OBI 
 355 
 
 UC-NRLF 
 
 YFQ2600 
 
 TABLES 
 
 FOR THE 
 
 TRUE ANOMALY 
 
 IN ELLIPTIC ORBITS 
 
 BY 
 
 FRANK SCHLESINGER AND STELLA UDICK 
 
 REPRINTED FROM THE PUBLICATIONS OF THE ALLEGHENY OBSERVATORY, VOLUME II 
 
 PRESS OF 
 
 THE NEW ERA PRINTING COMPANY 
 LANCASTER, PA. 
 
 1912 
 
S4 
 
 .-uron. D 
 

 TABLES FOR THE TRUE ANOMALY IN ELLIPTIC ORBITS. 
 
 BY FRANK SCHLESINGER AND STELLA UDICK. 
 
 The following tables have been compiled to facilitate the computation of the 
 orbits of spectroscopic and visual binaries. They should also prove useful for 
 the computation of finding ephemerides for asteroids. 
 
 The true anomaly (r) of a body moving in an elliptic orbit is the angle be- 
 tween its radius-vector and the major axis; it is counted from periastron, or that 
 end of the axis that corresponds to closest approach to the attracting body. The 
 mean anomaly (M) is what this angle would be were the angular motion uni- 
 form. These two anomalies are connected by the equations: 
 
 Ee sin E = ^f, (i) 
 
 (2) 
 
 in which is an auxiliary called the eccentric anomaly. As the first of these 
 equations is transcendental, the task of computing from M is one of classic 
 difficulty and is known as Kepler's problem. Among the numerous devices that 
 have been provided for the solution of this problem, the two most useful are the 
 " Tafel zur Berechnung der ivahre Anomalie " published by the Berlin Rechen- 
 Institut in 1892, and Astrand's " Hiilfstafeln zurAuflosung der Kepler 'schen Prob- 
 lems," Leipzig, 1890. The former gives the values of v M to the hundredth 
 part of a minute of arc; the arguments are each degree in M and each 20' in <, 
 up to 20 20', being the angle whose sine is equal to the eccentricity of the 
 orbit. Astrand's tables give the values of to the thousandth part of a degree; 
 the arguments are each degree in M and each hundredth in the eccentricity from 
 o.oi to i.oo. In addition each half-degree in M from o-5 to 19. 5 is included. 
 Both these tables were designed more especially with a view to facilitating the 
 computation of asteroid orbits. The present tables give the values of v directly, 
 to the hundredth part of a degree, the arguments being each degree in M and 
 each hundredth in e from o.oi to 0.77 inclusive. Any greater accuracy than 
 
FOR THE TRUE ANOMALY. 
 
 o.oi is superfluous for either spectroscopic or visual binaries. As it is frequently 
 necessary to interpolate for the thousandths in the eccentricity, the tables have 
 been arranged with this in view, and successive values of v for the same value 
 of M (but different values of e) are found in the same horizontal line. 
 
 The usefulness of tables depends so largely upon their freedom from error 
 that compilers should always state how they were computed and what precau- 
 tions were taken to insure the accuracy of their printing. In the present case, v 
 has been computed from the corresponding in Astrand's tables by means of 
 Equation (2) above. Bremiker's five-place logarithms were employed and the 
 work was carried out to three decimal places. It was then checked in the fol- 
 lowing way: from <? = o.oi to e = o.io, v was computed to three decimal places 
 from the formula, 
 
 v M+ 2(E M} + ^ sin zM+ $e? sin 3^/+ etc. 
 
 E M was taken from Astrand's tables. This expression is not conveniently 
 convergent beyond ? = o.io; and v was therefore computed in duplicate from 
 ^ = o.ii to = 0.23. Next, by means of the second differences (and the third 
 whenever necessary) the computed values of v were checked throughout the 
 whole extent of the tables. For the larger values of e, the method of differences 
 is not servicable at the beginning of each table, and these values of v were accord- 
 ingly checked by duplicate computations. The tables were now copied on sheets 
 for the printer and were rounded off to two decimal places. The copying was 
 checked by taking the differences upon these printer's sheets, that is the differences 
 in v for successive values of M. When the first proof was received from the 
 printer, it was subjected to three revisions; (i) it was compared with the original 
 manuscript, one of us reading the manuscript while the other followed the proof. 
 (2) The differences in v for successive values of M (but for the same values of e} 
 were constructed from the printed tables and compared with the differences that 
 had already been set into type. (3) The differences in v for successive values of 
 e (but for the same values of M) were constructed from the printed table and 
 were seen to run smoothly. The care with which the tables had been computed, 
 copied and set into type may be inferred from the fact that two and one half 
 errors were, on the average, found on each page of the proof. The second and 
 third revisions together revealed about twenty-five errors. 
 
 Although the computations were carried out to three decimal places, and then 
 rounded off to the nearest hundredth, the error in the printed numbers will occa- 
 sionally exceed o.oo5. In all doubtful cases the computations were repeated 
 with seven-place logarithms. But in order to make certain in some cases, it would 
 have been necessary to start with values of E that extend beyond the third decimal 
 place. 
 
TABLES FOR THE TRUE ANOMALY. 3 
 
 To obtain v corresponding to a value of M greater than 180, the latter should 
 be entered with the argument 360 - M and the resulting value of v counted as 
 negative. Thus for ^ = 0.07 and M = 250, we find opposite no that v = - 
 ii7.3o, and this is equal to 242. 70. 
 
 Simple or linear interpolation for the fractional part of M is almost always 
 sufficient; thus, if e does not exceed 0.50 the neglect of second differences cannot 
 cause an error of more than o.oi. With higher values of e this error becomes 
 appreciable for a small portion of the tables near the beginning. Thus for 
 e = 0.77 and M near 4 this error may reach o.i3. The computer may take this 
 into account by always adding a correction to the numerical value of v that has 
 been obtained by simple interpolation. This correction is obtained by multiply- 
 ing the second difference (the difference between two successive tabular differ- 
 ences) by the number in the following table. The argument, (x\, is the frac- 
 tional part of M, and may have any value from zero to unity. 
 
 x. Factor for the Second Diff< 
 
 0.0 0.00 
 
 O.I 0.04 
 
 0.2 OX>8 
 
 0.3 0.10 
 
 04 o.u 
 
 0.5 o.xz 
 
 0.6 o.iz 
 
 0.7 o.io 
 
 0.8 ox>8 
 
 0.9 0x14 
 
 I.O . . O.OO 
 
TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 e = .01 
 
 .02 
 
 .03 
 
 e = .04 
 
 .05 
 
 .06 
 
 e = .07 
 
 
 
 1 
 
 2 
 3 
 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
 o.oo 
 
 1.02 
 
 2.04 
 
 9.18 
 
 IO.2O 
 11.22 
 12.24 
 13.26 
 14.28 
 
 20.4O 
 21.41 
 22.43 
 23-45 
 24-47 
 
 25-49 
 
 27-53 
 28.54 
 
 31.60 
 32.61 
 33-63 
 34-65 
 
 35-66 
 36.68 
 37-70 
 38-71 
 39-73 
 40.74 
 
 42-77 
 43-79 
 44.80 
 
 49.87 
 50.88 
 
 53-92 
 54-93 
 
 55-94 
 
 57-97 
 58-98 
 59-99 
 61.00 
 
 .02 
 
 .02 
 
 ' 
 
 
 
 O.OO 
 
 1.04 
 2.08 
 
 3-12 
 4.16 
 
 5.20 
 6.25 
 7.29 
 
 8-33 
 
 9-37 
 
 10.41 
 
 u-45 
 12.49 
 
 15.61 
 
 18.72 
 19.76 
 
 20.80 
 21.84 
 
 22.88 
 
 23.92 
 24-95 
 
 25.99 
 27.03 
 28.06 
 
 1.04 
 1.04 
 
 1.04 
 1.04 
 
 i. os 
 
 1.04 
 
 1.04 
 1.04 
 
 1.04 
 
 1.04 
 1.04 
 1.04 
 
 1.04 
 1.03 
 1.04 
 1.04 
 
 1.04 
 
 1.04 
 1.03 
 
 36.34 
 37-37 
 38.41 
 
 39-44 
 40.47 
 
 1.03 
 
 1.03 
 
 1.03 
 
 1.03 
 
 49-73 
 
 51.78 
 52-81 
 53-83 
 54-86 
 55-88 
 
 59-97 
 60.99 
 
 62.01 
 
 s 
 
 , 
 
 1.02 
 
 O.OO 
 
 1. 06 
 
 2.12 
 
 10.62 
 11.68 
 
 I9.IO 
 2O.I6 
 
 21.22 
 
 22.28 
 23-33 
 
 28.61 
 29.67 
 
 31.78 
 32.83 
 
 33-88 
 34-93 
 35-98 
 
 37-03 
 38.08 
 
 39-13 
 40.18 
 
 42-27 
 43-32 
 44-36 
 
 s 
 
 i. 06 
 1.06 
 
 1.06 
 
 "S 
 
 .06 
 
 47-50 
 48.54 
 49.58 
 50.62 
 
 52.70 
 
 53-73 
 54-77 
 55-81 
 
 57-88 
 58.91 
 59-94 
 60.97 
 62.00 
 
 63-03 
 
 .05 
 .05 
 .05 
 OS 
 
 .os 
 .05 
 
 OS 
 
 - 
 
 n-i 
 
 0.00 
 
 1. 08 
 2.17 
 3-25 
 
 4-34 
 
 i. 08 
 
 ,.08 
 
 8.67 
 
 9-7? 
 
 SS 
 
 i. 08 
 i. 08 
 i. 08 
 
 1.09 
 1. 08 
 
 1949 
 
 21.64 
 
 23.80 
 24.88 
 
 27.03 
 28.10 
 29.18 
 30.25 
 
 32.40 
 
 33-47 
 34-54 
 35-6i 
 36-67 
 
 , 
 T . 
 
 I06 
 I ' 6 
 1.07 
 
 37-74 . OT 
 
 ss 
 
 42.00 
 
 49.41 
 50.47 
 51-52 
 52.57 
 
 53.63 
 54-68 
 55-72 
 56.77 
 57-82 
 
 60.95 
 
 i. 06 
 
 05 OS 
 
 i. os 
 
 1. 06 
 
 i. os 
 
 1.04 
 
 '- 04 
 
 O.OO 
 I. II 
 2.21 
 
 5-53 
 6.64 
 
 7-74 
 8.85 
 
 9-95 
 
 11.06 
 12. 16 
 
 15-47 
 16.58 
 
 18.78 
 
 20.98 
 
 22.08 
 23.18 
 24.28 
 25.37 
 26-47 
 
 A 
 i. ii 
 
 I ' xo 
 1. 1 1 
 
 '- 10 
 
 1. 10 
 
 i. 09 
 
 I.IO 
 
 1.09 
 
 28!66 '' 
 
 3'-94 
 
 m 
 
 37-38 ;;g 
 
 38.46 ' 
 
 4279 I ' 8 
 
 ' 1.07 
 
 43-86 
 
 44-94 -g 
 46.02 
 
 47-9 I'll 
 
 48.16 |' 7 
 
 49-23 . 
 
 5 -3 ,: 
 
 54-57 
 55-63 
 56-69 
 
 57-75 
 58-81 
 
 59-86 
 60.92 
 
 A 
 
 1. 13 
 1. 13 
 
 T 
 "- 13 
 
 x ' 13 
 
 1. 13 
 
 O.OO 
 
 1-13 
 
 2.26 
 3-39 
 
 5-65 
 6.78 
 7-90 
 9-03 
 10.16 
 
 11.29 
 
 12.42 
 
 13-54 
 14.67 
 
 15-79 
 16.92 
 18.04 
 19.17 
 20.29 
 21.41 
 
 22.53 
 23-65 
 24-77 
 25-89 
 27.00 
 
 28.12 
 29.23 
 30.34 
 31-45 
 
 33-67 
 34-78 
 35-89 
 36.99 
 38.10 
 
 39-20 
 40.30 
 
 43-59 I'] 
 
 1. 12 
 1. 12 
 
 11 II 
 
 1. 12 
 
 I. II 
 I. II 
 I. II 
 
 . 
 
 ' 
 
 !'" 
 
 ;; 
 
 '" 
 
 1. 10 
 
 64.07 
 
 64.07 
 65.12 
 
 i. 05 
 
 49-04 
 50.13 
 
 53-37 
 54-45 
 
 55-52 
 56.60 
 57-67 
 58-74 
 59-81 
 
 60.87 
 61.94 
 63.00 
 64.06 
 
 66.17 
 
 1.09 
 
 r - 8 
 
 '- 07 
 1 - 07 
 
 O.OO 
 
 1-15 
 
 2.31 
 
 3.46 
 
 4.61 
 
 5-77 
 6.92 
 8.07 
 9.22 
 10.38 
 
 13.82 
 4-97 
 
 i. if> 
 
 I. IS 
 
 18.41 
 19-56 
 20.70 
 21.85 
 
 22.99 
 24-13 
 
 26.41 
 
 28.68 
 29.81 
 
 30.95 
 32-08 
 
 33-21 
 
 34-33 
 35-46 
 36.59 
 37-71 
 38-83 
 
 39-95 
 41.07 
 42.18 
 43-30 
 
 1.14 
 
 I. IS 
 
 1. 14 
 
 15 IS 
 
 1.14 
 1.14 
 
 1. 14 
 
 1. 13 
 
 , 
 ' 3 
 
 ' 3 
 
 45-52 
 46.62 
 
 47-73 
 48.83 
 49-93 
 
 51-03 
 52-13 
 53-23 
 54-32 
 55-41 
 
 59-75 
 60.82 
 
 61.90 
 
 62.97 
 64.04 
 65.11 
 66.18 
 
 67.24 
 
 ! 
 
 r - 07 
 1 - 07 
 
 I ' 07 
 i. 06 
 
 2 
 3 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 
 52 
 53 
 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
 
 
TABLES FOR THE TRUE ANOMALY. 
 
 If 
 
 .01 
 
 e = .02 
 
 .03 
 
 e = .04 
 
 e = .05 
 
 .06 
 
 .07 
 
 M 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
 61.00 
 62.01 
 63.02 
 64.03 
 
 66.04 
 67-05 
 68.06 
 69.07 
 70.08 
 
 71.08 
 
 73-09 
 74.10 
 
 76.11 
 77-12 
 78.12 
 79.12 
 80.13 
 
 81.13 
 82.13 
 
 86.14 
 87.14 
 
 SS 
 
 93 ' 15 
 
 94- '4 
 
 95-14 
 
 3:3 
 
 J 
 
 102.12 
 
 .01 
 .01 
 
 01 
 
 M 
 oo 
 
 0, 
 
 oo I 
 
 .00 
 
 .00 
 .00 
 
 Jft 
 
 
 099 
 
 106.10 
 
 107.10 1 - 
 108.09 ' 99 I 
 109.08 - 99 i 
 
 110.08 I - 00 ' 
 
 0.99 
 
 111.07 
 112.06 
 113-06 
 
 114.05 
 
 116.03 
 117.02 
 118.01 
 119.01 
 I2O.OO 
 
 120.99 
 
 ' 99 
 ' 99 
 '- 00 
 
 '" 
 0.99 
 
 62.01 
 
 63.03 
 64.05 
 65.06 
 66.08 
 
 67.10 
 68.12 
 
 71.16 
 
 72.17 
 73-18 
 74-20 
 75-21 
 
 77-23 
 78.24 
 
 79-25 
 80.25 
 81.26 
 
 82.27 
 
 83-27 
 84.28 
 85-28 
 86.29 
 
 88.29 
 
 S3 
 
 '4:3 
 
 5 o 
 
 104.23 
 
 105.22 
 
 106.21 
 
 .02 
 .02 
 .01 
 .02 
 
 .02 
 
 .02 
 
 o.oo 
 
 - 99 
 
 ' 99 
 0.99 
 
 ' 99 
 
 IO7.2O 
 108.19 
 109.18 
 
 116.16 ' 98 
 
 1 11.15 " 
 
 0.99 
 117.06 
 118.04 ' 98 
 119-02 ' 98 
 I20.OO g 
 
 120.98 ' 9 . 
 0.98 , 
 
 121.96 
 
 64.06 
 65.09 
 
 66.il 
 
 68.16 
 69.19 
 70.21 
 
 73-27 
 74-29 
 75-30 
 76.32 
 
 78.35 
 79.36 
 
 82.40 
 
 8441 
 86!42 
 
 88.43 
 
 89-44 
 90.44 
 91.44 
 
 93-44 
 94-43 
 
 97.42 
 
 0.09 
 
 0.99 
 
 101.38 -99 
 
 IO2.37 ' 
 
 " 0.99 
 
 103-36 
 
 0.09 
 IO8.29 
 109-27 - 9 
 110.25 ' 
 
 "5:1! 
 
 118.06 
 1 19-04 
 120.0! 
 
 - 
 
 ' 98 
 - 97 
 
 65.10 
 66.14 
 67.18 
 
 68.21 
 
 69-24 
 70.27 
 
 7I-30 
 72-33 
 73-35 
 
 74-38 
 75-40 
 76.42 
 77-44 
 
 80.50 
 81.51 
 82.52 
 
 84-55 
 85-56 
 
 87-57 
 88.58 
 
 89.58 
 
 93-58 
 
 04 
 
 .03 
 
 .03 
 
 > O < 
 
 97-56 
 98-55 ;; 
 
 99-54 . 00 
 
 IOO -53 o 9 9 ' 
 101.52 
 
 102.50 ' 
 
 I0 3-49 ;^ 
 
 104-47 
 
 !33 
 
 118.10 ' 97 
 0.97 
 
 122.92 
 
 122 QI "'* 
 
 '9 0.96 
 123.87 
 
 66.16 
 67.20 
 68.25 
 
 70-33 
 
 72.40 
 
 73-43 
 74.46 
 
 75-49 
 76-52 
 77-55 
 78.57 
 79-59 
 80.62 
 81.64 
 82.65 
 83.67 
 84.68 
 
 85.70 
 
 87.71 
 88.72 
 
 90-73 
 
 93-73 
 94-72 
 
 .03 
 
 97.70 
 98.69 
 99-68 
 
 100.67 
 101.65 
 102.63 
 103.61 
 104-59 
 105-57 
 
 109.47 
 
 ' 
 
 '" 
 
 0.99 
 0.98 
 
 0.97 
 
 "3-34 
 
 117.18 
 
 120.05 
 
 0.95 
 
 121.01 -<* 
 121-96 ' 9 * 
 122-91 
 
 I24.8I 
 
 68.28 
 69-33 
 
 72-47 
 73-51 
 
 74-54 
 75.58 
 
 76.62 
 
 77-65 
 78.68 
 
 79-71 
 
 81.76 
 82.78 
 83.80 
 84.81 
 
 86.84 
 87.85 
 88.86 
 89.87 
 90.88 
 
 91.88 
 92.88 
 93-88 
 94.87 
 95-87 
 
 04 
 
 
 
 106.67 
 107.64 
 
 108.61 
 
 110.54 o' 9 ^ 
 
 m 
 
 "5-33 ;^ 
 
 116.29 
 
 I IT ->, - S 
 
 Ii 9 :i4- 95 i 
 120.08 ' 94 ' 
 
 0.95 
 
 - 94 
 
 122.91 
 
 iss - 
 
 V 0.94 
 125-73 
 
 69.36 
 70.42 
 
 73-58 
 
 74-62 
 75-67 
 76.71 
 
 77-75 
 78.78 
 79.81 
 80.85 
 81.88 
 
 82.90 
 83.92 
 84-95 
 85-97 
 86.98 
 
 88.00 
 89.01 
 90.02 
 91.02 
 92.02 
 
 93-03 
 94-02 
 95-02 
 96.01 
 
 97-99 
 
 98.98 
 
 99.96 
 
 100.95 
 
 101.93 
 
 05 
 
 79 
 
 1 11.60 "' 
 
 0.95 
 
 114.46 " 9S 
 IIS 41 ' 9S 
 
 "6^35 ' 94 
 
 00 0.95 
 117.30 
 118.24 - 94 
 II9I8 ' 94 
 120.12 ' 94 
 
 124.79 
 125-71 
 126.64 
 
 0.93 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 .01 
 
 e = .02 
 
 .03 
 
 e = .04 
 
 .05 
 
 .06 
 
 .07 
 
 M 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
 j;^! -" 
 i22 -97 ::ii 
 
 I2 3'95 99 
 124.94 
 
 0.99 
 
 126.92 
 
 !3S 
 
 0.99 
 
 '33-83 
 '34-82 
 
 0"-/V 9 g 
 
 138:76 ' 99 
 
 I) 75 ' 99 
 
 '39.75 0-98 
 
 '4-73 o 98 
 141.71 
 
 isi 
 If = 
 
 149-58 ' 9 
 
 '5-57 
 
 . 08 
 
 - 98 
 
 '54-50 
 
 157-44 
 158.43 
 159-41 
 160.39 
 
 - 98 
 
 168.24 
 169.22 
 
 170.20 
 
 - 98 
 0.98 
 
 0.98 
 
 '77^ ; 98 
 179.02 
 
 180.00 
 
 8 
 
 121.96 
 
 
 126.85 
 127.83 - 98 
 128.80 - 9 ' 
 129.78 - 98 
 '30-75 - 
 
 133-67 
 134-65 
 135-62 
 
 146.48 
 
 - 97 
 0.97 
 
 143-38 " 
 144-35 * 
 145-32 HI 
 
 146.29 
 147.26 - 9 ' 
 
 148.22 ' 96 
 '49-19 ' 9 I 
 150.15 
 
 151.12 
 
 0.97 
 0.97 
 
 154.02 
 
 '54-98 
 
 157-88 
 158.84 
 159.80 
 
 160.77 
 
 0.97 
 
 0.96 
 0.96 
 
 0.96 
 
 179-04 \l 
 180.00 
 
 122.92 
 
 285 
 
 S 
 
 
 
 0.96 
 
 ss 
 
 140.24 
 
 143.10 
 144.05 
 145.01 
 I45.96 
 146.91 
 
 0.95 
 
 151.67 94 
 
 53 "95 
 
 154-51 
 
 15546 ' 
 
 
 
 157-35 
 158.30 
 
 7 0.95 
 161.14 
 162.08 ' 94 
 163.02 Ol 
 
 163-97 ' 
 164.91 Q 4 
 
 165.86 
 166.80 ' 94 
 
 167.75 ' 
 168.69 ' 
 
 1 69-63 ' 9 ! 
 
 172.46 
 
 '73-40 
 '74-35 
 
 177.17 
 
 179.06 
 180.00 
 
 - 94 
 - 9s 
 
 0.94 
 
 
 128.65 
 
 -9-60 ::ii 
 
 0.95 
 
 'SS HI 
 
 US - 
 
 '37-'8 :- 
 
 140.01 
 140.96 ' 9S 
 
 O.QA 
 
 '4'-9 0.94 
 142.84 
 
 149-39 
 150.33 
 
 152.20 
 
 0.01 
 
 
 154-99 .: 
 I55-92 
 
 156.85 
 157.78 * 
 158.71 93 
 
 159-64 ' 93 
 160.57 ' 93 
 
 ' 0.93 
 161.50 
 162.42 ' 92 
 
 I63-35 
 164.28 
 
 165.21 ' 93 
 0.92 
 
 166.13 
 167.06 ' 93 
 167.98 ' 92 
 168.91 ' 93 
 '69.83 - 9 * 
 
 I72.6I 
 
 173-53 
 174.46 
 
 175.38 
 
 ' 93 
 
 179.08 
 iSo.OO 
 
 I24?8l A 
 
 125-75 ' 94 
 
 126.70 ' 9S 
 
 127.64 ' 94 
 
 128.59 ' 9S 
 
 y 0.94 
 
 I2 9-53 . 94 
 130.47 
 
 lg o 
 
 '33- 2 0.93 
 134.21 
 
 136.08 " 93 
 137.02 ' 94 
 137.95 ' 93 
 
 J/ - y;> 0.93 
 138.88 
 
 139-81 ' 93 
 
 I4O.73 " 9 
 
 141.66 ' 93 
 
 142.59 ; 93 
 
 143-51 
 144-43 
 145-36 
 146.28 
 147.20 
 
 
 - 92 
 0.92 
 
 ' 93 
 
 148.12 
 149-05 
 149-97 " 
 150.88 - 91 
 151.80 - 92 
 
 0.92 
 
 152.72 
 
 (. 0.91 
 
 T e ee O.9 2 
 
 iig - 91 
 
 0.92 
 O.9I 
 
 159.12 
 160.03 
 
 I6I.85 
 162.76 
 163.67 
 164.58 ' 91 
 165.49 Q - 
 
 I66.4O 
 
 167.31 ' 91 
 168.21 
 169.12 ' 91 
 
 170.03 ' 91 
 0.91 
 
 I7O.94 
 
 171-84 - 9 
 172.75 . 
 173.66 " 
 
 174.56 ' 
 0.91 
 
 177-28 
 178.19 
 179.09 
 
 180.00 
 
 127.60 
 
 132.25 
 134.10 
 
 136.86 
 139.61 
 
 . 93 
 093 
 
 0.92 
 
 0.92 
 0.92 
 
 142.35 
 143.26 
 
 144.18 
 145.08 
 
 145-99 
 146.90 
 
 0.92 
 
 0.90 
 
 iss 
 
 162.20 
 163.09 ' 89 
 '63.98 ' 89 
 164.87 ' 89 
 
 '65-77 n 9 
 166.66 
 
 ,.- ,, 0.89 
 
 
 O.89 
 0.89 
 
 0.89 
 
 175.56 
 176.45 
 
 179.11 
 ISO.OO 
 
 8Q 
 
 9 
 
 '30-33 
 
 '33-07 
 '33-99 
 '34-90 
 
 '3 8 -53 
 '39-43 
 
 . 
 
 142.13 
 I43.03 
 
 I44.83 
 
 O.90 
 0.89 
 
 147.51 
 148.40 
 
 149.29 
 
 - 
 
 - o. 
 
 153-73 
 154.61 
 
 155-49 
 156.38 
 157.26 
 
 158.14 
 159-02 
 159.90 l^l 
 l6O.78 ' 
 
 161.66 ' 88 
 0.87 
 
 162.53 n 8R 
 
 l6 3-4' o M 
 164.29 ' 88 
 
 165.16 ' 
 166.04 
 
 166.91 
 167.79 
 168.66 
 169.54 
 
 .88 
 
 171.28 
 172.16 
 I73.03 
 I73.90 
 174-77 
 
 175.64 
 176.52 
 
 177-39 
 
 179.13 
 180.00 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 e = .08 
 
 e = .09 
 
 .10 
 
 e = .11 
 
 .12 
 
 .13 
 
 .14 
 
 M 
 
 
 
 1 
 
 2 
 3 
 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 
 56 
 57 
 58 
 59 
 
 60 
 
 o.oo 
 1.18 
 2.36 
 3-53 
 4.71 
 
 5-89 
 7.06 
 
 9-42 
 10.59 
 
 14.11 
 15-28 
 
 17-63 
 18.79 
 19.96 
 
 22.29 
 
 23-46 
 24.62 
 25-78 
 26.94 
 
 29.26 
 30.41 
 
 32.71 
 33-86 
 
 35-01 
 36-16 
 37-30 
 38.44 
 39-58 
 
 40.72 
 41.85 
 42-98 
 44.11 
 
 45-24 
 
 46.37 
 47-49 
 48.61 
 
 49-73 
 50-84 
 
 5I-96 
 53-07 
 54-17 
 55-28 
 56.38 
 
 57-48 
 
 59-67 
 60.76 
 
 65.10 
 66.18 
 67-25 
 
 68-33 
 
 18 
 
 18 
 
 17 
 18 
 
 a 
 
 17 
 
 >I7 
 .18 
 .17 
 .17 
 
 .16 
 .17 
 
 17 
 .16 
 
 17 
 
 O.OO 
 1.20 
 2. 4 I 
 
 3-61 
 
 A 
 
 1.20 
 
 9.6l *' 20 
 
 I0 ' 81 \\ll 
 
 12.01 
 
 13-21 '- 20 
 
 * T on 
 
 17-99 
 19.18 
 20.37 
 21.56 
 22.75 
 
 23-94 
 25.12 
 
 66.17 
 
 28.67 
 
 29-84 
 31.02 
 32.19 
 33-36 
 34-53 
 
 35-70 
 36.87 
 38.03 
 39-19 
 40.34 
 41.50 
 42-65 
 43.80 
 
 44-95 
 
 47-23 
 49-51 
 
 1. 19 
 
 1.18 
 
 1. 19 
 
 1.18 
 1.18 
 1. 17 
 
 1. 17 
 1. 17 
 
 i 
 
 ;:;* 
 
 1.14 
 1.14 
 
 1.14 
 1. 13 
 
 52.89 
 
 54-02 
 
 55-14 
 56-26 
 
 57-37 
 58.48 
 
 59-59 
 60.70 
 61.80 
 
 I 13 
 
 3 
 
 I 12 
 
 '- 09 
 
 o.oo 
 
 1-23 
 2.46 
 
 3.69 
 4.91 
 
 6.14 
 7-37 
 8-59 
 9.82 
 11.04 
 
 15-93 
 17-15 
 
 23 
 '" 
 
 1.23 
 
 22 
 
 20.80 I-22 
 
 22.01 '" 
 
 II 
 
 69.42 
 
 37-59 
 38-77 
 39-95 
 4I.I3 
 
 42-30 
 43-47 
 44.64 
 45.80 
 46.96 
 
 48.11 
 
 b < :: * 
 51.57 i'i* 
 52.71 
 
 53.85 
 
 54-99 
 56-12 
 
 57-25 
 58-38 
 
 59-50 
 60.62 
 
 61.74 
 62.85 
 
 1.18 
 1.18 
 
 I.IS 
 1. 17 
 
 1. 17 
 1. 17 
 
 1.16 
 I.IS 
 
 . 14 
 
 * 
 
 67.26 
 
 68.35 
 69.44 
 
 70.53 
 
 O.OO 
 
 1-25 
 2.51 
 
 3-77 
 
 5-02 
 
 6.27 
 
 7-52 
 
 8.78 
 
 10.03 
 
 11.28 
 
 13^8 
 15-02 
 16.27 
 
 I7-5I 
 18.76 
 20.00 
 21.24 
 22.47 
 23.71 
 
 24-94 
 26.17 
 
 28^63 
 29-85 
 
 31-07 
 32.29 
 33-50 
 34-71 
 35-92 
 
 37-13 
 39-54 
 
 A 
 i. 25 
 
 r je 
 5 
 
 I.2S 
 
 ** 
 
 i. 25 
 
 1.25 
 
 1.23 
 i. 33 
 
 1.23 
 
 1.22 
 1.22 
 
 1.22 
 1. 21 
 1. 21 
 
 . ,. 
 
 ' 
 
 " 
 
 ' 9 
 
 43-H 
 44-30 
 45-48 
 46.66 
 47.84 
 
 49.01 
 50.18 
 
 1.18 
 1.18 
 1.18 
 1.17 
 
 S6 ' I.is 
 
 54-82 
 55-97 * 
 57-ii 
 58-26 '* 
 
 59-39 ,;,* 
 
 60.53 . 
 61.66 3 
 
 62.78 r 
 
 63-90 '" 
 
 66.13 
 67.24 
 
 71.64 
 
 r 
 
 
 0.00 
 
 1.28 
 2.56 
 3.85 
 
 7.69 
 
 8-97 
 10.24 
 
 11.52 
 
 12.80 
 14.07 
 
 15-34 
 16.62 
 
 20.42 
 21.68 
 
 22.94 
 24.20 
 
 25.46 
 26.72 
 
 30.46 
 
 32-94 
 34.18 
 
 35-41 
 36.64 
 
 39-09 
 40.31 
 41-53 
 42-74 
 
 43-95 
 45-15 
 46.35 
 47-55 
 48.74 
 
 49-93 
 51.11 
 52.29 
 53-47 
 54-64 
 
 55-8i 
 
 58.13 
 
 59-28 
 
 6i-57 
 62.71 
 
 63-85 
 64.98 
 66.10 
 
 67-23 
 68.34 
 
 69-45 
 70.56 
 
 72.76 
 
 .28 
 
 .27 
 .28 
 .28 
 
 .27 
 
 .27 
 
 27 
 
 .26 
 
 
 22 
 
 22 
 21 
 21 
 
 20 
 20 
 20 
 If 
 
 10 
 
 ll 
 
 18 
 It 
 
 
 14 
 
 14 
 .13 
 
 .12 
 
 .13 
 
 .II 
 .II 
 
 O.OO 
 2.62 
 
 3-93 
 
 22.14 
 23-43 
 
 34-87 
 36-13 
 37.38 
 
 38-63 
 39-87 
 
 42-34 
 43-57 
 
 44.80 
 46.02 
 47-24 
 48-45 
 49.66 
 
 50.86 
 
 53-25 
 54-44 
 55-63 
 
 56-81 
 57.98 
 59-15 
 
 61.48 
 
 62.63 
 63.78 
 
 64-93 
 66.07 
 67.20 
 
 68.33 
 
 
 
 6.55 ' 
 
 7-85 ' 3 
 9.16 
 
 10.47 *' 31 
 
 "77 ;:*: 
 
 ,8.27 
 
 1.29 
 
 1.29 
 
 2 5-99 . . 
 2 7- 2 7 I'll 
 
 28.55 *! 
 
 
 I 4 
 
 ' 
 
 1.22 
 1.22 
 1. 21 
 1. 21 
 1.20 
 
 I. 2O 
 1. 19 
 1. 19 
 
 70-57 
 71.69 
 
 73-90 
 
 I.IS 
 
 I.IS 
 I.IS 
 
 1.14 
 
 1. 13 
 1. 13 
 
 1. 12 
 1. 12 
 1. 12 
 
 0.00 
 
 i-34 
 2.68 
 4.02 
 5-35 
 6.69 
 
 9-36 
 10.70 
 12.03 
 
 14.69 
 16.01 
 
 17-34 
 18.66 
 
 19.98 
 21.30 
 22.62 
 23-93 
 
 1.34 
 
 1.33 
 1.33 
 
 1.33 
 
 1.32 
 32 
 
 '- 30 
 
 26.54 
 27-84 
 
 29 -'4 ;;-; 
 30.44 ' 
 
 34-30 
 35-58 
 36.86 
 
 50.59 
 51.81 
 
 53-02 
 
 1. 25 
 
 I.2S 
 
 1.25 
 1.23 
 
 1.22 
 1.23 
 1.22 
 
 1. 21 
 I. 21 
 1. 21 
 
 60.19 
 
 61.37 
 
 66.02 
 
 67.17 
 68.31 
 
 70.57 
 71.70 
 72.82 
 
 73-93 
 75-04 
 
 o 
 
 '- 18 
 
 1.16 
 I.IS 
 
 1. 13 
 
 1. 13 
 
 1.13 
 
 
 1 
 
 2 
 3 
 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
8 
 
 TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 e = .08 
 
 .09 
 
 .10 
 
 .11 
 
 .12 
 
 e = .13 
 
 e = .14 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
 
 A 
 
 i. 06 
 1.07 
 i. 06 
 i. 06 
 1.06 
 
 i. 06 
 
 I u- 1 tj 
 
 76.80 
 
 77.84 
 
 78.88 
 79.92 
 80.96 
 81.99 
 
 84.05 
 85.08 
 
 86.10 
 87.12 
 88.13 
 
 89.15 
 90.16 
 91.17 
 92.17 
 93-17 
 
 99-13 
 100.11 
 
 1.04 
 1.04 
 
 i. 02 
 
 1.02 
 
 103.04 
 
 I04.O2 
 104.99 
 
 106.92 
 107.88 
 
 108.84 
 I09.8O 
 110.75 
 
 112.65 
 II3.60 
 114-54 
 115-49 
 
 0.99 
 0.99 
 0.99 
 
 0.98 
 
 0.97 
 0.98 
 
 0.97 
 0.96 
 
 O*97 
 0.96 
 
 0.96 
 
 0.9S 
 
 
 ' 94 
 
 122.02 
 
 122.95 
 123.87 
 124.79 
 125.71 
 126.62 
 
 127-54 
 
 ' 93 
 0.93 
 
 70.50 
 71.57 
 
 7 2 ' 6 4 
 73-70 
 
 05 
 04 
 
 03 
 
 77-93 
 78-98 
 
 80.03 
 81.07 
 82.11 
 83.14 
 84.18 
 
 85.21 
 86.23 
 
 87-25 
 88.27 
 
 89-29 
 90.30 
 91-31 
 92.32 
 93-32 
 94-32 
 
 97-30 " 
 98.29 ' 99 
 99.28 
 
 100.26 
 101.24 
 
 IO2.2I 
 
 .01 
 .01 
 
 ' 99 
 0.98 
 
 ' 9 
 ' 97 
 
 105.12 
 106.09 ' 97 
 107-05 
 108.00 
 
 ' 96 
 
 ' 9S 
 ' 94 
 
 III.8I 
 112.75 
 113.6$ ' 94 
 114.63 
 
 115-57 
 116.50 
 II744 
 
 0.94 
 0.94 
 0.93 
 0.94 
 
 0.92 
 
 119.29 
 120.22 
 121.14 
 I22.O6 
 122-97 
 
 123.89 
 124.80 
 125.71 
 126.62 
 127.52 
 
 128.43 
 
 ' 93 
 
 0.92 
 
 - 9 
 
 0.91 
 
 72.69 *- 
 
 73-76 ' 
 
 75-9 r 06 
 
 76.96 l *"5 
 
 78.02 '- * 
 
 79-08 '- 06 
 
 
 83.26 
 
 1.03 
 1.03 
 
 86.36 
 
 S7-39 ^ 
 
 90.45 ;;;; 
 
 92 '47 |'oo 
 93-47 
 
 94-47 . 
 
 95-47 j; oo 
 96.47 
 
 97-46 ' 99 
 
 
 
 
 101.39 
 102.36 - 97 
 
 "' 
 
 106.22 
 
 107.18 - 96 
 
 108.13 - 9 f 
 
 109.09 - 96 
 
 116.03 - 94 
 
 0.95 
 IIO.98 
 
 111.92 ' 94 
 
 112.86 ' 94 
 
 113.80 - 94 
 114-73 
 
 ' 93 
 ' 92 
 
 ' 92 
 0.91 
 
 117.52 
 119-36 
 
 120.27 
 121.19 
 
 122. IO 
 123.01 
 123.91 
 
 124.82 
 125.72 
 
 126.62 -? 
 
 129.30 
 
 0.91 
 
 74-89 
 
 75-97 
 77.04 
 
 i. 08 
 i. 08 
 1.07 
 
 I. O6 
 
 1.06 
 
 
 
 84.42 
 85.46 
 86.49 
 
 87.52 
 88.55 
 89-57 
 
 92.61 
 93.62 
 94.62 
 
 1.03 
 
 - 98 
 
 o.oo 
 
 
 ' 
 
 - 9 
 
 109.21 
 110.16 ' 9S 
 
 III. 10 ' 94 
 0.94 
 112.04 
 112.97 ' 93 
 I: 3-90 "* 
 
 116.68 
 
 117.60 - 92 
 118.51 - 91 
 119.42 - 91 
 
 121.24 
 !>> iT 
 
 122. 14 
 
 
 78.19 
 
 80^32 
 81.38 
 
 83-49 
 
 85^58 
 86.62 
 87.66 
 
 88.69 
 89.71 
 90.73 
 91-75 
 92.76 
 
 r 
 
 I.OO 
 
 S 
 
 
 1.04 
 
 1.03 
 
 1.02 
 1.02 
 1.02 
 I .OI 
 I.OI 
 
 95-77 I00 
 96.77 
 
 97-76 ' 99 
 
 0.99 
 
 99 71 ' 98 
 
 lOC^I ' 98 
 
 101.68 " 97 
 
 102.65 ' 97 
 
 0.97 
 IO3.62 
 
 -4.58 ; 9 6 
 
 Io6 -5 ' 9 t 
 
 I08 '4 0.94 
 
 109.34 
 
 110.28 ' 94 
 
 1 1 1.22 ' 94 
 
 112.15 ' 93 
 
 0.93 
 II3.O8 
 
 0.93 
 
 117.68 
 118-59 
 119.50 ~" 
 I2O.4O 
 121.30 - 9 
 
 122.19 
 
 0.00 
 
 !li a 
 
 130.16 
 
 I26 ' 6 4 
 
 131.01 
 
 0.88 
 
 73-9 
 75.00 
 
 76.09 
 77-18 
 
 81.48 
 
 82.55 
 
 84.66 
 85-70 
 86.75 
 87-79 
 88.82 
 
 89.85 
 90.87 
 91.89 
 92.91 
 93-92 
 94.92 
 95-92 
 96.92 
 
 97-91 
 
 03 
 
 - 99 
 
 ; 99 
 
 101.84 
 
 102.80 
 
 -3-77 
 
 106.64 - 9 
 
 ' 92 
 
 l^.2S ' 93 
 
 113.20 - 92 
 
 0.92 
 114.12 
 
 115.04 
 
 115.96 "" 
 
 116.86 - 90 
 
 "7-77 ; 9 | 
 118.68 
 
 0.90 
 0.89 
 0.89 
 
 0.88 
 0.88 
 
 126.66 
 
 127-53 
 128.40 
 129.27 
 
 131-85 
 
 a 
 
 A 
 
 7p4 ;: 
 80.50 
 
 S a 
 
 1.04 
 
 1.03 
 1.03 
 
 86.88 
 87.92 
 88.96 
 89.99 
 
 91.02 
 
 92.04 *' 
 93-06 ' 
 
 94-07 . 
 95-oS i ' Qo 
 
 96.08 
 97.07 ' 99 
 98.07 
 99.06 - 99 
 
 IOO -4 o^s 
 
 IOI.O2 
 101.99 9 ' 
 102.96 ' 97 
 1 03-92 ' 9 , 
 
 107.74 - 9S 
 
 108.68 ' 94 
 
 109.62 ' 94 
 0.93 
 
 - 93 
 
 112.40 
 
 0.91 
 
 116.97 
 117.87 
 
 119.66 
 
 a 
 
 124.08 
 
 I2 4-95 
 125.82 
 126.69 
 
 0.88 
 ).8 7 
 
 ' 7 
 
 
 132.67 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 e = .08 
 
 e = .09 
 
 .10 
 
 e = .11 
 
 e = .12 
 
 e = .13 
 
 .14 
 
 Jtf 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
 130.27 
 I3i. i8 
 
 132.08 
 
 136-58 
 137.48 
 138.37 
 
 0.90 
 
 0.91 
 0.90 
 0.90 
 
 
 0.89 
 
 145.47 
 
 146.35 
 147-22 
 
 0.87 
 
 0.88 
 0.87 
 
 0.88 
 0.87 
 
 '53-34 ; 8 ; 
 
 ig: 8 - 87 
 
 155-95 H 
 156.82 ' 87 
 157.68 
 
 158.55 
 15942 
 160.28 
 161.14 
 162.00 
 
 162.86 
 163-73 
 ' 6 4-59 u '" 
 165-45 
 166.30 ^ll 
 
 167.16 
 '68.02 - 8 * 
 168.88 ' 8 , 
 
 86 
 
 - g, 
 
 
 
 0.86 
 0.87 
 
 
 174.87 
 
 175-73 
 176.58 
 
 177-44 
 178.29 
 
 "" 
 
 129.33 
 130.22 
 
 ' 89 
 
 '35-58 I' 8 
 ^46 
 
 142.61 
 143-48 
 144-35 
 145.22 
 
 146.09 
 146.96 
 147.82 
 148.69 
 149-55 
 
 
 0.87 
 0.87 
 0.87 
 0.87 
 
 0.87 
 0.87 
 
 Rfi 
 
 - 8 < 
 
 !* 
 
 I53.84 
 
 I54-69 
 155-55 
 156.40 
 I57.25 
 158.10 u o - t l 
 
 158.95 
 '59-80 O BS 
 160.65 1* 
 161.49 
 162.34 
 
 163.19 
 164.03 
 164.88 
 165.72 
 166.56 
 
 167.41 
 168.25 
 169.09 
 
 0.85 
 
 180.00 
 
 174-97 
 175.81 
 176.65 
 
 1/7-49 
 178.32 
 179.16 
 
 180.00 
 
 a 
 
 
 ' 
 
 129.30 
 
 g 
 
 134.6 
 
 137.23 
 138.10 
 
 0.88 
 
 * 
 
 087 
 
 '45-85 
 
 
 :- 
 
 
 158.51 
 159-34 
 161.01 
 
 163.50 
 
 165.16 
 
 165-99 
 166.82 
 
 167.64 
 
 
 
 . 
 
 ; 
 
 g, 
 
 : 
 
 
 '75-07 
 
 
 
 138.84 
 
 '39-69 
 '4'54 
 141.40 
 
 143.09 
 '43-94 
 144.79 
 
 I45.63 
 146.47 
 
 H7.3I 
 148.15 
 
 
 
 '54-80 
 
 '59-73 
 
 163.81 
 164.63 
 
 167.88 
 168.69 
 
 82 
 
 
 * 
 
 
 
 '73-54 
 
 180.00 
 
 179.19 
 180.00 
 
 0.81 
 . 8I 
 
 131.01 . 
 131.88 ' 87 
 
 3 2 -74 ; 86 
 
 133-60 
 '34-46 3 
 
 lyjtn - 8 s 
 '38-72 \ll 
 
 139-56 
 140.41 - 8 * 
 
 142.08 ' 83 
 
 '43-75 
 144-59 
 I45-42 
 146.25 
 
 I47.07 
 
 147.90 
 
 152.01 
 
 156.07 
 
 156.88 
 
 i6o.n 
 
 g 
 
 
 - 8 
 
 162.52 
 
 0.80 
 
 165.71 " 79 
 166.51 ' 8 
 
 l68.il 
 168.90 ' 79 
 169.70 Ol 
 170.49 ' 
 
 0.79 
 172.08 
 172.87 ' 79 
 '73-67 ' 8 
 
 
 180.00 
 
 - 
 
 0.79 
 
 
 136.09 
 136.93 
 137-77 
 138.61 
 
 139-44 
 
 141-93 
 142.76 
 
 H6: 4 - 8 * 
 146.86 ' 82 
 
 147.67 
 
 ' 0.81 
 
 148-48 . 
 
 III; 
 
 160.48 
 161.27 '" 
 162.05 ' 78 
 162.84 ' 79 
 
 164.41 
 165.20 
 
 
 168.33 
 169.11 ' 
 169.89 ' 78 
 170.67 
 '''45 
 
 0.78 
 0.78 
 0.78 
 
 174 56 ' 77 
 175-34 I'.H 
 176.12 
 176.89 ' 77 
 177.66 ' 77 
 
 'o ., 0.78 
 
 178-44 , 
 
 179.22 ' 78 
 
 0.78 
 
 180.00 
 
 ss 
 
 
 136.02 
 
 136-85 
 137-68 
 138-51 
 139-34 
 
 3 
 
 . 8I 
 
 145.04 
 
 
 149-05 
 149.85 
 
 *- 
 
 150-64 
 
 
 '56-95 
 '57-73 
 '5 8 -5' 
 '59- 2 8 
 
 0.79 
 
 0.78 
 0.78 
 
 
 164-70 
 
 I6 5'47 I'll 
 166.24 
 167.01 ' 77 
 
 - 76 
 
 176.08 
 
 
 175-43 
 176.19 
 
 178.48 
 179.24 
 
 180.00 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
10 
 
 TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 .15 
 
 e = .16 
 
 .17 
 
 .18 
 
 .19 
 
 .20 
 
 .21 
 
 M 
 
 
 
 1 
 
 2 
 3 
 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
 o.oo 
 1-37 
 2-74 
 4.10 
 
 5-47 
 6.84 
 8.20 
 
 9-57 
 10.93 
 
 13-65 
 15-01 
 16.36 
 
 r - 37 
 
 1.36 
 
 
 I9 ' 7 1-34 
 20.41 
 
 21.76 X ' 3S 
 
 23-10 J' 34 
 
 " 
 
 i 31 
 
 : : 
 
 '- 30 
 
 27.IO 
 28.43 
 29.76 
 31.08 
 
 33-70 
 
 
 
 8 
 
 
 50.31 
 51-55 
 
 52.78 
 54.01 
 
 55-23 
 56.45 
 
 57-66 
 
 58.86 
 60.06 
 61.25 
 62.44 
 63.62 
 
 64.79 
 65.96 
 67.12 
 68.28 
 69-43 
 
 
 
 3 
 
 1.20 
 1. 19 
 
 I.I7 
 
 I.I4 
 I.I4 
 
 72.84 
 
 73-97 
 75-09 
 
 76.20 
 
 o.oo 
 1.40 
 2.80 
 
 5-59 
 6.99 
 
 8-39 
 
 9.78 
 
 11.17 
 
 13-95 
 15-34 
 16.72 
 18.10 
 19.48 
 
 20.86 
 22.23 
 23.60 
 24.96 
 
 , 
 'to 
 
 .39 
 
 8 
 
 29.03 
 
 33 
 
 .36 
 .36 
 1.36 
 
 1.35 
 1.35 
 
 33-07 l\H 
 
 34-40 
 35-73 . 
 37-06 '" 
 38.38 I' 3 ' 
 59-69 I3I 
 41.00 
 42.30 ' 
 43.6O * 
 
 & I- 
 
 5- 
 
 55-01 
 
 57-47 
 58-69 
 
 59-91 
 61.12 
 62.32 
 
 ! 
 
 . Ig 
 
 
 65.89 
 67.07 
 68.24 II17 
 
 69.40 ? 
 
 70-56 l? s 
 
 73-99 
 75-12 
 76.24 
 
 o.oo 
 
 1-43 
 2.86 
 4.29 
 
 5-72 
 
 IO.OO 
 
 11.42 
 
 12.84 
 
 14.26 
 
 1.43 
 1.42 
 
 1.43 
 
 1.42 
 
 
 22 
 
 24 -" 
 
 25.50 ' 
 
 74.01 
 
 75.15 
 76.28 
 
 77.41 
 78.53 
 
 Mi 
 
 28 - 2 7 
 
 35-12 
 36-47 
 37-82 
 
 40.50 
 
 41.83 
 43-15 
 44-47 
 45-78 
 47.08 
 
 50.95 
 52.23 
 53-50 
 
 54-77 
 56.02 
 
 57-27 
 
 59-75 
 60.98 
 62.20 
 63.41 
 64.62 
 65-82 
 
 67.01 
 69.37 
 
 1.38 
 1.38 
 1.37 
 1.36 
 1.36 
 
 1.35 
 
 3 
 
 '- 30 
 1.30 
 
 . 2! 
 ' 
 
 i. 20 
 
 1. 19 
 
 1.18 
 1.18 
 1. 17 
 
 1.13 
 1.13 
 1. 12 
 
 0.00 
 
 2.93 
 
 4-39 
 
 5-85 
 
 7-31 
 8-77 
 
 14.58 
 
 i6 - 3 
 
 17-47 
 
 21.78 
 23.21 
 24.64 
 26.06 
 
 28.88 
 
 33-08 
 34-47 
 35-86 
 
 37-23 
 38.60 
 
 39.96 
 
 44.02 
 
 45-35 
 46.68 
 48.00 
 
 49-32 
 
 53-22 
 54-51 
 
 55-79 
 57-o6 
 
 59-57 
 
 62.06 
 63.29 
 64.51 
 
 65-73 
 66.94 
 
 68.14 
 69-33 
 70.51 
 71.69 
 
 74.02 
 75-17 
 76.32 
 77.46 
 78.59 
 
 79-71 
 
 A 
 .46 
 
 47 
 
 
 
 
 s 
 
 ; 
 
 
 
 o.oo 
 
 A 
 1.50 
 
 4-49 
 5-98 
 
 7.48 
 8.97 
 
 1.50 
 
 I 4-9 I 
 
 1.47 
 1.48 
 
 1.47 
 22.27 
 
 Si8 [H 
 26.63 
 
 28.07 '' 44 
 ' 1-44 
 
 5o ; 94 ;; 
 
 55-7? \ 4 ' 
 35-20 j"Jj 
 
 36.61 . 
 
 38.01 x 
 
 39-40 !' 
 
 40.79 T ' 
 
 45-54 
 44-90 
 
 ,?, 
 
 50.28 
 
 51.60 3 
 
 52-92 I' 3 ' 
 
 54-23 T , 
 
 55-; 
 56.82 
 
 1.29 
 
 63.16 
 
 64.40 
 
 65.63 
 
 66.86 
 
 
 72.85 
 
 74-03 
 
 
 79-77 
 80.90 
 
 o.oo 
 
 1-53 
 3.06 
 
 4-59 
 
 A 
 1.53 
 
 . 
 9' 17 5 
 
 ' 
 
 13.73 l\ll 
 
 15.25 . 
 16.76 
 
 T o - 1.51 
 
 22.76 
 24.25 
 
 f 
 
 g 
 
 28 - 68 
 
 33.06 
 34-51 
 
 35-95 
 
 37-38 
 38.81 
 40.22 
 41.63 
 43-03 
 
 J.iO 
 
 1.44 
 
 1-43 
 1.43 
 
 1.41 
 
 47-18 
 
 49-91 z 
 
 51.26 
 52.60 ' 
 
 53-93 . 
 55-26 
 
 56-57 , 
 
 57-88 
 59.18 
 
 :-s 
 
 ts ::" 
 
 69.22 '" 
 
 * 1.22 
 
 72.84 
 74.03 
 
 76.38 
 
 78.69 
 
 79.83 
 80.97 
 
 82.10 
 
 I. IS 
 
 1.14 
 1.14 
 
 1. 13 
 
 o.oo 
 1-56 
 3-i3 
 
 I.S7 
 1. 57 
 
 10.94 
 12.50 
 I4.05 
 
 18.68 
 
 20.22 
 
 53! 
 
 X ' S * 
 
 
 33-78 
 36.72 
 
 38.17 
 39.62 
 4I.O6 
 
 45-33 
 
 ^ 
 I>47 
 1.45 
 
 49-51 
 
 . , 
 - 3 
 
 52.26 
 
 55-62 x - 3 
 
 54.96 x ' 34 
 
 56.30 ' 34 
 
 57-63 ,;" 
 58.95 ,' 
 
 60.26 I-3X 
 
 61.56 r - 3 
 
 62.85 ;'' 
 
 - 
 
 67.91 
 
 69-15 
 70.38 
 
 71.60 
 72.82 
 74.02 
 75-21 
 76.40 
 
 77-57 
 78-73 
 
 81.03 
 82.17 
 
 83-30 
 
 1.17 
 1.16 
 
 
 
 1 
 
 2 
 3 
 
 4 
 
 5 
 6 
 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
TABLES FOR THE TRUE ANOMALY. 
 
 II 
 
 M 
 
 .15 
 
 e = .16 
 
 e = .17 
 
 e = .18 
 
 e = .19 
 
 .20 
 
 e = .21 
 
 M 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 77-31 
 79-50 
 
 81.67 
 
 83*82 
 84.89 
 85-95 
 87.00 
 88.05 
 89.09 
 
 90.13 
 91.16 
 
 92.19 
 
 as 
 
 i. 08 
 
 1.07 
 
 
 - , o 
 
 98-23 
 
 0.97 
 
 105.04 
 105.99 
 106.94 
 107.88 
 108.82 
 
 ' 94 
 
 II2 '53 
 
 "3-45 
 
 ft- 
 
 "9-75 
 I*?'* 4 
 
 0.88 
 
 I22 '4 
 
 0.87 
 
 I26 '73 
 
 s a 
 
 130.97 
 '3'- 8 ' oil 
 
 120 I 133.48 
 
 77.36 
 
 79-57 
 80.67 
 
 83-93 
 85.00 
 
 88.18 
 
 90-27 
 9I-30 
 
 93-35 
 94-37 
 95.38 
 
 97-39 
 
 98-38 
 99-37 
 
 .11 
 .10 
 
 I01 '33 
 I02 '3 
 
 M 
 05 
 
 00 
 . 99 
 
 o 97 
 0.97 
 
 106.14 - 95 
 107.09 - 95 
 
 ' 0.94 
 
 109.90 
 116.83 ' 93 
 
 111.75 
 '* 
 
 112.67 
 "3-58 
 
 114.49 
 
 9 
 0.92 
 
 " 8 -97 
 "9-85 
 
 ! 123-34 
 
 s 
 .? 7 
 
 I25 ' 92 
 
 a 
 a 
 
 130.14 
 
 78.53 
 
 8075 
 81.85 
 
 85-11 
 86.18 
 
 87-25 
 88.31 
 
 89.36 
 90.40 
 91.44 
 92-47 
 93-50 
 
 94-52 
 
 .04 
 .04 
 .03 
 
 99-53 
 
 I00 -si 
 
 I01 '49 
 I02 '47 
 
 O.99 
 
 0.98 
 0.98 
 
 I0 4'39 
 
 ' 94 
 
 106.30 
 107.24 
 
 108.18 
 
 0.94 
 IO9.I2 
 IIO.O5 ' 
 IIO-97 
 111.89 ' 
 
 II2.8I ' 9 
 O.9I 
 
 "7-30 
 
 79-71 
 80.83 
 81.94 
 
 85-22 
 86.30 
 
 8S! 4 3 
 89-49 
 
 90.54 
 
 92.62 
 
 93-65 
 94.67 
 
 95.69 
 96.70 
 
 97-70 
 98.70 
 99.69 
 
 100.68 
 101.66 
 102.63 
 
 107.40 
 
 ogg 
 1 
 
 :s 
 
 134.28 
 
 126.82 
 
 127.66 -* 4 
 
 "8-50 -* 
 
 !:!? - 82 
 f 0.82 
 
 0.82 
 
 0.8 1 
 1 **"* 0.81 
 I35-07 
 
 :ss 
 
 126.88 
 
 131-82 
 
 133-44 
 134-25 
 I35-05 
 
 135.85 
 
 .08 
 
 .02 
 .02 
 
 .00 
 
 .00 
 0.09 
 
 0.97 
 
 
 
 0.93 
 
 I IO.2O 
 III.I2 
 112.04 
 
 "7-43 
 
 120.06 
 120.92 
 
 0.85 
 0.85 
 0.84 
 
 0.83 
 
 0.83 
 0.83 
 0.82 
 0.82 
 0.81 
 
 0.81 
 
 . 80 
 
 82.02 ' 
 
 86.41 
 87.49 
 88.56 
 89.62 
 90.68 
 
 91.72 
 
 93-80 
 94.82 
 95-84 
 96.86 
 97-86 
 98.86 
 
 0.98 
 101.82 
 102.79 ' 97 
 
 104.72 0-96 
 105.67 ' 9S 
 
 ' 0.95 
 IO6.62 
 
 107.56 ' 94 
 
 108.50 ' 94 
 
 109-43 I 
 
 110-35 I'H 
 111.27 
 
 112.19 ' 92 
 
 113-09 ' 9 
 
 114.00 ' 91 
 
 I 4.89 - 89 
 v 0.90 
 
 i TC in 
 
 0.88 
 
 0.88 
 0.88 
 0.87 
 0.87 
 120.17 A 
 
 "*s 
 
 si 4 
 
 a 
 
 128.59 
 
 82 
 
 : 
 a 
 
 I35-83 
 136.62 
 
 82.10 
 83-21 
 84.32 
 85.42 
 
 .08 
 
 04 
 
 88.68 
 
 89.75 
 90.81 
 91.86 
 
 93-95 
 94.98 
 96.00 
 
 98.03 
 
 99-03 
 1 00.02 
 101.01 
 
 102.96 
 
 103-93 
 104.89 
 105.84 "'" 
 106.79 ' 9S 
 
 " 0.94 
 
 109.59 r 
 110.51 
 
 '"43 : 9 ; 
 
 II2 -34 
 
 "5-93 . 88 
 116.81 
 "7-69 !" 
 
 I2 7'83 
 
 129.46 
 
 S 
 
 ' 
 
 
 is? 
 
 i 
 
 0.79 
 
 137-37 
 
 83-30 
 84.42 
 
 85-53 
 86.63 
 
 88.80 
 89.88 
 
 90.94 
 92.00 
 
 93-05 
 
 96.16 
 97.18 
 
 99.19 
 100.19 
 101.17 
 102.15 
 
 ' 98 
 
 106.95 ' 94 
 107.11 ' 94 
 
 108.82 
 
 109-75 
 1 10.67 
 
 "1-59 
 112.50 
 
 113.40 
 114.29 
 
 0.93 
 0.93 
 
 0.90 
 
 o 
 .T 7 
 
 I I6.O7 
 
 117.82 
 118.69 "" 
 
 "9-55 I 
 120.41 
 
 121.26 - 8S 
 0.85 
 
 122 05 ' 84 
 
 :ss ; 
 
 125-45 '. 3 
 
 127.9 
 
 I28.fi 
 
 131.91 
 
 - 79 
 
 136.58 
 
 138.11 
 
 - 77 
 
 ' 77 
 , 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
12 
 
 TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 e = .15 
 
 e = .16 
 
 .17 
 
 e = .18 
 
 e = .19 
 
 e = .20 
 
 e = .21 
 
 M 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
 '33-48 
 '34-31 
 '35-H 
 
 
 
 140.86 
 
 0.81 
 
 . 8o 
 
 '44-87 
 
 . 7 g 
 
 1SJS - 
 AS ::;,* 
 
 '55-06 
 155.83 
 
 157-37 
 
 161.19 
 
 164.99 
 
 165.74 
 166.50 
 167.25 
 168.01 
 
 168.76 
 
 170.26 
 171.02 
 
 0.77 
 0.76 
 0.77 
 0.76 
 0.76 
 
 0.76 
 0.76 
 0.76 
 0.76 
 0.76 
 
 0.75 
 0.76 
 0.7S 
 
 0.75 
 
 0.75 
 0.75 
 0.76 
 
 174.02 
 174.76 
 I75-5I 
 176.26 
 177.01 
 
 0.75 
 0.75 
 
 179-25 
 iSo.OO 
 
 135-92 
 
 '36-73 
 '37-54 
 
 ' 
 
 - . 8o 
 '39-15 . 8I 
 '39-96 - 
 '4-75 
 
 I43.I4 
 143-93 
 144.71 
 I45-50 
 
 146.28 
 147.06 
 147.84 
 148.61 
 I49-38 
 150.16 
 150.93 
 
 I53-23 
 
 153-99 
 I54.76 
 155.51 
 
 0.79 
 
 0.80 
 0.79 
 0.78 
 
 o 78 
 ' 8 
 ' If 
 ' 77 
 
 .77 
 
 ., 6 
 
 >-75 
 ).76 
 
 15778 
 158.54 
 
 
 161.54 07 , 
 162.29 
 163.03 ' 74 
 I63-78 
 
 0.74 
 
 ' 6 -3 :: 7 ; 
 168.97 
 
 l6 9-7i o ; 74 
 
 - 74 
 
 0.74 
 
 171.18 
 171.92 
 
 172.66 
 173-39 
 
 175-60 
 176.33 
 177.80 
 
 S:" - 74 
 0.73 
 
 180.00 
 
 -V3 
 
 135.07 
 '35-88 
 136.68 
 
 14 - uu 0.79 
 
 0.78 
 o. 78 
 
 l -7 
 
 146.88 
 
 I47-65 
 148.42 
 149.18 
 149.94 
 
 150.70 
 
 0.77 
 
 
 153.72 
 
 154-47 
 155-22 
 
 159.67 
 160.41 
 I6I.I5 
 
 161.88 
 162.62 
 
 163.35 
 164.08 
 
 165.54 
 166.27 
 167.00 
 167.72 
 168.45 
 
 169.18 
 169.90 
 170.62 
 
 172.79 
 
 '73-52 
 
 0.74 
 0.73 
 
 0.74 
 
 0.73 
 0.73 
 
 0.73 
 0.73 
 
 0.73 
 0.73 
 
 0.72 
 
 
 
 73 
 
 '75-68 ; 72 
 176.40 
 
 177.12 " 72 
 
 177.84 ' 72 
 
 178.56 ' 72 
 
 179.28 - 72 
 0.72 
 
 180.00 
 
 142.13 
 142.90 
 
 143.67 
 144.44 
 
 0.79 
 0.78 
 0.78 
 
 0.78 
 0.78 
 0.78 
 0.77 
 0.77 
 
 0.77 
 0.76 
 0.76 
 0.76 
 0.76 
 
 0.75 
 
 147-48 
 148.23 
 148.98 
 '49-74 
 150-48 
 
 152.72 "- 13 
 
 153-46 ; 74 
 
 '54-93 
 155.67 ',, 
 156.40 ' 73 
 157.13 
 
 157-86 
 
 ' 73 
 ' 73 
 
 I59-32 ' 73 
 160.05 ' 73 
 
 l6o -77 H 
 161.49 ' 
 * 0.72 
 
 162.21 
 162.94 " 73 
 163.66 ' 72 
 
 111 
 
 169.38 
 170.09 
 170.80 
 
 0.72 
 
 172.93 
 
 '73-64 
 
 0.71 
 
 ).7I 
 ).7I 
 
 176.47 
 177.17 
 177.88 
 
 178.59 
 179.29 
 
 iSo.OO 
 
 136.62 
 
 138.95 
 139-73 
 140.50 
 141.27 
 
 142.80 
 I43-56 
 
 I44-3I 
 I45-07 
 
 
 
 0.78 
 
 
 
 ' 7 
 
 ' O 75 
 
 '47-32 Q 7 * 
 148.06 
 148.80 ' 74 
 149-54 '? 4 
 
 '53-94 
 154-67 
 
 " 
 
 
 158.27 
 
 158.99 
 I59-70 
 
 161.83 
 
 162.54 
 
 163-25 
 163.96 
 164.66 
 165-37 
 
 71 
 
 
 - 70 
 
 167.47 
 168.17 
 168.87 
 
 169-57 
 170.27 
 170.97 
 171.67 
 172.36 
 
 0.70 
 0.70 
 
 174-45 
 I75.I4 
 175-84 
 
 176.53 
 177.23 
 177.92 
 178.61 
 
 180.00 
 
 l 
 
 137-37 
 
 139-68 
 140.44 
 
 I4L95 
 
 144.20 
 
 144-95 
 145-69 
 146.43 
 147.17 
 147.90 
 
 148.63 
 149-36 
 
 07S 
 7 f 
 
 H 
 
 0.7S 
 
 I5I-54 
 152.26 
 152.98 
 153.70 
 
 ; 
 
 . 
 
 I57-96 ' 7 
 
 158.67 ; 7 ^ 
 
 '59-37 
 160.07 - 7 
 160.77 ' 7 
 161.47 - 7 
 
 162.17 -r 
 
 ' 0.69 
 162.86 
 
 Tfil Cfi -' 
 
 167.71 
 168.39 
 169.08 
 
 16977 
 
 170.45 
 171.14 
 171.82 
 172.50 
 
 
 180.00 
 
 0.68 
 0.69 
 0.68 
 
 0.69 
 
 0.68 
 0.68 
 0.69 
 0.68 
 
 0.68 
 0.68 
 0.68 
 0.68 
 0.68 
 
 I38.n 
 
 140.38 
 
 3 
 
 
 
 ' 7S 
 
 O.74 
 
 4 
 7J 
 
 0.73 
 0.73 
 
 141.88 
 142.63 
 
 143-37 
 144.10 
 4l8 4 ' 74 
 
 145-57 
 146.30 
 
 '47-03 o" 
 147-75 '' 
 
 148.48 73 
 0.72 
 
 150.63 ' 
 
 '5'-34 ; 
 152.06 Q ' 
 
 152.76 
 
 153-47 
 
 0.71 
 0.70 
 
 
 
 '55- 
 
 0.69 
 0.70 
 0.69 
 
 '59-06 
 
 163.18 
 
 3 
 
 0.67 
 
 169.28 
 
 169.96 
 170.63 
 171.30 
 
 0.68 
 
 '73-31 
 
 
 175-99 
 176.66 
 
 177-33 
 178.00 
 178.66 
 179-33 
 iSo.OO 
 
 ' 66 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 e = .22 
 
 = .23 
 
 e = .24 
 
 e = .25 
 
 e = .26 
 
 e = .27 
 
 .28 
 
 M 
 
 
 
 1 
 
 2 
 3 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
 o.oo 
 1.60 
 3.21 
 4.81 
 6.41 
 
 8.01 
 9.60 
 
 11.20 
 
 12.79 
 
 20.68 
 
 25-35 
 
 26.90 
 
 28.44 
 29-97 
 
 33-01 
 
 37-50 
 38.98 
 
 4I-92 
 43-37 
 
 46.25 
 47.68 
 49.09 
 50.50 
 
 53-28 
 54-65 
 
 57-37 
 
 60.04 
 
 61-37 
 62.68 
 
 63-98 
 
 66.55 
 67.82 
 69.07 
 70.32 
 71-56 
 
 72.79 
 74.00 
 
 75-21 
 76.41 
 
 77-59 
 
 79-93 
 81.09 
 82.24 
 83-38 
 84.51 
 
 A 
 .60 
 .61 
 .60 
 .60 
 .60 
 
 -58 
 
 57 
 
 55 
 
 54 
 
 52 
 
 *> 
 
 ; 
 
 
 " 
 
 33 
 
 .25 
 .24 
 23 
 
 .21 
 .21 
 
 .20 
 
 II 
 
 O.OO 
 
 8.20 
 
 9-83 
 
 11.46 
 
 13.09 
 14.71 
 
 16.33 
 
 21.16 
 22.76 
 
 24-35 
 25-93 
 27-51 
 29.08 
 30.64 
 
 32.19 
 
 33-73 
 35-27 
 36.79 
 38-31 
 39.82 
 
 42.80 
 44-28 
 45-75 
 47-20 
 48-65 
 50.08 
 
 55-71 
 57-09 
 
 58-45 
 
 61.15 
 
 62.49 
 63-81 
 65.12 
 66.42 
 
 67.71 
 
 70.25 
 7I-50 
 72-75 
 
 73-98 
 75-20 
 76.41 
 77.61 
 78.80 
 
 79-98 
 81.15 
 82.31 
 83.46 
 
 85-72 
 
 A 
 
 1.64 
 
 1.64 
 
 .64 
 
 .64 
 .63 
 
 -63 
 
 62 
 
 
 
 39 
 
 * 
 
 .. 
 - 34 
 
 .29 
 
 23 
 
 O.OO 
 
 '" 68 
 
 3-36 [. 
 
 1.68 
 
 
 1.68 
 1.67 
 
 1.67 
 "2 ' 
 
 20.01 
 
 ii 
 
 32.91 , 
 
 3 
 
 4- 6 7 ,. s 
 
 
 3 
 
 
 53-96 [ 
 
 St! 3 
 
 _o _ 1-39 
 
 
 62.28 i 
 
 64^6 '* 
 66.28 '- 3 
 
 68.88 
 70.17 
 
 I 27 
 
 73-95 ;;:; 
 
 75.19 T 
 76.41 
 
 77-63 " 
 78.83 - 2 
 
 80.02 
 
 1.18 
 
 81.20 
 
 84^68 ;;; 
 86.94 ' 
 
 O.OO 
 
 1.72 
 
 3-44 
 5-16 
 6.88 
 
 8-59 
 10.30 
 
 I2.OI 
 
 13-72 
 
 1-72 
 
 - 
 
 MI 
 
 
 25.48 
 27-13 
 28.77 
 30.41 
 32.03 
 
 33-64 
 35-24 
 36.84 
 
 39-99 
 
 43-09 
 44-63 
 46.15 
 47.66 
 
 49.16 
 50.64 
 52.11 
 53-57 
 
 a: 
 
 " 
 
 ::: 
 - 
 
 66.12 Ic 
 
 67-45 ' 
 
 68 '77 "30 
 
 70-07 i>29 
 
 72.64 ;- 2 * 
 
 73.91 \ 
 
 75- 16 t \, 5 4 
 76.40 
 77.63 3 
 
 1. 17 
 
 I.IS 
 I. IS 
 
 1. 12 
 
 82.43 
 83.60 
 
 84.75 
 
 o.oo 
 1.76 
 3-53 
 5-29 
 
 12.30 
 15-79 
 
 A 
 
 1-77 
 1.76 
 
 1.75 
 1.75 
 1.75 
 
 1.73 
 1-73 
 
 26.08 
 
 29.44 
 31.10 
 32.76 
 
 34-40 
 36.03 
 37.66 
 
 39-27 
 40.86 
 
 42-44 
 44.01 
 
 1.66 
 1.66 
 1.64 
 
 1.63 
 1.63 
 
 i. M 
 
 , 
 = 7 
 
 3 
 
 57-55 . 
 
 60.41 
 61.82 
 
 64-59 
 65.96 
 
 67-3I 
 68.64 
 69.97 
 
 71.28 
 72.58 
 73-86 
 
 1-37 
 I.3S 
 1.33 
 
 1.31 
 
 77-63 
 78.86 
 80.08 
 81.29 
 
 87.04 
 88.16 
 
 85-99 
 87.14 
 88.27 
 
 89-39 
 
 
 
 O.OO 
 
 I.8I 
 
 7.22 
 
 9-O2 
 I0.8I 
 12.60 
 
 14-39 
 
 17-94 
 19.71 
 
 21-47 
 23.22 
 24.96 
 
 26.69 
 28.41 
 30.12 
 31.82 
 
 35-18 
 36-85 
 
 ;: : 
 
 T 
 
 i. So 
 
 1.77 
 1-77 
 
 1-73 
 
 '- 70 
 
 43-37 
 
 44.96 
 
 46.54 
 48.11 
 49.66 
 
 51.20 
 
 52.73 
 
 . ,. 
 
 
 ' * 
 
 1-54 
 1.53 
 
 iSS 
 
 
 65-77 , 3 g 
 
 ^s' ;* 
 
 69.85 ' 34 
 
 71.18 ; : 33 
 
 E - 
 
 i~ ^ 1.29 
 1.27 
 
 1.25 
 78.87 
 80.10 
 81-32 '" 
 
 84.91 
 86.07 
 
 88^7 
 89.50 
 
 9O.62 
 
 '" 
 
 1.14 
 
 O.OO 
 
 1.85 
 3-70 
 
 5-55 
 7.40 
 
 9.24 
 11.08 
 12.91 
 
 H-74 
 
 I.8 S 
 1.85 
 
 1.84 
 
 18.38 
 2O.I9 
 21.98 
 23-77 
 25-55 
 
 30.82 
 
 $& 
 
 47-54 
 49-13 
 
 52.26 
 53-80 
 55-33 
 
 1.81 
 
 1.78 
 
 1-77 
 1-74 
 
 ' 
 
 
 4 
 ' " 
 
 62.72 
 
 66.97 
 68.35 
 69.72 
 71.07 
 72.41 
 
 1.38 
 1.37 
 I.3S 
 1-34 
 1.32 
 
 73-73 , 3I 
 75-04 ^ 
 76.33 ! 
 77-61 T ' 28 
 78.87 
 
 80.12 
 
 I.2S 
 
 89.62 
 90.74 
 
 91.86 
 
 
 
 1 
 
 2 
 3 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 .22 
 
 e = .23 
 
 .24 
 
 .25 
 
 .26 
 
 .27 
 
 e = .28 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
 84.51 
 85-62 
 
 86-73 
 
 90.00 
 91.07 
 
 93-20 
 94.24 
 
 95-28 
 96.31 
 97-33 
 
 99-35 
 
 
 .07 
 
 .04 
 
 .00 
 
 0.99 
 0.98 
 0.98 
 
 107.12 - 94 
 
 108.06 ' 94 
 108.99 93 
 
 V 0.93 
 109.92 
 
 JJ- 8 4 I'll 
 
 "3-55 o.^ 
 
 "4-45 o^g 
 "5-33 . 88 
 
 "" 
 
 117.96 ' 
 
 118.82 
 119.68 
 
 122.22 
 
 123.06 
 123.89 
 
 0.86 
 
 0.86 
 0.85 
 0.85 
 0.84 
 0.84 
 
 127.17 
 
 33 
 
 0.82 
 0.82 
 0.81 
 
 0.81 
 0.80 
 0.80 
 0.79 
 0.79 
 
 0.79 
 0.78 
 
 U 
 
 137.34 
 
 138.85 
 
 I. 
 
 .1 S 6 
 
 8572 
 86.84 
 
 87-95 
 89.04 
 
 91.21 
 92.28 
 93-34 
 94-39 
 95-43 
 
 96.47 
 97-49 
 
 99-52 
 I00 '5 2 
 
 '03-47 
 
 
 .02 
 .01 
 
 .00 
 
 
 0.93 
 
 1^09 ' 92 
 * 0.92 
 
 III.OI 
 
 "if, a 
 ::ss a 
 
 
 II 9- 82 O g 
 
 I2a6 7 o S! 
 
 I2i -s' :: : 
 
 122.35 
 
 I2 3-' 8 0.82 
 
 124.00 
 
 - 
 
 
 128.06 
 128.86 
 
 I 3 2 - 00 
 
 . 77 
 
 - 
 
 
 0.74 
 
 86.94 
 88.05 
 89.16 
 90.26 
 91-34 
 
 94-54 
 95-59 
 
 97.66 
 
 98.68 
 
 99.69 
 100.69 
 101.68 ' 99 
 
 0.99 
 
 0.97 
 
 10747 
 IO8.4I 
 
 .01 
 
 .00 
 
 120.80 
 
 0.91 
 
 ''477 "!! 
 
 115-65 ; 87 
 116.52 
 ''7-39 ; 8 6 
 
 !.. 0.86 
 
 
 g. 
 
 0.78 
 0.76 
 
 0.77 
 0.76 
 0.75 
 
 124.94 
 
 132.82 
 
 139-57 
 
 137-34 
 138.08 
 138.82 
 139.55 
 140.28 
 
 88.16 
 89.28 
 
 1.09 
 
 94-69 
 
 95-74 
 96.78 
 97-82 
 
 98.84 
 
 99-85 
 100.86 
 101.86 
 
 106.70 
 -7-65 
 
 IIO -44 
 
 O.02 
 
 26 ' 91 
 0.90 
 
 113.16 
 
 T T ne O.o9 
 
 "4^3 'g 8 . 
 115-81 -f 
 
 1 16.68 '* 7 
 0.87 
 
 
 "343 
 
 :ss a 
 
 
 129.81 
 
 '30-58 
 
 132.88 
 
 I33.64 
 134-39 
 I35.I4 
 135-88 
 136.62 
 
 137.36 
 138.09 
 138.82 
 
 139-54 
 140.26 
 
 140.98 
 
 ; 
 
 ' 73 
 
 89.39 
 90.50 
 91.60 
 
 93-77 
 94.84 
 95-90 
 96.94 
 97.98 
 99.01 
 
 IOO.O2 
 
 102.03 
 103.02 
 104.00 
 
 104.97 o.po 
 
 Io6%8 - 9S 
 
 107.83 H 
 
 '77 0.93 
 
 "iS - 9i 
 
 " 2 '43 : 9 
 "3-33 . 8p 
 
 114.22 
 115.10 
 115.98 
 
 .01 
 i. 01 
 
 I.OO 
 0.99 
 0.98 
 0.97 
 
 0.88 
 * 
 
 0.86 
 0.86 
 
 0.8s 
 
 122.74 
 
 
 0.79 
 126.77 
 127.56 - 79 
 128.35 
 
 a 
 
 129.90 
 
 130.67 
 I3I.43 
 132.19 
 
 132.94 
 I33.69 
 
 o. 76 
 
 138.10 
 
 138.82 
 
 139-54 
 140.25 
 140.96 
 
 141.67 
 
 a 
 
 90.62 
 91-73 
 
 93-91 
 
 94-99 
 96.05 
 97.10 
 98.14 
 99.17 
 100.19 
 
 IOI.2I 
 102.21 
 
 08 
 
 ' 
 
 
 106.12 
 
 O.Q5 
 IO7.O7 
 
 108.01 ' 94 
 
 inS nc ' 94 
 
 I IO.8O 
 III.7I 
 II2.6I 
 
 - 90 
 
 a 
 
 "9-57 . 84 
 
 
 I2 3-7 
 
 g, 
 
 4.5j 
 
 126.89 
 127.68 
 
 79 
 
 0.79 
 
 133-02 
 
 a 
 
 " 
 
 a 
 
 I374I 
 
 138.84 
 139-55 
 140.25 
 
 o o 
 
 - 
 0.70 
 
 91.86 
 92.96 
 94.06 
 
 96.20 
 
 97.26 
 
 98.31 
 
 99-34 
 
 100.37 
 
 102.39 
 103.38 
 104.36 
 
 .06 
 
 03 
 
 107.26 
 
 108.20 ' 94 
 
 109.14 - 94 
 
 118.06 - 9J 
 
 \\lfo 
 
 "5-46 
 
 . 87 
 
 118.90 
 119.74 
 
 120.57 
 121.40 
 
 122.22 
 
 I2 4- 6 5 
 
 0.83 
 * 
 
 
 
 133-10 
 133-83 
 134.56 
 I35.29 
 136.01 
 136.73 
 
 
 0.74 
 0.7S 
 
 
 i4 2 -35 
 
 138.56 
 140.26 - 7 
 140.96 ' 7 
 
 ili (U 9 
 
 0.68 
 0.69 
 
 143.02 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 e = .22 
 
 e = -23 
 
 .24 
 
 e = .25 
 
 e = .26 
 
 .27 
 
 .28 
 
 M 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
 139-59 
 
 '42-55 
 143.29 
 
 0.74 
 0.73 
 
 0.74 
 0.73 
 0.72 
 
 '^ .H 
 146.19 
 146.9, -' 2 
 14762 ' 71 
 
 $33 ::; 
 ,49.04 
 * 0.71 
 
 149-75 . .. 
 ,50.46 -y^ 
 
 ,5,!86 - 7 
 '52.56 '? 
 
 
 \y. y. 0.68 
 
 158.08 ' 9 
 
 159-44 
 ,60.12 
 
 ,60.79 - 67 
 
 ,61.47 
 
 ,62.14 
 
 ,62.82 
 0.67 
 
 I6 4' 8 3 o'o6 
 
 iSue - 67 
 0.67 
 
 ,66.83 
 
 l6 7-49 ' 
 168.16 ' 67 
 168.82 - 
 
 '69-48 *2 
 
 '71.46 
 ? 
 
 '7-78 
 
 T-f 
 
 ,76.07 *T 
 ' o.6s 
 
 l~j\a - 66 
 
 ;g : " 
 
 
 
 ,80.00 
 
 139-57 
 ,40.30 
 
 ,41.04 
 
 141-77 
 ,42.49 
 
 0.74 
 
 141.37 
 146.08 
 
 
 146.79 
 
 !S - 
 ,48.90 - 7 
 
 ,49.60 - 7 
 0.70 
 
 '5-3 . 69 
 
 ;^:H -* 
 
 '53-74 
 
 . 6g 
 
 '56-46 
 
 159-15 
 159-82 
 
 ,60.48 
 
 ,67.07 
 
 ,67.72 o- 6 * 
 
 168.37 
 
 - 6s 
 
 171.62 - s 
 - 6s 
 
 O.O5 
 
 11 
 
 * 0.6s 
 
 0.64 
 0.64 
 
 ,78.7, ' 64 
 
 79-36 ; 6 * 
 ,80.00 
 
 ,41.00 
 ,42.44 
 
 0.72 
 0.72 
 
 145-99 
 '46-69 
 
 '48-77 
 
 '49-46 
 
 153-54 
 ,54.22 
 154-89 
 
 ,60.84 
 
 '^79 
 
 '63-44 
 
 0.66 
 
 o.6s 
 0.65 
 0.6s 
 
 . 6s 
 
 166.67 e 
 
 I 
 
 ,7l.?4 '^ 4 
 171-78 t 
 
 '73-68 
 '74-31 
 
 
 A 
 0.71 
 
 150.01 
 
 '50-68 
 
 ill 
 
 ,61.19 
 ,61.83 
 ,62.47 
 ,63.11 
 163.75 
 
 
 165-65 
 166.28 
 
 l &% *3 
 
 ,68.80 - 3 
 
 170.68 
 
 '7-55 ~ 
 '73- 1 ? . 03 
 
 |1 
 
 ,76.90 
 I77-52 
 178.14 
 ,78.76 
 I79-38 
 
 0.62 
 0.62 
 
 Hi 
 
 0.67 
 
 
 
 
 157-72 
 158.36 
 
 o 66 
 
 s 
 
 064 
 
 162.79 
 
 ,69.01 
 ,69.62 
 
 180.00 
 
 180.00 
 
 ,72.08 
 ,72.69 -* r 
 
 '73-30 a 
 
 II 
 
 '76-96 O6r 
 
 177-57 
 
 ,78.18 
 
 ,78.78 
 
 '79-39 
 
 180.00 
 
 '43-72 
 
 1 
 
 
 
 1 
 
 160.01 
 160.63 
 161.25 
 
 161.87 
 162.49 
 
 
 
 * 
 
 166.78 -* r 
 
 167.39 ;j 
 
 ,68.00 
 
 168.60 - 6 
 
 ,69.21 "-* 1 
 
 ,69.81 - 60 
 
 170.42 ' 
 0.60 
 
 ,72.82 
 
 1 74.02 
 '74.62 
 
 177.01 
 
 O.S9 
 0.60 
 
 ,78.8, 
 ,79.40 
 
 I8O.OO 
 
 
 0.68 
 0.68 
 
 0.67 
 
 145-71 
 
 146.38 
 147.04 
 147.70 
 148.36 
 149.02 
 
 149.67 
 150.32 
 150.96 
 I5I.60 
 
 152.88 
 I53-52 
 
 o.6s 
 
 5 
 
 '58-53 
 
 0.63 
 0.63 
 0.63 
 
 
 
 ,59.76 - 62 
 ,60.37 ' 61 
 160.98 ' 61 
 
 ,6, S9 
 
 " 0.6 1 
 
 ,62.20 
 ,62.81 6 ' 
 163.42 
 ,64.02 
 
 ,6l62 -' 
 0.6 1 
 
 166.43 
 167.02 
 167.62 
 
 168.22 
 
 168.81 
 169.4, 
 
 170.00 
 
 170.59 
 171.18 
 
 171.78 
 172.37 
 172.95 
 
 '73-54 
 
 0.60 
 0.59 
 
 175-31 - 59 
 I75-90 
 
 176.48 'f* 
 
 177.07 
 ,77.66 
 178.24 - ss 
 178.83 ' 59 
 179.41 5 
 
 0.59 
 iSO.OO 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
i6 
 
 TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 .29 
 
 e = .30 
 
 e = .31 
 
 -32 
 
 -33 
 
 -34 
 
 -35 
 
 Jlf 
 
 
 
 1 
 
 2 
 3 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
 a 
 o.oo 
 
 1.90 '- 90 
 
 II is 
 
 1.89 
 
 13-24 
 
 18.83 
 
 20.68 
 22.52 
 
 26.17 
 
 29-77 
 31-55 
 33-32 
 35-07 
 36.81 
 
 38.53 
 40.24 
 
 I'll 
 'g 3 
 
 , 
 i. 80 
 
 7 
 
 I.7O 
 
 57-97 
 
 - 
 
 u 
 
 " 
 
 1.48 
 1.46 
 
 1.43 
 
 1.41 
 
 6O.07 
 
 \J S 
 
 65.35 
 66.78 
 
 68.19 
 69.58 
 
 70.95 
 72.31 
 
 73-65 
 74.98 
 
 77-59 
 78.87 
 80.13 
 
 81.38 
 82.61 
 83-83 
 
 87-41 , I7 
 
 88.58 ' 7 
 
 89.73 
 
 90.86 I>13 
 
 91.99 - 13 
 
 y i. ii 
 
 93.10 
 
 i. 23 
 
 o.oo 
 1-95 
 3-89 
 
 5-84 
 
 13-57 
 15-49 
 17.40 
 
 19-30 
 21.19 
 
 24.94 
 26.80 
 
 28.64 
 
 54-44 
 56.02 
 
 57-58 
 59-12 
 60.65 
 
 62.16 
 
 65.12 
 
 66.57 
 68.00 
 
 69.42 
 70.82 
 72.20 
 73.56 
 74-91 
 76.24 
 
 77-55 
 78.85 
 80.13 
 81.40 
 
 82.65 
 83.88 
 85-10 
 86.31 
 87.50 
 
 88.67 
 89.83 
 90.98 
 
 94-34 
 
 A 
 
 1.95 
 1-94 
 1. 95 
 
 32.29 
 34.10 
 35-88 
 
 37-66 
 39-41 
 4I-I5 
 42.87 
 44-58 
 
 46.27 
 47-94 
 49-59 
 
 1.91 
 1.90 
 
 1.89 
 
 1.88 
 1.87 
 1.86 
 1.84 
 
 1.83 
 1.82 
 1.81 
 
 i.7S 
 *" 
 
 I.S6 
 I-S4 
 I. S3 
 
 LSI 
 
 1.48 
 1.48 
 
 1.43 
 
 1.42 
 
 1.40 
 1.36 
 
 1 ' 27 
 
 I.2S 
 
 1.22 
 1. 21 
 
 17 
 .16 
 
 O.OO 
 2.OO 
 
 1.98 
 
 15.88 
 17.84 
 
 19-79 
 21.72 
 
 23-64 
 
 3 1 ' 21 
 33- 06 
 34-90 
 
 40.32 
 42.09 
 43-84 
 
 45-57 
 47.28 
 
 50.66 
 52.31 
 53-95 
 
 I.9S 
 
 ' 13 
 
 S 
 
 66.34 
 67.80 
 
 70.67 
 72.07 
 73-46 
 74-83 
 
 77-51 
 78.83 
 80.13 
 
 82.68 
 
 83-93 
 85-16 
 86.38 
 87.58 
 
 88-77 
 
 89-94 
 91.09 
 
 92.24 
 93-37 
 94-48 
 
 95-58 
 
 I.2S 
 
 IS 
 -IS 
 
 o.oo 
 
 2.05 2 ' os 
 
 4.10 2 ' s 
 
 6.14 2 ' 04 
 
 8.18 2 ' 04 
 2.04 
 
 10.22 
 
 12.25 2 ' 3 
 2.02 
 
 2. 02 
 
 . 
 18.29 2 - 
 
 * 1- 
 
 99 
 
 3:3 - 
 
 - 
 
 *" 1.86 
 
 37-59 * 
 
 > 
 5-4 7 
 
 56.71 
 58.33 
 59-92 
 61.50 
 
 63.05 
 
 64.58 
 66.09 
 67.58 
 
 1-55 
 I. S3 
 
 LSI 
 
 70.50 
 71-93 
 
 j , 
 
 77.46 
 
 78.80 
 80.12 
 81.42 
 82.70 
 
 1.30 
 
 85.21 
 86.44 
 87.66 
 88.85 
 90.04 
 
 91.21 
 
 I.I7 
 
 93-50 
 94.62 2 
 
 95-73 ,; 
 96.82 
 
 o.oo 
 
 2.10 
 
 4.20 
 6.30 
 8.40 
 
 10.48 
 
 12.57 
 14.64 
 
 16.71 
 18.76 
 
 20.80 
 
 22.83 
 24.84 
 26.84 
 
 28.83 
 32.74 
 
 34-68 
 36.59 
 
 40.35 
 42.20 
 
 44-03 
 
 49.40 
 
 . 
 
 5 I - I 4 
 
 52.86 
 
 57.89 
 59-52 
 61-13 
 62.72 
 64.28 
 
 65.82 
 67-34 
 
 A 
 
 2.10 
 
 2.08 
 
 2 ' s 
 2.04 
 
 1.96 
 L95 
 
 
 3 !:S 
 
 1.43 
 73-21 
 
 77.40 
 78.76 
 
 80.10 
 81.41 
 82.71 
 
 1.34 
 
 86.50 
 
 87.73 
 88.94 
 
 92.48 
 93.63 
 94-76 
 
 95-88 
 96.98 
 
 98.07 
 
 1.24 
 1.23 
 
 1. 21 
 1.20 
 
 I. IS 
 
 1. 13 
 
 O.OO 
 2.16 
 
 2.16 
 
 8.62 
 
 10.76 
 12.90 
 15.02 
 17.14 
 19-25 
 
 21-34 
 23-41 
 25-48 
 27-52 
 29-55 
 
 2.14 
 
 2.14 
 
 2.12 
 
 SS 
 
 3.O9 
 
 2.07 
 
 2.O4 
 2.OI 
 
 1.99 
 1.97 
 I.9S 
 
 1.90 
 I''?' ! 
 
 1.79 
 
 46.89 
 48.70 
 
 50.49 
 52-26 
 54-00 
 
 59.08 
 60.73 
 62.36 
 63.96 
 
 67.08 
 68.61 
 70.12 
 71.61 
 
 
 '- 60 
 
 '" 
 
 74-51 
 75-93 
 77-33 
 78.71 
 80.07 
 
 81.40 
 
 82.72 
 
 1.30 
 
 87.80 
 89.03 
 90.24 
 
 91-43 
 92.60 
 
 93.76 
 94.90 
 96.02 
 
 99.31 
 
 1.24 
 
 1.16 
 1.14 
 
 1. 12 
 
 O.OO 
 2.22 
 
 4-43 
 6.64 
 
 8.85 
 
 I5-42 
 17-59 
 
 21.89 
 24.02 
 26.13 
 28.22 
 
 A 
 
 2.22 
 
 36.39 
 38.38 
 40-34 
 
 42.28 
 44.20 
 46.09 
 
 47-95 
 49-79 
 51.61 
 53-40 
 55-i6 
 
 2 - 13 
 
 
 1.94 
 
 63.60 
 65.22 
 66.80 
 
 68-37 
 69.91 
 71.42 
 72.91 
 74-38 
 75-82 
 
 78^5 
 80.03 
 81.39 
 
 82.72 
 84.04 
 
 85-33 
 86.61 
 
 87.87 
 89.11 
 
 1. 57 
 
 92.72 
 
 95-04 
 96-17 
 97.29 
 
 98.39 
 99.48 
 
 100.55 
 
 1.22 
 1.20 
 1. 19 
 
 
 
 1 
 
 2 
 3 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 .29 
 
 e = .30 
 
 e = -31 
 
 -32 
 
 -33 
 
 -34 
 
 -35 
 
 M 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 76 
 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
 93.10 
 94.20 
 95-29 
 
 97-4- 
 
 99-5 ' 
 100.54 
 
 . 04 
 .03 
 
 .99 
 
 ;3? :ll 
 0.94 
 
 - 
 
 "5.64 
 "6-51 
 
 "9-7 
 "9-91 
 
 "0.74 
 
 " 
 
 
 07 
 
 ' . 70 
 130.21 
 
 130-96 ' 7S 
 - 74 
 
 I27 '' 5 
 
 '36-07 \H 
 '36-79 . 70 
 
 'S- : ; 
 138.89 - 6y 
 
 '39-59 ;; 9 
 140.28 
 
 IffS "' 
 
 142-33 
 143-00 
 
 143-68 
 
 
 94-34 
 95-43 
 96-51 
 97-58 
 98.64 
 
 99-68 
 100.72 
 101.74 
 
 103.75 
 
 I08 '39 o 94 j I0 9-52 
 
 mr 1 1 "="* ijr r 
 
 .07 
 
 4 
 
 I05-7I ' 97 
 
 106.68 
 
 IO7.64 -!X) 
 
 108-58 ' 94 
 
 0.94 
 0.93 
 
 11045 
 
 1 1 1. 37 
 112.28 
 
 ' 92 
 
 II4.07 
 
 "4-95 
 
 118.40 
 119.24 
 I2O.08 
 120.91 
 
 122.54 
 
 0.7O 
 
 124.94 
 
 125.73 I'll 
 126.51 
 127.28 - 77 
 128.05 - 77 
 128.82 
 
 ' 77 
 
 I3 -3 2 
 131.07 
 
 131.81 
 132-54 
 
 133-27 
 
 75 
 
 136.85 o ~^ o 
 137-55 
 
 140.98 
 
 144-33 
 
 fi . 
 
 95-58 
 96.67 
 
 97-74 
 98.81 
 99-86 
 
 100.89 
 101.92 
 
 132.65 
 133-37 
 I34-09 
 134-80 
 
 1.03 
 1.03 
 
 I0 4-93 
 
 107.83 
 108.78 
 109.72 
 
 1 10.65 
 
 ' 94 
 
 0.93 
 
 116.88 
 117-74 
 
 119-43 
 
 121.08 
 
 121.90 
 
 -* 
 
 
 1313 
 
 128.95 
 129.70 
 
 
 !36-9i ' 7 
 '37-61 o - 6p 
 
 :SS a 
 
 SS- 
 
 141.01 
 
 141.68 
 
 0.67 
 
 0.66 
 
 144-97 
 
 96.82 
 
 97-91 
 
 98.97 
 
 100.03 
 
 102.10 
 103.12 
 IO4.I2 
 105.12 
 IO6.IO 
 
 107.07 
 
 0.97 
 
 0.06 
 
 108.03 
 108.98 - 9S 
 109.92 - 94 
 
 113-57 
 114.46 
 
 1 16.21 
 117.08 
 "7-93 
 
 120.44 o 
 121.26 ' 82 
 122.08 
 
 s* a 
 
 126.04 
 126.81 ; 77 
 
 '30-57 
 
 0.7 
 
 '33 
 
 
 '4'- 5 
 
 !JS? - 
 
 144-31 
 144.96 
 
 145-60 
 
 s 
 
 98.07 
 99-14 
 
 IOO.2O 
 101.25 
 IO2.29 
 
 107.27 
 
 ' ' 0.96 
 
 108.23 
 IO9.I8 
 
 111.05 
 111.97 
 
 112.88 
 
 ' 94 
 
 ' 93 
 
 - 92 
 
 0.91 
 
 0.86 
 0.86 
 
 119.80 
 120.63 
 
 121.45 
 
 123.86 
 
 -4-65 
 
 ' 0.77 
 I2 6- 20 o 
 I26 '97 o 70 
 
 0.7S 
 I2 9' 2 3 . 74 
 129-97 o 74 
 
 J30-7I o. 7 , 4 , 
 
 I3 2 'i6 ' 72 
 0.72 
 
 132.88 n 
 
 137.07 
 
 a 
 
 146.22 
 
 
 loTX '- 
 
 ' 02 "7 |; 
 
 as a 
 
 ',SS -- 
 
 '" : E 
 
 113-98 
 
 ' 4 
 
 "5-75 
 1 16.62 
 117.48 
 
 "8-33 
 119.17 
 
 124.04 
 
 127.89 - 76 
 128.64 ' 7S 
 129.38 ' 74 
 
 0.74 
 130.12 
 
 130.85 
 
 131-57 o H 
 132.29 ' 
 133-00 * 
 
 
 139-17 
 
 '39- 8 3 
 
 1 S 
 
 - 
 
 '43-07 
 
 '44-97 
 
 146.83 
 
 0.62 
 
 100.55 J06 
 101.61 ** 
 
 %S '> 
 
 '4-7i l'* 
 
 107.68 
 108.64 
 
 109.59 ; 9 s 
 
 "0-54 o 
 '"47 0^2 
 
 !ES 4 
 
 0.89 
 115.08 
 115.96 -" 
 116.83 
 
 . 83 
 
 
 - 8 * 
 
 ; 
 
 0.80 
 
 "9-37 
 
 120.20 
 121.02 
 
 I2 '- 8 4 
 
 I22 - 6 4 
 
 128.80 
 
 ' 2 9-54 
 
 131.00 
 
 5 
 
 
 33 - 
 
 1%% "* 
 
 141.20 
 
 33 
 
 
 '44-37 
 
 147-43 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
i8 
 
 TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 e = .29 
 
 e = .30 
 
 .31 
 
 .32 
 
 e = -33 
 
 -34 
 
 -35 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
 
 
 
 ~t*J' v 
 
 !SS 
 
 335 
 
 iil 
 
 !SS - 
 160.73 
 
 161.33 
 161.93 
 
 
 iss 
 
 166.68 
 167.26 
 
 ''7.85 
 
 
 
 - s8 
 
 * 
 
 166.60 - 58 
 176.18 - s8 
 
 '70-77 
 
 171.35 
 171.93 
 
 173.09 
 173.66 
 
 174.24 
 174.82 
 175.40 
 175.97 
 176.55 
 177.12 
 177.70 
 178.27 
 178.85 
 179.43 
 180.00 
 
 . 58 
 
 
 
 0.57 
 0.58 
 
 0.58 
 0.57 
 
 I44-33 
 
 '46-93 
 
 
 
 : 
 
 -* 4 
 
 < 
 
 148.86 
 149.49 
 150.12 
 
 !S3 2 
 
 !$? ol 
 
 '53-86 
 
 0.62 
 
 ii.fn 
 
 ss 
 
 5 
 
 160.49 -f 
 
 161.09 
 
 161.68 - 
 162.26 - 58 
 
 0.59 
 162.85 
 
 !& *S 
 
 0.58 
 
 166.34 'H 
 
 166.92 o l 8 
 
 167-50 '* 8 
 
 i68 -7 05 l 
 
 168.65 
 
 169.22 ' S7 
 
 169.79 
 170.37 ' 
 
 170.94 
 
 * 0.57 
 
 172.64 
 173.21 
 173.78 
 
 174.35 
 
 
 6 
 
 0.57 
 
 0.57 
 
 . 
 
 178.87 
 17944 
 
 iSo.OO 
 
 146.25 
 146.89 
 147-53 
 148.16 
 148.79 
 14942 
 
 
 
 153.12 
 
 '5^73 ;; 6 ; 
 
 :ss ~ 
 
 ;f 
 
 157-33 
 157-92 
 158.51 
 159-10 
 
 159-69 
 160.27 
 
 161.43 
 162.01 
 
 163.17 
 
 164.32 
 164.89 
 
 
 0.58 
 0.58 
 0.58 
 
 " 
 ' s8 
 
 0*7 
 
 Hi 
 
 171.66 
 172.22 
 172.78 
 
 '73-34 
 '73-90 
 
 
 176.67 
 
 177-23 
 177.78 
 
 178.34 
 178.89 
 
 179-45 
 180.00 
 
 
 0.60 
 0.60 
 0.59 
 
 '55-40 6 S 9 
 '55-99 ; S8 
 156.57 ' 
 
 157-16 o ;** 
 157-74 0-so 
 
 158.91 ' s8 
 159-48 
 160.06 ** 
 
 160.63 
 
 161.20 " 
 
 161.77 - 
 
 163-48 
 164.04 
 '64-60 
 
 166.29 
 166.84 "" 
 167.40 ' s 
 
 f f O. SO 
 
 167.96 * 
 
 170.72 I'll 
 
 171.82 
 172.91 ' S4 
 
 173.46 ' 
 174-01 'H 
 
 '74-55 
 175-10 '" 
 
 175.65 o 
 176.19 -* 4 
 
 177.28 
 177.82 
 178.37 o 
 
 178.91 
 179.46 
 
 180.00 
 
 0.54 
 
 146.22 
 
 146.84 - 6i 
 
 147.46 ' 2 
 
 148.08 0- ;" 2 
 
 148.70 C * 
 o.oi 
 
 '49-31 
 149-92 
 
 ill 
 
 '55-27 
 
 0.59 
 
 0.58 
 0.58 
 0.57 
 
 0.57 
 
 160.99 
 
 0.57 
 
 0.56 
 0.56 
 
 162.67 
 
 163.78 
 164.34 
 
 
 Igg 
 
 18:8 - 
 
 - 54 
 
 0-54 
 
 174.12 
 174.66 
 175.19 
 
 176.80 
 
 177-33 
 177.86 
 178.40 
 178.93 
 179-47 
 180.00 
 
 
 
 
 
 0.54 
 
 146.83 u 
 
 147.44 ' fi ' 
 
 148.05 -* r 
 
 148.66 '" 
 
 149.27 '* Q 
 
 140.87 
 
 * 0.59 
 
 I5i!o6 ' 60 
 
 TCI fit - S9 
 
 0.59 
 
 152.83 
 
 '53-41 
 153-99 
 
 la 
 
 
 
 57 
 
 158.55 
 159-12 
 
 I59.67 - 
 160.23 ' 
 l6O.79 
 
 ly 0.55 
 161.34 
 161.89 
 162.44 ' 
 162.99 
 
 163-54 ; 
 
 165.17 - S4 
 165.71 l\H 
 
 0.54 
 166.79 
 
 !g: 3 8i o- 
 
 170.53 o 
 171.06 OJ 
 
 171.59 I'll 
 
 172.12 
 
 172.65 ' S3 
 
 ,1, o 0-S3 
 
 17476 
 
 !?3:S - 
 176.33 
 
 '76-86 ; 
 
 '77-38 S2 
 177.90 
 
 '78-43 I'll 
 178.95 
 179.48 Q 
 
 180.00 
 
 147-43 
 148.04 
 
 '48.6? 
 
 '49-|3 
 '49-83 
 
 151.00 
 
 '53-32 
 
 O . s8 
 
 
 
 8 
 
 :: ; 
 
 3 
 
 168.61 
 
 
 159-50 
 160.05 
 
 S 
 
 161.68 
 
 162.77 
 163.30 
 
 164.38 
 164.91 
 
 165.97 
 
 : 
 
 ' S2 
 
 
 0S2 
 
 I73.30 
 173.82 
 
 174-34 
 
 I74.85 
 175-37 
 175-88 
 176.40 
 176.91 
 
 177-43 
 177-94 
 
 
 
 . 
 
 0.51 
 0.52 
 
 180.00 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 e = .36 
 
 e = .37 
 
 .38 
 
 -39 
 
 -4 
 
 .41 
 
 .42 
 
 M 
 
 
 
 1 
 
 2 
 3 
 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 
 59 
 60 
 
 O.OO 
 
 2.28 
 
 4-55 
 6.82 
 
 15-84 
 18.06 
 20.27 
 
 22.47 
 24.65 
 26.81 
 28.95 
 31-07 
 
 33-17 
 35-24 
 
 39-31 
 4I-3I 
 
 2.21 
 2. 2O 
 
 2.18 
 
 2.14 
 
 I.9S 
 
 " * 
 
 49-5 
 
 52-76 
 
 54-57 
 56-36 
 58.12 
 
 59-85 
 
 6i-55 
 63-23 
 
 64.88 
 
 3 
 
 69167 
 71.21 
 
 75-70 
 
 77-15 
 78.58 
 79.98 
 81.36 
 82.71 
 
 84-05 
 85-37 
 86.66 
 
 
 90.42 
 
 96.32 
 
 97-45 
 98.56 
 
 99-65 
 100.73 
 
 101.80 
 
 I.4S 
 
 1.34 
 
 
 
 ' 3 
 
 0.00 
 
 2.34 
 4.68 
 7.01 
 
 9-34 
 11.66 
 
 2 ' 34 
 2 ' 33 
 
 SB 
 
 2.25 
 
 25-30 
 
 27-5I 
 29.70 
 31-86 
 
 34-01 
 36.12 
 38.21 
 40.28 
 42-31 
 
 44-32 
 46.30 
 
 50-18 
 52-07 
 
 57-58 
 59-35 
 61.10 
 
 62.82 
 64.51 
 66.17 
 
 2.19 
 2.16 
 
 2.IS 
 2. 1 1 
 
 2.07 
 2.03 
 
 2.OI 
 
 UJl 
 
 I.SS 
 
 5 ;-s 
 
 75-57 H 
 
 78-49 
 79.92 
 
 82.70 
 84.06 
 
 85.39 
 86.70 
 87.99 
 
 .-43 
 
 1-33 
 
 97.60 
 
 98.72 
 
 99.82 
 
 100.91 
 
 101.98 
 
 103.04 
 
 1. 13 
 
 O.OO 
 
 2.41 
 4.81 
 
 7-21 
 
 A 
 
 2.41 
 2.40 
 2.40 
 
 11.98 
 
 33! 
 35 
 
 2.31 
 2.28 
 
 ss 
 
 43-35 2 ;, 
 
 45-39 2 
 
 47-40 ' 
 
 49-38 ' 
 
 55 - I4 
 5 7 ' 00 
 
 SS 
 
 64.11 
 
 I-S9 
 
 75-42 
 
 82.68 i - 4 
 
 86.74 
 88.04 
 89-33 
 90-59 
 91.84 
 
 93.06 
 94.26 
 
 1.33 
 1.30 
 
 98.89 
 
 100.00 
 
 101.09 
 
 103.23 
 
 104.28 
 
 O.OO 
 
 2.47 
 
 4-94 
 7-41 
 
 17.18 
 19-58 
 21-97 
 
 24-33 
 
 44.41 
 46.48 
 
 76.78 
 78.29 
 79-77 
 81.22 
 82.64 
 
 2.47 
 
 2.47 
 
 2.40 
 
 2.36 
 
 2.34 
 2.32 
 
 S S 
 
 33-54 
 
 ;:;; 
 :: 
 
 2.07 
 
 56.37 
 58-25 
 60.09 
 
 4 
 
 65-43 , 
 
 
 1.53 
 1.51 
 1.48 
 1.45 
 
 1.42 
 
 85.42 ' 
 
 86.77 
 
 1.32 
 
 88.09 , 
 
 93-17 
 
 94-39 
 95-58 
 96.76 
 
 97-91 
 
 99-05 
 
 100.17 
 
 101.27 
 
 102.36 
 
 1.24 
 
 1.22 
 
 1. 19 
 I.I8 
 
 I. IS 
 
 I. 10 
 1.09 
 1.07 
 
 1.03 
 
 105-51 
 
 O.OO 
 
 2-55 2 
 
 5-09 . 
 
 7-63 , 
 
 IO.I5 
 
 a 2.52 
 
 12.67 
 
 TC ti 2 ' s 
 
 2 ''3 
 
 ' 
 
 * 
 
 29-77 
 32.11 
 
 34-43 
 
 36-71 
 38-95 
 
 43-35 
 45-50 
 
 , 
 
 4 
 
 2 
 
 53-73 
 
 90 
 
 
 ss 
 
 78.17 
 
 82.60 
 84.02 
 
 8S-4 2 
 86.79 
 88.13 
 
 J 
 
 ** 
 
 I>34 
 
 1-33 
 
 90-75 
 92-03 
 
 94-51 
 
 1.23 
 i. 21 
 95-72 
 96.90 ' ' 
 98.07 I ' 17 
 
 
 101.45 
 
 102.55 
 103.62 
 104.68 
 105.72 
 
 106.75 
 
 1.07 
 
 1.06 
 1.04 
 1.03 
 
 O.OO 
 2.62 
 
 -45 
 
 32? 
 
 18.16 
 20.70 
 
 " 
 
 3-58 2 ; 
 
 35-34 
 
 42.22 
 44.44 
 46-63 
 
 48.77 
 50.88 
 
 52.95 
 54-98 
 56-97 
 
 58-92 
 
 64-56 
 66.36 
 
 68.13 
 
 83-99 
 85.41 
 86.81 
 88.17 
 89-51 
 
 S 
 
 I.9S 
 
 1.77 
 
 76.46 
 78.03 
 
 79-57 
 81.07 
 
 93-38 
 94-63 
 
 97-05 
 
 98.23 
 
 99-38 
 
 100.52 
 
 101.64 
 
 102.74 
 
 104.88 I ' 
 
 106.96 *' 3 
 
 I.OI 
 
 107.97 
 
 
 i. 60 
 
 I.S7 
 
 I-SO 
 
 ' 
 1.32 
 
 1.22 
 1. 2O 
 
 I.IS 
 I.IS 
 
 1.14 
 
 I. 12 
 I.IO 
 
 O.OO 
 
 '8.69 
 
 26.41 
 28.93 
 3I-42 
 33-87 
 
 2.S8 
 
 2.S4 
 2.49 
 
 38.66 
 4I.OO 
 43-30 
 45-56 
 47.78 
 
 49-96 
 52.10 
 
 54-20 
 
 92.20 
 93-49 
 
 94-74 
 95-98 
 97-19 
 
 98.38 
 99-55 
 
 2 ' 34 
 
 4 
 
 60.24 
 62.18 
 
 1-97 
 
 71.26 
 
 72-97 
 74.64 
 76.27 
 
 77-87 
 79-44 
 
 88.20 '' 3 
 
 
 1.24 
 
 1. 21 
 
 1. 19 
 
 1. 17 
 I.IS 
 
 IO4.O2 
 105.09 
 IO6.I4 
 IO7.I8 
 IO8.2O 
 
 IO9.20 
 
 
 
 1 
 2 
 3 
 
 4 
 
 5 
 6 
 
 7 
 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
20 
 
 TABLES FOR THE TRUE ANOMALY. 
 
 if 
 
 .36 
 
 e = .38 
 
 -39 
 
 .40 
 
 .41 
 
 .42 
 
 if 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
 
 101.80 
 102.85 
 103.88 
 104.90 
 105.91 
 
 106.90 
 107.88 
 108.85 
 109.81 
 110.75 
 
 115-30 
 116.17 
 
 I- S 
 
 1. 01 
 
 0.99 
 
 0.97 
 0.96 
 
 0.93 
 
 0.87 
 
 118.74 
 119-58 ; g 4 
 120.41 
 
 121 21 
 
 ' 3 0.81 
 
 123-63 '! 9 
 
 * 
 
 125.96 - 77 
 
 i26.? 3 :^ s 
 
 -748 ' 
 
 
 131.86 
 
 132.57 '! 
 133.27 ' 
 
 133-97 'go 
 134.66 o 'J^ 
 
 '35.34 ; 68 
 
 
 
 . 66 
 
 - 0.65 
 139-99 I s . 
 
 5E3 3 
 
 143.16 
 
 146.23 
 146.83 
 147-43 
 148.03 
 
 " J 
 
 3 
 
 . 6o 
 
 103.04 
 104.08 
 105.10 
 106.1 1 
 107.11 
 
 108.10 
 109.07 
 
 IIO.O2 
 110.97 
 111.90 
 
 112.82 
 
 A 
 1.04 
 
 1. 01 
 1. 00 
 0.99 
 
 0.95 
 0.95 
 0.93 
 0.92 
 
 117.26 
 
 Ii8.ii - 8s 
 118.96 ' 8s 
 119-79 
 
 123.0 
 
 0.78 
 
 126.91 ' 7 
 127.66 ' 7S 
 
 I28. 4 I ' 7S 
 0.73 
 129.14 
 
 129.87 "'I 3 . 
 
 132.02 
 
 132.72 
 133-42 
 I34.II 
 
 134-79 
 135-47 
 
 0.70 
 
 0.70 
 0.69 
 0.68 
 0.68 
 0.67 
 
 j 0.65 
 0.65 
 
 IB? 
 
 83 
 
 I42.6O 
 
 Q- O.6l 
 
 I43'"3 f. 
 
 /I * O.OI 
 
 - s9 
 
 146.85 
 147.44 
 
 148.62 
 
 105-31 
 106.32 
 
 107.32 
 108.31 
 
 109.28 
 110.24 
 111.19 
 
 112. 12 
 II3.04 
 
 ' 9S 
 
 0.91 
 
 II748 
 
 118-33 
 II9.I8 
 I2O.OI 
 
 124.04 
 
 I24\82 
 
 -5-59 
 
 - 80 
 
 - 79 
 
 ' 78 
 
 127.10 
 
 0.75 
 
 
 ' 7S 
 
 129.32 
 
 130.77 ' 7 
 131.48 
 132.18 ' 70 
 
 132.88 ' 70 
 0.69 
 
 133-57 
 
 Hi 
 
 
 
 139-53 
 
 I40.J7 
 140.80 
 
 I4I-43 
 
 143.28 
 I43-89 
 
 0.61 
 o.6r 
 
 
 I45-69 
 146.28 
 146.87 
 
 148.62 
 149.19 
 
 ii 
 
 110.46 
 111.41 
 112.35 
 
 116.84 - 
 
 119.40 
 120.23 
 121.06 
 121.87 
 122.67 
 
 123.46 
 124.25 
 125.02 
 
 0.80 
 0.79 
 
 0.79 
 0.77 
 
 127.30 
 128.05 ' 7S 
 128.78 ' 73 
 
 O 73 
 129.51 ' J 
 
 I30.23 7,. 
 
 130.94 
 
 III 
 
 '34-41 
 135-08 -l 
 
 140.90 
 
 
 146.90 
 
 H7.48 
 148.06 ' s8 
 4s.6 3 " " 
 149.20 
 
 149.76 
 
 - 57 
 - 57 
 
 0.56 
 
 
 - 9S 
 - 94 
 
 0.06 
 
 111.64 
 112.58 ' 94 
 II3-50 
 114.41 
 
 "5-3' 0^89 
 116.20 
 
 117.08 - 88 
 
 "7-94 : ' 
 
 " 8 -79 "I! 
 119.63 o ' g * 
 
 120.46 
 121.28 
 
 '22.09 ' a ' 
 
 122.89 
 
 123.68 
 
 124.47 
 125.24 
 I26.0O 
 126.76 
 
 "S3 
 
 -9-70 
 130.42 
 
 
 138-49 
 
 \j s i 
 
 140.38 
 141.00 
 
 141.62 
 
 0.62 
 0.62 
 
 0.61 
 0.60 
 0.60 
 
 144.62 
 
 0.79 
 0.79 
 
 0.77 
 
 150.33 
 
 107.97 
 108.97 
 109-95 
 116.92 
 
 113.74 
 114.65 
 
 "9.87 
 120.69 
 
 * 
 
 123.91 
 "4 69 
 
 126.97 
 127.72 
 128.45 
 
 129.18 
 
 3 
 
 0.82 
 
 /y 
 
 0.73 
 
 0.72 
 0.71 
 
 134-74 
 I35-40 
 
 136.06 
 136.71 
 137-35 
 137-99 
 138.63 
 
 139.26 
 139.88 
 
 
 0.60 
 
 141.72 
 
 142.32 
 142.92 
 
 ' 
 144.69 
 
 145.28 
 145.85 
 
 147-56 
 
 148.12 
 148.68 
 149.24 
 
 0.59 
 
 . 5 
 
 150.8 
 
 109.20 
 110.18 
 in.i6 
 
 112. II 
 "3-05 
 
 113.98 
 114.89 
 
 
 
 ' 98 
 ' 98 
 
 "7-56 
 
 120.11 
 
 : 2 
 
 4 
 
 3 
 
 122.56 
 123-35 
 
 124.92 
 125.69 
 
 126.44 
 127.19 
 
 127.93 ;;; 
 128.66 - 73 
 
 129-39 '! 3 
 
 0.78 
 0.77 
 0.75 
 
 0.75 
 
 133.57 
 134-24 
 134-91 
 135-57 
 136.22 
 
 136.87 
 137-51 
 
 . 67 
 .6 
 
 139-39 
 140.01 
 140.63 
 
 143-03 
 143.61 
 144.20 
 144.78 
 145-35 
 
 145-92 
 146.49 
 
 0.64 
 
 0.63 
 0.62 
 0.62 
 
 >.62 
 
 ).6o 
 
 , 8 
 ' 58 
 ' 59 
 - 
 
 a 
 
 149 27 - SS 
 149.81 ' 54 
 
 150.35 
 150.89 ' S4 
 
 * 0.54 
 151.43 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
TABLES FOR THE TRUE ANOMALY. 
 
 21 
 
 M 
 
 = .36 
 
 < = -37 
 
 .38 
 
 = -39 
 
 e = .40 
 
 e = .41 
 
 e = 42 
 
 M 
 
 148.03 
 
 ; 148.62 
 
 ! I49-2I 
 
 ! 149-80 
 
 I 150.38 
 
 I5I-54 
 152.11 
 
 152.68 - 57 
 '53-25 
 
 155.50 -~ 
 156.05 ^2 
 
 156.61 
 I57-I6 - ss 
 I57.7I 
 
 !S:S - 
 
 0.54 
 159-34 ., 
 
 159-88 '* 4 
 
 160.42 
 
 160.96 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 
 179 179-56 
 
 180 180.00 
 
 0.58 
 0.57 
 
 0.54 
 0.53 
 0.53 
 
 162.02 
 162.56 ' 54 
 163.09 
 163.61 s 
 164.14 - 53 
 
 164.67 
 165.19 
 165.71 
 166.23 
 166.75 
 
 167.27 
 
 l6 7-79 
 168.31 5 
 168.82 ' 51 
 169-34 5 s l 
 169.85 n 
 
 0.53 
 
 0.52 
 
 / '^ 0.51 
 
 17241 . SI 
 172.92 
 
 , ,, 0.51 
 
 1/343 0.50 
 
 73-93 * 
 
 74-44 :;> 5 ; 
 
 176.47 
 
 176.97 - S 
 / 0.51 
 
 177.48 
 ,77-98 - 50 
 1/8.49 
 
 148.62 * 
 
 '49-78 * 
 I5 .35 
 
 g;49 O . s 
 
 '52-62 'l 
 
 53-74 
 
 6 
 
 155-40 
 155.95 
 156.50 
 
 158.12 
 
 158.65 
 
 59-72 
 160.25 " 
 160.78 - s3 
 
 161.31 " S3 
 
 161.83 - 52 
 
 J 0.53 
 162.36 
 ,62.88 ' S2 
 163.40 
 ,63.92 * 
 ,64.44 
 
 164-95 
 '65.47 
 165.98 
 166.49 
 167.00 
 
 167.51 
 
 168.02 - SI 
 
 168.53 ' SI 
 
 169.03 
 
 169-54 ;^ 
 170.04 
 
 0.51 
 
 0.52 
 
 0.51 
 
 
 I72 ' 55 
 173.05 
 
 '5? 
 
 
 0.50 
 0.50 
 
 $: - 
 
 178.52 o 
 ,79.0, o ' 49 
 
 180.00 
 
 150-33 
 
 ss 
 
 
 154-23 
 
 '54-77 
 I55-32 
 155-86 
 
 . ss 
 
 
 
 156.93 
 
 157-47 
 158.00 
 
 158.53 
 I59-05 
 159-58 
 
 160.10 
 
 ,60.62 ' 52 
 
 ,61.14 ' 52 
 
 ,61.66 ' S2 
 
 ,62.17 ' SI 
 ' 0.52 
 
 162.69 
 
 '63-26 -f; 
 
 ~f O SO 
 
 166.24 
 ,f*. -7 -s 
 
 167.74 
 168.24 - S 
 168.74 
 169.24 
 
 0.49 
 
 
 172.20 
 172.69 
 
 174.16 
 
 '74-65 
 
 176.60 
 
 '77-08 
 
 '78-54 :} 
 179.03 
 
 179-52 
 180.00 
 
 
 149.76 
 
 150-33 
 150.88 
 
 153-09 
 
 "54-17 
 154-71 
 
 o.ss 
 
 0.54 
 i.S4 
 
 rs 
 
 
 
 156.84 ' S3 
 157-36 
 
 0.52 
 0.51 
 
 'S^ ; s s * 
 160.47 
 
 '60-98 05, 
 161.49 
 162.00 
 162.51 
 
 163.01 
 
 0.51 
 0.51 
 0.50 
 
 164.01 
 l6 4-5' 
 
 166.50 ' 49 
 166.99 
 
 167.48 ' 49 
 0.49 
 
 167.97 
 
 168.46 49 
 
 168.95 ' 49 
 
 ifinT. "* 
 
 ' 49 
 
 - 
 
 170.41 
 170.90 
 
 ^S 
 
 171.86 - 
 
 172.83 
 I73.3I 
 173-79 
 174-27 
 174-75 
 
 i75- 2 3 
 175-71 
 
 176^66 
 
 177-62 
 
 1 78^57 
 
 
 180.00 
 
 150.88 " 
 I5I-43 - SS 
 'Si-97 
 
 0.53 
 
 153-05 
 153-59 
 154-12 
 
 I54.65 
 155-18 
 
 157-27 : 
 
 157-78 ;* 2 
 
 158.30 
 
 158.81 - SI 
 159-32 
 159-83 
 
 160.33 _^ 
 
 160.84 
 
 161.34 
 161.84 ' s 
 162.34 ' so 
 
 162.83 0-49 
 
 0.50 
 
 0.51 
 
 0.49 
 0.49 
 
 164.31 - 49 
 
 165.80 ' 49 
 '65-29 
 165-78 _^ 
 
 '<|w *; 
 
 167.24 
 
 167.72 
 
 0.48 
 0.48 
 
 168.20 
 
 168.68 - 48 
 
 169.16 
 
 169.64 
 
 170.12 
 
 171.07 
 
 172.02 
 172.49 
 172.96 
 
 0.48 
 0.47 
 
 0.48 
 
 ' 47 
 
 0.47 
 
 0.47 
 
 
 
 O 47 
 
 I77.I9 
 
 0.47 
 
 177.66 
 I/8.I3 ' 47 
 
 178.66 - 47 
 179.06 ' 46 
 
 179-53 ; 47 , 
 180.00 
 
 15088 
 
 153-56 
 154-08 
 154.61 
 
 155-65 
 156.16 
 156.68 
 157-19 
 157-70 
 158.20 
 
 158.71 
 159.21 
 
 0.53 
 
 ' 
 
 0.51 
 
 0.51 
 
 0.50 
 0.50 
 
 160.70 
 
 0.49 
 0.50 
 
 161.20 
 
 161.69 - 49 
 
 1 62. 18 ' 49 
 162.67 ' 49 
 I63-I6 " 49 
 
 163.64 
 164.13 
 164.61 
 
 165.57 
 166.05 
 
 0.48 
 
 
 167.00 
 
 167.48 
 167.95 
 
 169.36 
 169.83 
 170.30 
 
 0.47 
 0.47 
 
 178.62 
 179.08 
 179-54 
 180.00 
 
 152.49 
 '53-01 
 '53-53 
 
 0.52 
 
 52 
 
 '54-57 . 
 155-08 ' SI 
 
 '55-59 
 156.10 
 
 156.61 
 
 '57-" 
 
 157.62 
 
 0.51 
 0.51 
 0.51 
 
 0.50 
 0.51 
 
 158.61 
 
 0.49 
 0.50 
 
 I59-" 
 159.60 
 160.09 ' 49 
 160.58 
 
 161.55 
 162.04 
 162.52 ' 4 * 
 163.00 ' 
 
 l6 3-47 o^g 
 163-95 
 
 165-37 l\H 
 166.31 '" 
 
 168.64 
 169.10 ' 46 
 
 ss Hi 
 
 170.49 
 " 0.45 
 
 '7-32 
 
 ,_^" 0.45 
 
 O.46 
 
 75-4 :;: s s 
 
 '75-49 6 
 '75-95 4 
 176.40 ' 4S 
 176.85 
 77-30 ; 
 
 '77-75 ., 
 178.20 ' 4S 
 
 178.65 ' 4S 
 179.10 ' 4S 
 
 179-55 ; 4 j 
 180.00 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
22 
 
 TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 -43 
 
 .44 
 
 -45 
 
 .46 
 
 .47 
 
 .48 
 
 -49 
 
 M 
 
 
 
 1 
 
 2 
 3 
 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
 o.oo 
 
 2.78 
 
 5-55 
 
 8.32 
 
 11.07 
 
 13-81 
 
 19.23 
 21.91 
 
 A 
 
 2.78 
 2.77 
 
 2.75 
 
 2.74 
 
 
 
 32.29 2 '" 
 34.80 
 
 37-26 2 ' 46 
 2.43 
 
 39-69 - , 
 42.08 
 
 44-42 2 ' 34 
 
 55.48 
 57.56 
 59-60 
 
 61.59 
 
 67.32 
 69.15 
 
 70-93 
 72.68 
 
 1.83 
 1.78 
 
 1.75 
 
 82.40 
 83.90 
 85.38 
 
 86.81 
 88.22 
 
 89.61 
 90.96 
 
 92.28 
 
 93.58 
 
 94.86 
 96.11 
 
 1.48 
 1.43 
 
 1.39 
 1. 35 
 
 1.30 
 
 1.28 
 1.25 
 
 1.22 
 
 . 
 
 8 -53 
 
 
 
 102.01 
 
 I.O? 
 
 105.30 , 
 
 106.36 '- 06 
 
 IO7.4O *" 4 
 
 108.42 J - 2 
 
 10 9-43 o'g 
 110.42 
 
 o.oo 
 2.86 
 5-72 
 8..S7 
 
 si 
 ss 
 
 2 ' 86 
 2 ' 8s 
 
 a 
 
 2.77 
 2.75 
 
 2.71 
 2.68 
 
 2.6S 
 
 3576 
 38.28 
 
 40.76 
 43-19 
 
 45-57 
 50.20 
 
 52.45 
 54-65 
 56.80 
 
 58.90 
 
 62.97 
 64.94 
 66.86 
 
 68.74 
 
 70-57 
 
 2.34 
 
 2.29 
 2.25 
 
 2.IS 
 
 - 
 
 75.83 I'll 
 
 80.75 
 82.31 
 83.84 
 85-34 
 
 86.81 
 
 88.24 
 89.64 
 91.02 
 92-36 
 93-68 
 
 94-97 
 96.24 
 
 9748 
 98.69 
 99.88 
 
 101.05 
 
 102.20 
 
 1.56 
 1.53 
 
 1.47 
 1-43 
 
 .29 
 
 27 
 
 1. 17 
 
 I. IS 
 
 
 
 104.43 
 105.51 
 106.58 
 
 10 7'63 [H 
 
 108.66 I>03 
 
 109.67 I ' I 
 
 110.66 -" 
 0.98 
 
 111.64 
 
 0.00 
 
 2.95 
 5.90 
 8.83 
 
 n-75 
 
 2.93 
 2.91 
 
 2.88 
 
 23.22 
 26.01 
 
 28.76 
 31-47 
 34-13 
 36.75 
 
 39-33 
 41.86 
 44-34 
 
 53-75 
 
 SS 
 
 60.27 
 
 68.29 
 
 2. 75 
 
 2.71 
 2.66 
 
 2.62 
 
 73-82 
 75-58 
 77.29 
 
 78.97 
 
 82.21 
 83.77 
 85-30 
 86-79 
 88.25 
 
 .48 
 
 
 
 
 
 71 
 
 91.07 
 93-77 
 
 96.36 
 
 97.61 
 
 98.84 
 
 100.05 
 
 102.39 
 103-52 
 104.64 
 
 105-73 
 106.80 
 
 107.85 
 108.89 
 109.90 
 
 o.oo 
 
 3.04 
 
 6.08 
 9.11 
 
 12.12 
 
 IS-" 
 1 8.08 
 21.02 
 23.92 
 26.78 
 
 29.60 
 
 A 
 
 3.04 
 3.04 
 3.03 
 
 3.01 
 
 2.99 
 
 2.97 
 2.94 
 
 
 43-00 
 50.41 
 
 55-08 
 57-33 
 
 2 . S2 
 
 63-77 
 65.81 
 67-80 '' 
 
 73-49 
 
 7878 '? 
 
 82 - 8 E 
 83.68 
 
 85.24 
 86.76 ; 
 
 88.25 !- 4 
 89.70 
 
 9-50 
 
 112.85 
 
 
 95.19 
 96.49 
 
 97.76 
 99.00 
 
 IOO.22 
 
 10372 
 104.84 
 
 105-95 
 107.03 
 I08.O9 
 
 109.13 
 110.15 
 
 IU.I5 
 112.13 
 
 114.05 
 
 1.42 
 
 - 
 
 1.27 
 
 1. 12 
 I. II 
 1. 08 
 
 1.06 
 1.04 
 
 1. 02 
 
 O.O7 
 
 O.OO 
 
 6^28 
 9.40 
 
 21.66 3 ' 02 
 24.64 2 ' 98 
 
 36:?2 2 - 8 
 
 38.86 2 ' 74 
 
 2 6O 
 
 41-55 36l 
 44- I 7 .,. 
 
 11 s 
 is s 
 
 63!?! 2 - 17 
 65.22 2-i1 
 
 2. OS 
 
 71.23 
 
 73-4 
 
 74-99 
 
 
 83.58 
 
 85.17 
 86.72 
 88.24 
 
 8971 
 9I.I6 
 
 1.47 
 1-45 
 1.41 
 
 I.I 
 
 93-94 , ' 
 95-29 . 
 96.61 ' 
 
 97-89 1;] 
 
 99-15 - 
 
 100.38 
 
 101.59 
 
 102.77 
 
 103.92 
 
 105.06 
 106.17 
 
 1. 21 
 
 1.18 
 
 1.14 
 
 110.39 
 
 ! 1 1.40 
 
 o.oo 
 
 6^8 
 
 9.70 
 
 12.91 
 
 1 6.08 
 
 3 ' 22 
 
 3 ' 21 
 3-17 
 
 39-97 
 
 45-39 
 48.01 
 
 50-56 
 53-05 
 55-48 
 
 62.39 
 64.58 
 66.70 
 
 68.77 
 70.78 
 
 72.74 
 
 78.31 
 80.07 
 81.79 
 
 86.67 
 88.21 
 89.72 
 91.19 
 92.62 
 
 94.02 
 95-39 
 96.73 
 98.03 
 
 99-30 
 
 100.55 
 101.77 
 102.96 
 104.13 
 105.27 
 
 106.39 
 107.49 
 108.56 
 109.61 
 
 1 1 1. 66 
 
 2 
 
 I>S4 
 
 1.47 
 
 : - 43 
 
 1.03 
 
 1.02 
 0.99 
 
 O.OO 
 6^69 
 
 3 ' 33 
 
 13-33 
 1 6.60 
 
 2 . 99 
 
 
 "- 2 .7 
 
 43-92 2 ; 7 
 46.65 , 
 
 54-43 
 56.89 
 
 59-29 
 61.62 
 63.88 
 66.08 
 68.22 
 
 70.30 
 
 s 
 
 2. 2O 
 2.14 
 2.08 
 
 .02 
 
 - 62 
 
 .55 
 
 39 
 
 115-25 
 
 116.45 
 
 83-32 
 84.98 
 86.60 
 
 88.18 
 89.72 
 91.22 
 92.68 
 94.10 
 
 95-49 
 96.84 
 98.16 
 99.46 
 100.72 
 
 101.95 
 103.16 
 104.34 
 
 105-49 
 106.62 
 
 107.72 
 108.80 
 109.86 
 110.90 
 111.92 
 
 112.92 
 113.90 
 114.86 
 115.80 ' 94 
 
 116.72 ' 92 
 0.91 
 
 117.63 
 
 21 
 
 18 
 
 IS 
 13 
 IO 
 
 - 02 
 
 .00 
 
 - 98 
 
 
 1 
 2 
 3 
 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 -43 
 
 -44 
 
 = -45 
 
 .46 
 
 -47 
 
 e = .49 
 
 if 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
 110.42 
 '"39 
 
 114:22 ' 93 
 0.92 
 
 115.14 
 116.04 - 9 
 
 " 6 '93 o" 8 ,?. 
 117.80 ' 87 
 
 118.66 ' 8 t 
 0.86 
 
 0.79 
 
 134-43 - 
 135.09 
 135.74 ' 
 
 '3 6 '39 * 6 
 137.03 ' 
 
 138.92 
 '39-54 
 
 140.76 
 141.36 
 141.96 
 
 H2.55 
 I43-I4 
 
 I43-72 
 
 145-44 "" 
 
 ' 46 - :: S 6 
 
 146.56 
 147.12 
 147.67 
 
 151-44 
 151.96 
 
 "'64 t, 
 
 112.65 0' 96 
 
 114.47 
 
 121.18 
 1 22.00 
 122.80 
 
 123.59 79 
 
 125 IS ' 77 
 
 125.92 " 77 
 126.67 ' 7S 
 
 0.75 
 127.42 
 
 128.76 ' 74 
 
 128.88 - 72 
 
 129.60 - 72 
 
 0.72 
 0.70 
 
 131.02 
 
 -* 
 
 - 60 
 
 0.58 
 0.58 
 
 ' s6 
 "" 
 
 148.22 - ss 
 148.77 ' ss 
 
 0.54 
 
 1M.&S ' S4 
 'S3 
 
 116.29 
 117.18 '* 9 
 
 118.06 ' 88 
 
 118.92 
 
 "9-77 
 
 120.60 
 
 0.83 
 
 122 2 S ' 82 
 123^5 - 8 
 123.84 '^ 9 
 
 124.62 
 
 :s - 
 126.91 - 7s 
 
 "7-65 ^ 
 
 128.38 
 129.11 
 129.83 
 
 130.54 
 131.24 
 
 I37.84 
 
 138-46 
 139.08 
 
 0.63 
 
 0.62 
 
 0.73 
 
 
 
 147.20 
 
 T JT T J *54 
 
 I 47-74 . .. 
 148.28 ' 54 
 148.82 ' S4 
 H9-36- 4 
 
 152.50 
 
 II2?85 A 
 "3-80 - 9S 
 
 " 4 '73 0^2 
 
 "*3 :i 
 
 120.03 
 
 120.86 
 
 0.83 
 
 :s5 "> 
 %s 3 
 
 128.62 - 73 
 0.72 
 
 I2 9'34 . 7I 
 
 0.71 
 0.70 
 0.68 
 
 0.68 
 66 
 
 '35-47 o ; o j 
 
 '36- 12 0.63 
 !^'75 0.64 
 
 '43-95 ;; 
 
 '45-8 O . ss 
 '45-63 IS 
 146.19 
 
 IS'S - s3 
 
 I 48 ;?? o.l 4 3 
 
 s, 
 
 o 
 
 150.46 
 150.98 
 
 152.01 
 153-02 
 
 
 "7-70 i;i 
 
 118.58 
 
 "9-44 ; a 
 120.29 
 
 122.76 
 
 
 75 
 
 126 ' 6 5 
 127.40 
 
 128.13 ' 73 
 
 128.86 ' 73 
 
 si 
 
 135.03 
 135.67 
 136.31 
 
 136.95 
 137.57 
 138.19 
 138.81 
 139.41 
 
 140.02 
 140.61 
 141.20 
 
 " 
 
 
 r 
 
 - 59 
 
 I 42 ' 94 0.57 
 \A4-64 - s6 
 
 ^'9 4 :- 
 
 ISS - 
 
 146.83 
 147.37 
 147.90 
 
 148.43 
 148.96 
 149.48 
 
 150.00 
 150.52 
 
 151-03 
 
 ' S4 
 
 0.53 
 
 ' S2 
 
 
 
 o.so 
 
 153.54 
 
 117.08 
 * 
 
 
 
 - 
 
 "303 
 
 
 '33-27 . 67 
 '33-94 . 6 7 5 
 
 m 
 
 '39-59 . 6o 
 '4-'9 . 59 
 
 
 150.07 
 
 S4 
 ' 46 '94 o 53 
 
 147.47 
 148.00 - 53 
 
 
 
 :; 
 
 o.so 
 
 154-05 
 
 isl 5 
 
 "* ::!! 
 
 ~.'fi 0.83 
 
 0.79 
 
 124.89 
 125.66 
 
 128.65 
 
 ' 76 
 
 0.72 
 
 130.78 "" 
 131.48 0-7 g 
 
 11 
 
 146.37 - 59 
 
 ' 4 -* :n 
 
 142.68 
 
 '44-36 
 144-90 
 '45-45 
 '45-99 
 
 148.10 
 148.62 
 149.13 
 149.64 
 
 - s7 
 
 * 
 
 
 
 
 
 152.14 
 
 152-6] 
 
 154.08 
 154-55 
 
 "3- 
 
 0.86 
 
 121.12 ' 8S 
 0.83 
 
 121.95 
 
 HI 
 
 - . 76 
 
 I26 '7 o 74 
 
 127.44 
 
 I28.il ' 74 
 
 131-73 
 
 '3 2 -4' IT 7 
 
 '33- 08 0.67 
 133-75 I II 
 
 1 "U..J.O 
 *^ 0.6S 
 
 '35-05 . 6 > 
 '35-69 . 6 ^ 
 
 '36-32 0-63 
 '36-95 . 6 , 
 
 1512 - 6 ' 
 
 138.78 
 '39-38 o _ sQ 
 
 141-14 O 'll 
 
 141-72 ;* 7 
 
 142.29 
 
 , Sc 'S 6 
 
 S4 
 
 145.05 
 
 '45-59 
 146.12 ' S3 
 
 146.65 ' 53 
 
 147.18 ' S3 
 0.52 
 
 147.70 
 
 148.21 - SI 
 
 148.72 ' SI 
 
 I49-23 
 
 149-74 
 
 150.24 
 
 150.73 
 
 151-23 
 
 151.72 
 
 152.20 
 
 0.50 
 
 0.49 
 0.50 
 
 0.48 
 0.48 
 
 0.47 
 
 I54-H 
 154-58 
 
 155-05 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
2 4 
 
 TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 -43 
 
 = -44 
 
 -45 
 
 .46 
 
 = -47 
 
 e = .48 
 
 e = .49 
 
 If 
 
 120 
 121 
 122 
 123 
 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
 152-49 
 
 153-52 
 154-03 
 
 154-54 
 155-05 
 155-55 
 156.06 
 
 156-56 
 
 o.si 
 
 0.52 
 
 ' SI 
 
 0.50 
 
 0.49 
 
 0.49 
 '0-OJ o 40 
 159.02 
 
 0.49 
 
 '59-51 
 
 159-99 
 
 '60-47 HI 
 
 16218 ' 48 
 
 162^5 ' 47 
 163.32 HI 
 
 163-79 ; 47 , 
 164.26 
 
 '65-19 ' 4 I 
 
 0.46 
 
 0.45 
 0.46 
 
 0.45 
 
 I66.I I 
 
 166.57 
 167.03 
 
 167.95 
 168.40 
 
 168.86 
 169.31 
 169.76 
 170.22 
 170.67 
 
 171.12 
 
 I7I-57 
 172.01 
 
 '73-36 
 
 '73-80 HI 
 174.25 
 174.69 ' 44 
 
 S3 rj 
 
 175.58 
 176.02 
 
 0.44 
 
 0.44 
 
 176.91 
 177-35 
 
 177-79 
 
 178^68 
 179-12 
 I79-56 
 
 iSo.OO 
 
 152.50 
 153-01 
 153.52 
 154-02 
 154-53 
 
 I55.03 
 155-53 
 156.02 
 
 156.51 
 157-00 
 
 157-49 o 
 I57-98 -2 
 158.46 
 
 158-94 o 
 
 159-42 ; 4 7 
 
 159.89 
 160.37 4 
 160.84 ' 47 
 
 0.50 
 0.50 
 
 0.49 
 0.49 
 0.49 
 0.49 
 
 161.78 
 
 162.25 
 162.71 
 163.18 
 163.64 
 164.10 
 
 164.56 
 165.02 
 
 0.47 
 
 0.46 
 
 166.38 
 
 0.45 
 166.83 
 167.28 
 
 \68' 7 i8 ' 4S 
 
 168.63 ' 4S 
 
 0.44 
 
 0.45 
 
 t%.g6 ' 44 
 170.40 ' 
 170.85 
 
 171.29 
 
 0.44 
 
 0.44 
 
 I7L73 
 
 172.61 
 173.04 
 
 17348 
 I73-92 
 I74.36 
 174-79 
 
 175-66 
 176.10 
 
 '6-97 n 4 
 
 '77-40 HI 
 
 178.70 
 I79-I3 
 179-57 
 
 0.44 
 
 153-52 
 154-02 
 I54-52 
 155-01 
 
 I55-50 
 155-99 
 156.48 
 156.96 
 157-44 
 
 A 
 
 0.50 
 0.50 
 
 0.47 
 0.46 
 
 158-87 
 
 159-34 
 159.81 
 
 160.28 
 160.74 
 161.21 
 161.67 
 162.13 
 
 162.59 
 163.04 
 
 163.95 ' 4S 
 
 164.46 - 4 5 
 
 0.45 
 
 as - 
 
 !S - 
 
 166.64 ' 4 . 4 . 
 167.08 
 
 0.44 
 
 0.44 
 
 0.43 
 
 0.43 
 
 180.00 
 
 0.43 
 
 167.96 
 168.40 - 44 
 i68.8 4 - 4 ? 
 
 169.28 
 169.72 
 170.15 
 
 170.59 
 171.02 
 
 \l\il M4 
 
 172.32 
 
 172.75 ' 43 
 
 J73-18 HI 
 
 174.04 ' 43 
 174.46 
 174-89 
 
 175-32 in 
 
 175-75 o 
 
 176.17 '*; 
 176.60 
 177.02 
 '77-45 4 4 l 
 177.88 
 178.30 ' 
 178-73 o 
 
 179-15 ' 
 179.58 43 
 0.42 
 
 180.00 
 
 153.54 
 154-03 
 154.52 
 155-01 
 155.49 
 
 155.97 
 156.45 
 
 157.40 
 157.88 
 
 158.34 
 158.81 
 159.28 
 159-74 
 
 160.20 
 
 
 0.46 
 
 160.66 
 l6l.II 
 
 !S:S - 
 162.47 
 
 162.92 
 
 .46 
 
 0.45 
 0.45 
 
 163.82 4s 
 164.26 - 44 
 164.70 - 44 
 
 165.14 
 
 0.44 
 
 166.02 
 166.46 - 44 
 166.90 - 44 
 
 167-33 
 
 Ibl'.lo ' 44 
 168.63 
 
 0.43 
 
 0.43 
 
 169-49 
 
 170.34 
 170.77 
 171.19 
 
 171.62 
 
 172.04 
 
 173-31 
 173-73 
 
 0.43 
 
 0.42 
 
 0.42 
 
 0.42 
 0.42 
 
 175-83 
 176.25 
 176.66 
 
 177-50 
 177.92 
 178.33 
 178.75 
 179.17 
 
 179-58 
 
 180.00 
 
 0.42 
 
 0.42 
 
 156.91 
 
 0.48 
 0.48 
 0.48 
 
 0.47 
 
 0.47 
 0.47 
 0.46 
 
 160.58 
 
 161.03 
 161.48 
 161.93 
 162.37 
 I62.8I 
 
 163-25 
 
 - 4S 
 
 0.4S 
 
 0.44 
 
 164.57 
 165.00 
 
 - 44 
 - 44 
 
 0.43 
 
 illsl - 43 
 166.29 - 43 
 166.72 - 43 
 167.15 - 43 
 
 ' J 0.43 
 167.58 
 
 168.00 ' 42 
 
 168.43 ' 43 
 
 168.85 - 42 
 169.27 - 42 
 
 ' 0.42 
 169.69 
 
 170.11 ' 42 
 170.53 ' 42 
 
 '70-95 n ' 4 T 
 171.36 
 
 171.78 
 172.20 ' 42 
 
 A * T 
 I72.6I 
 
 I73.03 
 173-44 
 
 173.85 
 174.26 
 
 0.42 
 
 ' 
 
 O.4I 
 
 
 I75-09 
 175-50 
 
 175.91 
 176.32 
 
 176.73 
 177.14 
 
 177-55 
 177.96 
 
 178.37 
 178.77 
 179.18 
 179-59 
 iSO.OO 
 
 154-55 
 
 A 
 
 0.48 
 0.47 
 
 156.90 
 157.36 Hi 
 157.82 ' 46 
 158-27 II 5 , 
 158-73 "Is 
 159.18 
 
 I59-63 
 160.07 
 160.52 ' 4S 
 
 I60. 9 6 ' 44 
 0-44 
 161.40 
 161.84 ' 44 
 162.28 ' 44 
 162.71 ' 43 
 
 164.44 
 164.87 
 165.29 
 
 165.72 
 
 0.43 
 
 0.41 
 
 ' 
 
 166.56 
 
 167.40 
 
 167.82 
 168.24 
 168.65 
 169.07 
 169.48 
 
 169.89 
 170.30 
 170.71 
 171.12 
 
 171.94 
 
 173.16 ' 4 
 
 '73-57 o^ 
 
 '73-97 ... 
 '74-38 ' 4 ' 
 174.78 
 175-18 ' 4 
 '75-59 olo 
 175-99 
 
 177.60 
 
 178.00 
 178.40 
 178.80 
 179.20 
 179.60 
 
 180.00 
 
 0.40 
 0.40 
 
 0.40 
 
 0.40 
 
 0.47 
 0.46 
 
 157-35 .. 
 157.80 - 4S 
 158.25 - 45 
 158.70 - 4S 
 '59-H - 
 
 160.46 u 
 160.90 ' 44 
 
 161.77 
 162.20 
 162.63 ' 43 
 
 163.48 ' 43 
 0.42 
 
 163.90 
 
 1*5 in 
 
 lAr lA O.42 
 
 0.42 
 
 0.41 
 
 0.40 
 
 166.00 
 I66.4I 
 166.83 
 
 167.65 
 
 168.06 
 168.47 ' 41 
 I68.8 7 - 4 
 
 169.28 - 4 ! 
 169.69 
 
 170.09 
 170.49 
 170.90 
 171.30 
 
 172.10 
 172.50 " 
 
 173-30 ' 4 
 
 '73-69 o^o 
 174.09 
 
 174-49 ' 4 
 
 174.88 39 
 
 175.28 - 4 
 
 '75-67 ; 39 , 
 176.07 
 
 176.46 ' 39 
 
 176.86 ' 4 
 
 I77-25 " 
 177.64 
 
 178.04 
 
 178-43 
 178.82 
 179.21 
 179.61 
 
 180.00 
 
 0.40 
 
 0.39 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 e = .50 
 
 e = .51 
 
 .52 
 
 -53 
 
 = -54 
 
 = -55 
 
 .V 
 
 
 
 1 
 
 2 
 3 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
 0.00 
 
 10.35 
 13-77 
 
 20-49 
 27-03 
 
 30.22 
 
 33-34 
 36-40 
 
 45-^7 
 
 3-38 
 
 3-12 
 
 2.09 
 
 a s 
 ss ^ 2 
 
 60.76 
 63.11 2 - 3 f 
 65.39 2 
 
 67-61 !!! 
 69.76 
 
 71-85 
 73-87 
 
 77-75 
 79.61 
 
 81.41 
 83.16 
 
 86^53 
 88.14 
 
 89.71 
 
 92.72 
 94-17 
 95.58 
 
 96.96 
 
 98.30 
 
 99-61 
 100.89 
 102.13 
 
 103-35 
 104-54 
 105.71 
 106.85 
 107.96 
 
 109.05 
 
 IIO.I2 
 III.I6 
 112.18 
 
 "3-19 - 
 
 "til 0.96 
 
 - 93 
 
 ' 91 
 0.90 
 
 7S 
 -71 
 
 .61 
 
 57 
 
 52 
 
 41 
 
 38 
 
 4 
 
 .07 
 
 117.01 
 117.92 
 
 II8.82 
 
 0.00 
 
 3-58 " 
 
 7-15 ** 
 
 10.70 J 
 
 14.23 3 " S3 
 
 h 3-49 
 17.72 
 
 21.16 3 ' 44 
 
 27.90 
 31.17 
 
 34-38 
 
 49 -3 
 
 3-27 
 3-31 
 
 3.14 
 3-06 
 2.98 
 
 2 7S 
 
 62.28 
 
 2 - 37 
 
 71 '33 2 'op 
 
 8S S 
 S3 *" 
 
 81.19 
 82.99 
 
 88.08 
 89.68 
 
 91.24 
 92.76 
 94-23 
 95-67 
 
 98.43 
 
 9976 
 
 101.05 
 
 102.32 
 
 103-55 
 
 104-75 
 105.93 
 107.08 
 108.20 
 
 110.37 
 111.42 
 
 112.45 
 
 M 
 
 Ml 
 
 7S 
 .69 
 
 29 
 
 27 
 
 .18 
 
 IS 
 
 .12 
 .IO 
 
 119.99 
 
 0.00 
 
 A 
 3-71 
 
 28.81 
 32.17 
 
 35.46 
 38.67 
 
 5 
 
 56.20 
 
 3-36 
 3-29 
 
 3.21 
 3-05 
 
 2.87 
 2.80 
 
 as 
 
 68.53 
 
 75-03 
 77.06 
 
 79-03 
 80.94 
 
 84.58 
 86.32 
 
 88.01 
 
 91.24 
 
 92.79 
 94.29 
 
 95-75 
 
 99.90 
 
 IOI.22 
 102.50 
 
 103-75 
 104.96 
 
 106.15 
 107.31 
 108.45 
 109-55 
 
 II2 -73 
 "3-74 
 114.74 
 
 2.03 
 
 -97 
 91 
 
 
 .55 
 
 32 
 .28 
 .25 
 
 .19 
 
 II6 ' 66 
 
 !?? 
 
 0.95 
 0.93 
 
 o.oo 
 
 ii. 4 6 3 - 8 
 
 '5-3 
 
 26.22 3 ' 6 
 
 29-75 * 
 33- 21 
 
 43-08 3 ' 20 
 
 46.19 
 
 49.21 
 
 3 ' 02 
 2.92 
 
 70.15 
 
 2 - 33 
 
 2.03 
 
 76.66 
 78.69 
 
 80.66 I ' 97 
 
 82.56 l'jj 
 
 86.19 ' 
 
 87-92 '' 73 
 
 89.60 j- 8 
 
 92.81 I-s8 
 
 1-53 
 
 94-34 , 
 
 97.28 
 
 98.68 
 
 100.05 
 
 101.38 
 102.68 
 
 103-95 
 105.18 
 106.38 
 
 107-55 
 108.69 
 
 110.90 
 
 1.37 
 
 1-33 
 
 1.27 
 
 1. 20 
 t.I7 
 
 1.14 
 
 116.96 ' 96 
 0.94 
 117.90 
 
 118.82 - 92 
 lr . _, 0.90 
 
 121.16 
 
 121.47 
 122.32 
 
 2 A 
 
 54-97 ' < 
 
 o.8s 
 
 
 O.OO 
 
 3 ' 97 I'll 
 7-94 3 
 
 15-77 
 19.62 
 
 27.12 3 ' 72 
 
 34-30 3 ;^ 
 
 4"3 3 
 
 KS HI 
 50.65 
 
 53-62 
 
 2.97 
 
 2.87 
 2.78 
 
 67.05 
 69.46 
 71-79 
 74-05 
 76.22 
 
 78.32 
 
 80.35 
 82.31 
 84.21 
 86.04 
 
 87.82 
 
 2.41 
 2.33 
 2.26 
 2.17 
 2. IO 
 
 2.03 
 
 1.78 
 
 92.82 
 94-38 
 
 95-90 
 
 97-37 
 98.81 
 1 00.20 
 101-55 
 102.87 
 104.15 
 
 105-39 
 106.61 
 107.79 
 
 108.95 
 110.07 
 111.17 
 112.25 
 II3-30 
 
 1.28 
 
 1 '" 
 
 o 88 
 
 o.oo 
 
 4' 12 i" 
 
 8 4- * 1 
 .2* 
 
 12.30 4 - 07 
 
 16.34 4 ' 04 
 
 * 3.97 
 
 20.31 
 
 2 4' 22 I'll 
 28.05 
 
 31.80 3 
 
 35-45 t 
 
 ' 4 
 
 
 42-44 
 
 45-78 
 
 49- 01 
 
 63-58 
 66.20 
 
 68.71 
 
 73^8 
 75-73 
 77-91 
 80.00 
 82.03 
 83.98 
 85-87 
 87-69 
 89.46 
 91.16 
 92.82 
 94.41 
 95-96 
 
 97-47 
 
 98.92 
 
 100.34 
 
 101.72 
 
 103.05 
 
 104-35 
 105.61 
 106.84 
 108.04 
 109.20 
 
 110.34 
 
 112.53 
 
 "3-59 
 114.62 
 
 2.SI 
 
 2.09 
 
 77 
 
 -n 
 
 t.', 
 
 H 
 
 55 
 ft 
 
 45 
 -? 
 
 33 
 30 
 
 ^3 
 
 1 6 
 1.14 
 
 I. II 
 1. 08 
 1. 06 
 I.O3 
 I.OI 
 
 0.96 
 
 123-47 
 
 120.35 
 
 121.24 
 122.96 
 
 123.79 
 
 124.61 
 
 0.89 
 
 O.OO 
 4.28 
 
 8-54 
 
 16.94 
 
 21.05 
 
 25-09 
 29.04 
 32.89 
 
 4.28 
 4.26 
 
 4.11 
 
 40.28 
 
 43- 80 I'll 
 
 47.21 3 4 
 
 5-50 3 3 H 
 
 53-68 g 
 
 75-19 : ,6 
 
 77-45 ai7 
 
 2.09 
 81.71 
 83-73 2 ' 2 
 85-67 
 87-55 
 
 92.80 
 
 94-44 
 96.02 
 
 97-55 
 
 99.04 
 
 100.48 
 
 101.88 
 
 103-23 
 
 105.83 
 107.08 
 108.29 
 109.47 
 110.62 
 
 1 1 1-73 
 112.83 
 113.89 
 "4-93 
 "5-94 
 
 .49 
 
 32 
 .28 
 
 -5 
 
 .II 
 .10 
 
 118.85 ' 9S 
 119.78 ' 93 
 
 120.68 - 9 
 0.89 
 
 l^-s? . 87 
 
 ,,'in - 8 5 
 
 125-75 
 
 
 
 1 
 
 2 
 3 
 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
26 
 
 TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 .50 
 
 .51 
 
 .52 
 
 e = -53 
 
 -54 
 
 e = -55 
 
 -56 
 
 If 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
 n88a 
 
 "isf - 81 
 
 ^V' 0.80 
 
 I2 5 ; 45 'I! 
 126.22 
 
 0.76 
 
 126.98 
 127.72 " 74 
 128.46 ' 74 
 129.18 ' 72 
 129.90 l^ 
 
 J 0.66 
 
 '33-99 
 
 '35-93 H 4 
 '36-55 6 6 l 
 
 Si::" 
 
 139.00 - 
 
 139-59 O 'll 
 140.18 
 
 140.76 - s8 
 
 i 11 -57 
 
 142.47 
 
 I43-03 
 I43-58 
 I44-I3 
 144.67 
 145-20 
 
 145-74 
 146.26 
 146.79 
 
 0.55 
 0.55 
 0.54 
 
 0.54 
 0.53 
 
 , . _ o uoi 
 
 147-82 
 
 0.51 
 
 148-33 
 148.84 ' SI 
 
 150.33 
 150.82 
 
 SO 
 
 - so 
 
 
 iis'3 
 
 155-54 
 
 ; 22 ;54 ZZ 
 
 0.8 1 
 
 124.17 
 
 I2 F 4 : 7 7 
 126.51 
 
 127.26 - 7s 
 0.75 
 128.01 
 128.74 
 129.46 
 130.18 
 130.88 
 
 " 
 
 '3' -57 
 
 . 69 
 
 '34-90 6 
 
 
 '37-41 
 
 143.76 
 
 
 145.37 
 145.89 
 146.41 
 
 54 
 
 147.95 
 148.46 
 
 149.45 
 149.95 
 
 
 
 
 - SI 
 
 0.50 
 
 '5-9 2 
 
 151-88 
 
 '53-29 
 
 ' 
 
 0.47 
 0.47 
 
 155.13 
 
 155.58 
 
 156.03 
 
 
 \\iil ^ 
 
 126.87 ' 77 
 127.56 ' 7S 
 
 II 
 
 '37-04 
 
 '39-44 
 
 140.61 
 '4"' 8 
 
 0.59 
 0.59 
 
 0.59 
 0.58 
 
 14340 
 143-94 
 144.48 
 145-01 
 
 145-54 
 146.06 
 
 H6.57 
 
 147-59 
 I48.IO 
 148.60 
 149.09 
 
 149.58 
 150.07 
 150.55 
 I5I-03 
 
 o.so 
 
 
 ' SI 
 - so 
 
 
 153-82 
 154.28 
 154-73 
 155-18 
 I55-63 
 156.07 
 
 156.51 
 
 0.47 
 0.46 
 0.45 
 0.46 
 
 0.45 
 
 ' 44 
 0.44 
 
 I22 3 2 
 
 
 127.86 ' 7S 
 128.60 ' 74 
 
 129-33 ;" 
 
 130.05 
 130.76 -?' 
 
 '33-48 
 
 0.67 
 0.66 
 
 0.62 
 
 139-68 
 140.26 
 
 4o.8 3 
 
 - s8 
 
 ' S7 
 
 ' 54 
 
 I45.I9 
 
 14572 
 146.23 
 146.74 
 I47-25 
 
 147-75 
 148.25 
 148.74 
 
 0.51 
 0.51 
 
 0.50 
 0.49 
 
 0.49 
 
 : 
 
 54.35 
 
 I2 3-47 
 
 1 26166 ' 78 
 0.76 
 
 127.42 
 I28.T 7 ' 7S 
 
 128.91 - 74 
 
 130.35 ; 7 i 
 
 131.06 
 ,f . _, 0.69 
 
 0.68 
 
 '33-77 05 
 
 II 
 
 138.76 ; 
 
 139-35 ,g 
 
 139-93 ; S7 
 140.50 ' 
 ! 4 !-Z o.ll 
 
 
 156.98 
 
 143-27 
 143.81 
 
 144-34 
 
 144.87 
 
 145-90 
 146.41 
 146.92 
 147.42 
 147.91 
 
 149.38 
 
 IKS 
 
 13 "** 
 
 .. 
 
 ; 4 
 
 0.51 
 
 0.51 
 
 0.51 
 
 
 0.47 
 0.47 
 
 '5 I -73 
 
 0.45 
 
 155-31 
 155-75 
 156.18 
 156.60 
 157-03 
 
 157-45 
 
 
 
 126.21 u 
 126.98 - 77 
 127.74 - 76 
 
 * 0.75 
 128.49 
 129-23 ' 74 
 
 '3''37 o 09 
 
 II 
 
 139-02 o 
 '39-60 - 5 l 
 140.18 ' s8 
 '40-75 - 7 
 
 142.42 
 142.96 
 I43-50 
 144.03 
 144-55 
 I45-07 
 145-59 
 
 146.60 
 147.10 
 147.60 
 148.09 
 
 I49.05 
 149-53 
 150.00 
 
 150-47 
 150.94 
 
 -* 
 
 0.55 
 
 " 
 
 - 4 
 
 - s 
 
 
 
 153.65 
 
 '54-09 
 
 ., 
 
 !56.66 
 
 157.91 
 
 ' 42 
 
 18:3 
 
 128.82 
 
 129.55 
 130.28 
 
 7 , 
 
 ; 
 
 - 
 
 
 
 SJi 
 
 0.59 
 
 
 142.11 
 142.66 o f 4 
 
 '4373 ;" 
 
 144-77 
 145-29 
 145.80 
 
 146-30 
 146.80 
 
 I47-30 
 
 0.51 
 0.50 
 0.50 
 0.50 
 
 0.49 
 0.48 
 0.48 
 
 
 152.88 
 
 I53-76 
 154-20 
 I54-63 . 
 155-06 ' 43 
 15548 
 155-90 
 
 156-32 
 
 o 
 
 
 157.56 
 157-97 
 
 158.37 
 
 : 
 
 4 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 e = .50 
 
 - -Si 
 
 e = .52 
 
 -53 
 
 - -54 
 
 = -55 
 
 120 
 121 
 122 
 123 
 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
 .55-54 
 156.00 
 
 156-45 
 
 157-35 
 157-79 
 
 0.45 
 
 0.44 
 
 0.44 
 159-12 ' 44 
 
 159-55 ; 43 
 
 159-99 
 ,60.42 - 43 
 ,60.85 ' 43 
 ,61.28 - 43 
 
 ,61.70 - 42 
 0.43 
 
 f.i'ce 0-42 
 
 164.22 
 
 165.05 
 
 
 ,66.27 
 
 ,66.68 ' 41 
 ,67.09 " 41 
 167-49 ' 4 
 l6 7- 8 9 ^ 
 168.29 
 
 ::;: 
 
 171.08 
 
 ,72.26 
 ,72.65 
 
 - 39 
 
 <" 39 
 ' 38 
 
 '75-76 
 
 
 I77-30 
 ,77.69 
 
 ,78.07 
 ,78.46 
 ,78.84 
 
 1/9-23 
 ,79.61 
 
 ,80.00 
 
 0.38 
 0.39 
 0.38 
 
 0.38 
 
 0.38 
 0.39 
 
 I56 3 
 '5 6 -4 8 
 
 157.36 ' 
 '57-80 - 44 
 
 ,58.24 
 ,58.67 ' 43 
 159-10 ' 43 
 159-53 
 '59-96 Q ; 43 
 
 160.39 
 ,60.8? ' 42 
 ,61.23 * 
 
 ,62.07 
 
 162.48 
 ,62.90 
 
 0.41 
 
 ,64.13 ' 41 
 * 0.40 
 
 Ii 
 
 ,66.15 
 0.40 
 
 
 
 0.39 
 
 ,69.3, 
 
 ,70.09 
 
 ,70.48 
 ,70.87 
 171-25 
 
 - 38 
 S 3 
 
 '73-94 . 3 8 
 
 '75-46 
 '75-84 
 
 '77-36 
 '77-73 
 
 0.38 
 0.38 
 
 0.38 
 0.38 
 0.37 
 0.38 
 
 0.38 
 
 157.38 rs 
 
 157-81 !' 43 . 
 
 158.24 
 
 ,58.67 
 ,59.10 
 159-52 
 159-94 
 ,60.36 
 
 ,60.78 
 
 0.43 
 0.43 
 
 0.42 
 
 ' 42 
 
 0.40 
 
 ,6, .6, 
 162.02 
 162.43 
 
 ,62.83 
 163.24 
 163.64 
 164-4 - 4 
 
 164-44 ' 40 
 * 0.40 
 
 ,64.84 
 
 i6 s- 2 4 :i: 
 165.64 
 
 .66.03 - 39 . 
 ,66.42 
 
 ,66.82 
 ,67.2, " 39 
 ,67.60 - 39 
 ,67.98 - 38 
 ,68.37 - 39 
 
 *' 0.39 
 ,68.76 
 
 169.14 ' 3 
 
 0.40 
 
 169.91 
 170.29 
 
 ,70.67 
 
 I72.,8 
 
 172.94 
 
 '73-31 
 '73-69 
 174.06 
 
 0.38 
 0.38 
 
 0.38 
 0.38 
 
 0.38 
 
 180.00 
 
 ,74.44 
 ,74.8, 
 175-18 - J7 
 
 175-55 : 
 175-92 03 l 
 ,76.30 
 ,76.67 ' 37 
 ,77.04 
 
 177-4. 
 ,77.78 
 
 178.15 
 178.52 - 37 
 ,78.89 - 37 
 ,79-26 - 37 
 .79-63 ; 3 ^ 
 ,80.00 
 
 
 ' 37 
 
 ' 37 
 
 ' 37 
 - 37 
 0.37 
 
 ,56.98 * 
 
 'Si; r 3 
 
 S 6 - 
 
 ,59.10 
 .59.52 
 
 .59.93 
 .60.35 
 
 0.42 
 
 .-n 
 
 ,61.17 
 ,61.57 
 ,61.98 
 ,62.38 
 ,62.78 
 
 ,63.18 
 .63.58 
 
 ss - 
 
 ,64.76 - 39 
 
 * ' 0.39 
 
 0.40 
 0.40 
 0.40 
 
 0.39 
 
 168.61 
 
 0.38 
 0.38 
 0.37 
 
 '74 3 
 ,70.1, " 
 
 '70-48 ^ 37 
 
 \\\ 2 <x> ' 37 
 I71 '97 ' 37 
 
 .72.34 ;" 
 
 ,72.7, 
 
 ,73.08 - 37 
 .73.45 * 
 
 180.00 
 
 S 
 
 .57.45 .. 
 157-87 1 
 
 '5 8 - 2 9 '*\ 
 '5 8 -70 - 4 
 
 i '59-' 2 0.41 
 
 '59-53 
 
 159-94 o 
 
 1 ,60.34 4 
 
 i j6o.7 5 o ; 4 Q 
 
 i6i.55 
 : ,61.95 
 
 .62.34 ' 39 
 
 163.52 
 
 163.91 - 39 
 164.30 - 39 
 
 8 : : i 
 
 ;ss - 
 
 0.38 
 
 ,67.08 
 
 I66 '97 
 
 .65-45 - ,o 
 
 .65-83 ' 
 
 l66 ' 21 3 & 
 0.38 
 0.37 
 
 lel'.T^ - 38 
 
 ,68.09 ' 37 
 ,68.46 ' 37 
 ,68.84 o 
 
 ,69.2, 
 ,69.58 ' 3 J. 
 ,69.94 ' 36 
 
 0.17 
 
 .70-3. : 37 
 
 ,70.68 37 
 0.36 
 
 ,71.04 o 
 
 172-13 
 ,72.50 
 
 ,72.86 
 173-22 
 173-58 
 
 
 
 
 0.37 
 0.36 
 
 175-37 
 175-73 
 ,76.09 
 
 176.45 
 ,76.80 - 
 
 ,77-16 ' 36 
 
 177-51 
 
 177-87 
 
 178.23 
 ,78.58 
 ,78.94 
 179-29 
 179-65 
 
 ,80.00 
 
 157-91 
 
 158.33 
 
 159-14 
 159-55 
 
 .59-95 
 
 ,6,:(4 - 39 
 
 ,61.54 - 4 
 
 " 0.39 
 ,61.93 
 ,62.32 
 
 ,62.7, 
 
 - 0.38 
 ,64.24 * 
 
 ,64.62 - 3 * 
 
 ,65.00 - 38 
 
 165-75 
 ,66.12 
 ,66.50 ' 38 
 ,66.87 ' 3 ! 
 
 170.51 "- J " 
 
 '7- 8 7 \? 6 
 
 171-23 . 
 
 171-58 " '" 
 
 I7L94 ' 
 ,72.30 
 
 172-65 - 3S 
 
 
 173.01 
 173-36 
 173-71 
 
 -" 
 3 
 
 175-47 I" 
 175.82 ~* 
 ,76.17 
 
 :?6:i7 o- 
 
 177.22 
 
 177.56 
 
 177-91 ;; 3 j 
 ,78.26 
 ,78.6, 
 ,78.96 - 3S 
 .79.30 - 34 
 .79-65 ; 3 * 
 ,80.00 
 
 - 3S 
 
 isVis - 4 , 
 159-57 - 
 
 I59 ' 97 ol j 
 
 %$ 3 
 
 ,61.92 3 " 
 
 I I62 '3 
 ,62.68 ' 38 
 
 I ,63.06 / 38 
 3" 0.37 
 
 - 34 
 
 
 
 ,79.66 
 180.00 
 
 5 s 
 
 165-31 
 
 166.04 
 ,66.4, - 37 
 ,66.78 ^; 37 
 
 0.36 
 0.36 
 
 3 
 
 ,67.86 
 
 ,68.22 
 
 ,68.58 
 ,68.94 
 ,69.29 " -** 
 
 \%& - 
 
 !S3? -* 
 ;7;-o6 ; 3S S 
 
 17,76 ' 3S 
 172.11 - 35 
 ,72.46 - 3s 
 
 ,72.80 - 34 
 
 0.3S 
 
 173.15 
 .73.50 ' 
 
 I"- 8 ;} oil 
 
 
 I75-56 
 
 .75-9. : 
 ,76.25 o "" 
 
 176.59 . 
 .76.93 ' 34 
 177-27 
 ,77.62 
 ,77-96 - 34 
 
 0.34 
 178.30 
 ,78.64 ' 
 
 0-34 
 
 0.34 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 
 157 
 158 
 159 
 
 160 
 161 
 
 163 
 164 
 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 e = -57 
 
 = -59 
 
 e = .60 
 
 e = .61 
 
 .62 
 
 .63 
 
 A/ 
 
 
 
 1 
 
 2 
 3 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
 o.oo 
 
 4-44 
 8.86 
 
 A 
 
 4-44 
 4-42 
 
 13-25 T 
 '7-57 4 ;*6 
 
 21.83 , 
 26.00 4 ' 17 
 30.07 
 34-04 
 
 4 ' 07 
 
 41.61 
 
 45' 22 3 J 
 
 48 -7 I'll 
 52.05 J 3 
 
 55-27 3- " 
 58.38 
 
 g 
 
 66.97 
 69.62 
 
 72.16 
 74.60 
 
 76.94 
 79.19 
 
 83-44 
 8545 
 87-38 
 
 91.04 
 
 92-78 
 94-45 
 96-07 
 97.64 
 
 100.62 
 102.04 
 103.42 
 104.76 
 106.06 
 
 107.32 
 108.54 
 109.73 
 110.89 
 
 II2.O2 
 
 113.12 
 114.19 
 115.24 
 II6.26 
 117.26 
 
 118.23 
 
 I2O.II 
 I2I.O2 
 121.91 
 
 122.78 
 
 126.8 
 
 2.54 
 
 2.44 
 
 74 
 67 
 
 57 
 
 51 
 47 
 
 ,3 
 
 34 
 
 ,26 
 
 22 
 
 19 
 
 07 
 .05 
 .02 
 
 0.97 
 0.95 
 
 O.OO 
 4.61 
 9-21 
 
 18.24 
 22.65 
 
 4.60 
 4-55 
 4.48 
 4.41 
 
 4.20 
 
 50.24 
 
 5 6 '9 2 l'.l 
 60.06 
 
 78.71 
 
 80.96 
 
 85.19 
 87.19 
 
 90.96 
 
 97.71 
 
 99.26 
 
 100.75 
 
 IO2.2O 
 103.60 
 104.96 
 106.28 
 107.56 
 
 108.80 
 IIO.OO 
 
 111.17 
 112.32 
 113.43 
 
 116.59 
 
 117.59 
 118.57 
 
 119.52 
 
 
 
 
 127.23 
 
 128.00 
 
 O.OO 
 
 4.80 
 
 9-57 
 
 A 
 4.80 
 
 4-77 
 4-73 
 
 . JC 
 
 : 
 
 36.50 
 40.56 
 
 44-47 
 48.23 
 51.84 
 55-31 
 58-63 
 
 61.80 
 
 3.91 
 
 
 75-74 
 78.18 
 80.52 
 
 82.75 
 84.90 
 
 86.96 
 
 88.95 
 90.85 
 
 94-44 
 
 9778 
 
 99-36 
 
 100.89 
 
 103.79 
 105.17 
 106.51 
 107.80 
 109.06 
 
 110.28 
 111.47 
 112.62 
 
 , , 
 2 ' 44 
 
 2 ' 23 
 
 *'* 
 
 0.77 
 
 ' 0.94 
 120.81 
 
 124-34 :ii 
 
 126.80 - 
 
 128.36 ' 77 
 0.76 
 
 129.12 
 
 O.OO 
 
 5.00 
 9.96 
 
 A 
 4.96 
 
 '9-7^ 
 
 33-51 
 
 37- 8 3 
 
 41.99 
 
 y 
 
 4 ' 47 
 
 4.00 
 
 3.84 
 3.68 
 3-51 
 3.36 
 3.21 
 63-59 , 07 
 
 66.66 3 ' 07 
 69-53 ' 9 o 
 
 72-37 'I: 
 
 45-99 
 
 ss 
 
 ss 
 
 80.02 
 82.35 
 84.58 
 
 2.54 
 2.44 
 
 76 !. 
 
 97-84 z . c 
 
 103.97 
 
 105.38 
 106.74 
 108.05 
 109.32 
 110.56 
 
 111.76 
 112.92 
 114.05 
 
 117.26 
 118.27 
 119.26 
 120.23 
 121.17 
 
 122.09 
 I2 3 !S6 
 
 124.71 
 125-55 
 
 , , 6 
 1>31 
 
 1.27 
 
 ' 
 
 I>24 
 i. 20 
 
 IlOX 
 
 "" 
 
 0.07 
 
 0.9! 
 0.92 
 
 127.96 
 128.73 
 
 129.48 
 130.22 
 
 - 7s 
 
 0.74 
 
 o.oo 
 
 5-21 
 
 10.38 
 15.48 
 
 20.50 
 
 25-40 
 
 39-22 
 
 43-49 
 
 47.58 
 51-50 
 
 5.17 
 5.10 
 5.02 
 4.90 
 
 4.77 
 4-44 
 
 3 ' 74 
 
 62.20 3 ' 4 
 3-24 
 
 65-44 , n o 
 
 79.46 
 81.89 
 84.21 
 86.42 
 
 88.54 
 
 2.54 
 2.32 
 
 2.21 
 2.03 
 
 94.38 
 
 96.17 
 
 97-89 
 
 102.67 
 
 106.97 
 IO8.3O 
 
 109-59 
 110.85 
 II2.O6 
 
 113.24 
 
 114.38 
 
 115-49 
 116.56 
 II7.6I 
 
 118.63 
 
 1-33 
 1.29 
 1.26 
 
 I. 21 
 
 1.18 
 
 1.14 
 i. ii 
 1.07 
 
 I. O2 
 
 121.54 
 
 I2 4-23 
 
 I2 5'9 
 125-93 
 
 0.84 
 
 I29.IO 
 129.86 
 I3O.6O 
 
 I3L32 
 
 ' 77 
 
 - 76 
 
 - 74 
 0.72 
 
 O.OO 
 
 5-43 
 10.82 
 16.14 
 
 26.43 
 
 36.11 
 40.68 
 45.06 
 
 49.24 
 
 64.07 
 ' 
 
 73.38 
 76.18 
 
 8i-37 
 83-79 
 
 116.92 
 
 "9-99 
 120.97 
 121.92 
 
 124.62 
 
 5.32 
 
 4 ' 57 
 
 ^.00 
 
 3 - 43 
 3.26 
 
 2.66 
 2 . 53 
 
 90.39 
 92.40 
 94-32 
 96.16 
 
 97-93 
 99-63 
 
 101.26 
 102.83 
 104.34 
 
 105.79 
 107.20 
 
 108.56 
 109.87 
 111.14 
 
 113-55 
 
 1.36 
 
 i. 09 
 1.05 
 
 I.OO 
 
 0.98 
 
 0.95 
 0.92 
 
 128.72 
 129.49 
 130.24 
 130.98 
 131.70 
 
 132.41 
 
 
 - 77 
 - 7S 
 - 74 
 
 - 72 
 0.71 
 
 O.OO 
 
 5.27 
 
 37-52 
 
 42.22 
 
 - 
 
 69.28 
 
 80.79 
 
 83.31 
 85.71 
 88.00 
 90.18 
 92.25 
 
 96.14 
 
 97-95 
 
 99.70 
 
 101.37 
 
 102.97 
 104.52 
 106.00 
 
 108.81 
 
 110.14 
 111.43 
 112.68 
 113.88 
 "5-05 
 116.18 
 
 118.34 
 H9-37 
 
 2.29 
 
 2.18 
 
 2.07 
 1.99 
 
 1.90 
 I.8i 
 1-75 
 
 T ? C 
 
 ' 
 
 1.33 
 
 121.36 
 
 122.31 
 
 123.24 
 
 
 129.89 
 130.64 
 
 132.09 
 132.80 
 
 133-49 
 
 - 95 
 - 93 
 
 ... 
 ' 7S 
 
 
 
 0.69 
 
 
 
 1 
 
 2 
 3 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 
 44 
 
 45 
 46 
 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
TABLES FOR THE TRUE ANOMALY. 
 
 2 9 
 
 M 
 
 = -57 
 
 -58 
 
 = -59 
 
 .60 
 
 e = .61 
 
 .62 
 
 .V 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
 12688 
 
 32 
 
 129.16 - 7S 
 
 129.89 
 
 * 
 
 A 
 
 "> 
 
 0.73 
 0.72 
 
 '3^32 - 
 .32.01 
 
 IE-S oil 
 
 0.66 
 
 .32-69 
 133-37 
 
 M 
 
 
 .38.40 
 .38-99 
 .39-57 OS7 
 140.14 
 140.71 -" 
 141.27 ' 56 
 141.82 - 55 
 
 142-37 ;" 
 142.91 
 .43.44 ' 53 
 
 '43-97 '* 3 
 .44-49 ' S 
 
 145.00 5 
 * 0.51 
 
 
 146.52 
 
 47.61 
 
 '47.50 
 
 148:94 - 48 
 .49-4. 
 149.87 - 4 
 0.46 
 
 .50.33 
 .50.79 
 
 '5.- 2 4 
 I5.-4 ' 45 
 .52.14 * 
 
 153-45 
 153.88 - 43 
 
 '54-3' 
 
 155-58 
 '55-99 
 156.41 
 
 156.82 
 .57-22 
 
 I57-63 
 .58.03 
 
 158.43 
 .58.83 
 
 : :: 
 
 ' 4 
 
 0.41 
 
 
 I2800 
 
 ' 28 -76 
 129.50 
 
 '3-3 
 
 '3-95 
 
 , 
 
 
 II 
 
 '37-50 o ; 6o 
 
 .38.10 
 138.70 
 .39-28 
 .39-86 ' 
 
 ' S4 
 
 - 
 
 O.SI 
 
 14*9 
 
 142.63 
 
 '43-7 
 
 .44-73 
 
 .45-24 : 
 
 .45-75 o'.jo 
 
 146.25 
 146.74 - 4 
 
 * 0.47 
 148.66 
 149-13 ' 4 ! 
 
 Is a 
 
 150.96 
 151-4. 
 
 152.29 
 152.73 
 
 I53-.6 
 .53-59 
 
 
 '54-86 
 
 '57-31 
 
 158.88 
 I59-27 
 
 0.39 
 
 129.12 
 129.86 - 74 
 
 '3-59 
 
 132.00 
 
 '33-37 
 134.04 
 
 0.69 
 
 '35-34 
 
 137-82 
 138.42 
 
 .39-00 
 .39-59 
 
 '4-8 
 
 142.91 
 
 143-44 
 I43-96 
 
 144.48 
 144.99 
 
 .45-49 
 
 45-99 
 146.48 ' 49 
 
 146.97 
 147-45 
 .47-93 
 148.40 
 148.87 
 
 .49-33 
 .49-79 
 
 
 
 0.49 
 
 0.46 
 
 - . 4 
 
 150.70 
 
 152.02 
 
 152.89 
 .53-3. 
 
 .53-74 
 I54-.5 
 .54-57 
 I54-98 
 .55-39 
 
 ' 44 
 0.44 
 
 157-40 
 
 .57-79 
 158.18 
 
 158.57 
 
 158.95 
 '59-34 
 
 I59-72 
 
 
 . 4 t 
 
 0.39 
 0.39 
 
 0.38 
 0.39 
 0.38 
 
 
 .33-05 
 
 .33-72 
 134-38 
 
 3 
 
 '39-32 
 
 .-02 
 
 142.66 
 
 is;? 
 
 _T 0.49 
 
 jjrja 0.48 
 
 4'" 0.48 
 147.69 
 ,7s TA -47 
 
 149.09 
 .49-55 
 150.00 
 
 .50.89 
 I5I.33 
 
 152.20 
 
 '53-47 : 
 .53-89 ' 4 * 
 
 '54-30 
 
 i 
 
 0.41 
 
 0.41 
 0.41 
 0.41 
 0.40 
 0.39 
 
 I59-78 
 160.15 
 
 .34-74 
 
 154.87 
 
 . 6s 
 
 137-88 
 138-48 
 I39-07 
 I39-65 
 140.22 
 
 140.78 
 141.88 
 
 .43-48 
 144.00 
 
 144-51 
 145.02 
 
 I45-52 
 146.01 
 
 0.57 
 0.56 
 
 * 
 
 146.98 
 147.46 
 .47-93 
 148.40 
 148.86 
 .49-32 
 .49-77 
 
 150.66 
 151.10 
 
 ' 44 
 
 .52-81 
 
 0.40 
 0.41 
 
 0.40 
 
 .58.37 ; 38 
 
 ' 58 -75 o 37 
 '59-' 2 o 37 
 .59-49 
 159.86 J 
 
 .60.23 ' 3 I 
 0.36 
 
 160.59 
 
 .33-79 
 .34-45 
 135-1. 
 
 .35-76 
 .36-39 
 137.01 
 
 .37-63 
 .38-23 
 
 138.82 
 139-4. 
 .39-98 
 140.55 
 141.11 
 
 141.66 
 
 142.74 
 143.26 
 .43-79 
 144.30 
 144.81 
 
 I45-3I 
 145.80 
 146.29 
 
 
 0.62 
 0.60 
 
 0.59 
 0.59 
 
 
 
 so 
 O.SS 
 
 o 
 
 147-72 
 
 1S8 
 
 150.00 
 
 .58-48 
 158.85 
 
 159.22 
 159.58 
 
 - 
 
 160.66 - 3S 
 0.36 
 
 161.02 
 
 0.47 
 0.46 
 0.45 
 
 0.45 
 
 0.44 
 
 .53-00 
 153-42 o "^ 
 
 itl 21 ' 4 
 '54^3 * 
 
 55-03 :; 4 : 
 
 .55-43 , 
 55-82 
 156.21 ^ j g 
 
 3349 ^ 8 
 
 ii 
 
 liS - 
 
 I39.76 
 
 
 IJSS 
 
 46.09 
 
 2 
 
 148.91 
 
 '49-36 
 
 152:31 
 
 '5-79 
 
 154.01 
 I54-4I 
 
 .55-59 
 
 0.40 
 0.40 
 
 O. 
 
 0.37 
 
 0.37 
 0.36 
 
 158.97 ' 37 
 .59-33 
 
 I59-69 
 160.04 f 
 
 ; 160.40 - 36 
 1 Kl : 
 
 0.34 
 I 161.44 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
3 
 
 TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 -57 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
 159-22 """ 
 
 159.61 39 
 160.00 " 39 
 
 160.39 ' 39 
 
 y 0.39 
 160.78 
 
 -t, ',, 0.38 
 
 " 
 
 
 ' 37 
 
 3 
 
 163.42 
 163.79 
 
 164.52 
 164.89 
 
 I65.25 
 165.61 
 
 165.98 
 
 166.34 
 166.69 
 167.05 
 167.41 
 167.76 
 
 I68.I I 
 168.47 
 168.82 
 
 169.86 
 I7O.2I 
 170.56 
 170.90 
 171.24 
 
 I7L59 
 I7L93 
 172.27 
 I72.6I 
 
 0.35 
 
 0.36 
 0.35 
 
 ' 3S 
 
 - 34 
 
 0.3S 
 
 0.34 
 0.34 
 0.34 
 
 *'" vo 0.34 
 
 I73.29 ,. 
 
 173.63 ' 34 
 
 173.97 
 
 I74-3I 
 
 I74-65 
 
 174.98 
 
 Ultt o- 34 
 175-99 ' 33 
 176.33 03 l 
 176.66 
 
 0.34 
 0.34 
 0.34 
 0.33 
 
 0.34 
 
 0.34 
 0.33 
 
 177.00 
 
 '77-33 , 
 177.67 ' 34 
 178.00 ' 33 
 
 0.33 
 178.33 
 178.67 
 179.00 
 
 179-33 
 179.67 
 
 iSo.OO 
 
 7 
 
 ' 34 
 
 e = .58 
 
 160.80 
 
 161.18 
 161.56 
 
 162.30 
 162.67 
 
 
 165.56 
 165.92 
 166.27 
 
 166.62 
 166.97 
 167.32 
 167.67 
 168.02 
 
 168.36 
 168.71 
 169.05 
 169.39 
 
 170.08 
 170.42 
 
 170.75 
 171.09 
 
 I7L43 
 
 171.76 
 172.10 
 
 172.43 
 172.77 
 
 0.38 
 0.38 
 
 - 37 
 
 0.37 
 
 3 
 3 
 
 0.35 
 
 0.34 
 
 0.35 
 0.34 
 
 - 34 
 
 0.33 
 0.34 
 
 ' 33 
 
 173-43 
 173-77 
 174.10 
 
 0.33 
 
 0.34 
 0.33 
 0.33 
 
 174-43 
 
 17476 ' 33 
 
 0.33 
 
 I75-09 
 I75-42 
 175-75 ,. 
 176.08 ' 33 
 176.40 - 32 
 
 176.73 
 177.06 
 
 177-39 
 I77.7I 
 178.04 
 
 178.37 
 178.69 
 I79.O2 
 
 179-35 
 179.67 
 
 iSo.OO 
 
 33 
 
 
 
 "'" 
 
 0.33 
 
 0.33 
 
 -59 
 
 
 I6O.O9 
 
 160.47 ' 38 
 T* n -*i 
 160.84 
 
 161.21 
 
 161.58 
 161.95 
 162.32 
 162.68 
 
 0.37 
 0.37 
 0.37 
 
 163.40 
 
 i6 3-76 
 
 164.11 
 
 ' 37 
 
 - 36 
 
 165.87 
 166.22 35 
 
 166.56 ' 34 
 0.35 
 
 0.34 
 0.34 
 
 ' 34 
 
 I67.93 
 168.27 
 
 168.61 
 168.95 ' 34 
 I6 9 .28 ' 33 
 169.62 
 
 170.29 
 170.62 ' 33 
 
 170.95 
 171.28 Q-*" 
 
 0.33 
 
 172.60 ' 33 
 172.92 - 32 
 173-25 
 
 173-57 
 173.90 
 174.22 
 
 174-55 
 174.87 
 
 175-19 
 175-52 
 175-84 
 176.16 
 176.48 
 
 176.80 
 177.12 
 
 177-44 
 177.76 
 178.08 
 
 178.40 
 
 179.04 
 179-36 
 179.68 
 
 180.00 
 
 0.32 
 
 0.33 
 0.32 
 
 '.32 
 
 ' 3 
 
 ' 32 
 0.32 
 
 e .60 
 
 160:89 ' 37 
 
 161.26 
 
 161.62 ' 3 ^ 
 0.36 
 
 161.98 
 
 162.34 ' 3 
 
 162.70 3 
 
 - 0.35 
 
 '63-76 
 164.11 
 164.46 
 
 176.56 
 
 176.87 
 177-18 
 I77.50 
 
 178.12 
 
 178.44 
 
 178.75 
 179.06 
 
 179-37 
 179.69 
 
 180.00 
 
 - 3S 
 - 34 
 
 166.18 
 166.52 
 166.85 
 
 167.19 
 
 167.53 
 167.86 
 168.19 
 168.53 
 
 168.86 
 169.19 
 169.52 
 169.84 
 
 170.50 
 170.82 
 
 172.76 
 I73.07 
 173-39 
 
 I737I 
 I74-03 
 174-35 
 174.66 
 174.98 
 
 - 33 
 
 0.34 
 
 ' 33 
 
 0.32 
 0.32 
 0.31 
 
 0.31 
 
 0.31 
 0.32 
 
 .61 
 
 161.67 
 
 ' 36 
 
 162.02 - 35 
 0.35 
 
 162 7 * ' 36 
 
 l6 3-o8 ' 3S , 
 
 164.46 - 3s 
 
 16^.80 ' 34 
 165.14 ' 34 
 
 166.48 - 33 
 
 166.81 " 33 
 
 168.13 :- 3 
 168.45 - 3 
 
 169.10 
 
 0.32 
 
 ' 32 
 
 0.32 
 
 169.74 
 170.07 
 170.39 
 
 170.70 
 I7I.O2 
 
 I7I-34 
 171.66 
 171.97 
 
 172.29 
 172.60 
 172.91 
 I73.23 
 173-54 
 
 173.85 
 174.16 
 
 174-47 
 174.78 
 
 I75-09 
 
 17540 
 I75.7I 
 176.02 -* 
 
 '76-32 3 
 
 176.63 ; 3I 
 176.94 
 177.25 ' 3 ' 
 177-55 
 177.86 O 6 t 
 
 178.47 . 
 178.78 - 31 
 179-08 
 
 180.00 
 
 0.31 
 0.31 
 0.31 
 0.31 
 
 0.31 
 
 = .62 
 
 161.02 
 161.37 
 161.72 
 162.07 
 162.42 
 
 '63-79 
 
 165.46 
 
 166.12 
 166.45 
 166.78 
 167.10 
 
 168.39 
 168.71 
 169.03 
 
 169-34 
 169.66 
 169.97 
 170.29 
 
 0.35 
 0.35 
 0.35 
 
 0.34 
 0.33 
 
 0.33 
 0.33 
 0.33 
 0.33 
 
 0.32 
 0.31 
 
 0.31 
 
 0.31 
 0.31 
 170.91 
 171.22 
 
 "71-84 ' 3 ! 
 172.15 
 
 172.46 
 '7-76 - 
 I73.07 
 173-38 3I 
 173-68 
 
 '74-59 
 
 0.30 
 
 '75-5 
 175.80 - 3 
 
 176.10 - 30 
 "76.40 - 3 
 176.71 
 
 177.01 
 
 177-31 
 177.61 
 177.91 
 178.21 
 
 . 
 
 0.30 
 0.30 
 
 0.29 
 
 179.70 
 180.00 
 
 0.30 
 
 JW 
 
 0.34 
 0.34 
 
 161.44 
 
 161.79 ' 3S 
 
 162.13 ' 34 
 .62.47 !" 34 
 162.81 
 
 163-15 
 
 I6 3'49 o' 3 . 4 
 
 163.82 ' 33 
 
 164.15 ' 33 
 
 164-48 ' 33 
 
 0.33 
 164.81 
 
 165.1 4 ' 33 
 165-47 
 
 "65-79 ':: 
 
 166.11 
 
 166.43 
 
 166.75 
 167.07 
 
 167-39 
 
 0.32 
 
 0.32 
 
 0.32 
 0.31 
 
 0.31 
 0.31 
 
 168.65 
 168.96 
 169.27 
 
 169.58 
 169.89 
 170.20 
 170.50 
 170.81 
 
 172.02 
 
 0.30 
 172.62 
 
 172.92 - 3 
 
 173.22 ' 3 
 I73.52 ' 3 
 
 "73-82 ' 3 
 
 !?K! 
 
 1 75-3 1 
 
 
 176.49 
 '76.78 ' 
 
 177.66 ' 29 
 '77-95 
 "78-25 - 3 
 
 179.71 
 180.00 
 
 0.29 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
TABLES FOR THE TRUE ANOMALY. 
 
 .65 
 
 e = .66 
 
 e = .67 
 
 = .68 
 
 e = .69 
 
 .70 
 
 M 
 
 
 
 1 
 
 2 
 3 
 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 
 24 
 
 25 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
 o.oo 
 
 5-92 
 
 11.79 
 
 I'll 
 ' 8 
 
 28.68 
 
 5-47 
 
 43.83 
 48.43 
 
 52-78 
 56.91 
 60.8, 
 
 
 fflr * 3-29 
 71.28 
 
 -4-4 *" 
 
 &% >? 
 
 82.78 I' 6 * 
 
 89-93 
 92.08 
 
 96.10 
 
 97-97 
 
 99-76 
 
 101.47 
 
 103.12 
 
 ,04.70 
 ,06.21 
 ,07.67 
 109.08 
 110.43 
 
 ,13.00 
 114.22 
 115.40 
 116.54 
 
 ,17.65 
 1,8.72 
 
 120.77 
 121-75 
 
 122.7, 
 123.64 
 
 -71 
 
 6s 
 
 S8 
 
 SI 
 
 .26 
 
 .22 
 
 .18 
 
 I26 ' 2 9 
 
 0.96 
 
 0.84 
 
 *> 
 
 ::: 
 
 O.OO 
 
 6.19 
 
 12.33 
 18.36 
 
 24-23 
 
 29-91 
 35-36 
 
 6.14 
 6.03 
 S-87 
 5.68 
 
 5-45 
 
 45-53 
 
 StS 
 
 62.81 
 
 73-34 , .. 
 76-45 3 
 79-39 
 
 96.04 
 
 97-97 
 99-81 
 
 103.26 
 104.87 
 
 106.42 
 107-91 
 109-34 
 1,0.72 
 1,2.05 
 
 113-33 
 114.56 
 
 115-75 
 ,16.90 
 ,18.02 
 
 '33-6 
 
 
 2.03 
 1.93 
 
 1.84 
 1.76 
 
 I-SS 
 
 1.38 
 1.33 
 1.28 
 
 1.23 
 
 , c I-I9 
 I. IS 
 
 122.16 
 123-12 
 
 -7-56 
 
 129.96 
 
 0.94 
 
 0.72 
 
 0.70 
 
 ; 
 
 O.OO 
 
 6.49 
 
 I2.9I 
 
 19.21 
 
 31.22 
 36.86 
 42.23 
 
 
 4.52 
 
 60.88 
 64-87 
 
 68.6, 
 72.13 
 
 75-44 
 78-55 
 81.48 
 84.24 
 86.85 
 
 91.64 
 93-85 
 95-95 
 97-95 
 
 i 99-85 
 ! 101.66 
 
 i 103-39 
 | 105.05 
 | 106.63 
 
 108.15 
 ,09.61 
 
 ! ill. 01 
 
 112.36 
 
 ' ,13.66 
 
 114.91 
 
 1,6.12 
 
 ,17.29 
 
 ! 118.41 
 II9-5I 
 120.56 
 121.59 
 122.58 
 
 124.49 
 
 128.81 
 
 3-31 
 
 3.II 
 2.93 
 
 2.46 
 
 134-57 
 
 135-64 
 
 58 
 
 S2 
 
 u 
 
 0.81 
 0.78 
 
 130.40 
 ,31.16 
 ,31.9, 
 132.64 ' 73 
 
 133-35 
 
 ' 7S 
 
 0.71 
 
 136.70 
 
 O.OO 
 
 6.81 
 13-53 
 
 26.49 
 32.61 
 
 s ' 21 
 54-09 *'jg 
 
 58.67 
 62.97 4 " 30 
 67.60 4 ' 3 
 
 7 ' 76 I'll 
 
 74.29 ** 
 
 * 3.30 
 
 77-59 . I0 
 80.69 3 ' 10 
 83-60 2 ' 9 ' 
 
 86.34 I'" 
 88.92 2 ' 58 
 
 2.44 
 
 95-84 
 97-91 
 99.87 
 
 101.74 
 103.52 
 105.22 
 ,06.85 
 108.40 
 
 109.89 
 
 1,2.68 
 114.00 
 II5-27 
 
 116.49 
 117.68 
 1,8.82 
 1 ,9.92 
 
 I22.O2 
 
 & 
 
 
 
 78 
 
 : 
 
 ;- 
 
 .19 
 14 
 .10 
 
 0.80 
 0.78 
 
 0.74 
 
 133-79 
 134-49 
 
 I37-I3 
 
 137-75 
 
 O.OO 
 
 45-81 
 51-15 
 
 60.80 
 
 65-15 
 69.20 
 
 72.97 
 76.50 
 
 79-79 
 
 82.87 
 
 91-03 
 
 93-43 
 95-70 
 9785 
 
 3-29 
 
 101.81 
 103.64 
 
 105-39 
 107.05 
 108.64 
 1,0.16 
 
 111.62 
 1,3.0, 
 
 "4-35 
 1,5.64 
 ,16.88 
 
 1 1 8.08 
 119.23 
 120.34 
 
 ,22.46 
 
 1.27 
 
 .83 
 .75 
 
 .46 
 
 39 
 34 
 
 IS 
 .II 
 
 ss :i; 
 
 ,27.20 
 
 0.86 
 128.06 
 ,28.9, 
 
 '33-54 
 
 I35.62 
 
 i ,36.28 
 
 136.93 
 
 137-57 
 
 ! 138.80 
 
 
 o.oo 
 
 7.51 
 14-93 
 
 A 
 
 7.51 
 7.42 
 
 7.21 
 
 5- 
 
 63.01 
 
 
 3.28 
 
 75-24 
 78.76 
 
 82.04 
 
 87^96 
 90.64 
 
 SS :;; 
 
 -.'i 
 
 , 
 It 
 tt 
 
 4 = 
 
 n 
 
 M 
 
 "5 
 
 ,24.91 
 ,25.86 - 9S 
 ,26.78 '' 2 
 127.67 ' 89 
 
 s 
 
 0.74 
 
 0.71 
 O.69 
 
 0.66 
 0.64 
 
 105-55 
 ,07.26 
 ,08.89 
 1,0.44 
 
 1 1 1-93 
 
 H3-35 
 ,14.72 
 ,16.02 
 1,7.28 
 ,18.49 
 
 ,19.66 
 ,20.78 
 ,21.86 
 122.91 
 
 131-01 
 131-79 
 
 I33-29 
 134-01 
 134-72 
 
 137-39 
 138.02 
 
 138.64 
 I39-25 
 
 I39-84 
 
 0.00 
 
 23.27 
 v> so 
 
 * 
 
 S 
 
 7 21 
 
 6.86 
 
 3.25 
 
 IS 
 
 101.90 
 ,03.86 
 
 109.14 
 1,0.73 
 ,12.25 
 ,13-70 
 
 1,5.08 
 1,6.41 
 1,7.69 
 1,8.92 
 120.09 
 
 121.23 
 122.32 
 123-38 
 ,24.40 
 
 126.34 
 128.17 
 
 '33-78 
 
 .85 
 .76 
 
 .67 
 
 38 
 
 33 
 
 I ; 
 
 - 87 
 
 
 
 '34-50 
 
 i 
 
 0.71 
 
 0.68 
 0.68 
 o.6s 
 0.64 
 
 137-86 
 
 138-49 ** 
 
 139-11 
 
 139-71 
 
 
 ,40.88 
 
 
 
 1 
 
 2 
 3 
 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 e = .64 
 
 e = .66 
 
 .68 
 
 .70 
 
 M 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
 135-88 * 
 
 
 '39-55 El 
 140.12 
 
 0.57 
 140.69 
 
 .41.25 ' 5 ' 
 141.80 5S 
 
 .42.34 "" 
 142.87 ;* 3 
 
 '43-39 
 143-9. 'I, 
 
 145.42 ^r 
 
 .45-9. 
 .46-39 -4 ! 
 146.87 - 48 
 
 .47-34 ' 47 
 147.81 
 
 \j,t}\j 
 
 148.27 
 148.73 ' 46 
 149.18 ' 4S 
 149.62 ' 44 
 150.06 ' 44 
 
 0.43 
 
 150.49 
 150.92 ' 43 
 
 151.35 ' 43 
 
 j^f :::: 
 152.60 
 
 '53-01 - 4 ' 
 
 154.61 
 155.00 
 
 155-39 
 155-77 
 
 .57.27 ' 37 
 
 .57.64 ' 37 
 
 158.0, ; 37 
 
 158.37 , 6 
 
 158.73 ' 3 * 
 
 159.09 - 3 
 
 159-45 
 
 159.80 J5 
 
 0.35 
 
 160.15 
 
 160.50 - 35 
 
 160.84 - 34 
 
 161.19 ' 3S 
 
 161.53 -3 J 
 161.87 
 
 183 ? 
 
 S5 s 
 
 .38.75 
 .39.35 
 .39.93 
 
 
 ;: 
 
 " 
 
 * 
 
 - s4 
 
 143.22 
 143.74 
 .44.25 
 
 .45.74 
 
 146.71 
 
 147.18 
 
 
 ' SI 
 
 - 47 
 
 149.01 
 
 .49.45 
 149.89 
 
 .50.33 ; 44 
 
 151.18 
 151.60 - 42 
 152.02 
 
 .52.43 
 152.84 
 
 ' 42 
 
 
 
 154.8. 
 
 .55-20 
 155-58 
 
 0.39 
 
 
 156.70 
 
 SS 
 
 '59.57 rn 
 
 .59-92 
 
 160.26 
 
 0.35 
 
 160.61 
 
 160.95 ' 34 
 
 ,61.28 ' 33 
 161.62 ' 34 
 .61.95 ' 33 
 
 3 0.33 
 162.28 
 
 136.70 
 '37-33 
 
 .39-74 
 140.32 
 140.88 
 141.44 
 141.99 
 
 143.06 
 .43-58 
 144.09 
 144.60 
 
 145.10 
 
 .45-59 
 146.08 
 
 . 
 
 - 3 
 
 ,. 
 
 3 
 
 ' s6 
 
 0.51 
 0.50 
 
 0.49 
 
 o s 
 
 - 45 
 
 148.86 - 45 
 
 '49-31 - 
 
 148.41 
 
 '50-61 
 
 151.86 
 
 0.42 
 0.42 
 0.41 
 
 0.41 
 
 II 5 
 
 .55-03 ', 
 
 .55.4. o ; 3 7 
 j 55-78 037 
 
 iseisf - 37 
 
 O O.37 
 
 ^ '_ 0.36 
 
 O.36 
 
 0.34 
 0.34 
 
 .59-37 
 I59.7I 
 160.05 
 
 .60.39 ' 34 
 
 160.73 J4 
 
 J 0.33 
 
 161.06 
 
 .61.39 ^ 33 
 161.72 ' 33 
 162.05 ' 33 
 162.38 
 
 162.70 
 
 
 140.72 
 141.28 
 141.83 
 
 0.57 
 0.56 
 
 0.55 
 
 145.46 
 
 .45-94 
 .46-43 
 146.90 
 
 153-33 
 
 ' 47 
 
 148.28 
 
 '48-73 
 
 150.05 Q " 
 150.47 
 
 . ., 
 
 .51.73 r 
 152.14 
 
 0.40 
 
 
 
 2 
 
 156.00 
 
 156.36 
 .56.73 
 .57-09 
 
 7 
 
 0.35 
 
 159.86 
 
 160.20 ' 34 
 
 ifeii - 
 ' 6 --'9 ::?, 
 161.51 
 
 161.84 - 33 
 
 162.16 - 32 
 
 162.48 - 32 
 
 162.80 - 32 
 0.31 
 163.11 
 
 1 388o 
 13940 
 139-99 
 '40-57 
 
 142.24 
 '4 2 '77 
 
 H4-34 
 
 146.31 
 146.78 
 
 0.55 
 0.53 
 0.53 
 0.52 
 0.52 
 
 0.50 
 
 0.47 
 
 148. 17 
 
 148.62 - 4s 
 0.44 
 
 149.06 
 149.50 - 44 
 
 .49.93 :i 3 
 .50.36 
 
 150.78 - 42 
 0.42 
 
 151.20 
 151.61 - 41 
 152.02 4 
 .52.42 - 4 
 
 152.82 - 4 
 0.39 
 
 .53-99 
 .54-37 
 .54-75 
 
 .55-12 
 .55-49 
 .55-86 
 156.22 
 156.58 
 
 ' 37 
 
 .57.64 " 3 * 
 
 .57-99 ,; 
 .58.34 034 
 158.68 
 159.02 - 34 
 
 IW-36 ' 34 
 
 159-69 '" 
 
 160.02 - 33 
 
 0.33 
 
 160^68 ' 33 
 161.00 ' 32 
 161.32 ' 32 
 
 161.64 ' 32 
 ' 0.32 
 
 161.96 
 162.28 ' 32 
 162.59 ' 31 
 
 162.90 - 3 ; 
 163.21 
 
 .39.84 
 140.43 
 141.00 
 .41.56 - s6 
 
 r * nee 
 142.11 
 
 142.66 
 .43.I9 
 .43-7. 
 
 - ss 
 
 0.55 
 
 '44-73 ;;! 
 
 1C -70 ' 49 
 
 8S ' 4 ' 
 
 ,46.68 - 47 
 
 '48-52 
 - 4s 
 
 
 150.68 - 4 
 
 1*21,2 ' 40 
 152.71 " 39 
 
 ' ^38 
 
 '53-49 :; 3 : 
 
 . 53-88 
 .54-26 ' 38 
 I54-63 ' 
 .55-00 " 
 
 .55-37 ;j 7 
 
 '55-74 o ; 36 
 156.10 
 
 .56.46 - 3 ! 
 
 158.20 - 34 
 
 .58.54 ' 
 158.87 - 33 
 
 .59-21 
 .59-54 ' 
 
 .63.52 
 
 0.31 
 
 160.84 
 ,6147 - 32 
 
 ' 62 '-' o^ 
 162.41 
 162.72 3t 
 
 163.02 - 30 
 
 :: 3 
 
 .63-93 
 
 140.88 
 
 .41-45 
 ,42.00 
 
 142-55 
 143-09 
 
 143-62 
 
 .44.13 
 ,44.64 
 
 145-15 
 .45-64 
 
 * 
 
 - SI 
 
 ' SI 
 
 - 
 
 0.45 
 
 ,47.07 
 .47-54 
 .47-99 
 ,48.44 
 ,48.89 ' 4S 
 
 '49-33 
 149.76 
 150.18 
 
 150.60 
 ,51.02 ' 42 
 51.43 ' 4 ' 
 
 .53-4. 
 153.79 
 I54.I7 
 
 .54-54 
 .54-91 
 
 
 0.35 
 
 .57.05 
 
 158.08 
 
 158.41 - 33 
 
 j^g 5 0.34 
 
 I59!o8 ' 33 
 
 '59.4. - 
 
 i^T 1 ' 32 
 160.69 32 
 
 ,61.01 ' 32 
 0.31 
 
 161.32 
 161.63 ' 31 
 ,61.94 ' 31 
 ,62.24 ' 3 
 I62 '55 o^o 
 
 ,62.85 
 .63.15 ' 3 " 
 .63.45 
 
 !:2{ - 
 
 0.29 
 
 .64.33 
 
TABLES FOR THE TRUE ANOMALY. 
 
 33 
 
 M 
 
 e = .64 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
 161.87 
 162.20 
 162.54 
 162.87 
 163.20 
 
 163.53 
 163.86 
 164.19 
 
 0.33 
 0.34 
 0.33 
 0.33 
 0.33 
 
 0.33 
 
 165.80 
 
 I66.ii 
 
 
 167.37 
 167.68 
 167.99 
 
 168.29 
 168.60 
 168.91 
 169.21 
 
 0.30 
 
 - 3 
 
 17042 ' 3 
 
 170-72 ' 3 
 I7I.O2 
 
 I7I.3I 
 I7I.6I 
 
 - 3 
 
 0.29 
 
 172.20 
 
 '7-50 
 
 si 
 
 I 1 A CA O.29 
 
 ,-,. e, - 2 9 
 
 
 '75-70 
 
 177.14 
 
 178.00 
 178.28 
 
 179.71 
 
 180.00 
 
 e = .65 
 
 * 
 
 0.29 
 
 - 28 
 
 - 29 
 - 28 
 
 I6228 
 
 162.61 ' 33 
 
 162.94 ' 33 
 
 ' 33 
 
 - 32 
 
 164.87 - 3 
 
 165.81 
 166.12 
 
 166.43 
 
 167.05 Q 3Q 
 
 167.66 ' 31 
 167.96 ' 3 
 
 168.26 ' 3 
 0.30 
 
 168.56 
 168.86 ' 3 
 169.16 ' 30 
 
 '69.46 : 3 
 
 
 
 - 3 
 - 29 
 
 0.29 
 
 .66 
 
 170.64 
 
 170.93 
 171.22 
 
 172.09 " 
 
 '7 2 -38 HI 
 
 '7 2 -67 ; 2 9 
 
 T . o. 28 
 
 0.29 
 0.28 
 
 '75-52 
 175-80 
 '76-08 ; 28 
 
 ..28 
 
 177.20 
 
 178.60 
 178.88 
 179.16 
 179.44 
 179.72 
 
 180.00 
 
 *! 
 
 - 2 
 
 162.70 
 163.02 ' 32 
 
 i6 3-34 :- 3 : 
 
 163.66 ' 32 
 163.98 ' 32 
 
 0.31 
 
 164.91 
 165.22 
 
 166.45 - 31 
 166.75 - 3 
 
 167.95 - 3 
 168.24 - 2 
 
 170.28 
 
 '73-' 2 . 28 
 |73-40 28 
 
 I73-96 'll 
 
 174-24 ; 27 
 174-51 
 
 J 74-79 ', 
 175-07 
 175-35 
 175-62 
 
 * 
 
 175.90 
 
 '7 6 -'7 
 '7 6 -45 
 
 "'28 
 " 
 
 '77-27 
 
 178.09 
 178.36 
 
 178.64 
 178.91 
 179.18 
 179-45 
 179-73 
 180.00 
 
 ' 27 
 
 0.31 
 
 164.36 ' 31 
 " 0.30 
 
 164.66 
 164.97 
 
 si 
 
 166.17 
 
 167.06 
 
 168.23 
 168.52 
 
 169.09 
 169.38 
 
 171.91 
 
 ' 
 
 - 29 
 
 e = .68 
 
 0.28 
 0.28 
 
 0.28 
 0.28 
 
 0.27 
 
 '73-01 
 
 174.37 
 
 174.65 
 174.92 
 
 175.19 
 175.46 
 175.73 
 
 175.99 
 176.26 
 
 176.53 
 176.80 
 177.07 
 
 27 
 
 
 ' 27 
 
 '78-94 He 
 179.20 ' 
 
 '79-47 H 
 '79-73 . 2? 
 180.00 
 
 l66 -5' o 20 
 166.80 ' 
 
 167.09 ' 29 
 
 167.38 I'll 
 
 167.95 - 
 168.23 - 28 
 
 I68 '5 2 oil 
 168.80 ' 28 
 
 169.08 ' 28 
 0.28 
 
 0.28 
 0.27 
 0.28 
 
 170.74 
 
 171*1 -*l 
 171.29 ' 28 
 171.56 ' 27 
 
 171.83 ' 27 
 
 
 
 172.10 
 
 172.9 
 
 '73-8 
 
 0.27 
 0.27 
 
 - 27 
 
 173.98 
 174.24 
 
 174.51 
 
 174-77 
 I75-04 
 
 176.09 
 
 176.35 
 176.62 
 176.88 
 
 177.92 
 178.18 
 
 '78-44 
 
 
 180.00 
 
 .69 
 
 sts 
 
 164.82 
 165.11 ' 29 
 
 0.29 
 
 165.40 
 
 166.27 ' 29 
 
 168.24 
 
 
 0.27 
 
 169.62 
 
 169.89 - 27 
 170.16 - 27 
 
 170.43 
 170.70 ; 2 7 
 
 170.97 27 
 
 171.24 ' 
 
 111 
 
 '73-35 
 
 174-39 
 174.64 - 2 
 
 * 0.2 
 
 T2 0.26 
 
 1.26 
 
 "2 
 ' 26 
 
 0.25 
 
 177.97 I'll 
 
 0.25 
 
 '79-4 :; 
 
 '79-49 ' 
 '79-75 
 
 175-93 I 
 176.70 
 
 e = .70 
 
 Af 
 
 180.00 
 
 
 164.91 - 2 
 
 !S3? - 
 
 ii 
 
 168.54 
 168.8? ' 27 
 169.08 ' 27 
 
 '^9-35 H 
 
 169.61 ' 26 
 
 0.27 
 
 169.88 
 170-14 ' 2 , 
 
 '70-93 
 
 1-2 7? 
 
 173:- 
 173-26 
 
 '73-5! 
 
 0.26 
 0.26 
 0.26 
 
 0.25 
 0.26 
 0.26 
 
 ,-. ,_ 
 
 0.2S 
 
 0.2S 
 
 '75-53 H 
 175.78 ' 2S 
 176.03 ' 2S 
 
 176.28 
 
 176.53 
 176.78 
 
 177.03 
 
 177-28 
 
 177-53 
 177-77 
 178.02 
 178.27 
 178.52 ' 2S 
 
 178.76 
 179.01 
 179-26 ' 2S 
 179.51 
 
 179-75 ; 2S 
 180.00 
 
 0.2S 
 
 0.2S 
 
 ' 2S 
 
 0.24 
 
 0.2S 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
34 
 
 TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 e = .71 
 
 .72 
 
 .73 
 
 e = .74 
 
 -75 
 
 .76 
 
 .77 
 
 M 
 
 
 
 1 
 
 2 
 3 
 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
 o.oo 
 8-35 
 
 32.04 
 
 * 
 
 7.94 
 
 7.12 
 6.65 
 
 62.88 5-23 
 
 4.81 
 
 67.69 
 
 72.12 4 ' 43 
 
 76.20 4 ' 08 
 
 79-96 I'll 
 
 86.67 
 89.66 
 
 99-77 
 101.92 
 
 103-95 
 105.86 
 107.67 
 
 109.39 
 1 1 1. 02 
 "2-57 
 114-05 
 115-47 
 116.82 
 n8.il 
 
 119-35 
 120.55 
 121.70 
 
 122.80 
 123.86 
 124.89 
 125.89 
 126.84 ' 9S 
 
 0.94 
 
 2.IS 
 
 2.03 
 
 .91 
 
 .72 
 
 63 
 
 55 
 ,.|8 
 
 29 
 
 33 
 
 
 '3 2 ' 02 o 78 
 132.80 ' 78 
 
 '33-55 I'" 
 I34-29 '* 
 
 140.19 
 
 '40-77 
 
 141.91 
 
 A 
 
 8.82 
 8.65 
 8.33 
 7.90 
 7-39 
 
 0.00 
 
 8.82 
 
 17-47 
 
 33-70 
 41.09 
 
 6O.O2 
 
 70.16 
 74.60 4 ' 44 
 
 78.6 7 4 ' 7 
 
 W > A T *5* /4 
 02.41 
 
 85-85 3 ' 44 
 
 2 ' 39 
 2.24 
 
 91.99 
 
 94-74 
 97.29 
 99.68 
 
 101.92 
 104.02 
 106.00 
 107.87 
 109.64 
 
 111.31 
 112.90 
 114.42 
 115.86 
 117-23 
 
 I2I.O2 
 122.18 
 
 .21 
 .16 
 
 .03 
 
 .00 
 0.97 
 
 ' 28 '30 
 
 ! 2 ?' 2 0.88 
 0.84 
 0.83 
 
 125.40 
 126.40 
 127.37 
 
 I34.8I 
 135-53 
 136.23 
 
 136.91 
 
 ss r 
 138.86 *** 
 
 139.48 - 2 
 0.60 
 
 140.08 
 140.68 
 141.26 
 
 0.72 
 0.70 
 
 0.68 
 0.67 
 
 ' 6 
 ' s8 
 
 O.OO 
 
 9-35 9 
 
 i8. 4 8 9 -; 3 
 
 2 7' 2 3 I'" 
 35-48 * 
 
 43-14 
 50.19 
 56.64 
 62.51 
 67.86 
 
 72.71 
 
 77-15 
 81.20 
 84.90 
 88.31 
 
 7.05 
 6.45 
 5.87 
 
 4.85 
 
 4-44 
 3-70 
 
 99-56 
 101.89 
 
 104.08 
 106.14 
 IO8.O7 
 109.89 
 III.6I 
 
 113.24 
 1 14.79 
 II6.26 
 117.66 
 Iig.OO 
 
 120.28 
 121.50 
 122.68 
 
 123.80 
 124.89 
 
 125.93 
 126.93 
 127.90 
 
 128.84 - 94 
 129-75 'll 
 
 2.19 
 2.06 
 
 .63 
 .55 
 
 .34 
 
 JK 
 
 12 
 
 09 
 
 1.04 
 
 0.97 
 
 I33.87 
 
 I34.62 
 I35.36 
 136.07 
 
 - 74 
 
 138.11 
 
 139.38 
 I40.OO 
 
 140.60 
 
 0.59 
 141.19 
 4l.76 '" 
 
 142.93 
 
 142.88 
 I4342 
 
 H3.95 
 
 
 0.00 
 
 9.91 
 
 19.57 
 28.78 
 
 37.40 
 
 45-34 
 52-59 
 59.16 
 65.11 
 
 75-35 
 
 79-77 
 
 133.66 
 134-44 
 I35-I9 
 
 I35-92 
 136.63 
 137-32 
 138.00 
 
 139-30 
 139-92 
 
 
 9.66 
 9.21 
 8.62 
 7-94 
 7.25 
 
 . 
 4 ' 4 
 
 9O.8I 
 
 93-90 
 96.75 
 
 99-39 
 
 106.26 
 108.26 
 110.14 
 111.91 
 H3-59 
 
 115-17 
 116.68 
 118.10 
 119.47 
 120.77 
 
 I22.OI 
 123.19 
 124-33 
 125-43 
 126.48 
 
 127.49 
 128.46 
 129.40 
 
 3.09 
 
 2.8 S 
 
 2.64 
 2.45 
 
 2.14 
 .88 
 
 142.29 
 142.84 
 143-39 
 143-93 
 144-45 
 
 144-97 
 
 - 97 
 - 94 
 
 0.78 
 0.75 
 0.73 
 
 0.71 
 0.69 
 0.68 
 
 
 
 ' ss 
 
 
 
 
 O.OO 
 
 10-53" 
 20.77 
 
 47.68 
 
 10.53 
 10.24 
 9.70 
 8.99 
 8.22 
 
 7-44 
 
 78.07 
 82. 4 6 4 ' 39 
 86.43 
 90.05 
 
 96.38 
 
 99-17 
 
 101.75 
 
 104-14 
 
 3 ' 97 
 3 ' 62 
 3-30 
 
 3.03 
 
 108.44 
 1 10.39 
 112.22 
 113-94 
 
 "5-57 
 117.10 
 118.56 
 
 119-95 
 121.27 
 
 123-73 
 124.88 
 
 125-99 
 127-05 
 128.06 
 
 129.05 
 129.99 
 130.90 
 
 g, 
 l '* 3 
 
 . -. 
 1>IS 
 
 0.99 
 
 0.94 
 
 135-02 "": 
 
 '35-78 - 7 
 '36-50 ^ 
 137.21 
 '37-90 o f 
 138.57 6 l 
 139.23 ' fi . 
 139.86 ' 63 
 
 O.02 
 
 '4-4 8 . 6I 
 141-09 
 
 142.26 
 142-83 
 
 143.38 
 I43-92 
 144-45 
 144-97 
 145.48 
 
 145.98 
 
 ' S7 
 0.55 
 
 ; 
 
 o.oo 
 
 22.08 I 
 
 32.30 1 
 
 4--70 
 
 ill 
 
 n: 
 
 64.60 6 - 7 
 
 76.04 
 
 80.88 
 85.22 
 
 92.69 
 95-92 
 
 98.89 
 101.61 
 104.12 
 106.45 
 108.62 
 
 114.30 
 115.97 
 117.55 
 119.04 
 120.45 
 121.79 
 123.07 
 124.29 
 
 125.46 
 126.57 
 
 128^66 
 
 132.39 
 133.24 
 134-07 
 
 134-86 
 
 4 ' 34 
 
 2 ' 72 
 2 ' SI 
 
 ; 9 
 
 1.17 
 
 0.73 
 0.70 
 0.69 
 
 0.67 
 0.64 
 
 141.67 
 
 142.83 
 143-39 
 143-93 
 144.47 
 144.99 
 
 a 
 
 O.OO 
 
 11.98 
 
 '37-02 
 
 
 52.87 
 
 60.65 
 67.51 
 
 73-57 
 83-75 
 
 95-37 3 
 
 104.07 
 106.52 
 108.78 
 110.88 
 
 112.84 
 114.67 
 116.39 
 118.00 
 
 120.97 
 122.34 
 123.64 
 124.87 
 126.05 
 
 127.18 
 128.26 
 129.29 
 
 131-23 
 132.15 
 
 26S 
 
 2 
 
 1.96 
 
 
 1.37 
 
 1.18 
 1. 13 
 
 1. 08 
 1.03 
 
 0.92 
 
 0.88 
 0.85 
 0.82 
 
 0.75 
 0.72 
 
 146.51 
 146.99 
 
 141.06 
 
 141.67 " 
 
 142.26 - 59 
 0.59 
 
 0.56 
 
 '44 ; 5i '* 4 
 
 145-04 OS2 
 
 145.56 
 
 146.07 ' SI 
 
 146.56 - 49 
 I47.05 
 
 '47-53 o ; 4 7 
 148.00 
 
 
 
 1 
 2 
 3 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 10 
 11 
 12 
 13 
 14 
 
 15 
 16 
 17 
 18 
 19 
 
 20 
 21 
 22 
 23 
 24 
 
 25 
 26 
 27 
 28 
 29 
 
 30 
 31 
 32 
 33 
 34 
 
 35 
 
 36 
 37 
 38 
 39 
 
 40 
 41 
 42 
 43 
 44 
 
 45 
 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 
TABLES FOR THE TRUE ANOMALY. 
 
 35 
 
 .71 
 
 .72 
 
 -74 
 
 -75 
 
 .77 
 
 M 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 105 
 106 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 141.91 
 
 143-00 
 
 143-54 
 144.06 
 
 144-57 
 145-07 
 
 0.51 
 
 0.50 
 0.50 
 
 
 147.93 
 
 
 
 152.17 
 152.57 
 152.95 
 
 153-34 
 I53.72 
 154.10 
 
 154-47 
 I54-84 
 
 155.92 
 
 0.40 
 0.40 
 0.40 
 0.38 
 0.39 
 
 I64-45 
 
 0.34 
 
 3 
 
 
 
 0.34 
 
 156.96 
 I57.30 
 157.64 
 I57.98 
 
 158.31 ~ 33 
 
 158.64 
 
 158.97 : 
 
 159-29 IT 
 
 159-62 " 
 
 159-94 ; 3I 
 
 160.25 
 
 .60.57 :~ 32 
 
 160.88 ' 31 
 
 161.19 ' 31 
 
 161.49 ' 3 
 
 * 0.31 
 
 161.80 
 
 162.10 ' 3 
 
 162.40 - 30 
 
 162.70 - 3 
 
 163.00 ' 30 
 
 J 0.29 
 
 .63.29 
 
 .63-58 :; 29 
 
 120 164.73 
 
 0.29 
 0.28 
 
 142.93 
 143-47 
 144.00 
 
 I44-5I 
 145-02 
 
 I45-52 
 146.01 
 146.49 
 146.97 
 147-43 
 147.89 
 148.34 
 148.79 
 
 I49.23 
 149.66 
 
 150.08 
 150.50 
 150.92 
 
 152.13 
 152.52 
 152.91 
 153-29 
 I53-67 
 
 154-05 
 
 0.50 
 
 0.49 
 0.48 
 
 ' 43 
 0.42 
 
 - 
 
 '43-95 
 '44-47 
 .44.99 
 
 146.46 
 
 46.94 
 
 I55.I4 
 I55-50 
 
 I55.85 
 156.20 
 
 156.55 
 156.89 
 
 I57.23 
 
 157-57 
 I57-90 
 158.23 
 158.56 
 158.88 
 
 159.21 
 159-52 
 159.84 - 
 160.15 ' 3 
 
 0.33 
 
 0.32 
 0.33 
 
 161.38 - 3 
 
 161.68 - 30 
 
 161.98 - 3 
 
 0.29 
 
 .62.27 
 
 .62.57 - 30 
 
 162.86 
 
 163-15 
 
 .63.44 ; 
 
 .64.85 
 165.13 
 
 
 
 !l-1r ' 46 
 H/-87 ., 
 
 .48-32 
 148.77 
 
 0.45 
 0.45 
 
 0.44 
 
 150.07 
 
 '50-49 
 
 -: 
 
 152.88 
 I53-27 
 I53-64 
 154.02 
 
 I54.38 
 154-75 
 
 0.38 
 0.36 
 0.37 
 0.36 
 
 I55-8I 
 156.16 
 
 156.51 
 156-85 
 I57.I8 
 157.52 
 157.85 
 158.17 
 158.50 
 158.82 " 
 
 I59.I4 
 
 159-45 ' 3 3l 
 
 159-76 
 160.07 
 160.38 - 31 
 160.69 - 31 
 160.99 ' 3 
 
 . . 
 ' 34 
 
 0.32 
 0.33 
 
 161.88 
 162.17 
 162.46 
 
 162.75 
 163.04 
 
 163-32 
 163.60 
 163.88 
 
 
 - 3 
 
 ' 29 
 0.29 
 
 
 165.26 
 165-53 
 
 '4497 
 '45-47 
 145-97 
 '46-46 
 '46-94 
 
 . 
 
 i47 7 n 
 
 148.32 - 45 
 
 148.77 ' 4S 
 149.21 
 
 0.43 
 
 152.50 
 
 153-64 
 154.01 
 
 154-38 
 154-74 
 155-09 
 
 155-45 
 
 ,. 
 
 : 
 
 156.48 
 .56.82 
 
 157-16 
 157-49 
 157-81 
 158.14 
 158.46 
 
 ' 33 
 
 0.33 
 
 0.32 
 1.31 
 
 1.31 
 
 159.09 
 15940 
 159-71 
 160.02 - J1 
 0.30 
 
 160.32 
 I6O.62 
 160.92 ' 3 
 161.22 ' 3 
 I6I.5I 
 
 161.80 
 162.09 
 162.38 
 162.66 
 162.94 
 
 0.29 
 
 164.05 
 I64-33 
 164.60 
 
 I OJ..o7 
 I o^. I ^ 
 
 165.40 
 165.66 
 
 
 
 0.26 
 
 '46-47 ** 
 
 
 150.09 
 
 ~ 
 
 0.42 
 
 153.28 8 
 
 155.10 "" 
 
 155-45 rr 
 155.80 ^ 
 
 156.14 
 156.48 - 34 
 .56.82 
 
 .57-15 
 157-48 ^; 33 
 
 157.80 
 158.12 - 32 
 
 158.44 - 3 l 
 158.76 - 3 
 
 159-07 3I 
 
 SiS E 
 
 its - 
 
 160.58 - 3 
 0.30 
 
 .60.88 
 
 161.17 - 29 
 
 161.46 - 29 
 
 161.75 ' 29 
 
 .62.03 i 
 j 0.28 
 
 .62.31 
 
 .62.59 ' 2 ! 
 162.87 
 
 18:2 -' 
 0.27 
 
 163.69 
 
 163.96 - 27 
 
 164.23 ~ 
 
 164.50 - 27 
 
 164.76 - 26 
 0.27 
 
 .65.03 
 .65.29 
 
 '65-55 in 
 .65.81 - 26 
 166.06 
 
 146.99 
 147.46 ' 47 
 
 165.92 i 166.32 
 
 .48.84 
 
 .49.28 
 149.71 
 150.14 
 150.56 
 150.97 
 
 151.38 
 151.78 
 .52.17 
 
 0.44 
 
 148.00 * 
 148.45 - 45 
 $ 
 
 149.35 
 149.78 
 
 150.2. 
 150.63 
 i 151.04 
 i 151-45 
 
 ! 151-85 
 
 '53-32 
 
 
 154-43 
 I54-78 
 
 155-14 
 155-49 
 155-83 
 156.17 
 156.51 
 
 156.84 
 157-17 
 157-49 
 
 3 
 
 159-07 
 
 159-97 
 160.27 
 160.56 
 160.86 
 161.14 
 
 - 31 
 
 0.29 
 
 0.28 
 0.29 
 
 161.99 - 2 ? 
 
 162.27 J^g 
 
 162.82 
 
 '63.IO ' 2 
 
 163.90 
 
 164.16 
 164.43 
 164.69 
 
 I64-95 
 165.20 
 
 165.46 
 165.71 
 165.96 
 166.22 
 166.46 
 
 .66.71 
 
 
 - 39 
 - 39 
 
 0.34 
 0.34 
 0.34 
 0.33 
 
 '-39 
 .53-76 
 
 
 0.37 
 
 155-54 
 
 182 - 
 
 '56-56 -I 
 
 
 ! 157-53 
 157.85 
 158.17 
 .58.48 
 158.79 
 
 0.31 
 
 
 159-99 !' 3 ' 
 
 160.28 - 29 
 
 0.29 
 
 160.57 
 160.86 - 29 
 .61.14 - 28 
 .61.43 ' 29 
 
 .61.70 - 27 
 ' 0.28 
 
 !SS - 28 
 !Sio - 
 
 0.2S 
 0.2 S 
 O.26 
 0.24 
 0.25 
 
 163.86 
 164.12 
 164.38 
 
 164.63 
 164.89 
 165.14 
 
 165.39 
 165.64 
 
 165.89 
 166.14 
 166.38 
 166.62 
 
 166.86 
 167.10 
 
 ' 2 
 
 - 26 
 
 0.25 
 0.24 
 0.24 
 0.24 
 0.24 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 67 
 68 
 69 
 
 70 
 71 
 72 
 73 
 74 
 
 75 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 90 
 91 
 92 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 100 
 101 
 102 
 103 
 104 
 
 107 
 108 
 109 
 
 110 
 111 
 112 
 113 
 114 
 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
TABLES FOR THE TRUE ANOMALY. 
 
 M 
 
 .71 
 
 .72 
 
 -73 
 
 - -74 
 
 -75 
 
 .76 
 
 .77 
 
 M 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 138 
 139 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
 ' 6 5-3 
 
 g 
 
 0.27 
 
 166.13 
 
 I66. 4 i ' 28 
 
 166.68 ' 27 
 
 166.96 ' 28 
 
 167.23 ' 27 
 
 3 0.27 
 
 167.50 
 
 167.77 
 
 168.04 I 
 
 168.30 Q 1 6 7 
 
 168.83 
 
 169.09 ' 26 
 
 169.36 ' 27 
 
 169.62 ' 2 ^ 
 
 169.88 0>2 
 0.26 
 
 170.39 
 170.65 
 170.91 
 
 0.26 
 
 171.42 
 
 171.67 ' 2 * 
 
 !?g " 
 '7 2 -43 .ii 
 
 ' 72 ' 68 o 25 
 172.93 
 173.18 ' 25 
 
 '73-43 
 
 173.68 5 
 '* 0.24 
 
 174.42 ' 2S 
 174.66 ' 24 
 174.91 - 2S 
 
 0.2S 
 
 '75-16 
 
 176 n ' 24 
 
 176.38 
 176.62 - 24 
 176.86 - 24 
 177.10 
 '77-35 I'H 
 
 177-59 
 '77-83 ' 4 
 
 178.55 ; 24 
 
 178.80 
 
 179-04 ' 2 ' 
 179.28 
 179-52 ' 24 
 
 179-76 ; 24 
 180.00 
 
 f 5 
 
 " 
 
 - 26 
 
 166.50 
 166.76 
 167.03 - 27 
 167.30 7 
 
 l6 7-56 ' 2 
 
 168.35 
 168.61 
 168.86 
 
 169.12 
 169.38 
 169.63 
 169.89 
 170.14 
 
 170.39 
 170.64 
 170.89 
 
 I7I-39 
 171.64 
 171.89 
 172.14 
 
 0.26 
 
 0.25 
 0.26 
 
 0.26 
 
 0.26 
 
 0.25 
 
 172.87 
 
 0.25 
 0.24 
 
 174.08 
 
 '74-32 
 
 ' 24 
 
 175.04 
 175.28 
 
 Ii^ 
 
 
 ' 24 
 
 176.47 
 176.71 
 176.94 ' 23 
 
 '77-18 - 4 
 
 177.42 
 
 0.', 
 
 IJSM ' 23 
 '78-36 ^ 4 
 178.59 
 
 
 '79-30 
 
 180.00 
 
 0.23 
 
 0.24 
 
 23 
 
 166.06 
 
 - 26 
 
 ' oy 0.27 
 166.86 
 
 167.12 ' 2 * 
 
 167.38 ' 2 ^ 
 
 167.64 ' 26 
 
 167.89 ' 2S 
 ' ' 0.26 
 
 168.15 
 
 168.40 ' 2 f 
 
 168.66 ' 26 
 
 168.91 ' 2S 
 
 169.16 0-2S 
 0.25 
 
 169.41 
 
 169.66 - 2s 
 
 169.91 - 2s 
 
 170.16 - 25 
 
 170.40 - 24 
 
 0.25 
 
 170.65 
 
 170.89 - 24 
 
 171.38 ' 24 
 
 171.62 - 24 
 
 0.24 
 
 171.86 
 
 172.10 - 24 
 
 172.58 - 24 
 
 172.82 - 24 
 
 0.24 
 173.06 
 '73-30 o ' 24 
 173-53 
 173-77 
 174.00 
 
 174.24 
 
 174-47 
 174.71 
 
 174-94 
 I75-I7 
 
 
 
 I''. 3 . 
 '' 4 
 
 S* o"- 
 
 !%g "' 
 
 '76.33 :- 
 176.56 
 
 176.79 - 23 
 177.02 
 
 $3 - 
 0.23 
 
 - 23 
 ' 
 
 178.40 - 23 
 
 178.63 - 23 
 0.23 
 
 178.86 
 179.09 - 23 
 
 * 0.22 
 0.23 
 
 0.23 
 
 17977 
 iSO.OO 
 
 165.92 
 I66.?8 
 166.44 
 
 . 
 
 167.72 
 I67.97 - 
 168.22 ' 2S 
 0.25 
 
 168.47 
 168.72 
 168.97 
 169.21 
 169.46 
 
 ' 2S 
 
 ' 24 
 
 0.24 
 169.70 
 169.94 
 l?I - 4 
 170.42 
 170.66 
 
 170.90 
 
 ' 24 
 
 ' 24 
 0.24 
 
 171.38 
 
 .24 
 
 0.23 
 
 172.08 
 172.32 
 172.55 
 172.79 
 173-02 
 
 I73.25 
 
 0.23 
 0.24 
 
 0.24 
 0.23 
 0.23 
 
 ' 0.23 
 174.40 
 174-62 ' 22 
 
 I74.85 ' 23 
 175.08 
 
 175-31 ; 2 3 
 
 175-53 
 '75-76 * 
 175-98 
 176.21 
 
 176.43 
 176.66 
 176.88 
 
 0.23 
 
 O.22 
 
 0.23 
 
 O.22 
 
 177.55 
 177.78 
 
 178.00 
 
 178.22 
 
 178.44 
 
 0.23 
 
 '79-33 2 
 
 iSO.OO 
 
 166.57 
 166.82 
 
 ' 26 
 
 1 68:06 - 24 
 168.31 ll 
 
 168.79 
 169.03 ' 24 
 
 169^51 - 24 
 
 I6 9-7S ' 24 
 
 170.46 ' 24 
 170.69 ' 23 
 
 170.92 ' 23 
 0.24 
 
 171.16 
 
 ll\:ll - 
 ;? 2 :oi - 3 
 
 0.23 
 
 0.22 
 
 172.76 ' 23 
 172.99 ' 23 
 
 '73-2' ; 23 
 
 173-44 ,. 
 173.66 
 173.88 - 22 
 
 ,', , , 0.23 
 
 174.99 
 
 / 1 yy 
 
 - 22 
 
 O 22 
 
 0.21 
 
 I'll 
 
 175.66 
 175.88 ' 22 
 I76.O9 ' 21 
 
 '76-3' I'" 
 '7 6 -53 ; 22 
 
 176.75 
 176.97 
 
 I77.I9 
 
 177.62 
 177.84 
 
 178.92 
 179.14 
 179-35 
 179-57 
 179.78 
 
 180.00 
 
 166.71 
 166.96 ' 2S 
 167.20 ' 24 
 167.45 ' 2S 
 
 167.69 ' 24 
 ' 0.24 
 
 167.93 
 168.17 ' 24 
 168.41 ' 24 
 168.64 ' 23 
 168.88 ' 24 
 
 169.12 
 
 0.24 
 
 '169.81 ' 23 
 
 170.04 ' 23 
 * 0.23 
 
 170.27 
 
 170.50 ' 23 
 
 170.73 ' 23 
 
 170.96 ' 23 
 
 171.18 ' 22 
 
 171.41 
 171.64 
 171.86 
 172.08 
 172.30 
 
 0.23 
 
 0.23 
 
 0.22 
 O.22 
 0.21 
 
 0.22 
 
 172.97 
 
 173.62 
 
 173.84 
 174.06 
 174.28 
 174-49 
 
 I747I 
 174.92 
 
 '75-57 2 
 
 176.42 
 
 176.63 
 
 176.84 
 
 177-06 ' 22 
 
 I77.27 
 
 17748 
 
 177-69 ; 2I 
 177.90 
 
 178.11 - 21 
 
 178.32 -" 
 
 0.21 
 0.21 
 
 1/y-3 21 
 179.79 
 
 9 0.21 
 
 ISO.OO 
 
 167.10 
 
 I67'58 - 24 
 167.82 ' 24 
 168.05 
 
 168.29 
 168.52 ' 23 
 168.75 ' 23 
 
 ,. * *' /\ - t 
 
 168.98 
 169.21 
 
 169.44 
 169.66 
 169.89 
 I7O.II 
 170.34 
 
 O.24 
 
 0.23 
 
 0.23 
 
 0.22 
 
 0.23 
 
 0.22 
 
 171.00 "' 
 
 171.22 - 22 
 
 171.44 -" 
 
 0.22 
 
 171.66 
 
 171.88 ' 22 
 
 I72.IO ' 22 
 
 172.31 
 
 172.53 
 
 173-17 
 
 173.81 
 174.02 
 
 174-23 
 174.44 
 
 174-65 
 174.86 
 
 175-07 
 175.28 
 
 175-49 
 175-70 
 
 175-90 
 176.11 
 176.32 
 176.52 
 176.73 
 176.94 
 177-14 
 
 177.76 
 
 177.96 
 178.17 
 178.37 
 178.57 
 178.78 
 
 178.98 
 179.19 
 
 O.2I 
 O.20 
 0.21 
 O.2O 
 
 179.80 
 iSO.OO 
 
 120 
 121 
 122 
 123 
 124 
 
 125 
 126 
 127 
 128 
 129 
 
 130 
 131 
 132 
 133 
 134 
 
 135 
 136 
 137 
 133 
 
 140 
 141 
 142 
 143 
 144 
 
 145 
 146 
 147 
 148 
 149 
 
 150 
 151 
 152 
 153 
 154 
 
 155 
 156 
 157 
 158 
 159 
 
 160 
 161 
 162 
 163 
 164 
 
 165 
 166 
 167 
 168 
 169 
 
 170 
 171 
 172 
 173 
 174 
 
 175 
 176 
 177 
 178 
 179 
 
 180 
 
67083S 
 
 A 
 
 UNIVERSITY OF CALIFORNIA LIBRARY 
 
 UNIVERSITY OF CALIFORNIA LIBRARY 
 BERKELEY 
 
 Return to desk from which borrowed. 
 This book is DUE on the last date stamped below. 
 
 ASTRdNQMY LIBRARY 
 
 Jyt 
 
 AUG ^969 
 
 LD 21-100m-ll,'49(B7146sl6)476