 
 
 8.7492 
 
 9.2767 
 
 8.7496 
 
 9.2782 
 
 8.7500 
 
 9.2798 
 
 8.7503 
 
 9.2813 
 
 9.1810 
 
 
 
 117 
 
 8.7527 
 
 9.2903 
 
 8.7531 
 
 9.2918 
 
 8.7535 
 
 9.2933 
 
 8.7539 
 
 9.2948 
 
 8.7543 
 
 9.2963 
 
 9.1734 
 
 
 
 118 
 
 8.7567 
 
 9.3050 
 
 8.7571 . 
 
 9.3064 
 
 8.7575 
 
 9.3079 
 
 8.7579 
 
 9.3093 
 
 8.7583 
 
 9.3108 
 
 9.1649 
 
 
 
 119 
 
 8.7608 
 
 9.3191 
 
 8.7612 
 
 9.3205 
 
 8.7616 
 
 9.3219 
 
 8.7621 
 
 9.3233 
 
 8.7625 
 
 9.3247 
 
 9.1555 
 
 
 
 120 
 
 8.7650 
 
 9.3328n 
 
 8.7655 
 
 9.3342n 
 
 8.7659 
 
 9.3355 
 
 8.7663 
 
 9.3369n 
 
 8.7668 
 
 9.3382 
 
 9.1451 
 
 
 
18 
 
 TABLE IX. 
 
 
 
 
 
 .0 
 
 .1 
 
 .2 
 
 .3 
 
 .4 
 
 Log 
 
 
 A 
 
 Log Diff. 
 
 Log Diff. 
 
 Log Diff. 
 
 Log Diff. 
 
 Log Diff. 
 
 Sec. Tar. 
 
 
 
 
 V 
 
 Logr 
 
 V 
 
 Logr 
 
 V 
 
 Logr 
 
 V 
 
 Logr 
 
 V 
 
 Log r 
 
 V 
 
 
 
 120 
 
 8.7629 
 
 9.3261n 
 
 8.7633 
 
 9.3274n 
 
 8.7638 
 
 9.3288n 
 
 8.7642 
 
 9.3301n 
 
 8.7646 
 
 9.3315 
 
 8.1685n 
 
 
 
 121 
 
 8.7672 
 
 9.3396 
 
 8.7676 
 
 9.3409 
 
 8.7681 
 
 9.3422 
 
 8.7685 
 
 9.3435 
 
 8.7690 
 
 9.3448 
 
 8.1810 
 
 
 
 122 
 
 8.7716 
 
 9.3526 
 
 8.7720 
 
 9.3539 
 
 8.7725 
 
 9.3551 
 
 8.7730 
 
 9.3564 
 
 8.7734 
 
 9.3576 
 
 8.1926 
 
 
 
 123 
 
 8.7762 
 
 9.3652 
 
 8.7767 
 
 9.3664 
 
 8.7771 
 
 9.3676 
 
 8.7776 
 
 9.3688 
 
 8.7781 
 
 9.3700 
 
 8.2039 
 
 
 
 124 
 
 8.7809 
 
 9.3773 
 
 8.7814 
 
 9.3785 
 
 8.7819 
 
 9.3797 
 
 8.7823 
 
 9.3808 
 
 8.7828 
 
 9.3820 
 
 8.2142 
 
 
 
 125 
 
 8.7857 
 
 9.3891 
 
 8.7862 
 
 9.3902 
 
 8.7867 
 
 9.3914 
 
 8.7872 
 
 9.3925 
 
 8.7877 
 
 9.3936 
 
 8.2243 
 
 
 
 126 
 
 8.7907 
 
 9.4004 
 
 8.7912 
 
 9.4015 
 
 8.7917 
 
 9.4026 
 
 8.7922 
 
 9.4037 
 
 8.7927 
 
 9.4048 
 
 8.2348 
 
 
 
 127 
 
 8.7958 
 
 9.4113 
 
 8.7963 
 
 9.4123 
 
 8.7968 
 
 9.4134 
 
 8.7974 
 
 9.4144 
 
 8.7979 
 
 9.4155 
 
 8.2450 
 
 
 
 128 
 
 8.8010 
 
 9.4218 
 
 8.8015 
 
 9.4228 
 
 8.8021 
 
 9.4238 
 
 8.8026 
 
 9.4249 
 
 8.8031 
 
 9.4259 
 
 8.2539 
 
 
 
 129 
 
 8.8063 
 
 9.4320 
 
 8.8068 
 
 9.4330 
 
 8.8074 
 
 9.4340 
 
 8.8079 
 
 9.4349 
 
 8.8085 
 
 9.4359 
 
 8.2625 
 
 
 
 130 
 
 8.8118 
 
 9.4418 
 
 8.8124 
 
 9.4427 
 
 8.8129 
 
 9.4437 
 
 8.8135 
 
 9.4446 
 
 8.8140 
 
 9.4456 
 
 8.2704 
 
 
 
 131 
 
 8.8174 
 
 9.4512 
 
 8.8180 
 
 9.4521 
 
 8.8185 
 
 9.4530 
 
 8.8191 
 
 9.4539 
 
 8.8197 
 
 9.4548 
 
 8.2782 
 
 
 
 132 
 
 8.8231 
 
 9.4601 
 
 8.8237 
 
 9.4610 
 
 8.8243 
 
 9.4618 
 
 8.8248 
 
 9.4627 
 
 8.8254 
 
 9.4636 
 
 8.2859 
 
 
 
 133 
 
 8.8289 
 
 9.4688 
 
 8.8295 
 
 9.4696 
 
 8.8301 
 
 9.4704 
 
 8.8307 
 
 9.4712 
 
 8.8313 
 
 9.4720 
 
 8.2929 
 
 
 
 134 
 
 8.8349 
 
 9.4769 
 
 8.8355 
 
 9.4777 
 
 8.8361 
 
 9.4785 
 
 8.8367 
 
 9.4792 
 
 8.8373 
 
 9.4800 
 
 8.2997 
 
 
 
 135 
 
 8.8409" 
 
 9.4847 
 
 8.8415 
 
 9.4854 
 
 8.8421 
 
 9.4862 
 
 8.8428 
 
 9.4869 
 
 8.8434 
 
 9.4876 
 
 8.3060 
 
 
 
 136 
 
 8.8471 
 
 9.4920 
 
 8.8477 
 
 9.4927 
 
 8.8483 
 
 9.4934 
 
 8.8490 
 
 9.4941 
 
 8.8496 
 
 9.4948 
 
 8.3116 
 
 
 
 137 
 
 8.8533 
 
 9.4990 
 
 8.8539 
 
 9.4996 
 
 8.8546 
 
 9.5003 
 
 8.8552 
 
 9.5009 
 
 8.8559 
 
 9.5016 
 
 8.3167 
 
 
 
 138 
 
 8.8597 
 
 9.5054 
 
 8.8603 
 
 9.5060 
 
 8.8610 
 
 9.5066 
 
 8.8616 
 
 9.5072 
 
 8.8623 
 
 9.5078 
 
 8.8212 
 
 
 
 139 
 
 8.8662 
 
 9.5115 
 
 8.8668 
 
 9.5120 
 
 8.8675 
 
 9.5126 
 
 8.8681 
 
 9.5131 
 
 8.8688 
 
 9.5137 
 
 8.3257 
 
 
 
 140 
 
 8.8727 
 
 9.5170 
 
 8.8734 
 
 9.5175 
 
 8.8740 
 
 9.5180 
 
 . 8.8747 
 
 9.5185 
 
 8.8753 
 
 9.5190 
 
 8.8291 
 
 
 
 141 
 
 8.8793 
 
 9.5220 
 
 8.8800 
 
 9.5224 
 
 8.8806 
 
 9.5229 
 
 8.8813 
 
 9.5233 
 
 8.8820 
 
 9.5238 
 
 8.3826 
 
 
 
 142 
 
 8.8860 
 
 9.5265 
 
 8.8867 
 
 9.5269 
 
 8.8878 
 
 9.5273 
 
 8.8880 
 
 9.5277 
 
 8.8887 
 
 9.5281 
 
 8.3355 
 
 
 
 143 
 
 8.8927 
 
 9.5304 
 
 8.8934 
 
 9.5307 
 
 8.8941 
 
 9.5311 
 
 8.8948 
 
 9.5314 
 
 8.8955 
 
 9.5317 
 
 8.3374 
 
 
 
 144 
 
 8.8996 
 
 9.5337 
 
 8.9002 
 
 9.5340 
 
 8.9010 
 
 9.5343 
 
 8.9016 
 
 9.5345 
 
 8.9023 
 
 9.5348 
 
 8.3388 
 
 
 
 145 
 
 8.9064 
 
 9.5365 
 
 8.9071 
 
 9.5367 
 
 8.9078 
 
 9.5370 
 
 8.9085 
 
 9.5372 
 
 8.9092 
 
 9.5374 
 
 8.3403 
 
 
 
 146 
 
 8.9133 
 
 9.5385 
 
 8.9140 
 
 9.5387 
 
 8.9147 
 
 9.5388 
 
 8.9154 
 
 9.5390 
 
 8.9161 
 
 9.5391 
 
 8.3407 
 
 
 
 147 
 
 8.9202 
 
 9.5398 
 
 8.9209 
 
 9.5399 
 
 8.9216 
 
 9.5400 
 
 8.9223 
 
 9.5401 
 
 8.9230 
 
 9.5401 
 
 8.3403 
 
 
 
 148 
 
 8.9272 
 
 9.5404 
 
 8.9279 
 
 9.5404 
 
 8.9286 
 
 9.5404 
 
 8.9293 
 
 9.5404 
 
 8.9300 
 
 9.5404 
 
 8.3393 
 
 
 
 149 
 
 8.9341 
 
 9.5402 
 
 8.9348 
 
 9.5401 
 
 8.9355 
 
 9.5401 
 
 8.9362 
 
 9.5400 
 
 8.9369 
 
 9.5399 
 
 8.3374 
 
 
 
 150 
 
 8.9410 
 
 9.5391 
 
 8.9417 
 
 9.5389 
 
 8.9424 
 
 9.5388 
 
 8.9431 
 
 9.5386 
 
 8.9438 
 
 9.5384 
 
 8.3345 
 
 
 
 151 
 
 8.9479 
 
 9.5371 
 
 8.9486 
 
 9.5368 
 
 8.9493 
 
 9.5366 
 
 8.9500 
 
 9.5363 
 
 8.9506 
 
 9.5360 
 
 8.3311 
 
 
 
 152 
 
 8.9548 
 
 9.5340 
 
 8.9555 
 
 9.5336 
 
 8.9562 
 
 9.5333 
 
 8.9568 
 
 9.5329 
 
 8.9575 
 
 9.5325 
 
 8.3257 
 
 
 
 153 
 
 8.9616 
 
 9.5300 
 
 8.9623 
 
 9.5295 
 
 8.9630 
 
 9.5290 
 
 8.9636 
 
 9.5285 
 
 8.9643 
 
 9.5280 
 
 8.3202 
 
 
 
 154 
 
 8.9684 
 
 9.5247 
 
 8.9691 
 
 9.5241 
 
 8.9697 
 
 9.5235 
 
 8.9704 
 
 9.5229 
 
 8.9710 
 
 9.5222 
 
 8.3137 
 
 
 
 155 
 
 8.9750 
 
 9.5181 
 
 8.9756 
 
 9.5174 
 
 8.9763 
 
 9.5166 
 
 8.9769 
 
 9.5159 
 
 8.9776 
 
 9.5151 
 
 8.8060 
 
 
 
 156 
 
 8.9815 
 
 9.5102 
 
 8.9821 
 
 9.5093 
 
 8.9828 
 
 9.5084 
 
 8.9834 
 
 9.5075 
 
 8.9841 
 
 9.5066 
 
 8.2966 
 
 
 
 157 
 
 8.9880 
 
 9.5008 
 
 8.9886 
 
 9.4998 
 
 8.9892 
 
 9.4987 
 
 8.9899 
 
 9.4977 
 
 8.9905 
 
 9.4966 
 
 8.2859 
 
 
 
 158 
 
 8.9942 
 
 9.4898 
 
 8.9948 
 
 9.4886 
 
 8.9954 
 
 9.4874 
 
 8.9960 
 
 9.4861 
 
 8.9966 
 
 9.4849 
 
 8.2732 
 
 
 
 159 
 
 9.0003 
 
 9.4769 
 
 9.0009 
 
 9.4755 
 
 9.0015 
 
 9.4741 
 
 9.0021 
 
 9.4726 
 
 9.0027 
 
 9.4712 
 
 8.2585 
 
 
 
 160 
 
 9.0062 
 
 9.4620 
 
 9.0068 
 
 9.4604 
 
 9.0073 
 
 9.4587 
 
 9.0079 
 
 9.4571 
 
 9.0085 
 
 9.4554 
 
 8.2426 
 
 
 
 161 
 
 9.0119 
 
 9.4449 
 
 9.0124 
 
 9.4480 
 
 9.0130 
 
 9.4412 
 
 9.0135 
 
 9.4393 
 
 9.0141 
 
 9.4374 
 
 8.2237 
 
 
 
 162 
 
 9.0173 
 
 9.4253 
 
 9.0178 
 
 9.4232 
 
 9.0183 
 
 9.4210 
 
 9.0189 
 
 9.4189 
 
 9.0194 
 
 9.4166 
 
 8.2032 
 
 
 
 163 
 
 9.0225 
 
 9.4029 
 
 9.0230 
 
 9.4005 
 
 9.0235 
 
 9.3980 
 
 9.0240 
 
 9.3955 
 
 9.0245 
 
 9.3930 
 
 8.1797 
 
 
 
 164 
 
 9.0274 
 
 9.3772 
 
 9.0279 
 
 9.3745 
 
 9.0283 
 
 9.3717 
 
 9.0288 
 
 9.3689 
 
 9.0292 
 
 9.3660 
 
 8.1526 
 
 
 
 165 
 
 9.0320 
 
 9.3479 
 
 9.0324 
 
 9.3448 
 
 9.0329 
 
 9.3416 
 
 9.0333 
 
 9.3383 
 
 9.0337 
 
 9.3351 
 
 8.1221 
 
 
 
 166 
 
 9.0363 
 
 9.3143 
 
 9.0367 
 
 9.3107 
 
 9.0371 
 
 9.3071 
 
 9.0375 
 
 9.3032 
 
 9.0379 
 
 92994 
 
 8.0859 
 
 
 
 167 
 
 9.0403 
 
 9.2755 
 
 9.0407 
 
 9.2714 
 
 9.0410 
 
 9.2672 
 
 9.0414 
 
 9.2628 
 
 9.0417 
 
 9.2584 
 
 8.0463 
 
 
 
 168 
 
 9.0439 
 
 9.2308 
 
 9.0442 
 
 9.2259 
 
 9.0445 
 
 9.2209 
 
 9.0449 
 
 9.2158 
 
 9.0452 
 
 9.2106 
 
 8.0008 
 
 
 
 169 
 
 9.0471 
 
 9.1783 
 
 9.0474 
 
 9.1725 
 
 9.0477 
 
 9.1665 
 
 9.0479 
 
 9.1605 
 
 9.0481 
 
 9.1546 
 
 7.9487 
 
 
 
 170 
 
 9.0499 
 
 9.1158 
 
 9.0501 
 
 9.1088 
 
 9.0504 
 
 9.1018 
 
 9.0506 
 
 9.0947 
 
 9.0509 
 
 9.0873 
 
 7.8855 
 
 
 
 171 
 
 9.0523 
 
 9.0400 
 
 9.0525 
 
 9.0316 
 
 9.0527 
 
 9.0229 
 
 9.0529 
 
 9.0139 
 
 9.0531 
 
 9.0050 
 
 7.8082 
 
 
 
 172 
 
 9.0543 
 
 8.9453 
 
 9.0544 
 
 8.9345 
 
 9.0546 
 
 8.9233 
 
 9.0548 
 
 8.9118 
 
 9.0549 
 
 8.9001 
 
 7.7121 
 
 
 
 173 
 
 9.0558 
 
 8.8209 
 
 9.0559 
 
 8.8062 
 
 9.0560 
 
 8.7910 
 
 9.0561 
 
 8.7749 
 
 9.0562 
 
 8.7582 
 
 7.5885 
 
 
 
 174 
 
 9.0569 
 
 8.6425 
 
 9.0570 
 
 8.6196 
 
 9.0570 
 
 8.5955 
 
 9.0571 
 
 8.5700 
 
 9.0572 
 
 8.5422 
 
 7.4111 
 
 
 
 175 
 
 9.0576 
 
 8.3284 
 
 9.0576 
 
 8.2799 
 
 9.0576 
 
 8.2240n 
 
 9.0576 
 
 8.1614n 
 
 9.0576 
 
 8.0882 n 
 
 7.1060n 
 
 
 
 176 
 
 9.0578 
 
 7.1140 
 
 9.0578 
 
 7.5623 
 
 9.0578 
 
 7.7745 
 
 9.0578 
 
 7.9165 
 
 9.0578 
 
 8.0212 
 
 5.8588 
 
 
 
 177 
 
 9.0575 
 
 8.3766 
 
 9.0575 
 
 8.4183 
 
 9.0574 
 
 8.4281 
 
 9.0574 
 
 8.4942 
 
 9.0578 
 
 8.5211 
 
 7.1526 
 
 
 
 178 
 
 9.0568 
 
 8.6702 
 
 9.0567 
 
 8.6920 
 
 9.0566 
 
 8.7093 
 
 9.0565 
 
 8.7259 
 
 9.0564 
 
 8.7419 
 
 7.4348 
 
 
 
 179 
 
 9.0557 
 
 8.8401 
 
 9.0555 
 
 8.8525 
 
 9.0554 
 
 8.8645 
 
 9.0552 
 
 8.8762 
 
 9.0551 
 
 8.8910 
 
 7.6044 
 
 
 
 180 
 
 9.0541 
 
 8.9619 
 
 9.0539 
 
 8.9694 
 
 9.0537 
 
 8.9786 
 
 9.0535 
 
 8.9877 
 
 0.0532 
 
 8.9042 
 
 7.7241 
 
 
 
TABLE IX. 
 
 19 
 
 
 
 
 A 
 
 .5 
 
 .6 
 
 .7 
 
 .8 
 
 .9 
 
 Log 
 Sec. Tar. 
 
 Log Diff. 
 
 Log Diff. 
 
 Log Diff. 
 
 Log Dlff. 
 
 Log Dlff. 
 
 V 
 
 Logr 
 
 V 
 
 Logr 
 
 V 
 
 Logr 
 
 V 
 
 Logr 
 
 V 
 
 Log r 
 
 tog r 
 
 
 120 
 
 8.7650 
 
 9.3328n 
 
 S.7655 
 
 9.3342n 
 
 8.7659 
 
 9.3355n 
 
 8.7663 
 
 9.3369n 
 
 8.7668 
 
 9.3382 
 
 9.1451 
 
 
 
 1-21 
 
 8.7694 
 
 9.3461 
 
 8.7698 
 
 9.3474 
 
 8.770S 
 
 9.3487 
 
 8.7707 
 
 9.3500 
 
 8.7712 
 
 9.3513 
 
 9.134S 
 
 
 
 122 
 
 8.7739 
 
 9.3589 
 
 8.7744 
 
 9.3602 
 
 8.7748 
 
 9.3614 
 
 8.7753 
 
 9.3627 
 
 8.7757 
 
 9.3639 
 
 9.1296 
 
 
 
 123 
 
 8.7785 
 
 9.3712 
 
 8.7790 
 
 9.3725 
 
 ' 8.7795 
 
 9.3737 
 
 8.7800 
 
 9.3749 
 
 8.7804 
 
 9.3761 
 
 9.1117 
 
 
 
 124 
 
 8.7833 
 
 9.3832 
 
 8.7838 
 
 9.3844 
 
 8.7843 
 
 9.3856 
 
 8.7847 
 
 9.3867 
 
 8.7852 
 
 9.3879 
 
 9.0985 
 
 
 
 125 
 
 8.7882 
 
 9.3947 
 
 8.7887 
 
 9.3959 
 
 8.7892 
 
 9.3970 
 
 8.7897 
 
 9.3981 
 
 8.7902 
 
 9.3993 
 
 9.0841 
 
 
 
 126 
 
 8.7982 
 
 9.4058 
 
 8.7938 
 
 9.4069 
 
 8.7943 
 
 9.4080 
 
 8.7948 
 
 9.4091 
 
 8.7953 
 
 9.4102 
 
 0.0683 
 
 
 
 127 
 
 8.7984 ' 
 
 9.4165 
 
 8.7989 
 
 9.4176 
 
 8.7994 
 
 9.4186 
 
 8.8000 
 
 9.4197 
 
 8.8005 
 
 9.4207 
 
 9.0510 
 
 
 
 128 
 
 8.8036 
 
 9.4269 
 
 8.8042 
 
 9.4279 
 
 8.8047 
 
 9.4289 
 
 8.8052 
 
 9.4300 
 
 8.8058 
 
 9.4810 
 
 9.0320 
 
 
 
 129 
 
 8.8090 
 
 9.4369 
 
 8.8096 
 
 9.4379 
 
 8.8101 
 
 9.4389 
 
 8.8107 
 
 9.4398 
 
 8.8112 
 
 9.4408 
 
 9.0101 
 
 
 
 130 
 
 8.8146 
 
 9.4465 
 
 8.8152 
 
 9.4474 
 
 8.8157 
 
 9.4484 
 
 8.8163 
 
 9.4493 
 
 8.8168 
 
 9.4503 
 
 8.9859 
 
 
 
 131 
 
 8.8202 
 
 9.4556 
 
 8.8208 
 
 9.4565 
 
 8.8214 
 
 9.4574 
 
 8.8220 
 
 9.4583 
 
 8.8225 
 
 9.4592 
 
 8.9603 
 
 
 
 132 
 
 8.8260 
 
 9.4644 
 
 8.8266 
 
 9.4653 
 
 8.8272 
 
 9.4662 
 
 8.8277 
 
 9.4671 
 
 8.8283 
 
 9.4679 
 
 8.9319 
 
 
 
 133 
 
 8.8319 
 
 9.4728 
 
 8.8325 
 
 9.4737 
 
 8.8331 
 
 9.4745 
 
 8.8337 
 
 9.4753 
 
 8.8343 
 
 9.4761 
 
 8.8989 
 
 
 
 134 
 
 8.8379 
 
 9.4808 
 
 8.8385 
 
 9.4816 
 
 8.8391 
 
 9.4824 
 
 8.8397 
 
 9.4831 
 
 8.8403 
 
 9.4839 
 
 8.8603 
 
 
 
 135 
 
 8.8440 
 
 9.4883 
 
 8.8446 
 
 9.4891 
 
 8.8452 
 
 9.4898 
 
 8.8459 
 
 9.4905 
 
 8.8465 
 
 9.4913 
 
 8.8163 
 
 
 
 136 
 
 8.8502 
 
 9.4955 
 
 8.8508 
 
 9.4962 
 
 8.8514 
 
 9.4969 
 
 8.8521 
 
 9.4976 
 
 8.8527 
 
 9.4983 
 
 8.7655 
 
 
 
 137 
 
 8.8565 
 
 9.5022 
 
 8.8571 
 
 9.5028 
 
 8.8578 
 
 9.5035 
 
 8.8584 
 
 9.5041 
 
 8.8591 
 
 9.5048 
 
 8.7060 
 
 
 
 138 
 
 8.8629 
 
 9.5084 
 
 8.8636 
 
 9.5091 
 
 8.8642 
 
 9.5097 
 
 8.8649 
 
 9.5103 
 
 8.8655 
 
 9.5109 
 
 8.6346 
 
 
 
 139 
 
 8.8694 
 
 9.5142 
 
 8.8701 
 
 9.5148 
 
 8.8707 
 
 9.5153 
 
 8.8714 
 
 9.5159 
 
 8.8720 
 
 9.5164 
 
 8.5461 
 
 
 
 140 
 
 8.8760 
 
 9.5195 
 
 8.8767 
 
 9.5200 
 
 8.8773 
 
 9.5205 
 
 8.8780 
 
 9.5210 
 
 88786 
 
 9.5215 
 
 8.4309 
 
 
 
 141 
 
 8.8826 
 
 9.5242 
 
 8.8833 
 
 9.5247 
 
 8.8840 
 
 9.5251 
 
 8.8847 
 
 9.5256 
 
 8.8853 
 
 9.5260 
 
 8.2682 
 
 
 
 142 
 
 8.8893 
 
 9.5284 
 
 8.8900 
 
 9.5288 
 
 8.8907 
 
 9.5292 
 
 8.8914 
 
 9.5296 
 
 8.8920 
 
 9.5300 
 
 7.9945 
 
 
 
 143 
 
 8.8961 
 
 9.5320 
 
 8.8968 
 
 9.5324 
 
 8.8975 
 
 9.5327 
 
 8.8982 
 
 9.5330 
 
 8.8989 
 
 9.5334 
 
 6.6827 
 
 
 
 144 
 
 8.9030 
 
 9.5351 
 
 8.9037 
 
 9.5354 
 
 8.9044 
 
 9.5357 
 
 8.9050 
 
 9.5359 
 
 8.9057 
 
 9.5362 
 
 7.9499n 
 
 
 
 145 
 
 8.9098 
 
 9.5376 
 
 8.9105 
 
 9.5378 
 
 8.9112 
 
 9.5380 
 
 8.9119 
 
 9.5382 
 
 8.9126 
 
 9.5383 
 
 8.2682 
 
 
 
 146 
 
 8.9167 
 
 9.5392 
 
 8.9174 
 
 9.5394 
 
 8i9181 
 
 9.5395 
 
 8.9188 
 
 9.5396 
 
 8.9195 
 
 9.5397 
 
 8.4536 
 
 
 
 147 
 
 8.9237 
 
 9.5402 
 
 8.9244 
 
 9.5402 
 
 8.9251 
 
 9.5403 
 
 8.9258 
 
 9.5403 
 
 8.9265 
 
 9.5404 
 
 8.5858 
 
 
 
 148 
 
 8.9306 
 
 9.5404 
 
 8.9313 
 
 9.5404 
 
 8.9320 
 
 9.5403 
 
 8.9327 
 
 9.5403 
 
 8.9334 
 
 9.5403 
 
 8.6892 
 
 
 
 149 
 
 8.9375 
 
 9.5398 
 
 8.9382 
 
 95397 
 
 8.9389 
 
 9.5395 
 
 8.9396 
 
 9.5394 
 
 8.9403 
 
 9.5393 
 
 8.7726 
 
 
 
 150 
 
 8.9444 
 
 9.5382 
 
 8.9451 
 
 9.5380 
 
 8.9458 
 
 9.5378 
 
 8.9465 
 
 9.5376 
 
 8.9472 
 
 9.5373 
 
 8.8441 
 
 
 
 151 
 
 8.9513 
 
 9.5357 
 
 8.9520 
 
 9.5354 
 
 8.9527 
 
 9.5350 
 
 8.9534 
 
 9.5347 
 
 8.9541 
 
 9.5344 
 
 8.9054 
 
 
 
 152 
 
 8.9582 
 
 9.5321 
 
 8.9589 
 
 9.5317 
 
 8.9596 
 
 9.5313 
 
 8.9602 
 
 9.5308 
 
 8.9609 
 
 9.5304 
 
 8.9603 
 
 
 
 153 
 
 8.9650 
 
 9.5275 
 
 8.9657 
 
 9.5270 
 
 8.9664 
 
 9.5264 
 
 8.9670 
 
 9.5259 
 
 8.9677 
 
 9.5253 
 
 9.0101 
 
 
 
 154 
 
 8.9717 
 
 9.5216 
 
 8.9724 
 
 9.5209 
 
 8.9730 
 
 9.5202 
 
 8.9737 
 
 9.5195 
 
 8.9743 
 
 9.5188 
 
 9.0538 
 
 
 
 155 
 
 8.9782 
 
 9.5143 
 
 8.9789 
 
 9.5135 
 
 8.9795 
 
 9.5127 
 
 8.9802 
 
 9.5119 
 
 8.9808 
 
 9.5110 
 
 9.0943 
 
 
 
 156 
 
 8.9847 
 
 9.5057 
 
 8.9854 
 
 9.5047 
 
 8.9860 
 
 9.5038 
 
 8.9867 
 
 9.5028 
 
 8.9873 
 
 9.5018 
 
 9.1307 
 
 
 
 157 
 
 8.9911 
 
 9.4955 
 
 8.9917 
 
 9.4944 
 
 8.9923 
 
 9.4933 
 
 8.9930 
 
 9.4921 
 
 8.9936 
 
 9.4910 
 
 9.1635 
 
 
 
 158 
 
 8.9972 
 
 9.4836 
 
 8.9979 
 
 9.4823 
 
 8.9985 
 
 9.4810 
 
 8.9991 
 
 9.4796 
 
 8.9997 
 
 9.4783 
 
 91939 
 
 
 
 159 
 
 9.0032 
 
 9.4697 
 
 9.0038 
 
 9.4682 
 
 9.0044 
 
 9.4667 
 
 9.0050 
 
 9.4651 
 
 9.0056 
 
 9.4636 
 
 9.2212 
 
 
 
 160 
 
 9.0090 
 
 9.4537 
 
 9.0096 
 
 9.4520 
 
 9.0102 
 
 9.4503 
 
 9.0108 
 
 9.4485 
 
 9.0118 
 
 9.4467 
 
 9.2468 
 
 
 
 161 
 
 9.0146 
 
 9.4354 
 
 9.0151 
 
 9.4334 
 
 9.0157 
 
 9.4314 
 
 9.0162 
 
 9.4294 
 
 9.0168 
 
 9.4274 
 
 9.2704 
 
 
 
 162 
 
 9.0199 
 
 9.4144 
 
 9.0204 
 
 9.4121 
 
 9.0209 
 
 9.4098 
 
 9.0215 
 
 9.4075 
 
 9.0220 
 
 9.4052 
 
 9.2923 
 
 
 
 163 
 
 9.0249 
 
 9.3904 
 
 9.0254 
 
 9.3878 
 
 9.0259 
 
 9.3853 
 
 9.0264 
 
 9.3826 
 
 9.0269 
 
 9.3800 
 
 9.3116 
 
 
 
 164 
 
 9.0297 
 
 9.3632 
 
 9.0302 
 
 9.3602 
 
 9.0306 
 
 9.3571 
 
 9.0311 
 
 9.3540 
 
 9.0315 
 
 9.3510 
 
 9.3296 
 
 
 
 165 
 
 9.0341 
 
 9.3317 
 
 9.0346 
 
 9.3283 
 
 9.0350 
 
 9.3249 
 
 9.0354 
 
 9.3213 
 
 9.0359 
 
 9.3179 
 
 9.3460 
 
 
 
 166 
 
 9.0383 
 
 9.2957 
 
 9.0387 
 
 9.2918 
 
 9.0391 
 
 9.2878 
 
 9.0395 
 
 9.2838 
 
 9.0399 
 
 9.2796 
 
 9.3608 
 
 
 
 167 
 
 9.0421 
 
 9.2540 
 
 9.0425 
 
 9.2495 
 
 9.0428 
 
 9.2449 
 
 9.0432 
 
 9.2403 
 
 9.0435 
 
 9.2356 
 
 9.3743 
 
 
 
 168 
 
 9.0455 
 
 9.2054 
 
 9.0458 
 
 9.2001 
 
 9.0461 
 
 9.1948 
 
 9.0465 
 
 9.1894 
 
 9.0468 
 
 9.1839 
 
 9.3860 
 
 
 
 169 
 
 9.0485 
 
 9.1483 
 
 9.0488 
 
 9.1419 
 
 9.0491 
 
 9.1355 
 
 9.0493 
 
 9.1291 
 
 9.0496 
 
 9.1224 
 
 9.3957 
 
 
 
 170 
 
 9.0511 
 
 9.0797 
 
 90513 
 
 9.0721 
 
 9.0516 
 
 9.0643 
 
 9.0518 
 
 9.0564 
 
 9.0521 
 
 9.0483 
 
 9.4050 
 
 
 
 171 
 
 9.0533 
 
 8.9957 
 
 9.0535 
 
 8.9859 
 
 9.0537 
 
 8.9761 
 
 9.0539 
 
 8.9662 
 
 9.0541 
 
 8.9560 
 
 9.4128 
 
 
 
 172 
 
 9.0550 
 
 8.8876 
 
 9.0552 
 
 8.8754 
 
 9.0553 
 
 8.8625 
 
 9.0555 
 
 8.8488 
 
 9.0556 
 
 8.8351 
 
 9.4191 
 
 
 
 173 
 
 9.0563 
 
 8.7408 
 
 9.0565 
 
 8.7231 
 
 9.0566 
 
 8.7046 
 
 9.0567 
 
 8.6844 
 
 9.0568 
 
 8.6637 
 
 9.4235 
 
 
 
 174 
 
 9.0572 
 
 8.5132 
 
 9.0573 
 
 8.4829 
 
 9.0574 
 
 8.4495 
 
 9.0575 
 
 8.4125 
 
 9.0575 
 
 8.3720 
 
 9.4266 
 
 
 
 175 
 
 9.0576 
 
 7.9978n 
 
 9.0577 
 
 7.8865n 
 
 9.0577 
 
 7.7324n 
 
 9.0577 
 
 7.4914n 
 
 9.0577 
 
 6.9543n 
 
 9.4286 
 
 
 
 176 
 
 9.0577 
 
 8.1055 
 
 9.0577 
 
 8.1761 
 
 9.0577 
 
 8.2368 
 
 9.0577 
 
 8.2912 
 
 9.0576 
 
 8.3395 
 
 9.4294 
 
 
 
 177 
 
 9.0573 
 
 8.5465 
 
 9.0572 
 
 8.5705 
 
 9.0571 
 
 8.5999 
 
 9.0570 
 
 8.6253 
 
 9.0569 
 
 8.6454 
 
 9.4286 
 
 
 
 178 
 
 9.0563 
 
 8.7649 
 
 9.0561 
 
 8.7796 
 
 9.0560 
 
 8.8007 
 
 9.0559 
 
 8.8075 
 
 9.0559 
 
 8.8249 
 
 9.4266 
 
 
 
 179 
 
 9.0549 
 
 8.9042 
 
 9.0547 
 
 8.9149 
 
 9.0546 
 
 8.9253 
 
 9.0544 
 
 8.9355 
 
 9.0543 
 
 8.9513 
 
 9.4231 
 
 
 
 180 
 
 9.0531 
 
 9.0051 
 
 9.0529 
 
 9.0162 
 
 9.0527 
 
 9.0261 
 
 9.0525 
 
 9.0342 
 
 9.0523 
 
 9.0422 
 
 9.4183n 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
20 
 
 TABLE X. 
 
 
 
 
 T 
 
 4 
 
 8 
 
 12 
 
 16 
 
 20 
 
 
 V 
 
 6u 
 
 Diff. 
 
 r 
 
 iv 
 
 Diff. 
 
 r 
 
 iv 
 
 Diff 
 
 f 
 
 iv 
 
 Diff. 
 
 f 
 
 iv 
 
 Diff. 
 
 r 
 
 iv 
 
 Diff. 
 
 r 
 
 
 
 
 
 25.19 
 
 +1.95 
 
 68 
 
 25.95 
 
 +2.40 
 
 77 
 
 26.50 
 
 +2.91 
 
 86 
 
 26.61 
 
 +3.48 
 
 95 
 
 25.90 
 
 +3.96 
 
 102 
 
 24.41 
 
 +4.18 
 
 106 
 
 
 
 1 
 
 27.16 
 
 1.92 
 
 56 
 
 28.36 
 
 2.35 
 
 63 
 
 29.44 
 
 2.88 
 
 72 
 
 30.14 
 
 3.47 
 
 83 
 
 29.94 
 
 4.00 
 
 95 
 
 28.71 
 
 4.28 
 
 104 
 
 
 
 2 
 
 29.03 
 
 1.74 
 
 43 
 
 30.66 
 
 2.15 
 
 49 
 
 32.26 
 
 2.65 
 
 58 
 
 33.56 
 
 3.24 
 
 72 
 
 33.90 
 
 3.79 
 
 87 
 
 32.98 
 
 4.14 
 
 101 
 
 
 
 3 
 
 30.64 
 
 1.43 
 
 31 
 
 32.66 
 
 2.78 
 
 35 
 
 34.75 
 
 2.23 
 
 44 
 
 36.63 
 
 2.79 
 
 59 
 
 37.52 
 
 3.33 
 
 78 
 
 37.00 
 
 3.73 
 
 97 
 
 
 
 4 
 
 31.89 
 
 1.02 
 
 20 
 
 34.22 
 
 1.28 
 
 23 
 
 36.73 
 
 1.65 
 
 30 
 
 39.14 
 
 2.15 
 
 47 
 
 40.57 
 
 2.67 
 
 69 
 
 40.45 
 
 3.08 
 
 93 
 
 
 
 5 
 
 32.67 
 
 +O.B2 
 
 12 
 
 35.23 
 
 0.70 
 
 13 
 
 38.06 
 
 0.96 
 
 20 
 
 40.93 
 
 1.36 
 
 87 
 
 42.86 
 
 1.82 
 
 60 
 
 43.16 
 
 2.24 
 
 87 
 
 
 
 6 
 
 32.93 
 
 0.01 
 
 7 
 
 35.62 
 
 +0.06 
 
 6 
 
 38.65 
 
 +0.20 
 
 12 
 
 41.86 
 
 +0.47 
 
 28 
 
 44.21 
 
 +0.85 
 
 52 
 
 44.93 
 
 1.24 
 
 80 
 
 
 
 7 
 
 32.64 
 
 0.34 
 
 6 
 
 35.35 
 
 O.B9 
 
 2 
 
 38.46 
 
 0.68 
 
 7 
 
 41.87 
 
 0.45 
 
 21 
 
 44.56 
 
 0.12 
 
 45 
 
 45.64 
 
 +021 
 
 74 
 
 
 
 8 
 
 31.84 
 
 1.03 
 
 8 
 
 34.44 
 
 1.20 
 
 2 
 
 37.49 
 
 1.32 
 
 5 
 
 40.96 
 
 1.32 
 
 17 
 
 43.88 
 
 1.17 
 
 39 
 
 45.35 
 
 0.83 
 
 67 
 
 
 
 9 
 
 30.57 
 
 1.46 
 
 13 
 
 32.96 
 
 1.72 
 
 5 
 
 35.82 
 
 1.96 
 
 6 
 
 39.24 
 
 2.10 
 
 16 
 
 42.23 
 
 2.08 
 
 35 
 
 43.99 
 
 1 82 
 
 60 
 
 
 
 10 
 
 28.92 
 
 1.76 
 
 21 
 
 31.01 
 
 2.13 
 
 13 
 
 33.56 
 
 2.49 
 
 11 
 
 36.76 
 
 2.80 
 
 18 
 
 39.73 
 
 2.86 
 
 32 
 
 41.70 
 
 268 
 
 54 
 
 
 
 11 
 
 27.04 
 
 1.95 
 
 32 
 
 28.71 
 
 2.40 
 
 23 
 
 30.85 
 
 2.85 
 
 19 
 
 33.71 
 
 3.24 
 
 22 
 
 36.53 
 
 3.45 
 
 33 
 
 38.63 
 
 3.39 
 
 49 
 
 
 
 12 
 
 25.01 
 
 2.04 
 
 45 
 
 26.22 
 
 2.51 
 
 36 
 
 27.86 
 
 804 
 
 30 
 
 30.28 
 
 3.51 
 
 29 
 
 32.84 
 
 3.82 
 
 34 
 
 34.98 
 
 3.82 
 
 45 
 
 
 
 13 
 
 22.96 
 
 1.99 
 
 51 
 
 23.69 
 
 2.47 
 
 50 
 
 24.78 
 
 3.02 
 
 42 
 
 26.69 
 
 3.66 
 
 38 
 
 28.89 
 
 3.96 
 
 38 
 
 30.99 
 
 4.05 
 
 43 
 
 
 
 14 
 
 21.04 
 
 1.82 
 
 74 
 
 21.27 
 
 2.29 
 
 65 
 
 21.81 
 
 2.34 
 
 56 
 
 23.15 
 
 3.41 
 
 48 
 
 24.93 
 
 3.86 
 
 43 
 
 26.89 
 
 4.02 
 
 41 
 
 
 
 15 
 
 19.33 
 
 1.54 
 
 88 
 
 19.10 
 
 1.98 
 
 80 
 
 19.10 
 
 2.49 
 
 70 
 
 19.87 
 
 3.10 
 
 59 
 
 21.18 
 
 3.53 
 
 49 
 
 22.94 
 
 3.76 
 
 42 
 
 
 
 16 
 
 17.97 
 
 1.16 
 
 100 
 
 17.31 
 
 1.64 
 
 93 
 
 16.83 
 
 1.99 
 
 83 
 
 17.04 
 
 2.52 
 
 70 
 
 17.87 
 
 2.99 
 
 56 
 
 19.36 
 
 3.16 
 
 43 
 
 
 
 17 
 
 17.01 
 
 0.73 ' 
 
 111 
 
 16.02 
 
 1.01 
 
 105 
 
 15.11 
 
 1.39 
 
 95 
 
 14.82 
 
 1.86 
 
 80 
 
 15.19 
 
 2.29 
 
 63 
 
 16.38 
 
 2.60 
 
 44 
 
 
 
 18 
 
 16.51 
 
 0.26 
 
 118 
 
 15.28 
 
 0.45 
 
 114 
 
 14.05 
 
 0.70 
 
 104 
 
 13.34 
 
 1.07 
 
 89 
 
 13.29 
 
 1.46 
 
 70 
 
 14.15 
 
 1.79 
 
 51 
 
 
 
 19 
 
 16.50 
 
 +0.23 
 
 123 
 
 15.12 
 
 +0.14 
 
 120 
 
 13.70 
 
 +0.01 
 
 111 
 
 12.68 
 
 0.29 
 
 96 
 
 12.26 
 
 0.66 
 
 76 
 
 12.79 
 
 0.89 
 
 55 
 
 
 
 20 
 
 16.97 
 
 0.68 
 
 124 
 
 15.56 
 
 0.71 
 
 122 
 
 14.06 
 
 0.70 
 
 114 
 
 1 2.83 
 
 +0.66 
 
 101 
 
 12.16 
 
 +0.34 
 
 82 
 
 12.37 
 
 +0.05 
 
 61 
 
 
 
 21 
 
 17.87 
 
 1.09 
 
 122 
 
 16.54 
 
 1.21 
 
 121 
 
 15.09 
 
 1.32 
 
 115 
 
 13.79 
 
 1.31 
 
 103 
 
 12.94 
 
 1.19 
 
 86 
 
 12.89 
 
 0.95 
 
 67 
 
 
 
 22 
 
 19.15 
 
 1.40 
 
 116 
 
 17.97 
 
 1.61 
 
 116 
 
 16.69 
 
 1.83 
 
 112 
 
 15.45 
 
 1.95 
 
 102 
 
 14.54 
 
 1.94 
 
 88 
 
 14.27 
 
 1.75 
 
 72 
 
 
 
 23 
 
 20.67 
 
 1.59 
 
 108 
 
 19.76 
 
 1.89 
 
 108 
 
 18.75 
 
 2.20 
 
 106 
 
 17.68 
 
 2.42 
 
 99 
 
 16.82 
 
 2.52 
 
 89 
 
 16.39 
 
 2.41 
 
 77 
 
 
 
 24 
 
 22.34 
 
 1.67 
 
 98 
 
 21.75 
 
 2.01 
 
 98 
 
 21.09 
 
 2.38 
 
 97 
 
 19.28 
 
 2.69 
 
 94 
 
 19.58 
 
 2.99 
 
 88 
 
 19.08 
 
 2.84 
 
 80 
 
 
 
 25 
 
 24.02 
 
 1.61 
 
 86 
 
 23.78 
 
 2.96 
 
 86 
 
 23.51 
 
 2.37 
 
 89 
 
 23.06 
 
 2.74 
 
 86 
 
 22.59 
 
 3.02 
 
 85 
 
 22.10 
 
 3.07 
 
 83 
 
 
 
 26 
 
 25.55 
 
 1.40 
 
 74 
 
 25.67 
 
 1.75 
 
 74 
 
 25.84 
 
 2.17 
 
 75 
 
 25.77 
 
 2.58 
 
 78 
 
 25.61 
 
 2.90 
 
 81 
 
 25.21 
 
 3.02 
 
 85 
 
 
 
 27 
 
 26.82 
 
 1.08 
 
 61 
 
 27.29 
 
 1.40 
 
 61 
 
 27.86 
 
 1.78 
 
 63 
 
 28.23 
 
 2.20 
 
 68 
 
 28.39 
 
 2.55 
 
 76 
 
 28.15 
 
 2.74 
 
 84 
 
 
 
 28 
 
 27.70 
 
 0.65 
 
 52 
 
 28.47 
 
 0.92 
 
 50 
 
 29.42 
 
 1.24 
 
 52 
 
 30.17 
 
 1.61 
 
 59 
 
 30.71 
 
 1.94 
 
 70 
 
 30.69 
 
 2.23 
 
 83 
 
 
 
 29 
 
 28.12 
 
 +0.16 
 
 43 
 
 29.13 
 
 +0.35 
 
 40 
 
 30.37 
 
 +0.60 
 
 42 
 
 31.46 
 
 0.91 
 
 50 
 
 32.37 
 
 1.25 
 
 64 
 
 32.61 
 
 1.53 
 
 80 
 
 
 
 30 
 
 28.02 
 
 0.36 
 
 37 
 
 29.18 
 
 0.26 
 
 33 
 
 30.63 
 
 -0.11 
 
 34 
 
 32.99 
 
 +0.11 
 
 42 
 
 33.21 
 
 _|_0.39 
 
 57 
 
 33.75 
 
 +0.fit 
 
 76 
 
 
 
 T 48 
 
 52 
 
 56 
 
 60 
 
 64 
 
 68 
 
 
 
 V 
 
 60 
 
 Diff. 
 
 f 
 
 iv Biff- 
 
 f- 
 
 6v 
 
 Diff. 
 
 f 
 
 6v 
 
 Diff. 
 
 f 
 
 du 
 
 Diff. 
 
 r 
 
 6v 
 
 Diff. 
 
 f 
 
 
 
 
 
 J8.86 
 
 +l'.'77 
 
 64 
 
 l'9.19 
 
 +1.59 
 
 59 
 
 19.49 
 
 +1.49 
 
 57 
 
 i'9.68 
 
 +1.47 
 
 58 
 
 19.76 
 
 +1.47 
 
 62 
 
 19.80 
 
 +1.52 
 
 70 
 
 
 
 i 
 
 20.75 
 
 1.96 
 
 71 
 
 20.89 
 
 1.77 
 
 65 
 
 21.09 
 
 1.66 
 
 60 
 
 21.24 
 
 1.60 
 
 58 
 
 21.32 
 
 1.60 
 
 60 
 
 21.40 
 
 1.64 
 
 65 
 
 
 
 2 
 
 22.78 
 
 2.04 
 
 81 
 
 22.72 
 
 1.84 
 
 72 
 
 22.78 
 
 1.70 
 
 65 
 
 22.88 
 
 1.63 
 
 60 
 
 22.96 
 
 1.63 
 
 59 
 
 23.07 
 
 1.65 
 
 62 
 
 
 
 3 
 
 24.82 
 
 1.99 
 
 91 
 
 24.56 
 
 1.78 
 
 79 
 
 24.48 
 
 1.64 
 
 70 
 
 24.51 
 
 1.57 
 
 62 
 
 24.58 
 
 1.56 
 
 58 
 
 24.70 
 
 1.57 
 
 59 
 
 
 
 4 
 
 26.76 
 
 1.82 
 
 100 
 
 26.29 
 
 1.63 
 
 86 
 
 26.07 
 
 1.49 
 
 75 
 
 26.03 
 
 1.42 
 
 65 
 
 26.08 
 
 1.89 
 
 59 
 
 26.22 
 
 1.40 
 
 56 
 
 
 
 5 
 
 28.47 
 
 1.55 
 
 108 
 
 27.82 
 
 1.38 
 
 93 
 
 27.46 
 
 1.25 
 
 80 
 
 27.36 
 
 1.17 
 
 69 
 
 27.36 
 
 1.14 
 
 60 
 
 27.50 
 
 1.13 
 
 55 
 
 
 
 6 
 
 29.87 
 
 1.20 
 
 114 
 
 29.06 
 
 1.06 
 
 99 
 
 28.58 
 
 0.96 
 
 86 
 
 28.40 
 
 0.88 
 
 73 
 
 28.36 
 
 0.84 
 
 62 
 
 28.48 
 
 0.81 
 
 55 
 
 
 
 7 
 
 30.87 
 
 0.79 
 
 119 
 
 29.94 
 
 0.69 
 
 104 
 
 29.37 
 
 0.61 
 
 90 
 
 29.12 
 
 0.54 
 
 76 
 
 29.04 
 
 0.50 
 
 65 
 
 29.12 
 
 +0.47 
 
 56 
 
 
 
 8 
 
 31.45 
 
 +037 
 
 121 
 
 30.44 
 
 +0.31 
 
 107 
 
 29.80 
 
 +0.25 
 
 94 
 
 29.49 
 
 +0.20 
 
 80 
 
 29.37 
 
 +0.16 
 
 68 
 
 29.42 
 
 -0.13 
 
 58 
 
 
 
 9 
 
 31.61 
 
 0.06 
 
 121 
 
 30.55 
 
 -0.07 
 
 109 
 
 29.87 
 
 0.08 
 
 95 
 
 29.52 
 
 0.13 
 
 83 
 
 29.36 
 
 -0.18 
 
 71 
 
 29.38 
 
 0.21 
 
 61 
 
 
 
 10 
 
 31.33 
 
 0.46 
 
 119 
 
 30.30 
 
 0.42 
 
 110 
 
 29.61 
 
 0.41 
 
 99 
 
 29.24 
 
 0.42 
 
 86 
 
 29.05 
 
 0.45 
 
 75 
 
 29.00 
 
 0.61 
 
 ' 64 
 
 
 
 11 
 
 30.69 
 
 0.80 
 
 115 
 
 29.71 
 
 0.73 
 
 108 
 
 29.05 
 
 0.68 
 
 100 
 
 28.69 
 
 0.67 
 
 88 
 
 28.46 
 
 0.69 
 
 78 
 
 28.37 
 
 0.73 
 
 68 
 
 
 
 12 
 
 29.73 
 
 1.08 
 
 109 
 
 28.85 
 
 0.97 
 
 105 
 
 28.25 
 
 0.89 
 
 99 
 
 27.90 
 
 0.87 
 
 90 
 
 27.68 
 
 0.86 
 
 81 
 
 27.55 
 
 0.90 
 
 72 
 
 
 
 13 
 
 28.53 
 
 1.28 
 
 102 
 
 27.78 
 
 1.14 
 
 101 
 
 27.27 
 
 1.03 
 
 97 
 
 26.96 
 
 0.98 
 
 90 
 
 26.74 
 
 0.98 
 
 83 
 
 26.58 
 
 1.01 
 
 76 
 
 
 
 14 
 
 27.17 
 
 1.40 
 
 94 
 
 26.58 
 
 1.24 
 
 95 
 
 26.19 
 
 1.11 
 
 95 
 
 25.94 
 
 1.04 
 
 90 
 
 25.73 
 
 1.02 
 
 85 
 
 25.54 
 
 1.03 
 
 79 
 
 
 
 15 
 
 25.74 
 
 1.43 
 
 86 
 
 25.31 
 
 1.251 
 
 90 
 
 25.06 
 
 1.12 
 
 92 
 
 24.88 
 
 1.04 
 
 89 
 
 24.70 
 
 1.01 
 
 86 
 
 24.51 
 
 1.01 
 
 82 
 
 
 
 16 
 
 24.31 
 
 1.38 
 
 77 
 
 24.07 
 
 1.19 
 
 83 
 
 23.95 
 
 1.06 
 
 88 
 
 23.85 
 
 0.98 
 
 88 
 
 23.71 
 
 0.94 
 
 86 
 
 23.52 
 
 0.92 
 
 84 
 
 
 
 17 
 
 22.98 
 
 1.24 
 
 70 
 
 22.92 
 
 1.08 
 
 78 
 
 22.93 
 
 0.96 
 
 84 
 
 22.91 
 
 0.87 
 
 86 
 
 22.83 
 
 0.81 
 
 86 
 
 22.67 
 
 0.77 
 
 85 
 
 
 
 18 
 
 21.83 
 
 1.03 
 
 64 
 
 21.91 
 
 0.89 
 
 73 
 
 22.05 
 
 0.78 
 
 81 
 
 22.11 
 
 0.70 
 
 83 
 
 22.10 
 
 0.64 
 
 85 
 
 21.97 
 
 0.60 
 
 85 
 
 
 
 19 
 
 20.92 
 
 0.76 
 
 60 
 
 21.13 
 
 0.67 
 
 79 
 
 21.37 
 
 0.66 
 
 78 
 
 21.50 
 
 0.49 
 
 81 
 
 21.55 
 
 0.44 
 
 84 
 
 21.47 
 
 0.38 
 
 85 
 
 
 
 20 
 
 20.31 
 
 0.44 
 
 58 
 
 20.60 
 
 0.38 
 
 67 
 
 20.92 
 
 0.31 
 
 75 
 
 21.13 
 
 0.25 
 
 79 
 
 21.22 
 
 -0.20 
 
 82 
 
 21.20 
 
 0.15 
 
 84 
 
 
 
 21 
 
 20.03 
 
 -0.11 
 
 57 
 
 20.37 
 
 0.08 
 
 66 
 
 20.74 
 
 -6.06 
 
 74 
 
 21.00 
 
 -0.01 
 
 78 
 
 21.15 
 
 +0.05 
 
 80 
 
 21.17 
 
 +0.10 
 
 82 
 
 
 
 22 
 
 20.08 
 
 +0.22 
 
 60 
 
 20.43 
 
 +0.21 
 
 67 
 
 20.82 
 
 +0.21 
 
 74 
 
 21.11 
 
 +0.23 
 
 71 
 
 21.31 
 
 0.27 
 
 79 
 
 21.39 
 
 0.33 
 
 80 
 
 
 
 23 
 
 20.46 
 
 0.63 
 
 64 
 
 20.78 
 
 0.48 
 
 69 
 
 21.15 
 
 0.44 
 
 75 
 
 21.45 
 
 0.44 
 
 7G 
 
 21.69 
 
 0.47 
 
 78 
 
 21.82 
 
 0.52 
 
 78 
 
 
 
 24 
 
 21.13 
 
 0.78 
 
 70 
 
 21.39 
 
 0.70 
 
 73 
 
 21.70 
 
 0.63 
 
 77 
 
 21.99 
 
 0.62 
 
 77 
 
 22.25 
 
 0.63 
 
 77 
 
 22.43 
 
 0.67 
 
 76 
 
 
 
 25 
 
 22.02 
 
 0.96 
 
 77 
 
 22.18 
 
 0.85 
 
 78 
 
 22.41 
 
 0.76 
 
 80 
 
 22.68 
 
 0.73 
 
 78 
 
 22.94 
 
 0.72 
 
 77 
 
 23.15 
 
 0.75 
 
 74 
 
 
 
 26 
 
 23.04 
 
 1.06 
 
 85 
 
 23.09 
 
 0.93 
 
 89 
 
 23.22 
 
 0.82 
 
 84 
 
 23.44 
 
 0.76 
 
 80 
 
 23.68 
 
 0.73 
 
 77 
 
 23.93 
 
 0.70 
 
 73 
 
 
 
 27 
 
 24.13 
 
 1.06 
 
 93 
 
 24.04 
 
 0.92 
 
 90 
 
 24.05 
 
 0.80 
 
 88 
 
 24.20 
 
 0.72 
 
 83 
 
 24.41 
 
 0.69 
 
 79 
 
 24.67 
 
 0.69 
 
 73 
 
 
 
 28 
 
 25.16 
 
 0.96 
 
 101 
 
 24.94 
 
 0.84 
 
 96 
 
 24.83 
 
 0.71 
 
 93 
 
 24.89 
 
 0.62 
 
 87 
 
 25.06 
 
 0.57 
 
 81 
 
 25.30 
 
 0.54 
 
 74 
 
 
 
 29 
 
 26.06 
 
 0.79 
 
 108 
 
 25.72 
 
 0.68 
 
 102 
 
 25.48 
 
 0.55 
 
 98 
 
 25.45 
 
 0.46 
 
 91 
 
 25.56 
 
 0.40 
 
 84 
 
 25.76 
 
 0.35 
 
 75 
 
 
 
 30 
 
 26.75 
 
 +0.56 
 
 113 
 
 26.30 
 
 +0.46 
 
 107 
 
 25.94 
 
 f 0.34 . 
 
 103 
 
 25.82 
 
 +0.26 
 
 95 
 
 25.86 
 
 fO.18 
 
 87 
 
 26.01 +0.12 
 
 78 
 
 
 
 NOTE. When T exceeds 88, subtract 88 from it, and add 46.98 to V, 
 
TABLE X. 
 
 21 
 
 
 
 
 T 24 
 
 28 
 
 32 
 
 38 
 
 40 
 
 44 
 
 
 V 
 
 iv 
 
 Diff. 
 
 r 
 
 6v 
 
 Diff. 
 
 / 
 
 (to 
 
 Diff. 
 
 f 
 
 iv 
 
 Diff. 
 
 f 
 
 do 
 
 Diff. 
 
 r 
 
 Av 
 
 Diff. 
 
 r 
 
 
 
 
 
 22.60 
 
 +i'.08 
 
 100 
 
 21.01 
 
 .74 
 
 102 
 
 19.90 
 
 3.27 
 
 95 
 
 i'g.25 
 
 2.78 
 
 87 
 
 18.89 
 
 2.36 
 
 78 
 
 18.81 
 
 2.03 
 
 70 
 
 
 
 1 
 
 2G.83 
 
 4.26 
 
 110 
 
 24.91 
 
 3.06 
 
 110 
 
 23.33 
 
 3.50 
 
 107 
 
 22.19 
 
 3.02 
 
 100 
 
 21.40 
 
 2.59 
 
 90 
 
 20.98 
 
 2.24 
 
 81 
 
 
 
 9 
 
 31.12 
 
 4.18 
 
 113 
 
 28.92 
 
 3.94 
 
 119 
 
 26.90 
 
 3.53 
 
 118 
 
 25.28 
 
 3.07 
 
 112 
 
 24.06 
 
 2.65 
 
 103 
 
 23.29 
 
 2.32 
 
 92 
 
 
 
 3 
 
 35.19 
 
 3.84 
 
 114 
 
 32.80 
 
 3.68 
 
 125 
 
 30.39 
 
 3.34 
 
 128 
 
 28.34 
 
 2.94 
 
 124 
 
 26.71 
 
 2.57 
 
 115 
 
 25.61 
 
 2.26 
 
 103 
 
 
 
 4 
 
 38.80 
 
 3.27 
 
 114 
 
 36.29 
 
 3.21 
 
 129 
 
 33.59 
 
 2.97 
 
 136 
 
 31.17 
 
 2.64 
 
 134 
 
 29.20 
 
 2.34 
 
 126 
 
 27.79 
 
 2.05 
 
 113 
 
 
 
 5 
 
 41.73 
 
 2.60 
 
 112 
 
 39.22 
 
 2.56 
 
 132 
 
 36.33 
 
 2.42 
 
 142 
 
 33.63 
 
 2.20 
 
 142 
 
 31.39 
 
 1.97 
 
 134 
 
 29.71 
 
 1.74 
 
 122 
 
 
 
 6 
 
 43.80 
 
 1.58 
 
 109 
 
 41.40 
 
 1.74 
 
 131 
 
 38.43 
 
 1.73 
 
 144 
 
 35.58 
 
 1.63 
 
 146 
 
 33.14 
 
 1.49 
 
 140 
 
 31.27 
 
 1.33 
 
 128 
 
 
 
 7 
 
 44.89 
 
 +0.58 
 
 103 
 
 42.70 
 
 +0.83 
 
 127 
 
 39.80 
 
 . 0.96 
 
 142 
 
 36.90 
 
 +0.98 
 
 147 
 
 34.37 
 
 0.95 
 
 143 
 
 32.38 
 
 0.87 
 
 132 
 
 
 
 8 
 
 44.96 
 
 0.45 
 
 96 
 
 43.07 
 
 0.09 
 
 121 
 
 40.36 
 
 +0.16 
 
 139 
 
 37.55 
 
 0.30 
 
 144 
 
 35.04 
 
 +0.37 
 
 142 
 
 3301 
 
 +0.37 
 
 133 
 
 
 
 9 
 
 44.00 
 
 1.42 
 
 88 
 
 42.52 
 
 0.99 
 
 112 
 
 40.12 
 
 0.63 
 
 130 
 
 87.51 
 
 0.37 
 
 138 
 
 35.12 
 
 -0.20 
 
 138 
 
 33.13 
 
 0.12 
 
 132 
 
 
 
 10 
 
 42.12 
 
 2.28 
 
 79 
 
 41.09 
 
 1.81 
 
 102 
 
 39.11 
 
 134 
 
 118 
 
 36.81 
 
 0.99 
 
 128 
 
 34.65 
 
 0.73 
 
 131 
 
 32.77 
 
 0.58 
 
 127 
 
 
 
 11 
 
 39.44 
 
 2.90 
 
 70 
 
 38.90 
 
 2.60 
 
 90 
 
 37.42 
 
 1.97 
 
 106 
 
 35.53 
 
 1.53 
 
 117 
 
 33.67 
 
 1.19 
 
 121 
 
 31.98 
 
 0.97 
 
 120 
 
 
 
 12 
 
 36.13 
 
 3.51 
 
 Gl 
 
 36.10 
 
 3.01 
 
 77 
 
 35.17 
 
 2.46 
 
 92 
 
 33.75 
 
 1.96 
 
 103 
 
 32.27 
 
 1.57 
 
 109 
 
 30.84 
 
 1.29 
 
 111 
 
 
 
 13 
 
 32.42 
 
 3.80 
 
 52 
 
 32.88 
 
 3.34 
 
 64 
 
 32.51 
 
 2.78 
 
 77 
 
 31.61 
 
 2.26 
 
 88 
 
 30.54 
 
 1.83 
 
 96 
 
 29.41 
 
 1.52 
 
 101 
 
 
 
 14 
 
 28.53 
 
 3.86 
 
 45 
 
 29.43 
 
 3.46 
 
 52 
 
 29.61 
 
 2.93 
 
 63 
 
 29.24 
 
 2.41 
 
 78 
 
 28.61 
 
 1.98 
 
 83 
 
 27.80 
 
 1.66 
 
 90 
 
 
 
 15 
 
 24.70 
 
 3.68 
 
 39 
 
 25.97 
 
 3.36 
 
 42 
 
 26.66 
 
 2.90 
 
 49 
 
 26.79 
 
 2.42 
 
 59 
 
 26.58 
 
 2.01 
 
 70 
 
 26.11 
 
 1.68 
 
 79 
 
 
 
 16 
 
 21.17 
 
 3.29 
 
 35 
 
 22.70 
 
 3.07 
 
 34 
 
 23.81 
 
 2170 
 
 38 
 
 24.40 
 
 2.29 
 
 47 
 
 24.59 
 
 1.91 
 
 58 
 
 24.44 
 
 1.61 
 
 69 
 
 
 
 17 
 
 18.11 
 
 2.71 
 
 34 
 
 19.83 
 
 2.69 
 
 28 
 
 21.26 
 
 2.33 
 
 30 
 
 22.21 
 
 2.02 
 
 87 
 
 22.75 
 
 1.68 
 
 48 
 
 22.89 
 
 1.44 
 
 60 
 
 
 
 18 
 
 15.74 
 
 1.97 
 
 35 
 
 if. 5 1 
 
 1.97 
 
 26 
 
 19.14 
 
 1.84 
 
 25 
 
 20.36 
 
 1.63 
 
 31 
 
 21.17 
 
 1.40 
 
 41 
 
 21.55 
 
 1.19 
 
 53 
 
 
 
 19 
 
 14.17 
 
 1.13 
 
 37 
 
 15.88 
 
 1.25 
 
 26 
 
 17.58 
 
 1.24 
 
 23 
 
 18.95 
 
 1.15 
 
 27 
 
 19.94 
 
 1.02 
 
 87 
 
 20.50 
 
 0.87 
 
 49 
 
 
 
 20 
 
 13.47 
 
 0.34 
 
 42 
 
 15.01 
 
 0.46 
 
 30 
 
 16.66 
 
 0.63 
 
 25 
 
 18.06 
 
 0.61 
 
 28 
 
 19.12 
 
 -0.68 
 
 36 
 
 19.81 
 
 0.60 
 
 49 
 
 
 
 21 
 
 13.68 
 
 +0.64 
 
 49 
 
 14.95 
 
 +0.32 
 
 36 
 
 16.41 
 
 +0.09 
 
 31 
 
 17.73 
 
 -0.05 
 
 32 
 
 18.77 
 
 +0.12 
 
 89 
 
 19.50 
 
 0.10 
 
 48 
 
 
 
 22 
 
 14.74 
 
 1.46 
 
 56 
 
 15.65 
 
 107 
 
 ! 44 
 
 16.84 
 
 0.74 
 
 89 
 
 17.95 
 
 +0.49 
 
 39 
 
 18.88 
 
 0.34 
 
 44 
 
 19.58 
 
 +0.27 
 
 52 
 
 
 
 23 
 
 16.60 
 
 2.10 
 
 64 
 
 17.08 
 
 1.73 
 
 55 
 
 17.89 
 
 1.31 
 
 49 
 
 18.70 
 
 0.98 
 
 49 
 
 19.44 
 
 0.75 
 
 52 
 
 20.04 
 
 0.63 
 
 58 
 
 
 
 24 
 
 18.94 
 
 2.56 
 
 72 
 
 19.07 
 
 2.19 
 
 66 
 
 19.45 
 
 1.75 
 
 62 
 
 19.90 
 
 1.87 
 
 61 
 
 20.38 
 
 1.09 
 
 63 
 
 20.83 
 
 0.92 
 
 66 
 
 
 
 25 
 
 21.72 
 
 2.87 
 
 80 
 
 20.46 
 
 2.49 
 
 77 
 
 21 39 
 
 2.05 
 
 75 
 
 21.44 
 
 1.44 
 
 74 
 
 21.61 
 
 1.33 
 
 74 
 
 21.88 
 
 1.13 
 
 75 
 
 
 
 26 
 
 24.67 
 
 2.90 
 
 86 
 
 24.05 
 
 2.59 
 
 88 
 
 23.55 
 
 2.18 
 
 88 
 
 22.18 
 
 1.77 
 
 87 
 
 23.03 
 
 1.45 
 
 86 
 
 23.08 
 
 1.23 
 
 85 
 
 
 
 27 
 
 27.52 
 
 2.69 
 
 92 
 
 26.64 
 
 2.47 
 
 97 
 
 25.74 
 
 2.11 
 
 100 
 
 24.98 
 
 1.75 
 
 100 
 
 24.51 
 
 1.46 
 
 98 
 
 24.44 
 
 1.23 
 
 95 
 
 
 
 28 
 
 30.06 
 
 2.28 
 
 95 
 
 28.99 
 
 2.1.3 
 
 104 
 
 27.78 
 
 1.88 
 
 109 
 
 26.68 
 
 1.58 
 
 112 
 
 25.93 
 
 1.33 
 
 108 
 
 25.55 
 
 1.13 
 
 105 
 
 
 
 29 
 
 32.08 
 
 1.67 
 
 96 
 
 30.91 
 
 1.65 
 
 109 
 
 29.50 
 
 1.49 
 
 117 
 
 28.15 
 
 1.29 
 
 119 
 
 27 17 
 
 1.09 
 
 117 
 
 26.60 
 
 0.92 
 
 113 
 
 
 
 30 
 
 33.40 + o.91 
 
 95 
 
 3-2. ->'J 
 
 t-1.03 
 
 111 
 
 30.77 
 
 +0.99 
 
 120 
 
 29.26 
 
 +0.88 
 
 124 
 
 28.12 
 
 +0.77 
 
 122 
 
 27.40 
 
 +0.65 
 
 118 
 
 
 
 T 72 
 
 76 
 
 80 
 
 84 
 
 88 
 
 92 
 
 
 
 r 
 
 <fo 
 
 Diff. 
 
 r 
 
 to 
 
 Diff. 
 
 f 
 
 in 
 
 Diff. 
 
 f 
 
 6v 
 
 Diff. 
 
 r 
 
 6v 
 
 Diff. 
 
 r 
 
 <tw 
 
 Diff. 
 
 f 
 
 
 
 
 
 i'9.73 
 
 +1.61 
 
 80 
 
 19.47 
 
 +1.'78 
 
 92 
 
 18.86 
 
 l'.99 
 
 104 
 
 lV.73 
 
 +2.24 
 
 116 
 
 16.13 
 
 t-2.52 
 
 127 
 
 14.08 
 
 +2'!83 
 
 132 
 
 
 
 i 
 
 21.42 
 
 1.72 
 
 74 
 
 21.33 
 
 1.89 
 
 84 
 
 20.94 
 
 2.12 
 
 95 
 
 20.08 
 
 2.40 
 
 106 
 
 18.79 
 
 2.73 
 
 117 
 
 17.09 
 
 3.11 
 
 123 
 
 
 
 2 
 
 23.17 
 
 1.74 
 
 67 
 
 23.25 
 
 1.89 
 
 76 
 
 23.09 
 
 2.12 
 
 85 
 
 22.53 
 
 2.42 
 
 95 
 
 21.59 
 
 2.78 
 
 105 
 
 20.29 
 
 3.20 
 
 112 
 
 
 
 3 
 
 24.90 
 
 1.65 
 
 62 
 
 25.12 
 
 1.78 
 
 68 
 
 25.18 
 
 2.00 
 
 75 
 
 24.92 
 
 2.29 
 
 83 
 
 24.35 
 
 2.65 
 
 92 
 
 23.48 
 
 3.09 
 
 100 
 
 
 
 4 
 
 26.47 
 
 1.44 
 
 57 
 
 26.82 
 
 1.66 
 
 65 
 
 27.09 
 
 1.75 
 
 66 
 
 27.12 
 
 2.03 
 
 72 
 
 26.90 
 
 2.38 
 
 80 
 
 26.46 
 
 2.80 
 
 88 
 
 
 
 5 
 
 27.79 
 
 1.16 
 
 54 
 
 28.24 
 
 1.25 
 
 55 
 
 28.68 
 
 1.40 
 
 58 
 
 28.99 
 
 1.66 
 
 62 
 
 29.11 
 
 1.98 
 
 69 
 
 29.08 
 
 237 
 
 77 
 
 
 
 6 
 
 28.79 
 
 0.82 
 
 51 
 
 29.32 
 
 0.88 
 
 50 
 
 29.90 
 
 1.00 
 
 51 
 
 30.44 
 
 1.20 
 
 54 
 
 30.86 
 
 1.47 
 
 59 
 
 31.20 
 
 1.81 
 
 68 
 
 
 
 7 
 
 29.43 
 
 0.45 
 
 51 
 
 30.00 
 
 +0.47 
 
 48 
 
 30.68 
 
 0.56 
 
 47 
 
 31.40 
 
 +0.70 
 
 48 
 
 32.06 
 
 0.85 
 
 52 
 
 32.G9 
 
 1.17 
 
 56 
 
 
 
 8 
 
 29.70 
 
 +0.09 
 
 51 
 
 30.27 
 
 0.07 
 
 47 
 
 31.00 
 
 +0.10 
 
 44 
 
 31.84 
 
 0.19 
 
 34 
 
 32.67 
 
 +0.33 
 
 47 
 
 33.53 
 
 +0.51 
 
 54 
 
 
 
 9 
 
 29.61 
 
 0.26 
 
 53 
 
 30.14 
 
 0.31 
 
 48 
 
 30.88 
 
 0.33 
 
 44 
 
 31.78 
 
 0.29 
 
 43 
 
 32.72 
 
 0.21 
 
 :46 
 
 33.71 
 
 -0.14 
 
 52 
 
 
 
 10 
 
 29.18 
 
 0.57 
 
 56 
 
 29.66 
 
 0.63 
 
 50 
 
 30.35 
 
 0.69 
 
 46 
 
 31.27 
 
 0.71 
 
 45 
 
 32.25 
 
 0.72 
 
 47 
 
 33.26 
 
 0.72 
 
 53 
 
 
 
 11 
 
 28.48 
 
 0.80 
 
 60 
 
 28.88 
 
 0.90 
 
 54 
 
 29.50 
 
 0.98 
 
 51 
 
 30.37 
 
 1.05 
 
 49 
 
 31.29 
 
 1.13 
 
 51 
 
 32.27 
 
 1.21 
 
 57 
 
 
 
 12 
 
 27.58 
 
 0.97 
 
 65 
 
 27.87 
 
 1.08 
 
 60 
 
 28.40 
 
 1.19 
 
 56 
 
 29.17 
 
 1.30 
 
 55 
 
 30.00 
 
 1.42 
 
 57 
 
 30.85 
 
 1.66 
 
 63 
 
 
 
 13 
 
 26.54 
 
 1.07 
 
 79 
 
 26.73 
 
 1.17 
 
 65 
 
 27.13 
 
 131 
 
 63 
 
 27.77 
 
 1.45 
 
 62 
 
 28.45 
 
 1.60 
 
 65 
 
 29.15 
 
 1.79 
 
 71 
 
 
 
 14 
 
 25.45 
 
 1.09 
 
 74 
 
 25.53 
 
 1.19 
 
 71 
 
 25.79 
 
 1.32 
 
 70 
 
 26.28 
 
 1.48 
 
 70 
 
 26.80 
 
 1.65 
 
 74 
 
 27.27 
 
 1.89 
 
 80 
 
 
 
 15 
 
 24.36 
 
 1.05 
 
 78 
 
 24.34 
 
 1.14 
 
 77 
 
 24.48 
 
 1.26 
 
 77 
 
 24.80 
 
 1.42 
 
 79 
 
 25.15 
 
 1.69 
 
 83 
 
 25.38 
 
 1.83 
 
 89 
 
 
 
 16 
 
 23.34 
 
 0.95 
 
 82 
 
 23.24 
 
 1.02 
 
 81 
 
 23.26 
 
 1.12 
 
 83 
 
 23.44 
 
 1.26 
 
 86 
 
 23.61 
 
 1.43 
 
 92 
 
 23.61 
 
 1.64 
 
 99 
 
 
 
 17 
 
 22.46 
 
 0.79 
 
 85 
 
 22.30 
 
 0.83 
 
 86 
 
 22.23 
 
 0.91 
 
 88 
 
 22.28 
 
 1.03 
 
 93 
 
 22.29 
 
 1.16 
 
 99 
 
 22.10 
 
 1.33 
 
 106 
 
 
 
 18 
 
 21.76 
 
 0.58 
 
 86 
 
 21.57 
 
 0.60 
 
 88 
 
 21.44 
 
 0.65 
 
 92 
 
 21.38 
 
 0.74 
 
 98 
 
 21.28 
 
 0.82 
 
 105 
 
 20.95 
 
 096 
 
 112 
 
 
 
 19 
 
 21.29 
 
 035 
 
 87 
 
 21.09 
 
 0.34 
 
 90 
 
 20.93 
 
 0.36 
 
 94 
 
 20.80 
 
 0.39 
 
 100 
 
 20.65 
 
 0.43 
 
 108 
 
 20.23 
 
 -0.47 
 
 116 
 
 
 
 20 
 
 21.05 
 
 +0.10 
 
 86 
 
 20.88 
 
 -006 
 
 89 
 
 20.73 
 
 0.04 
 
 94 
 
 20.59 
 
 0.01 
 
 100 
 
 20.41 
 
 0.02 
 
 1'08 
 
 20.01 
 
 +0.03 
 
 116 
 
 
 
 21 
 
 21.08 
 
 0.16 
 
 84 
 
 20.96 
 
 +023 
 
 87 
 
 20.85 
 
 +0.28 
 
 91 
 
 20.75 
 
 +0.33 
 
 98 
 
 20.63 
 
 +0.42 
 
 105 
 
 20.29 
 
 0.63 
 
 113 
 
 
 
 22 
 
 21.37 
 
 0.40 
 
 81 
 
 21.33 
 
 0.48 
 
 83 
 
 21.29 
 
 0.57 
 
 87 
 
 21.25 
 
 0.67 
 
 92 
 
 21.25 
 
 0.80 
 
 99 
 
 21.06 
 
 0.99 
 
 107 
 
 
 
 23 
 
 21.87 
 
 0.59 
 
 78 
 
 21.91 
 
 0.68 
 
 79 
 
 21.99 
 
 0.80 
 
 81 
 
 22.08 
 
 0.94 
 
 85 
 
 22.22 
 
 1.12 
 
 91 
 
 22.26 
 
 1.38 
 
 98 
 
 
 
 24 
 
 22.55 
 
 0.74 
 
 75 
 
 22.69 
 
 0.81 
 
 74 
 
 22.89 
 
 0.97 
 
 75 
 
 23.13 
 
 1.13 
 
 77 
 
 23.49 
 
 1.35 
 
 81 
 
 23.81 
 
 1.65 
 
 87 
 
 
 
 25 
 
 23.34 
 
 081 
 
 71 
 
 23.56 
 
 0.91 
 
 69 
 
 23.92 
 
 1.05 
 
 67 
 
 24.33 
 
 1.22 
 
 67 
 
 24.91 
 
 1.46 
 
 69 
 
 25.56 
 
 1.79 
 
 74 
 
 
 
 26 
 
 24.16 
 
 0.80 
 
 68 
 
 24.50 
 
 0.89 
 
 64 
 
 24.98 
 
 1.01 
 
 59 
 
 25.56 
 
 1.19 
 
 56 
 
 26.39 
 
 1.42 
 
 56 
 
 27.38 
 
 1.77 
 
 56 
 
 
 
 27 
 
 24.G9 
 
 0.72 
 
 66 
 
 25.37 
 
 0.79 
 
 59 
 
 25.95 
 
 0.89 
 
 52 
 
 26.71 
 
 1.05 
 
 46 
 
 27.76 
 
 1.27 
 
 43 
 
 29.10 
 
 1.61 
 
 45 
 
 
 
 28 
 
 25.61 
 
 0.66 
 
 65 
 
 26.08 
 
 0.60 
 
 56 
 
 26.76 
 
 0.68 
 
 46 
 
 27.67 
 
 0.81 
 
 38 
 
 28.93 
 
 1.00 
 
 31 
 
 30.60 
 
 1.29 
 
 32 
 
 
 
 29 
 
 26.07 
 
 0.33 
 
 65 
 
 26.07 
 
 0.36 
 
 54 
 
 27.32 
 
 0.39 j 
 
 42 
 
 28.33 
 
 0.48 
 
 31 
 
 29.96 
 
 0.61 
 
 22 
 
 31.67 
 
 0.83 
 
 18 
 
 
 
 30 
 
 26.28 
 
 +0.08 
 
 66 
 
 26.78 
 
 +0.05 
 
 53 
 
 27.54 
 
 +00.5 
 
 40 
 
 28.63 
 
 (-0.08 
 
 26 
 
 30.16 
 
 +0.15 
 
 11 
 
 32.26 
 
 4-0.30 
 
 8 
 
 
 
 NOTE. When T exceeds 88, subtract 88 from it, and add 46.98 to V, 
 
22 
 
 TABLE X. 
 
 
 
 
 T 
 
 4 
 
 8 
 
 12 
 
 16 
 
 20 
 
 
 r 
 
 60 
 
 Diff. 
 
 r 
 
 dy 
 
 Diff. 
 
 t 
 / 
 
 io 
 
 Diff. 
 
 f 
 
 60 
 
 Diff. 
 
 f 
 
 tv 
 
 Diff. 
 
 r 
 
 do 
 
 Diff. 
 
 r 
 
 
 
 30 
 
 28.02 
 
 O.S6 
 
 37 
 
 29.18 
 
 0.26 
 
 33 
 
 30.63 
 
 -0.11 
 
 34 
 
 32.99 
 
 +0.11 
 
 42 
 
 33:21 
 
 +0.39 
 
 57 
 
 33. 7o 
 
 +0.69 
 
 76 
 
 
 
 31 
 
 27.40 
 
 0.87 
 
 35 
 
 28.61 
 
 0.88 
 
 29 
 
 30.15 
 
 0.85 
 
 29 
 
 31.68 
 
 -0.72 
 
 36 
 
 33.16 
 
 0.51 
 
 51 
 
 34.00 
 
 0.23 
 
 71 
 
 
 
 32 
 
 26.28 
 
 1.34 
 
 35 
 
 27.43 
 
 1.46 
 
 28 
 
 28.94 
 
 1.55 
 
 26 
 
 30.55 
 
 1.55 
 
 33 
 
 32.19 
 
 1.44 
 
 47 
 
 33.30 
 
 1.21 
 
 60 
 
 
 
 33 
 
 24.72 
 
 1.73 
 
 39 
 
 25.70 
 
 1.95 
 
 31 
 
 27.06 
 
 2.18 
 
 27 
 
 28.58 
 
 1.29 
 
 31 
 
 30.33 
 
 2.26 
 
 43 
 
 31.69 
 
 2.04 
 
 60 
 
 
 
 34 
 
 22.81 
 
 2.03 
 
 46 
 
 23.53 
 
 2.33 
 
 37 
 
 24.62 
 
 2.66 
 
 32 
 
 25.98 
 
 2.88 
 
 33 
 
 27.68 
 
 2.98 
 
 41 
 
 29.23 
 
 2.86 
 
 55 
 
 
 
 35 
 
 20.06 
 
 2.21 
 
 56 
 
 21.04 
 
 2.59 
 
 46 
 
 21.74 
 
 3.01 
 
 39 
 
 22.82 
 
 3.34 
 
 37 
 
 24.38 
 
 3.53 
 
 40 
 
 26.08 
 
 3.44 
 
 50 
 
 
 
 36 
 
 18.39 
 
 2.26 
 
 68 
 
 18.36 
 
 2.69 
 
 58 
 
 18.61 
 
 8.17 
 
 49 
 
 19.30 
 
 3.60 
 
 43 
 
 20.63 
 
 3.88 
 
 42 
 
 22.36 
 
 3.88 
 
 46 
 
 
 
 37 
 
 16.14 
 
 2.18 
 
 80 
 
 15,66 
 
 2.63 
 
 71 
 
 15.40 
 
 8.15 
 
 61 
 
 15.62 
 
 3.64 
 
 51 
 
 16.63 
 
 3.99 
 
 45 
 
 18.34 
 
 4.06 
 
 42 
 
 
 
 38 
 
 14.03 
 
 1.98 
 
 94 
 
 13.09 
 
 2.42 
 
 85 
 
 12.30 
 
 2.95 
 
 74 
 
 12.01 
 
 3.46 
 
 61 
 
 12.65 
 
 3.88 
 
 49 
 
 14.24 
 
 4.02 
 
 41 
 
 
 
 39 
 
 12.19 
 
 1.65 
 
 107 
 
 10.81 
 
 2.06 
 
 100 
 
 9.50 
 
 2.56 
 
 87 
 
 8.69 
 
 3.08 
 
 72 
 
 8.87 
 
 S.53 
 
 55 
 
 10.30 
 
 3.74 
 
 41 
 
 
 
 40 
 
 10.74 
 
 1.21 
 
 119 
 
 8.97 
 
 1.56 
 
 113 
 
 7.17 
 
 2.02 
 
 100 
 
 5.85 
 
 2.50 
 
 82 
 
 5.58 
 
 2.96 
 
 62 
 
 6.76 
 
 3.23 
 
 42 
 
 
 
 41 
 
 09.78 
 
 0.68 
 
 130 
 
 7.68 
 
 0.96 
 
 124 
 
 5.46 
 
 1.83 
 
 112 
 
 3.68 
 
 1.7< 
 
 93 
 
 2.95 
 
 2.21 
 
 69 
 
 3.83 
 
 2.52 
 
 45 
 
 
 
 42 
 
 09.38 
 
 0.09 
 
 137 
 
 7.04 
 
 0.28 
 
 134 
 
 4.50 
 
 0.55 
 
 122 
 
 2.32 
 
 0.85 
 
 102 
 
 1.16 
 
 1.30 
 
 76 
 
 1.71 
 
 1.64 
 
 49 
 
 
 
 43 
 
 09.60 
 
 +052 
 
 141 
 
 7.11 
 
 +0.44 
 
 140 
 
 4.35 
 
 +0.29 
 
 130 
 
 1.88 
 
 +0.04 
 
 110 
 
 0.35 
 
 0.30 
 
 83 
 
 0.53 
 
 0.63 
 
 54 
 
 
 
 44 
 
 10.43 
 
 1.13 
 
 142 
 
 7.91 
 
 1.18 
 
 143 
 
 5.07 
 
 1.13 
 
 135 
 
 2.39 
 
 0.99 
 
 116 
 
 0.56 
 
 +0.73 
 
 K) 
 
 0.38 
 
 +0.37 
 
 61 
 
 
 
 45 
 
 11.87 
 
 1.65 
 
 140 
 
 9.42 
 
 1.82 
 
 142 
 
 6.60 
 
 1.91 
 
 136 
 
 3.85 
 
 1.90 
 
 120 
 
 1.80 
 
 1.72 
 
 96 
 
 1.27 
 
 1.89 
 
 67 
 
 
 
 46 
 
 14.83 
 
 2.17 
 
 134 
 
 11.55 
 
 2.39 
 
 139 
 
 8.89 
 
 2.60 
 
 133 
 
 6.18 
 
 2.70 
 
 121 
 
 4.00 
 
 2.62 
 
 100 
 
 3.16 
 
 2.32 
 
 75 
 
 
 
 47 
 
 16.21 
 
 2.52 
 
 127 
 
 14.20 
 
 283 
 
 132 
 
 11.80 
 
 3.14 
 
 131 
 
 9.24 
 
 333 
 
 121 
 
 7.03 
 
 B.85 
 
 104 
 
 5.91 
 
 3.10 
 
 82 
 
 
 
 48 
 
 18.88 
 
 2.73 
 
 116 
 
 17.21 
 
 3.10 
 
 123 
 
 15.16 
 
 3.49 
 
 124 
 
 12.84 
 
 3.77 
 
 118 
 
 10.70 
 
 3.88 
 
 106 
 
 9.36 
 
 3.69 
 
 88 
 
 
 
 49 
 
 21.67 
 
 2.78 
 
 105 
 
 20.40 
 
 3.18 
 
 112 
 
 18.77 
 
 3.62 
 
 116 
 
 16.78 
 
 3.98 
 
 115 
 
 14.78 
 
 4.15 
 
 106 
 
 13.28 
 
 4.03 
 
 95 
 
 
 
 50 
 
 24.43 
 
 2.66 
 
 92 
 
 23.57 
 
 3.07 
 
 100 
 
 22.40 
 
 3.53 
 
 106 
 
 20.80 
 
 3.93 
 
 108 
 
 19.00 
 
 4.16 
 
 106 
 
 17.41 
 
 4.10 
 
 100 
 
 
 
 51 
 
 26.98 
 
 2.38 
 
 80 
 
 26.54 
 
 2.78 
 
 88 
 
 25.84 
 
 3.24 
 
 96 
 
 24.64 
 
 3.64 
 
 102 
 
 23.11 
 
 8.S2 
 
 105 
 
 21.48 
 
 3.91 
 
 104 
 
 
 
 52 
 
 29.18 
 
 1.97 
 
 69 
 
 29.14 
 
 2.34 
 
 77 
 
 28.89 
 
 2.77 
 
 86 
 
 28.09 
 
 3.17 
 
 95 
 
 26.8S 
 
 3.45 
 
 103 
 
 25.27 
 
 3.53 
 
 107 
 
 
 
 53 
 
 3091 
 
 1.46 
 
 59 
 
 31.23 
 
 1.78 
 
 67 
 
 31.38 
 
 2.15 
 
 78 
 
 30.98 
 
 2.52 
 
 89 
 
 30.01 
 
 2.78 
 
 100 
 
 28.48 
 
 2.86 
 
 109 
 
 
 
 54 
 
 32.10 
 
 0.90 
 
 52 
 
 32.70 
 
 1.14 
 
 59 
 
 33.19 
 
 1.44 
 
 71 
 
 33.13 
 
 1.74 
 
 84 
 
 32.42 
 
 1.99 
 
 98 
 
 31.00 
 
 2.11 
 
 110 
 
 
 
 55 
 
 32.70 
 
 +0.32 
 
 48 
 
 33.52 
 
 +0.49 
 
 54 
 
 34.26 
 
 +0.69 
 
 66 
 
 34.46 
 
 0.91 
 
 80 
 
 33.99 
 
 1.12 
 
 96 
 
 32.70 
 
 1.25 
 
 110 
 
 
 
 56 
 
 32.73 
 
 0.23 
 
 46 
 
 33.68 
 
 -0.15 
 
 52 
 
 34.57 
 
 -0.05 
 
 64 
 
 34.95 
 
 +0.09 
 
 78 
 
 34.66 
 
 +0.23 
 
 95 
 
 33.50 
 
 +0.36 
 
 110 
 
 
 
 57 
 
 32.24 
 
 0.72 
 
 47 
 
 33.22 
 
 0.73 
 
 53 
 
 34.17 
 
 0.71 
 
 64 
 
 34.54 
 
 068 
 
 78 
 
 34.46 
 
 0.60 
 
 94 
 
 33.43 
 
 0.48 
 
 109 
 
 
 
 58 
 
 31.28 
 
 1.13 
 
 51 
 
 32.22 
 
 1.21 
 
 57 
 
 33.13 
 
 1.29 
 
 67 
 
 33.60 
 
 1.34 
 
 80 
 
 33.47 
 
 1.32 
 
 94 
 
 32.55 
 
 1.22 
 
 107 
 
 
 
 59 
 
 29.98 
 
 1.43 
 
 57 
 
 30.80 
 
 1.57 
 
 63 
 
 31.59 
 
 1.73 
 
 72 
 
 31.97 
 
 1.85 
 
 83 
 
 31.82 
 
 1.90 
 
 96 
 
 30.99 
 
 1.83 
 
 106 
 
 
 
 GO 
 
 28.43 
 
 -1.62 
 
 65 
 
 29.09 
 
 1.79 
 
 71 
 
 29.X 
 
 2.01 
 
 79 
 
 211.1)1 
 
 2.19 
 
 88 
 
 :'iu;> 
 
 2.20 
 
 98 
 
 28.89 
 
 227 
 
 105 
 
 
 
 T 48 
 
 52 
 
 56 
 
 60 
 
 64 
 
 68 
 
 
 
 V 
 
 <ii> 
 
 Diff. 
 
 f 
 
 So 
 
 Hill. 
 
 f 
 
 eJw 
 
 Diff. 
 
 f 
 
 iv 
 
 Biff. 
 
 r 
 
 Sv 
 
 Diff. 
 
 r 
 
 Sv 
 
 Diff. 
 
 r 
 
 
 
 30 
 
 26.75 
 
 +0.56 
 
 11. '! 
 
 26.30 
 
 +0.46 
 
 107 
 
 25.94 
 
 +0.34 
 
 108 
 
 25.82 
 
 +0.26 
 
 95 
 
 25.86 
 
 +0.18 
 
 87 
 
 26.01 
 
 +0.12 
 
 78 
 
 
 
 31 
 
 27.18 
 
 +0.28 
 
 117 
 
 26.55 
 
 +0.21 
 
 111 
 
 26.17 
 
 +0.11 
 
 107 
 
 25.97 
 
 0.02 
 
 99 
 
 25.92 
 
 0.06 
 
 91 
 
 26.00 
 
 0.13 
 
 80 
 
 
 
 32 
 
 27.31 
 
 0.03 
 
 118 
 
 26.72 
 
 -0.06 
 
 114 
 
 26.17 
 
 0.13 
 
 110 
 
 25.87 
 
 0.22 
 
 102 
 
 25.74 
 
 0.30 
 
 95 
 
 25.74 
 
 0.38 
 
 85 
 
 
 
 33 
 
 27.13 
 
 0.34 
 
 118 
 
 26.53 
 
 0.33 
 
 114 
 
 25.92 
 
 0.37 
 
 112 
 
 25.54 
 
 0.44 
 
 106 
 
 25.32 
 
 0.62 
 
 99 
 
 25.24 
 
 0.62 
 
 90 
 
 
 
 34 
 
 26.64 
 
 0.63 
 
 114 
 
 26.06 
 
 0.58 
 
 113 
 
 25.43 
 
 0.59 
 
 113 
 
 25.00 
 
 0.64 
 
 108 
 
 24.70 
 
 0.71 
 
 103 
 
 24.50 
 
 0.82 
 
 95 
 
 
 
 35 
 
 25.87 
 
 0.88 
 
 109 
 
 25.37 
 
 0.8Q 
 
 110 
 
 24.75 
 
 0.77 
 
 112 
 
 24.27 
 
 0.60 
 
 109 
 
 23.90 
 
 0.87 
 
 106 
 
 23.61 
 
 0.95 
 
 100 
 
 
 
 36 
 
 24.88 
 
 1.09 
 
 102 
 
 24.47 
 
 0.97 
 
 105 
 
 23.90 
 
 0.91 
 
 110 
 
 23.40 
 
 0.92 
 
 109 
 
 22.97 
 
 0.96 
 
 109 
 
 22.60 
 
 1.04 
 
 105 
 
 
 
 37 
 
 23.70 
 
 1.23 
 
 93 
 
 23.44 
 
 1.08 
 
 99 
 
 22.94 
 
 0.99 
 
 106 
 
 22.44 
 
 0.97 
 
 108 
 
 21.98 
 
 1.00 
 
 110 
 
 21.54 
 
 1.07 
 
 110 
 
 
 
 38 
 
 22.42 
 
 1.30 
 
 83 
 
 22.32 
 
 1.13 
 
 92 
 
 21.92 
 
 1.01 
 
 101 
 
 21.46 
 
 0.96 
 
 107 
 
 20.98 
 
 0.97 
 
 111 
 
 20.46 
 
 1.03 
 
 113 
 
 
 
 39 
 
 21.11 
 
 1.28 
 
 73 
 
 21.18 
 
 1.10 
 
 84 
 
 20.92 
 
 0.96 
 
 96 
 
 20.52 
 
 0.90 
 
 104 
 
 20.03 
 
 0.89 
 
 111 
 
 19.48 
 
 0.92 
 
 116 
 
 
 
 40 
 
 19.85 
 
 1.20 
 
 63 
 
 20.11 
 
 1.01 
 
 76 
 
 19.99 
 
 0.86 
 
 90 
 
 19.65 
 
 0.79 
 
 100 
 
 19.19 
 
 0.75 
 
 109 
 
 18.62 
 
 0.76 
 
 117 
 
 
 
 41 
 
 18.71 
 
 1.03 
 
 53 
 
 19.15 
 
 0.86 
 
 68 
 
 19.19 
 
 0.70 
 
 83 
 
 18.93 
 
 0.61 
 
 95 
 
 18.53 
 
 0.55 
 
 107 
 
 17.96 
 
 0.53 
 
 117 
 
 
 
 42 
 
 17.79 
 
 0.79 
 
 45 
 
 18.39 
 
 0.63 
 
 60 
 
 18.58 
 
 0.49 
 
 76 
 
 18.43 
 
 0.38 
 
 90 
 
 18.08 
 
 0.32 
 
 103 
 
 17.55 
 
 0.27 
 
 115 
 
 
 
 43 
 
 17.13 
 
 0.49 
 
 38 
 
 17.88 
 
 0.36 
 
 54 
 
 18.21 
 
 0.23 
 
 70 
 
 18.16 
 
 -0.13 
 
 84 
 
 17.89 
 
 0.06 
 
 99 
 
 17.42 
 
 +0.02 
 
 112 
 
 
 
 44 
 
 16.80 
 
 0.15 
 
 34 
 
 17.66 
 
 0.06 
 
 48 
 
 18.12 
 
 +0.06 
 
 65 
 
 18.17 
 
 +0.15 
 
 79 
 
 17.98 
 
 +0.24 
 
 94 
 
 17.59 
 
 0.32 
 
 108 
 
 
 
 45 
 
 16.83 
 
 +0.21 
 
 31 
 
 17.76 
 
 +0.26 
 
 45 
 
 18.32 
 
 0.35 
 
 60 
 
 18.46 
 
 0.43 
 
 73 
 
 18.37 
 
 0.53 
 
 88 
 
 18.06 
 
 0.62 
 
 103 
 
 
 
 46 
 
 17.21 
 
 0.55 
 
 31 
 
 18.18 
 
 0.56 
 
 42 
 
 18.81 
 
 0.62 
 
 56 
 
 19.03 
 
 0.69 
 
 68 
 
 19.03 
 
 0.79 
 
 83 
 
 18.83 
 
 0.89 
 
 97 
 
 
 
 47 
 
 17.92 
 
 0.85 
 
 33 
 
 18.88 
 
 0.82 
 
 42 
 
 19.55 
 
 0.85 
 
 53 
 
 19.84 
 
 0.91 | 
 
 64 
 
 19.94 
 
 1.00 
 
 77 
 
 19.85 
 
 1.10 
 
 91 
 
 
 
 48 
 
 18.91 
 
 1.10 
 
 37 
 
 19.82 
 
 .1.03 
 
 43 
 
 20.51 
 
 1.03 
 
 52 
 
 20.84 
 
 1.08 
 
 60 
 
 21.03 
 
 1.14 
 
 72 
 
 21.03 
 
 1.23 
 
 84 
 
 
 
 49 
 
 20.11 
 
 1.25 
 
 42 
 
 20.93 
 
 1.15 
 
 45 
 
 21.60 
 
 1.12 
 
 51 
 
 21.99 
 
 1.16 
 
 58 
 
 22.21 
 
 1.21 
 
 67 
 
 22.31 
 
 1.80 
 
 78 
 
 
 
 50 
 
 21.40 
 
 1.30 
 
 48 
 
 22.12 
 
 1.18 
 
 49 
 
 22.75 
 
 113 
 
 52 
 
 23.15 
 
 1.18 
 
 56 
 
 23.44 
 
 1.19 
 
 63 
 
 23.62 
 
 1.27 
 
 71 
 
 
 
 51 
 
 22.70 
 
 1.25 
 
 55 
 
 23.29 
 
 1.12 
 
 53 
 
 23.86 
 
 1.05 
 
 54 
 
 24.26 
 
 1.04 
 
 55 
 
 24.59 
 
 1.07 
 
 59 
 
 24.86 
 
 1.13 
 
 06 
 
 
 
 52 
 
 23.91 
 
 1.11 
 
 62 
 
 24.36 
 
 0.97 
 
 58 
 
 24.85 
 
 0.89 
 
 56 
 
 25.23 
 
 0.87 
 
 55 
 
 25.59 
 
 O.S9 
 
 57 
 
 25.92 
 
 0.94 
 
 61 
 
 
 
 53 
 
 24.93 
 
 0.89 
 
 69 
 
 25.24 
 
 0.76 
 
 62 
 
 25.65 
 
 0.67 
 
 58 
 
 26.01 
 
 0.65 
 
 55 
 
 26.37 
 
 0.65 
 
 55 
 
 26.75 
 
 0.68 
 
 57 
 
 
 
 54 
 
 25.90 
 
 0.61 
 
 75 
 
 25.88 
 
 0.49 
 
 66 
 
 26.20 
 
 0.41 
 
 61 
 
 26.53 
 
 0.48 
 
 56 
 
 26.89 
 
 0.37 
 
 54 
 
 27.29 
 
 0.38 
 
 55 
 
 
 
 55 
 
 26.16 
 
 +0.29 
 
 79 
 
 26.23 
 
 +0.20 
 
 70 
 
 26.47 
 
 +0.13 
 
 63 
 
 26.77 
 
 +0.09 
 
 57 
 
 27.11 
 
 +0.07 
 
 54 
 
 27.52 
 
 +0.08 
 
 53 
 
 
 
 56 
 
 26.29 
 
 -0.03 
 
 82 
 
 26.29 
 
 -0.10 
 
 72 
 
 26.46 
 
 -0.15 
 
 65 
 
 26.72 
 
 0.19 
 
 59 
 
 27.04 
 
 0.21 
 
 00 
 
 27.44 
 
 -0.21 
 
 52 
 
 
 
 57 
 
 26.11 
 
 0.84 
 
 83 
 
 26.04 
 
 0.38 
 
 73 
 
 26.17 
 
 0.42 
 
 66 
 
 26.40 
 
 0.44 
 
 60 
 
 26.70 
 
 0.47 
 
 56 
 
 27.10 
 
 0.49 
 
 53 
 
 
 
 58 
 
 25.32 
 
 0.62 
 
 82 
 
 25.53 
 
 0.63 i 
 
 74 
 
 25.63 
 
 0.64 
 
 67 
 
 25.85 
 
 0.65 
 
 61 
 
 26.11 
 
 0.68 
 
 57 
 
 26.48 
 
 0.67 
 
 54 
 
 
 
 59 
 
 24.87 
 
 0.85 
 
 79 
 
 24.78 
 
 0.82 
 
 72 
 
 24.89 
 
 0.82 
 
 67 
 
 25.10 
 
 0.83 
 
 62 
 
 25.34 
 
 0.85 
 
 58 
 
 25.66 
 
 0.88 
 
 56 
 
 
 
 60 
 
 23.92 
 
 -1.03 
 
 76 
 
 23.89 
 
 0.97 
 
 70 
 
 24.00 
 
 095 
 
 66 
 
 24.20 
 
 0.95 
 
 62 
 
 24.42 
 
 -0.96 
 
 59 
 
 24.72 : _ .99 
 
 58 
 
 
 
 i 
 
 
 
 NOTE. When T exceeds 88, subtract 88 from it, and add 46.98 to V 
 
TABLE X. 
 
 
 
 3$\&W_ 
 
 
 T 24 
 
 28 
 
 32 
 
 36 
 
 ^^^^% j V i 
 
 TO-^ . 
 
 li^-^44 
 
 
 V 
 
 tv 
 
 Diff. 
 
 r 
 
 tv 
 
 Diff. 
 
 r 
 
 tv 
 
 Diff 
 
 f 
 
 to 
 
 Diff. 
 
 r 
 
 to 
 
 Diff. 
 
 r 
 
 tv 
 
 Diff. 
 
 f 
 
 
 
 30 
 
 33.40 
 
 +0.91 
 
 95 
 
 32.59 
 
 +i'.03 
 
 111 
 
 30.77 
 
 +0-99 
 
 120 
 
 29.26 
 
 +0.88 
 
 124 
 
 2812 
 
 +0.77 
 
 122 
 
 27.40 
 
 +0.63 
 
 118 
 
 
 
 31 
 
 33.90 
 
 +0.06 
 
 92 
 
 32.97 
 
 +0.28 
 
 109 
 
 31.48 
 
 +0.39 
 
 121 
 
 29.92 
 
 +0.40 
 
 126 
 
 28.71 
 
 +0.38 
 
 125 
 
 27.90 
 
 +0.32 
 
 122 
 
 
 
 32 
 
 33.52 
 
 0.82 
 
 87 
 
 32.85 
 
 0.50 
 
 105 
 
 31.55 
 
 0.27 
 
 117 
 
 30.07 
 
 0.12 
 
 124 
 
 28.88 
 
 0.05 
 
 124 
 
 28.05 
 
 -0.04 
 
 122 
 
 
 
 33 
 
 32.27 
 
 1.67 
 
 80 
 
 31.97 
 
 1.26 
 
 97 
 
 30.95 
 
 0.90 
 
 111 
 
 29.69 
 
 0.64 
 
 118 
 
 28.62 
 
 0.48 
 
 121 
 
 27.83 
 
 0.40 
 
 120 
 
 
 
 34 
 
 30.18 
 
 2.44 
 
 71 
 
 30.34 
 
 1.96 
 
 88 
 
 29.75 
 
 1.49 
 
 101 
 
 28.80 
 
 1.14 
 
 109 
 
 27.93 
 
 0.89 
 
 113 
 
 27.26 
 
 0.74 
 
 115 
 
 
 
 35 
 
 27.39 
 
 3.08 
 
 62 
 
 28.05 
 
 2.56 
 
 75 
 
 27.97 
 
 2.02 
 
 88 
 
 27.42 
 
 1.58 
 
 97 
 
 26.85 
 
 1.25 
 
 103 
 
 26.35 
 
 1.05 
 
 107 
 
 
 
 36 
 
 24.03 
 
 3.54 
 
 53 
 
 25.22 
 
 3.02 
 
 64 
 
 25.71 
 
 2.44 
 
 74 
 
 25.65 
 
 1.92 
 
 83 
 
 25.44 
 
 1.54 
 
 91 
 
 25.17 
 
 1.29 
 
 97 
 
 
 
 37 
 
 20.32 
 
 3.80 
 
 45 
 
 22.02 
 
 3.29 
 
 51 
 
 23.10 
 
 2.71 
 
 59 
 
 23.59 
 
 2.16 
 
 68 
 
 23.78 
 
 1.74 
 
 77 
 
 23.78 
 
 1.46 
 
 85 
 
 
 
 38 
 
 16.43 
 
 3.84 
 
 37 
 
 18.64 
 
 3.40 
 
 39 
 
 20.30 
 
 2.83 
 
 44 
 
 21 33 
 
 2.28 
 
 53 
 
 21.96 
 
 1.84 
 
 63 
 
 22.26 
 
 1.64 
 
 73 
 
 
 
 39 
 
 12.64 
 
 3.64 
 
 31 
 
 15.23 
 
 3.29 
 
 28 
 
 17.45 
 
 2.77 
 
 31 
 
 19.03 
 
 2.25 
 
 38 
 
 20.10 
 
 1.83 
 
 49 
 
 20.70 
 
 1.53 
 
 61 
 
 
 
 40 
 
 9.14 
 
 3.25 
 
 27 
 
 12.05 
 
 2.97 
 
 19 
 
 14.75 
 
 2.55 
 
 19 
 
 16.82 
 
 2.09 
 
 25 
 
 18.29 
 
 1.72 
 
 36 
 
 19.19 
 
 1.43 
 
 49 
 
 
 
 41 
 
 6.16 
 
 2.62 
 
 25 
 
 9.28 
 
 2.48 
 
 13 
 
 12.35 
 
 2.22 
 
 9 
 
 14.84 
 
 1.80 
 
 14 
 
 16.66 
 
 1.49 
 
 25 
 
 17.83 
 
 1.24 
 
 38 
 
 
 
 42 
 
 3.89 
 
 1.84 
 
 25 
 
 7.08 
 
 1.84 
 
 10 
 
 10.40 
 
 1.66 
 
 4 
 
 13.21 
 
 1.40 
 
 7 
 
 15.31 
 
 1.16 
 
 16 
 
 16.71 
 
 0.96 
 
 30 
 
 
 
 43 
 
 2.47 
 
 0.95 
 
 28 
 
 5.60 
 
 1.07 
 
 10 
 
 9.02 
 
 1.04 
 
 1 
 
 12.04 
 
 0.90 
 
 2 
 
 14.33 
 
 0.76 
 
 11 
 
 15.91 
 
 061 
 
 24 
 
 
 
 44 
 
 1.99 
 
 +0.01 
 
 33 
 
 4.93 
 
 -0.24 
 
 13 
 
 8.32 
 
 0.35 
 
 2 
 
 11.40 
 
 0.34 
 
 2 
 
 13.80 
 
 0.29 
 
 8 
 
 15.48 
 
 -0.22 
 
 20 
 
 
 
 45 
 
 2.49 
 
 0.98 
 
 41 
 
 5.12 
 
 +0.62 
 
 20 
 
 8.32 
 
 +0.37 
 
 8 
 
 11.35 
 
 +0.25 
 
 4 
 
 13.75 
 
 +0.19 
 
 9 
 
 15.46 
 
 +0.19 
 
 19 
 
 
 
 46 
 
 3.95 
 
 1.88 
 
 49 
 
 6.16 
 
 1.43 
 
 Z9 
 
 9.05 
 
 1.06 
 
 16 
 
 11.89 
 
 0.81 
 
 12 
 
 14.18 
 
 0.46 
 
 12 
 
 15.86 
 
 0.60 
 
 21 
 
 
 
 47 
 
 6.25 
 
 2.65 
 
 59 
 
 7.97 
 
 2.13 
 
 40 
 
 10.43 
 
 1.66 
 
 27 
 
 12.97 
 
 1.32 
 
 22 
 
 15.06 
 
 1.08 
 
 21 
 
 16.65 
 
 0.95 
 
 26 
 
 
 
 48 
 
 9.25 
 
 3.28 
 
 69 
 
 10.42 
 
 2.tj8 
 
 53 
 
 12.37 
 
 2.15 
 
 40 
 
 14.52 
 
 1.72 
 
 33 
 
 16.33 
 
 1.42 
 
 31 
 
 17.75 
 
 1.23 
 
 32 
 
 
 
 49 
 
 12.73 
 
 3.62 
 
 80 
 
 13.33 
 
 3.04 
 
 67 
 
 14.72 
 
 2.47 
 
 55 
 
 16.41 
 
 2.00 
 
 47 
 
 17.89 
 
 1.65 
 
 42 
 
 19.11 
 
 1.42 
 
 41 
 
 
 
 50 
 
 16.48 
 
 3.74 
 
 91 
 
 16.50 
 
 3.20 
 
 79 
 
 17.30 
 
 2.62 
 
 70 
 
 18.51 
 
 2.12 
 
 61 
 
 19.62 
 
 1.75 
 
 54 
 
 20.59 
 
 1.49 
 
 50 
 
 
 
 51 
 
 20.22 
 
 3.62 
 
 100 
 
 19.73 
 
 3.13 
 
 93 
 
 19.95 
 
 2.58 
 
 84 
 
 20.65 
 
 2.09 
 
 75 
 
 21.38 
 
 1.71 
 
 67 
 
 22.09 
 
 1.45 
 
 60 
 
 
 
 52 
 
 23.73 
 
 3.28 
 
 107 
 
 22.77 
 
 2.86 
 
 104 
 
 22.46 
 
 2.36 
 
 97 
 
 22.69 
 
 1.91 
 
 88 
 
 23.04 
 
 1.66 
 
 78 
 
 23.49 
 
 1.30 
 
 69 
 
 
 
 53 
 
 26.79 
 
 2.74 
 
 114 
 
 25.46 
 
 2.41 
 
 114 
 
 24.68 
 
 2.00 
 
 108 
 
 24.48 
 
 1,60 
 
 99 
 
 24.50 
 
 1.29 
 
 88 
 
 24.70 
 
 1.07 
 
 78 
 
 
 
 54 
 
 29.22 
 
 2.05 
 
 118 
 
 27.60 
 
 1.82 
 
 120 
 
 26.46 
 
 1.51 
 
 115 
 
 25.90 
 
 1.20 
 
 107 
 
 25.63 
 
 0.95 
 
 96 
 
 25.63 
 
 0.76 
 
 85 
 
 
 
 55 
 
 30.89 
 
 1 26 
 
 120 
 
 29.10 
 
 1.16 
 
 123 
 
 27.71 
 
 0.95 
 
 121 
 
 26.88 
 
 +0.73 
 
 113 
 
 26.40 
 
 0.55 
 
 103 
 
 26.22 
 
 0.41 
 
 90 
 
 
 
 56 
 
 31.75 
 
 +0.45 
 
 120 
 
 29.90 
 
 +0.43 
 
 125 
 
 28.36 
 
 +0.35 
 
 123 
 
 27.37 
 
 0.24 
 
 115 
 
 26.74 
 
 +0.13 
 
 106 
 
 26.45 
 
 +0.04 
 
 93 
 
 
 
 57 
 
 31.79 
 
 0.36 
 
 111 
 
 29.97 
 
 0.27 
 
 123 
 
 28.41 
 
 0.24 
 
 122 
 
 27.36 
 
 0.26 
 
 115 
 
 26.66 
 
 0.28 
 
 106 
 
 26.31 
 
 0.32 
 
 93 
 
 
 
 58 
 
 31.05 
 
 1.07 
 
 116 
 
 2936 
 
 0.91 
 
 1 L'O 
 
 27.88 
 
 0.79 
 
 118 
 
 26.86 
 
 0.71 
 
 111 
 
 26.19 
 
 0.65 
 
 103 
 
 25.82 
 
 0.64 
 
 92 
 
 
 
 59 
 
 29.66 
 
 1.66 
 
 112 
 
 28.15 
 
 1.45 
 
 114 
 
 26.84 
 
 1.24 
 
 112 
 
 25.95 
 
 1.08 
 
 105 
 
 25.36 
 
 0.87 
 
 97 
 
 25.03 
 
 0.90 
 
 88 
 
 
 
 60 
 
 27.74 
 
 2.00 
 
 108 
 
 2(1.17 
 
 1.85 
 
 108 
 
 -'.-..in 
 
 1.59 
 
 mi 
 
 24.70 
 
 -1.38 
 
 97 
 
 24.25 
 
 1.21 
 
 90 
 
 24.02 
 
 1.11 
 
 82 
 
 
 
 T 72 
 
 76 
 
 80 
 
 84 
 
 88 
 
 92 
 
 
 
 V 
 
 tv 
 
 Diff. 
 
 r 
 
 tv 
 
 Diff. 
 
 f 
 
 tv 
 
 Diff. 
 
 r 
 
 tv 
 
 Diff. 
 
 r 
 
 tv 
 
 Diff. 
 
 
 tv 
 
 Diff. 
 
 f 
 
 
 
 30 
 
 26.28 
 
 +0.08 
 
 66 
 
 26.78 
 
 +0.05 
 
 53 
 
 27.54 
 
 +0.05 
 
 40 
 
 28.63 
 
 +0.08 
 
 26 
 
 30.16 
 
 +0.15 
 
 14 
 
 32.26 +0.30 
 
 8 
 
 
 
 31 
 
 26.23 
 
 0.20 
 
 69 
 
 26.68 
 
 0.26 
 
 55 
 
 27.42 
 
 0.31 
 
 40 
 
 28.51 
 
 0.33 
 
 16 
 
 30.07 
 
 -0.34 
 
 20 
 
 32.27 
 
 -0.30 
 
 2 
 
 
 
 32 
 
 25.89 
 
 0.48 
 
 73 
 
 26.26 
 
 0.67 
 
 59 
 
 26.93 
 
 0.67 
 
 42 
 
 27.97 
 
 0.74 
 
 17 
 
 29.48 
 
 0.84 
 
 19 
 
 31.66 
 
 0.92 
 
 1 
 
 
 
 33 
 
 25.28 
 
 0.72 
 
 79 
 
 25.55 
 
 0.85 
 
 64 
 
 26.09 
 
 0.99 
 
 48 
 
 27.02 
 
 1.13 
 
 30 
 
 28.40 
 
 1.30 
 
 12 
 
 30.46 
 
 1.48 
 
 
 
 
 
 34 
 
 24.45 
 
 0.93 
 
 85 
 
 24.57 
 
 1.08 
 
 71 
 
 24.95 
 
 1.25 
 
 55 
 
 25.71 
 
 1.46 
 
 37 
 
 26.89 
 
 1.69 
 
 19 
 
 28.71 
 
 1.97 
 
 5 
 
 
 
 35 
 
 23.42 
 
 1.09 
 
 92 
 
 23.39 
 
 1.25 
 
 79 
 
 2359 
 
 1.45 
 
 65 
 
 24.11 
 
 1.74 
 
 47 
 
 25.03 
 
 2.00 
 
 29 
 
 26.52 
 
 2.36 
 
 12 
 
 
 
 36 
 
 22.28 
 
 1.17 
 
 99 
 
 22.08 
 
 1.34 
 
 89 
 
 22.05 
 
 1.57 
 
 76 
 
 22.32 
 
 1.83 
 
 60 
 
 22.90 
 
 2.18 
 
 42 
 
 24.00 
 
 2.62 
 
 24 
 
 
 
 37 
 
 21.09 
 
 1.17 
 
 106 
 
 20.72 
 
 1.34 
 
 98 
 
 20.46 
 
 1.67 
 
 87 
 
 20.45 
 
 1.86 
 
 74 
 
 20.67 
 
 2.23 
 
 54 
 
 21.28 
 
 2.73 
 
 39 
 
 
 
 38 
 
 19.93 
 
 1.11 
 
 112 
 
 19.39 
 
 1.27 
 
 107 
 
 18.91 
 
 1.48 
 
 100 
 
 18.60 
 
 1.78 
 
 88 
 
 18.44 
 
 2.16 
 
 74 
 
 18.54 
 
 2.67 
 
 56 
 
 
 
 39 
 
 18.86 
 
 0.99 
 
 118 
 
 18.17 
 
 1.12 
 
 116 
 
 17.49 
 
 1.31 
 
 111 
 
 16.88 
 
 1.59 
 
 103 
 
 16.35 
 
 1.96 
 
 90 
 
 15.94 
 
 2.47 
 
 73 
 
 
 
 40 
 
 17.94 
 
 0.80 
 
 122 
 
 17.14 
 
 0.89 
 
 123 
 
 16.28 
 
 1.06 
 
 122 
 
 15.41 
 
 1.30 
 
 117 
 
 14.51 
 
 1.64 
 
 107 
 
 13.61 
 
 2.12 
 
 91 
 
 
 
 41 
 
 1 7.25 
 
 0.55 
 
 124 
 
 16.38 
 
 0.61 
 
 129 
 
 15.36 
 
 0.74 
 
 131 
 
 14.27 
 
 0.94 
 
 129 
 
 13.06 
 
 1.22 
 
 122 
 
 11.70 
 
 1.64 
 
 107 
 
 
 
 42 
 
 16.83 
 
 0.26 
 
 126 
 
 15.92 
 
 0.28 
 
 133 
 
 14.80 
 
 -0.35 
 
 138 
 
 13.53 
 
 0.50 
 
 139 
 
 12.06 
 
 0.73 
 
 135 
 
 10.33 
 
 1.06 
 
 122 
 
 
 
 43 
 
 16.73 
 
 +0.07 
 
 125 
 
 15.81 
 
 +008 
 
 135 
 
 14.65 
 
 +0.06 
 
 143 
 
 13.26 
 
 0.02 
 
 147 
 
 11.60 
 
 -0.17 
 
 145 
 
 9.59 
 
 0.42 
 
 135 
 
 
 
 44 
 
 16.96 
 
 0.40 
 
 122 
 
 16.08 
 
 0.45 
 
 134 
 
 14.91 
 
 0.48 
 
 144 
 
 13.48 
 
 +0.46 
 
 151 
 
 11.71 
 
 +0.40 
 
 152 
 
 9.50 
 
 +0.25 
 
 144 
 
 
 
 45 
 
 17.52 
 
 0.72 
 
 118 
 
 16.71 
 
 081 
 
 131 
 
 15.60 
 
 0.89 
 
 143 
 
 14.18 
 
 0.93 
 
 152 
 
 12.39 
 
 0.95 
 
 155 
 
 10.10 
 
 0.92 
 
 149 
 
 
 
 46 
 
 18.39 
 
 1.00 
 
 112 
 
 17.69 
 
 1.13' 
 
 126 
 
 16.68 
 
 1.25 
 
 139. 
 
 15.33 
 
 1.35 
 
 149 
 
 13.60 
 
 1.44 
 
 154 
 
 11.34 
 
 1.52 
 
 152 
 
 
 
 47 
 
 19.52 
 
 1.22 
 
 105 
 
 18.96 
 
 1.37 
 
 119 
 
 18.09 
 
 1.53 
 
 132 
 
 16.87 
 
 1.68 
 
 144 
 
 15.27 
 
 2.84 
 
 150 
 
 13.14 
 
 2.02 
 
 150 
 
 
 
 48 
 
 20.83 
 
 1.37 
 
 98 
 
 20.43 
 
 1.53 
 
 111 
 
 19.73 
 
 1.71 
 
 124 
 
 18.69 
 
 1 90 
 
 135 
 
 17.28 
 
 2.13 
 
 143 
 
 15.38 
 
 2.38 
 
 145 
 
 
 
 49 
 
 22.26 
 
 1.43 
 
 89 
 
 22.01 
 
 1.59 
 
 101 
 
 21.50 
 
 1.78 
 
 114 
 
 20.67 
 
 2.00 
 
 125 
 
 19.52 
 
 226 
 
 134 
 
 17.90 
 
 2.58 
 
 137 
 
 
 
 50 
 
 23.69 
 
 1.39 
 
 80 
 
 23.61 
 
 1.54 
 
 92 
 
 23.29 
 
 1.73 
 
 103 
 
 22.69 
 
 1.97 
 
 114 
 
 21.80 
 
 2.25 
 
 122 
 
 20.54 
 
 2.61 
 
 127 
 
 
 
 51 
 
 25.04 
 
 1.25 
 
 74 
 
 25.10 
 
 1.38 
 
 82 
 
 24.97 
 
 1.58 
 
 92 
 
 24.61 
 
 1.81 
 
 101 
 
 24.03 
 
 2.10 
 
 110 
 
 23.11 
 
 2.46 
 
 115 
 
 
 
 52 
 
 26.20 
 
 1.03 
 
 67 
 
 26.38 
 
 1.15 
 
 73 
 
 26.45 
 
 1.31 
 
 81 
 
 26.31 
 
 1.53 
 
 89 
 
 26.01 
 
 1.80 
 
 97 
 
 25.46 
 
 2.16 
 
 103 
 
 
 
 53 
 
 27.10 
 
 0.74 
 
 61 
 
 27.40 
 
 0.84 
 
 66 
 
 27.59 
 
 0.96 
 
 71 
 
 27.67 
 
 1.16 
 
 78 
 
 27.64 
 
 1.40 
 
 85 
 
 27.43 
 
 1.72 
 
 92 
 
 
 
 54 
 
 27.69 
 
 0.42 
 
 56 
 
 28.07 
 
 0.49 
 
 59 
 
 28.38 
 
 0.58 
 
 63 
 
 28.62 
 
 0.73 
 
 68 
 
 28.81 
 
 0.92 
 
 75 
 
 28.89 
 
 1.18 
 
 81 
 
 
 
 55 
 
 27.95 
 
 +0.23 
 
 53 
 
 28.38 
 
 +0.12 
 
 54 
 
 28.76 
 
 +0.17 
 
 57 
 
 29.13 
 
 +0.27 
 
 61 
 
 29.48 
 
 0.41 
 
 66 
 
 29.78 
 
 +1.59 
 
 73 
 
 
 
 56 
 
 27.88 
 
 0.23 
 
 51 
 
 28.32 
 
 0.23 
 
 52 
 
 28.72 
 
 0.22 
 
 53 
 
 29.17 
 
 -0.18 
 
 56 
 
 29.63 
 
 +0.10 
 
 60 
 
 30.07 
 
 -0.00 
 
 67 
 
 
 
 57 
 
 27.50 
 
 0.51 
 
 51 
 
 27.92 
 
 0.55 
 
 50 
 
 28.32 
 
 0.57 
 
 51 
 
 28.78 
 
 0.58 
 
 53 
 
 29.28 
 
 0.57 
 
 57 
 
 29.79 
 
 0.54 
 
 64 
 
 
 
 58 
 
 26.86 
 
 0.76 
 
 52 
 
 27.22 
 
 0.81 
 
 51 
 
 27.59 
 
 0.87 
 
 51 
 
 28.02 
 
 0.92 
 
 53 
 
 28.50 
 
 097 
 
 57 
 
 28.98 
 
 1.04 
 
 63 
 
 
 
 59 
 
 25.99 
 
 0.94 
 
 54 
 
 26.31 
 
 1.00 
 
 53 
 
 26.59 
 
 1.09 
 
 54 
 
 26.95 
 
 1.18 
 
 55 
 
 27.34 
 
 1.29 
 
 59 
 
 27.71 
 
 1.43 
 
 66 
 
 
 
 CO 
 
 24.99 
 
 1.04 
 
 57 
 
 25.23 
 
 1.12 
 
 57 
 
 25.42 
 
 1.22 
 
 57 
 
 25.67 
 
 -1.84 
 
 60 
 
 25.93 
 
 1.49 
 
 64 
 
 26.13 -1.67 
 
 71 
 
 
 
 NOTE. When T exceeds 88, subtract 88 from it, and add 46.98 to V. 
 
24 
 
 TABLE X. 
 
 
 
 
 T 
 
 4 
 
 8 
 
 12 
 
 16 
 
 20 
 
 
 V 
 
 to 
 
 Diff. 
 
 r 
 
 6v 
 
 Diff. 
 
 r 
 
 <5 
 
 Diff. 
 
 r 
 
 <5 
 
 Diff. 
 
 f 
 
 <Sy 
 
 Diff. 
 
 r 
 
 6 
 
 1 Diff. 
 
 r 
 
 
 
 60 
 
 28 43 
 
 -1.62 
 
 65 
 
 29.09 
 
 1'.79 
 
 71 
 
 29.68 
 
 2.01 
 
 79 
 
 29.91 
 
 2.19 
 
 88 
 
 29.68 
 
 -2.30 
 
 98 
 
 28.89 
 
 2.27 
 
 105 
 
 
 
 61 
 
 2C.77 
 
 1.65 
 
 74 
 
 27.22 
 
 1.88 
 
 80 
 
 27.57 
 
 2.13 
 
 87 
 
 27.60 
 
 2.34 
 
 95 
 
 27.23 
 
 2.50 
 
 101 
 
 26.45 
 
 2.50 
 
 104 
 
 
 
 62 
 
 25.12 
 
 1.60 
 
 84 
 
 25.34 
 
 1.82 
 
 89 
 
 25.43 
 
 2.07 
 
 96 
 
 25.23 
 
 2.30 
 
 101 
 
 24.69 
 
 2.48 
 
 104 
 
 23.89 
 
 2.51 
 
 104 
 
 
 
 63 
 
 23.57 
 
 1.43 
 
 92 
 
 23.58 
 
 1.63 
 
 99 
 
 23.43 
 
 2.86 
 
 104 
 
 22.99 
 
 2.08 
 
 108 
 
 22.26 
 
 2.27 
 
 108 
 
 21.42 
 
 2.32 
 
 104 
 
 
 
 64 
 
 22.25 
 
 1.16 
 
 100 
 
 22.08 
 
 1.32 
 
 106 
 
 21.70 
 
 1.52 
 
 112 
 
 21.06 
 
 1.75 
 
 114 
 
 20.14 
 
 1.87 
 
 112 
 
 19.23 
 
 1.95 
 
 105 
 
 
 ! 65 
 
 21.24 
 
 0.82 
 
 105 
 
 20.94 
 
 0.92 
 
 112 
 
 19.39 
 
 1.05 
 
 118 
 
 19.58 
 
 1.18 
 
 119 
 
 18.53 
 
 1.30 
 
 115 
 
 17.52 
 
 1.39 
 
 106 
 
 
 66 
 
 20.61 
 
 0.42 
 
 108 
 
 20.23 
 
 0.46 
 
 116 
 
 19.60 
 
 0.50 
 
 121 
 
 18.70 
 
 0.60 
 
 1-2'-' 
 
 17.53 
 
 0.63 
 
 118 
 
 16.44 
 
 -0.71 
 
 107 
 
 
 
 67 
 
 20.39 
 
 0.02 
 
 108 
 
 20.02 
 
 +0.04 
 
 116 
 
 19.38 
 
 +0.08 
 
 122 
 
 18.47 
 
 +0.13 
 
 ] -23 
 
 17.26 
 
 +0.12 
 
 119 
 
 16.10 
 
 +0.07 
 
 109 
 
 
 
 68 
 
 20.60 
 
 +0.41 
 
 105 
 
 20.31 
 
 0.54 
 
 113 
 
 19.75 
 
 0.67 
 
 120 
 
 18.96 
 
 0.77 
 
 122 
 
 17.77 
 
 0.90 
 
 119 
 
 16.57 
 
 0.88 
 
 110 
 
 
 
 69 
 
 21.23 
 
 0.81 
 
 100 
 
 21.09 
 
 0.99 
 
 107 
 
 20.72 
 
 1.22 
 
 114 
 
 20.10 
 
 1.45 
 
 118 
 
 19.05 
 
 1.63 
 
 117 
 
 17.85 
 
 1.66 
 
 111 
 
 
 
 70 
 
 22.21 
 
 1.12 
 
 91 
 
 22.29 
 
 1.37 
 
 98 
 
 22.19 
 
 1.68 
 
 105 
 
 21.86 
 
 2.01 
 
 111 
 
 21.02 
 
 2.27 
 
 113 
 
 19.88 
 
 2.35 
 
 111 
 
 
 
 71 
 
 23.46 
 
 134 
 
 81 
 
 23.83 
 
 1.65 
 
 87 
 
 24.07 
 
 2.01 
 
 94 
 
 24.11 
 
 2.42 
 
 102 
 
 23.58 
 
 2.76 
 
 107 
 
 22.55 
 
 2.91 
 
 110 
 
 
 
 72 
 
 24.89 
 
 1.46 
 
 69 
 
 25.58 
 
 1.78 
 
 74 
 
 26.21 
 
 2.19 
 
 81 
 
 26.70 
 
 2.65 
 
 91 
 
 26.53 
 
 3.05 
 
 100 
 
 25.69 
 
 3.27 
 
 108 
 
 
 
 73 
 
 26.37 
 
 1.42 
 
 56 
 
 27.39 
 
 1.75 
 
 59 
 
 28.44 
 
 2.18 
 
 67 
 
 29.40 
 
 2.66 
 
 78 
 
 29.67 
 
 3.12 
 
 92 
 
 29.08 
 
 3.40 
 
 105 
 
 
 
 74 
 
 27.74 
 
 1.27 
 
 43 
 
 29.09 
 
 1.68 
 
 44 
 
 30.57 
 
 1.99 
 
 51 
 
 32.03 
 
 2.48 
 
 64 
 
 32.78 
 
 2.96 
 
 82 
 
 32.48 
 
 3.28 
 
 100 
 
 
 
 75 
 
 28.91 
 
 1.00 
 
 31 
 
 30.56 
 
 1.26 
 
 31 
 
 32.42 
 
 1.63 
 
 37 
 
 34.36 
 
 2.08 
 
 50 
 
 35.60 
 
 2.57 
 
 71 
 
 35.65 
 
 2.93 
 
 94 
 
 
 
 76 
 
 29.74 
 
 0.61 
 
 22 
 
 31.62 
 
 0.81 
 
 18 
 
 33.83 
 
 0.91 
 
 23 
 
 36.20 
 
 1.51 
 
 37 
 
 37.92 
 
 1.96 
 
 60 
 
 38.35 
 
 2.36 
 
 87 
 
 
 
 77 
 
 30.14 
 
 +0.15 
 
 14 
 
 32.19 
 
 +0.08 
 
 8 
 
 34.64 
 
 +0.47 
 
 11 
 
 37.38 
 
 +0.79 
 
 25 
 
 39.53 
 
 1.19 
 
 49 
 
 40.37 
 
 1.59 
 
 79 
 
 
 
 78 
 
 30.05 
 
 0.34 
 
 10 
 
 32.18 
 
 0.32 
 
 2 
 
 34.77 
 
 -0.23 
 
 3 
 
 37.78 
 
 0.03 
 
 15 
 
 40.30 
 
 +0.30 
 
 39 
 
 41.54 
 
 +0.70 
 
 70 
 
 
 
 79 
 
 29.46 
 
 0.83 
 
 10 
 
 31.56 
 
 0.92 
 
 1 
 
 34.18 
 
 0.95 
 
 3 
 
 37.33 
 
 0.88 
 
 7 
 
 40.14 
 
 0.64 
 
 30 
 
 41.77 
 
 0.28 
 
 61 
 
 
 
 80 
 
 28.39 
 
 1.29 
 
 13 
 
 30.35 
 
 1.48 
 
 
 
 32.87 
 
 1.64 
 
 5 
 
 36.02 
 
 1.70 
 
 3 
 
 39.02 
 
 1.58 
 
 22 
 
 40.99 
 
 1.27 
 
 52 
 
 
 
 81 
 
 26.88 
 
 1.69 
 
 19 
 
 28.60 
 
 1.97 
 
 5 
 
 30.90 
 
 2.26 
 
 3 
 
 33.93 
 
 2.44 
 
 1 
 
 36.98 
 
 2.44 
 
 17 
 
 39.24 
 
 2.19 
 
 43 
 
 
 
 82 
 
 25.01 
 
 1.99 
 
 29 
 
 26.41 
 
 2.35 
 
 13 
 
 28.36 
 
 2.76 
 
 3 
 
 31.14 
 
 3.07 
 
 3 
 
 34.14 
 
 3.18 
 
 13 
 
 36.61 
 
 3.06 
 
 35 
 
 
 
 83 
 
 22.91 
 
 2.17 
 
 42 
 
 23.90 
 
 2.61 
 
 25 
 
 25.40 
 
 3.09 
 
 13 
 
 27.80 
 
 3.53 
 
 7 
 
 30.62 
 
 3.76 
 
 12 
 
 33.22 
 
 3.67 
 
 27 
 
 
 
 84 
 
 20.67 
 
 2.23 
 
 57 
 
 21.20 
 
 2.71 
 
 40 
 
 22.18 
 
 3.26 
 
 25 
 
 24.09 
 
 3.78 
 
 15 
 
 26.63 
 
 4.13 
 
 14 
 
 29.28 
 
 4.11 
 
 22 
 
 
 
 85 
 
 18.45 
 
 2.15 
 
 74 
 
 18.48 
 
 2.65 
 
 57 
 
 18.89 
 
 3.23 
 
 39 
 
 20.24 
 
 3.81 
 
 25 
 
 22.40 
 
 4.24 
 
 .17 
 
 25.00 
 
 433 
 
 18 
 
 
 
 86 
 
 16.36 
 
 1.96 
 
 90 
 
 15.89 
 
 2.44 
 
 74 
 
 15.71 
 
 3.03 
 
 56 
 
 16.46 
 
 8.65 
 
 37 
 
 18.16 
 
 4.14 
 
 23 
 
 20.63 
 
 4.29 
 
 16 
 
 
 
 87 
 
 14.53 
 
 1.64 
 
 107 
 
 13.59 
 
 2.09 
 
 92 
 
 12.83 
 
 264 
 
 72 
 
 12.94 
 
 3.27 
 
 50 
 
 14.15 
 
 3.78 
 
 30 
 
 16.41 
 
 4.03 
 
 16 
 
 
 
 88 
 
 13.08 
 
 1.23 
 
 122 
 
 11.71 
 
 1.61 
 
 108 
 
 10.42 
 
 2.11 
 
 89 
 
 9.92 
 
 2.68 
 
 64 
 
 10.60 
 
 3.22 
 
 39 
 
 12.57 
 
 3.53 
 
 19 
 
 
 
 89 
 
 12.09 
 
 0.72 
 
 135 
 
 10.36 
 
 1.03 
 
 123 
 
 8.fil 
 
 1.44 
 
 104 
 
 7.57 
 
 1.96 
 
 78 
 
 7.71 
 
 2.48 
 
 49 
 
 9.34 
 
 2.84 
 
 23 
 
 
 
 90 
 
 11.64 
 
 -0.17 
 
 145 
 
 9.64 
 
 039 
 
 136 
 
 7.53 
 
 0.70 
 
 117 
 
 :>.!)!) 
 
 1.14 
 
 90 
 
 5.63 
 
 1.61 
 
 59 
 
 6.89 
 
 1.94 
 
 29 
 
 
 
 T 48 
 
 52 
 
 56 
 
 60 
 
 64 
 
 68 
 
 
 
 V 
 
 to 
 
 Diff. 
 
 f 
 
 dv Diff. 
 
 f 
 
 iv 
 
 Diff. 
 
 f 
 
 6v 
 
 Diff. 
 
 r 
 
 So 
 
 Diff. 
 
 r 
 
 fv Diff. 
 
 r 
 
 
 
 60 
 
 23.92 
 
 i'.oa 
 
 76 
 
 23.89 
 
 0.97 
 
 70 
 
 24.00 
 
 6'.95 
 
 66 
 
 24.40 
 
 0.91 
 
 62 
 
 24.42 
 
 0.96 
 
 59 
 
 24.72 
 
 6.99 
 
 58 
 
 
 
 61 
 
 22.82 
 
 1.13 
 
 71 
 
 22.85 
 
 1.07 
 
 67 
 
 23.00 
 
 1.03 
 
 64 
 
 23.41 
 
 1.00 
 
 62 
 
 23.43 
 
 1.00 
 
 60 
 
 23.69 
 
 1.04 
 
 60 
 
 
 
 62 
 
 21.65 
 
 1.18 
 
 66 
 
 21.76 
 
 1.09 
 
 64 
 
 21.95 
 
 1.04 
 
 62 
 
 22.20 
 
 1.00 
 
 61 
 
 22.41 
 
 1.00 
 
 61 
 
 22.65 
 
 1.02 
 
 61 
 
 
 
 63 
 
 20.47 
 
 1.14 
 
 61 
 
 20.67 
 
 1.06 
 
 60 
 
 20.92 
 
 0.99 
 
 59 
 
 21.20 
 
 0.96 
 
 60 
 
 21.41 
 
 0.95 
 
 61 
 
 21.64 
 
 0.97 
 
 63 
 
 
 
 64 
 
 19.36 
 
 1.04 
 
 56 
 
 19.64 
 
 0.96 
 
 56 
 
 19.96 
 
 0.90 
 
 57 
 
 20.27 
 
 0.86 
 
 59 
 
 20.50 
 
 0.84 
 
 61 
 
 20.71 
 
 0.85 
 
 64 
 
 
 
 65 
 
 18.38 
 
 0.87 
 
 52 
 
 18.75 
 
 0.81 
 
 53 
 
 19.12 
 
 0.75 
 
 54 
 
 19.47 
 
 0.71 
 
 57 
 
 19.72 
 
 0.69 
 
 60 
 
 19.94 
 
 0.67 
 
 64 
 
 
 
 66 
 
 17.62 
 
 0.62 
 
 50 
 
 18.04 
 
 0.60 
 
 51 
 
 18.46 
 
 0.54 
 
 53 
 
 18.85 
 
 0.51 
 
 56 
 
 19.12 
 
 0.49 
 
 60 
 
 19.36 
 
 0.47 
 
 64 
 
 
 
 67 
 
 17.13 
 
 0.32 
 
 50 
 
 17.57 
 
 -0.31 
 
 50 
 
 18.03 
 
 0.29 
 
 51 
 
 18.44 
 
 0,27 
 
 55 
 
 18.74 
 
 0.25 
 
 58 
 
 19.00 
 
 0.23 
 
 63 
 
 
 
 68 
 
 16,97 
 
 +0.02 
 
 51 
 
 17.41 
 
 0.00 
 
 51 
 
 17.88 
 
 0.01 
 
 51 
 
 18.30 
 
 +0.00 
 
 54 
 
 18.62 
 
 +0.01 
 
 57 
 
 18.90 t+o.OS 
 
 62 
 
 
 
 69 
 
 17.16 
 
 0.38 
 
 55 
 
 17.57 
 
 +0.32 
 
 53 
 
 18.01 
 
 +0.29 
 
 52 
 
 18.43 
 
 0.28 
 
 54 
 
 18.76 
 
 0.29 
 
 56 
 
 19.07 
 
 0.32 
 
 60 
 
 
 
 70 
 
 17.72 
 
 0.74 
 
 61 
 
 18.05 
 
 0.64 
 
 57 
 
 18.45 
 
 0.59 
 
 54 
 
 18.85 
 
 0.55 
 
 54 
 
 19.19 
 
 0.56 
 
 55 
 
 19.53 
 
 0.59 
 
 58 
 
 
 
 71 
 
 18.63 
 
 1.06 
 
 68 
 
 18.85 
 
 0.94 
 
 63 
 
 19.18 
 
 0.86 
 
 58 
 
 19.53 
 
 0.81 
 
 56 
 
 19.87 
 
 0.80 
 
 55 
 
 20.24 
 
 0.81 
 
 56 
 
 
 
 72 
 
 19.85 
 
 1.34 
 
 77 
 
 19.93 
 
 1.19 
 
 70 
 
 20.16 
 
 1.08 
 
 62 
 
 20.46 
 
 1.02 
 
 58 
 
 20.78 
 
 0.99 
 
 55 
 
 21.14 
 
 0.99 
 
 55 
 
 
 
 73 
 
 21.31 
 
 1.54 
 
 87 
 
 21.23 
 
 1.37 
 
 78 
 
 21.34 
 
 1.24 
 
 68 
 
 21.56 
 
 1.15 
 
 62 
 
 21.85 
 
 1.11 
 
 56 
 
 22.22 
 
 1.11 
 
 53 
 
 
 
 74 
 
 22.92 
 
 1.63 
 
 98 
 
 22.66 
 
 1.45 
 
 86 
 
 22.63 
 
 1.31 
 
 75 
 
 22.76 
 
 1.21 
 
 66 
 
 23.00 
 
 1.16 
 
 58 
 
 23.35 
 
 1.13 
 
 53 
 
 
 
 75 
 
 24.56 
 
 1.61 
 
 109 
 
 24.13 
 
 1.44 
 
 95 
 
 23.96 
 
 1.29 
 
 82 
 
 23.98 
 
 1.19 
 
 71 
 
 24.16 
 
 1.12 
 
 61 
 
 24.48 
 
 1.08 
 
 53 
 
 
 
 76 
 
 26.15 
 
 1.50 
 
 118 
 
 25.54 
 
 1.33 
 
 104 
 
 25.22 
 
 1.19 
 
 89 
 
 25.14 
 
 1.08 
 
 77 
 
 25.24 
 
 1.00 
 
 65 
 
 25.52 
 
 0.95 
 
 55 
 
 
 
 77 
 
 27.57 
 
 1.29 
 
 127 
 
 26.80 
 
 1.15 
 
 112 
 
 26.34 
 
 1.01 
 
 '96 
 
 26.15 
 
 0.90 
 
 82 
 
 26.17 
 
 0.81 
 
 69 
 
 26.38 
 
 0.74 
 
 57 
 
 
 
 78 
 
 28.73 
 
 1.00 
 
 134 
 
 27.84 
 
 0.89 
 
 119 
 
 27.25 
 
 0.77 
 
 103 
 
 26.95 
 
 0.67 
 
 89 
 
 26.87 
 
 0.57 
 
 74 
 
 27.00 
 
 0.48 
 
 60 
 
 
 
 79 
 
 29.57 
 
 0.65 
 
 139 
 
 28.58 
 
 0.58 
 
 125 
 
 27.89 
 
 0.49 
 
 109 
 
 27.49 
 
 0.39 
 
 94 
 
 27.32 
 
 0.31 
 
 79 
 
 27.35 
 
 +0.21 
 
 64 
 
 
 
 80 
 
 30.04 
 
 +0.28 
 
 141 
 
 29.00 
 
 +0.24 
 
 129 
 
 28.23 
 
 +0.18 
 
 114 
 
 27.74 
 
 -f-0.10 
 
 100 
 
 27.49 
 
 4-0.02 
 
 85 
 
 27.43 
 
 _0.07 
 
 70 
 
 
 
 81 
 
 30.14 
 
 -0.10 
 
 141 
 
 29.07 
 
 _0.09 
 
 131 
 
 28.26 
 
 0.12 
 
 117 
 
 27.70 
 
 -0.17 
 
 105 
 
 27.37 
 
 -0.25 
 
 90 
 
 27.22 
 
 0.35 
 
 75 
 
 
 
 82 
 
 29.85 
 
 0.47 
 
 138 
 
 28.82 
 
 0.41 
 
 131 
 
 27.99 
 
 0.40 
 
 119 
 
 27.40 
 
 0.42 
 
 109 
 
 26.99 
 
 0.49 
 
 95 
 
 26.74 
 
 0.78 
 
 81 
 
 
 
 83 
 
 29.21 
 
 0.78 
 
 132 
 
 28.26 
 
 0.68 
 
 128 
 
 27.47 
 
 0.64 
 
 120 
 
 26.86 
 
 0.64 
 
 112 
 
 26.40 
 
 0.68 
 
 100 
 
 26.06 
 
 0.76 
 
 87 
 
 
 
 84 
 
 28.29 
 
 1.04 
 
 125 
 
 27.46 
 
 0.91 
 
 124 
 
 26.72 
 
 0.83 
 
 119 
 
 26.12 
 
 0.81 
 
 114 
 
 25.63 
 
 0.83 
 
 104 
 
 25.22 
 
 0.84 
 
 93 
 
 
 
 85 
 
 27.13 
 
 1.24 
 
 115 
 
 26.45 
 
 1.07 
 
 119 
 
 25.81 
 
 0.97 
 
 117 
 
 25.24 
 
 0.92 
 
 114 
 
 24.75 
 
 0.92 
 
 108 
 
 24.28 
 
 0.96 
 
 99 
 
 
 
 86 
 
 25.82 
 
 1.33 
 
 105 
 
 25.32 
 
 1.16 
 
 112 
 
 24.79 
 
 1.04 
 
 113 
 
 24.29 
 
 0.96 
 
 114 
 
 23.80 
 
 0.94 
 
 110 
 
 23.30 
 
 0.95 
 
 104 
 
 
 
 87 
 
 24.44 
 
 1.37 
 
 94 
 
 24.13 
 
 1J8 
 
 103 
 
 23.74 
 
 1.03 
 
 108 
 
 23.32 
 
 0.95 
 
 112 
 
 22.87 
 
 0.90 
 
 111 
 
 22.37 
 
 0.90 
 
 107 
 
 
 
 88 
 
 23.07 
 
 1.32 
 
 83 
 
 22.96 
 
 1.12 
 
 95 
 
 22.72 
 
 0.98 
 
 103 
 
 22.39 
 
 0.88 
 
 109 
 
 21.99 
 
 0.82 
 
 111 
 
 21.50 
 
 0.80 
 
 110 
 
 
 
 89 
 
 21.80 
 
 1.18 
 
 73 
 
 21.88 
 
 1.00 
 
 87 
 
 21.78 
 
 0.86 
 
 97 
 
 21.56 
 
 0.76 
 
 106 
 
 21.23 
 
 0.68 
 
 110 
 
 20.78 
 
 0.62 
 
 111 
 
 
 
 90 
 
 20.71 
 
 0.97 
 
 63 
 
 20.96 
 
 -0.81 
 
 79 
 
 21.00 
 
 -0.68 
 
 91 
 
 20.88 
 
 -0.58 
 
 101 
 
 20.63 
 
 -0.49 
 
 108 
 
 20.25 
 
 -0.42 
 
 111 
 
 
 
 NOTE. When T exceeds 88, subtract 88 from it, and add 46.98 to F. 
 
TABLE X. 
 
 25 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 T 
 
 
 24 
 
 
 
 28 
 
 
 
 32 
 
 
 
 36 
 
 
 
 40 
 
 
 
 44 
 
 
 
 
 V 
 
 io 
 
 Diff. 
 
 r 
 
 iv 
 
 Diff. 
 
 f 
 
 60 
 
 Diff. 
 
 r 
 
 de 
 
 Diff. 
 
 r 
 
 iv 
 
 Diff. 
 
 r 
 
 iv 
 
 Diff. 
 
 r 
 
 
 
 60 
 
 27.74 
 
 2.09 
 
 108 
 
 26.47 
 
 1.85 
 
 108 
 
 25.40 
 
 i'.59 
 
 104 
 
 2'4.70 
 
 i'.38 
 
 97 
 
 24.25 
 
 i'.21 
 
 90 
 
 24.02 
 
 'i.n 
 
 82 
 
 
 
 61 
 
 25.48 
 
 2.35 
 
 104 
 
 24.46 
 
 2.10 
 
 100 
 
 23.66 
 
 1.81 
 
 95 
 
 23.20 
 
 1.57 
 
 89 
 
 22.94 
 
 1.37 
 
 82 
 
 22.82 
 
 1.25 
 
 75 
 
 
 
 62 
 
 23.05 
 
 2.39 
 
 100 
 
 22.28 
 
 2.16 
 
 93 
 
 21.78 
 
 1.89 
 
 86 
 
 21.57 
 
 1.64 
 
 80 
 
 21.51 
 
 1.43 
 
 74 
 
 21.53 
 
 1.29 
 
 70 
 
 
 
 63 
 
 20.69 
 
 2.24 
 
 96 
 
 20.13 
 
 2.06 
 
 87 
 
 19.89 
 
 1.81 
 
 78 
 
 19.93 
 
 1.58 
 
 71 
 
 20.08 
 
 1.39 
 
 66 
 
 20.24 
 
 1.26 
 
 63 
 
 
 
 64 
 
 18.56 
 
 1.92 
 
 94 
 
 18.16 
 
 1.78 
 
 82 
 
 18.15 
 
 1.59 
 
 72 
 
 18.40 
 
 1.41 
 
 64 
 
 18.73 
 
 1.25 
 
 59 
 
 19.01 
 
 1.14 
 
 57 
 
 
 
 65 
 
 16.85 
 
 1.41 
 
 93 
 
 16.56 
 
 1.35 
 
 79 
 
 16.70 
 
 1.24 
 
 68 
 
 17.11 
 
 1.12 
 
 59 
 
 17.57 
 
 1.01 
 
 55 
 
 17.96 
 
 0.93 
 
 53 
 
 
 
 66 
 
 15.73 
 
 0.77 
 
 93 
 
 15.46 
 
 -0.79 
 
 79 
 
 15.66 
 
 0.77 
 
 66 
 
 16.16 
 
 0.73 
 
 57 
 
 16.70 
 
 0.69 
 
 52 
 
 17.14 
 
 0.66 
 
 50 
 
 
 
 67 
 
 15.31 
 
 0.03 
 
 95 
 
 14.98 
 
 +0.13 
 
 80 
 
 15.15 
 
 0.20 
 
 67 
 
 15.65 
 
 0.26 
 
 58 
 
 16.19 
 
 0.29 
 
 52 
 
 16.63 
 
 -0.31 
 
 50 
 
 
 
 68 
 
 15.66 
 
 +0.75 
 
 97 
 
 15.19 
 
 0.58 
 
 84 
 
 15.25 
 
 +0.41 
 
 71 
 
 15.64 
 
 +0.26 
 
 61 
 
 16.11 
 
 +0.15 
 
 56 
 
 16.51 
 
 +0.08 
 
 53 
 
 
 
 69 
 
 16.80 
 
 1.53 
 
 101 
 
 16.14 
 
 1.30 
 
 89 
 
 15.97 
 
 1.03 
 
 78 
 
 16.17 
 
 0.80 
 
 68 
 
 16.48 
 
 0.61 
 
 62 
 
 16.78 
 
 0.48 
 
 58 
 
 
 
 70 
 
 18.71 
 
 2.23 
 
 105 
 
 17.78 
 
 1.96 
 
 96 
 
 17.31 
 
 1.63 
 
 86 
 
 1 7.24 
 
 1.32 
 
 78 
 
 17.33 
 
 1.07 
 
 70 
 
 17.46 
 
 0.88 
 
 65 
 
 
 
 71 
 
 21.26 
 
 2.80 
 
 109 
 
 20.05 
 
 1.52 
 
 104 
 
 19.23 
 
 2.15 
 
 97 
 
 18.80 
 
 1.78 
 
 89 
 
 18.62 
 
 1.48 
 
 81 
 
 18.54 
 
 1.25 
 
 75 
 
 
 
 72 
 
 24.31 
 
 3.21 
 
 113 
 
 22.82 
 
 2.94 
 
 112 
 
 21.61 
 
 2.54 
 
 10S 
 
 20.80 
 
 2.15 
 
 102 
 
 20.28 
 
 1.80 
 
 94 
 
 19.96 
 
 1.65 
 
 85 
 
 
 
 73 
 
 27.67 
 
 3.40 
 
 115 
 
 25.92 
 
 3.17 
 
 120 
 
 24.31 
 
 2.78 
 
 120 
 
 23.09 
 
 2.37 
 
 115 
 
 22.22 
 
 2.03 
 
 107 
 
 21.64 
 
 1.76 
 
 97 
 
 
 
 74 
 
 31.11 
 
 3.35 
 
 117 
 
 29.15 
 
 3.18 
 
 127 
 
 27.16 
 
 2.83 
 
 130 
 
 25.54 
 
 2.46 
 
 128 
 
 24.33 
 
 2.12 
 
 120 
 
 23.47 
 
 1.86 
 
 109 
 
 
 
 75 
 
 34.38 
 
 3.07 
 
 116 
 
 32.28 
 
 2.98 
 
 132 
 
 29.98 
 
 2.71 
 
 140 
 
 28.00 
 
 2.38 
 
 139 
 
 26.46 
 
 3:07 
 
 132 
 
 25.35 
 
 1.S3 
 
 121 
 
 
 
 76 
 
 37.26 
 
 2.58 
 
 114 
 
 35.12 
 
 2.59 
 
 135 
 
 32.59 
 
 2.41 
 
 147 
 
 30.30 
 
 2.15 
 
 149 
 
 28.47 
 
 1.89 
 
 143 
 
 27.14 
 
 1.68 
 
 132 
 
 
 
 77 
 
 39.54 
 
 1.89 
 
 110 
 
 37.46 
 
 2.00 
 
 135 
 
 34.80 
 
 1.93 
 
 150 
 
 32.30 
 
 1.77 
 
 155 
 
 30.25 
 
 1.60 
 
 151 
 
 28.72 
 
 143 
 
 141 
 
 
 
 78 
 
 41.04 
 
 1.05 
 
 104 
 
 39.12 
 
 1.77 
 
 132 
 
 36.46 
 
 133 
 
 150 
 
 33.85 
 
 1.26 
 
 158 
 
 31.67 
 
 1.21 
 
 157 
 
 30.01 
 
 1.10 
 
 147 
 
 
 
 79 
 
 41.65 
 
 +0.13 
 
 95 
 
 40.01 
 
 +0.45 
 
 126 
 
 37.47 
 
 +0.64 
 
 147 
 
 34.87 
 
 0.72 
 
 157 
 
 32.65 
 
 0.73 
 
 158 
 
 31.93 
 
 0.70 
 
 150 
 
 
 
 80 
 
 41.30 
 
 0.83 
 
 85 
 
 40.03 
 
 -0.41 
 
 117 
 
 37.75 
 
 -0.09 
 
 140 
 
 35.29 
 
 +0.11 
 
 152 
 
 33.13 
 
 +0.12 
 
 155 
 
 31.42 
 
 +0.27 
 
 150 
 
 
 
 81 
 
 40.00 
 
 1.75 
 
 74 
 
 39.20 
 
 1.23 
 
 105 
 
 37.29 
 
 0.81 
 
 129 
 
 35.09 
 
 0.60 
 
 144 
 
 33.09 
 
 -0.29 
 
 149 
 
 31.47 
 
 0.17 
 
 147 
 
 
 
 82 
 
 37.81 
 
 2.57 
 
 62 
 
 37.57 
 
 2.02 
 
 100 
 
 36.13 
 
 1.49 
 
 115 
 
 34.29 
 
 1.08 
 
 132 
 
 32.55 
 
 0.78 
 
 140 
 
 31.08 
 
 0.59 
 
 141 
 
 
 
 83 
 
 34.86 
 
 3.25 
 
 50 
 
 35.17 
 
 2.69 
 
 76 
 
 34.32 
 
 2.08 
 
 99 
 
 32.94 
 
 1.58 
 
 117 
 
 31.53 
 
 1.21 
 
 129 
 
 30.30 
 
 0.96 
 
 132 
 
 
 
 84 
 
 31.31 
 
 3.75 
 
 39 
 
 32.20 
 
 3.18 
 
 59 
 
 31.98 
 
 2.54 
 
 81 
 
 31.13 
 
 1.99 
 
 100 
 
 30.13 
 
 1.56 
 
 113 
 
 29.17 
 
 1.26 
 
 121 
 
 
 
 85 
 
 27.36 
 
 4.04 
 
 28 
 
 28.82 
 
 3.49 
 
 44 
 
 29.24 
 
 2.86 
 
 63 
 
 28.97 
 
 2.27 
 
 82 
 
 28.42 
 
 1.81 
 
 97 
 
 27.78 
 
 1.48 
 
 108 
 
 
 
 86 
 
 23.23 
 
 4.09 
 
 19 
 
 25.22 
 
 3.61 
 
 29 
 
 26.27 
 
 3.01 
 
 45 
 
 26.59 
 
 2.42 
 
 63 
 
 26.51 
 
 1.95 
 
 80 
 
 26.22 
 
 1.60 
 
 94 
 
 
 
 87 
 
 19.17 
 
 3.92 
 
 12 
 
 21.60 
 
 3.52 
 
 13 
 
 23.23 
 
 2.96 
 
 29 
 
 24.14 
 
 2.42 
 
 46 
 
 24.52 
 
 1.97 
 
 64 
 
 24.58 
 
 1.63 
 
 80 
 
 
 
 88 
 
 15.39 
 
 3.53 
 
 7 
 
 28.17 
 
 3.22 
 
 6 
 
 20.34 
 
 2.76 
 
 15 
 
 21.74 
 
 2.29 
 
 31 
 
 22.56 
 
 1.88 
 
 49 
 
 22.95 
 
 1.56 
 
 67 
 
 
 
 89 
 
 12.11 
 
 2.93 
 
 4 
 
 15.16 
 
 2.76 
 
 1 
 
 17.71 
 
 2.41 
 
 4 
 
 19.56 
 
 2.02 
 
 18 
 
 20.76 
 
 1.67 
 
 36 
 
 21.46 
 
 1.39 
 
 55 
 
 
 
 90 
 
 9.52 
 
 2.18 
 
 6 
 
 12.65 
 
 2.16 
 
 5 
 
 15.51 
 
 1.92 
 
 3 
 
 17.70 
 
 -1.64 
 
 8 
 
 19.22 
 
 -1.37 
 
 25 
 
 20.16 
 
 1.15 
 
 -45 
 
 
 
 T 
 
 
 72 
 
 
 
 76 
 
 
 
 80 
 
 
 
 84 
 
 
 
 88 
 
 
 
 92 
 
 
 
 
 V 
 
 iv 
 
 Diff. 
 
 f 
 
 iv 
 
 Diff. 
 
 f 
 
 iv 
 
 Diff. 
 
 r 
 
 iv 
 
 Diff. 
 
 r 
 
 Sv 
 
 Diff. 
 
 r 
 
 iv 
 
 Diff. 
 
 r 
 
 
 
 60 
 
 24.99 
 
 f.04 
 
 57 
 
 25.23 
 
 i'l2 
 
 57 
 
 25.42 
 
 i'.22 
 
 57 
 
 25.67 
 
 1.34 
 
 60 
 
 25.93 
 
 i'.49 
 
 64 
 
 26". 13 
 
 -L67 
 
 71 
 
 
 
 61 
 
 23.91 
 
 1.08 
 
 60 
 
 24.07 
 
 1.17 
 
 61 
 
 24.15 
 
 1.28 
 
 62 
 
 24.27 
 
 1.41 
 
 66 
 
 24.37 
 
 1.68 
 
 71 
 
 24.37 
 
 1.80 
 
 77 
 
 
 
 62 
 
 22.83 
 
 1.06 
 
 63 
 
 22.90 
 
 1.14 
 
 65 
 
 22.87 
 
 1.24 
 
 6X 
 
 22.85 
 
 1.38 
 
 73 
 
 22.78 
 
 1.55 
 
 79 
 
 22.54 
 
 1.79 
 
 85 
 
 
 
 63 
 
 21.78 
 
 1.00 
 
 66 
 
 21.79 
 
 1.04 
 
 69 
 
 21.67 
 
 1.13 
 
 74 
 
 21.51 
 
 1.26 
 
 80 
 
 21.26 
 
 1.42 
 
 87 
 
 20.79 
 
 1.64 
 
 94 
 
 
 
 64 
 
 20.83 
 
 0.86 
 
 68 
 
 20.81 
 
 0.89 
 
 73 
 
 20.60 
 
 0.95 
 
 79 
 
 20.33 
 
 1.03 
 
 86 
 
 19.94 
 
 1.18 
 
 95 
 
 19.26 
 
 1.36 
 
 102 
 
 
 
 65 
 
 20.05 
 
 0.67 
 
 70 
 
 20.01 
 
 0.68 
 
 76 
 
 19.77 
 
 0.70 
 
 84 
 
 19.40 
 
 0.77 
 
 92 
 
 18.89 
 
 0.86 
 
 101 
 
 18.07 
 
 0.99 
 
 110 
 
 
 
 66 
 
 19.48 
 
 0.44 
 
 70 
 
 19.44 
 
 -043 
 
 78 
 
 19.19 
 
 0.42 
 
 86 
 
 18.79 
 
 0.43 
 
 96 
 
 18.22 
 
 0.46 
 
 106 
 
 1 7.29 
 
 0.62 
 
 115 
 
 
 
 67 
 
 19.16 
 
 0.19 
 
 70 
 
 19.14 
 
 +0.14 
 
 78 
 
 18.92 
 
 0.09 
 
 87 
 
 18.53 
 
 -0.06 
 
 98 
 
 17.96 
 
 0.02 
 
 109 
 
 17.03 
 
 +0.00 
 
 118 
 
 
 
 68 
 
 19.10 
 
 +0.08 
 
 69 
 
 19.15 
 
 0.17 
 
 77 
 
 19.01 
 
 +026 
 
 86 
 
 18.67 
 
 +0.34 
 
 97 
 
 18.17 
 
 +0.44 
 
 109 
 
 17.32 
 
 0.57 
 
 119 
 
 
 
 69 
 
 19.32 
 
 0.37 
 
 66 
 
 19.47 
 
 0.47 
 
 74 
 
 19.43 
 
 0.59 
 
 83 
 
 19.21 
 
 0.73 
 
 94 
 
 18.84 
 
 0.90 
 
 106 
 
 18.17 
 
 1.11 
 
 116 
 
 
 
 70 
 
 19.84 
 
 0.65 
 
 63 
 
 20.09 
 
 075 
 
 70 
 
 20.18 
 
 C.90 
 
 78 
 
 20.12 
 
 1.08 
 
 88 
 
 19.96 
 
 1.30 
 
 100 
 
 19.53 
 
 1.59 
 
 110 
 
 
 
 71 
 
 20.61 
 
 0.87 
 
 60 
 
 20.97 
 
 0.99 
 
 65 
 
 21.23 
 
 1.16 
 
 72 
 
 20.36 
 
 1.37 
 
 81 
 
 21.43 
 
 1.62 
 
 91 
 
 21.35 
 
 2.00 
 
 101 
 
 
 
 72 
 
 21.58 
 
 1.06 
 
 56 
 
 22.06 
 
 1.16 
 
 60 
 
 22.49 
 
 1.34 
 
 65 
 
 22.76 
 
 1.57 
 
 73 
 
 23.20 
 
 1.87 
 
 80 
 
 23.53 
 
 2.29 
 
 90 
 
 
 
 73 
 
 22.70 
 
 1.15 
 
 52 
 
 23.29 
 
 1.25 
 
 54 
 
 23.90 
 
 1.43 
 
 57 
 
 24.50 
 
 1.66 
 
 61 
 
 25.16 
 
 1.97 
 
 68 
 
 25'.92 
 
 2.41 
 
 78 
 
 
 
 74 
 
 23.87 
 
 1.16 
 
 49 
 
 24.56 
 
 1.24 
 
 48 
 
 25.34 
 
 1.40 
 
 48 
 
 26.18 
 
 1.63 
 
 51 
 
 27.14 
 
 1.93 
 
 55 
 
 28.34 
 
 2.37 
 
 64 
 
 
 
 75 
 
 25.01 
 
 1.08 
 
 47 
 
 25.78 
 
 1.14 
 
 43 
 
 26.70 
 
 1.27 
 
 41 
 
 27.56 
 
 1.47 
 
 40 
 
 29.03 
 
 1.76 
 
 43 
 
 30.66 
 
 2.18 
 
 50 
 
 
 
 76 
 
 26.04 
 
 0.93 
 
 46 
 
 26.85 
 
 0.95 
 
 40 
 
 27.88 
 
 1.04 
 
 34 
 
 29.13 
 
 1.31 
 
 31 
 
 30.65 
 
 1.44 
 
 30 
 
 32.69 
 
 1.81 
 
 36 
 
 
 
 77 
 
 26.88 
 
 0.70 
 
 46 
 
 27.69 
 
 0.69 
 
 37 
 
 28.79 
 
 0.74 
 
 29 
 
 30.19 
 
 0.85 
 
 23 
 
 31.92 
 
 1.03 
 
 20 
 
 34.28' 
 
 1.31 
 
 23 
 
 
 
 78 
 
 27.44 
 
 0.41 
 
 48 
 
 28.23 
 
 038 
 
 37 
 
 29.36 
 
 4-0.37 
 
 26 
 
 30.84 
 
 fO.42 
 
 17 
 
 32.71 
 
 -1-0.53 
 
 12 
 
 35.31 
 
 0.72 
 
 13 
 
 
 
 79 
 
 27.71 
 
 +0.12 
 
 51 
 
 28.45 
 
 -0.04 
 
 38 
 
 29.55 
 
 -0.04 
 
 26 
 
 31.04 
 
 -0.02 
 
 15 
 
 32.98 
 
 -0.00 
 
 7 
 
 35.71 
 
 fO.07 
 
 06 
 
 
 
 80 
 
 27.68 
 
 -0.18 
 
 55 
 
 28.31 
 
 +030 
 
 41 
 
 29.34 
 
 0.40 
 
 27 
 
 30.80 
 
 0.46 
 
 15 
 
 32.72 
 
 0.54 
 
 5 
 
 35.45 
 
 -0.68 
 
 02 
 
 
 
 81 
 
 27.35 
 
 0.46 
 
 60 
 
 27.85 
 
 0.60 
 
 46 
 
 28.75 
 
 0.75 
 
 32 
 
 30.12 
 
 0.88 
 
 18 
 
 31.92 
 
 1.03 
 
 7 
 
 34.55 
 
 1.19 
 
 02 
 
 
 
 82 
 
 26.76 
 
 0.71 
 
 67 
 
 27.11 
 
 0.87 
 
 53 
 
 27.84 
 
 1.04 
 
 38 
 
 29.04 
 
 1.23 
 
 24 
 
 30.66 
 
 1.45 
 
 12 
 
 33.08 
 
 1.71 
 
 05 
 
 
 
 83 
 
 25.94 
 
 0.90 
 
 74 
 
 26.12 
 
 1.07 
 
 61 
 
 26.68 
 
 1.26 
 
 47 
 
 27.66 
 
 1.49 
 
 33 
 
 29.03 
 
 1.77 
 
 20 
 
 31.13 
 
 2 13 | 
 
 13 
 
 
 
 84 
 
 24.97 
 
 1.01 
 
 82 
 
 24.98 
 
 1.18 
 
 70 
 
 25.33 
 
 1.40 
 
 57 
 
 26.06 
 
 1.65 
 
 44 
 
 27.12 
 
 1.98 
 
 31 
 
 28.82 
 
 2.41 
 
 23 
 
 
 
 85 
 
 23.92 
 
 1.06 
 
 89 
 
 23.76 
 
 1.22 
 
 79 
 
 23.89 
 
 1.43 
 
 68 
 
 24.36 
 
 1.70 
 
 56 
 
 25.08 
 
 2.05 
 
 44 
 
 26.32 
 
 2.53 
 
 86 
 
 
 
 86 
 
 22.86 
 
 1.03 
 
 96 
 
 22.54 
 
 1.18 
 
 88 
 
 22.47 
 
 1.42 
 
 79 
 
 22.66 
 
 1.66 
 
 69 
 
 23.02 
 
 2.00 
 
 59 
 
 23.77 
 
 2.50 
 
 49 
 
 
 
 87 
 
 21.85 
 
 096 
 
 102 
 
 21.40 
 
 1.07 
 
 95 
 
 21.14 
 
 1.24 
 
 90 
 
 21.06 
 
 1.49 
 
 82 
 
 21.08 
 
 1.83 
 
 73 
 
 21.33 
 
 2.32 
 
 64 
 
 
 
 88 
 
 20.94 
 
 082 
 
 107 
 
 20.40 
 
 0.90 
 
 104 
 
 19.98 
 
 1.04 
 
 100 
 
 19.67 
 
 125 
 
 94 
 
 19.36 
 
 1.65 
 
 87 
 
 19.14 
 
 2.01 
 
 79 
 
 
 
 89 
 
 20.20 
 
 0.63 
 
 111 
 
 19.60 
 
 0.67 
 
 110 
 
 19.06 
 
 0.77 
 
 108 
 
 18.55 
 
 0.94 
 
 105 
 
 17.97 
 
 1.18 
 
 100 
 
 17.32 
 
 1.57 i 
 
 92 
 
 
 
 90 
 
 19.68 
 
 0.39 
 
 113 
 
 19.06 
 
 0.40 
 
 114 
 
 18.44 
 
 -0.45 
 
 115 
 
 17.79 
 
 -057 H 
 
 114 
 
 16.99 . 
 
 -074 
 
 111 
 
 16.01 
 
 -1.04 
 
 104J 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 NOTE. When T exceeds 88, subtract 88 from it, and add 46.98 to V 
 
26 
 
 TABLE X. 
 
 
 
 
 T 
 
 4 
 
 8 
 
 12 
 
 16 
 
 20 
 
 
 V 
 
 to 
 
 Diff. 
 
 f 
 
 Sv 
 
 Diff. 
 
 / 
 
 to 
 
 Diff. 
 
 f 
 
 <iw 
 
 Diff. 
 
 f 
 
 i 
 
 Diff. 
 
 r 
 
 it 
 
 Diff. 
 
 r 
 
 
 
 90 
 
 l'i.64 
 
 -0.17 
 
 145 
 
 "9.64 
 
 0.39 
 
 136 
 
 "7.53 
 
 -0.70 
 
 117 
 
 5.99 
 
 i'.u 
 
 90 
 
 "5.63 
 
 -1.61 
 
 59 
 
 6.89 
 
 1.94 
 
 29 
 
 
 
 91 
 
 11.75 
 
 +0.40 
 
 151 
 
 9.58 
 
 +0.28 
 
 145 
 
 7.21 
 
 +0.09 
 
 128 
 
 5 28 
 
 0.65 
 
 101 
 
 4.48 
 
 0.65 
 
 69 
 
 5.35 
 
 1.05 
 
 36 
 
 
 
 92 
 
 12.43 
 
 096 
 
 155 
 
 10.20 
 
 0.94 
 
 150 
 
 7.70 
 
 0.87 
 
 135 
 
 5'.48 
 
 +0.65 
 
 111 
 
 4.32 
 
 +0.32 
 
 79 
 
 4.78 
 
 0.07 
 
 45 
 
 
 
 93 
 
 13.64 
 
 1.44 
 
 155 
 
 11.45 
 
 1.53 
 
 152 
 
 8.94 
 
 1.58 
 
 140 
 
 658 
 
 1.48 
 
 117 
 
 5.11 
 
 1.24 
 
 87 
 
 5.20 
 
 +0.8ii 
 
 54 
 
 
 
 94 
 
 15.31 
 
 1.84 
 
 150 
 
 13.25 
 
 202 
 
 150 
 
 10.85 
 
 2.18 
 
 141 
 
 8^44 
 
 2.14 
 
 122 
 
 6.79 
 
 2.07 
 
 94 
 
 6.54 
 
 1.74 
 
 64 
 
 
 
 95 
 
 17.31 
 
 2.12 
 
 143 
 
 15.49 
 
 2.38 
 
 145 
 
 13.30 
 
 2.64 
 
 139 
 
 10.96 
 
 2.76 
 
 123 
 
 9.22 
 
 2.71 
 
 100 
 
 8.67 
 
 2.45 
 
 73 
 
 
 
 96 
 
 19.54 
 
 2.32 
 
 133 
 
 18.01 
 
 2.58 
 
 137 
 
 16.12 
 
 2.91 
 
 134 
 
 13.95 
 
 3.12 
 
 123 
 
 12.21 
 
 3.16 
 
 105 
 
 11.43 
 
 2.95 
 
 83 
 
 
 
 97 
 
 21.83 
 
 2.24 
 
 121 
 
 20.64 
 
 2.69 
 
 127 
 
 19.11 
 
 2.97 
 
 127 
 
 17.19 
 
 3.25 
 
 120 
 
 15.53 
 
 3.36 
 
 108 
 
 14.57 
 
 3.22 
 
 91 
 
 
 
 98 
 
 24.03 
 
 2.08 
 
 109 
 
 23.20 
 
 2.44 
 
 115 
 
 22.07 
 
 2.84 
 
 118 
 
 20.45 
 
 3.16 
 
 116 
 
 18.93 
 
 3.35 
 
 109 
 
 17.87 
 
 3.25 
 
 98 
 
 
 
 99 
 
 26.00 
 
 1.79 
 
 96 
 
 25.52 
 
 2.13 
 
 103 
 
 24.80 
 
 2.52 
 
 108 
 
 23.51 
 
 2.85 
 
 111 
 
 22.19 
 
 3.06 
 
 109 
 
 21.07 
 
 3.03 
 
 104 
 
 
 
 100 
 
 27.62 
 
 1.40 
 
 84 
 
 27.47 
 
 1.69 
 
 92 
 
 27.12 
 
 2.04 
 
 99 
 
 26.16 
 
 2.36 
 
 101 
 
 25.06 
 
 2.58 
 
 109 
 
 23.94 
 
 2.60 
 
 109 
 
 
 
 101 
 
 28.79 
 
 0.91 
 
 74 
 
 28.91 
 
 1.05 
 
 81 
 
 28.89 
 
 1.45 
 
 90 
 
 28.24 
 
 1.73 
 
 99 
 
 27.35 
 
 1.93 
 
 107 
 
 26.27 
 
 1.98 
 
 112 
 
 
 
 102 
 
 29.45 
 
 +0.40 
 
 66 
 
 29.78 
 
 +0.58 
 
 73 
 
 30.03 
 
 0.79 
 
 83 
 
 29.63 
 
 1.01 
 
 94 
 
 28.93 
 
 1.18 
 
 105 
 
 27.91 
 
 1.25 
 
 114 
 
 
 
 103 
 
 29.60 
 
 0.11 
 
 60 
 
 30.06 
 
 0.01 
 
 67 
 
 30.48 
 
 +0.11 
 
 77 
 
 30.26 
 
 +0.25 
 
 90 
 
 29.71 
 
 +0.37 
 
 103 
 
 28.78 
 
 +0.45 
 
 114 
 
 
 
 104 
 
 29.24 
 
 0.58 
 
 57 
 
 29.76 
 
 0.58 
 
 64 
 
 30.25 
 
 0.54 
 
 74 
 
 30.13 
 
 0.49 
 
 87 
 
 29.68 
 
 -0.47 
 
 102 
 
 28.82 
 
 0.36 
 
 114 
 
 
 
 105 
 
 28.45 
 
 0.97 
 
 57 
 
 2894 
 
 1.05 
 
 63 
 
 29.40 
 
 1.10 
 
 73 
 
 29.29 
 
 1.16 
 
 86 
 
 28.87 
 
 1.15 
 
 100 
 
 28.07 
 
 1.10 
 
 113 
 
 
 
 106 
 
 27.30 
 
 1.28 
 
 59 
 
 27.67 
 
 1.42 
 
 66 
 
 28.03 
 
 1.57 
 
 75 
 
 27.84 
 
 1.69 
 
 87 
 
 27.38 
 
 1.76 
 
 100 
 
 26.62 
 
 1.75 
 
 111 
 
 
 
 107 
 
 25.90 
 
 1.48 
 
 64 
 
 26.10 
 
 1.67 
 
 71 
 
 26.26 
 
 1.89 
 
 79 
 
 25.92 
 
 2.07 
 
 90 
 
 25.35 
 
 2.22 
 
 100 
 
 24.58 
 
 2.24 
 
 109 
 
 
 
 108 
 
 24.35 
 
 1.57 
 
 71 
 
 24.33 
 
 1.80 
 
 77 
 
 24.26 
 
 2.05 
 
 85 
 
 23.70 
 
 2.29 
 
 94 
 
 22.95 
 
 2.48 
 
 101 
 
 22.15 
 
 2.56 
 
 107 
 
 
 
 109 
 
 22.77 
 
 1.54 
 
 79 
 
 22.51 
 
 1.77 
 
 85 
 
 22.16 
 
 2.06 
 
 92 
 
 21.34 
 
 2.32 
 
 99 
 
 20-39 
 
 2.54 
 
 103 
 
 19.50 
 
 2.67 
 
 105 
 
 
 
 110 
 
 21.27 
 
 1.41 
 
 87 
 
 20.78 
 
 1.62 
 
 94 
 
 20."l4 
 
 1.89 
 
 100 
 
 19.06 
 
 2.16 
 
 105 
 
 17.86 
 
 2.40 
 
 106 
 
 16.86 
 
 2.53 
 
 104 
 
 
 
 111 
 
 19.95 
 
 1.17 
 
 95 
 
 19.26 
 
 1.25 
 
 102 
 
 18.37 
 
 1.58 
 
 108 
 
 17.02 
 
 1.81 
 
 111 
 
 15.59 
 
 2.05 
 
 109 
 
 14.44 
 
 2.20 
 
 103 
 
 
 
 112 
 
 18.92 
 
 0.84 
 
 102 
 
 18.08 
 
 0.97 
 
 110 
 
 16.98 
 
 1.14 
 
 115 
 
 15.43 
 
 1.32 
 
 116 
 
 13.75 
 
 1.52 
 
 112 
 
 12.45 
 
 1.67 
 
 102 
 
 
 
 113 
 
 18.26 
 
 0.45 
 
 106 
 
 17.32 
 
 -0.50 
 
 115 
 
 16.09 
 
 -0.59 
 
 120 
 
 14.38 
 
 0.70 
 
 120 
 
 12.54 
 
 0.84 
 
 114 
 
 11.10 
 
 1.00 
 
 103 
 
 
 
 114 
 
 18.01 
 
 0.02 
 
 108 
 
 17.07 
 
 +0.03 
 
 118 
 
 15.79 
 
 +0.04 
 
 124 
 
 14.03 
 
 +0.03 
 
 123 
 
 12.06 
 
 0.05 
 
 116 
 
 10.45 
 
 0.20 
 
 103 
 
 
 
 115 
 
 18.22 
 
 +0.43 
 
 109 
 
 17.37 
 
 0.58 
 
 119 
 
 16.15 
 
 0.65 
 
 124 
 
 14.43 
 
 0.79 
 
 124 
 
 12.43 
 
 +0.80 
 
 117 
 
 10.69 
 
 +0.76 
 
 104 
 
 
 
 116 
 
 18.87 
 
 0.89 
 
 106 
 
 18.22 
 
 1.11 
 
 116 
 
 17.17 
 
 1.33 
 
 122 
 
 15.60 
 
 1.65 
 
 123 
 
 13.66 
 
 1.66 
 
 117 
 
 11.85 
 
 1.61 
 
 106 
 
 
 
 117 
 
 20.00 
 
 1.31 
 
 100 
 
 19.58 
 
 1.59 
 
 110 
 
 18.81 
 
 1.92 
 
 117 
 
 17.42 
 
 2.26 
 
 119 
 
 15.74 
 
 2.51 
 
 116 
 
 13.91 
 
 2.48 
 
 106 
 
 
 
 118 
 
 21.48 
 
 1.63 
 
 91 
 
 20.40 
 
 2.00 
 
 101 
 
 21.00 
 
 2.41 
 
 109 
 
 20.10 
 
 2.84 
 
 113 
 
 18.58 
 
 3.16 
 
 113 
 
 16.80 
 
 3.22 
 
 107 
 
 
 
 119 
 
 23.25 
 
 1.86 
 
 81 
 
 23.57 
 
 2.28 
 
 90 
 
 23.62 
 
 2.75 
 
 99 
 
 23.19 
 
 3.26 
 
 105 
 
 22.03 
 
 3.66 
 
 108 
 
 20.35 
 
 3.81 
 
 107 
 
 
 
 120 
 
 25.19 
 
 1.96 
 
 68 
 
 25.95 
 
 +2.40 
 
 77 
 
 26.50 
 
 +2.91 
 
 86 
 
 L'i;.li 1 
 
 +3.48 
 
 95 
 
 25.90 
 
 3.90 
 
 102 
 
 24.41 
 
 +4.18 
 
 106 
 
 
 
 T 48 
 
 52 
 
 56 
 
 60 
 
 64 
 
 68 
 
 
 
 V 
 
 60 
 
 Diff. 
 
 r 
 
 60 \ Diff. 
 
 r 
 
 fc 
 
 Diff. 
 
 r 
 
 6v 
 
 Diff. | 
 
 r 
 
 . ia. 
 
 Diff. 
 
 r 
 
 6n Diff. 
 
 r 
 
 
 
 90 
 
 20.71 
 
 -O.W 
 
 63 
 
 20.96 
 
 0.81 
 
 79 
 
 21.00 
 
 0.68 
 
 91 
 
 20.88 
 
 0.58 
 
 101 
 
 20.63 
 
 0.49 
 
 108 
 
 20.25 042 
 
 111 
 
 
 
 91 
 
 19.86 
 
 0.70 
 
 56 
 
 20.26 
 
 0.67 
 
 73 
 
 20.41 
 
 0.47 
 
 85 
 
 20.40 
 
 0.37 
 
 97 
 
 20.24 
 
 0.27 
 
 105 
 
 19.93 i-0.20 
 
 110 
 
 
 
 92 
 
 19.31 
 
 0.38 
 
 50 
 
 19.81 
 
 0.30 
 
 67 
 
 20.06 
 
 0.12 
 
 80 
 
 20.14 
 
 0.15 
 
 93 
 
 20.08 
 
 0.04 
 
 101 
 
 19.85 
 
 +0.04 
 
 108 
 
 
 
 93 
 
 19.09 
 
 0.06 
 
 47 
 
 19.65 
 
 -0.01 
 
 63 
 
 19.97 
 
 +0.04 
 
 75 
 
 20.13 
 
 +0.11 
 
 88 
 
 20.15 
 
 +0.19 
 
 97 
 
 20.01 
 
 0.28 
 
 104 
 
 
 
 94 
 
 19.19 
 
 +0.26 
 
 46 
 
 19.78 
 
 +0.26 
 
 60 
 
 20.14 
 
 0.29 
 
 72 
 
 20.36 
 
 0.33 
 
 84 
 
 20.45 
 
 0.41 
 
 93 
 
 20.41 
 
 0.49 
 
 100 
 
 
 
 I 95 
 
 19.60 
 
 0.54 
 
 47 
 
 20.17 
 
 0.60 
 
 59 
 
 20.54 
 
 0.60 
 
 70 
 
 20.79 
 
 0.52 
 
 81 
 
 20.96 
 
 0.68 
 
 89 
 
 20.99 
 
 066 
 
 96 
 
 
 
 96 
 
 20.26 
 
 0.76 
 
 50 
 
 20.78 
 
 0.69 
 
 60 
 
 21.13 
 
 0.66 
 
 68 
 
 21.40 
 
 0.67 
 
 78 
 
 21.61 
 
 0.70 
 
 86 
 
 21.73 
 
 0.79 
 
 91 
 
 
 
 97 
 
 21.11 
 
 0.90 
 
 55 
 
 21.55 
 
 0.81 
 
 64 
 
 21.85 
 
 0.75 
 
 68 
 
 22.12 
 
 0.74 
 
 77 
 
 22.36 
 
 0.77 
 
 82 
 
 2256 
 
 0.82 
 
 87 
 
 
 
 98 
 
 22.06 
 
 0.94 
 
 60 
 
 22.39 
 
 0.84 
 
 67 
 
 22.63 
 
 0.77 
 
 69 
 
 22.87 
 
 0.73 
 
 76 
 
 23.14 
 
 0.76 
 
 79 
 
 23.38 
 
 0.78 
 
 83 
 
 
 
 99 
 
 23.00 
 
 u.90 
 
 67 
 
 23.23 
 
 0.79 
 
 69 
 
 23.39 
 
 0.71 
 
 71 
 
 23.59 
 
 0.66 
 
 75 
 
 23.86 
 
 0.65. 
 
 78 
 
 24.12 
 
 0.68 
 
 79 
 
 
 
 100 
 
 23.86 
 
 0.77 
 
 73 
 
 23.98 
 
 0.66 
 
 73 
 
 24.05 
 
 0.58 
 
 73 
 
 24.20 
 
 0.52 
 
 76 
 
 24.45 
 
 0.60 
 
 77 
 
 24.74 
 
 051 
 
 77 
 
 
 
 101 
 
 24.55 
 
 0.57 
 
 79 
 
 24.56 
 
 0.47 
 
 77 
 
 24.55 
 
 0.39 
 
 76 
 
 24.64 
 
 0.33 
 
 77 
 
 24.86 
 
 0.29 
 
 76 
 
 25.15 
 
 0.28 
 
 75 
 
 
 
 102 
 
 25.00 
 
 +0.30 
 
 84 
 
 24.92 
 
 +0.24 
 
 81 
 
 24.84 
 
 +0.19 
 
 78 
 
 24.87 
 
 +0.12 
 
 78 
 
 25.04 
 
 +0.05 
 
 77 
 
 25.31 
 
 +0.02 
 
 74 
 
 
 
 103 
 
 25.16 
 
 0.00 
 
 88 
 
 25.03 
 
 -0.03 
 
 84 
 
 24.88 
 
 0.09 
 
 80 
 
 24.85 
 
 -0.15 
 
 80 
 
 24.97 
 
 -0.20 
 
 78 
 
 25.20 
 
 0.25 
 
 75 
 
 
 
 104 
 
 25.01 
 
 0.30 
 
 90 
 
 24.86 
 
 0.31 
 
 86 
 
 24.66 
 
 0.34 
 
 82 
 
 24.58 
 
 0.39 
 
 81 
 
 24.65 
 
 0.44 
 
 79 
 
 24.82 
 
 0.60 
 
 76 
 
 
 
 105 
 
 24.56 
 
 0.59 
 
 91 
 
 24.41 
 
 0.68 
 
 86 
 
 24.20 
 
 0.57 
 
 83 
 
 24.07 
 
 0.61 
 
 83 
 
 24.09 
 
 0.87 
 
 81 
 
 24.20 
 
 0.73 
 
 78 
 
 
 
 106 
 
 23.83 
 
 0.85 
 
 89 
 
 23.71 
 
 0.80 
 
 86 
 
 23.52 
 
 0.78 
 
 83 
 
 23.36 
 
 0.80 
 
 83 
 
 23.32 
 
 0.86 
 
 83 
 
 23.36 
 
 0.93 
 
 80 
 
 
 
 107 
 
 22.86 
 
 1.07 
 
 86 
 
 22.81 
 
 0.99 
 
 84 
 
 22.64 
 
 0.94 
 
 82 
 
 22.47 
 
 0.96 
 
 84 
 
 22.38 
 
 1.00 
 
 84 
 
 22.34 
 
 1.07 
 
 83 
 
 
 
 108 
 
 21.70 
 
 1.23 
 
 81 
 
 21.74 
 
 1.12 
 
 81 
 
 21.64 
 
 1.05 
 
 81 
 
 21.45 
 
 1.05 
 
 84 
 
 21.33 
 
 1.08 
 
 85 
 
 21.23 
 
 1.18 
 
 86 
 
 
 
 109 
 
 20.41 
 
 1.81 
 
 75 
 
 20.57 
 
 1.19 
 
 76 
 
 20.54 
 
 1.11 
 
 78 
 
 20.38 
 
 1.08 
 
 83 
 
 20.23 
 
 1.10 
 
 86 
 
 20.08 
 
 1.13 
 
 89 
 
 
 
 110 
 
 19.08 
 
 1.32 
 
 69 
 
 19.36 
 
 1.19 
 
 72 
 
 19.42 
 
 1.10 
 
 75 
 
 19.30 
 
 1.05 
 
 81 
 
 19.13 
 
 1.06 
 
 86 
 
 18.93 
 
 1.11 
 
 91 
 
 
 
 111 
 
 17.77 
 
 1.24 
 
 63 
 
 18.19 
 
 1.12 
 
 66 
 
 18.34 
 
 1.02 
 
 71 
 
 18.27 
 
 0.98 
 
 79 
 
 18.10 
 
 0.97 
 
 86 
 
 17.86 
 
 1.00 
 
 93 
 
 
 
 112 
 
 16.59 
 
 1.08 
 
 56 
 
 17.12 
 
 0.98 
 
 61 
 
 17.37 
 
 0.88 
 
 67 
 
 17.34 
 
 0.83 
 
 76 
 
 17.18 
 
 0.82 
 
 85 
 
 16.93 
 
 0.82 
 
 93 
 
 
 
 113 
 
 15.60 
 
 0.85 
 
 51 
 
 16.23 
 
 0.76 
 
 57 
 
 16.57 
 
 0.68 
 
 63 
 
 16.60 
 
 0.62 
 
 73 
 
 16.46 
 
 0.60 
 
 83 
 
 16.21 
 
 0.59 
 
 93 
 
 
 
 114 
 
 14.89 
 
 0.54 
 
 47 
 
 15.59 
 
 0.48 
 
 53 
 
 16.01 
 
 0.42 
 
 60 
 
 16.09 
 
 0.36 
 
 70 
 
 15.98 
 
 0.33 
 
 80 
 
 15.75 
 
 0.30 
 
 92 
 
 
 
 115 
 
 14.52 
 
 0.17 
 
 45 
 
 15.26 
 
 0.14 
 
 50 
 
 15.73 
 
 -0.10 
 
 57 
 
 15.87 
 
 0.06 
 
 C6 
 
 15.80 
 
 -0.02 
 
 77 
 
 15.60 
 
 +0.01 
 
 90 
 
 
 
 116 
 
 14.56 
 
 +0.25 
 
 45 
 
 15.30 
 
 +0.23 
 
 49 
 
 15.80 
 
 +0.25 
 
 54 
 
 15.97 
 
 +0.28 
 
 63 
 
 15.94 
 
 +0.31 
 
 74 
 
 15.77 
 
 0.35 
 
 87 
 
 
 
 117 
 
 15.02 
 
 0.68 
 
 47 
 
 15.72 
 
 0.42 
 
 49 
 
 16.22 
 
 0.60 
 
 53 
 
 16.42 
 
 0.62 
 
 61 
 
 16.42 
 
 0.66 
 
 71 
 
 16.29 
 
 0.70 
 
 83 
 
 
 
 118 
 
 15.92 
 
 1.10 
 
 51 
 
 16.53 
 
 1.00 
 
 51 
 
 16.99 
 
 0.95 
 
 53 
 
 17.21 
 
 0.95 
 
 59 
 
 17.25 
 
 0.98 
 
 68 
 
 17-17 
 
 1.04 
 
 79 
 
 
 
 119 
 
 17.22 
 
 1.47 
 
 56 
 
 17.71 
 
 1.33 
 
 54 
 
 18.11 
 
 1.25 
 
 54 
 
 18.31 
 
 1.24 
 
 58 
 
 18.38 
 
 1.26 
 
 64 
 
 18.36 
 
 1.32 
 
 74 
 
 
 
 120 
 
 18.86 
 
 +1.77 
 
 64 
 
 19.19 
 
 +1.59 
 
 59 
 
 19.49 
 
 +1.47 . 
 
 57 
 
 19.68 
 
 +1.47 
 
 58 
 
 19.76 
 
 1.47 
 
 62 
 
 19.80 +1.52 
 
 70 
 
 
 
 NOTE. When T exceeds 88, subtract 88 from it, and add 46.98 to V. 
 
TABLE X. 
 
 27 
 
 
 
 
 T 24 
 
 28 
 
 32 
 
 36 
 
 40 
 
 44 
 
 
 V 
 
 So 
 
 Diff. 
 
 f 
 
 tv 
 
 Diff. 
 
 f 
 
 So 
 
 Diff. 
 
 r 
 
 fa 
 
 Diff. 
 
 f 
 
 fa 
 
 Diff. 
 
 r 
 
 iv 
 
 Diff. 
 
 r 
 
 
 
 90 
 
 9.52 
 
 2.18 
 
 6 
 
 12.65 
 
 2.16 
 
 5 
 
 15.51 
 
 i'.92 
 
 -3 
 
 17.70 
 
 -i'.64 
 
 8 
 
 19.22 
 
 -1.37 
 
 25 
 
 20.16 
 
 1.15 
 
 45 
 
 
 
 91 
 
 7.74 
 
 1.33 
 
 10 
 
 10.83 
 
 1.41 
 
 -5 
 
 13.86 
 
 1.33 
 
 -7 
 
 16.28 
 
 1.16 
 
 2 
 
 18.02 
 
 0.99 
 
 18 
 
 19.16 
 
 0.82 
 
 37 
 
 
 
 92 
 
 6.85 
 
 0.42 
 
 17 
 
 9.82 
 
 0.61 
 
 -1 
 
 12.85 
 
 0.6T 
 
 -6 
 
 15.37 
 
 0.64 
 
 
 
 17.24 
 
 0.65 
 
 14 
 
 18.51 
 
 0.46 
 
 32 
 
 
 93 
 
 6.90 
 
 +0.49 
 
 26 
 
 9.60 
 
 +0.18 
 
 6 
 
 12.51 
 
 0.01 
 
 -1 
 
 15.00 
 
 0.09 
 
 3 
 
 16.91 
 
 0.10 
 
 14 
 
 18.23 
 
 0.09 
 
 30 
 
 
 
 , 94 
 
 7.83 
 
 1.32 
 
 36 
 
 10.17 
 
 0.92 
 
 16 
 
 12.83 
 
 40.62 
 
 7 
 
 15.18 
 
 +0.44 
 
 9 
 
 17.03 
 
 +0.33 
 
 18 
 
 18.34 
 
 +0.27 
 
 31 
 
 
 
 95 
 
 , 9.53 
 
 2.01 
 
 48 
 
 11.43 
 
 1.56 
 
 29 
 
 13.75 
 
 1.17 
 
 19 
 
 15.87 
 
 0.89 
 
 18 
 
 17.56 
 
 0.71 
 
 24 
 
 18.79 
 
 0.61 
 
 35 
 
 
 
 96 
 
 11.85 
 
 2.53 
 
 61 
 
 13.27 
 
 2.05 
 
 43 
 
 15.17 
 
 1.60 
 
 32 
 
 16.96 
 
 1.26 
 
 30 
 
 18.45 
 
 1.01 
 
 33 
 
 19.55 
 
 0.87 
 
 40 
 
 
 
 97 
 
 14.59 
 
 2.84 
 
 73 
 
 15.52 
 
 2.34 
 
 58 
 
 16.94 
 
 1.87 
 
 47 
 
 18.36 
 
 1.49 
 
 43 
 
 19.58 
 
 1.21 
 
 44 
 
 20.52 
 
 1.03 
 
 48 
 
 
 
 98 
 
 17.53 
 
 2.91 
 
 85 
 
 17.95 
 
 2.46 
 
 73 
 
 18.91 
 
 1.98 
 
 63 
 
 19.93 
 
 1.58 
 
 57 
 
 20.86 
 
 1.29 
 
 56 
 
 21.60 
 
 1.09 
 
 57 
 
 
 
 99 
 
 20.42 
 
 2.76 
 
 96 
 
 20.43 
 
 2.36 
 
 86 
 
 20.90 
 
 1.90 
 
 79 
 
 21.52 
 
 1.52 
 
 72 
 
 22.15 
 
 1.24 
 
 68 
 
 22.69 
 
 1.04 
 
 66 
 
 
 
 100 
 
 23.05 
 
 2.40 
 
 105 
 
 22.68 
 
 2.05 
 
 99 
 
 22.72 
 
 1.67 
 
 92 
 
 22.98 
 
 1.34 
 
 85 
 
 23.34 
 
 1.07 
 
 79 
 
 23.68 
 
 0.89 
 
 75 
 
 
 
 101 
 
 25.23 
 
 1.87 
 
 113 
 
 24.54 
 
 1.60 
 
 109 
 
 24.24 
 
 1.30 
 
 103 
 
 24.18 
 
 1.02 
 
 96 
 
 24.34 
 
 0.81 
 
 89 
 
 24.48 
 
 ' 0.67 
 
 83 
 
 
 
 102 
 
 26.79 
 
 1.19 
 
 118 
 
 25.89 
 
 1.04 
 
 117 
 
 25.33 
 
 0.82 
 
 112 
 
 25.02 
 
 0.63 
 
 105 
 
 24.97 
 
 0.48 
 
 97 
 
 25.02 
 
 0.37 
 
 90 
 
 
 
 103 
 
 27.62 
 
 +0.46 
 
 121 
 
 26.62 
 
 +0.39 
 
 122 
 
 25.89 
 
 +0.28 
 
 118 
 
 25.44 
 
 +0.18 
 
 111 
 
 25.26 
 
 +0.09 
 
 102 
 
 25.23 
 
 -j-0.03 
 
 94 
 
 
 
 104 
 
 27.71 
 
 0.29 
 
 121 
 
 26.68 
 
 0.27 
 
 123 
 
 25.89 
 
 -0.28 
 
 120 
 
 25.38 
 
 0.30 
 
 113 
 
 25.15 
 
 -0.31 
 
 105 
 
 25.08 
 
 _0.32 
 
 97 
 
 
 
 105 
 
 27.04 
 
 1.01 
 
 120 
 
 26.08 
 
 0.92 
 
 122 
 
 25.34 
 
 0.83 
 
 119 
 
 24.85 
 
 0.75 
 
 113 
 
 24.65 
 
 0.69 
 
 104 
 
 24.60 
 
 0.64 
 
 97 
 
 
 
 106 
 
 25.69 
 
 1.64 
 
 117 
 
 24.85 
 
 1.48 
 
 118 
 
 24.24 
 
 1.32 
 
 115 
 
 23.88 
 
 1.16 
 
 109 
 
 23.77 
 
 1.04 
 
 101 
 
 23.80 
 
 0.94 
 
 94 
 
 
 
 107 
 
 23.77 
 
 2.12 
 
 113 
 
 23.12 
 
 1.92 
 
 113 
 
 22.71 
 
 1.70 
 
 109 
 
 22.53 
 
 1.49 
 
 103 
 
 22.58 
 
 1.82 
 
 96 
 
 22.72 
 
 1.19 
 
 90 
 
 
 
 108 
 
 21.45 
 
 2.44 
 
 108 
 
 21.01 
 
 2.23 
 
 105 
 
 20.85 
 
 1.97 
 
 101 
 
 20.90 
 
 1.72 
 
 94 
 
 21.14 
 
 1.52 
 
 88 
 
 21.42 
 
 1.86 
 
 84 
 
 
 
 109 
 
 18.89 
 
 2.57 
 
 103 
 
 18.66 
 
 2.37 
 
 98 
 
 18.77 
 
 2.12 
 
 91 
 
 19.09 
 
 1.84 
 
 85 
 
 19.54 
 
 1.63 
 
 80 
 
 20.00 
 
 1.46 
 
 77 
 
 
 
 110 
 
 16.31 
 
 2.49 
 
 98 
 
 16.27 
 
 2.32 
 
 90 
 
 16.64 
 
 2.08 
 
 82 
 
 17.22 
 
 1.83 
 
 75 
 
 17.89 
 
 1.62 
 
 71 
 
 18.51 
 
 1.46 
 
 69 
 
 
 
 111 
 
 13.91 
 
 2.21 
 
 93 
 
 14.02 
 
 2.09 
 
 83 
 
 14.61 
 
 1.90 
 
 73 
 
 15.43 
 
 1.69 
 
 66 
 
 16.30 
 
 1.51 
 
 62 
 
 17.08 
 
 1.37 
 
 61 
 
 
 
 112 
 
 11.89 
 
 1.74 
 
 90 
 
 12.08 
 
 1.69 
 
 77 
 
 12.83 
 
 1.57 
 
 65 
 
 13.84 
 
 1.42 
 
 58 
 
 14.86 
 
 1.30 
 
 54 
 
 15.77 
 
 1.18 
 
 54 
 
 
 
 113 
 
 10.42 
 
 1.11 
 
 88 
 
 10.63 
 
 1.13 
 
 73 
 
 11.47 
 
 1.10 
 
 60 
 
 12.59 
 
 1.03 
 
 52 
 
 13.70 
 
 0.96 
 
 48 
 
 14.71 
 
 0.90 
 
 48 
 
 
 
 114 
 
 9.67 
 
 0.33 
 
 87 
 
 9.81 
 
 0.45 
 
 71 
 
 10.63 
 
 0.51 
 
 57 
 
 11.78 
 
 0.53 
 
 48 
 
 12.93 
 
 0.54 
 
 44 
 
 13.97 
 
 0.54 
 
 44 
 
 
 
 115 
 
 9.75 
 
 +O.B2 
 
 88 
 
 9.78 
 
 +0.33 
 
 71 
 
 10.45 
 
 +0.17 
 
 57 
 
 11.52 
 
 +0.04 
 
 47 
 
 12.61 
 
 0.06 
 
 43 
 
 13.62 
 
 -0.12 
 
 42 
 
 
 
 116 
 
 10.71 
 
 1.42 
 
 90 
 
 10.47 
 
 1.16 
 
 74 
 
 10.97 
 
 0.89 
 
 60 
 
 11.87 
 
 0.67 
 
 50 
 
 12.81 
 
 +0.48 
 
 45 
 
 13.73 
 
 +0.35 
 
 43 
 
 
 
 117 
 
 12.58 
 
 2.28 
 
 93 
 
 12.04 
 
 1.97 
 
 79 
 
 12.23 
 
 1.62 
 
 66 
 
 12.86 
 
 1.30 
 
 56 
 
 13.57 
 
 1.03 
 
 51 
 
 14.32 
 
 0.84 
 
 47 
 
 
 
 118 
 
 1527 
 
 3.05 
 
 97 
 
 14.40 
 
 2.70 
 
 86 
 
 14.20 
 
 2.29 
 
 74 
 
 14.46 
 
 1.89 
 
 64 
 
 14.87 
 
 1.56 
 
 57 
 
 15.40 
 
 1.30 
 
 52 
 
 
 
 119 
 
 18.67 
 
 8.67 
 
 102 
 
 17.43 
 
 3.31 
 
 94 
 
 16.80 
 
 2.85 
 
 84 
 
 16.63 
 
 2.40 
 
 75 
 
 16.68 
 
 2.01 
 
 67 
 
 16.92 
 
 1.71 
 
 60 
 
 
 
 120 
 
 22.60 
 
 4.08 
 
 106 
 
 21.01 
 
 +3.74 
 
 102 
 
 19.90 '+3.27 
 
 95 
 
 19.25 
 
 +2.78 
 
 87 
 
 is.s;i 
 
 +2.36 
 
 78 
 
 18.81 
 
 +2.03 
 
 70 
 
 
 
 T 72 
 
 76 
 
 80 
 
 84 
 
 88 
 
 92 
 
 
 
 V 
 
 fc 
 
 Diff. 
 
 r 
 
 Sv 
 
 Diff. 
 
 r 
 
 tv 
 
 Diff. 
 
 r 
 
 60 
 
 Diff. 
 
 f 
 
 to 
 
 Diff. 
 
 r 
 
 to 
 
 Diff. 
 
 r 
 
 
 
 90 
 
 19.68 
 
 0.39 
 
 113 
 
 l'9.06 
 
 -0.40 
 
 114 
 
 18.44 
 
 6'.45 
 
 115 
 
 i'7.79 
 
 0.67 
 
 114 
 
 16.99 
 
 0.74 
 
 111 
 
 #.01 
 
 f'04 
 
 104 
 
 
 
 91 
 
 19.41 
 
 0.04 
 
 114 
 
 18.80 
 
 -0.11 
 
 116 
 
 18.15 
 
 0.11 
 
 119 
 
 17.41 
 
 -0.17 
 
 120 
 
 16.48 
 
 -0.27 
 
 118 
 
 15.25 
 
 0.47 
 
 114 
 
 
 
 92 
 
 19.40 
 
 +0.12 
 
 113 
 
 18.84 
 
 +0.19 
 
 117 
 
 18.21 
 
 +0.24 
 
 120 
 
 17.45 
 
 +0.24 
 
 123 
 
 16.45 
 
 +0.22 
 
 123 
 
 15.08 
 
 +0.13 
 
 120 
 
 
 
 93 
 
 19.65 
 
 0.38 
 
 110 
 
 19.18 
 
 0.47 
 
 115 
 
 18*62 
 
 0.56 
 
 119 
 
 17.88 
 
 0.62 
 
 123 
 
 16.91 
 
 0.68 
 
 124 
 
 15.50 
 
 0.70 
 
 122 
 
 
 
 94 
 
 20.15 
 
 0.61 
 
 106 
 
 19.78 
 
 0.72 
 
 111 
 
 19.33 
 
 0.84 
 
 116 
 
 18.68 
 
 0.96 
 
 120 
 
 17.80 
 
 1.08 
 
 122 
 
 16.47 
 
 1.20 
 
 121 
 
 
 
 95 
 
 20.86 
 
 0.78 
 
 101 
 
 20.62 
 
 091 
 
 106 
 
 20.29 
 
 1.05 
 
 111 
 
 19.79 
 
 1.21 
 
 114 
 
 19.06 
 
 1.40 
 
 117 
 
 17.90 
 
 1.61 
 
 116 
 
 
 
 96 
 
 21.71 
 
 0.89 
 
 96 
 
 21.60 
 
 ].03 
 
 99 
 
 21.43 
 
 1.19 
 
 103 
 
 21.10 
 
 1.87 
 
 107 
 
 20.60 
 
 1.61 
 
 108 
 
 19.69 
 
 1.90 
 
 108 
 
 
 
 97 
 
 22.64 
 
 0.93 
 
 90 
 
 22.67 
 
 1.06 
 
 92 
 
 22.66 
 
 1.22 
 
 95 
 
 22.53 
 
 1.41 
 
 97 
 
 22.27 
 
 1.68 
 
 98 
 
 21.69 
 
 2.02 
 
 98 
 
 
 
 98 
 
 23.57 
 
 0.88 
 
 84 
 
 23.72 
 
 0.99 
 
 85 
 
 23.87 
 
 1.15 
 
 . 86 
 
 23.93 
 
 1.34 
 
 86 
 
 23.96 
 
 1.61 
 
 87 
 
 23.73 
 
 1.98 
 
 86 
 
 
 
 99 
 
 24.40 
 
 0.75 
 
 79 
 
 24.66 
 
 0.84 
 
 78 
 
 24.96 
 
 0.97 
 
 77 
 
 25.22 
 
 1.16 
 
 76 
 
 25.50 
 
 1.41 
 
 75 
 
 25.65 
 
 1.78 
 
 74 
 
 
 
 100 
 
 25.07 
 
 0.55 
 
 75 
 
 25.41 
 
 0.62 
 
 72 
 
 25.82 
 
 0.71 
 
 69 
 
 26.26 
 
 0.87 
 
 66 
 
 26.79 
 
 1.09 
 
 63 
 
 27.28 
 
 1.42 
 
 61 
 
 
 
 101 
 
 25.51 
 
 0.30 
 
 72 
 
 25.90 
 
 0.34 
 
 67 
 
 26.39 
 
 0.39 
 
 62 
 
 26.97 
 
 0.50 
 
 57 
 
 27.68 
 
 0.66 
 
 52 
 
 28.48 
 
 0.94 
 
 50 
 
 
 
 102 
 
 25.68 
 
 +0.02 
 
 70 
 
 2609 
 
 +0.01 
 
 64 
 
 26.61 
 
 +0.03 
 
 57 
 
 27.27 
 
 +0.08 
 
 50 
 
 28.12 
 
 +0.18 
 
 44 
 
 29.16 
 
 +0.39 
 
 40 
 
 
 
 103 
 
 25.55 
 
 0.28 
 
 69 
 
 25.93 
 
 0.32 
 
 62 
 
 26.45 
 
 0.36 
 
 54 
 
 27.13 
 
 0.37 
 
 46 
 
 28.04 
 
 0.34 
 
 38 
 
 29.23 
 
 0.24 
 
 33 
 
 
 
 104 
 
 25 13 
 
 0.68 
 
 70 
 
 25.45 
 
 0.64 
 
 63 
 
 25.90 
 
 0.72 
 
 54 
 
 26.54 
 
 0.80 
 
 44 
 
 27.44 
 
 0.86 
 
 35 
 
 28.68 
 
 0.86 
 
 29 
 
 
 
 105 
 
 24.44 
 
 0.81 
 
 73 
 
 24.66 
 
 0.92 
 
 65 
 
 25.01 
 
 1.05 
 
 56 
 
 25.54 
 
 1.18 
 
 46 
 
 26.33 
 
 1.33 
 
 36 
 
 27.51 
 
 1.45 
 
 28 
 
 
 
 106 
 
 23.52 
 
 1.02 
 
 76 
 
 23.61 
 
 1.15 
 
 69 
 
 23.81 
 
 1.31 
 
 60 
 
 24.18 
 
 1.51 
 
 50 
 
 24.79 
 
 1.72 
 
 39 
 
 25.78 
 
 1.95 
 
 81 
 
 
 
 107 
 
 22.41 
 
 1.16 
 
 80 
 
 22.37 
 
 1.81 
 
 74 
 
 22.39 
 
 1.50 
 
 66 
 
 22.53 
 
 1.75 
 
 57 
 
 22.89 
 
 2.05 
 
 46 
 
 23.61 
 
 2.34 
 
 37 
 
 
 
 108 
 
 21.20 
 
 1.24 
 
 85 
 
 21.00 
 
 1.40 
 
 80 
 
 20.81 
 
 1.61 
 
 74 
 
 20.69 
 
 1.88 
 
 66 
 
 20.74 
 
 2.21 
 
 56 
 
 21.11 
 
 2.60 
 
 46 
 
 
 
 109 
 
 19.93 
 
 1.25 
 
 89 
 
 19.58 
 
 1.40 
 
 87 
 
 19.18 
 
 1.61 
 
 83 
 
 18.77 
 
 1.90 
 
 76 
 
 18.47 
 
 2.28 
 
 68 
 
 18.42 
 
 2.71 
 
 57 
 
 
 
 110 
 
 18.70 
 
 1.19 
 
 94 
 
 18.20 
 
 1.33 
 
 94 
 
 17.58 
 
 1.53 
 
 92 
 
 16.88 
 
 1.82 
 
 88 
 
 16.19 
 
 2.19 
 
 8"! 
 
 15.70 
 
 2.65 
 
 70 
 
 
 
 111 
 
 1 7.55 
 
 1.07 
 
 98 
 
 16.92 
 
 1.18 
 
 100 
 
 16.11 
 
 1.36 
 
 101 
 
 15.12 
 
 1.63 
 
 99 
 
 14.09 
 
 2.07 
 
 94 
 
 13.12 
 
 2.45 
 
 84 
 
 
 
 112 
 
 16.56 
 
 0.88 
 
 101 
 
 15.83 
 
 0.96 
 
 100 
 
 14.86 
 
 1.10 
 
 109 
 
 13.62 
 
 1.33 
 
 110 
 
 12.24 
 
 2.66 
 
 107 
 
 10.81 
 
 2.09 
 
 99 
 
 
 
 113 
 
 15.80 
 
 0.62 
 
 103 
 
 15.00 
 
 0.66 
 
 110 
 
 13.90 
 
 0.77 
 
 116 
 
 12.45 
 
 0.95 
 
 120 
 
 10.77 
 
 1.22 
 
 119 
 
 8.95 
 
 1.59 
 
 112 
 
 
 
 114 
 
 15.32 
 
 +0.31 
 
 103 
 
 14.50 
 
 -032 
 
 113 
 
 13.32 
 
 -0.37 
 
 121 
 
 11.71 
 
 -0.50 
 
 128 
 
 9.80 
 
 0.69 
 
 129 
 
 7.63 
 
 0.99 
 
 124 
 
 
 
 115 
 
 15.18 
 
 -0.04 
 
 102 
 
 14.36 
 
 +0.07 
 
 114 
 
 13.15 
 
 +0.07 
 
 124 
 
 11.45 
 
 +0.01 
 
 133 
 
 9.38 
 
 -0.11 
 
 137 
 
 6.97 
 
 -0.31 
 
 133 
 
 
 
 116 
 
 15.39 
 
 0.40 
 
 100 
 
 14.63 
 
 0.48 
 
 113 
 
 13.45 
 
 0.48 
 
 125 
 
 11.72 
 
 0.54 
 
 135 
 
 9.58 
 
 fO.61 
 
 141 
 
 7.02 
 
 fO.42 
 
 140 
 
 
 
 117 
 
 15.98 
 
 0.77 
 
 96 
 
 15.31 
 
 0.87 
 
 110 
 
 14.20 
 
 0.97 
 
 123 
 
 12.53 
 
 1.06 
 
 135 
 
 10.40 
 
 1.12 
 
 142 
 
 7.81 
 
 1.14 
 
 143 
 
 
 
 118 
 
 16.92 
 
 1.11 
 
 92 
 
 16.37 
 
 1.24 
 
 105 
 
 15.39 
 
 1.39 
 
 119 
 
 13.84 
 
 1.54 
 
 131 
 
 11.81 
 
 1.68 
 
 140 
 
 9.30 
 
 1.81 
 
 143 
 
 
 
 119 
 
 18.20 
 
 1.41 
 
 86 
 
 17.78 
 
 1.65 
 
 99 
 
 16.97 
 
 1.74 
 
 112 
 
 15.61 
 
 1.95 
 
 125 
 
 13.76 
 
 2.16 
 
 135 
 
 11.42 
 
 2.39 
 
 139 
 
 
 
 120 
 
 19.73 
 
 +1.61 
 
 80 
 
 19.47 +1 . 78 
 
 92 
 
 18.86 
 
 fl.99 
 
 104 
 
 17.73 
 
 f2.24 
 
 116 
 
 16.13 '+2.52 
 
 127 
 
 14.08 '+2 82 
 
 132 
 
 
 
 NOTE. When T exceeds 88. subtract 88 from it, and add 46.98 to V. 
 
28 
 
 TABLE XI. 
 
 
 
 
 T 
 
 4 
 
 8 
 
 12 
 
 16 
 
 20 
 
 24 
 
 28 
 
 32 
 
 36 
 
 40 
 
 44 
 
 
 J 
 
 fc 
 
 r 
 
 tv 
 
 r 
 
 Sv 
 
 r 
 
 in 
 
 r 
 
 So 
 
 r 
 
 Sv 
 
 r 
 
 Sv 
 
 r 
 
 Sv 
 
 r 
 
 Sv 
 
 r 
 
 So 
 
 r 
 
 Sv 
 
 r 
 
 So 
 
 r 
 
 
 
 
 
 2.26 
 
 45 
 
 1.79 
 
 SI 
 
 1.69 
 
 2.' 
 
 2.03 
 
 15 
 
 2.79 
 
 ': 
 
 3.87 
 
 
 5.09 
 
 ] 
 
 6.24 
 
 3 
 
 7.15 
 
 5 
 
 7.64 
 
 15 
 
 7.75 
 
 26 
 
 7.61 
 
 35 
 
 
 
 1 
 
 2.51 
 
 52 
 
 1.83 
 
 43 
 
 1.49 33 
 
 1.58 
 
 >- 
 
 2.12 
 
 12 
 
 3.03 
 
 
 4.20 
 
 i 
 
 
 
 5.41 
 
 
 6.46 
 
 6 
 
 7.14 U 
 
 7.43 21 
 
 7.44 
 
 29 
 
 
 
 2 
 
 2.88 
 
 58 
 
 2.05 
 
 of 
 
 1.47 
 
 41 
 
 1.29 
 
 30 
 
 1.57 
 
 19 
 
 2.30 10 
 
 3.36 
 
 1 
 
 4.56 
 
 * 
 
 5.72 
 
 4 
 
 6.55 
 
 
 
 7.08 16 
 
 7.24 
 
 23 
 
 
 
 3 
 
 3.40 
 
 54 
 
 2.41 
 
 57 
 
 1.63 
 
 4X 
 
 1.2-2 
 
 88 
 
 1.22 
 
 27 
 
 1.70 
 
 1( 
 
 2.60 
 
 ^ 
 
 3.73 
 
 r 
 
 4.92 
 
 4 
 
 5.88 
 
 
 6.58 
 
 12 
 
 6.94 
 
 18 
 
 
 
 4 
 
 3.98 
 
 69 
 
 2.93 
 
 6-1 
 
 1.98 
 
 5( 
 
 1.31 
 
 46 
 
 1.05 
 
 35 
 
 1.28 
 
 2 
 
 1.97 
 
 15 
 
 2.97 
 
 ( 
 
 4.14 
 
 1 
 
 5.17 
 
 
 6.05 
 
 1C 
 
 6.54 
 
 15 
 
 
 
 5 
 
 4.68 
 
 72 
 
 3.59 
 
 69 
 
 2.50 
 
 6; 
 
 1.62 
 
 55 
 
 1.09 
 
 44 
 
 1.04 
 
 32 
 
 1.50 
 
 22 
 
 2.32 
 
 13 
 
 3.42 
 
 c 
 
 3.47 
 
 8 
 
 5.4C 
 
 1 
 
 6.07 
 
 13 
 
 
 
 6 
 
 5.42 
 
 75 
 
 4.3-2 
 
 71 
 
 8.15 
 
 6!) 
 
 2.10 
 
 61. 
 
 1.82 
 
 52 
 
 1.00 
 
 41 
 
 1.17 
 
 8( 
 
 1.81 
 
 21 
 
 2.76 
 
 14 
 
 3.80 
 
 1C 
 
 4.77 
 
 c 
 
 5.55 
 
 11 
 
 
 
 7 
 
 6.15 
 
 70 
 
 5.13 
 
 71 
 
 3.93 
 
 74 
 
 2.74 
 
 IS 
 
 1.75 
 
 61 
 
 . 1.17 
 
 50 
 
 1.08 
 
 38 
 
 1.44 
 
 28 
 
 2.23 
 
 21 
 
 3.17 
 
 14 
 
 4.15 
 
 11 
 
 5.00 
 
 11 
 
 
 
 8 
 
 6.90 
 
 75 
 
 5.98 
 
 78 
 
 4.79 
 
 78 
 
 3.54 
 
 U 
 
 2.38 
 
 68 
 
 1.54 
 
 5.8 
 
 1.16 
 
 47 
 
 1.25 
 
 31 
 
 1.82 
 
 27 
 
 2.65 
 
 19 
 
 8.59 
 
 u 
 
 4.46 12 
 
 
 
 9 
 
 7.57 
 
 73 
 
 6.82 
 
 78 
 
 5.70 
 
 8(. 
 
 4.41 
 
 79 
 
 3.14 
 
 74 
 
 2.10 
 
 66 
 
 1.44 
 
 56 
 
 1.27 
 
 44 
 
 1.59 
 
 34 
 
 2.23 
 
 25 
 
 3.08 
 
 19 
 
 3.96 
 
 15 
 
 
 
 10 
 
 8.18 
 
 69 
 
 7.61 
 
 71 
 
 6.62 
 
 80 
 
 5.37 
 
 81 
 
 4.02 
 
 79 
 
 2.81 
 
 73 
 
 1.91 
 
 63 
 
 1.47 
 
 53 
 
 1.52 
 
 42 
 
 1.98 
 
 82 
 
 2.67 
 
 25 
 
 3.50 
 
 19 
 
 
 
 11 
 
 8.66 
 
 65 
 
 8.31 
 
 73 
 
 7.53 
 
 79 
 
 6.37 
 
 8L 
 
 5.00 
 
 82 
 
 3.67 
 
 78 
 
 2.56 
 
 7( 
 
 1.8-7 
 
 6i 
 
 1.63 
 
 51. 
 
 1.88 
 
 3! 
 
 2.39 
 
 31 
 
 3.11 
 
 24 
 
 
 
 12 
 
 9.04 
 
 59 
 
 8.93 
 
 68 
 
 8.35 
 
 76 
 
 7.33 
 
 81 
 
 6.04 
 
 83 
 
 4.63 
 
 82 
 
 '8.37 
 
 76 
 
 2.43 
 
 67 
 
 1.94 
 
 57 
 
 1.92 
 
 47 
 
 2.26 
 
 38 
 
 2.84 
 
 29 
 
 
 
 13 
 
 9.28 
 
 53 
 
 9.41 
 
 6'2 
 
 9.07 
 
 71 
 
 8.25 
 
 79 
 
 7.05 
 
 83 
 
 5.66 
 
 84 
 
 4.29 
 
 80 
 
 3.16 
 
 73 
 
 2.43 
 
 64 
 
 2.15 
 
 54 
 
 2.27 
 
 14 
 
 2.68 
 
 36 
 
 
 
 14 
 
 9.35 
 
 46 
 
 9.73 
 
 56 
 
 9.66 
 
 66 
 
 9.07 
 
 74 
 
 8.05 
 
 81 
 
 6.71 
 
 84 
 
 5.29 
 
 83 
 
 4.02 
 
 78 
 
 3.05 
 
 70 
 
 2.54 
 
 61 
 
 2.4-2 51 
 
 2.64 
 
 42 
 
 
 
 15 
 
 9.27 
 
 39 
 
 9.89 
 
 48 
 
 10.09 
 
 69 
 
 9.76 
 
 69 
 
 8.95 
 
 77 
 
 7.74 
 
 82 
 
 6.33 
 
 83 
 
 4.96 
 
 81 
 
 3.81 
 
 75 
 
 3.07 
 
 67 
 
 2.7258 
 
 2.74 
 
 49 
 
 
 
 16 
 
 9.03 
 
 32 
 
 9.87 
 
 41 
 
 10.34 
 
 51 
 
 10.29 
 
 J2 
 
 9.78 
 
 72 
 
 8.71 
 
 7! 
 
 7.37 
 
 82 
 
 5.96 
 
 82 
 
 4.67 
 
 78 
 
 3.74 
 
 71 
 
 3.16 63 
 
 2.98 
 
 55 
 
 
 
 17 
 
 8.66 
 
 2li 
 
 9.67 
 
 !t 
 
 10.41 
 
 13 
 
 10.65 
 
 54 
 
 10.37 
 
 65 
 
 9.56 
 
 74 
 
 8.35 
 
 79 
 
 6.96 
 
 81 
 
 5.59 
 
 79 
 
 4.51 
 
 75 
 
 3.73|68 
 
 3.34 
 
 61 
 
 
 
 18 
 
 8.14 
 
 20 
 
 9.33 
 
 27 
 
 10.29 
 
 35 
 
 10.79 
 
 16 
 
 10.82 
 
 57 
 
 10.27 
 
 I r 
 
 9.25 
 
 75 
 
 7.95 
 
 79 
 
 6.56 
 
 80 
 
 5.36 
 
 77 
 
 4.40172 
 
 3.80 
 
 65 
 
 
 
 19 
 
 7.54 
 
 15 
 
 8.81 
 
 20 
 
 9.97 
 
 28 
 
 10.75 
 
 38 
 
 11.08 
 
 49 
 
 10.81 
 
 60 
 
 10.02 
 
 ;s 
 
 8.87 
 
 75 
 
 7.51 
 
 78 
 
 6.24 
 
 77 
 
 5.15 
 
 74 
 
 4.37 
 
 69 
 
 
 
 20 
 
 6.84 
 
 12 
 
 8.17 
 
 15 
 
 9.48 
 
 21 
 
 10.49 
 
 >D 
 
 11.12 
 
 40 
 
 11.15 
 
 52 
 
 10.63 
 
 62 
 
 9.67 
 
 70 
 
 8.40 
 
 75 
 
 7.12 
 
 76 
 
 5.95 
 
 75 
 
 5.02 
 
 72 
 
 
 
 21 
 
 6.09 
 
 Oil 
 
 7.44 
 
 10 
 
 8.84 
 
 15 
 
 10.05 
 
 22 
 
 10.94 
 
 32 
 
 11.28 
 
 43 
 
 11.06 
 
 5-1 
 
 10.33 
 
 63 
 
 9.21 
 
 70 
 
 7.97 
 
 74 
 
 6.76 75 
 
 5.72 
 
 78 
 
 
 
 22 
 
 5.34 
 
 08 
 
 6.62 
 
 8 
 
 8.07 
 
 10 
 
 9.44 
 
 R 
 
 10.56 
 
 23 
 
 11.20 
 
 34 
 
 11.28 
 
 46 
 
 10.83 
 
 56 
 
 9.90 
 
 64 
 
 8.77 
 
 70 
 
 7.55 73 
 
 6.44 73 
 
 
 
 23 
 
 4.59 
 
 0!) 
 
 5.77 
 
 6 
 
 7.21 
 
 6 
 
 8.66 
 
 9 
 
 9.99 
 
 16 
 
 10.89 
 
 26 
 
 11.28 
 
 37 
 
 11.14 
 
 18 
 
 10.45 
 
 58 
 
 9.45 65 
 
 8.29 69 
 
 7.16 72 
 
 
 
 24 
 
 3.90 
 
 11 
 
 4.90 
 
 6 
 
 6.29 
 
 4 
 
 7.80 
 
 5 
 
 9.26 
 
 10 
 
 10.38 
 
 18 
 
 11.09 
 
 28 
 
 11.23 
 
 40 
 
 10.82 
 
 50 
 
 10.02 59 
 
 8.97 65 
 
 7.85 69 
 
 
 
 25 
 
 8.26 
 
 15 
 
 4.11 
 
 8 
 
 5.36 
 
 4 
 
 6.82 
 
 3 
 
 8.39 
 
 5 
 
 9.72 
 
 12 
 
 10.68 
 
 21 
 
 11.12 
 
 31 
 
 11.00 
 
 42 
 
 10.41 52 
 
 9.5259 
 
 8.47 65 
 
 
 
 26 
 
 2.75 
 
 19 
 
 3.37 
 
 11 
 
 4.44 
 
 5 
 
 5.83 
 
 2 
 
 7.43 
 
 2 
 
 8.88 
 
 6 
 
 10.09 
 
 14 
 
 10.81 24 
 
 10.99 
 
 34 
 
 10.65 45 
 
 9.96 53 
 
 9.0260 
 
 
 
 27 
 
 2.36 
 
 25 
 
 2.71 
 
 16 
 
 3.59 
 
 8 
 
 4.84 
 
 3 
 
 6.38 
 
 1 
 
 7.94 
 
 2 
 
 9.32 
 
 8 
 
 10.31J17 
 
 10.78 
 
 27 
 
 10.72:37 
 
 10.2246 
 
 9.44 54 
 
 
 
 28 
 
 2.10 
 
 31 
 
 2.21 
 
 33 
 
 2.83 
 
 13 
 
 3.88 
 
 5 
 
 5.35 
 
 1 
 
 6.90! 
 
 8.42 
 
 4 
 
 9.62 
 
 11 
 
 10.38 
 
 20 
 
 10.59 30 
 
 10.34 40 
 
 9.74 48 
 
 
 
 29 
 
 2.01 
 
 
 
 1.85 
 
 28 
 
 2.19 
 
 1,8 
 
 3.04 
 
 10 
 
 4.32 
 
 3 
 
 5.851 
 
 7.44 
 
 1 
 
 8.81 
 
 , 
 
 9.82 14 
 
 10.28 23 
 
 10.30 33 
 
 9.90.42 
 
 
 
 30 
 
 2.06145 
 
 1.65 36 
 
 1.71 25 
 
 2.29 
 
 15 
 
 8.37 
 
 7 
 
 4.791 2 
 
 6.39 
 
 1 
 
 7.88 
 
 3 
 
 9.09 9 
 
 9.8217 
 
 10.09 26 
 
 9.9235 
 
 
 
 T 48 
 
 52 
 
 56 
 
 60 
 
 64 
 
 68 
 
 72 
 
 76 
 
 80 
 
 84 
 
 88 
 
 92 
 
 
 
 J 
 
 6v 
 
 r 
 
 So 
 
 r' 
 
 & 
 
 r 
 
 Sv 
 
 f 
 
 So 
 
 r 
 
 Sv 
 
 r 
 
 Sv 
 
 ^ 
 
 iv 
 
 r 
 
 Sv 
 
 r 
 
 So 
 
 r 
 
 So 
 
 r 
 
 Sv 
 
 f 
 
 
 
 
 
 7.10 
 
 44 
 
 6.60 
 
 51 
 
 6.19 
 
 58 
 
 5.88 
 
 64 
 
 5.69 
 
 68 
 
 5.52 
 
 70 
 
 5.26 
 
 70 
 
 4.82 
 
 69 
 
 4.20 
 
 65 
 
 3.41 
 
 60 
 
 2.57 
 
 53 
 
 l'.88 
 
 44 
 
 
 
 i 
 
 7.17 
 
 37 
 
 6.79 
 
 45 
 
 6.42 
 
 53 
 
 614 
 
 59 
 
 5.98 
 
 65 
 
 5.85 
 
 68 
 
 5.66 70 
 
 5.29 
 
 70 
 
 4.7069 
 
 3.90 
 
 65 
 
 2.98:60 
 
 2.13 
 
 51 
 
 
 
 2 
 
 7.15 
 
 31 
 
 6.87 
 
 39 
 
 6.59 
 
 17 
 
 6.36 
 
 55 
 
 6.24 
 
 61 
 
 6.17 
 
 66 
 
 6.04 
 
 69 
 
 5.75 
 
 71 
 
 5.24 
 
 71 
 
 4.47 
 
 6i) 
 
 3.51 65 
 
 2.52 : 58 
 
 
 
 3 
 
 7.00 
 
 26 
 
 6.87 
 
 33 
 
 6.68 
 
 II 
 
 6.50 
 
 19 
 
 6.45 
 
 56 
 
 6.44 
 
 62 
 
 6.39 
 
 67 
 
 6.21 
 
 70 
 
 5.79 
 
 72 
 
 5.08 
 
 72 
 
 4.12170 
 
 3.08J65 
 
 
 
 4 
 
 6.77 
 
 21 
 
 6.78 
 
 28 
 
 6.68 
 
 35 
 
 6.58 
 
 13 
 
 6.59 
 
 50 
 
 6.65 
 
 58 
 
 6.69 
 
 63 
 
 6.63 
 
 68 
 
 6.34 
 
 72 
 
 5.73 
 
 73 
 
 4.82 
 
 73 
 
 3.75 
 
 70 
 
 
 
 5 
 
 6.47 
 
 17 
 
 6.61 23 
 
 6.60 
 
 30 
 
 6.59 
 
 37 
 
 6.67 
 
 -15 
 
 6.81 
 
 52 
 
 6.93 
 
 59 
 
 .7.00 
 
 65 
 
 6.85 
 
 70 
 
 6.38 
 
 73 
 
 5.55 
 
 75 
 
 4.50 
 
 74 
 
 
 
 6 
 
 6.07 
 
 14 
 
 6.36 
 
 19 
 
 6.47 
 
 25 
 
 6.52 
 
 32 
 
 6.68 
 
 89 
 
 6.87 
 
 47 
 
 7.11 
 
 5-1 
 
 7.31 
 
 61 
 
 7.32 
 
 67 
 
 7.01 
 
 72 
 
 6.30 
 
 75 
 
 5.32 
 
 76 
 
 
 
 7 
 
 5.64 
 
 13 
 
 6.03 
 
 16 
 
 6.25 
 
 20 
 
 6.40 
 
 26 
 
 6.61 
 
 33 
 
 6.88 
 
 41 
 
 7.20 
 
 48 
 
 7.54 
 
 56 
 
 7.69 
 
 63 
 
 7.56 
 
 6!) 
 
 7.02 
 
 74 
 
 6.16 
 
 78 
 
 
 
 8 
 
 5.19 
 
 12 
 
 5.66 
 
 14 
 
 5.98 
 
 17 
 
 5.07 
 
 22 
 
 6.47 
 
 28 
 
 6.80 
 
 35 
 
 7.21 
 
 13 
 
 7.66 
 
 51 
 
 7.98 
 
 -><8 
 
 8.03 
 
 16 
 
 7.68 
 
 72 
 
 6.99 
 
 78 
 
 
 
 9 
 
 4.71 
 
 13 
 
 5.28 
 
 13 
 
 5.66 
 
 15 
 
 5.97 
 
 18 
 
 6.29 
 
 24 
 
 6.66 
 
 29 
 
 7.13 
 
 37 
 
 7.69 
 
 15 
 
 8.16 
 
 53 
 
 8.41 
 
 61 
 
 8.28 
 
 68 
 
 7.76 
 
 76 
 
 
 
 10 
 
 4.25 
 
 15 
 
 4.87 
 
 14 
 
 5.32 
 
 11 
 
 5.67 
 
 16 
 
 6.02 
 
 19 
 
 6.43 
 
 25 
 
 6.97 
 
 31 
 
 7.61 
 
 39 
 
 8.22 
 
 47 
 
 8.66 
 
 56 
 
 8.74 
 
 64 
 
 8.45 
 
 72 
 
 
 
 11 
 
 3.85 
 
 19 
 
 4.48 
 
 15 
 
 4.97 
 
 11 
 
 5.36 
 
 14 
 
 5.74 
 
 16 
 
 6.17 
 
 20 
 
 6.73 
 
 26 
 
 7.45 
 
 33 
 
 8.17 
 
 40 
 
 8.77 
 
 49 
 
 9.09 
 
 58 
 
 9.04 
 
 17 
 
 
 
 12 
 
 3.50 
 
 23 
 
 4.12 
 
 18 
 
 4.62 
 
 15 
 
 5.04 
 
 14 
 
 5.42 
 
 1-1 
 
 5.86 
 
 17 
 
 6.43 
 
 21 
 
 7.18 
 
 27 
 
 8.00 
 
 !4 
 
 8.77 
 
 42 
 
 9.30 
 
 51 
 
 9.48 
 
 61 
 
 
 
 13 
 
 3.24 
 
 28 
 
 3.81 
 
 22 
 
 4.31 
 
 18 
 
 4.71 
 
 14 
 
 5.09 
 
 14 
 
 5.52 
 
 15 
 
 6.07 
 
 1,8 
 
 6.85 
 
 22 
 
 7.72 
 
 28 
 
 8.61 
 
 16 
 
 9.35 
 
 14 
 
 9.77 
 
 55 
 
 
 
 14 
 
 3.08 
 
 34 
 
 3.56 
 
 27 
 
 4.03 
 
 21 
 
 4.42 
 
 17 
 
 4.77 
 
 14 
 
 5.16 
 
 14 
 
 5.70 
 
 15 
 
 6.43 
 
 18 
 
 7.84 
 
 23 
 
 8.32 
 
 29 
 
 9.23 
 
 17 
 
 9.89 
 
 47 
 
 
 
 15 
 
 3.02 
 
 40 
 
 3.41 
 
 18 
 
 8.81 
 
 26 
 
 4.16 
 
 20 
 
 4.46 
 
 16 
 
 4.81 
 
 14 
 
 5.29 
 
 14 
 
 5.99 
 
 15 
 
 6.83 
 
 19 
 
 7.92 
 
 21 
 
 8.97 
 
 31 
 
 9.73 
 
 10 
 
 
 
 16 
 
 3.08 
 
 17 
 
 3.34 
 
 S9 
 
 3.65 
 
 il 
 
 3.95 
 
 25 
 
 4.19 
 
 19 
 
 4.48 
 
 16 
 
 4.88 
 
 14 
 
 5.51 
 
 14 
 
 6.36 
 
 15 
 
 7.42 
 
 19 
 
 8.57 
 
 24 
 
 9.60 
 
 33 
 
 
 
 17 
 
 3.24 
 
 53 
 
 3.37 
 
 15 
 
 3.59 
 
 !7 
 
 3.81 
 
 29 
 
 3.97 
 
 23 
 
 4.18 
 
 18 
 
 4.50 
 
 15 
 
 5.03 
 
 13 
 
 5.80 
 
 13 
 
 6.83 
 
 15 
 
 8.03 
 
 111 
 
 9.22 
 
 26 
 
 
 
 18 
 
 3.54 
 
 58 
 
 3.50 
 
 51 
 
 3.60 
 
 11 
 
 3.74 
 
 US 
 
 3.82 
 
 28 
 
 3.94 
 
 22 
 
 4.17 
 
 17 
 
 4.58 
 
 11 
 
 5.24 
 
 12 
 
 6.21 
 
 12 
 
 7.40 
 
 14 
 
 8.67 
 
 19 
 
 
 
 19 
 
 3.93 
 
 63 
 
 3.72 
 
 56 
 
 3.71 
 
 19 
 
 3.74 
 
 41 
 
 3.74 
 
 r.', 
 
 3.77 
 
 26 
 
 8.87 
 
 20 
 
 4.1516 
 
 4.67 
 
 12 
 
 5.5511 
 
 6.71 
 
 11 
 
 8.01 
 
 14 
 
 
 
 20 
 
 4.41 
 
 67 
 
 4.05 
 
 61 
 
 3.92 
 
 54 
 
 8.83 
 
 17 
 
 3.74 
 
 19 
 
 3.67 
 
 i2 
 
 3.67 
 
 25 
 
 3.79 19 
 
 4.16 
 
 14 
 
 4.88 11 
 
 5.96 
 
 9 
 
 7.26 
 
 10 
 
 
 
 21 
 
 4.97 
 
 70 
 
 4.46 
 
 i5 
 
 4.18 
 
 19 
 
 4.01 
 
 52 
 
 3.81 
 
 48 
 
 3.66 
 
 17 
 
 3.51 
 
 io 
 
 3.49 23 
 
 3.70 
 
 16 
 
 4.25 12 
 
 5.20 
 
 9 
 
 6.43 
 
 8 
 
 
 
 22 
 
 5.57 
 
 71 
 
 4.94 
 
 (8 
 
 4.54 
 
 14 
 
 4.25 
 
 )8 
 
 3.97 
 
 5i 
 
 3.7243 
 
 3.47 
 
 15 
 
 3.28 28 
 
 3.32 
 
 21 
 
 3.69 15 
 
 4.46 
 
 9 
 
 5.58 
 
 6 
 
 
 
 23 
 
 6.20 
 
 72 
 
 5.47 
 
 70 
 
 4.97 
 
 i7 
 
 4.56 
 
 i2 
 
 4.21 
 
 -,6 
 
 3.8649 
 
 3.50 
 
 41 
 
 3.1933 
 
 8.03 
 
 26 
 
 3.2018 
 
 3.78 
 
 12 
 
 4.73 
 
 6 
 
 
 
 24 
 
 685 
 
 71 
 
 6.02 
 
 71 
 
 5.43 
 
 19 
 
 4.94 
 
 ;e 
 
 4.50 
 
 il 
 
 4.09 55 
 
 3.63 
 
 47 
 
 3.17 
 
 19 
 
 2.86131 
 
 2.81 23 
 
 3.16 
 
 16 
 
 3.95 
 
 8 
 
 
 
 25 
 
 7.47169 
 
 6.59 
 
 70 
 
 5.92 
 
 70 
 
 5.37 
 
 i8 
 
 4.87 
 
 65 
 
 4.3959 
 
 8.85 
 
 53 
 
 3.28 
 
 15 
 
 2.7937 
 
 2.54 29 
 
 2.69 
 
 21 
 
 3.22 
 
 12 
 
 
 
 26 
 
 8.0365 
 
 7.14 
 
 II) 
 
 6.42 
 
 70 
 
 5.82 
 
 70 
 
 5.27 
 
 18 
 
 4.75 64 
 
 4.15 
 
 58 
 
 3.4951 
 
 2.86 44 
 
 2.4235 
 
 2.3 2 1 26 
 
 2.40 
 
 17 
 
 
 
 27 
 
 8.5261 
 
 7.67 
 
 i6 
 
 6.92 
 
 69 
 
 6.28 
 
 70 
 
 5.71 
 
 70 
 
 5.1667 
 
 4.51 63 
 
 3.7957 
 
 3.05 50 
 
 2.42|42 
 
 2.08:33 
 
 2.13 
 
 23 
 
 
 
 28 
 
 8.95 56 
 
 8.13 
 
 IS 
 
 7.39 
 
 Hi 
 
 6.74 
 
 19 
 
 6.16 
 
 70 
 
 5.59 69 
 
 4.94 
 
 66 
 
 4.1762 
 
 3.34 56 
 
 2.57i48 
 
 2.0r40 
 
 1.81 
 
 29 
 
 
 
 29 
 
 9.25 50 
 
 8.51 
 
 -,1 
 
 7.82 
 
 >3 
 
 7-.17 
 
 j? 
 
 6.60 
 
 70 
 
 6.06 70 
 
 5.39 69 
 
 4.6366 
 
 3.7461 
 
 2.8655 
 
 2.1047 
 
 1.6537 
 
 
 
 30 
 
 9.44 44 
 
 8.82 
 
 n 
 
 8.17 
 
 58 
 
 7.56 
 
 ;i 
 
 7.03 
 
 i8 
 
 6.50 70 
 
 5.88 70 
 
 5.1269 
 
 4.22 65 
 
 3.25 60 2.33 53 
 
 1.6644 
 
 
 
 NOTE. When T exceeds 88, subtract 88 from it, and add 1.22 to Argument J. 
 
TABLE XI. 
 
 29 
 
 
 
 
 T 
 
 4 
 
 8 
 
 12 
 
 16 
 
 20 
 
 24 
 
 28 
 
 32 
 
 36 
 
 40 
 
 44 
 
 
 j 
 
 So r 
 
 dv 
 
 r 
 
 So f 
 
 & 
 
 r 
 
 &> 
 
 r 
 
 tv 
 
 r 
 
 So 
 
 r 
 
 to 
 
 r 
 
 iv 
 
 p 
 
 iv 
 
 r 
 
 iv 
 
 /' 
 
 iv 
 
 r 
 
 
 
 30 
 
 2.06 
 
 45 
 
 1.65 
 
 .-it; 
 
 '.71 25 
 
 i'.29 
 
 15 
 
 3.37 
 
 7 
 
 4.79 
 
 > 
 
 6.39 
 
 1 
 
 7.88 
 
 3 
 
 9.09 
 
 9 
 
 9.82 
 
 17 
 
 10.09 
 
 26 
 
 9.92 
 
 35 
 
 
 
 31 
 
 2.27;52 
 
 1.6343 
 
 .4l|33 
 
 1.70 
 
 22 
 
 2.54 
 
 12 
 
 3.79 
 
 5 
 
 5.34 
 
 2 
 
 6.89 
 
 2 
 
 8.26 
 
 (i 
 
 9.20 
 
 13 
 
 9.72 
 
 21 
 
 9.78 
 
 29 
 
 
 
 32 
 
 2.62:58 
 
 1.77 
 
 50 
 
 .2741 
 
 1.29 
 
 30 
 
 1.83 
 
 19 
 
 2.88 
 
 10 
 
 4.32 
 
 5 
 
 5.86 
 
 3 
 
 7.34 
 
 4 
 
 8.47 
 
 9 
 
 9.20 
 
 Hi 
 
 9.50 
 
 23 
 
 
 
 33 
 
 3.10 64 
 
 2.07 
 
 57 
 
 .3348 
 
 1.06 
 
 38 
 
 1.32 
 
 27 
 
 2.10 
 
 16 
 
 3.36 
 
 9 
 
 4.83 
 
 5 
 
 6.36 
 
 4 
 
 7.64 
 
 7 
 
 8.58 
 
 12 
 
 9.10 
 
 18 
 
 
 
 34 
 
 3.G9J69 
 
 2.55 
 
 64 
 
 .5856 
 
 1.03 
 
 46 
 
 0.97 
 
 35 
 
 1.48 
 
 24 
 
 2.51 15 
 
 3.87 
 
 9 
 
 5.39 
 
 5 
 
 6.75 
 
 7 
 
 7.86 
 
 10 
 
 8.58 
 
 15 
 
 
 
 35 
 
 4.36 72 
 
 3.13 
 
 69 
 
 2.00 63 
 
 1 20 
 
 55 
 
 0.83 
 
 44 
 
 1.04 
 
 32 
 
 1-.82S2 
 
 3.00 
 
 13 
 
 4.44 
 
 9 
 
 5.83 
 
 8 
 
 7.06 
 
 9 
 
 7.97 
 
 13 
 
 
 
 36 
 
 5.08 75 
 
 3.82 
 
 74 
 
 2.5769 
 
 1.56 
 
 62 
 
 0.92 
 
 52 
 
 .82 
 
 41 
 
 1.31 
 
 30 
 
 2.25 
 
 >\ 
 
 3.58 
 
 14 
 
 4.94 
 
 10 
 
 6.23 
 
 9 
 
 7.27 
 
 11 
 
 
 
 37 
 
 5.81176 
 
 4.59 76 
 
 3.27 74 
 
 2.08 
 
 (i!) 
 
 1.19 
 
 61 
 
 .79 
 
 50 
 
 .98 
 
 38 
 
 1.66 
 
 28 
 
 2.79 20 
 
 4.09 
 
 11 
 
 5.41 
 
 11 
 
 6.54 
 
 11 
 
 
 
 38 
 
 6.54 75 
 
 5.38 78 
 
 4.05 78 
 
 2.76 
 
 75 
 
 1.64 
 
 68 
 
 .98 
 
 58 
 
 .86 
 
 47 
 
 1.25 
 
 36 
 
 2.16 27 
 
 3.33 
 
 19 
 
 4.61 
 
 15 
 
 5.80 
 
 12 
 
 
 
 39 
 
 7.21 
 
 73 
 
 6.20 78 
 
 4.90 
 
 
 
 3.53 
 
 79 
 
 2.26 
 
 71 
 
 1.36 
 
 66 
 
 .92 
 
 56 
 
 1.03 
 
 44 
 
 1.67 
 
 34 
 
 2.67 
 
 25 
 
 3.88 
 
 19 
 
 5.06 
 
 16 
 
 
 
 40 
 
 7.82 
 
 69 
 
 6.95 
 
 76 
 
 5.76 
 
 so 
 
 3.41 
 
 81 
 
 3.02 
 
 7!) 
 
 1.91 
 
 73 
 
 1.21 
 
 63 
 
 1.01 
 
 53 
 
 1.38 
 
 42 
 
 2.16 
 
 32 
 
 3.23 
 
 25 
 
 4.38 
 
 1!) 
 
 
 
 41 
 
 8.32165 
 
 7.65 
 
 73 
 
 659 
 
 7!) 
 
 5.29 
 
 82 
 
 3.86 
 
 S2 
 
 2.61 
 
 78 
 
 1.64 
 
 70 
 
 1.17 
 
 60 
 
 1.25 
 
 50 
 
 1.80 
 
 89 
 
 2.69 
 
 31 
 
 3.77 
 
 24 
 
 
 
 42 
 
 8.70J59 
 
 8.27 
 
 (is 
 
 7.37 
 
 76 
 
 6.21 
 
 81 
 
 4.7883 
 
 3.41 
 
 S2 
 
 2.27 
 
 76 
 
 1.53 
 
 67 
 
 1.30 
 
 57 
 
 1.60 
 
 17 
 
 2.30 
 
 38 
 
 3.24 
 
 29 
 
 
 
 43 
 
 8.94 53 
 
 8.7362 
 
 8.07 
 
 71 
 
 7.05 
 
 71) 
 
 5.71 
 
 83 
 
 4.32 
 
 81 
 
 3.03 
 
 80 
 
 2.06 
 
 73 
 
 1.55 
 
 64 
 
 1.59 
 
 54 
 
 2.05 
 
 11 
 
 2.82 
 
 36 
 
 
 
 44 
 
 9.03 46 
 
 9.05 56 
 
 S.G4 
 
 66 
 
 7.81 
 
 71 
 
 6.61 
 
 81 
 
 5,23 
 
 84 
 
 3.85 
 
 83 
 
 2.72 
 
 78 
 
 1.95 
 
 70 
 
 1.72 
 
 (il 
 
 1.94 
 
 51 
 
 2.54 
 
 42 
 
 
 
 45 
 
 8.97 
 
 39 
 
 9.23 48 
 
 9.07 
 
 5!) 
 
 8.48 
 
 68 
 
 7.45 
 
 77 
 
 6.16 
 
 82 
 
 4.75 
 
 S3 
 
 .3.48 
 
 SI 
 
 2.51 
 
 75 
 
 2.03 
 
 67 
 
 2.00 
 
 58 
 
 2.38 
 
 49 
 
 
 
 46 
 
 8.75 32 
 
 9.23 41 
 
 9.32 
 
 51 
 
 8.99 
 
 62 
 
 8.17 
 
 72 
 
 7.03 
 
 70 
 
 5.65 
 
 82 
 
 4.30 
 
 82 
 
 3.17 
 
 78 
 
 2.48 
 
 71 
 
 2.20 
 
 63 
 
 2.36 
 
 55 
 
 
 
 47 
 
 8.40 26 
 
 9.07 34 
 
 9.41 
 
 13 
 
 9.33 
 
 54 
 
 9.79 
 
 (i.-, 
 
 7.82 
 
 74 
 
 6.53 
 
 79 
 
 5.18 
 
 81 
 
 3.91 
 
 7!) 
 
 3.03 
 
 75 
 
 2.55 
 
 68 
 
 2.48 
 
 (il 
 
 
 
 48 
 
 7.92 20 
 
 8.75 27 
 
 9.31 
 
 86 
 
 9.49146 
 
 9.20 
 
 57 
 
 8.49 
 
 67 
 
 7.35175 
 
 6.05 
 
 711 
 
 4.72 
 
 80 
 
 3.68 
 
 77 
 
 3.00 
 
 72 
 
 2.72 
 
 (i.-, 
 
 
 
 49 
 
 7.34 15 
 
 8.27 20 
 
 9.03 
 
 28 
 
 9.47 
 
 88 
 
 9.46 
 
 49 
 
 8.99 
 
 60 
 
 8.06 69 
 
 6.85 
 
 75 
 
 5.53 
 
 78 
 
 4.40 
 
 77 
 
 3.53 
 
 74 
 
 3.07 
 
 69 
 
 
 
 50 
 
 6.68 
 
 12 
 
 7.67 
 
 15 
 
 8.58 
 
 21 
 
 9.25 
 
 29 
 
 9.5240 
 
 9.33 
 
 52 
 
 8.61 
 
 62 
 
 7.57 
 
 70 
 
 6.30 
 
 75 
 
 5.14 
 
 7(i 
 
 4.15 
 
 75 
 
 3.50 
 
 72 
 
 
 
 51 
 
 5.97 09 
 
 6.98 10 
 
 8.00 
 
 15 
 
 8.85 22 
 
 9.38|32 
 
 9.46 
 
 43 
 
 9.02 54 
 
 8.17 
 
 61! 
 
 7.01 
 
 70 
 
 5.85 
 
 74 
 
 4.80 
 
 75 
 
 4.02 
 
 73 
 
 
 
 52 
 
 5.26 08 
 
 6.22 8 
 
 7.29 
 
 10 
 
 8.30 15 
 
 9.06 23 
 
 9.40 
 
 34 
 
 9.26 
 
 56 
 
 8.63 
 
 66 
 
 7.64 
 
 64 
 
 6.53 
 
 70 
 
 5.45 
 
 73 
 
 4.58 
 
 73 
 
 
 
 53 
 
 4.53 09 
 
 5.43 
 
 (i 
 
 6.51 
 
 6 
 
 7.60 9 
 
 8.55 16 
 
 9.15 26 
 
 9.26 
 
 37 
 
 8.92 
 
 48 
 
 8.13 
 
 58 
 
 7.13 
 
 66 
 
 6.07 
 
 (il) 
 
 5.14 
 
 72 
 
 
 
 ;54 
 
 3.88 11 
 
 4.64 
 
 6 
 
 5.67 
 
 4 
 
 6.81 
 
 5 
 
 7.90 
 
 Id 
 
 8.72J18 
 
 9.11 
 
 28 
 
 9.03 
 
 40 
 
 8.48 
 
 SO 
 
 7.64 
 
 59 
 
 6.63 
 
 65 
 
 5.69 
 
 69 
 
 
 
 55 
 
 3.30|15 
 
 3.89 
 
 8 
 
 4.82 
 
 4 
 
 5.96 
 
 3 
 
 7.13 
 
 5 
 
 8.12 
 
 12 
 
 8.76 
 
 21 
 
 8.96 
 
 31 
 
 8.66 
 
 42 
 
 8.01 
 
 52 
 
 7.14 
 
 59 
 
 6.21 
 
 65 
 
 
 
 56 
 
 2.81119 
 
 3.23 
 
 11 
 
 4.00 
 
 5 
 
 5.07 
 
 2 
 
 6.27 
 
 2 
 
 7.40 
 
 6 
 
 8.27 
 
 14 
 
 8.71 
 
 24 
 
 8.69 
 
 31 
 
 8.23 
 
 45 
 
 7.53 
 
 53 
 
 6.66 
 
 60 
 
 
 
 57 
 
 2.46 25 
 
 2.65 
 
 16 
 
 3.25 
 
 8 
 
 4.20 
 
 3 
 
 5.36 
 
 1 
 
 6.58 
 
 2 
 
 7.60 
 
 8 
 
 8.29 
 
 17 
 
 8.54 
 
 27 
 
 8.32 
 
 37 
 
 7.78 
 
 46 
 
 7.04 
 
 54 
 
 
 
 58 
 
 2.24 31 
 
 2.21 22 
 
 2.59 
 
 13 
 
 3.37 5 
 
 4.45 
 
 1 
 
 5.68 
 
 (1 
 
 6.82 
 
 4 
 
 7.72 
 
 11 
 
 8.20 
 
 20 
 
 8.23 
 
 30 
 
 7.90 40 
 
 7.32 48 
 
 
 
 59 
 
 2.17138 
 
 1.93 28 
 
 2.08 
 
 18 
 
 2.64 
 
 10 
 
 3.58 
 
 3 
 
 4.77 
 
 
 
 5.98 
 
 1 
 
 7.01 
 
 6 
 
 7.74 
 
 14 
 
 8.02 
 
 23 
 
 7.90 33 
 
 7.48 
 
 42 
 
 
 
 60 
 
 2.26)45 
 
 1.7936 
 
 1.69 
 
 26 
 
 2.03 15 
 
 2.79 7 
 
 3.87 
 
 2 
 
 5.09 
 
 1 
 
 6.24 3 
 
 7.15 
 
 1) 
 
 7.64ll7 
 
 7.75 26 
 
 7.52 35 
 
 
 
 T 48 
 
 52 
 
 56 
 
 60 
 
 64 
 
 68 
 
 72 
 
 76 
 
 80 
 
 84 
 
 88 
 
 92 
 
 
 
 J 
 
 & 
 
 r 
 
 da 
 
 /' 
 
 da 
 
 r 
 
 iv 
 
 r 
 
 *. 
 
 r 
 
 iv f 
 
 6u \f 
 
 iv 
 
 r 
 
 iv 
 
 r 
 
 iv 
 
 r 
 
 iv 
 
 r 
 
 iv 
 
 r 
 
 
 
 30 
 
 9.44 
 
 44 
 
 8.82 
 
 51 
 
 8.17 
 
 68 
 
 7.56 
 
 64 
 
 7.03 
 
 68 
 
 6.50 70 
 
 5.88 70 
 
 5.12 
 
 69 
 
 4.22 
 
 65 
 
 3.25 
 
 60 
 
 2.33 
 
 53 
 
 i'.66 
 
 44 
 
 
 
 31 
 
 9.49 37 
 
 9.01 45 
 
 8.46 
 
 53 
 
 7.90 
 
 59 
 
 7.42 
 
 65 
 
 6.9368 
 
 6.36 70 
 
 5.65 
 
 70 
 
 4.7669 
 
 3.74 
 
 65 
 
 2.7060 
 
 1.84 
 
 51 
 
 
 
 32 
 
 943 31 
 
 9.09 39 
 
 8.65 
 
 17 
 
 8.16 
 
 55 
 
 7.76 
 
 61 
 
 7.33|66 
 
 6.8269 
 
 6.19 
 
 71 
 
 5.34 
 
 71 
 
 4.33 
 
 (i!l 
 
 3.21165 
 
 2.17 
 
 58 
 
 
 
 33 
 
 9.22 
 
 26 
 
 9.07 33 
 
 8.74 
 
 11 
 
 8.34 
 
 49 
 
 8.01 
 
 56 
 
 7.66 62 
 
 7.2367 
 
 6.69 
 
 70 
 
 5.93 
 
 72 
 
 4.94 
 
 72 
 
 3.82 70 
 
 2.68 
 
 65 
 
 
 
 34 
 
 8.91 
 
 21 
 
 8.94 
 
 28 
 
 8.72 
 
 86 
 
 8.44 
 
 43 
 
 8.19 
 
 50 
 
 7.93 58 
 
 7.59 
 
 63 
 
 7.17 
 
 68 
 
 6.52 
 
 72 
 
 5.61 
 
 73 
 
 4.48 
 
 73 
 
 3.28 
 
 70 
 
 
 
 35 
 
 8.47 
 
 17 
 
 8.67 
 
 23 
 
 8.62 
 
 30 
 
 8.45 
 
 37 
 
 8.29 
 
 45 
 
 8.11 
 
 52 
 
 7.89 
 
 59 
 
 7.58 
 
 65 
 
 7.07 
 
 70 
 
 6.28 
 
 73 
 
 5.21 
 
 75 
 
 3.99 
 
 74 
 
 
 
 36 
 
 7.95 
 
 14 
 
 8.32 
 
 19 
 
 8.41 
 
 25 
 
 8.36 
 
 32 
 
 8.30 
 
 89 
 
 8.21 47 
 
 8.11 54 
 
 7.93 
 
 til 
 
 7.56 
 
 67 
 
 6.91 
 
 72 
 
 5.94 
 
 75 
 
 4.77 
 
 76 
 
 
 
 37 
 
 7.36 13 
 
 7.89 
 
 16 
 
 8.11 
 
 20 
 
 8.18 
 
 26 
 
 8.23 
 
 33 
 
 8.2241 
 
 8.2248 
 
 8.18 
 
 56 
 
 7.97 
 
 63 
 
 7.48 
 
 69 
 
 6.66 
 
 7-1 
 
 5.56 
 
 78 
 
 
 
 38 
 
 6.73 12 
 
 7.38 
 
 14 
 
 7.74 
 
 17 
 
 7.93 
 
 22 
 
 8.05 
 
 2.s 
 
 8.14 
 
 35 
 
 8.2543 
 
 8.34 
 
 51 
 
 8.28 
 
 58 
 
 7.97 
 
 66 
 
 7.32 
 
 72 
 
 6.37 
 
 78 
 
 
 
 39 
 
 6.07 
 
 13 
 
 6.84 
 
 13 
 
 7.30 
 
 10 
 
 7.59 
 
 18 
 
 7.81 
 
 24 
 
 7.98 
 
 29 
 
 8.17 
 
 37 
 
 8.39 
 
 45 
 
 8.48 
 
 53 
 
 8.35 
 
 (il 
 
 7.92 
 
 68 
 
 7.10 
 
 76 
 
 
 
 40 
 
 5.41 
 
 IB 
 
 6.25 
 
 11 
 
 6.82 
 
 14 
 
 7.21 
 
 Hi 
 
 7.50 
 
 19 
 
 7.73 
 
 25 
 
 8.01 
 
 31 
 
 8.33 
 
 39 
 
 8.58 
 
 47 
 
 8.64 
 
 55 
 
 8.38 
 
 64 
 
 7.79 
 
 72 
 
 
 
 41 
 
 4.79 
 
 19 
 
 5.68 
 
 If 
 
 6.31 
 
 1 1 
 
 6.78 
 
 14 
 
 7.12 
 
 16 
 
 7.41 
 
 20 
 
 7.75 
 
 26 
 
 8.15 
 
 33 
 
 8.53 
 
 40 
 
 8.77 
 
 4!) 
 
 8.73 
 
 58 
 
 8.37 
 
 67 
 
 
 
 42 
 
 4.22 
 
 23 
 
 5.10 
 
 IS 
 
 5.80 
 
 15 
 
 6.32 
 
 14 
 
 6.72 
 
 II 
 
 7.04 
 
 17 
 
 7.45 
 
 21 
 
 7.88 
 
 27 
 
 8.36 
 
 34 
 
 8.77 
 
 12 
 
 8.96 
 
 51 
 
 8.80 
 
 61 
 
 
 
 43 
 
 3.70 
 
 28 
 
 4.59 
 
 22 
 
 5.29 
 
 18 
 
 5.85 
 
 14 
 
 6.27 
 
 14 
 
 6.62 
 
 15 
 
 7.03 
 
 18 
 
 7.53 
 
 22 
 
 8.10 
 
 js 
 
 8.63 
 
 36 
 
 9.01 
 
 11 
 
 9.09 
 
 55 
 
 
 
 44 
 
 3.30 
 
 34 
 
 4.12 
 
 27 
 
 4.81 
 
 21 
 
 5.40 
 
 17 
 
 5.83 
 
 11 
 
 6.18 
 
 14 
 
 6.60 
 
 15 
 
 7.11 
 
 18 
 
 7.72 
 
 23 
 
 8.36 
 
 29 
 
 8.93 
 
 37 
 
 9.23 
 
 47 
 
 
 
 45 
 
 3.00 
 
 40 
 
 3.73 
 
 :::! 
 
 4.39 
 
 26 
 
 4.96 
 
 20 
 
 5.38 
 
 16 
 
 5.73 
 
 14 
 
 6.13 
 
 14 
 
 6.63 
 
 15 
 
 7.26 
 
 19 
 
 7.98 
 
 24 
 
 8.69 
 
 31 
 
 9.20 
 
 40 
 
 
 
 46 
 
 2.8247 
 
 342 
 
 39 
 
 4.03 
 
 :il 
 
 4.57 
 
 25 
 
 4.97 
 
 HI 
 
 5.30 
 
 16 
 
 5.62 
 
 14 
 
 6.11 
 
 14 
 
 6.74 
 
 16 
 
 7.50 
 
 19 
 
 8.31 
 
 24 
 
 9.00 
 
 33 
 
 
 
 47 
 
 2.74 
 
 53 
 
 3.23 
 
 46 
 
 3.73 
 
 37 
 
 4.23 
 
 I'll 
 
 4.59 
 
 23 
 
 4.88 
 
 18 
 
 5.20 
 
 15 
 
 5.59 
 
 13 
 
 6.18 
 
 13 
 
 6.93 15 
 
 7.81 
 
 1!) 
 
 8.64 
 
 26 
 
 
 
 48 
 
 2.80 
 
 58 
 
 3.12 
 
 51 
 
 3.54 
 
 11 
 
 3.98 
 
 86 
 
 4.28 
 
 2.S 
 
 4.52 
 
 22 
 
 4.77 
 
 17 
 
 5.08 
 
 14 
 
 5.60 
 
 12 
 
 6.33!l2 
 
 7.22 
 
 14 
 
 8.14 
 
 1!) 
 
 
 
 49 
 
 2.95 
 
 68 
 
 3.12 
 
 M 
 
 3.45 
 
 49 
 
 3.80 
 
 11 
 
 4.04 
 
 B8 
 
 4.21 
 
 26 
 
 4.39 
 
 20 
 
 5.61 
 
 16 
 
 5.03 
 
 12 
 
 5.67 
 
 11 
 
 6.55 
 
 11 
 
 7.52 
 
 14 
 
 
 
 50 
 
 3.21 
 
 07 
 
 3.23 
 
 61 
 
 3.42 
 
 54 
 
 8.69 
 
 17 
 
 8.86 
 
 in 
 
 3.97 
 
 32 
 
 4.07 
 
 25 
 
 4.19 
 
 19 
 
 4.48 
 
 14 
 
 5.02 
 
 11 
 
 5.84 
 
 9 
 
 6.81 
 
 10 
 
 
 
 51 
 
 3.57 
 
 70 
 
 3.42 
 
 65 
 
 3.50 
 
 59 
 
 3.67 
 
 52 
 
 3.77 
 
 US 
 
 3.8237 
 
 8.83 
 
 30 
 
 3.83 
 
 23 
 
 3.98 
 
 16 
 
 4.39(12 
 
 5.12 
 
 9 
 
 6.05 
 
 8 
 
 
 
 52 
 
 3.99 
 
 71 
 
 3.70 
 
 (is 
 
 3.66 
 
 114 
 
 3 73 
 
 58 
 
 3.75 
 
 -.1 
 
 3.74143 
 
 8.67 
 
 35 
 
 3.46 
 
 28 
 
 8.58 
 
 21 
 
 3.83 15 
 
 4.42 
 
 9 
 
 5.26 
 
 6 
 
 
 
 53 
 
 4.44 
 
 n 
 
 4.05 
 
 70 
 
 3.87 
 
 (17 
 
 3.86 
 
 62 
 
 3.83 
 
 "16 
 
 3.76 
 
 49 
 
 3.60 
 
 41 
 
 3.38 
 
 33 
 
 3.27 
 
 26 
 
 3.361 18 
 
 3.78 
 
 12 
 
 4.48 
 
 6 
 
 
 
 54 
 
 4.93 71 
 
 4.42 
 
 71 
 
 4.17 
 
 (ill 
 
 4.06 
 
 66 
 
 8.96 
 
 il 
 
 3.83 
 
 55 
 
 3.63 
 
 47 
 
 3.31 
 
 39 
 
 8.06 
 
 31 
 
 2.99 23 
 
 3.22 
 
 1G 
 
 3.74 
 
 8 
 
 
 
 55 
 
 5.43 
 
 69 
 
 4.85 
 
 70 
 
 4.50 
 
 70 
 
 4.31 
 
 68 
 
 4.17 
 
 65 
 
 4.01 
 
 59 
 
 3.73 
 
 53 
 
 3.34 
 
 45 
 
 2.97 
 
 37 
 
 2.72 29 
 
 2.75 
 
 21 
 
 3.11 
 
 12 
 
 
 
 56 
 
 5.89 
 
 86 
 
 5.26 
 
 6? 
 
 4.86 
 
 70 
 
 4.60 
 
 70 
 
 4.43 
 
 68 
 
 4.23 64 
 
 3.93 58 
 
 3.47 
 
 51 
 
 3.00 
 
 44 
 
 2.60:35 
 
 2.42 
 
 2(1 
 
 2.56 
 
 17 
 
 
 
 57 
 
 6.30 
 
 61 
 
 5.67 
 
 (it; 
 
 5.22 
 
 (ill 
 
 4.92 
 
 70 
 
 4.71 
 
 7n 
 
 4.50 67 
 
 4.19 63 
 
 3.71 
 
 57 
 
 3.15 
 
 50 
 
 2.60 42 
 
 2.22 
 
 33 
 
 2.15 
 
 23 
 
 
 
 58 
 
 6.67 
 
 56 
 
 6.03 
 
 68 
 
 5.57 
 
 66 
 
 5.26 
 
 (ill 
 
 5.04 
 
 70 
 
 4.83 69 
 
 4.5266 
 
 4.01 
 
 62 
 
 3.40 
 
 56 
 
 2.75 48 
 
 2.19 
 
 40 
 
 1.90 
 
 29 
 
 
 
 59 
 
 6.93 
 
 50 
 
 6.37 
 
 57 
 
 5.90 
 
 (i;i 
 
 5.57 
 
 67 
 
 5.36 
 
 7(1 
 
 5.17J70 
 
 4.87 
 
 69 
 
 4.39 
 
 66 
 
 3.76 
 
 (il 
 
 8.0255 2.30 
 
 47 
 
 1.83 
 
 37 
 
 
 
 60 
 
 7.10 
 
 44 6.60 
 
 51 
 
 6.19 
 
 58 
 
 5.88 
 
 64 
 
 5.69 
 
 liS 
 
 5.52170 
 
 5.26 
 
 70 
 
 4.82 69 
 
 4.20 65 
 
 3.41 60 2.57 
 
 58 
 
 1.88 44 
 
 
 
 NOTE. When T exceeds 88, subtract 88 from it, and add 1.22 to Argument J. 
 
3O 
 
 TABLE XII. 
 
 
 
 
 T 
 
 4 
 
 8 
 
 12 
 
 16 
 
 20 
 
 24 
 
 28 
 
 32 
 
 36 
 
 40 
 
 44 
 
 
 E 
 
 &v 
 
 iv 
 
 60 
 
 iv 
 
 iv 
 
 iv 
 
 iv 
 
 iv 
 
 iv 
 
 iv 
 
 iv 
 
 iv 
 
 
 
 
 
 2.33 
 
 2.21 
 
 2.09 
 
 f.95 
 
 i'.83 
 
 1.74: 
 
 1.65 
 
 i'.62 
 
 i'.ei 
 
 i'.ei 
 
 l'.65 
 
 i'.69 
 
 
 
 1 
 
 2.66 
 
 2.58 
 
 2.51 
 
 2.42 
 
 2.30 
 
 2.20 
 
 2.08 
 
 2.01 
 
 1.94 
 
 1.88 
 
 1.85 
 
 1.85 
 
 
 
 2 
 
 2.88 
 
 2.85 
 
 2.81 
 
 2.77 
 
 2.67 
 
 2.58 
 
 2.43 
 
 2.32 
 
 2.20 
 
 2.10 
 
 2.02 
 
 1.97 
 
 
 
 3 
 
 2.94 
 
 2.95 
 
 2.98 
 
 2.95 
 
 2.87 
 
 2.75 
 
 2.66 
 
 2.52 
 
 2.39 
 
 2.24 
 
 2.14 
 
 2.07 
 
 
 
 4 
 
 2.88 
 
 2.93 
 
 2.96 
 
 2.95 
 
 2.87 
 
 2.76 
 
 2.67 
 
 2.53 
 
 2.40 
 
 2.28 
 
 2.17 
 
 2.10 
 
 
 
 5 
 
 2.71 
 
 2.76 
 
 2.78 
 
 2.77 
 
 2.72 
 
 2.61 
 
 2.52 
 
 2.42 
 
 2.29 
 
 2.19 
 
 2.09 
 
 2.05 
 
 
 
 6 
 
 2.47 
 
 2.52 
 
 2.49 
 
 2.48 
 
 2.42 
 
 2.31 
 
 2.24 
 
 2.16 
 
 2.08 
 
 2.00 
 
 1.95 
 
 1.91 
 
 
 
 7 
 
 2.22 
 
 2.23 
 
 2.19 
 
 2.14 
 
 2.05 
 
 1.95 
 
 1.89 
 
 1.82 
 
 1.77 
 
 1.74 
 
 1.74 
 
 1.75 
 
 
 
 8 
 
 1.98 
 
 1.99 
 
 1.91 
 
 1.81 
 
 1.71 
 
 1.59 
 
 1.53 
 
 1.46 
 
 1.48 
 
 1.48 
 
 1.50 
 
 1.56 
 
 
 
 9 
 
 1.82 
 
 1.80 
 
 1.69 
 
 1.59 
 
 1.45 
 
 1.33 
 
 1.27 
 
 1.21 
 
 1.22 
 
 1.25 
 
 1.31 
 
 1.39 
 
 
 
 10 
 
 1.75 
 
 1.72 
 
 1.63 
 
 1.50 
 
 1.35 
 
 1.23 
 
 1.15 
 
 1.08 
 
 1.09 
 
 1.13 
 
 1.20 
 
 1.28 
 
 
 
 11 
 
 1.78 
 
 1.78 
 
 1.69 
 
 1.56 
 
 1.44 
 
 1.31 
 
 1.20 
 
 1.14 
 
 1.11 
 
 1.11 
 
 1.20 
 
 1.24 
 
 
 
 12 
 
 1.91 
 
 1.96 
 
 1.91 
 
 1.82 
 
 1.72 
 
 1.57 
 
 1.45 
 
 1.35 
 
 1.30 
 
 1.26 
 
 1.29 
 
 1.33 
 
 
 
 13 
 
 2.12 
 
 2.19 
 
 2.22 
 
 2.18 
 
 2.12 
 
 2.00 
 
 1.85 
 
 1.75 
 
 1.63 
 
 1.55 
 
 1.50 
 
 1.48 
 
 
 
 14 
 
 2.33 
 
 2.45 
 
 2.58 
 
 2.61 
 
 2.60 
 
 2.53 
 
 . 2.38 
 
 2.24 
 
 2.08 
 
 1.92 
 
 1.82 
 
 1.74 
 
 
 
 15 
 
 2.51 
 
 2.69 
 
 2.89 
 
 8.01 
 
 3.07 
 
 3.05 
 
 2.93 
 
 2.76 
 
 2.57 
 
 2.36 
 
 2.19 
 
 2.04 
 
 
 
 16 
 
 2.60 
 
 2.83 
 
 3.11 
 
 3.33 
 
 3.46 
 
 3.49 
 
 3.40 
 
 3.25 
 
 3.04 
 
 2.78 
 
 2.56 
 
 2.37 
 
 
 
 17 
 
 2.58 
 
 2.86 
 
 3.18 
 
 3.45 
 
 3.67 
 
 3.76 
 
 3.74 
 
 3.62 
 
 3.40 
 
 3.15 
 
 2.89 
 
 2.65 
 
 
 
 18 
 
 2.43 
 
 2.71 
 
 8.07 
 
 3.41 
 
 3.66 
 
 3.83 
 
 3.86 
 
 3.80 
 
 3.61 
 
 3.38 
 
 3.12 
 
 2.86 
 
 
 
 19 
 
 2.16 
 
 2.43 
 
 2.77 
 
 8.14 
 
 3.44 
 
 3.66 
 
 3.77 
 
 3.76 
 
 3.64 
 
 3.45 
 
 3.24 
 
 2.99 
 
 
 
 20 
 
 1.80 
 
 2.03 
 
 2.34 
 
 2.66 
 
 8.00 
 
 3.26 
 
 3.45 
 
 3.51 
 
 3.47 
 
 3.37 
 
 3.21 
 
 3.01 
 
 
 
 21 
 
 1.41 
 
 1.57 
 
 1.80 
 
 2.09 
 
 2.41 
 
 2.69 
 
 2.95 
 
 3.09 
 
 3.15 
 
 3.16 
 
 3.06 
 
 2.92 
 
 
 
 22 
 
 1.03 
 
 1.11 
 
 1.24 
 
 1.46 
 
 1.75 
 
 2.05 
 
 2.33 
 
 2.55 
 
 2.70 
 
 2.81 
 
 280 
 
 2.75 
 
 
 
 23 
 
 0.72 
 
 0.70 
 
 0.74 
 
 0.88 
 
 1.11 
 
 1.38 
 
 1.70 
 
 1.97 
 
 2.23 
 
 2.41 
 
 2.50 
 
 2.53 
 
 
 
 24 
 
 0.52 
 
 0.43 
 
 0.37 
 
 0.42 
 
 0.56 
 
 0.83 
 
 1.13 
 
 1.43 
 
 1.75 
 
 2.02 
 
 2.19 
 
 2.28 
 
 
 
 25 
 
 0.46 
 
 0.32 
 
 0.18 
 
 0.13 
 
 0.22 
 
 0.43 
 
 0.70 
 
 1.02 
 
 1.36 
 
 1.68 
 
 1.91 
 
 2.07 
 
 
 
 26 
 
 0.58 
 
 0.38 
 
 0.19 
 
 0.10 
 
 0.11 
 
 0.25 
 
 0.48 
 
 0.79 
 
 1.11 
 
 1.44 
 
 1.72 
 
 1.89 
 
 
 
 27 
 
 0.83 
 
 0.61 
 
 0.41 
 
 0.27 
 
 0.22 
 
 0.30 
 
 0.47 
 
 0.72 
 
 1.04 
 
 1.34 
 
 1.60 
 
 1.80 
 
 
 
 28 
 
 1.18 
 
 0.97 
 
 0.78 
 
 0.60 
 
 0.51 
 
 0.55 
 
 0.65 
 
 0.85 
 
 1.10 
 
 1.37 
 
 1.61 
 
 1.81 
 
 
 
 29 
 
 1.56 
 
 1.40 
 
 1.23 
 
 1.09 
 
 0.96 
 
 0.95 
 
 0.98 
 
 1.12 
 
 1.29 
 
 1.50 
 
 1.68 
 
 1.85 
 
 
 
 ;-!( 
 
 1.97 
 
 1.83 
 
 1.71 
 
 1.59 
 
 1.47 
 
 1.42 
 
 1.41 
 
 1.46 
 
 1.55 
 
 1.69 
 
 1.83 
 
 1.95 
 
 
 
 T 48 
 
 52 
 
 56 
 
 60 
 
 64 
 
 68 
 
 72 
 
 76 
 
 80 
 
 84 
 
 88 
 
 92 
 
 
 
 
 
 iv 
 
 6v 
 
 6v 
 
 iv 
 
 iv 
 
 iv 
 
 <fo 
 
 iv 
 
 <iy 
 
 iv 
 
 Se 
 
 6v 
 
 
 
 
 
 1.75 
 
 1.77 
 
 1.79 
 
 i'.83 
 
 f.83 
 
 i'.86 
 
 i'.90 
 
 1.97 
 
 2.09 
 
 2.23 
 
 2.40 
 
 2.56 
 
 
 
 1 
 
 1.86 
 
 1.86 
 
 1.85 
 
 1.89 
 
 1.87 
 
 1.91 
 
 1.94 
 
 2.01 
 
 2.15 
 
 2.33 
 
 2.55 
 
 2.75 
 
 
 
 2 
 
 1.96 
 
 1.93 
 
 1.91 
 
 1.93 
 
 1.90 
 
 1.92 
 
 1.94 
 
 2.01 
 
 2.14 
 
 2.33 
 
 2.59 
 
 2.84 
 
 
 
 3 
 
 2.01 
 
 1.97 
 
 1.94 
 
 1.92 
 
 1.90 
 
 1.89 
 
 1.89 
 
 1.94 
 
 2.05 
 
 2.24 
 
 2.51 
 
 2.79 
 
 
 
 4 
 
 2.01 
 
 1.98 
 
 1.93 
 
 1.90 
 
 1.84 
 
 1.80 
 
 1.78 
 
 1.82 
 
 1.90 
 
 2.06 
 
 2.31 
 
 2.58 
 
 
 
 5 
 
 1.98 
 
 1.94 
 
 1.88 
 
 1.81 
 
 1.77 
 
 1.69 
 
 1.64 
 
 1.63 
 
 1.68 
 
 1.80 
 
 2.00 
 
 2.25 
 
 
 
 6 
 
 1.86 
 
 1.83 
 
 1.79 
 
 1.74 
 
 1.66 
 
 1.57 
 
 1.51 
 
 1.45 
 
 1.43 
 
 1.49 
 
 1.62 
 
 1.82 
 
 
 
 7 
 
 1.71 
 
 1.72 
 
 1.69 
 
 1.62 
 
 1.55 
 
 1.45 
 
 1.36 
 
 1.27 
 
 1.18 
 
 1.19 
 
 1.23 
 
 1.36 
 
 
 
 8 
 
 1.55 
 
 1.59 
 
 1.57 
 
 1.52 
 
 1.47 
 
 1.35 
 
 1.24 
 
 1.13 
 
 1.01 
 
 0.92 
 
 0.87 
 
 0.92 
 
 
 
 9 
 
 1.42 
 
 1.48 
 
 1.47 
 
 1.46 
 
 1.40 
 
 1.30 
 
 1.20 
 
 1.05 
 
 0.89 
 
 0.74 
 
 0.61 
 
 0.55 
 
 
 
 10 
 
 1.82 
 
 1.39 
 
 1.44 
 
 1.41 
 
 1.39 
 
 1.32 
 
 1.21 
 
 1.05 
 
 0.87 
 
 0.67 
 
 0.48 
 
 0.38 
 
 
 
 11 
 
 1.32 
 
 1.37 
 
 1.44 
 
 1.44 
 
 1.43 
 
 1.37 
 
 1.29 
 
 1.15 
 
 0.95 
 
 0.74 
 
 0.51 
 
 0.35 
 
 
 
 12 
 
 1.38 
 
 1.42 
 
 1.48 
 
 1.50 
 
 1.53 
 
 1.50 
 
 1.44 
 
 1.32 
 
 1.14 
 
 0.93 
 
 0.68 
 
 0.49 
 
 
 
 13 
 
 1.50 
 
 1.52 
 
 1.59 
 
 1.62 
 
 1.65 
 
 1.67 
 
 1.63 
 
 1.58 
 
 139 
 
 1.20 
 
 0.98 
 
 0.78 
 
 
 
 14 
 
 1.72 
 
 1.70 
 
 1.72 
 
 1.77 
 
 1.81 
 
 1.86 
 
 1.84 
 
 1.78 
 
 1.69 
 
 1.55 
 
 1.86 
 
 1.17 
 
 
 
 15 
 
 1.97 
 
 1.90 
 
 1.91 
 
 1.94 
 
 1.97 
 
 2.03 
 
 2.04 
 
 2.02 
 
 1.97 
 
 1.89 
 
 1.76 
 
 1.60 
 
 
 
 16 
 
 2.24 
 
 2.12 
 
 2.09 
 
 2.10 
 
 2.12 
 
 2.19 
 
 2.20 
 
 2.23 
 
 2.22 
 
 2.19 
 
 2.13 
 
 2.00 
 
 
 
 17 
 
 2.47 
 
 2.34 
 
 2.26 
 
 2.23 
 
 2.25 
 
 2.30 
 
 2.33 
 
 2.37 
 
 2.40 
 
 2.41 
 
 2.41 
 
 2.32 
 
 
 
 18 
 
 2.67 
 
 2.49 
 
 2.40 
 
 2.34 
 
 2.33 
 
 2.36 
 
 2.39 
 
 2.44 
 
 2.48 
 
 2.51 
 
 2.57 
 
 2.52 
 
 
 
 19 
 
 2.79 
 
 2.61 
 
 2.48 
 
 2.39 
 
 2.36 
 
 2.36 
 
 2.38 
 
 2.43 
 
 2.47 
 
 2.53 
 
 2.59 
 
 2.56 
 
 
 
 20 
 
 2.81 
 
 2.65 
 
 2.50 
 
 2.40 
 
 2.34 
 
 2.32 
 
 2.31 
 
 2.35 
 
 2.39 
 
 2.43 
 
 2.49 
 
 2.48 
 
 
 
 21 
 
 2.75 
 
 2.62 
 
 2.46 
 
 2.37 
 
 2.29 
 
 2.25 
 
 2.23 
 
 2.23 
 
 2.25 
 
 2.28 
 
 2.31 
 
 2.29 
 
 
 
 22 
 
 2.63 
 
 2.54 
 
 2.42 
 
 2.29 
 
 2.22 
 
 2.14 
 
 2.11 
 
 2.10 
 
 2.11 
 
 2.10 
 
 2.08 
 
 2.04 
 
 
 
 23 
 
 2.49 
 
 2.42 
 
 2.32 
 
 2.21 
 
 2.13 
 
 2.06 
 
 2.02 
 
 1.99 
 
 1.95 
 
 1.90 
 
 1.86 
 
 1.79 
 
 
 
 24 
 
 2.31 
 
 2.30 
 
 2.22 
 
 2.14 
 
 2.05 
 
 1.99 
 
 1.95 
 
 1.87 
 
 1.84 
 
 1.76 
 
 1.68 
 
 1.60 
 
 
 
 25 
 
 2.15 
 
 2.17 
 
 2.14 
 
 2.07 
 
 2.03 
 
 1.94 
 
 1.92 
 
 1.87 
 
 1.81 
 
 1.70 
 
 1.59 
 
 1.51 
 
 
 
 26 
 
 2.03 
 
 2.08 
 
 2.06 
 
 2.05 
 
 2.01 
 
 1.96 
 
 1.93 
 
 1.90 
 
 1.83 
 
 1.75 
 
 1.62 
 
 1.53 
 
 
 
 27 
 
 1.97 
 
 2.03 
 
 2.04 
 
 2.06 
 
 2.03 
 
 2.02 
 
 2.00 
 
 1.97 
 
 1.92 
 
 1.87 
 
 1.75 
 
 1.68 
 
 
 
 28 
 
 1.95 
 
 2.02 
 
 2.06 
 
 2.09 
 
 2.08 
 
 2.07 
 
 - 2.08 
 
 2.07 
 
 2.07 
 
 2.04 
 
 1.99 
 
 1.93 
 
 
 
 29 
 
 2.00 
 
 2.08 
 
 2.11 
 
 2.15 
 
 2.15 
 
 2.16 
 
 2.18 
 
 2.21 
 
 2.23 
 
 2.25 
 
 2.26 
 
 2.23 
 
 
 
 30 
 
 2.07 
 
 2.13 
 
 2.17 
 
 2.21 
 
 2.21 
 
 2.24 
 
 2.26 
 
 2.31 
 
 2.37 
 
 2.43 
 
 2.50 
 
 2.54 
 
 
 
 NOTE. When T exceeds a, subtract 88 from it, and add 14.45 to E. 
 
TABLE XII. 
 
 
 
 
 T 
 
 4 
 
 8 
 
 12 
 
 16 
 
 20 
 
 24 
 
 28 
 
 32 
 
 36 
 
 40 
 
 44 
 
 48 
 
 
 E 
 
 tv 
 
 tv 
 
 iv 
 
 <?t> 
 
 Se 
 
 tv 
 
 tv 
 
 tv 
 
 tv 
 
 to 
 
 iv 
 
 tv 
 
 tv 
 
 
 
 30 
 
 f.97 
 
 i'.83 
 
 1. 71 
 
 f.59 
 
 i'.47 
 
 l'.42 
 
 i'.4i 
 
 1.46 
 
 l'.55 
 
 i'.69 
 
 i'.83 
 
 l'.95 
 
 2.07 
 
 
 
 31 
 
 2.28 
 
 2.20 
 
 2.13 
 
 2.04 
 
 1.94 
 
 1.86 
 
 1.80 
 
 1.81 
 
 1.84 
 
 1.90 
 
 1.97 
 
 2.07 
 
 2.16 
 
 
 
 32 
 
 2.50 
 
 2.47 
 
 2.43 
 
 2.39 
 
 2.31 
 
 2.22 
 
 2.11 
 
 2.08 
 
 2.04 
 
 2.06 
 
 2.10 
 
 2.15 
 
 2.22 
 
 
 
 33 
 
 2.58 
 
 2.57 
 
 2.60 
 
 2.57 
 
 2.49 
 
 2.39 
 
 2.30 
 
 2.24 
 
 2.19 
 
 2.14 
 
 2.16 
 
 2.19 
 
 2.23 
 
 
 
 34 
 
 2.54 
 
 2.55 
 
 2.58 
 
 2.57 
 
 2.49 
 
 2.40 
 
 2.31 
 
 2.21 
 
 2.16 
 
 2.14 
 
 2.13 
 
 2.18 
 
 2.19 
 
 
 
 35 
 
 2.39 
 
 2.40 
 
 2.40 
 
 2.39 
 
 2.34 
 
 2.22 
 
 2.16 
 
 2.08 
 
 2.01 
 
 1.99 
 
 1.99 
 
 2.07 
 
 2.10 
 
 
 
 36 
 
 2.17 
 
 2.16 
 
 2.13 
 
 2.10 
 
 2.04 
 
 1.93 
 
 1.88 
 
 1.80 
 
 1.76 
 
 1.76 
 
 1.79 
 
 1.87 
 
 1.94 
 
 
 
 37 
 
 1.94 
 
 1.89 
 
 1.83 
 
 1.76 
 
 1.67 
 
 1.57 
 
 1.51 
 
 1.46 
 
 1.43 
 
 1.46 
 
 1.54 
 
 1.65 
 
 1.73 
 
 
 
 38 
 
 1.74 
 
 1.67 
 
 1.55 
 
 1.45 
 
 1.33 
 
 1.21 
 
 1.15 
 
 1.10 
 
 1.12 
 
 1.16 
 
 1.26 
 
 1.40 
 
 1.53 
 
 
 
 39 
 
 1.62 
 
 1.52 
 
 1.37 
 
 1.23 
 
 1.09 
 
 0.95 
 
 0.89 
 
 0.83 
 
 0.86 
 
 0.91 
 
 1.03 
 
 1.19 
 
 1.34 
 
 
 
 40 
 
 1.59 
 
 1.48 
 
 1.31 
 
 1.14 
 
 0.99 
 
 0.85 
 
 0.77 
 
 0.70 
 
 0.73 
 
 0.77 
 
 0.88 
 
 1.04 
 
 1.20 
 
 
 
 41 
 
 1.68 
 
 1.58 
 
 1.41 
 
 1.24 
 
 1.08 
 
 0.93 
 
 0.82 
 
 0.76 
 
 0.73 
 
 0.75 
 
 0.88 
 
 0.96 
 
 1.12 
 
 
 
 42 
 
 1.89 
 
 1.80 
 
 1.67 
 
 1.50 
 
 1.36 
 
 1.21 
 
 1.07 
 
 5-97 
 
 0.92 
 
 0.88 
 
 0.93 
 
 1.01 
 
 1.14 
 
 
 
 43 
 
 2.14 
 
 2.09 
 
 2.02 
 
 1.90 
 
 1.78 
 
 1.64 
 
 1.49 
 
 1.37 
 
 1.25 
 
 1.17 
 
 1.14 
 
 1.16 
 
 1.24 
 
 
 
 44 
 
 2.41 
 
 2.41 
 
 2.42 
 
 2.37 
 
 2.28 
 
 2.17 
 
 2.02 
 
 1.86 
 
 1.70 
 
 1.54 
 
 1.44 
 
 1.38 
 
 1.42 
 
 
 
 45 
 
 2.63 
 
 2.71 
 
 2.79 
 
 2.81 
 
 2.79 
 
 2.71 
 
 2.57 
 
 2.40 
 
 2.19 
 
 1.98 
 
 1.81 
 
 1.68 
 
 1.65 
 
 
 
 46 
 
 2.78 
 
 2.91 
 
 3.05 
 
 3.17 
 
 3.22 
 
 3.17 
 
 3.04 
 
 2.89 
 
 2.66 
 
 2.40 
 
 2.18 
 
 1.99 
 
 1.90 
 
 
 
 47 
 
 2.80 
 
 2.98 
 
 3.18 
 
 3.35 
 
 3.47 
 
 3.48 
 
 3.40 
 
 3.26 
 
 3.04 
 
 2.77 
 
 2.51 
 
 2.27 
 
 2.11 
 
 
 
 48 
 
 2.69 
 
 2.89 
 
 3.15 
 
 3.35 
 
 3.50 
 
 3.59 
 
 3.54 
 
 3.44 
 
 3.25 
 
 3.00 
 
 2.74 
 
 2.48 
 
 2.29 
 
 
 
 49 
 
 2.46 
 
 2.65 
 
 2.89 
 
 3.14 
 
 3.32 
 
 3.46 
 
 3.49 
 
 3.42 
 
 3.28 
 
 3.09 
 
 2.86 
 
 2.61 
 
 2.41 
 
 
 
 50 
 
 2.14 
 
 2.29 
 
 2.52 
 
 2.74 
 
 2.94 
 
 3.10 
 
 3.19 
 
 3.19 
 
 3.11 
 
 3.01 
 
 2.83 
 
 2.63 
 
 2.43 
 
 
 
 51 
 
 1.75 
 
 1.87 
 
 2.02 
 
 2.21 
 
 2.41 
 
 2.59 
 
 2.73 
 
 2.79 
 
 2.81 
 
 2.80 
 
 2.68 
 
 2.54 
 
 2.37 
 
 
 
 52 
 
 1.37 
 
 1.43 
 
 1.50 
 
 1.64 
 
 1.81 
 
 1.99 
 
 2.15 
 
 2.29 
 
 2.38 
 
 2.47 
 
 2.44 
 
 2.87 
 
 2.25 
 
 
 
 53 
 
 1.08 
 
 1.04 
 
 1.04 
 
 1.10 
 
 1.21 
 
 1.38 
 
 1.58 
 
 1.75 
 
 1.93 
 
 2.07 
 
 2.14 
 
 2.15 
 
 2.11 
 
 
 
 54 
 
 0.88 
 
 0.77 
 
 0.69 
 
 0.68 
 
 0.75 
 
 0.89 
 
 1.07 
 
 1.25 
 
 1.49 
 
 1.70 
 
 1.83 
 
 1.90 
 
 1.93 
 
 
 
 55 
 
 0.82 
 
 0.68 
 
 0.52 
 
 0.43 
 
 0.44 
 
 0.53 
 
 0.70 
 
 0.88 
 
 1.14 
 
 1.38 
 
 1.57 
 
 1.69 
 
 1.77 
 
 
 
 56 
 
 0.96 
 
 0.74 
 
 0.55 
 
 0.42 
 
 0.37 
 
 0.43 
 
 0.54 
 
 0.71 
 
 0.93 
 
 1.18 
 
 1.38 
 
 1.55 
 
 1.65 
 
 
 
 57 
 
 1.21 
 
 0.99 
 
 0.77 
 
 0.61 
 
 0.50 
 
 0.52 
 
 0.57 
 
 0.72 
 
 0.90 
 
 1.12 
 
 1.30 
 
 1.46 
 
 1.59 
 
 
 
 58 
 
 1.56 
 
 1.35 
 
 1.14 
 
 0.96 
 
 0.83 
 
 0.81 
 
 0.81 
 
 0.91 
 
 1.02 
 
 1.19 
 
 1.35 
 
 1.47 
 
 1.59 
 
 
 
 59 
 
 1.94 
 
 1.78 
 
 1.61 
 
 1.45 
 
 1.32 
 
 1.23 
 
 1.18 
 
 1.22 
 
 1.29 
 
 1.36 
 
 1.46 
 
 1.55 
 
 1.66 
 
 
 
 60 
 
 2.33 
 
 2.21 
 
 2.09 
 
 1.95 
 
 1.83 
 
 1.74 
 
 1.65 
 
 1.62 
 
 1.61 
 
 1.61 
 
 1.65 
 
 1.69 
 
 1.75 
 
 
 
 T 52 
 
 56 
 
 60 
 
 64 
 
 68 
 
 72 
 
 76 
 
 80 
 
 84 
 
 88 
 
 
 
 
 E 
 
 So 
 
 tv 
 
 ta 
 
 to 
 
 iv 
 
 c!r 
 
 to 
 
 tv 
 
 tv 
 
 tv 
 
 TABLE Xm. 
 
 
 
 30 
 
 2.13 
 
 2.17 
 
 2.21 
 
 2.21 
 
 2.24 
 
 2.26 
 
 2.31 
 
 2.37 
 
 2.43 
 
 2.50 
 
 
 
 
 31 
 
 2.20 
 
 2.23 
 
 2.27 
 
 2.25 
 
 2.29 
 
 2.30 
 
 2.37 
 
 2.47 
 
 2.57 
 
 2.71 
 
 s 
 
 iv 
 
 Dif. 
 
 
 
 
 32 
 
 2.25 
 
 9 97 
 
 9 11 
 
 9 9A 
 
 9 ICt 
 
 9 ^9 
 
 OQ7 
 
 9 *1R 
 
 9 fil 
 
 27Q 
 
 
 
 
 
 
 
 33 
 
 2.27 
 
 jB*jBI 
 
 2.28 
 
 i.O L 
 
 2.30 
 
 AO 
 
 2.28 
 
 A*Ov 
 
 2.27 
 
 ,,*} 
 
 2.27 
 
 _> 1 
 
 2.30 
 
 4. 40 
 2.41 
 
 -' > l 
 
 2.56 
 
 f 
 
 2.75 
 
 
 
 0.40 
 
 .11 
 
 
 
 
 34 
 
 2.24 
 
 2.25 
 
 2.26 
 
 2.22 
 
 2.18 
 
 2.16 
 
 2.20 
 
 2.26 
 
 2.40 
 
 2.59 
 
 4 
 
 0.51 
 
 .10 
 
 
 
 
 35 
 
 2.18 
 
 2.18 
 
 2.17 
 
 2.13 
 
 2.07 
 
 2.02 
 
 2.01 
 
 2.04 
 
 2.16 
 
 2.32 
 
 8 
 
 0.61 
 
 .09 
 
 
 
 
 36 
 
 2.03 
 
 2.07 
 
 2.06 
 
 2.02 
 
 1.95 
 
 1.89 
 
 1.83 
 
 1.81 
 
 1.85 
 
 1.96 
 
 12 
 
 0.70 
 
 .06 
 
 
 
 
 37 
 
 1.86 
 
 1.93 
 
 1.94 
 
 1.91 
 
 1.81 
 
 1.74 
 
 1.65 
 
 1.58 
 
 1.55 
 
 1.59 
 
 16 
 
 0.76 
 
 .03 
 
 
 
 
 38 
 
 1.67 
 
 1.77 
 
 1.80 
 
 1.79 
 
 1.71 
 
 1.62 
 
 1.51 
 
 1.39 
 
 1.30 
 
 1.23 
 
 20 
 
 0.79 
 
 .01 
 
 
 
 
 39 
 
 1.50 
 
 1.63 
 
 1.70 
 
 1.72 
 
 1.66 
 
 1.56 
 
 1.43 
 
 1.27 
 
 1.12 
 
 0.97 
 
 24 
 
 0.80 
 
 .03n 
 
 
 
 
 40 
 
 1.37 
 
 1.54 
 
 1.61 
 
 1.67 
 
 1.64 
 
 1.57 
 
 1.43 
 
 1.25 
 
 1.05 
 
 0.84 
 
 28 
 
 0.77 
 
 .06 
 
 
 
 
 41 
 
 1.29 
 
 1.46 
 
 1.60 
 
 1.67 
 
 1.69 
 
 1.65 
 
 1.51 
 
 1.33 
 
 1.12 
 
 0.87 
 
 32 
 
 0.71 
 
 .08 
 
 
 
 
 42 
 
 1.30 
 
 1.46 
 
 1.60 
 
 1.73 
 
 1.78 
 
 1.76 
 
 1.68 
 
 1.52 
 
 1.31 
 
 1.06 
 
 36 
 
 0.63 
 
 .10 
 
 
 
 
 43 
 
 1.34 
 
 1.51 
 
 1.66 
 
 1.81. 
 
 1.91 
 
 1.95 
 
 1.89 
 
 1.75 
 
 1.58 
 
 1.36 
 
 40 
 
 0.53 
 
 .11 
 
 
 
 
 44 
 
 1.48 
 
 1.60 
 
 1.75 
 
 1.91 
 
 2.06 
 
 2.12 
 
 2.12 
 
 2.05 
 
 1.91 
 
 1.74 
 
 44 
 
 0.42 
 
 .11 
 
 
 
 
 45 
 
 1.64 
 
 1.73 
 
 1.86 
 
 2.03 
 
 2.19 
 
 2.28 
 
 2.34 
 
 2.33 
 
 2.25 
 
 2.14 
 
 48 
 
 0.31 
 
 .11 
 
 
 
 
 46 
 
 1.82 
 
 1.87 
 
 1.98 
 
 2.12 
 
 2.29 
 
 2.40 
 
 2.51 
 
 2.56 
 
 2.55 
 
 2.49 
 
 52 
 
 0.20 
 
 .09 
 
 
 
 
 47 
 
 2.00 
 
 2.00 
 
 2.05 
 
 2.17 
 
 2.36 
 
 2.49 
 
 2.61 
 
 2.70 
 
 2.77 
 
 2.77 
 
 56 
 
 0.11 
 
 .06 
 
 
 
 
 48 
 
 2.15 
 
 2.10 
 
 2.12 
 
 2.21 
 
 2.36 
 
 2.49 
 
 2.64 
 
 2.78 
 
 2.85 
 
 2.93 
 
 60 
 
 0.05 
 
 .04 
 
 
 
 
 49 
 
 2.25 
 
 2.14 
 
 2.13 
 
 2.18 
 
 2.30 
 
 2.44 
 
 2.59 
 
 2.73 
 
 2.85 
 
 2.95 
 
 64 
 
 0.01 
 
 .Oln 
 
 
 
 
 50 
 
 2.27 
 
 2.16 
 
 2.10 
 
 2.12 
 
 2.20 
 
 2.31 
 
 2.45 
 
 2.61 
 
 2.73 
 
 2.83 
 
 68 
 
 0.00 
 
 .02+ 
 
 
 
 
 51 
 
 2.24 
 
 2.12 
 
 2.03 
 
 2.03 
 
 2.07 
 
 2.17 
 
 2.29 
 
 2.43 
 
 2.54 
 
 2.63 
 
 72 
 
 0.02 
 
 .06 
 
 
 
 
 52 
 
 2.16 
 
 2.04 
 
 .95 
 
 1.92 
 
 1.92 
 
 .99 
 
 2.10 
 
 2.21 
 
 2.32 
 
 2.38 
 
 76 
 
 0.08 
 
 .07 
 
 
 
 
 53 
 
 2.04 
 
 1.94 
 
 .87 
 
 1.81 
 
 .80 
 
 .84 
 
 1.93 
 
 2.01 
 
 2.08 
 
 2.12 
 
 80 
 
 0.15 
 
 .10 
 
 
 
 
 54 
 
 1.92 
 
 1.84 
 
 .78 
 
 1.71 
 
 .69 
 
 .73 
 
 1.77 
 
 1.84 
 
 1.90 
 
 1.90 
 
 84 
 
 0.25 
 
 .11 
 
 
 
 
 55 
 
 1.79 
 
 1.76 
 
 .71 
 
 1.67 
 
 .62 
 
 .66 
 
 1.69 
 
 1.75 
 
 1.78 
 
 1.77 
 
 88 
 
 0.36 
 
 .12 
 
 
 
 
 56 
 
 1.70 
 
 1.68 
 
 .67 
 
 1.65 
 
 .62 
 
 .65 
 
 1.68 
 
 1.73 
 
 1.75 
 
 1.76 
 
 92 
 
 0.48 
 
 
 
 
 
 57 
 
 1.65 
 
 1.66 
 
 .68 
 
 1.67 
 
 .66 
 
 .68 
 
 1.71 
 
 1.78 
 
 1.81 
 
 1.83 
 
 
 
 
 58 
 
 1.64 
 
 1.68 
 
 .71 
 
 1.70 
 
 .71 
 
 .74 
 
 1.79 
 
 1.87 
 
 1.94 
 
 1.99 
 
 
 
 
 59 
 
 1.70 
 
 1.73 
 
 .77 
 
 1.77 
 
 .80 
 
 .82 
 
 1.89 
 
 1.99 
 
 2.09 
 
 2.20 
 
 Period = 89.43 
 
 
 
 60 
 
 1.77 
 
 1.79 
 
 .83 
 
 1.83 
 
 .86 
 
 .90 
 
 1.97 
 
 2.09 
 
 2.23 
 
 2.40 
 
 
 
 
 NOTE. When T exceeds 88, subtract 88 from it, and add 14.45 to E. 
 
32 
 
 TABLE XIV. 
 
 
 
 
 ARG. 
 
 o.o 
 
 0.1 
 
 0.2 
 
 O.3 
 
 0.4 
 
 V. 
 
 V. 
 
 V. 
 
 V. 
 
 V. 
 
 
 
 1 
 
 2 
 3 
 
 359 59 39.2 
 3 10 0.4 
 6 20 9.6 
 9 29 55.1 
 
 O 1 N 
 
 18 41.5 
 3 29 2.0 
 6 39 9.4 
 9 48 51.9 
 
 1 
 
 37 43.8 
 3 48 3.6 
 6 58 9.0 
 
 10 7 48.4 
 
 6 56 46.1 
 4 7 4.9 
 7 17 8.3 
 10 26 44.4 
 
 1 15 48.4 
 4 26 6.2 
 7 36 7.3 
 10 45 40.1 
 
 
 4 
 5 
 6 
 
 7 
 
 12 39 5.3 
 15 47 28.8 
 18 54 54.8 
 22 1 12.7 
 
 12 57 58.0 
 16 6 16.2 
 19 13 35.8 
 22 19 46.3 
 
 13 16 50.1 
 16 25 3.0 
 19 32 16.1 
 22 38 19.2 
 
 13 35 41.8 
 16 43 49.2 
 19 50 55.7 
 22 56 51.3 
 
 13 54 32.9 
 17 2 34.7 
 20 9 34.7 
 23 15 22.6 
 
 
 
 8 
 9 
 10 
 11 
 
 25 6 12.7 
 28 9 45.6 
 31 11 42.7 
 34 11 56.2 
 
 25 24 38.1 
 28 28 1.8 
 31 29 48.9 
 34 29 51.6 
 
 25 43 2.5 
 28 46 17.0 
 31 47 54.0 
 34 47 45.8 
 
 26 1 26.1 
 29 4 31.2 
 32 5 58.0 
 35 5 39.0 
 
 26 19 48.9 
 29 22 44.4 
 32 24 1.0 
 35 23 31.0 
 
 
 
 12 
 13 
 14 
 15 
 
 37 10 18.9 
 40 6 44.3 
 43 1 6.8 
 45 53 21.5 
 
 37 28 2.8 
 40 24 16.2 
 43 18 26.1 
 46 10 27.8 
 
 37 45 45.5 
 
 40 41 46.8 
 43 35 44.1 
 46 27 32.7 
 
 38 3 27.1 
 40 59 16.2 
 43 53 0.8 
 46 44 36.3 
 
 38 21 7.5 
 41 16 44.4 
 44 10 16.2 
 47 1 38.6 
 
 
 
 16 
 17 
 18 
 19 
 
 48 43 24.3 
 51 31 11.5 
 54 16 40.3 
 56 59 48.9 
 
 49 17.1 
 51 47 50.6 
 54 33 5.5 
 57 16 0.0 
 
 49 17 8.6 
 52 4 28.4 
 54 49 29.3 
 57 32 9.6 
 
 49 33 58.8 
 52 21 4.8 
 55 5 51.7 
 57 48 17.8 
 
 49 50 47.6 
 52 37 39.7 
 55 22 12.7 
 58 4 24.6 
 
 
 
 20 
 21 
 22 
 23 
 
 59 40 35.4 
 62 18 59.1 
 64 54 59.5 
 67 28 36.6 
 
 59 56 32.3 
 62 34 41.6 
 65 10 27.6 
 67 43 50.4 
 
 60 12 27.6 
 62 50 22.6 
 65 25 54.4 
 67 59 2.9 
 
 60 28 21.6 
 63 6 2.3 
 65 41 19.7 
 68 14 13.8 
 
 60 44 14.1 
 63 21 40.5 
 65 56 43.5 
 68 29 23.4 
 
 
 
 24 
 25 
 26 
 
 27 
 
 69 59 50.9 
 72 28 43.3 
 74 55 15.2 
 
 77 19 28.1 
 
 70 14 50.5 
 72 43 28.8 
 75 9 46.7 
 77 33 45.9 
 
 70 29 48.7 
 72 58 12.9 
 75 24 16.9 
 77 48 2.2 
 
 70 44 45.5 
 73 12 55.6 
 75 38 45.6 
 78 2 17.2 
 
 70 59 40.9 
 73 27 36.9 
 75 53 13.0 
 78 16 30.8 
 
 
 
 28 
 29 
 30 
 31 
 
 79 41 24.0 
 
 82 1 4.8 
 84 18 32.9 
 86 33 50.9 
 
 79 55 28.1 
 82 14 55.6 
 84 32 10.6 
 86 47 15.7 
 
 80 9 30.9 
 82 28 45.0 
 84 45 46.9 
 87 39.1 
 
 80 23 32.3 
 82 42 33.1 
 84 59 21.9 
 87 14 1.3 
 
 80 37 32.4 
 82 56 19.9 
 85 12 55.6 
 87 27 22.3 
 
 
 32 
 33 
 34 
 35 
 
 88 47 1.4 
 90 58 7.2 
 93 7 11.1 
 95 14 16.3 
 
 89 13.6 
 91 11 7.0 
 93 19 58.9 
 95 26 52.3 
 
 89 13 24.5 
 91 24 5.6 
 93 32 45.5 
 95 39 27.2 
 
 89 26 34.1 
 91 37 3.0 
 93 45 31.0 
 95 52 1.0 
 
 89 39 42.5 
 91 49 59.2 
 93 58 15.2 
 96 4 33.6 
 
 
 36 
 37 
 38 
 39 
 
 97 19 25.4 
 99 22 41.9 
 101 24 8.7 
 103 23 48.9 
 
 97 31 50.1 
 99 34 55.4 
 101 36 11.4 
 103 35 41.2 
 
 97 44 13.7 
 99 47 7.9 
 101 48 13.1 
 103 47 32.4 
 
 97 56 36.1 
 99 59 19.3 
 102 13.8 
 103 59 22.7 
 
 98 8 57.4 
 100 11 29.6 
 102 12 13.4 
 104 11 11.9 
 
 
 40 
 41 
 42 
 43 
 
 105 21 45.7 
 107 18 2.1 
 109 12 41.2 
 111 5 46.1 
 
 105 33 27.8 
 107 29 34.3 
 109 24 3.9 
 111 16 59.6 
 
 105 45 8.9 
 107 41 5.6 
 109 35 25.7 
 111 28 12.1 
 
 105 56 49.0 
 107 52 35.9 
 109 46 46.5 
 111 39 23.7 
 
 106 8 28.1 
 108 4 5.3 
 109 58 6.3 
 111 50 34.4 
 
 
 44 
 45 
 
 112 57 19.8 
 114 47 25.2 
 
 113 8 24.3 
 114 58 21.0 
 
 113 19 27.9 
 115 9 16.0 
 
 113 30 30.6 
 115 20 10.1 
 
 113 41 32.4 
 115 31 3.3 
 
 
 ARG. 
 
 0.0 
 
 0.1 
 
 0.3 
 
 O.3 
 
 0.4 
 
 
TABLE XIV. 
 
 33 
 
 
 
 
 ARG. 
 
 0.5 
 
 0.6 
 
 0.7 
 
 o.s 
 
 0.9 
 
 9. 
 
 V. 
 
 V. 
 
 V. 
 
 V. 
 
 
 
 1 
 
 2 
 3 
 
 I II 
 
 1 34 50.5 
 4 45 7.2 
 7 55 6.1 
 11 4 35.4 
 
 O 1 II 
 
 1 53 52.7 
 5 4 8.1 
 8 14 4.5 
 11 23 30.2 
 
 O 1 II 
 
 2 12 54.7 
 5 23 8.8 
 8 33 2.7 
 11 42 24.7 
 
 1 II 
 
 2 31 56.7 
 5 42 9.3 
 8 52 0.5 
 
 12 1 18.7 
 
 2 50 58.6 
 6 1 9.6 
 9 10 58.0 
 12 20 12.2 
 
 
 4 
 5 
 
 6 
 
 7 
 
 14 13 23.6 
 17 21 19.6 
 20 28 12.9 
 23 33 53.0 
 
 14 32 13.7 
 17 40 4.0 
 20 46 50.3 
 23 52 22.6 
 
 14 51 3.3 
 
 17 58 47.7 
 21 5 27.0 
 24 10 51.4 
 
 15 9 52.4 
 18 17 30.7 
 21 24 3.0 
 24 29 19.4 
 
 15 28 40.9 
 18 36 13.1 
 21 42 38.2 
 24 47 46.5 
 
 
 
 8 
 9 
 10 
 11 
 
 26 38 10.6 
 29 40 56.7 
 32 42 2.9 
 35 41 21.8 
 
 26 56 31.5 
 29 59 7.9 
 33 3.7 
 35 59 11.5 
 
 27 14 51.4 
 30 17 18.2 
 33 18 3.5 
 36 17 0.1 
 
 27 33 10.4 
 30 35 27.4 
 33 36 2.1 
 36 34 47.5 ' 
 
 27 51 28.5 
 30 53 35.6 
 33 53 59.7 
 36 52 33.8 
 
 
 
 12 
 13 
 14 
 15 
 
 38 38 46.6 
 41 34 11.3 
 44 27 30.4 
 47 18 39.6 
 
 38 56 24.6 
 41 51 36.9 
 44 44 43.2 
 47 35 39.2 
 
 39 14 1.3 
 42 9 1.3 
 45 1 54.7 
 47 52 37.5 
 
 39 31 36.9 
 42 26 24.4 
 45 19 5.0 
 48 9 34.4 
 
 39 49 11.2 
 42 43 46.2 
 45 36 13.9 
 48 26 300 
 
 
 
 16 
 17 
 
 18 
 19 
 
 50 7 35.0 
 52 54 13.3 
 55 38 32.3 
 58 20 30.0 
 
 50 24 21.0 
 53 10 45.5 
 55 54 50.4 
 58 36 34.0 
 
 50 41 5.7 
 53 27 16.3 
 56 11 7.2 
 58 52 36.5 
 
 50 57 49.0 
 53 43 45.7 
 56 27 22.5 
 59 8 37.6 
 
 51 14 30.9 
 54 13.7 
 56 43 36.4 
 59 24 37.3 
 
 
 
 20 
 21 
 22 
 23 
 
 61 5.2 
 63 37 17.2 
 66 12 5.9 
 68 44 31.6 
 
 61 15 54.8 
 63 52 52.5 
 66 27 26.9 
 68 59 38.3 
 
 61 31 43.0 
 64 8 26.4 
 66 42 46.5 
 69 14 43.6 
 
 61 47 29.8 
 64 23 58.9 
 66 58 4.6 
 69 29 47.4 
 
 62 3 15.2 
 64 39 29.9 
 67 )3 21.3 
 69 44 49.9 
 
 
 
 24 
 25 
 
 26 
 
 27 
 
 71 14 34.8 
 73 42 16.8 
 76 7 38.9 
 78 30 43.1 
 
 71 29 27.3 
 73 56 55.2 
 76 22 3.5 
 78 44 54.0 
 
 71 44 18.5 
 74 11 32.3 
 76 36 26.8 
 78 59 3.5 
 
 71 59 8.2 
 74 26 8.0 
 76 50 48.6 
 79 13 11.7 
 
 72 13 56.5 
 74 40 42.3 
 77 5 9.1 
 79 27 18.5 
 
 
 
 28 
 29 
 30 
 31 
 
 80 51 31.2 
 83 10 5.3 
 85 26 28.0 
 87 40 41.9 
 
 81 5 28.6 
 83 23 49.5 
 85 39 59.2 
 87 54 0.3 
 
 81 19 24.6 
 83 37 32.3 
 85 53 29.0 
 88 7 17.5 
 
 81 33 19.4 
 83 51 13.8 
 86 6 57.6 
 88 20 33.4 
 
 81 47 12.8 
 84 4 54.0 
 86 20 24.9 
 88 33 48.0 
 
 
 
 32 
 33 
 34 
 35 
 
 89 52 49.7 
 92 2 54.2 
 94 10 58.3 
 96 17 5.1 
 
 90 5 55.7 
 92 15 48.0 
 94 23 40.2 
 96 29 35.5 
 
 90 19 0.4 
 92 28 40.6 
 94 36 21.0 
 96 42 4.6 
 
 90 32 3.9 
 92 41 31.9 
 94 49 0.6 
 96 54 32.7 
 
 90 45 6.1 
 92 54 22.1 
 95 1 39.0 
 97 6 59.6 
 
 
 
 36 
 37 
 38 
 39 
 
 98 21 17.6 
 100 23 38.8 
 102 24 11.9 
 104 23 0.0 
 
 98 33 36.6 
 100 35 46.9 
 102 36 9.4 
 104 34 47.2 
 
 98 45 54.6 
 100 47 54.0 
 102 48 5.8 
 104 46 33.3 
 
 98 58 11.5 
 100 59 59.9 
 103 1.2 
 104 58 18.5 
 
 99 10 27.2 
 101 12 4.8 
 103 11 55.6 
 105 10 2.6 
 
 
 40 
 41 
 42 
 43 
 
 106 20 6.3 
 108 15 33.6 
 110 9 25.3 
 112 1 44.2 
 
 106 31 43.4 
 
 108 27 1.1 
 110 20 43.3 
 112 12 53.1 
 
 106 43 19.5 
 108 38 27.5 
 110 32 0.4 
 112 24 1.1 
 
 106 54 54.7 
 108 49 53.0 
 110 43 16.6 
 112 35 8.2 
 
 107 6 28.9 
 109 1 17.6 
 110 54 31.8 
 112 46 14.5 
 
 
 44 
 45 
 
 113 52 33.3 
 
 115 41 55.8 
 
 114 3 33.4 
 115 52 47.3 
 
 114 14 32.7 
 116 3 38.1 
 
 114 25 31.0 
 116 14 28.0 
 
 114 36 28.5 
 116 25 17.1 
 
 
 ARG. 
 
 0.5 
 
 0.6 
 
 o.r 
 
 0.8 
 
 0.9 
 
 
TABLE XIV. 
 
 
 
 
 AR3. 
 
 o.o 
 
 0.1 
 
 O.2 
 
 O.3 
 
 0.4 
 
 V. 
 
 V. 
 
 V. 
 
 V. 
 
 V. 
 
 45 
 46 
 
 47 
 
 48 
 
 114 47 25.2 
 116 36 5.3 
 118 23 23.1 
 120 9 21.3 
 
 114 58 21.0 
 116 46 52.8 
 118 34 2.5 
 120 19 52.9 
 
 115 9 16.0 
 116 57 39.4 
 118 44 41.1 
 120 30 23.7 
 
 115 20 10.1 
 117 8 25.2 
 118 55 18.8 
 120 40 53.7 
 
 O | n 
 
 115 31 3.3 
 117 19 10.2 
 119 5 55.9 
 120 51 23.0 
 
 
 49 
 50 
 51 
 52 
 
 121 54 2.7 
 123 37 30.1 
 125 19 46.2 
 127 53.6 
 
 122 4 26.8 
 123 47 46.9 
 125 29 56.0 
 127 10 56.6 
 
 122 14 50.1 
 123 58 3.0 
 125 40 5.1 
 127 20 59.0 
 
 122 25 12.6 
 124 8 18.3 
 125 50 13.5 
 127 31 0.8 
 
 122 35 34.5 
 124 18 33.0 
 126 21.3 
 127 41 1.8 
 
 
 
 53 
 54 
 55 
 56 
 
 128 40 54.7 
 130 19 52.3 
 131 57 48.7 
 133 34 46.3 
 
 128 50 51.3 
 130 29 42.7 
 132 7 33.1 
 133 44 25.0 
 
 129 47.3 
 130 39 32.4 
 132 17 16.9 
 133 54 3.1 
 
 129 10 42.6 
 130 49 21.6 
 132 27 0.1 
 134 3 40.6 
 
 129 20 37.3 
 130 59 10.1 
 132 36 42.7 
 134 13 17.6 
 
 
 
 57 
 58 
 59 
 60 
 
 135 10 47.7 
 136 45 54.9 
 138 20 10.2 
 139 53 35.9 
 
 135 20 20.8 
 136 55 22.7 
 138 29 33.0 
 140 2 53.9 
 
 135 29 53.4 
 137 4 50.1 
 138 38 55.3 
 140 12 11.4 
 
 135 39 25.4 
 137 14 16.8 
 138 48 17.0 
 140 21 28.3 
 
 135 48 57.0 
 137 23 43.1 
 138 57 38.3 
 140 30 44.9 
 
 
 
 61 
 62 
 63 
 64 
 
 141 26 14.2 
 142 58 7.0 
 144 29 16.6 
 145 59 44.9 
 
 141 35 27.5 
 143 7 16.0. 
 144 38 21.3 
 146 8 45.6 
 
 141 44 40.4 
 143 16 24.4 
 144 47 25.5 
 146 17 45.8 
 
 141 53 52.8 
 143 25 32.4 
 144 56 29.4 
 146 26 45.7 
 
 142 3 4.7 
 143 34 40.0 
 145 5 32.8 
 146 35 45.2 
 
 
 
 65 
 66 
 67 
 68 
 
 147 29 33.9 
 148 58 45.5 
 150 27 21.6 
 151 55 24.2 
 
 147 38 30.7 
 149 7 38.7 
 150 36 11.4 
 152 4 10.8 
 
 147 47 27.2 
 149 16 31.5 
 150 45 0.8 
 152 12 56.9 
 
 147 56 23.2 
 . 149 25 24.0 
 150 53 49.9 
 152 21 42.8 
 
 148 5 18.9 
 149 34 16.1 
 151 2 38.7 
 152 30 28.3 
 
 
 
 69 
 70 
 71 
 72 
 
 153 22 55.0 
 154 49 55.7 
 156 16 28.2 
 157 42 34.2 
 
 153 31 38.5 
 154 58 36.3 
 156 25 6.0 
 157 51 * 9.4 
 
 153 40 21.6 
 155 7 16.5 
 156 33 43.5 
 157 59 44.4 
 
 153 49 4.4 
 155 15 56.4 
 156 42 20.7 
 158 8 19.1 
 
 153 57 46.9 
 155 24 36.0 
 156 50 57.7 
 158 16 53.6 
 
 
 
 73 
 
 74 
 75 
 76 
 
 159 8 15.4 
 160 33 33.5 
 161 58 30.1 
 163 23 6.9 
 
 159 16 48.3 
 160 42 4.2 
 162 6 58.7 
 163 31 33.6 
 
 159 25 20.9 
 160 50 34.6 
 162 15 27.1 
 163 40 0.1 
 
 159 33 53.2 
 160 59 4.7 
 162 23 55.2 
 163 48 26.4 
 
 159 42 25.4 
 161 7 34.7 
 162 32 23.2 
 163 56 52.5 
 
 
 
 77 
 78 
 79 
 80 
 
 164 47 25.5 
 166 11 27.5 
 167 35 14.3 
 
 168 58 47.7 
 
 164 55 50.5 
 166 19 50.9 
 167 43 36.3 
 
 169 7 8.4 
 
 165 4 15.3 
 166 28 14.1 
 167 51 58.1 
 169 15 28.9 
 
 165 12 39.8 
 166 36 37.1 
 168 19.7 
 169 23 49.4 
 
 165 21 4.3 
 166 45 0.0 
 168 8 41.3 
 169 32 9.7 
 
 
 
 81 
 82 
 83 
 84 
 
 170 22 9.2 
 171 45 20.1 
 173 8 22.1 
 174 31 16.8 
 
 170 30 28.7 
 171 53 38.7 
 173 16 40.0 
 174 39 34.0 
 
 170 38 48.1 
 172 1 57.2 
 173 24 57.7 
 174 47 51.0 
 
 170 47 7.5 
 172 10 15.6 
 173 33 15.3 
 174 56 8.0 
 
 170 55 26.7 
 172 18 34.0 
 173 41 32.9 
 175 4 25.0 
 
 
 
 85 
 86 
 87 
 88 
 
 175 54 5.5 
 
 177 16 49.8 
 178 39 31.2 
 180 2 11.2 
 
 176 2 22.2 
 177 25 6.1 
 178 47 47.3 
 180 10 27.3 
 
 176 10 38.7 
 177 33 22.3 
 178 56 3.4 
 180 18 43.2 
 
 176 18 55.3 
 177 41 38.5 
 179 4 19.4 
 180 26 59.2 
 
 176 27 11.7 
 177 49 54.7 
 179 12 35.4 
 180 35 15.2 
 
 
 
 89 
 90 
 
 181 24 51.2 
 182 47 32.8 
 
 181 33 7.8 
 182 55 49.1 
 
 181 41 23.4 
 183 4 5.4 
 
 181 49 39.5 
 183 12 21.8 
 
 181 57 55.6 
 183 20 38.1 
 
 
 AUG. 
 
 O.O 
 
 O.I 
 
 0.3 
 
 0.3 
 
 O.4 
 
 
TABLE XIV. 
 
 35 
 
 
 
 
 ARG. 
 
 O.5 
 
 O.6 
 
 O.7 
 
 0.8 
 
 O.9 
 
 V. 
 
 V. 
 
 V. 
 
 V. 
 
 V. 
 
 45 
 46 
 47 
 
 48 
 
 115 41 55.8 
 117 29 54.4 
 119 16 32.0 
 121 1 51.5 
 
 115 52 47.3 
 117 40 37.7 
 119 27 7.4 
 121 12 19.2 
 
 116 3 38.1 
 117 51 20.3 
 119 37 42.0 
 121 22 46.2 
 
 116 14 28.0 
 118 2 2.1 
 119 48 15.9 
 121 33 12.5 
 
 O / H 
 
 116 25 17.1 
 118 12 43.0 
 119 58 49.0 
 121 43 38.0 
 
 
 49 
 50 
 51 
 52 
 
 122 45 55.5 
 124 28 46.9 
 126 10 28.3 
 127 51 2.3 
 
 122 56 15.9 
 124 39 0.2 
 126 20 34.7 
 128 1 2.0 
 
 123 6 35.6 
 124 49 12.7 
 126 30 40.4 
 128 11 1.2 
 
 123 16 54.5 
 124 59 24.6 
 126 40 45.4 
 128 20 59.7 
 
 123 27 12.7 
 125 9 35.7 
 126 50 49.8 
 128 30 57.5 
 
 
 
 53 
 54 
 55 
 
 56 
 
 129 30 31.3 
 131 8 58.0 
 132 46 24.7 
 134 22 54.0 
 
 129 40 24.8 
 131 18 45.3 
 132 56 6.2 
 134 32 29.8 
 
 129 50 17.6 
 131 28 32.1 
 133 5 47.1 
 134 42 5.1 
 
 130 9.8 
 131 38 18.2 
 133 15 27.4 
 134 51 39.9 
 
 130 10 1.4 
 131 48 3.7 
 133 25 7.2 
 135 1 14.1 
 
 
 
 57 
 58 
 59 
 60 
 
 135 58 27.9 
 137 33 8.9 
 139 6 59.1 
 140 40 0.9 
 
 136 7 58.4 
 137 42 34.2 
 139 16 19.5 
 140 49 16.5 
 
 136 17 28.3 
 137 51 58.9 
 139 25 39.3 
 140 58 31.7 
 
 136 26 57.7 
 138 1 23.3 
 139 34 58.7 
 141 7 46.3 
 
 136 36 26.6 
 138 10 47.0 
 139 44 17.5 
 141 17 0.5 
 
 
 
 61 
 62 
 63 
 
 64 
 
 142 12 16.2 
 143 43 47.1 
 145 14 35.8 
 146 44 44.2 
 
 142 21 27.3 
 143 52 53.9 
 145 23 38.4 
 146 53 42.9 
 
 142 30 37.9 
 144 2 0.2 
 145 32 40.7 
 147 2 41.3 
 
 142 39 48.1 
 144 11 6.1 
 145 41 42.5 
 147 11 39.2 
 
 142 48 57.8 
 144 20 11.6 
 145 50 43.9 
 147 20 36.7 
 
 
 
 65 
 66 
 67 
 
 68 
 
 148 14 14.3 
 149 43 7.9 
 151 11 27.1 
 152 39 13.6 
 
 148 23 9.2 
 149 51 59.3 
 151 20 15.2 
 
 152 47 58.5 
 
 148 32 3.8 
 150 50.4 
 151 29 2.9 
 152 56 43.1 
 
 148 40 58.0 
 150 9 41.2 
 151 37 50.4 
 153 5 27.4 
 
 148 49 52.0 
 150 18 31,6 
 151 46 37.5 
 153 14 11.4 
 
 
 
 69 
 70 
 71 
 
 72 
 
 154 6 29.1 
 155 33 15.4 
 156 59 34.5 
 
 158 25 27.8 
 
 154 15 11.0 
 155 41 54.5 
 157 8 10.9 
 158 34 1.8 
 
 154 23 52.6 
 155 50 33.3 
 157 16 47.1 
 158 42 35.6 
 
 154 32 34.0 
 155 59 11.9 
 157 25 23.1 
 158 51 9.1 
 
 154 41 15.0 
 156 7 50.2 
 157 33 58.8 
 158 59 42.4 
 
 
 
 73 
 
 74 
 75 
 
 76 
 
 159 50 57.3 
 161 16 4.5 
 162 40 51.0 
 164 5 18.5 
 
 159 59 29.0 
 161 24 34.0 
 162 49 18.6 
 164 13 44.2 
 
 160 8 0.5 
 161 33 3.4 
 162 57 46.0 
 164 22 9.8 
 
 160 16 31.7 
 161 41 32.5 
 163 6 13.2 
 164 30 35.3 
 
 160 25 2.8 
 161 50 1.5 
 163 14 40.2 
 164 39 0.5 
 
 
 
 77 
 78 
 79 
 80 
 
 165 29 28.5 
 166 53 22.7 
 168 17 2.7 
 169 40 29.9 
 
 165 37 52.7 
 167 1 45.3 
 168 25 23.9 
 169 48 49.9 
 
 165 46 16.6 
 167 10 7.8 
 168 33 45.1 
 169 57 9.9 
 
 165 54 40.4 
 167 18 30.1 
 168 42 6.1 
 170 5 29.8 
 
 166 3 4.1 
 167 26 52.3 
 168 50 27.0 
 170 13 49.5 
 
 
 
 81 
 
 82 
 83 
 
 84 
 
 171 3 45.9 
 172 26 52.2 
 173 49 50.4 
 175 12 41.9 
 
 171 12 4.9 
 172 35 10.4 
 
 173 58 7.7 
 175 20 58.7 
 
 171 20 23.9 
 172 43 28.4 
 174 6 25.0 
 175 29 15.5 
 
 171 28 42.7 
 172 51 46.4 
 174 14 42.2 
 175 37 32.3 
 
 171 37 1.5 
 173 4.4 
 174 22 59.5 
 175 45 49.0 
 
 
 
 85 
 86 
 
 87 
 88 
 
 176 35 28.2 
 177 58 10.9 
 179 20 51.4 
 180 43 31.2 
 
 176 43 44.6 
 178 6 27.0 
 179 29 7.4 
 180 51 47.2 
 
 176 52 1.0 
 178 14 43.1 
 179 37 23.3 
 181 3.2 
 
 177 17.3 
 178 22 59.2 
 179 45 39.3 
 181 8 19.2 
 
 177 8 33.6 
 178 31 15.2 
 179 53 55.3 
 181 16 35.3 
 
 
 
 89 
 90 
 
 182 6 11.8 
 183 28 54.6 
 
 182 14 27.9 
 183 37 11.0 
 
 182 22 44.1 
 183 45 27.5 
 
 182 31 0.3 
 183 53 44.1 
 
 182 39 16.5 
 184 2 0.7 
 
 
 ARG. 
 
 O.5 
 
 0.6 
 
 0.7 
 
 0.8 
 
 0.9 
 
 
36 
 
 TABLE XIV. 
 
 
 ARG. 
 
 o.o 
 
 O.I 
 
 0.2 
 
 O.3 
 
 0.4 
 
 V. 
 
 V. 
 
 V. 
 
 V. 
 
 V. 
 
 90 
 91 
 92 
 93 
 
 182 47 32.8 
 184 10 17.3 
 185 33 6.3 
 186 56 1.4 
 
 182 55 49.1 
 184 18 34.0 
 185 41 23.6 
 187 4 19.3 
 
 O 1 It 
 
 183 4 5.4 
 184 26 50.7 
 185 49 40.9 
 187 12 37.3 
 
 183 12 21.8 
 184 35 7.5 
 
 185 57 58.2 
 187 20 55.3 
 
 183 20 38.1 
 184 43 24.3 
 186 6 15.6 
 187 29 13.5 
 
 94 
 95 
 96 
 
 97 
 
 188 19 3.9 
 189 42 15.5 
 191 5 37.6 
 192 29 11.8 
 
 188 27 22.7 
 189 50 35.3 
 191 13 58.5 
 192 37 34.0 
 
 188 35 41.5 
 189 58 55.1 
 191 22 19.5 
 192 45 56.2 
 
 188 44 0.4 
 190 7 15.0 
 191 30 40.6 
 192 54 18.7 
 
 188 52 19.5 
 190 15 35.1 
 191 39 1.8 
 193 2 41.2 
 
 98 
 99 
 100 
 101 
 
 193 52 59.5 
 195 17 2.4 
 196 41 22.1 
 198 6 0.1 
 
 194 1 23.1 
 195 25 27.7 
 196 49 49.1 
 198 14 29.0 
 
 194 9 46.9 
 195 33 53.0 
 196 58 16.2 
 198 22 58.1 
 
 194 18 10.8 
 195 42 18.6 
 197 6 43.6 
 198 31 27.3 
 
 194 26 34.8 
 195 50 44.3 
 197 15 11.1 
 
 198 39 56 8 
 
 102 
 103 
 104 
 105 
 
 199 30 58.0 
 200 56 17.4 
 202 22 0.1 
 
 203 48 7.7 
 
 199 39 29.0 
 201 4 50.7 
 202 30 35.8 
 203 56 45.9 
 
 199 48 0.1 
 201 13 24.1 
 202 39 11.7 
 204 5 24.4 
 
 199 56 31.5 
 
 201 21 57.8 
 202 47 47.8 
 204 14 3.1 
 
 200 5 3.1 
 201 30 31.7 
 202 56 24.1 
 204 22 42.1 
 
 106 
 107 
 108 
 109 
 
 205 14 41.8 
 206 41 44.3 
 208 9 17.1 
 209-37 21.6 
 
 205 23 22.8 
 206 50 28.2 
 208 18 4.1 
 209 46 12.0 
 
 205 32 4.0 
 206 59 12.4 
 208 26 51.4 
 209 55 2.6 
 
 205 40 45.5 
 207 7 56.9 
 208 35 39.0 
 210 3 53.6 
 
 205 49 27.3 
 207 16 41.7 
 208 44 27.0 
 210 12 44.9 
 
 110 
 111 
 112 
 113 
 
 211 5 59.9 
 212 35 13.7 
 214 5 5.1 
 215 35 35.8 
 
 211 14 53.7 
 212 44 11.2 
 214 14 6.4 
 215 44 41.2 
 
 211 23 47.8 
 212 53 9.0 
 214 23 8.0 
 215 53 46.9 
 
 211 32 42.3 
 213 2 7.2 
 214 32 10.1 
 216 2 53.1 
 
 211 41 37.1 
 213 11 5.7 
 214 41 12.6 
 216 11 59.7 
 
 114 
 115 
 116 
 117 
 
 217 6 48.0 
 218 38 43.6 
 220 11 24.7 
 221 44 53.4 
 
 217 15 57.6 
 218 47 57.6 
 220 20 43.5 
 221 54 17.0 
 
 217 25 7.6 
 218 57 12.1 
 220 30 2.6 
 222 3 41.1 
 
 217 34 18.1 
 219 6 27.1 
 220 39 22.3 
 222 13 5.7 
 
 217 43 28.9 
 219 15 42.5 
 220 48 42.4 
 222 22 30.8 
 
 118 
 119 
 120 
 121 
 
 223 19 11.9 
 224 54 22.3 
 226 30 27.0 
 
 228 7 28.2 
 
 223 28 40.6 
 225 3 56.4 
 226 40 6.6 
 228 17 13.6 
 
 223 38 9.8 
 225 13 30.9 
 226 49 46.7 
 228 26 59.5 
 
 223 47 39.5 
 225 23 6.0 
 226 59 27.4 
 228 36 46.0 
 
 223 57 9.7 
 225 32 41.6 
 227 9 8.6 
 228 46 33.1 
 
 122 
 123 
 124 
 125 
 
 229 45 28.3 
 231 24 29.7 
 233 4 34.9 
 234 45 46.4 
 
 229 55 19.7 
 231 34 27.3 
 233 14 39.0 
 234 55 57.3 
 
 230 5 11.6 
 231 44 25.6 
 233 24 43.8 
 235 6 8.9 
 
 230 15 4.2 
 231 54 24.5 
 233 34 49.3 
 235 16 21.2 
 
 230 24 57.4 
 232 4 24.0 
 233 44 55.4 
 235 26 34.1 
 
 126 
 127 
 128 
 129 
 
 236 28 6.7 
 238 11 38.6 
 239 56 24.6 
 241 42 27.6 
 
 236 38 24.7 
 238 22 3.8 
 240 6 57.5 
 241 53 8.3 
 
 236 48 43.3 
 238 32 29.8 
 240 17 31.0 
 242 3 49.8 
 
 236 59 2.7 
 238 42 56.5 
 240 28 5.4 
 242 14 32.0 
 
 237 9 22.7 
 238 53 24.0 
 240 38 40.5 
 242 25 15.0 
 
 130 
 131 
 132 
 133 
 
 243 29 50.4 
 245 18 35.7 
 247 8 46.4 
 249 25.5 
 
 243 40 39.2 
 245 29 32.9 
 247 19 52.3 
 249 11 40.5 
 
 243 51 28.8 
 245 40 30.9 
 247 30 59.1 
 249 22 56.3 
 
 244 2 19.2 
 245 51 29.8 
 247 42 6.7 
 249 34 13.0 
 
 244 13 10.4 
 246 2 29.6 
 247 53 15.3 
 249 45 30.7 
 
 134 
 135 
 
 250 53 36.1 
 252 48 21.2 
 
 251 5 0.4 
 252 59 55.0 
 
 251 16 25.5 
 253 11 29.8 
 
 251 27 51.6 
 253 23 5.6 
 
 251 39 18.7 
 253 34 42.3 
 
 ARG. 
 
 O.O 
 
 0.1 
 
 0.2 
 
 0.3 
 
 0.4 
 
 
TABLE XIV. 
 
 
 
 
 ARG. 
 
 O.3 
 
 0.6 
 
 o.r 
 
 0.8 
 
 O.9 
 
 V. 
 
 V. 
 
 V. 
 
 V. 
 
 V. 
 
 90 
 91 
 92 
 93 
 
 183 28 54.6 
 184 51 41.2 
 186 14 33.1 
 187 37 31.7 
 
 183 37 li'.O 
 184 59 58.1 
 186 22 50.6 
 187 45 50.0 
 
 183 45 27.5 
 185 8 15.1 
 186 31 8.2 
 187 54 8.3 
 
 183 53 44.1 
 185 16 32.0 
 186 39 25.9 
 
 188 2 26.8 
 
 O I ft 
 
 184 2 0.7 
 185 24 49.1 
 186 47 43.6 
 188 10 45.4 
 
 
 94 
 95 
 96 
 
 97 
 
 189 38.6 
 190 23 55.2 
 191 47 23.2 
 193 11 3.9 
 
 189 8 57.8 
 190 32 15.5 
 191 55 44.6 
 193 19 26.7 
 
 189 17 17.1 
 190 40 35.9 
 192 4 6.2 
 193 27 49.7 
 
 189 25 36.5 
 190 48 56.3 
 192 12 28.0 
 193 36 12.9 
 
 189 33 56.0 
 190 57 16.9 
 192 20 49.8 
 193 44 36.1 
 
 
 
 98 
 99 
 100 
 101 
 
 194 34 59.0 
 195 59 10.1 
 197 23 38.8 
 198 48 26.5 
 
 194 43 23.6 
 196 7 36.2 
 197 32 6.6 
 198 56 56.4 
 
 194 51 47.9 
 196 16 2.4 
 197 40 34.7 
 199 5 26.5 
 
 195 12.6 
 
 196 24 28.8 
 197 49 3.0 
 199 13 56.8 
 
 195 8 37.5 
 196 32 554 
 197 57 31.5 
 199 22 27.3 
 
 
 
 102 
 103 
 104 
 105 
 
 200 13 35.0 
 201 39 5.8 
 203 5 0.8 
 204 31 21.4 
 
 200 22 7.0 
 201 47 40.2 
 203 13 37.6 
 204 40 0.9 
 
 200 30 39.3 
 201 56 14.8 
 203 22 14.8 
 204 48 40.8 
 
 200 39 11.8 
 202 4 49.7 
 203 30 52.2 
 204 57 20.9 
 
 200 47 44.5 
 202 13 24.8 
 203 39 29.8 
 205 6 1.2 
 
 
 
 106 
 107 
 108 
 109 
 
 205 58 9.4 
 207 25 26.8 
 208 53 15.3 
 210 21 36.5 
 
 206 6 51.8 
 207 34 12.2 
 209 2 3.9 
 210 30 28.5 
 
 206 15 34.5 
 207 42 58.0 
 209 10 52.8 
 210 39 20.8 
 
 206 24 17.5 
 207 51 44.0 
 209 19 42.1 
 210 48 13.5 
 
 206 33 0.8 
 208 30.4 
 209 28 31.7 
 210 57 6.6 
 
 
 
 110 
 111 
 112 
 113 
 
 211 50 32.3 
 213 20 4.6 
 214 50 15.4 
 216 21 6.7 
 
 211 59 27.9 
 213 29 4.0 
 214 59 18.7 
 216 30 14.1 
 
 212 8 23.8 
 213 38 3.7 
 215 8 22.4 
 216 39 21.9 
 
 212 17 20.1 
 213 47 3.8 
 215 17 26.5 
 216 48 30.2 
 
 212 26 16.8 
 213 56 4.2 
 215 26 31.0 
 216 57 38.9 
 
 
 
 114 
 115 
 116 
 117 
 
 217 52 40.3 
 219 24 58.4 
 220 58 3.0 
 222 31 56.3 
 
 218 1 52.0 
 219 34 14.7 
 221 7 24.1 
 222 41 22.4 
 
 218 11 4.2 
 219 43 31.5 
 221 16 45.7 
 222 50 49.0 
 
 218 20 16.9 
 219 52 48.8 
 221 26 7.8 
 223 16.1 
 
 218 29 30.0 
 220 2 6.5 
 221 35 30.4 
 223 9 43.8 
 
 
 
 118 
 119 
 120 
 121 
 
 224 6 40.5 
 225 42 17.8 
 227 18 50.5 
 228 56 20.8 
 
 224 16 11.8 
 225 51 54.5 
 227 28 32.9 
 229 6 9.1 
 
 224 25 43.6 
 226 1 31.8 
 227 38 15.8 
 229 15 58.0 
 
 224 35 16.0 
 226 11 9.7 
 227 47 59.4 
 229 25 47.5 
 
 224 44 48.9 
 226 20 48.1 
 227 57 43.5 
 229 35 37.6 
 
 
 
 122 
 123 
 124 
 125 
 
 230 34 51.2 
 232 14 24.2 
 233 55 2.2 
 
 235 36 47.8 
 
 230 44 45.6 
 232 24 25.0 
 234 5 9.7 
 235 47 2.2 
 
 230 54 40.7 
 232 34 26.5 
 234 15 17.8 
 235 57 17.3 
 
 231 4 36.4 
 232 44 28.6 
 234 25 26.6 
 236 7 33.0 
 
 231 14 32.7 
 232 54 31.4 
 234 35 36.2 
 236 17 49.5 
 
 
 
 126 
 127 
 128 
 129 
 
 237 19 43.6 
 239 3 52.2 
 240 49 16.4 
 242 35 58.9 
 
 237 30 5.1 
 239 14 21.1 
 240 59 53.1 
 242 46 43.6 
 
 237 40 27.4 
 239 24 50.9 
 241 10 30.5 
 242 57 29.1 
 
 237 50 50.4 
 239 35 21.4 
 241 21 8.8 
 243 8 15.4 
 
 238 1 14.1 
 239 45 52.6 
 241 31 47.8 
 243 19 2.5 
 
 
 
 130 
 131 
 132 
 133 
 
 244 24 2.5 
 246 13 30.2 
 
 248 4 24.8 
 249 56 49.3 
 
 244 34 55.5 
 246 24 31.7 
 248 15 35.1 
 
 250 8 8.8 
 
 244 45 49.3 
 246 35 34.1 
 248 26 46.3 
 250 19 29.2 
 
 244 56 43.9 
 246 46 37.3 
 248 37 58.5 
 250 30 50.6 
 
 245 7 39.4 
 246 57 41.4 
 248 49 11.6 
 250 42 12.9 
 
 
 
 134 
 135 
 
 251 50 46.7 
 253 46 20.1 
 
 252 2 15.7 
 253 57 58.8 
 
 252 13 45.6 
 254 9 38.5 
 
 252 25 16.5 
 254 21 19.2 
 
 252 36 48.3 
 254 33 1.0 
 
 
 ARG. 
 
 O.5 
 
 0.6 
 
 0.7 
 
 O.8 
 
 O.9 
 
 
TABLE XIV. 
 
 
 
 
 ARG. 
 
 0.0 
 
 0.1 
 
 0.3 
 
 O.3 
 
 0.4 
 
 V. 
 
 V. 
 
 V. 
 
 V. 
 
 V. 
 
 135 
 136 
 137 
 138 
 
 252 48 21.2 
 254 44 43.6 
 256 42 46.7 
 258 42 33.4 
 
 252 59 55\0 
 254 56 27.4 
 256 54 40.7 
 258 54 37.9 
 
 253 11 29.8 
 255 8 12.2 
 257 6 35.7 
 259 6 43.5 
 
 253 23 5.6 
 255 19 57.9 
 257 18 31.7 
 259 18 50.1 
 
 253 34 42.3 
 255 31 44.7 
 257 30 28.8 
 259 30 57.8 
 
 
 139 
 140 
 141 
 142 
 
 260 44 6.8 
 262 47 30.0 
 264 52 46.3 
 266 59 58.6 
 
 260 56 22.1 
 262 59 56.6 
 265 5 24.3 
 267 12 48.4 
 
 261 8 38.6 
 263 12 24.2 
 265 18 3.4 
 267 25 39.3 
 
 261 20 56.1 
 263 24 52.9 
 265 30 43.7 
 267 38 31.4 
 
 261 33 148 
 263 37 22.8 
 265 43 25.2 
 267 51 24.7 
 
 
 
 143 
 144 
 145 
 
 146 
 
 269 9 9.9 
 271 20 23.2 
 273 33 41.5 
 275 49 7.3 
 
 269 22 11.8 
 271 33 37.5 
 273 47 8.3 
 276 2 47.1 
 
 269 35 14.8 
 271 46 52.9 
 274 36.4 
 276 16 28.1 
 
 269 48 19.0 
 272 9.5 
 274 14 5.8 
 276 30 10.4 
 
 270 1 24.5 
 272 13 27.4 
 274 27 36.4 
 276 43 54.1 
 
 
 
 147 
 148 
 149 
 150 
 
 278 6 43.5 
 280 26 32.6 
 282 48 36.8 
 285 12 58.2 
 
 278 20 36.5 
 280 40 38.9 
 283 2 56.8 
 285 27 32.0 
 
 278 34 30.7 
 280 54 46.6 
 283 17 18.1 
 285 42 7.1 
 
 278 48 26.2 
 281 8 55.6 
 283 31 40.7 
 285 56 43.7 
 
 279 2 23.1 
 281 23 5.9 
 283 46 4.8 
 286 11 21.6 
 
 
 
 151 
 152 
 153 
 154 
 
 287 39 38.6 
 290 8 39.7 
 292 40 2.8 
 295 13 48.7 
 
 287 54 26.4 
 290 23 41.7 
 292 55 19.0 
 295 29 19.2 
 
 288 9 15.6 
 290 38 45.0 
 293 10 36.5 
 295 44 51.1 
 
 288 24 6.1 
 290 53 49.7 
 293 25 55.5 
 296 24.4 
 
 288 38 58.2 
 291 8 55.9 
 293 41 16.0 
 296 15 59.2 
 
 
 
 155 
 156 
 157 
 
 158 
 
 297 49 57.8 
 300 28 30.2 
 303 9 25.5 
 305 52 42.8 
 
 298 5 42.7 
 300 44 29.4 
 303 25 38.9 
 306 9 10.3 
 
 298 21 28.9 
 301 29.9 
 303 41 53.7 
 306 25 39.1 
 
 298 37 16.6 
 301 16 31.9 
 303 58 9.9 
 306 42 9.4 
 
 298 53 5.7 
 301 32 35.3 
 304 14 27.5 
 306 58 41.0 
 
 
 
 159 
 160 
 161 
 162 
 
 308 38 20.2 
 311 26 15.8 
 314 16 '26.7 
 317 8 49.5 
 
 308 55 1.6 
 311 43 10.9 
 314 33 35.2 
 317 26 10.8 
 
 309 11 44.4 
 312 7.3 
 314 50 44.9 
 317 43 33.4 
 
 309 28 28.5 
 312 17 5.0 
 315 7 55.9 
 318 57.3 
 
 309 45 14.0 
 312 34 4.2 
 315 25 8.3 
 318 18 22.5 
 
 
 
 163 
 164 
 165 
 166 
 
 320 3 19.6 
 322 59 52.4 
 325 58 22.0 
 328 58 42.1 
 
 320 20 53.5 
 323 17 38.2 
 326 16 19.2 
 329 16 49.9 
 
 320 38 28.5 
 323 35 25.2 
 326 34 17.5 
 329 34 58.7 
 
 320 56 4.8 
 323 53 13.3 
 326 52 1"6.8 
 329 53 8.6 
 
 321 13 42.3 
 324 11 2.6 
 327 10 17.2 
 330 11 19.4 
 
 
 
 167 
 168 
 169 
 170 
 
 332 45.3 
 335 4 23.8 
 338 9 28.9 
 341 15 51.2 
 
 332 19 3.1 
 335 22 50.6 
 338 28 3.8 
 341 34 33.4 
 
 332 37 21.7 
 335 41 18.2 
 338 46 39.5 
 341 53 16.2 
 
 332 55 41.3 
 335 59 46.7 
 339 5 15.9 
 342 11 59.6 
 
 333 14 1.8 
 336 18 16.0 
 339 23 53.1 
 342 30 43.7 
 
 
 
 171 
 172 
 173 
 174 
 
 344 23 21.1 
 
 347 31 477 
 350 41 0.4 
 353 50 47.7 
 
 344 42 9.4 
 347 50 41.1 
 350 59 57.8 
 354 9 47.9 
 
 345 58.2 
 348 9 35.0 
 351 18 55.5 
 354 28 48.3 
 
 345 19 47.6 
 348 28 29.2 
 351 37 53.5 
 354 47 49.0 
 
 '345 38 37.6 
 348 47 23.9 
 351 56 51.8 
 355 6 49.8 
 
 
 
 175 
 
 176 
 
 357 58.0 
 11 19.6 
 
 357 19 59.9 
 30 21.9 
 
 357 39 1.9 
 49 24.2 
 
 357 58 3.9 
 1 8 26.5 
 
 358 17 6.0 
 1 27 28.6 
 
 
 ARG. 
 
 0.0 
 
 O.I 
 
 0.3 
 
 0.3 
 
 0.4 
 
 
TABLE XIV. 
 
 39 
 
 
 
 
 ARG. 
 
 0.5 
 
 0.6 
 
 0.7 
 
 0.8 
 
 0.9 
 
 V. 
 
 V. 
 
 V. 
 
 V. 
 
 V. 
 
 135 
 
 136 
 137 
 138 
 
 253 46 20.1 
 255 43 32.5 
 257 42 26.9 
 259 43 6.7 
 
 253 57 58.8 
 255 55 21.3 
 257 54 26.1 
 259 55 16.4 
 
 254 9. 38.5 
 256 7 11.1 
 258 6 26.3 
 260 7 27.4 
 
 254 21 19.2 
 256 19 1.9 
 258 18 27.6 
 260 19 39.4 
 
 254 33 1.0 
 256 30 53.8 
 258 30 30.0 
 260 31 52.6 
 
 
 139 
 140 
 141 
 142 
 
 261 45 34.5 
 263 49 53.9 
 265 56 7.8 
 268 4 19.2 
 
 261 57 55.4 
 264 2 26.1 
 266 8 51.6 
 268 17 15.0 
 
 262 10 17.4 
 264 14 59.4 
 266 21 36.6 
 268 30 11.9 
 
 262 22 40.5 
 264 27 33.9 
 266 34 22.7 
 268 43 10.0 
 
 262 35 4.7 
 264 40 9.5 
 266 47 10.1 
 268 56 9.4 
 
 
 
 143 
 144 
 145 
 146 
 
 270 14 31.2 
 272 26 46.6 
 274 41 8.3 
 276 57 39.0 
 
 270 27 39.1 
 272 40 7.1 
 274 54 41.6 
 277 11 25.3 
 
 270 40 48.3 
 272 53 28.8 
 275 8 16.1 
 277 25 12.9 
 
 270 53 58.7 
 273 6 51.8 
 275 21 51.9 
 277 39 1.8 
 
 271 7 10.4 
 273 20 16.0 
 275 35 29.0 
 277 52 52.0 
 
 
 
 147 
 148 
 149 
 150 
 
 279 16 21.3 
 
 - 281 37 17.7 
 284 30.2 
 286 26 0.9 
 
 279 30 20.9 
 281 51 30.8 
 284 14 57.1 
 286 40 41.7 
 
 279 44 21.8 
 282 5 45.2 
 284 29 25.3 
 286 55 23.8 
 
 279 58 24.0 
 282 20 1.0 
 284 43 54.9 
 287 10 7.3 
 
 280 12 27.6 
 282 34 18.2 
 284 58 25.8 
 287 24 52.3 
 
 
 
 151 
 
 152 
 153 
 154 
 
 288 53 51.6 
 291 24 3.5 
 293 56 37.8 
 296 31 35.4 
 
 289 8 46.4 
 291 39 12.5 
 294 12 1.2 
 296 47 13.0 
 
 289 23 42.6 
 291 54 22.9 
 294 27 25.9 
 297 2 52.1 
 
 289 38 40.3 
 292 9 34.8 
 294 42 52.1 
 297 18 32.6 
 
 289 53 39.3 
 292 24 48.1 
 294 58 19.7 
 297 34 14.6 
 
 
 
 155 
 156 
 157 
 158 
 
 299 8 56.2 
 301 48 40.1 
 304 30 46.5 
 307 15 14.1 
 
 299 24 48.1 
 302 4 46.4 
 304 47 7.0 
 307 31 48.5 
 
 299 40 41.5 
 302 20 54.1 
 305 3 28.8 
 307 48 24.4 
 
 299 56 36.4 
 302 37 3.1 
 305 19 52.1 
 308 5 1.6 
 
 300 12.32.6 
 302 53 13.7 
 305 36 16.7 
 308 21 40.2 
 
 
 
 159 
 160 
 161 
 162 
 
 310 2 0.9 
 312 51 4.6 
 315 42 21.9 
 318 35 48.9 
 
 310 18 49.2 
 313 8 6.4 
 315 59 36.8 
 318 53 16.5 
 
 310 35 38.8 
 313 25 9.5 
 316 16 53.1 
 319 10 45.4 
 
 310 52 29.8 
 313 42 14.0 
 316 34 10.6 
 319 28 15.6 
 
 811 9 22.1 
 313 59 19.7 
 316 51 29.4 
 319 45 47.0 
 
 
 
 163 
 164 
 165 
 166 
 
 321 31 21.0 
 324 28 53.0 
 
 327 28 18.7 
 330 29 31.3 
 
 321 49 0.9 
 324 46 44.6 
 327 46 21.3 
 330 47 44.2 
 
 322 6 42.0 
 325 4 37.3 
 328 4 24.9 
 331 5 58.0 
 
 322 24 24.3 
 325 22 31.1 
 328 22 29.6 
 331 24 12.8 
 
 323 42 7.8 
 325 40 26.0 
 328 40 35.3 
 331 42 28.6 
 
 
 
 167 
 168 
 169 
 170 
 
 333 32 23.2 
 336 36 46.1 
 339 42 31.0 
 342 49 28.4 
 
 333 50 45.5 
 336 55 17.1 
 340 1 9.7 
 343 8 13.8 
 
 334 9 8.8 
 337 13 48.8 
 340 19 49.0 
 343 26 59.7 
 
 334 27 32.9 
 337 32 21.4 
 340 38 29.1 
 343 45 46.2 
 
 334 45 57.9 
 337 50 54.8 
 340 57 9.8 
 344 4 33.4 
 
 
 
 171 
 172 
 173 
 174 
 
 345 57 28.0 
 349 6 19.0 
 352 15 50.5 
 355 25 50.7 
 
 346 16 19.0 
 349 25 14.6 
 352 34 49.4 
 355 44 51.9 
 
 346 35 10.4 
 349 44 10.5 
 352 53 48.6 
 356 3 53.2 
 
 346 54 2.4 
 350 3 6.7 
 353 12 48.1 
 356 22 54.6 
 
 347 12 54.8 
 350 22 3.4 
 353 31 47.8 
 356 41 56.3 
 
 
 
 175 
 176 
 
 358 36 8.1 
 1 46 30.9 
 
 358 55 10.4 
 2 5 32.9 
 
 359 14 12.7 
 2 24 34.9 
 
 359 33 14.9 
 2 43 36.8 
 
 359 52 17.3 
 3 2 38.7 
 
 
 ARG. 
 
 0.5 
 
 O.6 
 
 0.7 
 
 O.8 
 
 0.9 
 
 
40 
 
 TABLE XV. 
 
 
 
 
 ARG. 
 
 o.o 
 
 0.1 
 
 0.9 
 
 O.3 
 
 0.4 
 
 ARG. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 
 
 1 
 
 2 
 3 
 
 9.4878495 
 .4879630 
 .4883030 
 
 .4888674 
 
 9.4878506 
 .4879868 
 .4883494 
 .4889361 
 
 9.4878540 
 .4880129 
 .4883980 
 .4890070 
 
 9.4878597 
 .4880413 
 .4884489 
 .4890801 
 
 9.4878677 
 .4880719 
 .4885020 
 .4891553 
 
 
 
 1 
 
 2 
 3 
 
 
 4 
 5 
 6 
 
 7 
 
 9.4896531 
 .4906558 
 .4918699 
 .4932890 
 
 9.4897437 
 .4907678 
 .4920027 
 .4934419 
 
 9.4898364 
 .4908819 
 .4921376 
 .4935968 
 
 9.4899314 
 .4909981 
 .4922744 
 .4937536 
 
 9.4900284 
 .4911164 
 .4924133 
 .4939124 
 
 4 
 5 
 6 
 
 7 
 
 
 
 8 
 9 
 10 
 11 
 
 9.4949055 
 .4967111 
 .4986967 
 .5008526 
 
 9.4950777 
 .4969017 
 .4989048 
 .5010772 
 
 9.4952518 
 .4970941 
 .4991146 
 .5013033 
 
 9.4954277 
 .4972883 
 .4993261 
 .5015311 
 
 9.4956055 
 .4974843 
 .4995392 
 .5017604 
 
 8 
 9 
 10 
 11 
 
 
 
 12 
 13 
 14 
 15 
 
 9.5031688 
 .5056345 
 .5082391 
 .5109715 
 
 9.5034088 
 .5058889 
 .5085068 
 .5112513 
 
 9.5036503 
 .5061447 
 .5087757 
 .5115323 
 
 9.5038933 
 .5064018 
 .5090459 
 .5118145 
 
 9.5041378 
 .5066603 
 .5093-173 
 .5120977 
 
 12 
 13 
 14 
 15 
 
 
 
 16 
 17 
 18 
 19 
 
 9.5138206 
 .5167756 
 .5198255 
 .5229598 
 
 9.5141115 
 .5170765 
 .5201353 
 .5232775 
 
 9.5144035 
 .5173783 
 .5204459 
 .5235959 
 
 9.5146965 
 .5176811 
 .5207574 
 .5239150 
 
 9.5149905 
 .5179848 
 .5210697 
 .5242348 
 
 16 
 17 
 IS 
 19 
 
 
 
 20 
 21 
 22 
 23 ' 
 
 9.5261681 
 .5294400 
 .5327660 
 .5361371 
 
 9.5264925 
 .5297703 
 .5331012 
 .5364763 
 
 9.5268176 
 .5301012 
 .5334369 
 .5368159 
 
 9.5271434 
 .5304325 
 .5337730 
 .5371558 
 
 9.5274697 
 .5307644 
 .5341095 
 .5374961 
 
 20 
 21 
 22 
 23 
 
 
 
 24 
 25 
 26 
 
 27 
 
 9.5395439 
 .5429781 
 .5464318 
 .5498973 
 
 9.5398862 
 .5433227 
 .5467779 
 .5502442 
 
 9.5402288 
 .5436675 
 .5471242 
 .5505912 
 
 9.5405716 
 .5440125 
 .5474705 
 .5509382 
 
 9.5409147 
 .5443577 
 .5478170 
 .5512852 
 
 24 
 25 
 26 
 
 27 
 
 
 
 28 
 29 
 30 
 31 
 
 9.5533676 
 .5568361 
 .5602963 
 .5637431 
 
 9.5537146 
 .5571826 
 .5606417 
 .5640868 
 
 9.5540617 
 .5575290 
 .5609869 
 .5644303 
 
 9.5544086 
 .5578753 
 .5613320 
 .5647736 
 
 9.5547556 
 .5582215 
 .5616769 
 .5651167 
 
 28 
 29 
 30 
 31 
 
 
 
 32 
 33 
 34 
 35 
 
 9.5671706 
 .5705740 
 
 .5739488 
 .5772908 
 
 9.5675121 
 .5709128 
 .5742845 
 .5776231 
 
 9.5678534 
 .5712514 
 .5746199 
 .5779549 
 
 9.5681944 
 .5715896 
 .5749550 
 
 .5782865 
 
 9.5685351 
 .5719276 
 .5752897 
 .5786176 
 
 32 
 33 
 34 
 35 
 
 
 
 36 
 37 
 38 
 39 
 
 9.5805963 
 .5838615 
 .5870835 
 .5902594 
 
 9.5809247 
 .5841857 
 .5874032 
 .5905743 
 
 9.5812527 
 .5845094 
 .5877225 
 .5908888 
 
 9.5815802 
 
 .5848328 
 .5880412 
 .5912027 
 
 9.5819074 
 .5851556 
 .5883596 
 .5915162 
 
 36 
 37 
 38 
 39 
 
 
 
 40 
 41 
 42 
 43 
 
 9.5933864 
 .5964622 
 .5994846 
 .6024521 
 
 9.5936963 
 .5967669 
 .5997839 
 .6027457 
 
 9.5940057 
 .5970710 
 .6000826 
 .6030388 
 
 9.5943146 
 .5973746 
 .6003807 
 .6033313 
 
 9.5946230 
 .5976777 
 .6006783 
 .6036232 
 
 40 
 41 
 42 
 43 
 
 
 
 44 
 45 
 
 9.6053625 
 .6082144 
 
 9.6056503 
 .6084963 
 
 9.6059376 
 .6087777 
 
 9.6062243 
 .6090584 
 
 9.6065104 
 .6093385 
 
 44 
 45 
 
 
 ARG. 
 
 0.0 
 
 0.1 
 
 0.2 
 
 0.3 0.4 
 
 ARG. 
 
 
TABLE XT. 
 
 41 
 
 
 
 
 ARG. 
 
 0.5 
 
 O.6 
 
 0.7 
 
 o.s 
 
 0.9 
 
 ARG. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 
 
 I 
 
 2 
 3 
 
 9.4878779 
 .4881048 
 .4885573 
 .4892328 
 
 9.4878904 
 .4881399 
 .4886149 
 .4893125 
 
 9.4879051 
 
 .4881773 
 .4886747 
 .4893944 
 
 9.4879221 
 .4882170 
 .4887367 
 .4894784 
 
 9.4879414 
 .4882589 
 .4888009 
 .4895647 
 
 
 
 1 
 
 2 
 3 
 
 
 4 
 5 
 6 
 
 7 
 
 9.4901276 
 .4912368 
 .4925543 
 .4940731 
 
 9.4902290 
 .4913593 
 .4926972 
 .4942357 
 
 9.4903325 
 .4914838 
 .4928422 
 .4944003 
 
 9.4904381 
 .4916105 
 .4929891 
 .4945668 
 
 9.4905458 
 .4917392 
 .4931381 
 .4947352 
 
 4 
 5 
 6 
 
 7 
 
 
 
 8 
 9 
 10 
 11 
 
 9.4957852 
 .4976820 
 .4997540 
 .5019913 
 
 9.4959667 
 .4978815 
 .4999705 
 .5022237 
 
 9.4961501 
 
 .4980827 
 .5001886 
 .5024577 
 
 9.4963353 
 .4982856 
 .5004083 
 .5026932 
 
 9.4965223 
 .4984902 
 .5006296 
 .5029303 
 
 8 
 9 
 10 
 11 
 
 
 
 12 
 13 
 14 
 15 
 
 9.5043837 
 .5069201 
 .5095900 
 .5123821 
 
 9.5046310 
 .5071813 
 .5098639 
 .5126677 
 
 9.5048798 
 .5074438 
 .5101390 
 .5129543 
 
 9.5051299 
 .5077076 
 .5104153 
 .5132420 
 
 9.5053815 
 .5079727 
 .5106928 
 .5135307 
 
 12 
 13 
 14 
 15 
 
 
 
 16 
 17 
 18 
 19 
 
 9.5152856 
 .5182894 
 .5213828 
 .5245553 
 
 9.5155816 
 .5185948 
 .5216966 
 .5248765 
 
 9.5158786 
 .5189012 
 .5220113 
 .5251984 
 
 9.5161766 
 .5192084 
 .5223267 
 .5255209 
 
 9.5164756 
 .5195165 
 .5226429 
 .5258441 
 
 16 
 17 
 18 
 19 
 
 
 
 20 
 21 
 22 
 23 
 
 9.5277967 
 .5310968 
 .5344465 
 .5378366 
 
 9.5281242 
 .5314297 
 .5347838 
 .5381775 
 
 9.5284523 
 .5317631 
 .5351216 
 .5385186 
 
 9.5287810 
 .5320969 
 .5354597 
 .5388601 
 
 9.5291102 
 .5324312 
 .5357982 
 .5392019 
 
 20 
 21 
 22 
 23 
 
 
 
 24 
 25 
 
 26 
 
 27 
 
 9.5412581 
 .5447030 
 .5481635 
 .5516323 
 
 9.5416016 
 .5450485 
 .5485101 
 .5519793 
 
 9.5419454 
 , .5453941 
 
 .5488568 
 .5523264 
 
 9.5422894 
 .5457399 
 .5492036 
 .5526735 
 
 9.5426337 
 .5460858 
 .5495504 
 .5530205 
 
 24 
 25 
 26 
 
 27 
 
 
 
 28 
 29 
 30 
 31 
 
 9.5551025 
 .5585676 
 .5620217 
 .5654596 
 
 9.5554493 
 .5589136 
 .5623663 
 .5658023 
 
 9.5557961 
 .5592595 
 .5627108 
 .5661447 
 
 9.5561429 
 .5596052 
 .5630551 
 .5664869 
 
 9.5564895 
 .5599508 
 .5633992 
 
 .5668289 
 
 28 
 29 
 30 
 31 
 
 
 
 32 
 33 
 34 
 35 
 
 9.5688756 
 .5722652 
 .5756241 
 
 .5789484 
 
 9.5692158 
 .5726026 
 .5759582 
 
 .5792787 
 
 9.5695558 
 .5729396 
 .5762919 
 .5796087 
 
 9.5698955 
 .5732763 
 .5766252 
 .5799383 
 
 9.5702349 
 .5736127 
 .5769582 
 .5802675 
 
 32 
 33 
 34 
 
 35 
 
 
 
 36 
 37 
 38 
 39 
 
 9.5822342 
 
 .5854781 
 .5886774 
 .5918292 
 
 9.5825605 
 .5858001 
 .5889948 
 .5921416 
 
 9.5828864 
 .5861216 
 .5893116 
 .5924536 
 
 9.5832119 
 .5864427 
 .5896280 
 .5927650 
 
 9.5835369 
 .5867633 
 .5899440 
 .5930760 
 
 36 
 37 
 38 
 39 
 
 
 
 40 
 41 
 42 
 43 
 
 9.5949308 
 .5979802 
 .6009753 
 .6039146 
 
 9.5952382 
 .5982822 
 .6012718 
 .6042053 
 
 9.5955450 
 .5985836 
 .6015677 
 .6044955 
 
 9.5958512 
 
 .5988845 
 .6018631 
 .6047851 
 
 9.5961570 
 .5991848 
 .6021579 
 .6050741 
 
 40 
 41 
 . 42 
 43 
 
 
 
 44 
 45 
 
 9.6067958 
 .6096180 
 
 9.6070807 
 .6098970 
 
 9.6073651 
 .6101753 
 
 9.6076488 
 .6104530 
 
 9.6079319 
 .6107301 
 
 44 
 45 
 
 
 ARG. 
 
 0.5 
 
 O.6 
 
 o.r 
 
 0.8 
 
 O.9 
 
 ARG. 
 
 
42 
 
 TABLE XV. 
 
 
 
 
 ARG. 
 
 o.o 
 
 0.1 
 
 0.3 
 
 0.3 
 
 0.4 
 
 ARG. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 45 
 46 
 
 47 
 
 48 
 
 9.6082144 
 .6110066 
 .6137377 
 .6164068 
 
 9.6084963 
 .6112825 
 .6140074 
 .6166703 
 
 9.6087777 
 .6115577 
 .6142765 
 .6169331 
 
 9.6090584 
 .6118324 
 .6145450 
 .6171953 
 
 9.6093385 
 .6121064 
 .6148128 
 .6174568 
 
 45 
 46 
 
 47 
 48 
 
 
 49 
 50 
 5*1 
 52 
 
 9.6190128 
 .6215551 
 .6240330 
 .6264459 
 
 9.6192699 
 .6218058 
 .6242772 
 .6266836 
 
 9.6195264 
 .6220558 
 .6245208 
 .6269206 
 
 9.6197822 
 .6223052 
 .6247637 
 .6271570 
 
 9.6200374 
 .6225540 
 .6250060 
 .6273927 
 
 49 
 50 
 51 
 52 
 
 
 
 53 
 54 
 55 
 56 
 
 9.6287932 
 .6310746 
 .6332895 
 .6354379 
 
 9.6290243 
 .6312991 
 .6335073 
 .6356491 
 
 9.6292548 
 .6315229 
 .6337245 
 .6358596 
 
 9.6294845 
 .6317461 
 .6339410 
 .6360694 
 
 9.6297137 
 .6319685 
 .6341568 
 .6362786' 
 
 53 
 54 
 55 
 56 
 
 
 
 57 
 58 
 59 
 60 
 
 9.6375196 
 .6395343 
 .6414819 
 .6433623 
 
 9.6377241 
 .6397321 
 .6416730 
 .6435466 
 
 9.6379279 
 .6399292 
 .6418634 
 .6437303 
 
 9.6381310 
 .6401256 
 .6420531 
 .6439133 
 
 9.6383335 
 .6403214 
 .6422421 
 .6440957 
 
 57 
 58 
 59 
 60 
 
 
 
 61 
 62 
 63 
 64 
 
 9.6451756 
 .6469216 
 .6486005 
 .6502122 
 
 9.6453532 
 
 .6470925 
 .6487647 
 .6503697 
 
 9.6455302 
 
 .6472627 
 .6489282 
 .6505265 
 
 9.6457065 
 .6474323 
 .6490911 
 .6506827 
 
 9.6458821 
 .6476012 
 .6492532 
 .6508381 
 
 61 
 62 
 63 
 64 
 
 
 
 65 
 66 
 67 
 
 68 
 
 9.6517568 
 .6532344 
 .6546450 
 .6559891 
 
 9.6519076 
 .6533785 
 .6547824 
 .6561198 
 
 9.6520577 
 .6535219 
 .6549191 
 .6562499 
 
 9.6522071 
 .6536646 
 .6550552 
 .6563793 
 
 9.6523559 
 .6538067 
 .6551906 
 .6565080 
 
 65 
 66 
 67 
 
 68 
 
 
 
 69 
 70 
 71 
 
 72 
 
 9.6572663 
 .6584769 
 .6596210 
 .6606988 
 
 9.6573904 
 .6585943 
 .6597318 
 .6608029 
 
 9.6575137 
 .6587110 
 .6598419 
 .6609064 
 
 9.6576365 
 
 .6588271 
 .6599513 
 .6610092 
 
 9.6577585 
 .6589425 
 .6600601 
 .6611114 
 
 69 
 70 
 71 
 
 72 
 
 
 
 73 
 
 74 
 75 
 76 
 
 9.6617104 
 .6626560 
 .6635355 
 .6643493 
 
 9.6618079 
 .6627469 
 .6636198 
 .6644271 
 
 9.6619048 
 .6628372 
 .6637035 
 .6645042 
 
 9.6620010 
 .6629268 
 .6637865 
 .6645806 
 
 9.6620966 
 .6630157 
 .6638689 
 .6646564 
 
 73 
 74 
 75 
 
 76 
 
 
 
 77 
 78 
 79 
 80 
 
 9.6650973 
 .6657798 
 .6663967 
 .6669482 
 
 9.6651685 
 .6658444 
 .6664548 
 .6669997 
 
 9.6652390 
 .6659084 
 .6665122 
 .6670506 
 
 9.6653089 
 .6659718 
 .6665690 
 .6671008 
 
 9.6653782 
 .6660344 
 .6666251 
 .6671504 
 
 77 
 78 
 79 
 80 
 
 
 
 81 
 82 
 83 
 
 84 
 
 9.6674343 
 
 .6678553 
 .6682110 
 .6685017 
 
 9.6674793 
 
 .6678938 
 .6682430 
 .6685272 
 
 9.6675237 
 .6679317 
 .6682743 
 .6685520 
 
 9.6675674 
 .6679689 
 .6683050 . 
 .6685762 
 
 9.6676105 
 .6680054 
 .6683351 
 .6685997 
 
 81 
 82 
 83 
 
 84 
 
 
 
 85 
 86 
 87 
 88 
 
 9.6687273 
 
 .6688877 
 .6689832 
 .6690138 
 
 9.6687463 
 .6689002 
 .6689892 
 .6690133 
 
 9.6687646 
 .6689120 
 .6689945 
 .6690121 
 
 9.6687823 
 .6689232 
 .6689992 
 .6690103 
 
 9.6687993 
 .6689337 
 .6690032 
 .6690078 
 
 85 
 86 
 87 
 
 88 
 
 
 - * 
 
 89 
 90 
 
 9.6689793 
 .6688798 
 
 9.6689723 
 .6688663 
 
 9.6689646 
 
 .6688521 
 
 9.6689563 
 .6688373 
 
 9.6689473 
 .6688218 
 
 89 
 90 
 
 
 ARG. 
 
 0.0 
 
 0.1 
 
 0.3 
 
 0.3 
 
 0.4 
 
 ARG. 
 
 
 
TABLE XV. 
 
 
 
 
 ARG. 
 
 0.5 
 
 O.6 
 
 0.7 
 
 0.8 
 
 0.9 
 
 ARG. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 45 
 46 
 47 
 
 48 
 
 9.6096180 
 .6123798 
 .6150801 
 .6177177 
 
 9.6098970 
 .6126527 
 .6153467 
 .6179780 
 
 9.6101753 
 .6129248 
 .6156127 
 .6182377 
 
 9.6104530 
 .6131964 
 .6158780 
 .6184967 
 
 9.6107301 
 .6134674 
 .6161427 
 .6187551 
 
 45 
 46 
 
 47 
 48 
 
 
 49 
 50 
 51 
 52 
 
 9.6202920' 
 .6228021 
 .6252476 
 
 .6276278 
 
 9.6205459 
 .6230496 
 .6254886 
 .6278622 
 
 9.6207991 
 .6232964 
 .6257289 
 .6280959 
 
 9.6210518 
 .6235426 
 .6259685 
 
 .6283289 
 
 9.6213038 
 .6237881 
 .6262076 
 .6285614 
 
 49 
 50 
 51 
 
 52 
 
 
 
 53 
 51 
 55 
 56 
 
 9.6299422 
 .6321904 
 .6343720 
 .6364871 
 
 9.6301700 
 .6324115 
 .6345865 
 .6366949 
 
 9.6303971 
 .6326320 
 .6348004 
 .6369021 
 
 9.6306236 
 .6328518 
 .6350135 
 .6371086 
 
 9.6308494 
 .6330710 
 .6352261 
 .6373144 
 
 53 
 54 
 55 
 56 
 
 
 
 57 
 58 
 59 
 60 
 
 9.6385353 
 .6405165 
 .6424305 
 .6442773 
 
 9.6387365 
 .6407109 
 .6426182 
 .6444583 
 
 9.6389369 
 .6409047 
 .6428052 
 .6446387 
 
 9.6391367 
 .6410978 
 .6429916 
 .6448183 
 
 9.6393358 
 .6412902 
 .6431773 
 .6449973 
 
 57 
 58 
 59 
 60 
 
 
 
 61 
 62 
 63 
 61 
 
 9.6460570 
 .6477694 
 .6494147 
 .6509929 
 
 9.6462313 
 .6479370 
 .6495756 
 .6511471 
 
 9.6464049 
 .6481039 
 .6497357 
 .6513004 
 
 9.6465778 
 .6482701 
 .6498952 
 .6514532 
 
 9.6467500 
 .6484356 
 .6500541 
 .6516054 
 
 61 
 62 
 63 
 64 
 
 
 
 65 
 66 
 67 
 63 
 
 9.6525040 
 .6539481 
 .6553254 
 .6566361 
 
 9.6526514 
 .6540888 
 .6554594 
 .6567635 
 
 9.6527982 
 .6542289 
 .6555929 
 .6568902 
 
 9.6529442 
 .6543682 
 .6557256 
 .6570162 
 
 9.6530897 
 .6545070 
 .6558577 
 .6571416 
 
 65 
 66 
 
 67 
 68 
 
 
 
 69 
 70 
 71 
 72 
 
 9.6578799 
 .6590573 
 .6601682 
 .6612129 
 
 9.6580007 
 .6591713 
 .6602756 
 .6613137 
 
 9.6581207 
 .6592848 
 .6603824 
 .6614139 
 
 9.6582401 
 .6533975 
 .6604885 
 .6615134 
 
 9.6583588 
 .6595096 
 .6605940 
 .6616122 
 
 69 
 70 
 71 
 72 
 
 
 
 73 
 74 
 75 
 
 76 
 
 9.6621915 
 .6631040 
 .6639506 
 .6647315 
 
 9.6622857 
 .6631916 
 .6640317 
 .6648060 
 
 9.6623793 
 .6632786 
 .6641121 
 
 .6648798 
 
 9.6624722 
 .6633649 
 .6641918 
 .6649530 
 
 9.6625644 
 .6634505 
 .6642709 
 .6650255 
 
 73 
 74 
 75 
 76 
 
 
 
 77 
 78 
 79 
 80 
 
 9.6654467 
 .6660964 
 .6666806 
 .6671993 
 
 9.6655147 
 .6661578 
 .6667354 
 .6672476 
 
 9.6655819 
 .6662185 
 .6667896 
 .6672953 
 
 9.6656485 
 .6662786 
 .6668431 
 .6673423 
 
 9.6657145 
 .6663380 
 .6668959 
 .6673886 
 
 77 
 78 
 79 
 80 
 
 
 
 81 
 82 
 83 
 
 84 
 
 9.6676529 
 .6680413 
 .6683645 
 .6686226 
 
 9.6676947 
 .6680766 
 .6683932 
 .6686449 
 
 9.6677358 
 .6681111 
 .6684213 
 .6686665 
 
 9.6677763 
 .6681451 
 
 ' .6684488 
 .6686874 
 
 9.6678161 
 .6681784 
 .6684756 
 .6687077 
 
 81 
 
 82 
 83 
 
 84 
 
 
 
 85 
 86 
 87 
 88 
 
 9.6688156 
 .6689436 
 .6690066 
 .6690047 
 
 9.6688314 
 .6689528 
 .6690094 
 .6690009 
 
 9.6688461 
 .6689614 
 .6690114 
 .6689965 
 
 9.6688608 
 .6689693 
 .6690129 
 .6689914 
 
 9.6688746 
 .6689766 
 .6690137 
 .6689857 
 
 85 
 86 
 87 
 88 
 
 
 
 89 
 90 
 
 9.6689377 
 .6688057 
 
 9.6689274 
 .6687890 
 
 9.6689165 
 .6687715 
 
 ,9.6689049 
 .6687535 
 
 9.6688927 
 .6687348 
 
 89 
 90 
 
 
 AHG. 
 
 O.5 
 
 O.6 
 
 o.r 
 
 0.8 
 
 0.9 
 
 ARG. 
 
 
44 
 
 TABLE XV. 
 
 
 4 
 
 
 ARG. 
 
 o.o 
 
 0.1 
 
 0.3 
 
 0.3 
 
 0.4 
 
 ARG. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 90 
 91 
 92 
 93 
 
 9.6688798 
 .6687154 
 .6G84858 
 .6681911 
 
 9.6688663 
 .6686954 
 .6684593 
 .6681581 
 
 9.6688521 
 .6686747 
 .6681321 
 .6681244 
 
 9.6688373 
 .6686534 
 .6684042 
 .6680900 
 
 9.6688218 
 .6686314 
 .6683757 
 .6680550 
 
 90 
 
 91 
 92 
 93 
 
 
 94 
 95 
 96 
 
 97 
 
 9.6678314 
 .6674064 
 .6669162 
 .6663608 
 
 9.6677918 
 .6673603 
 .666^636 
 .6663017 
 
 9.6677516 
 .6673136 
 .6668103 
 .6662419 
 
 9.6677108 
 .6672662 
 .6667564 
 .6661814 
 
 9.6676692 
 .6672181 
 .6667019 
 .6661203 
 
 94 
 95 
 96 
 
 97 
 
 
 
 98 
 99 
 100 
 101 
 
 9.6657399 
 .6650534 
 .6643013 
 .6634835 
 
 9.6656742 
 .6649811 
 .6642225 
 .6633981 
 
 9.6656078 
 .66490^2 
 .6641430 
 .6633120 
 
 9.6655408 
 .6648347 
 .6640629 
 .6632253 
 
 9.6654732 
 .6647604 
 .6639821 
 .6631380 
 
 98 
 99 
 100 
 101 
 
 
 
 102 
 103 
 104 
 105 
 
 9.6625998 
 .6616503 
 .6606347 
 .6595528 
 
 9.6625079 
 .6615517 
 .6605295 
 .6594410 
 
 9.6624153 
 .6614524 
 .6604236 
 .6593285 
 
 9.6623219 
 .6613525 
 .6603171 
 .6592153 
 
 9.6622280 
 .6612520 
 .6602099 
 .6591015 
 
 102 
 103 
 104 
 105 
 
 
 
 106 
 
 107 
 108 
 109 
 
 9.6584046 
 .6571899 
 .6559086 
 .6545605 
 
 9.6582861 
 .6570618 
 .6557768 
 .6544220 
 
 9.6581670 
 .6569390 
 .6556443 
 .6542829 
 
 9.6580472 
 .6568125 
 .6555112 . 
 .6541430 
 
 9.6579267 
 .6566854 
 .6553774 
 .6540026 
 
 106 
 107 
 108 
 109 
 
 
 
 110 
 111 
 112 
 113 
 
 9.6531457 
 .6516640 
 .6501153 
 .6484995 
 
 9.6530005 
 .6515121 
 .6499567 
 .6483342 
 
 9.6528547 
 .6513596 
 .6497975 
 .6481683 
 
 9.6527082 
 .6512064 
 .6496376 
 .6480017 
 
 9.6525611 
 .6510526 
 .6494770 
 .6478344 
 
 110 
 111 
 112 
 113 
 
 
 
 114 
 115 
 116 
 117 
 
 9.6468165 
 .6450664 
 .6432490 
 .6413645 
 
 9.6466445 
 .6448877 
 .6430636 
 .6411724 
 
 9.6464718 
 .6447083 
 .6428775 
 .6409795 
 
 9.6462985 
 .6445282 
 .6426907 
 .6407860 
 
 9.6461245 
 .6443475 
 .6425032 
 .6405919 
 
 114 
 115 
 
 116 
 117 
 
 
 
 118 
 119 
 120 
 121 
 
 9.6394128 
 .6373940 
 .6353082 
 .6331557 
 
 9.6392139 
 .6371884 
 .6350960 
 .6329368 
 
 9.6390144 
 .6369822 
 .6348830 
 .6327172 
 
 9.6388142 
 .6367753 
 .6346695 
 .6324970 
 
 9.6386133 
 .6365677 
 .6344552 
 .6322761 
 
 118 
 119 
 120 
 121 
 
 
 
 122 
 123 
 124 
 125 
 
 9.6309367 
 .6286512 
 .6262999 
 .6238829 
 
 9.6307111 
 .6284190 
 .6260612 
 .6236376 
 
 9.6304849 
 
 .6281862 
 .6258218 
 .6233917 
 
 9.6302581 
 .6279527 
 .6255817 
 .6231452 
 
 9.6300305 
 .6277186 
 .6253410 
 .6228980 
 
 122 
 123 
 124 
 125 
 
 
 
 126 
 127 
 
 128 
 129 
 
 9.6214011 
 .6188549 
 .6162450 
 .6135720 
 
 9.6211494 
 .6185968 
 .6159805 
 .6133013 
 
 9.6208970 
 .6183380 
 .6157154 
 .6130299 
 
 9.6206440 
 
 .6180786 
 .6154497 
 .6127580 
 
 9.6203903 
 
 .6178185 
 .6151833 
 .6124855 
 
 126 
 
 127 
 128 
 129 
 
 
 
 130 
 131 
 132 
 133 
 
 9.6108372 
 .6080413 
 .6051858 
 .6022718 
 
 9.6105603 
 .6077584 
 .6048970 
 .6019772 
 
 9.6102829 
 .6074749 
 .6046076 
 .6016821 
 
 9.6100048 
 .6071908 
 .6043177 
 .6013864 
 
 9.6097261 
 .6069062 
 .6040272 
 .6010902 
 
 130 
 131 
 132 
 133 
 
 
 
 134 
 135 
 
 9.5993008 
 .5962751 
 
 9.5990007 
 .5959696 
 
 9.5987000 
 .5956035 
 
 9.5983988 
 .5953569 
 
 9.5980970 
 .5950498 
 
 134 
 135 
 
 
 ARG. 
 
 O.O 
 
 01. 
 
 O.3 
 
 0.3 
 
 0.4 
 
 ARG. 
 
 - 
 
TABLE XV. 
 
 45 
 
 
 
 
 
 O.5 
 
 0.6 
 
 0.7 
 
 O.8 
 
 0.9 
 
 
 
 ARG. 
 
 
 
 
 
 
 ARG. 
 
 
 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 
 
 
 90 
 
 9.6688057 
 
 9.6687890 
 
 9.6687715 
 
 9.6687535 
 
 9.6687348 
 
 SO 
 
 
 
 91 
 
 .6686088 
 
 .6685855 
 
 .6685615 
 
 .6685370 
 
 .6685117 
 
 91 
 
 
 
 92 
 
 .6683466 
 
 .6683168 
 
 .6682864 
 
 .6682553 
 
 .6682235 
 
 92 
 
 
 
 93 
 
 .6680194 
 
 .6679831 
 
 .6679461 
 
 .6679086 
 
 .6678703 
 
 93 
 
 
 
 94 
 
 9.6676271 
 
 9.6675842 
 
 9.6675408 
 
 9.6674966 
 
 9.6674518 
 
 94 
 
 
 
 95 
 
 .6671694 
 
 .6671201 
 
 .6670701 
 
 .6670194 
 
 .6669681 
 
 95 
 
 
 
 96 
 
 .6666466 
 
 .6665908 
 
 .6665343 
 
 .6664771 
 
 .6664193 
 
 96 
 
 
 
 97 
 
 .6660585 
 
 .6659961 
 
 .6659330 
 
 .6658693 
 
 .6658049 
 
 97 
 
 
 
 98 
 
 9.6654048 
 
 9.6653358 
 
 9.6652662 
 
 9.6651959 
 
 9.6651250 
 
 C8 
 
 
 
 99 
 
 .6646856 
 
 .6646100 
 
 .6645338 
 
 .6644570 
 
 .6643795 
 
 99 
 
 
 
 100 
 
 .6639006 
 
 .6638185 
 
 .6637357 
 
 .6636523 
 
 .6635682 
 
 100 
 
 
 
 101 
 
 .6630499 
 
 .6629612 
 
 .6628719 
 
 .6627819 
 
 .6626912 
 
 101 
 
 
 
 102 
 
 9.6621334 
 
 9.6620381 
 
 9.6619421 
 
 9.6618455 
 
 9.6617482 
 
 102 
 
 
 
 103 
 
 .6611507 
 
 .6610489 
 
 .6609463 
 
 .6608431 
 
 .6607392 
 
 103 
 
 
 
 105 
 
 .6601020 
 
 .6599935 
 
 .6598843 
 
 .6597745 
 
 .6596640 
 
 104 
 
 
 
 105 
 
 .6589870 
 
 .6588719 
 
 .6587560 
 
 .6586396 
 
 .6585224 
 
 105 
 
 
 
 106 
 
 9.6578056 
 
 9.6576838 
 
 9.6575613 
 
 9.6574382 
 
 9.6573144 
 
 106 
 
 
 
 107 
 
 .6565576 
 
 .6564291 
 
 .6563000 
 
 .6561702 
 
 .6560397 
 
 107 
 
 
 
 108 
 
 .6552430 
 
 .6551078 
 
 .6549720 
 
 .6548355 
 
 .6546983 
 
 108 
 
 
 
 109 
 
 .6538614 
 
 .6537196 
 
 .6535771 
 
 .6534340 
 
 .6532902 
 
 109 
 
 
 
 110 
 
 9.6524132 
 
 9.6522647 
 
 9.6521155 
 
 9.6519657 
 
 9.6518152 
 
 110 
 
 
 
 111 
 
 .6508980 
 
 .6507428 
 
 .6505869 
 
 .6504304 
 
 .650-2732 
 
 111 
 
 
 
 112 
 
 .6493158 
 
 .6491539 
 
 .6489913 
 
 .6488280 
 
 .6486641 
 
 112 
 
 
 
 113 
 
 .6476664 
 
 .6474978 
 
 .6473284 
 
 .6471585 
 
 .6469878 
 
 113 
 
 
 
 114 
 
 9.6459498 
 
 9.6457745 
 
 9.6455985 
 
 9.6454218 
 
 9.6452444 
 
 114 
 
 
 
 115 
 
 .6441661 
 
 .6439840 
 
 .6438013 
 
 .6436179 
 
 .6434338 
 
 115 
 
 
 
 116 
 
 .6423151 
 
 .6421263 
 
 .6419369 
 
 .6417468 
 
 .6415560 
 
 116 
 
 
 
 117 
 
 .6403970 
 
 .6402015 
 
 .6400054 
 
 .6398085 
 
 .6396110 
 
 117 
 
 
 . 
 
 118 
 
 9.6384118 
 
 9.6382096* 
 
 9.6380067 
 
 9.6378031 
 
 9.6375989 
 
 118 
 
 
 
 119 
 
 .6363595 
 
 .6361506 
 
 .6359410 
 
 .6357307 
 
 .6355198 
 
 119 
 
 
 
 120 
 
 .6342403 
 
 .6340247 
 
 .6338085 
 
 .6335915 
 
 .6333740 
 
 120 
 
 
 
 121 ' 
 
 .6320545 
 
 .6318323 
 
 .6316094 
 
 .6313858 
 
 .6311616 
 
 121 
 
 
 
 122 
 
 9.6298023 
 
 9.6295733 
 
 9.6293437 
 
 9.6291135 
 
 9.6288827 
 
 122 
 
 
 
 123 
 
 .6274838 
 
 .6272483 
 
 .6270122 
 
 .6267754 
 
 .6265380 
 
 123 
 
 
 
 124 
 
 .6250996 
 
 .6248576 
 
 .6246149 
 
 .6243715 
 
 .6241275 
 
 124 
 
 
 
 125 
 
 .6226501 
 
 .6224016 
 
 .6221525 
 
 .6219027 
 
 .6216522 
 
 125 
 
 
 
 126 
 
 9.6201360 
 
 9.6198811 
 
 9.6196255 
 
 9.6193693 
 
 9.6191124 
 
 126 
 
 
 
 127 
 
 .6175579 
 
 .6172965 
 
 .6170346 
 
 .6167721 
 
 .6165088 
 
 127 
 
 
 
 128 
 
 .6149163 
 
 .6146487 
 
 .6143805 
 
 .6141116 
 
 .6138421 
 
 128 
 
 
 
 129 
 
 .6122123 
 
 .6119385 
 
 .6116641 
 
 .6113891 
 
 .6111135 
 
 129 
 
 
 
 130 
 
 9.6094468 
 
 9.6091669 
 
 9.6088864 
 
 9.6086053 
 
 9.6083236 
 
 130 
 
 
 
 131 
 
 .6066209 
 
 .6063351 
 
 .6060486 
 
 .6057616 
 
 .6054740 
 
 131 
 
 
 
 132 
 
 .6037360 
 
 .6034444 
 
 .6031521 
 
 .6028592 
 
 .6025658 
 
 132 
 
 
 
 133 
 
 .6007933 
 
 .6004960 
 
 .6001980 
 
 .5998995 
 
 .599-004 
 
 133 
 
 
 
 134 
 
 9.5977947 
 
 9.5974918 
 
 9.5971884 
 
 9.5968845 
 
 9.5965801 
 
 134 
 
 
 
 135 
 
 .5947422 
 
 .5944340 
 
 .5941253 
 
 .5938162 
 
 .5935064 
 
 135 
 
 
 
 ARG. 
 
 O.5 
 
 06. 
 
 0.7 
 
 O.8 
 
 0.9 
 
 ARG. 
 
 
 
46 
 
 TABLE XV. 
 
 
 
 
 ARG. 
 
 0.0 
 
 O.I 
 
 0.2 
 
 O.3 
 
 0.4 
 
 ARG. 
 
 Log .}. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 Log }. 
 
 135 
 136 
 137 
 138 
 
 9.5962751 
 .5931962 
 .5900661 
 
 .5868873 
 
 9.5959696 
 .5928855 
 .5897504 
 .5865668 
 
 9.5956635 
 .5925742 
 .5894342 
 .5862459 
 
 9.5953569 
 .5922624 
 .5891175 
 .5859246 
 
 9.5950498 
 .5919502 
 .5888003 
 .5856027 
 
 J35 
 136 
 
 137 
 .138 
 
 
 139 
 140 
 141 
 142 
 
 9.5836625 
 .5803947 
 .5770869 
 .5737427 
 
 9.5833376 
 .5800657 
 .5767541 
 .5734065 
 
 9.5830123 
 
 .5797362 
 .5764208 
 .5730699 
 
 9.5826866 
 .5794064 
 .5760873 
 .5727329 
 
 9.5823604 
 .5790762 
 .5757534 
 
 .5723958 
 
 139 
 110 
 141 
 142 
 
 
 
 143 
 
 144 
 145 
 146 
 
 9.5703662 
 .5669612 
 .5635323 
 .5600845 
 
 9.5700269 
 .5666193 
 .5631883 
 .5597389 
 
 9.5696873 
 .5662772 
 .5628441 
 .5593932 
 
 9.5693475 
 .5659348 
 .5624997 
 .5590474 
 
 9.5690073 
 .5655923 
 .5621551 
 .5587015 
 
 143 
 144 
 145 
 146 
 
 
 
 147 
 148 
 149 
 150 
 
 9.5566237 
 .5531548 
 .5496847 
 .5462196 
 
 9.5562771 
 .5528078 
 .5493378 
 .5458736 
 
 9.5559303 
 .5524607 
 .5489911 
 .5455278 
 
 9.5555836 
 .5521137 
 .5486443 
 .5451821 
 
 9.5552367 
 .5517666 
 .5482977 
 .5448366 
 
 ,147 
 148 
 149 
 150 
 
 
 
 151 
 152 
 153 
 154 
 
 9.5427669 
 .5393341 
 .5359293 
 .5325607 
 
 9.5424226 
 .5389922 
 .5355906 
 .5322262 
 
 9.5420785 
 .5386506 
 .5352524 
 .5318921 
 
 9.5417346 
 .5383094 
 .5349145 
 .5315586 
 
 9.5413909 
 .5379684 
 .5345770 
 .5312255 
 
 151 
 152 
 153 
 154 
 
 
 
 155 
 156 
 157 
 158 
 
 9.5292377 
 .5259694 
 .5227654 
 .5196359 
 
 9.5289082 
 .5256459 
 .5224489 
 .5193275 
 
 9.5285793 
 .5253231 
 .5221332 
 .5190199 
 
 9.5282510 
 .5250010 
 .5218183 
 .5187132 
 
 9.5279233 
 
 .5246795 
 .5215042 
 .5184074 
 
 155 
 
 156 
 157 
 158 
 
 
 
 159 
 160 
 161 
 162 
 
 9.5165916 
 .5136428 
 .5108005 
 .5080756 
 
 9.5162922 
 .5133536 
 .5105225 
 .5078100 
 
 9.5159939 
 .5130654 
 .5102458 
 .5075457 
 
 9.5156964 
 .5127784 
 .5099702 
 
 .5072827 
 
 9.5154000 
 
 .5124925 
 .5096958 
 .5070211 
 
 159 
 160 
 161 
 162 
 
 
 
 
 163 
 164 
 165 
 166 
 
 9.5054792 
 .5030224 
 .5007157 
 .4985699 
 
 9.5052270 
 .5027848 
 .5004937 
 .4983646 
 
 9.5049763 
 .5025487 
 .5002733 
 
 .4981609 
 
 9.5047270 
 .5023141 
 .5000546 
 .4979590 
 
 9.5044791 
 .5020811 
 .4998375 
 .4977589 
 
 163 
 164 
 165 
 166 
 
 
 
 167 
 168 
 169 
 170 
 
 9.4965951 
 .4948008 
 .4931962 
 .4917895 
 
 9.4964074 
 .4946317 
 .4930465 
 .4916600 
 
 9.4962215 
 .4944644 
 .4928987 - 
 .4915326 
 
 9.4960374 
 .4942991 
 .4927531 
 .4914072 
 
 9.4958552 
 .4941357 
 .4926093 
 .4912839 
 
 167 
 168 
 169 
 170 
 
 
 
 171 
 172 
 173 
 174 
 
 9.4905882 
 .4895986 
 
 .4888264 
 .4882757 
 
 9.4904796 
 
 .4895115 
 .4887613 
 .4882329 
 
 9.4903731 
 .4894266 
 
 .4886984 
 .4881924 
 
 9.4902688 
 .4893439 
 .4886377 
 .4881541 
 
 9.4901666 
 .4892633 
 
 .4885793 
 
 .4881181 
 
 171 
 172 
 173 
 174 
 
 
 
 175 
 
 176 
 
 9.4879495 
 .4878499 
 
 9.4879293 
 
 .4878524 
 
 9.4879114 
 
 ..4878572 
 
 9.4878958 
 .4878643 
 
 9.4878824 
 .4878736 
 
 175 
 176 
 
 
 ARG. 
 
 0.0 
 
 01. 
 
 0.3 
 
 0.3 
 
 0.4 
 
 ARG. 
 
 
TABLE XV. 
 
 47 
 
 
 
 
 ARG. 
 
 O.5 
 
 O.6 
 
 0.7 
 
 O.8 
 
 0.9 
 
 ARG. 
 
 Log }. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 Log r. 
 
 135 
 136 
 137 
 138 
 
 9.5947422 
 .5916374 
 
 .5884826 
 .5852805 
 
 9.5944340 
 .5913241 
 
 .5881645 
 .5849578 
 
 9.5941253 
 .5910104 
 .5878459 
 .5846346 
 
 9.5938162 
 .5906961 
 .5875268 
 .5843110 
 
 9.5935064 
 .5903814 
 .5872073 
 .5839870 
 
 135 
 136 
 137 
 
 138 
 
 
 139 
 140 
 141 
 142 
 
 9.5820338 
 .5787456 
 .5754191 
 .5720583 
 
 9.5817068 
 .5784146 
 .5750845 
 .5717205 
 
 9.5813794 
 .5780832 
 .5747496 
 .5713823 
 
 9.5810516 
 .5777515 
 .5744143 
 .5710439 
 
 9.5807234 
 .5774194 
 .5740787 
 .5707052 
 
 139 
 140 
 141 
 142 
 
 
 
 143 
 144 
 
 145 
 146 
 
 9.5686669 
 .5652495 
 .5618104 
 .5583554 
 
 9.5683263 
 .5649064 
 .5614655 
 .5580092 
 
 9.5679854 
 .5645632 
 .5611205 
 .5576630 
 
 9.5676442 
 .5642198 
 .5607753 
 .5573166 
 
 9.5673028 
 
 .5638762 
 .5604300 
 .5569702 
 
 143 ' 
 144 
 145 
 146 
 
 
 
 147 
 148 
 149 
 150 
 
 9.5548898 
 .5514195 
 .5479511 
 .5444912 
 
 9.5545429 
 .5510725 
 .5476046 
 .5441460 
 
 9.5541959 
 .5507255 
 .5472582 
 .5438010 
 
 9.5538489 
 .5503785 
 .5469119 
 .5434561 
 
 9.5535019 
 .5500316 
 .5465657 
 .5431114 
 
 147 
 
 148 
 149 
 150 
 
 
 
 151 
 152 
 153 
 154 
 
 9.5410475 
 .5376277 
 .5342399 
 .5308929 
 
 9.5407043 
 .5372873 
 .5339032 
 .5305609 
 
 9.5403614 
 .5369473 
 .5335669 
 .5302293 
 
 9.5400187 
 .5366076 
 .5332311 
 
 .5298982 
 
 9.5396762 
 .5362683 
 .5328957 
 .5295677 
 
 151 
 152 
 153 
 154 
 
 
 
 155 
 
 156 
 157 
 158 
 
 9.5275961 
 .5243587 
 .5211907 
 .5181025 
 
 9.5272695- 
 .5240396 
 
 .5208781 
 .5177985 
 
 9.5269436 
 .5237192 
 .5205663 
 .5174954 
 
 9.5266182 
 .5234005 
 .5202554 
 .5171932 
 
 9.5262935 
 .5230826 
 .5199452 
 .5168919 
 
 155 
 156 
 157 
 158 
 
 
 
 159 
 160 
 161 
 162 
 
 9.5151046 
 .5122076 
 .5094227 
 .5067607 
 
 9.5148102 
 .5119239 
 .5091508 
 .5065017 
 
 9.5145168 
 .5116413 
 .5088801 
 .5062440 
 
 9.5142245 
 .5113599 
 .5086106 
 .5059877 
 
 9.5139332 
 .5110796 
 .5083425 
 .5057328 
 
 159 
 160 
 161 
 162 
 
 
 
 163 
 164 
 165 
 166 
 
 9.5042327 
 .5018496 
 .4996220 
 .4975605 
 
 9.5039877 
 .5016196 
 .4994083 
 .4973638 
 
 9.5037441 
 .5013912 
 .4991961 
 .4971689 
 
 9.5035021 
 .5011645 
 
 .4989857 
 .4969758 
 
 9.5032615 
 .5009393 
 .4987770 
 .4967845 
 
 163 
 164 
 165 
 166 
 
 
 
 167 
 168 
 169 
 170 
 
 9.4956748 
 .4939743 
 ;4924676 
 .4911627 
 
 9.4954963 
 .4938148 
 .4923279 
 .4910436 
 
 9.4953196 
 .4936572 
 .4921903 
 .4909266 
 
 9.4951448 
 .4935016 
 .4920546 
 .4908117 
 
 9.4949718 
 .4933479 
 .4919211 
 .4906989 
 
 167 
 168 
 169 
 170 
 
 
 
 171 
 172 
 173 
 174 
 
 9.4900665 
 .4891850 
 .4885231 
 .4880844 
 
 9.4899686 
 .4891089 
 .4884692 
 .4880529 
 
 9.4898729 
 .4890349 
 .4884174 
 .4880236 
 
 9.4897793 
 .4889632 
 .4883679 
 .4879966 
 
 9.4896879 
 '.4888937 
 .4883207 
 .4879719 
 
 171 
 172 
 173 
 174 
 
 
 
 175 
 176 
 
 9.4878713 
 
 .4878853 
 
 9.4878625 
 .4878991 
 
 9.4878559 
 .4879153 
 
 9.4878517 
 .4879338 
 
 9.4878497 
 .4879544 
 
 175 
 176 
 
 
 ARG. 
 
 0..1 O.6 
 
 o.r 
 
 O.8 
 
 0.9 
 
 ARG. 
 
 
TABLE XVI. 
 
 
 
 
 Argument of 
 Latitude. 
 
 Reduction 
 to the 
 Ecliptic. 
 
 Log Diff. 
 for 1". 
 
 Var. in 
 100 
 
 Years. 
 
 Argument of 
 Latitude. 
 
 Reduction 
 to the 
 Ecliptic. 
 
 Log Diff. 
 for 1". 
 
 Var. in 
 100 
 Years. 
 
 
 
 
 + 
 
 
 
 + 
 
 
 
 
 
 
 + 
 
 
 
 + 
 
 
 
 
 
 o 
 
 
 
 180 
 
 180 
 
 360 
 
 0.0 
 
 7.8725 
 
 o'!oo 
 
 o 
 
 45 
 
 
 
 135 
 
 225 
 
 o 
 
 315 
 
 12 51.9 
 
 +5.4437 
 
 0'.43 
 
 
 1 
 
 179 
 
 181 
 
 359 
 
 26.8 
 
 7.8722 
 
 0.01 
 
 46 
 
 134 
 
 226 
 
 314 
 
 12 51.5 
 
 6.3680 
 
 0.43 
 
 
 
 2 
 
 178 
 
 182 
 
 358 
 
 53.6 
 
 7.8714 
 
 0.02 
 
 47 
 
 133 
 
 227 
 
 313 
 
 12 50.2 
 
 6.6917 
 
 0.43 
 
 
 
 3 
 
 177 
 
 183 
 
 357 
 
 1 20.4 
 
 7.8702 
 
 0.04 
 
 48 
 
 132 
 
 2-28 
 
 312 
 
 12 48.0 
 
 6.8783 
 
 0.43 
 
 
 
 4 
 
 176 
 
 184 
 
 356 
 
 1 47.0 
 
 7.8684 
 
 0.05 
 
 49 
 
 131 
 
 229 
 
 311 
 
 12 44.8 
 
 7.0060 
 
 0.42 
 
 
 
 5 
 
 175 
 
 185 
 
 355 
 
 2 13.6 
 
 7.8660 
 
 0.07 
 
 50 
 
 130 
 
 230 
 
 310 
 
 12 40.6 
 
 7.1055 
 
 0.42 
 
 
 
 6 
 
 174 
 
 186 
 
 354 
 
 2 39.9 
 
 7.8630 
 
 009 
 
 51 
 
 129 
 
 231 
 
 309 
 
 12 35.6 
 
 7.1849 
 
 0.42 
 
 
 
 7 
 
 173 
 
 187 
 
 353 
 
 3 6.1 
 
 7.8595 
 
 0.10 
 
 52 
 
 128 
 
 232 
 
 308 
 
 12 29.6 
 
 7.2519 
 
 0.41 
 
 
 
 8 
 
 172 
 
 188 
 
 352 
 
 3 32.0 
 
 7.8555 
 
 0.12 
 
 53 
 
 127 
 
 233 
 
 307 
 
 12 22.7 
 
 7.30S8 
 
 0.41 
 
 
 
 9 
 
 171 
 
 189 
 
 351 
 
 3 57.7 
 
 7.8509 
 
 0.13 
 
 54 
 
 126 
 
 234 
 
 306 
 
 12 15.0 
 
 7.3596 
 
 0.41 
 
 
 
 10 
 
 170 
 
 190 
 
 350 
 
 4 23.1 
 
 7.8456 
 
 0.14 
 
 55 
 
 125 
 
 235 
 
 305 
 
 12 6.3 
 
 7.4047 
 
 0.40 
 
 
 
 11 
 
 169 
 
 191 
 
 349 
 
 4 48.2 
 
 7.8401 
 
 0.15 
 
 56 
 
 124 
 
 236 
 
 304 
 
 11 56.7 
 
 7.4146 
 
 0.40 
 
 
 
 12 
 
 168 
 
 192 
 
 348 
 
 5 12.9 
 
 7.8338 
 
 0.17 
 
 57 
 
 123 
 
 237 
 
 303 
 
 11 46.2 
 
 7.4811 
 
 0.39 
 
 
 
 13 
 
 167 
 
 193 
 
 347 
 
 5 37.2 
 
 7.8266 
 
 0.18 
 
 58 
 
 122 
 
 238 
 
 302 
 
 11 34.9 
 
 7.5137 
 
 0.39 
 
 
 
 14 
 
 166 
 
 194 
 
 346 
 
 6 1.2 
 
 7.8190 
 
 0.19 
 
 59 
 
 121 
 
 239 
 
 301 
 
 11 22.7 
 
 7.5437 
 
 0.38 
 
 
 
 15 
 
 165 
 
 195 
 
 345 
 
 6 24.7 
 
 7.8107 
 
 0.21 
 
 60 
 
 120 
 
 240 
 
 300 
 
 11 9.7 
 
 7.5715 
 
 0.37 
 
 
 
 16 
 
 164 
 
 196 
 
 344 
 
 6 47.7 
 
 7.8018 
 
 0.22 
 
 61 
 
 119 
 
 241 
 
 299 
 
 10 55.9 
 
 7.5972 
 
 0.36 
 
 
 
 17 
 
 163 
 
 197 
 
 343 
 
 7 10.3 
 
 7.7920 
 
 0.24 
 
 62 
 
 118 
 
 242 
 
 298 
 
 10 41.3 
 
 7.6207 
 
 0.35 
 
 
 
 18 
 
 162 
 
 198 
 
 342 
 
 7 32.3 
 
 7.7814 
 
 0.25 
 
 63 
 
 117 
 
 243 
 
 297 
 
 10 25.8 
 
 7.6424 
 
 0.35 
 
 
 
 19 
 
 161 
 
 199 
 
 341 
 
 7 53.8 
 
 7.7700 
 
 0.26 
 
 64 
 
 116 
 
 244 
 
 296 
 
 10 9.7 
 
 7.6628 
 
 0.34 
 
 
 
 20 
 
 160 
 
 200 
 
 340 
 
 8 14.7 
 
 7.7582 
 
 0.28 
 
 65 
 
 115 
 
 245 
 
 295 
 
 9 52.7 
 
 7.6818 
 
 0.33 
 
 
 
 21 
 
 159 
 
 201 
 
 339 
 
 8 35.1 
 
 7.7450 
 
 0.29 
 
 66 
 
 114 
 
 246 
 
 294 
 
 9 35.1 
 
 7.69S5 
 
 0.32 
 
 
 
 22 
 
 158 
 
 202 
 
 338 
 
 8 54.8 
 
 7.7308 
 
 0.30 
 
 67 
 
 113 
 
 247 
 
 293 
 
 9 16.7 
 
 7.7158 
 
 0.31 
 
 
 
 23 
 
 157 
 
 203 
 
 337 
 
 9 13.8 
 
 7.7160 
 
 0.31 
 
 68 
 
 112 
 
 248 
 
 292 
 
 8 57.6 
 
 7.7311 
 
 0.30 
 
 
 
 24 
 
 156 
 
 204 
 
 336 
 
 9 32.2 
 
 7.6999 
 
 0.32 
 
 69 
 
 111 
 
 249 
 
 291 
 
 8 37.9 
 
 7.7454 
 
 0.29 
 
 
 
 25 
 
 155 
 
 205 
 
 335 
 
 9 49.9 
 
 7.6825 
 
 0.33 
 
 70 
 
 110 
 
 250 
 
 290 
 
 8 17.6 
 
 7.7588 
 
 0.28 
 
 
 
 26 
 
 154 
 
 206 
 
 334 
 
 10 6.9 
 
 7.6641 
 
 0.34 
 
 71 
 
 109 
 
 251 
 
 289 
 
 7 56.6 
 
 7.7711 
 
 0.27 
 
 
 
 27 
 
 153 
 
 207 
 
 333 
 
 10 23.1 
 
 7.6443 
 
 0.35 
 
 72 
 
 108 
 
 252 
 
 288 
 
 7 35.1 
 
 7.7828 
 
 0.25 
 
 
 
 28 
 
 152 
 
 208 
 
 332 
 
 10 38.6 
 
 7.6230 
 
 0.36 
 
 73 
 
 107 
 
 253 
 
 287 
 
 7 13.0 
 
 7.7936 
 
 0.24 
 
 
 
 29 
 
 151 
 
 209 
 
 331 
 
 10 53.3 
 
 7.5996 
 
 0.37 
 
 74 
 
 106 
 
 254 
 
 286 
 
 6 50.3 
 
 7.8034 
 
 0.22 
 
 
 
 30 
 
 150 
 
 210 
 
 330 
 
 11 7.2 
 
 7.5747 
 
 0.37 
 
 75 
 
 105 
 
 255 
 
 285 
 
 6 27.2 
 
 7.8125 
 
 0.21 
 
 
 
 31 
 
 149 
 
 211 
 
 329 
 
 11 20.3 
 
 7.5479 
 
 0.38 
 
 76 
 
 104 
 
 256 
 
 284 
 
 6 3.6 
 
 7.8212 
 
 0.20 
 
 
 
 32 
 
 148 
 
 212 
 
 328 
 
 11 32.6 
 
 7.5182 
 
 0.38 
 
 77 
 
 103 
 
 257 
 
 283 
 
 5 39.5 
 
 7.8288 
 
 0.18 
 
 
 
 33 
 
 147 
 
 213 
 
 327 
 
 11 44.1 
 
 7.4863 
 
 0.39 
 
 78 
 
 102 
 
 258 
 
 282 
 
 5 15.0 
 
 7.8359 
 
 0.17 
 
 
 
 34 
 
 146 
 
 214 
 
 326 
 
 11 54.7 
 
 7.4506 
 
 0.39 
 
 79 
 
 101 
 
 259 
 
 281 
 
 4 50.2 
 
 7.8425 
 
 0.16 
 
 
 
 35 
 
 145 
 
 215 
 
 325 
 
 12 4.4 
 
 7.4117 
 
 0.40 
 
 80 
 
 100 
 
 260 
 
 280 
 
 4 24.9 
 
 7.8484 
 
 0.14 
 
 
 
 36 
 
 144 
 
 216 
 
 324 
 
 12 13.3 
 
 7.3680 
 
 0.41 
 
 81 
 
 99 
 
 261 
 
 279 
 
 3 59.4 
 
 7.8538 
 
 0.13 
 
 
 
 37 
 
 143 
 
 217 
 
 323 
 
 12 21.2 
 
 7.3188 
 
 0.41 
 
 82 
 
 98 
 
 262 
 
 278 
 
 3 33.5 
 
 7.8583 
 
 0.11 
 
 
 
 38 
 
 142 
 
 218 
 
 322 
 
 12 28.3 
 
 7.2639 
 
 0.42 
 
 83 
 
 97 
 
 263 
 
 277 
 
 3 7.4 
 
 7.8625 
 
 0.10 
 
 
 
 39 
 
 141 
 
 219 
 
 321 
 
 12 34.4 
 
 7.2003 
 
 0.42 
 
 84 
 
 96 
 
 264 
 
 276 
 
 2 41.1 
 
 7.8661 
 
 0.09 
 
 
 
 40 
 
 140 
 
 220 
 
 320 
 
 12 39.7 
 
 7.1231 
 
 0.43 
 
 85 
 
 95 
 
 265 
 
 275 
 
 2 14.5 
 
 7.8689 
 
 0.08 
 
 
 
 41 
 
 139 
 
 221 
 
 319 
 
 12 44.0 
 
 7.0292 
 
 0.43 
 
 86 
 
 94 
 
 266 
 
 274 
 
 1 47.8 
 
 7.8715 
 
 0.06 
 
 
 
 42 
 
 138 
 
 -222 
 
 318 
 
 12 47.4 
 
 6.9091 
 
 0.43 
 
 87 
 
 93 
 
 267 
 
 273 
 
 1 21.0 
 
 7.8735 
 
 0.04 
 
 
 
 43 
 
 137 
 
 223 
 
 317 
 
 12 49.8 
 
 6.7404 
 
 0.43 
 
 88 
 
 92 
 
 268 
 
 272 
 
 54.0 
 
 7.8746 
 
 0.03 
 
 
 
 44 
 
 136 
 
 224 
 
 316 
 
 12 51.3 
 
 6.4607 
 
 0.43 
 
 89 
 
 91 
 
 269 
 
 271 
 
 27.0 
 
 7.8754 
 
 0.01 
 
 
 
 45 
 
 135 
 
 225 
 
 315 
 
 12 51.9 
 
 5.4437 
 
 0.43 
 
 90 
 
 90 
 
 270 
 
 270 
 
 0.0 
 
 7.8757 
 
 0.00 
 
 
 
TABLE XVII. 
 
 49 
 
 
 
 
 Argument of 
 Latitude. 
 
 Latitude. 
 
 Log Diff. 
 for 1". 
 
 Var. in 
 100 
 Years. 
 
 Argument of 
 Latitude. 
 
 Latitude. 
 
 Log Diff. 
 for 1". 
 
 Var. in 
 100 
 Years. 
 
 
 180 
 
 
 
 | II 
 
 0.0 
 
 9.0860 
 
 0.00 
 
 
 
 135 
 
 
 
 45 
 
 O 1 II 
 
 4 56 40.1 
 
 8.9371 
 
 5.01 
 
 
 
 179 
 
 1 
 
 7 18.8 
 
 9.0859 
 
 0.12 
 
 134 
 
 46 
 
 5 1 48.8 
 
 8.9294 
 
 5.09 
 
 
 
 178 
 
 2 
 
 14 37.4 
 
 9.0857 
 
 0.25 
 
 133 47 
 
 5 6 52.1 
 
 8.9-215 
 
 5.18 
 
 
 
 177 
 
 3 
 
 21 55.8 
 
 90854 
 
 0.37 
 
 132 i 48 
 
 5 11 49.7 
 
 8.9133 
 
 5.27 
 
 
 
 176 
 
 4 
 
 29 13.8 
 
 9.0849 
 
 0.49 
 
 131 
 
 49 
 
 5 16 41.7 
 
 8.9048 
 
 5.35 
 
 
 
 175 
 
 5 
 
 36 31.3 
 
 9.0843 
 
 0.61 
 
 130 
 
 50 
 
 5 21 27.9 
 
 8.8959 
 
 5.43 
 
 
 
 174 
 
 6 
 
 43 48.1 
 
 9.0836 
 
 0.74 
 
 129 
 
 51 
 
 5 26 8.2 
 
 8.8868 
 
 5.51 
 
 
 
 173 
 
 7 
 
 51 4.1 
 
 9.0828 
 
 086 
 
 128 52 
 
 5 30 42.7 
 
 8.8773 
 
 5.58 
 
 
 
 172 
 
 8 
 
 58 19.2 
 
 9.0818 
 
 0.98 
 
 127 53 
 
 5 35 11.1 
 
 8.8675 
 
 5.66 
 
 
 
 171 
 
 9 
 
 1 5 33.3 
 
 9.0807 
 
 1.10 
 
 126 
 
 54 
 
 5 39 33.3 
 
 8.8573 
 
 5.74 
 
 
 
 170 
 
 10 
 
 1 12 46.2 
 
 9.0794 
 
 1.22 
 
 125 
 
 55 
 
 5 43 49.4 
 
 8.8467 
 
 5.81 
 
 
 
 169 
 
 11 
 
 1 19 57.7 
 
 9.0780 
 
 1.34 
 
 124 
 
 56 
 
 5 47 59.2 
 
 8.8.','57 
 
 5.88 
 
 
 
 168 
 
 12 
 
 1 27 7.9 
 
 9.0765 
 
 1.47 
 
 123 
 
 57 
 
 5 52 2.7 
 
 8.8243 
 
 5.95 
 
 
 
 167 
 
 13 
 
 1 34 16.4 
 
 90748 
 
 1.59 
 
 122 I 58 
 
 5 55 59.7 
 
 8.8125 
 
 G.02 
 
 
 
 166 
 
 14 
 
 1 41 23.3 
 
 9.0731 
 
 1.71 
 
 121 
 
 59 
 
 5 59 50.2 
 
 8.8002 
 
 6.09 
 
 
 
 165 
 
 15 
 
 1 48 28.3 
 
 9.0711 
 
 1.83 
 
 120 
 
 60 
 
 6 3 34.2 
 
 8.7874 
 
 6.15 
 
 
 
 164 
 
 16 
 
 1 55 31.4 
 
 9.0690 
 
 1.95 
 
 119 
 
 61 
 
 6 7 11.5 
 
 8.7740 
 
 6.21 
 
 
 
 163 
 
 17 
 
 2 2 32.4 
 
 9.0668 
 
 2.07 
 
 118 
 
 62 
 
 6 10 42.1 
 
 8.7601 
 
 6.27 
 
 
 
 162 
 
 18 
 
 2 9 31.1 
 
 9.0645 
 
 2.18 
 
 117 
 
 63 
 
 6 14 5.9 
 
 8.7456 
 
 6.33 
 
 
 
 161 
 
 19 
 
 2 16 27.6 
 
 9.0620 
 
 2.30 
 
 116 
 
 64 
 
 6 17 22.9 
 
 8.7304 
 
 6.38 
 
 
 
 160 
 
 20 
 
 2 23 21.5 
 
 9.0593 
 
 2.41 
 
 115 
 
 65 
 
 6 20 32.9 
 
 8.7146 
 
 6.44 
 
 
 
 159 
 
 21 
 
 2 30 12.9 
 
 9.0565 
 
 2.52 
 
 114 
 
 66 
 
 6 23 36.0 
 
 8.6980 
 
 6.49 
 
 
 
 158 
 
 22 
 
 2 37 1.6 
 
 9.0536 
 
 2.64 
 
 113 
 
 67 
 
 6 26 32.1 
 
 8.6806 
 
 6.54 
 
 
 
 157 
 
 23 
 
 2 43 47.4 
 
 9.0505 
 
 2.76 
 
 112 
 
 68 
 
 6 29 21.1 
 
 8.6623 
 
 6.59 
 
 
 
 156 
 
 24 
 
 2 50 30.3 
 
 9.0472 
 
 2.87 
 
 111 
 
 69 
 
 6 32 3.0 
 
 8.6431 
 
 6.64 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 155 
 
 25 
 
 2 57 10.1 
 
 9.0438 
 
 2.99 
 
 110 
 
 70 
 
 6 34 37.6 
 
 8.6229 
 
 6.68 
 
 
 
 151 
 
 26 
 
 3 3 46.7 
 
 9.0402 
 
 3.10 
 
 109 
 
 71 
 
 6 37 5.1 
 
 8.6015 
 
 6.72 
 
 
 
 153 
 
 27 
 
 3 10 20.0 
 
 9.0365 
 
 3.21 
 
 108 
 
 72 
 
 6 39 25.3 
 
 8.5789 i 6.76 
 
 
 
 152 
 
 28 
 
 3 16 49.9 
 
 9.0326 
 
 3.32 
 
 107 
 
 73 
 
 6 41 38.1 
 
 8.5549 i 6.80 
 
 
 
 151 
 
 29 
 
 3 23 16.1 
 
 9.0285 
 
 3.43 
 
 106 
 
 74 
 
 6 43 43.6 
 
 8.5293 
 
 6.83 
 
 
 
 150 
 
 30 
 
 3 29 38.7 
 
 9.0243 
 
 3.54 
 
 105 
 
 75 
 
 6 45 41.7 
 
 8.5020 
 
 6.87 
 
 
 
 149 
 
 31 
 
 3 35 57.6 
 
 9.0199 
 
 3.64 
 
 104 
 
 76 
 
 6 47 32.3 
 
 8.4727 
 
 6.90 
 
 
 
 148 
 
 32 
 
 3 42 12.5 
 
 9.0153 
 
 3.75 
 
 103 
 
 77 
 
 6 49 15.5 
 
 8.4411 
 
 6.93 
 
 
 
 147 
 
 33 
 
 3 48 23.3 
 
 9.0105 
 
 3.85 
 
 102 
 
 78 
 
 6 50 51.1 
 
 8.4070 
 
 6.95 
 
 
 
 146 
 
 34 
 
 3 54 30.1 
 
 9.0055 
 
 3.95 
 
 101 
 
 79 
 
 6 52 19.3 
 
 8.3697 
 
 6.98 
 
 
 
 145 
 
 35 
 
 4 32.6 
 
 9.0004 
 
 4.05 
 
 100 
 
 80 
 
 6 53 39.8 
 
 8.3286 
 
 7.00 
 
 
 
 144 
 
 36 
 
 4 6 30.7 
 
 8.9950 
 
 4.16 
 
 99 
 
 81 
 
 6 54 52.8 
 
 8.2835 
 
 7.02 
 
 
 
 143 
 
 37 
 
 4 12 24.4 
 
 8.9895 
 
 4.26 
 
 98 
 
 82 
 
 6 55 58.1 
 
 8.2327 
 
 7.04 
 
 
 
 142 
 
 38 
 
 4 18 13.5 
 
 8.9837 
 
 4.36 
 
 97 
 
 83 
 
 6 56 55.8 
 
 8.1751 
 
 7.06 
 
 
 
 141 
 
 39 
 
 4 23 57.9 
 
 8.9777 
 
 4.45 
 
 96 
 
 84 
 
 6 57 45.8 
 
 8.1085 
 
 7.07 
 
 
 
 140 
 
 40 
 
 4 29 37.5 
 
 8.9716 
 
 4.55 
 
 95 
 
 85 
 
 6 58 28.2 
 
 8.0295 
 
 7.08 
 
 
 
 139 
 
 41 
 
 4 35 12.2 
 
 8.9651 
 
 4.65 
 
 94 
 
 86 
 
 6 59 2.9 
 
 7.9328 i 7.09 
 
 
 
 138 
 
 42 
 
 4 40 41.9 
 
 8.9585 
 
 4.74 
 
 93 
 
 87 
 
 6 59 29.9 7.8081 
 
 7.10 
 
 
 
 137 
 
 43 
 
 4 46 6.6 
 
 8.9516 
 
 4.85 
 
 92 
 
 88 
 
 6 59 49.2 7.6321 
 
 7.11 
 
 
 
 136 
 
 44 
 
 4 51 26.0 
 
 8.9445 
 
 4.92 
 
 91 
 
 89 
 
 7 0.7 7.3313 7.11 
 
 
 
 135 
 
 45 
 
 4 56 40.1 
 
 8.9371 
 
 5.01 
 
 90 
 
 90 
 
 7 4.6 oo 
 
 7.11 
 
 
 
5O 
 
 TABLE XVIII. 
 
 
 
 
 A v 
 
 .0 
 
 .1 
 
 .2 
 
 .3 
 
 .4 
 
 . 
 
 .6 
 
 . 
 
 .8 
 
 .9 
 
 
 Arg. 
 
 Log Diff. v. 
 
 Log Diff. 
 
 Log Diff. . 
 
 Log Diff. v. 
 
 Log Diff. v 
 
 Log Diff. v. 
 
 Log Diff. v. 
 
 Log Diff. v. 
 
 Log Diff. v. 
 
 Log Diff. v. 
 
 
 
 
 
 9.05779 
 
 9.05779 
 
 9.05778 
 
 9.05777 
 
 9.05775 
 
 9.05773 
 
 9.05771 
 
 9.05768 
 
 9.05764 
 
 9.05760 
 
 
 
 1 
 
 9.05756 
 
 9.05751 
 
 9.05746 
 
 9.05740 
 
 9.05734 
 
 9.05728 
 
 9.05721 
 
 9.05713 
 
 9.05705 
 
 9.05697 
 
 
 
 2 
 
 9.05688 
 
 9.05679 
 
 9.05669 
 
 9.05659 
 
 9.05648 
 
 9.05637 
 
 9.05626 
 
 9.05614 
 
 9.05601 
 
 9.05588 
 
 
 
 3 
 
 9.05575 
 
 9.05561 
 
 9.05547 
 
 9.05533 
 
 9.05517 
 
 9.05502 
 
 9.05486 
 
 9.05470 
 
 9.05453 
 
 9.05436 
 
 
 
 4 
 
 9.05418 
 
 9.05400 
 
 9.05381 
 
 9.05362 
 
 9.05343 
 
 9.05323 
 
 9.05303 
 
 9.05282 
 
 9.05261 
 
 9.05239 
 
 
 
 5 
 
 9.05217 
 
 9.05195 
 
 9.05172 
 
 9.05149 
 
 9.05125 
 
 9.05101 
 
 9.05077 
 
 9.05052 
 
 9.05027 
 
 9.05001 
 
 
 
 6 
 
 9.04975 
 
 9.04948 
 
 9.04922 
 
 9.04894 
 
 9.04866 
 
 9.04838 
 
 9.04810 
 
 9.04781 
 
 9.04751 
 
 9.04721 
 
 
 
 7 
 
 9.04691 
 
 9.04660 
 
 9.04629 
 
 9.04598 
 
 9.04566 
 
 9.04534 
 
 9.04501 
 
 9.04468 
 
 9.04435 
 
 9.04401 
 
 
 
 8 
 
 9.04367 
 
 9.04333 
 
 9.04298 
 
 9.04263 
 
 9.04227 
 
 9.04191 
 
 9.04155 
 
 9.04118 
 
 9.04081 
 
 9.04044 
 
 
 
 9 
 
 9.04006 
 
 9.03968 
 
 9.03929 
 
 9.03891 
 
 9.03852 
 
 9.03812 
 
 9.03772 
 
 9.03732 
 
 9.03691 
 
 9.03650 
 
 
 
 10 
 
 9.03609 
 
 9.03567 
 
 9.03526 
 
 9.03483 
 
 9.03441 
 
 9 03398 
 
 9.03354 
 
 9.03311 
 
 9.03267 
 
 9.03223 
 
 
 
 11 
 
 9.03178 
 
 9.03133 
 
 9.03088 
 
 9.03042 
 
 9.02997 
 
 9.02951 
 
 9.02904 
 
 9.02857 
 
 9.02810 
 
 9.02763 
 
 
 
 12 
 
 9.02715 
 
 9.02667 
 
 9.02619 
 
 9.02570 
 
 9.02521 
 
 9.02472 
 
 9.02422 
 
 9.02372' 
 
 9.02322 
 
 9.02272 
 
 
 
 13 
 
 9.02221 
 
 9.02170 
 
 9.02119 
 
 9.02068 
 
 9.02016 
 
 9.01964 
 
 9.01912 
 
 9.01859 
 
 9.01806 
 
 9.01753 
 
 
 
 14 
 
 9.01700 
 
 9.01647 
 
 9.01593 
 
 9.01539 
 
 9.01485 
 
 9.01430 
 
 9.01375 
 
 9.01320 
 
 9.01265 
 
 9.01210 
 
 
 
 15 
 
 9.01154 
 
 9.01098 
 
 9.01042 
 
 9.00986 
 
 9.00929 
 
 9.00872 
 
 9.00815 
 
 9.00758 
 
 9.00700 
 
 9.00642 
 
 
 
 16 
 
 9.00581 
 
 9.00526 
 
 9.00467 
 
 9.00409 
 
 9.00350 
 
 9.00291 
 
 9.00232 
 
 9.00173 
 
 9.00113 
 
 9.00053 
 
 
 
 17 
 
 8.99993 
 
 8.99933 
 
 8.99873 
 
 8.99812 
 
 8.99751 
 
 8.99690 
 
 8.99629 
 
 8.99568 
 
 8.99507 
 
 8.99445 
 
 
 
 18 
 
 8.99383 
 
 8.99321 
 
 8.99259 
 
 8.99197 
 
 8.99135 
 
 8.99072 
 
 8.9G009 
 
 8.98946 
 
 8.98883 
 
 8.98820 
 
 
 
 19 
 
 8.98757 
 
 8.98694 
 
 8.98630 
 
 8.98566 
 
 8.98502 
 
 8.98438 
 
 8.98374 
 
 8.98309 
 
 8.98245 
 
 8.98180 
 
 
 
 20 
 
 8.98115 
 
 8.98050 
 
 8.97985 
 
 8.97920 
 
 8.97855 
 
 8.97790 
 
 8.97724 
 
 8.97658 
 
 8.97593 
 
 8.97527 
 
 
 
 21 
 
 8.97461 
 
 8.97395 
 
 8.97329 
 
 8.97263 
 
 8.97196 
 
 8.97130 
 
 8.97063 
 
 8.96997 
 
 8.96930 
 
 8.96863 
 
 
 
 22 
 
 8.96796 
 
 8.96729 
 
 8.96662 
 
 8.96595 
 
 8.96527 
 
 8.96460 
 
 8.96392 
 
 8.96325 
 
 8.96257 
 
 8.96189 
 
 
 
 23 
 
 8.96121 
 
 8.96053 
 
 8.95985 
 
 8.95917 
 
 8.95849 
 
 8.95781 
 
 8.95713 
 
 8.95645 
 
 8.95577 
 
 8.95508 
 
 
 
 21 
 
 8.95440 
 
 8.95372 
 
 8.95303 
 
 8.95235 
 
 8.95166 
 
 8.95097 
 
 8.95029 
 
 8.94960 
 
 8.94891 
 
 8.94822 
 
 
 
 25 
 
 8.94753 
 
 8.94684 
 
 8.94615 
 
 8.94546 
 
 8.94477 
 
 8.94408 
 
 8.94333 
 
 8.94270 
 
 8.94201 
 
 8.94131 
 
 
 
 26 
 
 8.94062 
 
 8.93993 
 
 8.93924 
 
 8.93854 
 
 8.93785 
 
 8.93716 
 
 8.9364G 
 
 8.93577 
 
 8.93508 
 
 8.93438 
 
 
 
 27 
 
 8.93369 
 
 8.93300 
 
 8.93230 
 
 8.93161 
 
 8.93092 
 
 8.93022 
 
 8.92953 
 
 8.92883 
 
 8.32814 
 
 8.92744 
 
 
 
 28 
 
 8.92675 
 
 8.92606 
 
 8.92536 
 
 8.92467 
 
 8.92397 
 
 8.92328 
 
 8.92259 
 
 8.92189 
 
 8.92120 
 
 8.92050 
 
 
 
 29 
 
 8.91981 
 
 8.91912 
 
 8.91842 
 
 8.91773 
 
 8.91704 
 
 8.91635 
 
 8.91566 
 
 8.91496 
 
 8.91427 
 
 8.91358 
 
 
 
 147 
 
 8.92024 
 
 8.92093 
 
 8.92163 
 
 8.92232 
 
 8.92301 
 
 8.92370 
 
 8.92440 
 
 8.92509 
 
 8.92578 
 
 8.92648 
 
 
 
 148 
 
 8.92717 
 
 8.92786 
 
 8.92856 
 
 8.92925 
 
 8.92994 
 
 8.93064 
 
 8.93133 
 
 8.93203 
 
 8.93272 
 
 8.93342 
 
 
 
 149 
 
 8.93411 
 
 8.93480 
 
 8.93550 
 
 8.93619 
 
 8.93688 
 
 8.93758 
 
 8.93827 
 
 8.93896 
 
 8.93965 
 
 8.94035 
 
 
 
 150 
 
 8.94104 
 
 8.94173 
 
 8.94242 
 
 8.94312 
 
 8.94381 
 
 8.94450 
 
 8.94519 
 
 8.94588 
 
 8.94657 
 
 8.94726 
 
 
 
 151 
 
 8.94795 
 
 8.94864 
 
 8.94933 
 
 8.95002 
 
 8.95070 
 
 8.95139 
 
 8.95208 
 
 8.95276 
 
 8.95345 
 
 8.95413 
 
 
 
 152 
 
 8.95482 
 
 8.95550 
 
 8.95619 
 
 8.95687 
 
 8.95755 
 
 8.95823 
 
 8.95891 
 
 8.95959 
 
 8.96027 
 
 8.96095 
 
 
 
 153 
 
 8.96163 
 
 8.96231 
 
 8.96298 
 
 8.96366 
 
 8.96433 
 
 8.96501 
 
 8.96568 
 
 8.96636 
 
 8.96703 
 
 8.96770 
 
 
 
 154 
 
 8.96837 
 
 8.96904 
 
 8.96971 
 
 8.97037 
 
 8.97104 
 
 8.97170 
 
 8.97237 
 
 8.97303 
 
 8.97369 
 
 8.97435 
 
 
 
 155 
 
 8.97501 
 
 8.97567 
 
 8.97633 
 
 8.97698 
 
 8.97764 
 
 8.97829 
 
 8.97895 
 
 8.97960 
 
 8.98025 
 
 8.98090 
 
 
 
 156 
 
 8.98155 
 
 8.98220 
 
 8.98284 
 
 8.98349 
 
 8.98413 
 
 8.98477 
 
 8.98541 
 
 8.98605 
 
 8.98669 
 
 8.98732 
 
 
 
 157 
 
 8.98796 
 
 8.98859 
 
 8.98922 
 
 8.98985 
 
 8.99048 
 
 8.99111 
 
 8.99173 
 
 8.99236 
 
 8.99298 
 
 8.99360 
 
 
 
 158 
 
 8.99422 
 
 8.99484 
 
 8.99545 
 
 8.99606 
 
 8.99667 
 
 8.99728 
 
 8.99789 
 
 8.99849 
 
 8.9D910 
 
 8.99970 
 
 
 
 159 
 
 9.00030 
 
 9.00090 
 
 9.00149 
 
 9.00209 
 
 9.00268 
 
 9.00327 
 
 9.00386 
 
 9.00445 
 
 9.00503 
 
 9.00562 
 
 
 
 160 
 
 9.00620 
 
 9.00678 
 
 9.00735 
 
 9.00793 
 
 9.00850 
 
 9.00907 
 
 9.00964 
 
 9.01021 
 
 9.01077 
 
 9.01133 
 
 
 
 161 
 
 9.01189 
 
 9.01245 
 
 9.01300 
 
 9.01355 
 
 9.01410 
 
 9.01464 
 
 9.01518 
 
 9.01572 
 
 9.01626 
 
 9.01680 
 
 
 
 162 
 
 9.01733 
 
 9.01786 
 
 9.01839 
 
 9.01891 
 
 9.01944 
 
 9.01996 
 
 9.02047 
 
 9.02099 
 
 9.02150 
 
 9.02201 
 
 
 
 163 
 
 9.02252 
 
 9.02302 
 
 9.02353 
 
 9.02402 
 
 9.02452 
 
 9 02501 
 
 9.02550 
 
 9.02599 
 
 9.02648 
 
 9.02696 
 
 
 
 164 
 
 9.02744 
 
 9.02791 
 
 9.02839 
 
 9.02886 
 
 9.02932 
 
 9.02978 
 
 9.03024 
 
 9.03070 
 
 9.03115 
 
 9.03160 
 
 
 
 165 
 
 9.03205 
 
 9.03249 
 
 9.03293 
 
 9.03337 
 
 9.03381 
 
 9.03424 
 
 9.03467 
 
 9.03509 
 
 9.03551 
 
 9.03593 
 
 
 
 166 
 
 9.03635 
 
 9.03676 
 
 9.03717 
 
 9.03757 
 
 9.03797 
 
 9.03837 
 
 9.03876 
 
 9.03915 
 
 9.03954 
 
 9.03992 
 
 
 
 167 
 
 9.04030 
 
 9.04067 
 
 9.04105 
 
 9.04141 
 
 9.04178 
 
 9.04214 
 
 9.04249 
 
 9.04284 
 
 9.04319 
 
 9.04354 
 
 
 
 168 
 
 9.04388 
 
 9.04422 
 
 9.04455 
 
 9.04488 
 
 9.04521 
 
 9.04553 
 
 9.04585 
 
 9.04617 
 
 9.04648 
 
 9.04679 
 
 
 
 169 
 
 9.04709 
 
 9.04739 
 
 9.04769 
 
 9.04798 
 
 9.04826 
 
 9.04855 
 
 9.04883 
 
 9.04910 
 
 9.04938 
 
 9.04965 
 
 
 
 170 
 
 9.04991 
 
 9.05017 
 
 9.05042 
 
 9.05067 
 
 9.05092 
 
 9.05116 
 
 9.05140 
 
 9.05163 
 
 9.05186 
 
 9.05209 
 
 
 
 171 
 
 9.05231 
 
 9.05253 
 
 9.05274 
 
 9.05295 
 
 9.05315 
 
 9.05335 
 
 9.05355 
 
 9.05374 
 
 9.05393 
 
 9.05411 
 
 
 
 172 
 
 9.05429 
 
 9.05446 
 
 9.05463 
 
 9.05480 
 
 9.05496 
 
 9.05512 
 
 9.05527 
 
 9.05541 
 
 9.05556 
 
 9.05570 
 
 
 
 173 
 
 9.05583 
 
 9.05596 
 
 9.05609 
 
 9.05621 
 
 9.05632 
 
 9.05644 
 
 9.05654 
 
 9.05665 
 
 9.05675 
 
 9.05684 
 
 
 
 174 
 
 9.05693 
 
 9.05702 
 
 9.05710 
 
 9.05717 
 
 9.05725 
 
 9.05732 
 
 9.05738 
 
 9.05744 
 
 9.05749 
 
 9.05754 
 
 
 
 175 
 
 9.05759 
 
 9.05763 
 
 9.05767 
 
 9.05770 
 
 9.05773 
 
 9.05775 
 
 9.05777 
 
 9.05778 
 
 9.05779 
 
 9.05779 
 
 
 
 176 
 
 9.05779 9.05778 9.05777 
 
 9.05776 
 
 9.05774 
 
 9.05771 
 
 9.05768 
 
 9.05765 
 
 9.05761 
 
 9.05757 
 
 
 
UNIVERSITY OF CALIFORNIA LIBRARY