REESE LIBRARY UNIVERSITY OF CALIFORNIA. ASTRONOMY '/< 35. 5M 82f 17. i> 36. 2M ^ 18. M+ 2f 37. 3M 2^ 19. M 3^ The elliptical elements which have been used in the construction of the Tables are as follows: 1851, Jan. o.o. WASHINGTON MEAN TIME. Mean Anomaly 66 6' 49^.79 Longitude of Perihelion 301 39 25 .02 ) Referred to the Mean Equinox Longitude of Ascending Node .... 235 34 41 .74 j of 1851, Jan. o. Inclination 823 1 7 .74 Angle of Excentricity 1238 44 .90 Mean Daily Motion 994*.8347237 Logarithm of half Great Axis ... 0.3681389 Though the Tables need no further explanation, I will give here, as an example, the computation of the heliocentric co-ordinates of Victoria for 1857 August 13.5, Washington Mean Time. We must form first the different Arguments from Table I. i. 2. 3. 4. 5. 6. 7. 8. 1857 Aug. 13 12 hours 311.071 40.972 2-513 96 310.283 23.357 !-433 55 261.355 64.328 3-944 151 0.786 17.613 1.080 42 309-497 5-744 0.352 13 51.29 11.87 0-73 2 101.79 6.13 0.38 i 259.78 29.10 1.78 7 354.652 335- I2 8 329-778 19.521 315.606 63.91 108.31 290.73 9. 10. 11. 12. 13. 14. 15. 16. 1857 Aug. 13 12 hours 212.42 105.30 6.46 2 5 311.858 58.585 3-592 138 H-I73 213.99 1 40.5 3 8.62 33 211.64 87.69 5.38 20 210.06 52.46 3.21 12 292.81 44.40 2.72 ii 262.92 99.56 6.1 1 24 302.33 51.49 3.16 12 32443 347 304-9 1 265.85 340.04 8-83 357-10 17. 18. 19. 20. 21. 22. 23. 24. 1857 Aug. *3 12 hours 9.52 7.09 0.44 i 312.6 76.1 4-7 2 283-3 37-3 2.3 i 163.5 H6.3 9.0 4 235- 1 95-9 5-8 2 52.1 29.5 1.8 214.8 158.1 9-6 4 3I3.4 93-8 5-7 2 17.06 33-6 323-0 319.2 337-0 834 22.9 53-1 25. 26. 27. 28. 29. 30. 31. 32. 1857 Aug. 13 12 hours 165.1 181.5 ii. i 5 314.2 111.4 6.8 2 161.9 III.O 6.8 2 52.8 47.1 2.9 i 264.5 134.8 8.2 2 209.3 34-9 2.1 I 1 14.6 I8/-3 11.5 5 1 16.2 222.5 13.6 5 358.2 72.6 279.9 102.9 47-7 246.4 3*3-9 352.8 - 33. 34. 35. 36. 37. 1857 Aug. '3 1 2 hours 53.6 64.7 4.0 i 113.8 169.6 10.4 4 113.0 152.0 9.2 4 254.1 I I O.I 6.8 2 196.6 161.6 9-9 4 ' 122.4 294.2 274.6 II. 2 8-5 6 With these Arguments we find, then, the following perturbations: Arg. 2. 335-128 3. 329.778 4. 19.521 5. 315.606 6. 63.91 7. 108.31 8. 290.73 9- 3 2 4-43 10. 14.173 11- 3-47 12. 304.91 13. 265.85 14. 340.04 15. 8.83 16. 357.10 17. 17.06 18. 33-6 19. 323.0 20. 319.2 21. 337.0 22. 83.4 23. 22.9 24. 53.1 25. 358.2 26. 72.6 27. 279.9 28. 102.9 29. 47.7 30. 246.4 31- 33.9 32. 352.8 33. 122.4 34. 294.2 35. 274.6 36. 1 1. 2 37. 8.5 Terms mult, by t Perturbations SM. 249.71 318.27 0.17 60.71 162.29 0.97 5.69 7.62 1 1. 06 18.14 3-44 o-37 7-31 16.31 11.87 9-39 1.23 2.45 4.28 2.79 2.04 1.46 1.36 1.24 0.14 -93 0.26 0.03 0.15 O.I I 0.8 1 0.70 0.19 0.62 0.27 0.31 0.47 $ Tog. r. 4336- 3932 3052 500 1932 166 64 188 405 18 411 140 179 21 224 19 6 92 6 40 7 25 29 36 36 17 3 10 17 2 10 9 o 6 i 4 279.9 268.5 69.6 25- 1 70.5 0.2 1.0 9-9 25.1 3-3 2-3 5.6 11.4 3-2 36.9 1.9 46.8 0.8 1.2 0.0 2-5 4.6 O.I o-3 4-4 4-3 6.1 M. t. 1857 311 23 1.22 +6.OOI Aug. 58 35 4.96 580 13 days 3 35 32.85 35 12 hours 8 17.4-2 i M 13 4 1 56.45 +6.617 SM 13 38.40 M 13 55 34.85 Eq. ofC. +8 8 59.53 from Table XII. v 22 4 34.38 log. r 0.2655504 from Table XIII. 5 log. r !549 log. r 0.2670913 Then one takes A, B, C, log. , log. bj and log. c from Table XIV., and finds: A + v 53 31 45.58 IB + v 321 ii 38.29 C + v 343 6 53.06 ar 0.2639174 sin (A + v) 9.9053431 Or 0.2438883 sin (JB + v) 9.797049971 cr 9.7990453 sin (C + v) 9.4630805^ X +1.4765918 Corr. +169 from Table XV. y -1.0988493 Corr. +448 from Table XV. 2 0.1828630 Corr. -1322 from Table XV. 905.16 13.11 1 15974 -85.45 = +6.617 892.3 2.76 The heliocentric co-ordinates, re- ferred to the equator and the mean equinox of 1857.0, are, therefore: x = +1.4766087 y = 1.0988045 z 0.1829952 - 86.76 818.40 565 15409 -18.3 874.0 If one wishes to calculate only an approximate place, it will be sufficient to take into account only the first five equations in M., *Log.r, and { , together, with the Terms multiplied in t In this case, one-must take M. and Log.r Table XVII, and corrections of the three co-ordinates a, y, 2, from Table XVI. TA.BLES. TABLE Arguments for the Perturbations (Referred to the Meridian Year. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 1850 176.906 28.564 205.470 148.342 240.221 268.12 27.90 268.79 22.37 325-249 319.06 234.03 1851 247.446 68.778 316.224 178.667 250.1 10 288.55 38.45 318.89 203.66 66.1 14 2OI.OO 25.00 18525 318.179 109.102 67.281 209.076 260.025 309.05 49-03 9-' 3 25-45 167^55 83.61 176.38 1853 28.718 1 49-3*7 178.035 239.401 269.914 32949 59-57 59-24 206.75 268.120 325.56 327.35 1854 99.258 189.530 288.789 269.727 279.803 349.92 70.12 109.34 28.04 8.985 207.50 118.32 1855 169.798 229.745 39-544 300.052 289.692 10.35 80.67 159-44 209.33 109.851 89.45 269.29 1856.6 240.531 270.069 150.601 330.461 299.608 30.85 91.24 209.68 31.12 210.992 332.05 60.67 1857 311.071 310.283 261.355 0.786 309-497 51.29 101.79 25978 212.42 311.858 213.99 21 1.64 1858 2 1 .6 1 350.498 12.109 3I.I 12 319.386 71.72 112.34 309.89 33-7' 52-723 95-94 2.6 I 1859 92.150 30.712 122.863 61.438 329.275 92.16 122.88 359-99 2 I 5 .0 I 153.588 337.89 '53-57 1860.8 162.883 71.036 2 33-9'9 91.847 339-' 8 9 112.66 133.47 50.23 36.80 254-730 220.49 304.95 1861 233.423 1 11.250 344-673 122.172 349.078 133- 10 144.02 100.33 218.09 355-595 102.43 95.92 1862 303-963 151.465 95427 152.498 358-967 '53-53 154.56 15044 39-39 96.460 344-38 246.89 1863 14.502 191.679 206.181 182.823 8.856 '73-97 165.11 200.54 220.68 197.326 226.32 37-86 18645 85-235 232.004 317-239 213.232 18.772 194.46 175.69 250.78 42-47 298.467 108.93 189.24 1865 '55-775 272.218 67.994 243-557 28.661 214.90 186.23 300.88 223.77 39.332 350.88 340.21 1866 226.315 312.433 178.748 273.883 38.55 235-34 196.78 350-99 45.06 140.197 232.82 131.18 1867 296.855 352.647 289.502 304.209 48.439 255-77 207.33 41.09 226.35 241.063 114.77 282.15 18685 7-588 32.972 40.560 334.6I7 58.355 276.27 217.90 9L33 48-15 342.204 357.38 73-53 1869 78.128 73.186 '5'-3'4 4.942 68.244 296.70 228.45 ' 4' -43 229.44 83.069 239.32 224.50 1870 148.667 113.401 262.067 35.267 78.133 3'7-'3 239.00 I9I-53 5073 183-934 121.27 '5-47 1871 219.207 153.616 12.822 65.592 88.023 337-57 249.55 241.63 232.02 284-799 3-2' 166.44 18725 289.940 193.940 123.880 96.OOO 97.940' 358.06 260.12 291.88 53-82 25.940 245.82 317-82 1873 0.480 234-I55 234-635 126.326 107.829 18.49 270.67 341.98 235.11 126.806 127.76 108.79 1874 71.020 274.370 345-39 156.651 117.719 38.93 281.21 32.08 56.41 227.671 9.71 259.76 1875 141.560 3H-584 96.145 186.976 127.608 59.36 291.76 82.19 237.70 328.536 251.65 50.73 18765 212.294 354-99 207.203 217.384 137-525 79.86 302.33 '32-43 59-49 69.678 134.26 2O2. 12 1877 282.834 35-124 317.958 247709 '47-4' 5 100.29 312.88 182.53 240.79 I70.543 1 6.2 I 353.09 187-8 353-374 '75-339 68.713 278.034 157.304 120.73 323-42 232.64 62.08 271.408 258.15 I 44.06 1879 63-9 '4 '15-554 179.467 308.360 167.194 141.16 333-97 282.74 243-38 12.273 140.10 295.03 i88o5 134.647 I55-879 290.526 338.768 177.111 161.66 344-55 332.99 65-17 "34'5 22.71 86.40 1881 205.187 196.094 41.281 9-93 187.001 182.09 355-10 23-09 246.46 214.280 264.65 237.37 1882 275.727 236.309 152.036 39-4 18 196.891 202.53 5.64 73.20 . 67.76 3'5-'45 146.60 28.34 1883 346.267 276.524 262.791 69743 206.781 222.96 16.19 123.30 249.05 56.011 28.54 '79-3' 18845 57.001 316.849 13.850 100.152 216.698 243.46 26.76 '73-55 70.85 157.152 271.15 330.69 1885 127.541 357.064 124.605 130.477 226.588 263.89 37-3 223.65 252.14 258.017 153.10 121.66 1886 198.081 37.279 235.360 160.802 236.478 284-33 47-85 273.76 73-44 358.882 35-04 272.63 1887 268.621 77-494 346.H5 191.127 246.368 304.76 58.39 323.86 254-73 99.748 276.99 63.60 18885 339-354 117.820 97-174 221.535 256.285 325- z 5 68.96 14.10 76.52 200.889 159.60 214.98 1889 49.894 158.035 207.929 251.860 266.175 345.69 79-5 ' 64.21 257.82 301-754 41.54 5-95 1890 120.435 198.250 318.684 282.185 276.065 6.12 90.05 114.31 79-12 42.620 283.49 156.93 1891 190.975 238.465 69439 312.510 285.955 26.55 100.59 164.41 260.41 143.485 165.43 307.90 18925 261.709 278.791 180.498 342.918 295.873 47.05 111.17 2 I 4.66 82.20 244.627 48.04 99.28 i93 332.249 319.006 291.254 13.244 305-763 67.48 121.71 264.76 263.49 345-492 289.99 250.25 1894 42.789 359.221 42.009 43-568 3 I 5- 6 53 87.92 132.26 3I4.87 84.79 86-357 '7'-93 41.22 1895 113-33 39-43 6 152.765 73-894 325-543 108.35 142.80 4-97 266.09 187.222 53-88 192.19 18965 184.063 79.762 263.824 104.302 335-46i 128.84 '53-38 55-21 87.88 288.364 296.49 343.58 1897 254.603 119.977 '4-579 134.627 345-35 1 149.28 163.92 105.32 269.18 29.229 17843 '34-55 1898 325-I44 160.192 125-334 164.951 355-24 1 169.71 174-47 155.42 90.48 1 30.094 60.38 285.52 1899 35.684 200.407 236.089 195.276 5-3 190.15 185.01 205-53 271.78 230.959 302.32 76.49 1900- 106.223 240.622 346.845 225.601 15.021 210.58 195.56 255.64 93-07 331.824 184.27 227.47 I. for the Different Years. of Waftiington. MBWB^^H 1 3 t^a^mmmmf 14. HK^Knm 15. B^K>K 16. w*m i 17. 18. - 19. mxmmmfs*^*' 20. ^mfwmmm^ 21. Bie 22. , 23. M^MB 24. ^^ 25. , * 26. 27. Year. i. O. 297-34 27.66 118.22 208.54 298.86 29.18 119.74 210.06 300.38 30.70 121.26 211.58 301.90 32.21 117.28 193.72 270.18 346.^2 63.27 i 39-7 i 216.37 292.81 9.26 85.71 162.37 238.82 315.26 3 I -7 I 142.15 3I3.55 12543 296.83 108.24 279.64 9 I -5 2 , 262.92 : 74-3 3 j 245-73 57.60 229.00 40.41 211.81 41.26 129.91 2 1 8.8 1 307.47 36.12 124.78 213.68 302.33 30-99 119.64 208.54 297.20 25.85 114.51 283.99 H3.6 296.2O 244.8 308.44 l6.3 320.65 H7.5 ; 332.86 278.7 ! 345-07 49-9 1 357.31 181.4 9.52 312.6 21.73 ! 83.8 33-94 215.0 '' 46.18 346.6 58.39 117-8 70.60 249.0 82.8l 20.2 193-3 257-5 321.9 26.2 90.4 154.6 219.0 283.3 347-5 5^-7 I 1 6. 2 180.4 244.7 308.9 199-3 91.1 343-7 235-5 127.3 19.1 j 271.7 163-5 55-3 307.2 199.7 91.5 343-4 235-2 158.5 323-6 129.1 294.2 99-3 264.4 70.0 235-1 40.2 205.3 10.9 176.0 34 1 - 1 146.2 56.4 107.4 107.2 19.7 158.1 292.7 208.8 205.0 259.6 117.2 3104 29.5 1.3 302.5 52.1 214.8 102.9 ; 127.0 153-7 ! 39-3 204.5 312.3 255-3 224.6 306.0 136.9 356.8i 49.1 261.9 634 2254 26.9 188.4 349-9 151.9 3 '34 114.9 2764 784 239-9 414 203.0 136.0 88.5 41.8 354-3 306.8 i 259.3 212.6 165.1 II7.6 7O.I 234 335-9 2884 240.9 T r\ A t 50.3 242.1 74-5 266.3 98.2 290.0 122.4 3H- 2 146.1 337-9 170.3 2.1 194.0 25.8 2l8.2 262.6 93-8 285.5 116.7 307.9 139.0 330.7 161.9 353- 1 184.3 1 6.0 207.2 38.4 229.6 6l T, 1850 1851 1852.6 1853 1854 1855 1856,5 1857 1858 1859 1860.5 1861 1862 1863 1864^8 122.78 213.10 30342 33.74 124.30 214.62 304-94 35-26 125.83 216.14 306.46 36.78 127.35 217.67 37-99 38.30 128.87 219.19 309-5 1 39.83 130.40 220.72 311.04 41.36 i3'-93 222.25 312.56 42.88 133-45 223.77 3 ' 4-9 44.41 134.98 225.30 315.62 45-95 136.27 108.37 23.68 203.41 : 184.81 195.09 292.06 261.26 6.50 20.72 337-7 1 I 77-9 I0 9-37 54.36 349.78 198.27 : 130.81 161.19 286.93 207.25 332.60 15.59 283.69 144.01 104.24 0.34 315.88 193.14 76.79 127.29 281.79 153.23 298.69 10.45 229.67 1 10. 10 99.10 306.32 281.97 188.00 22.77 93-38 276.65 99.21 264.79 5.31 175.65 ! 7 6 -20 93.96 2^2.31 i 248.06 182.86 328.75 i 59-47 271.51 45.19 ': 230.87 O.l6 121.63 ; 42.28 88.82; i 198.28 ; 214.15 I77-7 1 274.72 ! 25.56 266.36 351.16 i 196.97 355- 01 67.60 8.37 83.67 144.25 180.25 172.56 220.69 '351.65 261.21 297.12 163.05 349.87 i3-57i334-4 6 78.53 90.23 146.33 l6 7-43 166.68 : 317.74 256.08 243.13 129.14 344-74 3'9-57 i 300-55 73-4 36.23 112.42 162.30 112.68:283.83 250.95 189.13! 95.24 339.61 265.58 i 266.65 68.27 342.02 78.05 156.92 95.05 107.26 119.47 131.68 H3-93 156.14 168.34! 180.55 ' 192.79 205.00 , 217.21 229.42 ; 241.67 253.88 266.09 278.30 290.55 302.76 3 1 4-97 327-19 339-43 354 3-86 16.07 28.32 40.53 52.75 64.96 77.20 89.41 101.62 113-83 126.07 138.28 150.48 162.69 174.90 151.7 J 3'3 I2 7-7 282.9 77.5 19-5 54.1 141.81271.4 185.3 206.0 163.2 316.8 270.4, 55.7 88.0 334.6 307.6 219.2 ; 38.9 199.4 350.4 103.1 91.2 121.9 167.5 343-8 253.1 : 231.8 235.6 24.3 296.0 127.4 155.5 ; 0.2 19.2 287.1 ; 64.6 271.8 58.3 128.9 163.6 1894 193.1 55-4 320.6 i 257.3 307.3 92.2 i 321.8 199.8 223.4 26.0 91.6 354.6 90.2 343.5 125.8 154.4 235.3 257.3 218.8 127.8 28.5 : 283.1 19.6 159-7 347-3 271.5 290.9 51.5 163.3 62.4 1 1 5.9 55-8 193.6 180.1 307.7 324.8 244.4 199.6 96.0 308.6 91.4 227.5 ! !3- 344-o 358.7 77.2 235.8 129.9 141.5 127.6 261.1 i 205.7 19.4 32.7 270.1 272.0 163.9 334-4 l6 3- 8 295.1 38.6 55.6 66.3 102.8 307.5 197.4 167.1 199.3 3 JI -7 1 1 6.8 281.9 87.0 252.6 57-7 222.8 27.9 193-4 358.5 163.6 328.7 134-3 299.4 104.5 269.6 75-2 240.3 45-4 210.5 1 6.0 iBi.i 346.2 151-3 316.8 121.9 287.0 92.1 257-6 62.7 227.8 32.9 198.5 3-6 168.7 333-8 138-9 47-7 98.5 149.2 2OO.O 250.9 3 OI -7 3524 43-2 94.1' 144.8 195.6 246.3 297.2 348-o 38.8 89.5 H04 191.2 241.9 292.7 343-6 34-3 85.1 135-8 186.7 237-5 288.3 339- 1 30.0 80.7 131-5 182.2 233-' 283.9 334-7 25-4 76.2 yt.i ^-.y L yt'" 234.4 166.4 146.7 146.7 328.0 99.2 59-o I2 9-5 5 1 -? 332.0 2914 5.0 244.3 92.9 3 i 7-5 156.5 254.5 269.9 68.8 56.0 . 2224 341.8 218.0 175.7 254.1 19.5 128.2 166.3 181.0 80.7 78.6 : 342-5 33-2 351.6 144.5 346-6 263.9 36.o 299.0 176.2 107.5 2 S l -S 88.5 : 269.1 , 204.0 1.5 7-9 1 5 74 273.8 2324 109.9 1 86.1 ; 33.9 624 98-3 i 195-5 H-9 11.3 3574 328.2 283.6; 158.9 280.7 195-9 320.5 233.2 108.2 122.0 185.7 21.2:283.9 139.0 293.5 85.5! 91.5 2057 247.0 43-9 1 1 8.0 j 48.5 356.4 31.01210.5 1309.7 303.3 i I2.O j 262.2 215.6 173.5 214.7 127.8 335-0 167.2 40.8 : 137.0 120.6 313.11298.5 73.1 2254, 100,0 25.5 137.7 1 261.5 338.0 49.9 ! 63.0 290.5 50.0 ; 241.8 73-6 266.0 97-8 289.7 121.5 3 ! 3-9 1 45 -7 337-5 1694 i-7 193.6 254 217.2 49-7 ,241.5 734 265.2 97-6 289.4 I 2 1. 2 3 I 3- 1 45 4 337.2 169.1 0.9 I93.3 25.1 216.9 ! 48.8 241.1 73-0 264.8 96.6 288.5 j 252.5 837 274-8 1 06.6 297-8 129.0 320.2 151.9 343- 1 174-3 5-5 197.2 28.4 219.6 50.7 242-5 73-7 264.9 96.1 287.8 119.0 310.2 141.3 333-o 164.2 355-3 186.5 i 1 8.2 209.4 40.6 231.8 63.5 254-7 85-9 277.0 108.1 1865 1866 1867 18685 1869 1870 1871 18725 1873 1874 1875 1876^ 1877 1878 1879 1880^6 1881 1882 1883 1884.2 1885 1886 1887 1888^ 1889 1890 1891 1892^ 1893 1894 1895 1896^ 1897 1898 1899 1900 [9] TABLE I. CONCLUDED. Aguments of. the Perturbations for the Different Years. (Referred to the Meridian of Wafhington.) Year. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 1850 204.8 78.8 149.0 1 6.2 312.9 353-1 227.9 79-5 6-5 47.8 1851 285.9 310.9 209.0 338.6 335-9 104.5 159.9 341-2 I 95-9 326.0 18525 7.2 183.6 269.2 301.8 o.o 216.2 92.8 243-7 26.0 244.9 1853 88.3 55-6 329.2 264.2 23.0 327.6 24.8 H5-4 215.5 163.1 1854 169.4 287.7 29.2 226.6 46.1 79.0 316.9 47-i 45-o 81.3 1855 250.4 159-7 8^.2 189.0 69.1 190.5 248.9 308.8 234-5 359-5 18565 331-7 32-4 H-3 152.2 93-2 302.2 181.8 21 1.3 64.6 278.4 1857 52.8 264.5 209.3 1 14.6 I 1 6.2 53-6 113.8 II3.0 254.1 196.6 1858 133-9 '36.5 269.3 77-0 139.2 165.0 45-9 H-7 83.6 114.7 1859 215.0 8.6 329-3 39-4 162.3 276.4 337-9 276.5 273.1 32.9 1 860 B 296.3 2 4* -3 29.4 2.6 186.3 28.2 270.8 178.9 103.2 311.8 1 86 1 174 11 3-3 894 325.0 209.3 139.6 202.9 80.6 292.7 230.0 1862 98.5 345-4 149.4 287-4 232.4 251.0 134-9 342.4 122.2 148.2 1863 179-5 217.4 209.4 249-7 255.4 2.4 67.0 244.1 3II.8 66.3 18645 260.9 90.1 269.5 213.0 279-5 114.1 359-8 146.5 I4I.8 345-3 1865 34 J -9 322.2 329-5 175-4 302.5 225-5 291.9 48.2 331-3 263.5 1866 63.0 194.2 29.5 137-8 325.5 337-0 223.9 310.0 160.8 iSi.6 1867 144.1 66.3 89.5 IOO.I 348.5 88.4 156.0 211.7 350-4 99-8 18685 225.4 299.0 149.6 63.4 12.6 200.1 88.8 1 14.2 180.4 18.7 1869 306.5 171.0 209.6 25.8 35-6 3H-5 20.9 15.9 9-9 296.9 1870 27.7 43-i 269.6 348.1 58.6 63.0 312.8 277.5 '99-5 215.1 1871 108.8 275.1 329.6 310.5 81.6 174.4 244.9 179.2 29.0 133.3 18725 190.1 147.8 29.8 273.7 105.7 286.1 177.7 81.7 219.0 52.2 i8?3 271.2 19.9 89.8 236.1 128.7 37-5 109.7 343-4 48.5 330.4 1874 352-3 251.9 149.8 198.5 151.8 148.9 41.8 245.1 238.0 248.6 1875 73-3 124.0 209.8 160.9 174.8 260.3 333-8 146.9 67.6 1 66.8 18765 154.6 35 6 -7 270.0 124.1 198.9 12. 1 266.7 49-3 257.6 85.7 1877 2 35-7 228.7 33- 86.5 221.9 '23.5 198.8 311.0 87.1 3-9 1878 316.8 100.8 30.0 48.9 244-9 234-9 130.8 212.8 276.6 282.0 1879 37-9 332-8 90.0 "-3 267.9 346.3 62.8 II4.5 106.2 2O0.2 i88o5 119.2 205.6 150.1 334-5 291.9 98.0 355-7 16.9 296.3 II9.I 1881 200.3 77.6 210. 1 296.9 3 1 4-9 209.4 287.8 278.6 125.8 37-3 1882 281.4 39-7 270.1 259-3 338.o 320.8 219.8 180.4 3I5-3 3*5-5 1883 2.4 181.7 33-I 221.7 I.O 72.2 151.8 82.1 144.9 233-6 18845 83-7 54-4 3-3 185.0 25.1 183.9 847 344-5 334-9 152.6 1885 164.8 286.5 9-3 H7-3 48.1 295-3 16.7 246-3 164.4 70.8 1886 245.9 158.5 I50-3 109.7 71.1 46.8 308.8 148.0 353-9 348.9 1887 327.0 30.6 210.3 72.0 94.1 158.2 240.8 49-7 183-5 267.1 18885 48.3 263.3 270.3 35-3 118.2 269.9 173-7 312.2 13-5 1 86.0 1889 129.4 '35-3 330-3 357-7 Hi -3 21.3 105.7 213.9 203.0 104.2 1890 210.5 7-4 304 320.0 !64-3 132.6 37-8 1 15.6 32.5 22.4 1891 291.6 239-4 90.4 282.4 187-3 244.0 329-9 17-3 222.O 300.6 18925 12.9 112. 1 150.6 245.6 211.4 355-7 262.7 279-8 52.1 219.5 '893 94.0 344-2 2IO.6 208.0 234-4 107.1 194.7 181.5 241.6 137-7 1894 175.1 216.2 270.6 170.4 257-5 218.5 126.8 83.2 7I.I 55-9 1895 256.1 88.3 330.6 132.8 280.5 329-9 58.8 345-o 260.6 334- 1 18965 337-4 321.0 30.7 96.0 304.6 81.7 351-7 247.4 90.7 253.0 1897 58.5 193.0 90.7 58.4 327.6 J93-I 283.7 149.1 280.2 171.2 1898 139.6 65.1 150.7 20.8 350.6 304-5 215.8 50.9 1097 89-3 1899 220.7 297.1 210.7 343-2 13.6 55-9 147.9 312.6 299.2 7-5 1900 301.8 169.2 270.7 305-5 36.7 167.4 79-9 214-3 128.7 285.7 [10] TABLE II. Variation of the Arguments for the Different Months. ^i 1. .i^OM^M""" 2. 3. 4. 5. 6. 7. 8. 9. 10. " January . . . February. . March April o.ooo 5-99 1 11402 17.394 23.192 29.183 34-9 8 i 40.972 46.963 52.761 58.752 64.550 o.ooo 3.415 6.500 9.916 13.221 16.636 19.941 23-357 26.772 30.077 33-493 36.798 o.ooo 9.406 17-903 27.309 36.412 45.818 54.921 64.328 73-734 82.837 92.244 101.347 o.ooo 2-575 4.902 7-477 9.970 12.545 15.038 17.613 20.189 22.681 25.257 27.749 o.ooo 0.840 J-599 2.438 3-25 1 4.091 4.904 5-744 6.584 7-397 8.236 9-49 o.oo i-74 3-3 5.04 6.72 8.46 10.14 11.87 13.61 15.29 17.02 18.70 0.00 0.90 1.71 2.60 3-47 4.36 5-23 6.13 7.02 7.89 8.79 9.65 o.oo 4.25 8.10 12.35 16.47 20.73 24.85 29.10 33-35 37-47 4 I -73 45-85 O.OO 15.40 29.31 44.70 59.60 75-0 89.90 105.30 1 20.70 135.60 1 5 1 .00 165.90 o.ooo 8.567 16.304 24.871 33.161 41.728 50.018 53.585 67.151 75-44 1 84.008 92.298 o.oo 20.55 39- 11 59.66 79-55 JOO.IO 119.98 140.53 161.08 180.97 201.52 221.40 May Tune ...... Tuly. . . j u v August September. October . . November. December . TABLE III. Variation of the Arguments for the Different Days. M^BMBtai^BI Days. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. i 0.193 O.IIO 0.303 0.083 0.02 7 0.06 0.03 0.14 0.50 0.276 0.66 2 0.387 O.22O 0.607 0.166 0.054 O.I I 0.06 0.27 0.99 0.552 '33 3 4 6 7 8 9 10 20 0.580 0-773 0.966 1.160 1.353 1.546 1.740 1-933 3.866 o-3 3 1 0.441 . 0.551 0.66 1 0.771 0.882 0.992 I.IO2 2.204 0.910 1.214 1.517 1.820 2.124 2.427 2.731 3-034 6.068 0.249 0.332 0.415 0.499 0.582 0.665 0.748 0.831 1.662 o.o 8 1 0.108 0-135 0.163 0.190 0.217 0.244 0.271 0.542 0.17 0.22 0.28 o-34 0-39 0.45 0.50 0.56 1. 12 0.09 0.12 O.I4 0.17 O.2O 0.23 O.26 0.29 0.58 0.41 0.55 0.69 0.82 0.96 I.IO 1.23 1-37 2.74 1.49 1.99 2-49 2.98 348 3.98 4-47 4-97 9-94 0.829 1.105 1.381 1.658 !-934 2.2 1 I 2.487 2.763 5.527 . *-99 2.65 3-3 * 3.98 4.64 5-30 5-97 6.63 13.26 3 5-799 3-3 6 9.102 2-493 0.813 1.68 0.87 4.11 14.91 8.290 19.89 TABLE IV. Variation of the Arguments for the Different Hours. Hours. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. I 0.008 0.005 0.013 0.003 O.OO I o.oo o.oo o.oo O.O2 O.OI I 0.03 2 3 4 5 6 o.oi 6 0.024 0.032 0.040 0.048 0.009 0.014 0.018 0.023 0.028 0.025 0.038 0.050 0.063 0.076 0.007 O.OIO 0.014 0.017 0.021 O.OO2 O.O03 O.OO5 O.OO6 O.OO7 o.oo O.OI O.OI O.OI O.OI 0.00 o.oo o.oo O.OI O.OI O.OI O.02 O.O2 0.03 0.04 O.O4 O.o6 0.08 O.IO 0.12 0.023 0.034 0.046 0.058 0.069 0.05 0.08 O.I I 0.13- 0.16 7 8 9 10 0.056 0.064 0.072 0.080 0.032 0.037 0.041 0.046 0.088 O.IOI 0.113 0.126 0.024 O.O28 0.031 0.035 O.OO8 O.OO9 O.OIO 0.0 1 I O.02 O.O2 O.O2 0.02 O.OI O.OI O.OI O.OI 0.05 O.05 O.o6 O.o6 0.14 0.17 0.19 0.21 0.080 0.092 0.103 0.115 0.19 O.22 0.25 0.28 20 o.i 60 0.092 0.252 0.070 0.023 O.05 0.03 0.12 0.42 0.230 0.55 [11] TABLE II. CONTINUED. Variation of the Arguments for the Different Months. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. January . . . 0.00 0.00 o.oo 0.00 0.00 o.oo o.o 0.0 0.0 0.0 0.0 0.0 0.0 February. . 12.82 7.67 6.49 14.56 7-53 1.04 I I.I 5.5 21.4 14.0 4.3 23.1 J3-7 March 2440 14.60 12.36 27.71 H-33 1.97 21.2 10.4 40.7 26.7 8.2 44.0 26.1 April 37.22 22 27 18.85 4.2.27 21.86 3.OI 32.3 15.8 62.1 40.7 12. C 67.1 3Q.8 May j 1 ' 4-0.6 3 ""'" i 2Q,6Q 2C.I 3 T " / C6.3C 2Q.i <: j' 4-.OI J * j 43.1 J. 21. 1 82.8 T " / H.3 j l6.7 / 89.5 J7 1:3.1 June T7* J 62.4.6 7' 7 37.36 j* J 3 1.62 J ' Jj 70.01 7' j 36.68 T* ;.O5 T^ J C4.2 26.6 104.2 j 68.3 * / 2I.O y j I 12.6 j j 66.8 July. . . T 74.87 j i ' j" A.A..7Q j 37.01 / 7 8c.oo j 4-3.Q6 j j 6.06 J \ 6C.O 31.9 I 124.0 81.9 2C. 2 1 1C.O 80. i August / T* / 87.69 TT*/ 7 52.46 3fy 44.40 j 99.56 TJ.-7 51-49 7.09 J * 76.1 J 7 37-3 T^ y 146.3 y 95-9 j 29.5 J J 158.1 93-8 September. 100.51 60.13 50.90 114.1 1 59.02 8.13 87.3 42.8 167.7 109.9 33-8 181.2 107.5 October. . . 112.92 67.55 57.18 128.20 66.31 9-13 98.1 48.1 188.4 I2 3-5 38.0 203.6 120.8 November. 12574 75.22 63.67 142.76 73.84 10.17 109.2 53-6 209.8 137.5 42.3 226.7 134-5 December . 138.15 82.65 69.96 156.85 8I.I3 11.17 120.0 58.8 230.5 151.1 46.5 249.1 147.8 TABLE III. CONTINUED. Variation of the Arguments for the Different Days. Days. 12. 13. 14. 15. 16. M 18. 19. 20. 21. 22. 23. 24. I 0.41 0.25 0.21 0.47 0.24 0.03 0.4 O.2 0.7 0.4 O.I 0.7 0.4 2 0.83 0.49 0.42 0.94 0.49 0.07 0.7 0.4 1-4 0.9 -3 .| 0.9 3 1.24 0.74 0.63 1.41 0-73 O.IO I.I 0.5 2.1 i-3 0.4 2.2 1-3 4 1.66 0.99 0.84 1.88 0.97 0.14 1.4 0.7 2.8 1.8 0.6 3- 1.8 5 2.0*7 1.24 1.05 2 -35 1. 21 0.17 1.8 0.9 3-5 2.2 0.7 3-7 2.2 6 2.48 . 1.48 1.25 2.82 1.46 0.20 2.2 .1 4-i 2.7 0.8 4-4 2.6 7 2.90 -73 1.46 3- 2 9 1.70 0.24 2-5 3 4-8 3- 1 I.O 5-2 3-1 8 3-3i 1.98 1.6 7 3-76 1.94 O.27 2. 9 4 5-5 3-6 i.i 5-9 3-5 9 3-73 2.22 1.88 4. 2 3 2.19 0.31 3-2 .6 6.2 4.0 i-3 6-7 4.0 10 4.14 2.47 2.09 4.70 2-43 0-34 3.6 .8 6.9 4-5 1.4 7-4 4-4 20 8.28 4.94 4.18 9.40 4.86 0.68 7.2 3-6 13.8 9.0 2.8 14.9 8.8 3 12.42 7.41 6.27 14.10 7-29 1.02 10.8 5-4 20.7 13-5 4.2 22.3 13.2 TABLE IV. CONTINUED. Variation of the Arguments for the Different Hours. Hours. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. i 0.02 O.OI O.OI O.O2 O.OI o.oo o.o o.o 0.0 o.o o.o o.o o.o 2 0.03 O.O2 0.02 0.04 0.02 o.oo 0.0 0.0 O.I 0.0 0.0 O.I o.o 3 0.05 0.03 O.O3 O.o6 0.03 o.oo o.o 0.0 O.I o.o o.o O.I 0.0 4 O.O7 0.04 0.03 0.08 0.04 o.oo 0. o.o O.I 0. 0.0 O.I O.I 5 0.08 0.05 0.04 O.IO 0.05 O.OI o. 0.0 O.I o. o.o O.I O.I 6 0.10 O.o6 0.05 0.12 0.06 O.OI 0. o.o 0.2 o. o.o O.2 O.I 7 O.I 2 0.07 O.o6 0.14 O.O7 O.OI 0. O.I O.2 0. 0.0 0.2 O.I 8 0.14 0.08 0.07 o.i 6 0.08 O.OI o. O.I 0.2 o. o.o 0.2 O.I 9 O.I 5 0.09 0.08 0.18 O.09 O.OI 0. O.I O.2 o. 0.0 O.2 O.I 10 0.17 O.IO 0.09 O.2O O.IO . O.OI O.2 O.I 0-3 O.2 0.0 -3 O.2 20 o-34 O.2I 0.18 -39 0.20 0.02 -3 O.2 0.6 -3 O.I 0.6 0.3 , [12] TABLE II. CONCLUDED. Variation of the Arguments for the Different Months. ^iM* I^M 25. 26. BHn 27. HiH^BHi 28. m^nmxatma. 29. MM 30. Mi 31. . - 32. /c i 33. 34. 35. 36. 37. January . . . February. . March April o.o 26.5 50.5 77.0 102.7 129.3 155.0 181.5 208.0 233-7 260.2 285.9 o.o 16.3 31.0 47-3 63.1 79-4 95.1 111.4 127.7 H3-5 159.8 i75 5 0.0 I 6.2 3-9 47.1 62.9 79.1 94-8 I I I.O 127.2 143.0 159.2 174.9 o.o 6-9 I3- 1 20. 6 26.7 33-6 40.2 47.1 54.0 60.7 67.5 74.2 o.o 19.7 37-5 57-2 76.3 96.0 115.1 134.8 154-5 173.6 193-3 212.3 o.o 5-i 9-7 14.8 19.7 24.8 29.8 34-9 40.0 44-9 50.0 54-9 o.o 27.4 52.1 79-5 1 06.0 133-4 159-9 187.3 214.6 241.1 268.5 295.0 o.o 32.5 61.9 94-4 125.9 158.4 189.9 222.5 255.0 286.5 319.0 35-5 o.o 9-5 1 8.0 27.5 36.6 46.1 55-2 64.7 74.2 83-3 92.8 IO2.O o.o 24.8 47-2 72.0 96.0 120.8 144.8 169.6 194.4 218.4 243.2 267.2 o.o 22.2 42.3 64.5 86.0 108.3 129.8 152.0 174.2 195.8 218.0 239-5 0.0 16.1 30.6 46.7 62.3 78.4 94.0 I I O.I 126.2 141.8 157-9 173-5 o.o 23.6 45.0 68.6 91.5 115.1 138.0 161.6 185.2 208.1 23,1.7 254.6 May .... July. , . August .... September. October . . November. December . TABLE III. CONCLUDED. Variation of the Arguments for the Different Days. Days. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. i 0.9 0.5 0.5 O.2 0.6 O.2 0.9 I.O o-3 0.8 0.7 0.5 0.8 2 1.7 j I.O I.O 0.4 1.3 o-3 1.8 2.1 0.6 1.6 1.4 I.O x i-5 2.6 1.6 1.6 0.7 1.9 0.5 2-7 3.1 0.9 2-4 2.1 1.6 2-3 4 3-4 2.1 2.1 0.9 2-5 0.7 3-5 4 .2 1.2 3-2 2.9 2.1 3- i 5 4-3 2.6 2.6 I.I 3-2 0.8 4-4 5-2 I -5 4.0 3-6 2.6 . f. 6 i -J 5.1 3- 1 3- 1 1-3 3-8 I.O 5-3 6.3 x -9 4.8 4-3 3-i 4.6 7 6.0 3-7 3-7 4-4 1.2 6.2 7-3 2.2 5.6 5.0 3- 6 5-3 61 8 6. 8 4-2 4.2 1.8 5-i 1.3 7- 1 8.4 2-5 6-4 5-7 4-2 .i 60 9 7-7 4-7 4-7 2.0 5-7 1.5 8.0 9.4 2.8 7.2 c 6 ' 4 4-7 .0 n A 10 8 "C 5.2 2.2 6-3 1.6 8.8 10.5 3-1 8.0 7.1 5- 2 7.0 20 3 "O I7.I 25.6 10.5 15-7 10.5 '5-7 4-4 6.6 12.7 19.1 3-3 4-9 17.7 26.5 21.0 6.2 9-3 16.0 24.0 14-3 21.5 10.4 15.6 15.2 22.8 TABLE IV. CONCLUDED. Variation of the Arguments for the Different Hours. Hours. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. i o.o o.o o.o o.o o.o o.o o.o 0.0 0.0 o.o o.o o.o 0.0 2 O.I 0.0 0.0 o.o o.o o.o O.I O.I 0.0 O.I O.I 0.0 O.I 3 O.I o. o. 0.0 O.I o.o O.I O.I 0.0 O.I O.I o. O.I j A. O.I o. o. o.o O.I o.o O.I 0.2 0.0 O.I O.I 0. O.I T c O.2 o. 0. o.o O.I o.o 0.2 O.2 0. 0.2 O.I o. O.2 J 6 O.2 o. o. 0.0 O.I o.o 0.2 0.2 0. 0.2 0.2 o. O.2 1 0.2 0. 0. o.o 0.2 o.o O.2 O.2 o. O.2 0.2 o. O.2 / 8 0-3 0.2 0.2 O.I 0.2 O.I 0-3 0-3 o. 0-3 O.2 O.2 0-3 q *S 0.3 0.2 O.2 O.I O.2 O.I 0-3 0-3 o. o-3 -3 O.2 o-3 y IO J 0.4 0.2 0.2 O.I 0.2 O.I 0.4 0.4 0. -3 o-3 0.2 -3 2O - 0.8 0.4 0.4 0.2 0.5 0.2 0.8 0.8 o-3 0.7 0.6 0.4 o, __ucm>w> [13] TABLE V. Perturbations of the Mean Anomaly. Argument 1. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. I 2 3 227.02 223.00 219.08 215.24 4.02 3.92 3.84 3-74 45 46 47 48 164.49 165.96 167.51 169.15 1.47 i.55 1.64 1.73 \ 90 9 1 92 93 255.80 256.85 257.81 258.66 i.o5 0.96 o.85 0.76 '35 136 137 '38 200.46 197.12 193.72 190.25 3.34 3.40 3.47 3.52 4 21 1.50 3.65 49 170.88 1.81 94 259.42 o.65 139 186.73 3.58 5 207.85 5o 172.69 95 260.07 140 183.15 3.55 1.89 o.55 3.63 6 7 8 204.30 2OO.86 197.52 3.44 3.34 3.22 5i 52 53 174.58 176.54 178.56 1.96 2.02 2.O8 96 97 98 260.62 261.06 261.40 0.44 o.34 O 23 141 142 '43 179.52 175.84 172.11 3.68 3.73 3 __ 9 194.30 3.12 54 180.64 2.l5 99 261.63 O 1 2 144 168.34 *>T7 1 Ro 10 I9I.I8 55- 182.79 IOO 261.75 '45 164.52 V.Q3I 3.oo 2.20 O.OI 3.86 n 12 13 188.18 185.31 182.56 2.87 2.75 2.63 56 57 58 184.99 187.24 189.52 2.25 2.28 2.33 IOI 102 I0 3 261.76 261.66 261.45 0.10 0.21 O.32 146 '47 148 160.66 I56.774 152.85 3.8 9 3.92 3.g5 4 1 79-93 2.5o 59 191.85 2.36 104 261.13 0.43 '49 148.90 3.OT 15 17743 60 194.21 I0 5 260.70 150 '44-93 ***T / 2.37 2.39 o.54 4.00 16 7 18 '9 20 175.06 172.82 170.71 168.73 166.89 2.24 2. II 1.98 1.84 61 62 63 64 65 196.60 199.01 201.43 203.87 206.32 2.41 2.42 2.44 2.45 1 06 I0 7 108 109 I IO 260.16 259.51 258.75 257.89 256.91 o.65 0.76 0.86 0.98 '5' 152 '53 '54 '55 '40-93 136.92 132.89 128.86 124.81 4.01 4-o3 4.o3 4.65 1.70 2.45 1.09 4-o5 21 22 23 24 165.19 163.62 162.19 160.90 1.9] i.43 1.29 i.iS 66 67 68 69 208.77 211. 21 213.64 2l6.o6 2.44 2.43 2.42 2.41 in 112 "3 114 255.82 254.63 253-33 251.93 1.19 i.3o 1.40 i.5i 156 '57 158 '59 120.76 1 16.71 1 12.66 108.62 4.o5 4-o5 4.o4 4.o3 2 5 159-75 70 218.47 "5 250.42 1 60 104.59 I.OI 2.38 1.62 4.02 26 2 7 158.74 157.87 0.87 O.74 7' 72 220.85 223.19 2.34 2.3l 116 117 248.80 247.08 1.72 1.81 161 162 100.57 96.58 3.99 Q -- 28 I57.I3 O.l)0 73 225.50 o oft 118 245.27 163 92.61 O-97 1 ^/ 2 9 3 156.53 156.07 0.46 74 75 227.78 230.02 2. 2O 2.24 119 120 243.35 241.33 1.92 2.02 164 165 88.67 84-76 J.94 S.gl 0.32 2.19 2.12 3.88 3 15575 76 232.21 121 239.21 1 66 80.88 30 / 32 155.56 0. If) o.o5 77 234-34 2.12 1 nQ 122 237.00 2.21 2.3o 167 77.04 .04 7 Tft 33 34 '55-51 155.58 0.07 O.2I 78 79 236.42 238.44 c.OO 2.02 123 I2 4 234.70 232.31 2.39 2/n 168 169 73.26 69.52 -J.J& 3.74 1 in 35 1 55-79 80 240.41 1-97 125 229.82 49 170 65.82 *j.^\j o.34 1.89 2.58 3.64 36 37 38 39 40 156.13 156.59 I57-I7 157.88 158.71 0.46 o.58 0.71 o.83 81 82 83 84 85 242.30 244.12 245.87 247-54 249- '3 1.82 I. 7 5 1.6 7 i.5g 126 I2 7 128 129 I 3 227.24 224.58 221.84 219.02 2 1 6. 1 I 2.66 2.74 2.82 2.91 171 172 '73 '74 '75 62.18 58.62 55.12 51.69 48.32 3.56 3.5o 3.43 3.37 0.94 i.5i 2.99 3.28 4 1 42 43 159.65 160.71 161.86 i. 06 i.tS 1 . 26 86 8? 88 250.64 252.07 253.40 1.43 1.33 In / 131 132 '33 213.12 210.07 206.94 3.o5 3.i3 1 11 176 '77 178 45.04 41.84 38.74 3.20 3.io i n9 44 45 163.12 164.49 i.3 7 89 90 254.64 255.80 24 1.16 '34 '35 203.73 200.46 O. 2 I 3.27 '79 1 80 35.72 32.80 9m 2.92 [14] TABLE V. CONTINUED. Perturbations of the Mean Anomaly. Argument 1. Concluded- P^MBMM Arg. ^^i Eq. MB D. ^m^mxm^*^* Arg. Eq. D. Arg. Eq. t D. Arg. Eq. . / D. 180 181 182 183 184 185 32.80 29.98 27.27 24.67 22.17 19.79 2.82 2.71 2.60 2.5o 2.38 225 226 227 228 229 230 50.95 55-15 59-5 63-99 68.63 73-41 4.20 4.35 4-49 4-64 4-78 / rtO 270 271 272 273 274 275 316.90 322.51 328.00 333.38 338.63 343-77 5.6i 5.49 5.38 5.25 5.i4 5.oo 3i5 316 317 318 39 320 407.60 405.44 403.12 400.66 398.04 395-27 2.16 2.32 2.46 2.62 2.77 2.92 1 86 187 188 189 190 17-53 15.40 13.40 11.52 9.78 2.26 2.l3 2.OO 1.88 1.74 231 232 233 234 235 78-33 83.37 88.53 93.82 99-23 4.92 5.o4 5.i6 5.29 5.4i R K3 276 277 278 279 280 348.77 353.63 358.34 362.91 367-33 4-86 4-71 4.57 4-42 4.26 321 322 323 324 325 392.35 389-3I 386.14 382.84 379-4 1 3.O4 3.17 3.3o 3.43 3.55 191 192 !93 *94 *95 8.18 6.72 5-4 1 4.25 3-23 i. 60 1.46 i.3i 1.16 i. 02 236 237 238 239 240 104.76 110.38 ii6.n 121.93 127.85 J.J\j 5.62 5. 7 3 5.82 5.92 281 282 283 284 285 37M9 375-69 379-62 , 383-38 386.98 4.10 " 3. 9 3 3.76 3.6o 3.42 326 327 328 329 33 375-86 372.21 368.46 364.61 360.65 3.65 3.75 3.85 3.96 4-o5 196 197 198 J 99 200 2-37 1.67 1. 12 0.74 0.51 0.86 0.70 o.55 o.38 0.23 241 242 243 244 245 133-86 139-94 146.09 152.32 158.61 O.OI 6.08 6.i5 6.23 6.29 A TK 286 287 288 289 290 390.40 393.64 396.71 399-59 402.29 3.24 3.07 2.88 2.70 2.5l 33i 332 333 334 335 356.60 352.48 348.28 344.01 339-66 4.12 4.20 4.27 4.35 4.4i 201 2O2 203 204 205 0.46 0.57 0.85 I.3I i-93 o.o5 O.I I 0.28 0.46 0.62 _ Q.-. 246 247 248 249 250 164.96 i7i-35 177.79 184.26 190.77 U.O J 6.3 9 6.44 6.47 6.5i 6.53 291 292 293 294 295 404.80 407.12 409.25 411.18 412.93 2.32 2.13 1.93 1.75 i.55 336 337 338 339 340 335-25 330.80 326.30 321.76 W- 1 7 4-45 4.5o 4.54 4.59 4.62 2O6 2Oy 208 209 2IO 2-73 3-7 4.85 6.17 7.67 O.oO 0.97 i.i5 1.32 I. JO 251 252 253 254 255 197.30 203.85 210.40 216.95 223.51 6.55 6.55 6.55 6.56 296 297 298 299 300 414.48 45.83 416.99 417.96 4!8-73 i.35 1.16 0.97 0.77 r\ *\i 34 1 342 343 344 345 312.55 307.92 3 3.27 298.61 293.93 4.63 4.65 4.66 4-68 4.67 211 212 2I 3 214 215 9-35 II. 21 I3-24 15-44 17.82 1.68 1.86 2.03 2.20 2.38 256 257 258 259 260 230.06 236.58 243.08 249-55 255-99 6.55 6.52 6.5o 6.47 6.44 A / 301 302 33 34 35 419.30 419.68 419.87 419.87 419.67 0.37 o.38 0.19 O.OO 0.20 o.3o 346 347 348 349 35 289.26 284.60 279.95 275-32 270.70 4.66 4.65 4.63 4.62 4.59 216 217 218 219 22O 20.38 23.11 26.OI 29.07 32.31 2.56 2.73 2.90 3.06 3.24 261 262 263 264 265 262.39 268.73 275.01 281.23 287.39 6.40 6.34 6.28 6.22 6.l6 A r.Q 306 37 308 39 310 419.28 418.70 4 x 7-94 417.00 |i5.87 o.58 0.76 0.94 I.i3 i.3i 35 1 352 353 354 355 266.11 261.56 257.06 252.60 248.18 4.55 4-5o 4.46 4-42 4.37 221 222 22 3 224 225 35-72 39-29 43.02 46.90 5-95 3.4i 3.57 3. 7 3 3.88 4-o5 266 267 268 269 270 293-47 299.47 35-37 311.18 316.90 O.OO 6.00 5.90 5.8i 5.72 3 11 312 3'3 3H 3^5 414.56 4 I 3-7 411.42 409.60 407.60 1.49 i.65 1.82 2.OO 356 357 358 359 360 243.81 239-5 1 235.28 231.12 227.02 4.3o 4.23 ' 4.16 4.10 [15] TABLE V. CONTINUED. Perturbations of the Mean Anomaly. Argument 2. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. I 2 161.27 155.50 149.81 5.77 5.69 5.63 45 46 47 1.23 0.72 o-37 o.5i o.35 o, in 90 9 1 92 122. II 127.37 132.69 5.26 5.32 5.36 135 136 137 358.80 362.96 367.04 4.16 4.08 4.00 3 4 5 1 44. 1 8 138.62 I33'i3 5.56 5.49 48 49 5 0.18 0.15 0.27 o.o3 0.12 93 94 95 138.05 1 43-4 6 H8.93 5.4i 5.47 138 '39 140 37I-04 374.96 378.81 3.92 3.85 5.4i 0.28 5.5i 3.76 6 127.72 5.33 5 1 0.55 0.45 96 154.44 5.53 141 382.57 3.68 7 122.39 5.25 52 1. 00 O.6o 97 159-97 5.56 142 386.25 3.6o 8 117.14 5.17 53 1. 60 O.75 98 165-53 5.6o H3 389.85 3.53 9 10 111.97 106.88 / 5.09 54 55 2-35 3-27 0.92 99 100 171.13 176.75 5.62 144 H5 393.38 396.83 3.45 4.99 1.07 5.64 3.37 ii 12 101.89 96.98 4.91 4.82 56 57 4-34 5-57 1.23 i.38 101 102 182.39 188.04 5.65 5.66 146 147 400.20 403.49 3.29 3.23 13 92.16 4.72 58, 6.95 i.54 I0 3 193.70 5.67 148 406.72 3.i5 14 15 87.44 82.82 *** / 4.62 59 60 8-49 10.18 1.69 IO4 105 199-37 205.04 5.67 149 150 409.87 412.94 3.07 4.52 i.85 5.67 3.oo 16 17 78.30 73.88 4.42 / "<<> 61 62 12.03 14.03 2.0O 2 1 5 I 06 107 210.71 216.36 5.65 5.65 151 152 415.94 418.87 2.93 2.86 18 69.58 4"3(J 63 16.18 108 222.OI 5.63 *53 42L73 2 IO 19 20 65.37 61.28 4-21 4.09 64 65 18.47 20.92 2.29 2.45 109 I IO 227.64 233.26 5.62 '54 155 424.52 427.25 * /y 2. 7 3 3. 9 8 ,2.5g 5.6o 2.66 21 57-3 3.86 66 23-51 2.74 in 238.86 5.56 156 429.91 2.60 22 23 53-44 49.69 3.75 3.62 67 68 26.25 29.12 /H- 2.8 7 3.oi 112 IJ 3 244.42 249.96 5.54 5.5i '57 158 432-5 1 435-05 2.54 2.47 24 25 46.07 42.56 3.5i 69 70 32-13 35-28 3.i5 114 H5 25547 260.95 5.48 159 1 60 437.5 2 439-94 2.42 3.38 3.29 5.44 2.36 26 27 28 39.18 35-93 32.81 3.25 3.12 3.oo 7i 72 73 38.57 41.98 45.52 3.4i 3.54 3.66 116 117 118 266.39 271.78 2 77 .12 5.3 9 5.34 5.3o 161 162 163 442.30 444.60 446.86 2.3o 2.26 2.21 2 9 29.81 2.86 74 49.18 1 in 119 282.42 5.25 164 449.07 2.l5 30 26.95 75 52.97 0.79 1 20 28 7 .6 7 *5 45 1.22 2. 7 3 3.91 5.20 2. II 31 32 24.22 21.64 2.58 2.45 76 77 56.88 60.90 4.02 4. 1 3 121 122 292.87 298.01 5.i4 5.o8 1 66 167 453.33 455.40 2.07 2.03 33 19.19 9 7n 78 65.03 4nf{ I2 3 303.09 5 02 168 457-43 2.0O 34 35 16.89 14.72 i.ou 2.17 79 80 69.28 73.63 . JL J 4.35 I2 4 125 3O8.I I 3 ! 3-7 4.96 169 170 459-43 461.38 J.95 2.02 4-46 4.89 1.92 36 37 38 12.70 10.83 9.10 1.8 7 i. 7 3 i.58 81 82 83 78.09 82.64 87.28 4.55 4.64 4.73 126 127 128 317.96 322.79 327-55 4.83 4.76 4.68 171 172 173 463-30 465.18 467.04 io o o 1.88 1.86 1.84 39 4 7.52 6.09 1.43 84 85 92.01 96.84 4.83 I2 9 I 3 332.23 336.85 4.62 74 '75 408.08 470.69 1.81 1.28 4.91 4-54 1.78 4i 42 43 44 45 4.81 3-69 2-73 1.90 1.23 1. 12 0.96 o.83 0.67 86 87 88 89 90 101.75 106.73 111.79 1 16.91 122. II 4.98 5.o6 5.12 5. 20 131 132 133 134 '35 34M9 345-85 35 -24 354-56 358.80 4-46 4.39 4-32 4-24 176 177 178 179 1 80 472.47 474-24 475.99 477-73 479-45 i-77 i. 7 5 1-74 1.72 [16] ^ / TABLE V. CONTINUED. Perturbations of the Mean Anomaly. Argument 2. Concluded. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. 1 80 181 182 183 479-45 481.16 482.86 484.55 1.71 1.70 1.69 i. 60 225 226 227 228 564.59 566.70 568.81 570.90 2. II 2. II 2.09 2.O7 270 271 272 273 611.05 6lO.OO 608.83 607.54 i.o5 1.17 1.29 1.42 3!! $1? 445.50 439.58 433.60 427.56 5.92 5.98 6.04 6.09 184 486.24 V 1. 60 229 572.97 / 2.06 274 6o6.I2 i.55 319 421.47 6.14 185 487.93 i .^V 230 575-03 275 604.57 320 4 I 5-33 1.68 2.O4 1.68 6. 20 1 86 489.61 1.69 231 577.07 2.02 276 602.89 i. 80 321 409.13 6.23 187 491.30 i .60 232 579.09 2.00 ?77 601.09 1.94 322 402.90 6.28 188 492.99 i .60 233 581.09 I O7 278 599^5 2.o5 323 396.62 6.3i 189 494.68 i .70 234 583.06 1 *V / I C\fi 279 597.10 2 . 1 324 390-31 6.36 190 496.38 235 585.00 i i y i 280 594.91 325 383-95 1.70 I.gl 2.32 6.39 191 498.08 I T2 236 586.91 1.87 281 592.59 2-44 326 377.56 6.41 192 499.80 T* I 19 2 37 588.78 1.84 * 282 590.15 327 37LI5 A /./. 501.52 '7 a 238 590.62 1 .79 283 587.58 2. 7O 328 364-71 U.44 6.46 194 95 503.26 505.00 1-74 239 240 592.41 594.16 I. 7 5 284 285 584.88 582.08 / 2.82 329 330 358.25 35L76 6.49 1.76 1.70 2.95 6.5i 196 506.76 t TT 241 595.86 1.66 286 579.11 3.O7 33i 345.25 652 197 5o8.53 * / / 1-79 242 597.52 1.59 287 576.04 3.20 332 348.73 6.53 198 510.32 1. 8O 243 599.11 i.53 288 572.84 3.32 333 332.20 6.54 199 512.12 1.82 244 600.64 1.48 289 569-52 3.44 334 325.66 6.55 200 5 i 3-94 245 602.12 290 566.08 335 3-19.11 1.84 1.42 3.57 6.56 2OI 515.78 1.86 246 603.54 i.34 291 562.51 3.69 336 312.55 6.55 2O2 517.64 1.87 247 604.88 1.28 292 558.82 3.8i 337 306.00 6.55 203 519.51 1.90 248 606.16 1. 21 2 93 555-01 3.92 338 299.45 6.54 204 521.41 I OI 249 607.37 I il 294 551.09 4.04 339 292.91 205 523-32 i .y i 250 608.50 1 . 1 vj 295 547.05 34 286.36 ' 1.93 i.o5 4.i5 6.53 206 525.25 1. 06 251 609.55 296 542.9 4.26 34 1 279.83 6.52 207 527.21 V 1.97 252 610.52 0.97 0.88 297 538.64 4.37 342 273-3 1 6.5o 208 529.18 I .90 2 53 6 1 1 .40 298 534-27 A 48 343 266.81 6.48 209 53 I - I 7 2.0O 254 612.19 0.79 0.71 299 529.79 /l.lL> 4.58 344 260.33 6.47 2IO 533-J7 255 612.90 3 525.21 345 253.86 2.02 0.61 4.69 6.44 21 I 535-J9 2.04 256 613.51 O.52 301 520.52 4-79 346 247.42 6.41 212 537.23 2.o6 257 614.03 32 515.73 4.88 347 241.01 6.38 213 539- 2 9 2.o6 258 614.45 0.42 33 510.85 4.98 348 234-63 6.35 2I 4 541-35 2.08 259 614.77 O.32 34 505-87 5.OT 349 228.28 6.32 215 543-43 260 614.99 0. 22 305 500.80 *j.u i 350 221.96 2.10 O.I I 5.i 7 6.28 216 545-53 2 IO 261 615.10 36 495.63 5.25 351 215.68 6.24 217 547.63 262 615.10 o.oo 37 490.38 5.33 352 209.44 6 10 218 549-73 212 263 614.98 O. I 2 308 485.05 5.42 353 203.25 6. 1 5 219 551.85 2 12 264 614.77 O.2I C\ ^I 309 479.63 5.5o 354 197.10 22O 553-97 265 614.46 U.O I 310 474' 1 3 355 190.99 2.13 0.44 5.5 9 6.06 221 222 22 3 556.10 558.22 560.35 2.12 2.13 266 267 268 614.02 613-45 612.77 0.57 0.68 e\ Qn 312 468.54 462.87 457.15 5.67 5.72 t. -Q 356 357 358 184.93 178.93 172.99 6.00 5. 9 4 ^ Q/-. f S. . \ Z. 224 562.47 *t T/ 2.12 225 i 564.59 269 270 611.97 611.05 O.OO 0.92 3H* 315 451-37 445-5 3.70 6.87 359 360 167.10 161.27 3.09 5.83 [17] TABLE V. CONTINUED. Perturbations of the Mean Anomaly. Argument 3. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. o 42.77 2.66 45 219.67 x 8x 9 433-37 X IX 135 557-07 1 .01 i 45-43 2 48.16 3 50-96 2. 7 3 2.80 2 8l 46 47 -48 224.51 229.36 234-23 4.04 4.85 4.87 / 8r> 9 1 92 93 437-5 i 441.61 445.65 ** *^i 4.10 4.04 136 J 37 138 558.08 559.01 559-85 0.93 0.84 o 76 4 53-83 ^.o / f)/t 49 239.12 4.09 94 449.64 0.99 3 nX J 39 560.61 0.68 5 56.77 4.y4 5 244.02 4-9O ?5 453.58 0.94 140 561.29 3.01 4.92 3.89 o.58 6 59.78 7 62.86 8 | 66.00 9 69.21 10 72.49 3.o8 3.i4 3.21 3.28 5i 52 * 53 54 55 248.94 253.86 258.79 263.73 268.68 4.92 4.93 4-94 4.95 96 97 98 99 IOO 457-47 461.31 465-09 468.81 472.48 3.84 3.78 3.72 3.67 141 142 H3 144 H5 561.87 562.37 562.78 563.11 563-36 o.5o 0.41 o.33 0.25 3.35 4.95 3.6i 0.16 1 1 12 75.84 79.25 3.4i 3 Al 56 57 273.63 278.58 4.95 4.95 101 * 102 476.09 479-63 3.54 3.48 146 H7 563.52 563.60 0.08 o.oo '3 82.72 J.4 / 3.53 58 283.53 4.95 103 483.11 3.42 148 563.60 O. IO 1.4 86.25 3.5g 59 288.48 4.o5 104 486.53 3.36 149 563.50 0.18 15 ; 89.84 60 * 2 93-43 ** y-' I0 5 489.89 150 563.32 3.65 4.95 3.3o 0.27 16 i? 18 9349 97.20 100.96 3. 7 i 3.76 3.82 61 62 63 298.38 303-3 1 308.24 4.93 4-93 4.o3 1 06 107 108 493-^9 496.42 499-58 3.23 3.i6 3. 10 X 5' 152 ! 53 563.05 562.70 562.26 o.35 0.44 O.52 '9 104.78 1 R8 64 3I3-I7 t+.yv X..QI 109 502.68 3.o3 154 561.74 '0.61 20 108.66 o.oo 65 318.08 i*.y i no 505.71 !55 561.13 3. 9 3 4.90 2.96 0.69 21 112.59 66 322.98 X go III 508.67 2.89 156 560.44 22 116.58 3.99 / n/ 67 327.87 |.l>y 4.88 112 511.56 2.82 J 57 559-67 0.77 0.86 2 3 120.62 4.O4 4.08 68 332.75 4.86 H3 5H-38 2.74 158 558.81 0.94 24 124.70 4tX 69 337.6i 4.84 114 517.12 2.68 '59 557.87 i.o3 25 128.84 .14 70 342.45 "5 519.80 1 60 556.84 4.18 4.82 2.60 i. ii 26 133.02 4.23 7i 347-27 4.80 116 522.40 2.53 161 555-73 1.20 27 137.25 4 Of 72 352.07 4.78 117 524-93 2.46 . 162 554.53 1.27 28 141.52 .27 X "*-> 73 356.85 4.76 118 527-39 2.38 163 553.26 i.36 2 9 145.84 4>Oz X ^A 74 361.61 4. f\j 4.73 119 529.77 2.3o 164 551.90 1.44 30 150.20 4*"U 75 366.34 1 20 532.07 165 | 550.46 4.40 4.71 2.22 1.52 31 154.60 4.44 76 37i-o5 4.67 121 534-29 2.l5 1 66 548.94 i. 60 32 159.04 4.48 77 375-72 4.65 122 536.44 2 O1 167 547-34 1.67 33 163.52 4.5i 78 380.37 4.62 123 538.51 .\J I 168 545-67 1.77 34 168.03 4.55 79 384-99 4.5o 124 540.50 '99 I OI 169 543-9 i.83 35 172.58 80 389-58 *"-'y 125 542.41 1 V* 170' 542.07 4.58 4.55 1.84 1.92 36 37 177.16 181.78 4.62 X 6/5 81 82 394-13 398.65 4-52 f. /.R 126 127 544.25 546.00 i. 7 5 T f iS 171 172 540.15 538.15 2.00 2.O7 38 186.42 4.U4 4.67 83 403.13 4.40 4.44 128 547.68 1 .UO i.5g 173 536.08 2.13 39 191.09 4.70 84 407.57 4.40 129 549-27 V i.5i 174 533-93 2.23 40 '95-79 t+. |V 85 411.97 I 3 550.78 175 53^70 4.73 4.37 1.42 2.3o 4' 42 200.52 205.27 4.75 4.18 86 87 416.34 420.66 4.32 4.28 !3' I 3 2 552.20 553-54 i.34 1.26 176 177 529.40 527.03 2.3 7 2.44 43 210.05 ** / V 4.80 88 424.94 ' / n / 133 554.80 i iS 178 ; 524.59 2.53 44 45 214.85 219.67 4.82 89 90 429.18 433-37 4-24 4.19 34 '35 555-98 557-07 I . I o I.Og 179 522.06 1 80 519.47 2.59 [18] TABLE V. CONTINUED. Perturbations of the Mean Anomaly. Argument 3. Concluded. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. 180 1 8l 51947 516.80 2.67 225 226 344.18 339-41 4.77 4.78 270 271 132.79 128.66 4.i3 4.09 315 316 7-47 6-39 i. 08 I.OO 182 514.07 2. 8 1 227 334-63 *# (** 4.80 272 124.57 4.o3 317 5-39 0.91 183 511.26 2.88 228 3 2 9-83 4.82 273 120.54 3.OQ 3 J 8 4.48 o.83 184 508.38 2.94 229 325.01 4.83 274 116.55 vs.yy 3.94 319 3-65 0.74 185 505-44 230 320.18 275 112. 6l 320 2.91 3.oi 4.85 3.89 0.66 186 502.43 231 315-33 4.85 276 108.72 3.84 321 2.25 o.5i 187 499-36 31 / 232 310.48 4 87 277 104.88 ^ in 322 1.68 v.*y l 0.4.3 188 496.22 14 3. 20 233 305.61 4.87 278 101.09 j. /y 3.73 323 1.20 0.41 189 493.02 234 300.74 t* 1 -' / 4,88 279 97-36 3.68 324 -79 o.3i 190 489-75 0.2*7 235 295.86 280 93.68 3 2 5 0.48 3.33 4.88 3.62 0.23 191 486.42 i in 236 290.98 4.88 281 90.06 3.56 326 0.25 o. 14 192 483.03 0.09 3 /A 237 286.10 282 86.50 3.5o 327 O.I I o 06 193 479-57 .40 281.22 x 88 283 83.00 3.45 328 0.05 o.o3 194 476.06 3.57 239 276.34 4*00 4.89 284 79-55 3.38 329 0.08 O.I 2 195 472.49 240 271.45 285 76.17 33 O.2O 3.63 4.88 3.32 O.2O 196 468.86 3f 241 266.57 / QQ 286 72.85 331 0.40 o.3o 197 465.19 .67 3_ , 242 261.69 4.OO 287 69.59 o. 2o Q In 332 0.70 o.38 198 199 461.45 457-66 74 3.79 3.84 243 244 256.83 251.96 4.87 4.85 288 289 66.40 63.27 vj. i (y 3.i3 3.o6 333 334 1. 08 o.45 o.55 200 453-82 245 247.11 290 60.21 335 2.08 ,-, \ 3.90 4-84 2.99 o.63 201 449.92 3.94 246 242 27 4.83 291 57-22 2.93 336 2.71 0.71 202 445.98 247 237.44 x 8t 292 54.29 2.86 337 342 0.80 203 204 2O5 441.98 437-93 433-84 4>oo 4-o5 4.09 248 249 250 232.63 227.82 223.03 l\,O i 4-8l 4-79 293 294 295 543 48.65 45-93 2.78 2.72 338 339 34 4.22 5.II 6.08 0.89 0.97 4.14 4-77 2.65 i. 06 206 429.70 X 18 251 218.26 4.75 296 43.28 2.58 34 1 7.H 1. 14 207 425.52 252 213.51 ** /^ / "in 297 40.70 342 8.28 1.23 208 421.30 253 208.79 4-72 298 38.20 2* DO 343 9.51 209 417-03 4.^7 4.3 1 254 204.08 4.71 4.60 299 35-77 2.36 344 10.82 1.40 2IO 412.72 255 *99-39 *+"^ 300 33-4 1 345 12.22 4.35 4.67 2.28 1.47 211 408.37 4.3g 256 194.72 4.63 301 J3 2. 2O 346 13.69 1.56 212 213 214 2I 5 403.98 399-56 395-n 390.62 4.42 4.45 4.49 257 258 259 260 190.09 185.48 180.89 176.34 4.61 4.59 4.55 302 303 304 305 28.93 26.80 24-75 22.78 2.13 2.05 1.97 347 348 349 35 15.25 16.89 18.61 20.41 1.64 1.72 1. 80 4.52 4.52 20.88 1.90 1.89 216 217 218 219 22O 386.10 38L55 376.97 372.37 367-73 4.55 4.58 4.60 4.64 261 262 263 264 265 171.82 167.34 162.89 158.48 154.10 4-48 4-45 4-41 4.38 306 37 308 39 310 19.07 17-33 15.68 14.10 1.81 1-74 i.65 1.58 35 1 352 353 354 355 22.30 24.26 26.31 28.43 30.63 1.96 2.o5 2.12 2.20 4.66 4.34 i-49 2.28 221 222 363.07 358.38 4.69 266 H9.76 267 ! 145.46 4.3o 3 11 312 12. 6l 11.20 1.41 356 357 32.91 35.26 2.35 /I 223 353-67 268 ' 141.19 4.27 9.87 1 .33 358 37.69 2.40 224 348 - 9 t i* 269 136.97 4-22 4.l8 3H 8.63 1.24 1.16 359 40.19 2.5o 2.58 225 344.18 ; 270 132.79 3i5 7-47 360 ! 42.77 [19] TABLE V. CONTINUED. Perturbations of the Mean Anomaly. Argument 4. Arg. Eq. D. Arg Eq. D. Arg. Eq. D. Arg. Eq. D. o 71.69 0. 1 2 45 C 28.87 i.3o 90 0.65 0. 22 135 20.1 8 0.18 i 7*-57 0.18 4'6 27.57 1.29 9 1 0.87 0.24 136 20.36 o.i 5 2 3 71-39 71.17 0.22 0.26 47 48 26.28 25.01 1.27 1.25 92 93 I.I I 1.38 0.27 o.3o 137 138 20.51 20.63 O.I 2 0.09 4 70.91 0.32 49 23.76 1.24 94 1.68 o.33 139 20.72 0.06 5 70.59 5 22.52 95 2.OI 140 20.78 O.37 1. 21 o.35 o.o3 6 70.22 O.4l 51 21.31 I.I9 96 2.36 o.38 141 20.8 I o.oo 7 69.81 O.46 52 20.12 1.16 97 2.74 0.40 142 20.8 I o.o3 8 69.35 o.5i 53 18.96 1.14 98 3-H 0.42 H3 20.78 o.o5 9 68.84 o.56 54 17.82 1. 1 1 99 3-56 144 20.73 0.09 10 68.28 55 16.71 IOO 4.00 ' H5 20.64 0.61 i. 08 0.46 0.12 n 67.67 0.66 56 15.63 1. 06 101 4-46 0.48 146 20.52 0.14 12 67.01 0.70 57 H-57 1.02 IO2 4-94 o.5o H7 20.38 0.18 13 4 15 66.31 65.57 64.78 0.74 0.79 58 59 60 '3-55 12.56 1 1. 60 0.99 0.96 103 104 I0 5 5-44 5.96 6-47 0.52 o.5i 148 149 150 20.20 20.00 19.78 O.2O 0.22 o.83 0.92 0.53 O.25 16 18 9 20 63.08 62.17 61.22 60.24 0.87 0.91 o.g5 0.98 61 62 63 64 65 10.68 9-79 8.94 8.12 7-34 0.89 o.85 0.82 0.78 106 107 108 109 no 7.00 7.54 8.09 8.64 9.20 o.54 o.55 o.55 o.56 '5 1 152 54 '9-53 19.25 18.95 18.62 18.27 0.28 o.3o o.33 o.35 i. 02 0.74 o.55 o.36 21 22 23 24 25 59-22 58.16 57.08 55-96 54.82 1. 06 i. 08 1. 12 1.14 66 67 68 69 70 6.60 5.90 5-23 4.61 4.02 0.70 0.67 0.62 o.Sg in I 12 115 9-75 10.31 10.88 11.44 11.99 o.56 0.57 o.56 o.55 156 158 1 60 17.91 17.52 17.11 16.68 16.22 o.3g 0.41 o.43 0.46 1.17 o.54 o.55 0.47 26 53.65 1.20 7 1 348 o.5o 116 12.54 o.55 161 X* '5-75 0.48 27 28 2 9 30 52.45 51.24. 50.00 48.74 1. 21 1.24 1.26 72 73 74 75 2.98 2.51 2.09 1.71 0.47 0.42 o.38 117 118 119 1 20 13.09 13.62 14.14 14.66 o.53 0.52 0.52 IO2 163 164 165 15.27 14.78 14.28 13.76 0.49 o.5o 0.52 1.28 o.34 o.5o o.53 31 32 33 34 47.46 46.16 44.86 43-54 i.3o i.3o 1.32 1.32 76 77 78 79 1.07 0.80 0.58 o.3o 0.27 0.22 0.18 121 122 I2 3 124 15.16 15.65 1 6. 1 2 . 16.57 0.49 0.47 o.45 0.44 1 66 167 168 169 I 3- Z 3 12.70 12.17 11.63 o.53 o.53 o.54 o.55 35 42.22 80 0.40 I2 5 17.01 170 1 1. 08 i.34 0.14 0.42 o.55 36 37 38 40.88 39-55 38.21 1.33 i.34 i.35 81 82 83 0.26 o/i 6 O.IO O.IO 0.06 o.o3 126 I2 7 128 17.43 17.83 18.21 0.40 o.38 o.36 171 172 9-99 9-45 o.54 o.54 o.54 39 36.86 84 0.07 129 18.57 o 33 '74 8.91 o.53 40 35-52 1.34 85 0.08 O.O I 130 18.90 175 8.38 o.o5 o.3i o.53 4 2 43 34-7 32.84 31-51 1.35 i.33 i.33 1.33 86 87 88 0.13 O.2O 0.32 0.07 O.I 2 o.i 5 131 132 133 19.21 19.49 19.74 0.28 0.25 0.23 176 177 178 7.85 7-34 6.83 o.5i o.5i 0.49 44 45 30.18 28.87 t .31 89 90 0.47 0.65 0.18 134 '35 19.97 20. 1 8 O.2I 179 1 80 34 5.85 9.49 [20] TABLE V. CONTINUED. Perturbations of the Mean Anomaly. Argument 4. Concluded^ Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. 1 80 5.85 O.47 225 8.58 o.53 270 24-93 O.II 315 42.48 0.86 181 5-38 v>bf. y 0.45 226 9.II o.53 271 25.04 O.II 316 43-34 0.86 182 4-93 O.43 227 9.64 o.54 272 25.15 O.II 3 ! 7 44.20 0.88 183 4.50 O.42 228 IO.I8 o.54 273 25.26 O.II 3 l8 45.08 0.90 184 4.08 O.4O 229 10.72 o.54 274 25-37 O.II 3^9 45.98 0.90 185 3-68 230 11.26 275 25.48 320 46.88 o.38 o.54 O.II 0.92 1 86 3-3 o.35 231 1 1. 80 o.54 276 25.59 0.12 321 47.80 0.92 187 1 88 2.95 2.62 o.33 o.3i 232. 233 12.34 12.87 o.53 o.53 277 278 25.71 25.84 o.i3 o.i3 322 323 48.72 49-64 0.92 0.93 189 190 2.31 2.02 0.29 234 235 13.40 13.93 o.53 279 280 25-97 26.10 o.i3 324 325 5-57 51.51 0.94 0.26 0.52 o.iS 0.95 191 1.76 O.23 236 14.45 O.52 281 26.25 o.i5 326 52.46 o.o3 192 193 i-53. O.2O 0.18 237 238 14.97 15-47 o.5o o.5o 282 283 26.40 26.57 0.17 0.19 327 328 53-39 54-32 V 0.93 o.o3 194 ^95 1.15 I.OO p. 1 5 239 240 15-97 16.46 0.49 284 285 26.76 26.95 0.19 329 33 55-25 56.16 7 O.9I 0.12 0.48 O.2I O.9I ' 196 197 198 199 0.88 0.79 0.72 0.69 0.09 0.07 o.o3 O.Ol 241 242 243 244 16.94 17.41 17.87 18.32 0.47 0.46 o.45 o.43 286 287 288 289 27.16 27.38 27.62 27.88 O.22 0.24 0.26 O.28 333 334 57.07 57-97 58-85 59.72 0.90 0.88 0.87 n SA 200 0.68 245 18.75 290 28.16 335 60.58 o.oo O.02 0.42 o.3o 0.84 2OI 2O2 203 0.70 0.76 0.84 0.06 0.08 O.IO 246 247 248 19.17 19.96 0.40 o.3g o.38 291 292 293 28.46 28.78 29.12 0.32 o.34 o.36 336 337 338 61.42 62.23 63.02 0.81 0.79 O tt 204 205 0.94 i. 08 0.14 249 250 20.34 20.70 o.36 294 295 29.48 29.86 o.38 339 34 63-79 64-54 u. / I 0.75 0.16 o.34 0.40 O.TI 2O6 207 208 1.24 I -43 1.65 0.19 0.22 O.24 251 252 2 53- 21.04 21.38 21.69 o.34 o.3i 0.28 296 297 298 30.26 30.69 0.43 o.45 0.48 34 1 342 343 65-25 65.94 66.59 / '0.69 o.65 0.62 209 210 1.89 2.16 0.27 254 255 21.97 22.25 0.28' 299 300 31.62 32.12 o.5o 344 345 67.21 67.80 o.Sg o.3o 0.26 o.53 o.56 21 I 212 213 214 2.46 2.78' 3.12 3.48 0.32 o.34 o.36 o.3g 256 257 258 259 22.51 22.76 22.99 23.21 0.25 0.23 O.22 O.2I 301 302 33 304 32.65 33-20 33.78 34.38 o.55 o.58 0.60 0.62 346 347 348 349 68.36 68.88 69-37 69.81 0.52 0.49 0.44 215 3-87 260 23.42 35 35.00 35 70.22 ' 0.41 O.2O o.65 o.36 216 2I 7 4.28 4.70 0.42 261 262 23.62 23.80 0.18 306 37 36.32 0.67 352 70.58 70.88 o.3o 218 5.14 o.44 n /*> 263 23-97 0.17 308 37.02 0.70 353 71.15 0.27 219 22O 5-59 6.06 O.4J 0.47 264 265 24.14 24.29 0.17 o.i 5 39 310 37-74 38.48 0.74 354 355 71-37 7L54 0.22 0.17 0.49 0.14 0.76 0. 12 221 222 223 224 225 6-55 7.04 7-54 8.06 8.58 0.49 o.5o 0.52 o.52 266 267 268 269 270 24-43 24.57 24.69 24.81 24-93 0.14 0.12 O.I 2 O.I 2 312 3*3 3H 315 39.24 40.02 40.82 41.64 42.48 0.78 0.80 0.82 0.84 356 357 358 359 360 71.66 71.76 71.75 71.69 0.07 o.o3 O.OI 0.06 [21] TABLE V. CONTINUED. Perturbations of the Mean Anomaly. Argument 5. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. 3-9 1.23 45 246.47 Q.O7 90 730.36 '35 1187.52 i 4-32 1.45 46 255.54 0.18 9' 74L82 1 1 . 4-t) n/ / 136 "95-37 7 ' 2 5-77 1.65 47 264.72 o.3o 92 753.26 44 '37 1203.08 7.71 3 4 5 7.42 9.29 11.36 1.87 2.07 48 49 50 274.02 28343 292.96 9-4i 9.53 93 94 95 764.68 776.08 78745 1 1 .42 11.40 11.37 138 '39 140 1210.64 1218.06 1225.34 7-42 7.28 2.28 9.64 u.35 7.i3 6 7 8 9 '3-64 I 6. 1 2 18.81 21.70 2.48 2.69 2.89 3.io 53 54 302.60 312.34 322.18 332.13 9-74 9-84 9.95 1 0.0 A 96 97 98 99 798.80 8 1 o.i I 821.37 832.61 n. 3i 11.26 11.24 I I 2O 141 142 '43 '44 1232.47 1239.44 1246.26 1252.93 6.97 6.82 6.67 10 24.80 55 342.17 IOO 843.81 '45 1259.44 ' l 3.3o 10.14 n. i5 6.35 ii 28.10 3.5o 56 352.3' IO 22 101 854.96 146 1265.79 6 o 12 31.60 3.70 57 362.53 io.3o 102 866.07 1 1 ,o5 '47 1271.97 .18 '3 '4 '5 35-30 39-'9 43.28 3.89 4.09 58 372.83 383.22 393.70 10.39 10.48 103 104 105 877.12 888.11 899.06 10.99 10.95 148 '49 150 1277.99 1283.85 1289.54 6.02 5.86 5.69 4.28 10.56 10.89 5.53 16 47.56 4-47 61 404.26 10.62 1 06 909.95 10.82 '5' 1295.07 A TK '7 18 '9 20 52.03 56.69 61.54 66.57 4-66 4.85 5.o3 62 63 64 65 414.88 425.58 436.34 447.18 10.70 10.76 10.84 107 108 109 IIO 920.77 93'-53 942.22 952.84 10.76 10.69 10.62 152 '53 '54 '55 1300.42 1305.59 1310.60 '3 '5-43 J.O J 5.1 7 5.oi 4.83 5.22 10.90 10.55 4.65 21 22 7L79 77.20 5.4i 5.58 66 67 458.08 469.04 10.96 1 1 .01 in 112 963-39 973.86 10.47 io.38 156 '57 1320.08 '324-55 4-47 23 82.78 5.76 68 480.05 1 1. 06 "3 984.24 io.3i 158 1328.83 4.28 24 88.54 5.94 69 491.11 II II 114 994-55 '59 1332.93 4.10 25 94-48 70 5O2.22 "5 1004.78 IO. 23 1 60 1336.85 3.92 6. u 11.17 10.14 3.73 26 27 28 100.59 106.87 113-32 6.28 6.45 6.62 72 73 5'3-39 524.60 535.85 II. 21 11.25 1 1 . 2Q 116 "7 118 1014.92 1024.97 1034.92 io.o5 9.95 9.86 161 162 163 1340.58 1344.12 '347-47 3.54 3.35 29 30 119.94 126.72 6.78 74 75 547.H 558.46 11.32 "9 1 20 1044.78 1054.54 9.76 164 165 1350.64 '353-6i 3.17 2.97 6.95 H.36 9.67 o -18 3' '33-67 1 IO 76 569.82 ii.38 121 1064.21 1 66 '.356.39 2.70 32 140.77- /*" 736 77 581.20 1 1 .41 122 1073.77 167 '358.97 2.58 33 148.03 .^u 1 Xf 78 592.61 1 1.43 123 1083.22 O*43 168 1361.36 2.39 34 '55-44 7.41 79 604.04 1 1 .45 124 1092.57 9- 169 1363.56 2.20 35 163.01 7- 7 80 615.49 125 1101.81 9.24 170 1365.56 2.00 7.72 11.47 9-i3 . Q~ 36 170.73 81 626.96 1 1.48 126 1110.94 171 y' / 1 . OU 1367.36 | 37 38 178.59 186.60 8.01 8.i5 82 83 638.44 649.92 11.48 1 1 . 5o I2 7 128 1119.94 1128.83 9.00 8.89 ft -if, 172 '73 1368.96 1370.36 1. 6O I.4O 39 194.75 8 20 84 661.42 i i.5o I2 9 "37.59 O.j\J ft f\^ '74 1371.56 I. 2O 4 203.04 0.49 85 672.92 I3O 1 146.24 O.UJ '75 1372.56 I.OO 8.43 n. 5o 8.52 o 4' 211.47 8.55 86 684.42 '3' 1154.76 8 In 176 I373-36 O. oO 42 220.02 8.69 87 695.92 1 1 .00 1 1.48 132 1163.15 .09 Q 9 177 '373-95 o. 39 43 228.71 8.82 88 707.40 11.48 '33 1171.40 OfftJ 8.i3 178 '374-34 0.18 44 45 237-53 246.47 8.94 89 90 i 718.88 730.36 11.48 '34 '35 "79-53 1187.52 7-99 179 1 80 '374-52 '374-5' O.OI [22] TABLE V. CONTINUED. Perturbations of the Mean Anomaly. Argument 5. Concludrdr Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. 1 80 I374-5I 225 1165.63 8.89 270 658.84 315 l6 7- I 9 8o4 181 1374.28 0. 2o 0.43 226 1156.74 9.o3 271 646.37 12.47 12.45 316 '59-'5 7 ; 85 182 '83 184* 1373.85 1373.21 1372.36 0.64 o.85 227 228 229 1147.71 1138.52 1129.19 9.19 9.33 272 273 274 633.92 621.49 609.08 12.43 12.41 317 318 3'9 151.30 143.62 136.12 7.68 7-5o 1 32 185 I37I-3I 1 .00 230 1119.70 9.49 275 596.68 12.40 320 128.80 7*> 1.26 9.63 12.37 7.i3 1 86 187 188 1370.05 1368.59 1366.92 1.46 1.67 1.88 231 232 233 IIIO.O7 1100.30 1090.40 9-77 9.90 276 277 278 584.31 571.98 559^9 I 12.33 12.29 321 322 323 121.67 114.72 107.96 6. 9 5 6.76 6.56 189 1365.04 2.08 2 34 1080.36 10.04 10.18 279 547-44 12.25 12 21 324 101.40 6.38 190 1362.96 235 1070.18 280 535.23 325 95.02 2.29 io.3o 12. l6 6.18 191 192 ^93 1360.67 1358.17 1355.46 2.5o 2.71 Q n I 236 237 238 1059.88 1049.45 1038.91 10.43 10.54 281 282 283 523.07. 510.97 498.92 12.10- 12.05 n_Q 326 327 328 88.84 82.86 77.07 5. 9 8 5.79 5.58 194 95 1352.55 1 3 49-44 ^.91 3. ii 239 240 1028.24 1017.46 I O.O*7 10.78 284 285 486.94 475.02 .Qo 11.92 329 33- 7L49 66. i o 5.3 9 3.32 10.90 u.85 5.i8 196 1346.12 3.52 241 1006.56 1 1. 00 286 463.17 1 1 11 33i 60.92 4-97 197 1342.60 3 T2 242 995.56 287 451.40 1 * / / 332 55-95 A 11 198 199 1338.88 1 3 34.96 0.7^ 3.92 4. i3 243 244 98445 973.24 11*11 II. 21 li.3i 288 289 439-70 428.09 1 1 .70 n. 61 Tf K-l 333 334 51.18 46.62 4-77 4.56 4.35 2DO 1330-83 245 961.93 290 416.56 11. JO 335 42.27 4.33 11.41 11.44 4-14 201 1326.50 4.53 246 950.52 n.4o 291 405.12 ii.34 336 38.13 3.94 2O2 203 1321.97 1317.24 4.73 4.93 247 248 939-03 927.46 ^7 11.57 u.66 292 293 393.78 382.55 11.23 11.14 337 338 34-19 30.47 3. 7 2 3.5o 204 1312.31 5.i3 249 915.80 294 37I-4 1 339 26.97 3.3o 20 5 1307.18 250 904.06 11.74 295 360.37 11.04 340 23.67 5.32 11.82 10.93 3.o8 2O6 1301.86 5.52 251 892.24 1 1 88 296 349-44 10.81 34i 20.59 2.86 207 208 209 1296.34 1290.63 1284.73 5. 7 i 5.90 6.00 252 253 254 880.36 868.41 856.39 1 1 .00 11.95 12.02 1 2. 08 297 298 299 338.63 327-94 317.36 10.69 10.58 IO.46 342" 343 344 17.73 15.08 12.64 2.65 2.44 2.22 2IO 1278.64 255 8 44.3I 300 306.90 345 10.42 6.28* 12. l3 io.33 2.00 21 I 212 1272.36 1265.89 6.47 6.65 256 257 832.18 820.00 12. l8 12.23 301 302 296.57 286.38 10.19 1 0.06 346 347 8.42 6.63 1-79 i 5i 2I 3 1259.24 6.84 258 807.77 12.27 303 276.32 9.93 348 5.06 i . ^ i i.36 214 1252.40 7n9 259 795-50 / r o T i 34 266.39 349 3-70 I IA 2I 5 I2 45-38 .OJ 260 78^.19 1 4.3 I 35 256.60 9-79 350 2.56 i.i^ 7-20 12.35 9.64 0.92 216 1238.18 7.38 261 770.84 12.38 306 246.96 35i 1.64 O.TO 217 218 219 22O 1230.80 1223.25 1215.52 1207.62 7.55 7. 7 3 7.90 262 263 264 265 758.46 746.06 733.63 72I.I8 ' 12.40 12.43 12.45 37 308 39 310 237.46 228.12 218.94 209.90 Q. DO 9.34 9.18 9.04 352 353 354 355 0-94 0-45 o.i 8 0.13 0.49 0.27 O.OD 8.07 12.46 8.87 0.16 221 1199.55 o ? 266 708.72 3 11 201.03 fi -! 356 0.29 r> 38 222 223 224 225 1 1191.32 1182.92 1174.36 1165.63 O. 4-J 8.40 8.56 8. 7 3 267 268 269 270 696.25 683.78 671.31 658.84 12.47 12.47 12.47 12.47 312 3'3 3H 3i5 192.32 183.78 175.40 167.19 8.71 8.54 8.38 8.21 357 358 359 360 0.67 1.27 2.07 3-09 O.OO O.60 0.80 1.02 [23] TABLE V. CONTINUED. Perturbations of the Mean Anomaly. Argument 6. Argument 7. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. 21.94 0.45 1 80 26.40 o.36 36.58 o.i5 I 80 2.22 o.i5 5 19.68 0.45 185 28.18 o.35 5 35-75 0.18 185 3-05 0.18 10 17.46 0.44 190 29.94 o.35 10 34.80 0.20 190 4.OO O.2O 15 15.29 0.42 195 3'-64 o.34 15 33-73 0.22 95 5.07 0.22 20 13.21 0.41 200 33-31 o.33 20 32.56 0.25 2OO 6.24 *0.25 25 11.22 0.89 205 34-9 2 0.32 25 31.28 0.27 205 7.52 0.27 30 9-35 o.36 2IO 3 6 -47 o.3o 30 29.90 0.28 2IO 8.90 0.28 35 7.62 o.33 215 37-95 0.29 35 28.46 o.3o 215 10.34 o.3o 40 6.04 o.3o 220 39-36 0.27 40 26.94 o.3i 22O 11.86 o.3i 45 4.64 0.26 225 40.67 0.25 45 25.36 0.32 225 13-44 0.32 5 3-39 0.23 230 41.89 0.23 50 23-74 o.33 230 15.06 0.33 55 2-34 0.19 2 35 43-01 0.21 55 22.08 o.33 235 16.72 o.33 60 1.49 o.i5 240 44.01 0.19 60 20.41 o.33 240 18.39 o.33 65 0.84 O.I I 245 44.88 0.16 65 18.73 0.33 245 20.07 o.33 70 0.38 0.07 250 45.62 o.i3 70 17.06 0.33 250 21.74 o.33 75 0.14 o.o3 255 46.23 O.IO 75 15.40 o.33 255 23.40 o.33 80 0.09 O.OI 260 46.67 0.07 80 13.76 0.32 260 25.04 0.32 85 0.24 o.o5 265 46.96 0.04 85 12.18 o.3i 265 26.62 o.3i 90 0.57 0.09 270 47.09 O.OI 90 10.65 o.3o 270 28.15 o.3o 95 1. 10 0.12 275 47.04 o.o3 95 9.19 0.28 275 29.61 0.28 IOO 1.79 o.i5 280 46.81 0.06 IOO 7.80 0.27 280 31.00 0.27 105 2.65 0.18 285 46.41 O.IO 105 6.50 O.25 285 3 2 -3 O.25 no 3-64 O.2I 290 45.84 o.i3 no 5-30 0.23 290 33-5 0.23 "5 4-79 0.24 295 45.06 0.17 "5 4.21 0.21 295 34-59 0.21 120 6.07 0.26 3OO 44.11 0.21 1 20 3.23 0.18 300 35-57 0.18 125 744 0.28 305 42.99 0.24 125 2.39 0.16 35 36.41 0.16 130 8.91 o.3o . 310 41.69 0.28 130 1.66 o.i3 310 37-H o.i3 35 10.48 o.3i 315 40.22 o.3i 135 1.07 O.IO 3^5 37-73 O.IO 140 12.12 . o.33 320 38.60 o.34 140 0.62 0.08 320 3'8.i8 0.08 45 13.82 o.34 325 36.84 o.36 H5 0.31 o.o5 325 38.49 o.o5 . 150 15.56 0.35 330 34-95 0.39 150 0.14 O.02 33 38.66 O.O2 55 17-34 o.36 335 32.95 0.41 155 0.13 O.OI . 335 38.67 O.OI 1 60 19.15 o.36 34 30.85 o.43 1 60 0.26 0.04 34 38.54 O.O4 165 20.97 o.36 345 28.68 0.44 165 0.54 0.07 345 38-26 0.07 170 22.78 o.36 35 26.46 0.45 170 0.96 O.IO 35 37-84 O.IO 75 24.60 o.36 355 24.21 0.45 175 1.52 o.i3 355 37.28 o.i3 1 80 26.40 o.36 360 21.94 o.45 1 80 2.22 o. i5 360 36.58 o.i5 V * !t * The Differences are calculated for i Degree. [24] TABLE V. CONTINUED. Perturbations of the Mean Anomaly. Argument 8. Argument 9. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. 0.14 o.o3 1 80 28.46 o.o3 3.89 0.16 1 80 2 347 0.16 5 0-35 o.o5 I8 5 28.25 o.o5 5 3.12 o.i5 185 24.22 o. 14 10 0.66 0.07 190 27.94 0.07 10 2.42 o.i3 190 24.90 0.12 '5 i. 08 0.09 195 27.52 0.09 15 1.79 0.12 195 2547 O.II 20 i. 60 O.II 2OO 27.00 O.II 20 1.24 O.IO 200 25.96 O.Og 25 2.21 o.i3 205 26.39 o.i 3 2 5 0.80 0.08 205 26.35 0.07 3 2.92 o.i5 210 25.68 o.i 5 3 0.47 0.06 2IO 26.65 o.o5 35 3-72 0.17 2I 5 24.88 0.17 35 O.22 0.04 215 26.84 o.o3 40 4.60 0.18 22O 24.00 0.18 40 0.07 O.02 22O 26.93 O.OI 45 5-55 0.19 22 5 23.04 0.19 45 0.03 O.OO 225 26.92 O.O2 5 6-57 0.21 230 22.03 0.21 5 O.IO O.O2 230 26.82 o.o3 55 7.65 0.22 235 20.96 0.22 55 0.27 0.04 235 26.61 o.o5 60 8-77 0.23 240 19.83 0.23 60 -54 0.06 240 26.30 0.07 65 9-94 0.24 245 18.66 0.24 65 0.91 0.08 245 25.90 0.09 70 1 1.14 0.24 250 17.46 0.24 70 1.38 O.IO 250 25.42 O.II 75 12.36 0.25 255 16.24 0.25 75 1.94 O.I 2 255 24.84 o.i3 So 13.60 0.25 260 15.00 0.25 80 2.61 0.14 260 24.19 0.14 85 14.85 0.25 265 13.75 0.25 85 3.36 o. 16 265 23.46 o.i 5 90 16.09 0.25 270 12.51 0.25 90 4.19 0.17 270 22.65 0.17 95 17-3 1 0.24 275 11.29 0.24 95 5.09 0.19 275 21.77 0.18 IOO 18.52 0.24 280 I O.08 0.24 IOO 6.05 O.2O 280 20.83 0.19 105 19.69 0.23 285 8.91 0.23 105 7.09 0.21 285 19.84 0.20 I IO 20.82 O.22 290 7.78 0.22 no 8.18 0.22 290 18.82 O.2I H5 21.90 0.21 295 6.69 O.2I "5 9.31 0.23 295 1775 0.21 1 20 22.93 O.2O 3OO 5.67 0.20 1 20 10.45 0.23 3OO 16.64 O.22 125 23.88 O.lg 35 4.72 0.19 125 1 1.62 0.24 305 '5-52 0.22 130 24.77 0.17 310 3.83 O.I 7 130 12.82 0.24 310 H.38 0.23 135 25-57 o.i5 3^5 3.02 . o.i5 135 14.01 0.24 315 13.22 0.23 140 26.30 o.i3 32O 2.30 o.i 3 140 15.21 O.24 320 12.07 0.23 145 26.92 0.12 325 1.6 7 0.12 H5 16.39 0.23 325' 10.93 0.23 . 150 27.46 O. IO 33 I.I4 0.10 150 17.55 0.22 330 9.81 0.22 155 27.89 0.08 335 0. 7 I 0.08 155 18.67 O.2I 335 8.71 0.21 1 60 28.22 O.06 34 0.38 O.o6 1 60 '9-74 O.20 34 7.66 O.2I 165 28.44 0.04 345 o.i 6 O.04 165 20.74 0.19 345 6.64 0.2O 170 28.56 0.02 35 0.04 OJ02 170 21.70 O.lg 35 5.66 0.19 175 28.56 o.oo 355 0.04 O.OO 75 22.61 0.18 355 4-74 '0.18 1 80 28.46 o.o3 360 0.14 o.o3 1 80 23-47 0.17 360 3.89 O.l6 * %.*The Differences -are calculated for i Degree. [25] TABLE V. CONTINUED. Perturbations of the Mean Anomaly. Argument 10. Argument IT. Arg.< Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. '5-4 1 0.21 1 80 11.51 0.22 3-91 0.14 180 16.83 0.14 5 16.41 O.20 185 10.45 O.2I 5 3-25 o.i3 185 17.49 0.12 10 17.37 O.IQ 190 9.39 0.21 10 2.63 O.I2 190 18.09 O.II '5 18.29 0.18 195 8-35 O.2I 15 2.07 O.II '95 18.63 O.IO 20 19.17 0.17 200 7-33 0.20 20 1.57 0.09 200 19.1 1 0.09 25 19.98 0.16 205 6 -34 O.lg 25 1.14 0.08 205 19.51 0.07 3 20.74 o.i5 2IO 5.40 0.18 3 0.78 0.07 2IO 19.84 O.O6 35 21.42 0.14 215 4-51 0.17 35 0.48 0.06 215 20.1 I o.o5 40 22.04 0.12 220 3.68 0.16 40 0.27 0.04 22O 2O.3I o.o3 45 22.58 0.10 225 2.91 0.14 45 0.13 0.02 225 20.42 O.OI 5 23.07 0.09 230 2.23 o.i3 5 0.08 O.OI 230 20.46 o.oo 55 23-49 0.08 235 1.64 O.II 55 0.09 O.OI 235 20.43 O.OI 60 23.84 O.O6 240 1.14 0.09 60 0.19 o.o3 240 2O.32 o.o3 65 24.11 o.o5 245 0.71 0.07 65 0-37 0.04 245 20.13 o.o5 70 24.31 o.o3 250 0-39 o.o5 70 0.62 0.06 250 19.86 0.06 75 2443 0.02 255 0.19 o.o3 75 0.95 0.07 255 19.51 0.08 80 24.47 o.oo 260 0.09 O.OI 80 1-34 0.09 260 19.10 0.09 85 24.45 0.01 265 0.09 O.OI 85 1.81 O.IO 265 18.63 O.IO 90 24.36 o.o3 270 O.20 o.o3 90 2-35 O.II 270 i8.n O.II 95 24.20 0.04 275 0-43 0.06 95 2.94 o.i3 275 17.52 " o.i a IOO 23.96 0.06 280 0.76 0.08 IOO 3.60 0.14 280 16.88 o.i3 105 23.64 0.07 285 1.20 O.IO 105 4.3i o.i 5 285 16.19 0.14 no 23.24 0.09 290 i-74 O.II IIO 5.06 o.i 5 290 15.46 o.i5 "5 22.77 0.10 295 2.40 o.i3 "5 5.86 0.16 295 14.70 0.16 1 20 22.24 O.I I 300 3.10 o.i5 1 20 6.69 0.17 ' 3OO 13.89 0.17 125 21.63 o.i3 35 3-9i 0.17 125 7-54 0.17 305 1 3>S 0.17 130 20.96 0.14 310 4.80 0.18 130 8.42 0.18 3IO 12.20 0.17 '35 20.22 o.i5 3i5 5-74 0.19 135 9.3i 0.18 315 "33 0.17 140 f 943 0.16 320 6-75 0.20 140 IO.2I 0.18 32O 10.45 0.18 H5 18.58 0.18 325 1-11 0.21 H5 11. 1 I 0.18 325 9-57 0.18 150 17.67 0.19 330 8.83 0.22 150 I2.OO 0.18 33 8.70 0.17 - 155 16.72 0.19 335 9-93 0.22 155 12.87 0.17 335 7.83 0.17 1 60 15-73 0.20 34 11.05 0.22 1 60 '3-73 0.17 34 6.99 0.17 165 14.71 0.21 345 12. 16 0.22 165 14-57 0.16 345 6.18 o. 16 170 13.67 O.2I 35 13-25 0.22 170 15-37 o.i5 35 5-39 o.i 5 75 I 2.6 1 O.22 355 H-35 0.22 75 1 6. 1 2 o. i5 355 4-63 o.i5 1 80 11.51 0.22 360 15.41 0.21 1 80 16.83 o.i 4 360 3-9 1 0.14 %* The Differences are calculated for i Degree. [26] TABLE V. CONTINUED. Perturbations of the Mean Anomaly. Argument 12. Argument 13. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. 2.32 O.IO 1 80 15.18 O.IO 0.30 0.04 1 80 17.50 0.04 5 2.84 O.I I 185 14.65 O.I I 5 o-53 o.o5 185 17.27 o.o5 10 3-4 2 0.12 190 14.08 0.12 10 0.82 0.06 190 16.98 0.07 15 4-3 o.i3 '95 '13-47 o.i3 15 1.18 0.08 '95 16.62 0.08 20 4.68 o.i3 200 12.82 o.i3 20 1.59 0.09 200 16.21 0.09 25 5-36 0.14 205 12.15 0.14 25 2.06 O.IO 205 15.74 O.IO 3 6.07 0.14 2IO "43 0.14 30 2-57 O.I I 2IO 15.23 O.I I 35 6.79 o.i5 2I 5 10.71 o.i5 35 3-H O.I2 2I 5 14.65 0.12 40 7-53 o.i5 22O 9-97 o.i5 40 3-75 o.i3 22O 14.05 o.i 3 45 8.28 o.i 5 225 9.21 o.i5 45 4.40 o.i3 22 5 J 3-39 o.i3 5 9.04 o.i5 230 8.46 o.i 5 50 5.08 0.14 230 12.72 0.14 55 9-79 o.i 5 2 35 7.71 o.i5 55 5-79 o.i5 235 12.00 0.14 60 10.54 o.i5 240 6.96 o.i5 60 6.53 o.i5 240 11.27 o.i5 65 11.26 0.14 245 6.23 0.14 65 7.28 o.i5 245 IO.5I o.i5 70 11.97 0.14 250 5-53 0.14 70 8.06 o.i5 250 9-74 o.i 5 75 12.65 o.i3 2 55 4.85 o.i 3 75 8.83 o.i5 255 8.96 0.1 5 80 i3-3i o.i3 260 4.19 o.i3 80 9.61 o.i5 260 8.19 o.i5 85 13-93 0.12 265 3-56 O.I 2 85 10.37 o.i 5 265 7-43 o.i5 90 14.52 O.Il 270 2.98 O.I I 90 11.13 o.i5 270 6.67 o.i5 95 15.06 O.IO 275 2.44 O.IO 95 11.87 o.i5 275 5-93 o.i5 IOO 15-55 0.09 280 1.95 0.09 IOO 12.59 0.14 280 5-2i 0.14 105 15.98 0.08 285 1.52 0.08 105 13-28 o.i3 285 4.51 0.14 no 16.37 0.07 290 i.3 0.07 no 13-94 o.i3 290 3.86 o.i3 "5 16.70 0.06 295 0.80 0.06 "5 H-55 0. 12 295 3-24 0.12 1 20 16.96 o.o5 30O 0.54 o.o5 120 15. '3 O.I I 300 2.67 O.I I 125 17.16 o.o3 35 0-34 o.o3 125 15.66 O.IO 305 2.14 O.IO 130 17.30 O.O2 310 O.2O 0.02 130 16.14 0.09 310 1.66 0.09 '35 17-37 O.OI 3i5 O.I 2 O.OI 135 16.56 0.08 315 1.23 0.08 140 17-39 O.OI 320 O.I I O.OI 140 16.93 0.07 32O 0.87 0.07 45 17.33 0.02 325 0.17 O.02 H5 17.23 o.o5 325 0.57 o.o5 150 17.21 o.o3 33 0.29 o.o3 150 17.47 0.04 33 0-33 0.04 '55 17.01 0.04 335 0.48 0.04 155 17.64 o.o3 335 0.16 o.o3 1 60 16.76 0.06 34 0.74 0.06 1 60 17-75 O.OI 34 0.05 O.OI 165 16.45 0.07 345 1.05 0.07 165 17.79 o.oo 345 O.OI o.oo 170 1 6.08 0.08 350 1.42 p.o8 170 17.76 O.OI 35 0.04 O.OI 175 15.65 0.09 355 1.84 o 09 175 17.66 o.o3 355 0.14 o.o3 1 80 15.18 O.IO 360 2.32 O.IO 1 80 17.50 0.04 360 0.30 0.04 %* The Differences are calculated for i Degree. [27] TABLE V. CONTINUED. Perturbations of the Mean Anomaly. Argument 14. Argument 15. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. 18.55 0.09 180 i-43 0.09 12.47 0.06 180 0.07 0.00 5 18.96 0.08 185 i. 02 0.08 5 12.13 0.07 185 O.IO O.OI 10 19.30 0.06 190 0.68 0.06 10 11.79 0.07 190 0.21 o.o3 15 19-57 o.o5 *95 0.41 o.o5 '5 "43 0.07 1 95 -39 o.o5 20 19.77 o.o3 200 O.2I o.o3 20 1 1. 08 0.07 200 0.66 0.06 25 19.89 O.OI 205 0.08 O.O2 25 10.72 0.07 205 I.OO 0.07 30 19.94 0.00 2IO 0.04 0.00 3 10.37 0.07 2IO 1.41 0.09 35 19.91 O.OI 215 0.07 O.OI 35 10.01 0.07 215 1.90 O.IO 40 19.80 o.o3 22O 0.18 o.o3 40 9.65 0.07 220 2.45 O.I 2 45 19.62 0.04 225 0.36 0.04 45 9.29 0.07 225 3-7 o.i3 5 19-37 o.o5 230 0.61 o.o5 5 8.93 0.07 230 3-73 0.14 55 19.05 0.07 235 -93 0.07 55 8.59 0.07 235 4-43 o.i5 60 18.66 0.08 - 240 1.32 0.08 60 8.25 0.07 240 5-17 o".i5 65 18.20 0.09 245 1.78 0.09 65 7.91 0.07 245 5-94 0.16 70 17.68 O.II 250 2.30 0.11 70 7-57 0.07 250 6.73 0.16 75 17.09 0.12 255 2.89 0.12 75 7.21 0.07 255 7-5 i o.i5 80 16.46 o.i3 260 3-52 o.i3 80 6.85 0.07 260 8.27 o.i5 85 15.77 0.14 265 4.20 0.14 85 6.49 0.07 265 9-3 o.i 5 90 15.05 o.i 5 270 4-93 o.i5 90 6.12 0.08 270 9-74 o. 14 95 14.28 0.16 275 5.70 0.16 95 5-73 0.08 275 10.43 o.i3 100 '3-49 0.16 280 6.49 0.16 100 5-33 0.08 280 11.07 O.I 2 105 12.66 0.17 285 7-31 0.17 105 4.92 0.08 285 1 1.64 O.II no 11.82 0.17 290 8.16 0.17 no 4.51 0.08 290 12.15 0.09 115 10.95 0.17 295 9.02 0.17 i'5 4.08 0.09 295 12.59 0.08 1 20 10.09 0.17 3OO 9.89 0.17 120 3-65 0.09 300 12.97 0.07 125 9- 2 3 0.17 305 10.75 0.17 125 3.22 0.09 305 13.27 0.06 130 8-37 0.17 310 1 1. 6 1 0.17 130 2.79 0.08 310 i3-5i 0.04 135 7.52 0.17 315 12.46 0.17 135 2-37 0.08 315 13.67 o.o3 140 6.69 0.16 32O 13.29 0.16 140 1.97 0.08 32O 13-77 O.OI H5 5-89 0.16 325 14.09 0.16 H5 1.59 0.07 325 '3-79 0.00 150 5.11 o.i 5 33 14.87 o.i5 150 1.23 0.07 33 13-75 O.OI '55 4-37 0.14 335 15.60 o. 14 155 0.90 0.06 335 13.64 o.o3 1 60 3.68 o.i3 34 16.30 o.i3 1 60 0.62 o.o5 34 13.48 0.04 165 3-04 0. 12 345 16.94 O.I 2 I6 5 o-39 0.04 345 13.29 0.04 170 2-44 O.II 35 7-54 O.II 170 0.23 o.o3 35 13-0$ o.o5 '75 1.90 O.IO 355 18.07 O.IO 75 O.I 2 O.O2 355 12.78 0.06 1 80 i-43 0.09 360 18.55 0.09 ISO O.O7 O.'QO 360 12.47 0.06 *$* The Differences are calculated for i Degree. [28] TABLE V. CONTINUED. Perturbations of the Mean Anomaly. Argument 16. Argument 17. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. 9.69 O. IO 1 80 5-77 o.o3 2.41 0.08 1 80 1.64 o.o4 5 10.14 0.08 185 5.61 o.o4 5 2.OI 0.08 185 1.85 Q.Q4 10 10.54 0.07 190 5.41 o.o5 10 1.6 5 0.07 190 2.07 o.o4 15 10.83 o.o5 195 5-'5 0.06 15 i-34 0.06 '95 2.30 o.o5 20 11.03 o.o3 2OO 4.85 '0.06 20 1.08 o.o,5 2OO 2.55 o.o5 25 1 1.14 O.OI 205 4.50 o.o5 25 0.86 0.04 205 2.81 o.q5 30 1 1 . j 6 O.OI 210 4.11 0.08 3 0.69 o.o3 2IO 3.20 0.06 35 11.09 O.O2 215 3- 6 9 0.09 35 0.55 O.02 215 3-31 0.07 40 10.95 0.04 22O 3-25 0.09 40 0.44 O.Q2 22O 3-75 Q.Q7 45 10.73 o.o5 225 2.79 Q.Q9 45 0.36 o.oi 225 4.10 0.97 5 10.46 0.06 230 2.33 Q.Q9 5 0.31 O.OI 230 4-47 O.o8 55 10.12 0.07 235 1.88 q.09 55 0.26 O.OI 235 4.86 0.08 60 9-75 0.08 240 '45 0.08 60 O.22 O.OI 240 5.26 O.o8 65 9-35 0.08 245 1. 06 0.07 65 O.I9 O.OI 245 5.66 0.08 70 8.94 0.08 250 0.72 0.06 70 o.i 6 O.OI 250 6.05 O.o8 75 8.52 0.08 255 -43 o.o5 75 0.13 o.oo 255 6 -43 0.07 80 8.10 0.08 260 0.21 o.o3 80 O.II o.oo 260 6.79 O.07 85 7.70 0.08 265 0.07 O.Q2 85 0.08 O.OI 265 7.10 O.q6 90 7-33 0.07 270 O.OI O.QO 90 0.05 0.0^0 270 7.38 o.o5 95 6.99 0.06 275 0.04 O.OI 95 0.03 0.00 275 7.59 o.o4 IOO 6.69 o.o5 280 0.1-6 9-o3 IOO O.OI o.oo 280 7-75 O.Q2 105 6.44 0.04 285 0.38 o.o5 105 o.oo O.QO 285 7.83 O.OI no 6.23 o.o3 290 0.69 0.07 no o.oo O.QO 290 7.85 O.OI H5 6.07 O.O2 295 1.09 0.09 "5 O.OI o.oo 295 7.78 O.O2 120 5.96 O.O2 300 i-57 Q.IQ 1 20 0.05 O.OI 300 7.64 o.o3 125 5.88 O.OI 305 2.13 0.12 125 O.IO O.QI 35 7.41 o.o5 I 3 5.85 o.oo 310 2.75 O.l3 130 0.17 O.OI 310 7.12 0.07 135 5.84 o.oo 315 3-43 Q.I4 135 0.25 0.02 315 6.76 0.08 140 5.86 o.oo 320 4.15 o.i5 140 0.36 0.02 320 6.34 0.09 H5 5.89 O.OI 325 4.89 Q.l5 H5 0.47 O.O2 325 5.87 0.09 I 5 5-93 O.OI 33 5.66 o.i5 150 0.61 o.o3 33 5.39 O.IO '55 5-97 O.OI 335 6.42 Q.l5 155 0.75 o.o3 335 4.87 O.IO 1 60 5-99 o.oo 340 7.16 0.14 1 60 0.92 o.o3 34 4-35 O.IO 165 5-99 o.oo 345 7.87 0.14 165 1.09 p.o3 345 3.83 Q.10 170 5.96 O.OI 35 8.54 o.i3 170 1.26 Q.04 350 3.33 O.IO 75 5.88 O.02 355 9.14 0.12 175 1.45 0.04 355 2.85 0.09 1 80 5-77 o.o3 360 9.69 O.II 1 80 1.64 0.04 360 2.41 0.08 * s> * The Differences are calculated for I Degree. [29] TABLE V. CONTINUED. Perturbations of the Mean Anomaly. Argument 18 to 25, inclusive. s Arg. 18. D. 19. D. 20. D. 21. D. 22. 23.- 24. 25. IO 20 30 40 4-59 3-96 3-32 2.67 2.07 o.63 0.64 o.65 0.60 4.82 4-79 4.70 4-54 o.o3 0.09 o.i 6 0.23 i-75 1.48 1.20 o-93 0.69 0.27 0.28 0.27 0.24 2.21 2.24 2.22 2.18 2.10 o.o3 O.O2 0.04 0.08 2.47 2.46 2.42 2-35 2.24 44 .42 38 3 2 23 2.08 1.96 1.82 1.66 1.48 O.I 2 0.05 O.OI 0.00 O.OI 5 60 70 80 90 1.52 1.03 0.62 o.33 0.13 0.49 0.41 0.29 O.20 4.02 3-69 2.91 2.50 o.33 o.38 0.40 0.41 0.48 0.30 0.17 0.08 0.03 0.18 o.i3 0.09 o.o5 1.99 1.86 1.70 ^53 ^34 o.i3 0.16 0.17 0.19 2.09 1.92 1.74 1.32 .14 0.92 0.79 0.66 1.30 i. ii 0.91- o-73 0.55 0.05 O.II O.2I 0.32 0.45 0.08 0.42 O.OI 0.19 IOO no 1 20 130 140 150 1 60 170 1 80 0.05 O.IO 0.25 0.50 0.85 1.27 1.78 2.30 2.89 o.o5 o.i 5 0.25 0.35 0.42 o.5i 0.52 o.Sg 2.08 1.67 1.28 0-93 0.62 o-37 o.i 8 0.06 o.oo. 0.41 0.39 o.35 o.3i 0.25 0.19 O.I 2 0.06 0.04 0.09 O.20 o-34 0-53 0.75 1. 00 1.28 i-55 o.o5 O.II 0.14 0.19 O.22 0.25 0.28 0.27 1.15 0.96 0.77 0.59 43 0.29 0.17 0.08 0.03 0.19 0.19 0.18 0.16 0.14 0. 12 0.09 o.o5 i. ii 0.90 0.70 0.51 0.36 0.23 O.I 2 O.O6 0.03 -53 0.42 0.31 O.22 0.13 0.06- O.02 O.OO O.OO -39 0.25 0.15 0.06 O.O2 O.OO O.O2 0.08 0.16 O.6o 0.7*5 0.91 .07 23 38 51 63 72 o.Sg o.o3 0.27 o.o3 190 200 210 22O 348 4.06 5-'7 o.58 0.57 o.54 0.03 O.I2 0.28 0.51 0.09 o.i 6 O.23 1.82 2.10 2-37 2.6 1 0.28 0.27 0.24 o.oo O.02 O.06 O.I4 0.02 0.04 0.08 O.O4 0.08 0.15 O.26 O.O2 0.06 0.12 O.2I 0.28 0.42 0.58 0.76 79 83 84 83 230 240 250 260 270 5.68 6.1 1 6.48 6.79 6.99 o.43 0.37 o.3i O.20 0.80 1.13 1.51 1.91 2.32 o.33 o.38 0.40 0.41 2.82 3.00 3.13 3.22 3-27 0.18 o.i 3 0.09 o.o5 0.25 0.38 0.54 0.71 0.90 o.i3 0.16 0.17 0.19 0.41 0.58 0.76 0.97 1.18 0.30 0.41 0.52 0.65 0.78 0.94 13 33 5i .69 79 73 63 52 39 0.12 0.42 O.OI 0.19 280 290 30O 310 320 33 34 350 360 7.11 7.12 7.05 6.86 6-55 6.19 5.72 5.18 4-59 O.OI 0.07 0.19 o.3i 0.36 0.47 o.54 0.59 2.74 3-15 3-54 3-89 4.20 445 4.64 4-75 4.82 0.41 o.3g 0.35 o.3i 0.25 0.19 O.II 0.07 3.26 3.21 3.10 2.96 2.77 2-55 2.30 2.O2 '75 o.o5 O.II o.i 4 0.19 0.22 0.25 0.28 O.27 I.O9 1.28 '47 1.65 1.81 1.95 2.07 2.16 2.21 0.19 0.19 0.18 o.i 6 0.14 0.12 0.09 o.o5 i. 60 i. 80 1.99 2.14 2.27 2.38 2.44 2-47 0.91 .02 .22 3' 38 42 1.44 1.44 .85 99 2.09 2.18 2.22 2.24 2.22 2.l6 2.08 .24 .09 o-93 0.77 0.61 0.46 o-33 O.2I O.I 2 [30] TABLE V. CONCLUDED. Perturbations of the Mean Anomaly. Arguments 26 to 37, inclusive. Arg. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 0.99 o-34 0.45 0.32 1.83 0.91 0.70 0.84 0-53 o.oo 0.28 0.46 10 .04 0.50 0.36 0.29 2.12 0.90 0.68 0.84 0.48 0.00 0.31 0.47 20 .05 0.70 . 0.28 0.25 2.41 0.87 0.65 0.8 1 o-43 O.OI o.34 0.48 3 .06 0.90 O.20 O.2I 2.66 0.82 0.62 0.77 0.38 O.O2 0.36 0.48 40 .06 1. 12 O.I3 0.17 2.88 0.77 0.59 o-73 0.32 0.04 o-37 0.48 5 .04 i-34 0.08 O.I^J 3.08 0.71 0-53 0.68 0.26 0.07 0-39 0.47 60 .00 1-57 0.04 O.IO 3.23 0.64 0.47 0.62 O.2I O.IO 0.40 0.45 70 0.95 1.78 O.OI 0.08 3-32 0.57 0.41 0.54 0.16 0.14 0.40 0.42 80 0.88 1.98 o.oo 0.05 3.38 0.49 0-35 0.47 0.12 0.19 o-39 0.39 90 0.8 1 2.15 O.OI 0.03 3.38 0.40 0.29 0.40 0.08 0.23 0.38 0.35 IOO 0.72 2.30 0.02 O.OI 3-34 o-33 0.23 0-33 0.04 0.27 0.36 0.31 no 0.63 2.42 O.O7 o.oo 3- 2 4 0.25 o.i 8 0.26 O.O2 0.32 -34 0.27 IZO 0.54 2.51 O.I 2 o.oo 3 -.o 9 o.i 8 0.13 0.20 O.OI 0.36 0.32 0.23 130 0.44 2.56 o.i 8 o.oo 2.90 0.13 0.09 0.14 o.oo 0.41 0.29 0.19 140 0.36 2.56 0.25 O.OI 2.68 0.07 0.05 O.O9 o.oo 0.44 0.25 0.15 150 0.28 2.54 o-33 0.03 2.42 0.04 O.02 0.05 O.O2 0.48 O.22 O.I I 1 60 0.19 2.46 0.42 0.05 2.15 O.OI O.OI O.OI O.05 0.50 O.I9 0.08 170 0.12 2.36 0.52 0.09 1.86 o.oo 0.00 o.oo 0.08 0.52 0.15 0.05 1 80 O.07 2.22 0.61 O.I 2 1-57 O.OI o.oo o.oo O.I I 0.52 0.12 O.02 190 0.02 2.06 0.70 0.15 1.28 0.02 O.O2 o.oo 0.16 0.52 0.09 O.OI 200 0.0 1 1.86 0.78 0.19 0.99 0.05 O.O5 0.03 O.2I 0.51 O.o6 o.oo 2IO o.oo 1.66 0.86 0.23 0.74 O.IO 0.08 0.07 0.26 0.50 0.04 o.oo 220 o.oo 1.44 -93 0.27 0.52 0.15 O.I I O.I I 0.32 0.48 0.03 o.oo 230 O.O2 1.22 0.98 0.30 0.32 0.21 0.17 o.i 6 0.38 0.45 O.OI O.OI 240 O.O6 0.99 1.02 o-34 0.17 0.28 0.23 O.22 -43 0.42 o.oo 0.03 250 O.I I 0.78 1.05 0.36 0.08 -35 0.28 0.30 0.48 0.38 o.oo 0.06 260 o.i 8 0.58 1. 06 0.39 O.O2 o-43 o-35 0.37 0.52 -33 O.OI 0.09 270 0.25 0.41 1.05. 0.41 O.O2 0.52 0.41 0.44 0.56 0.29 0.02 0.13 280 -34 O.26 1.03 -43 O.o6 0.59 047 0.51 0.60 0.25 0.04 0.17 290 -43 0.14 0.99 0.44 0.16 0.67 0.52 0.58 0.62 0.2O 0.06 O.2I 300 0.52 O.O5 0.94 0.44 0.31 0.74 0.57 0.64 0.63 0.16 0.08 0.25 310 0.62 O.OO 0.88 0.44 0.50 0.79 0.61 0.70 0.64 O.I I O.I I 0.29 32O 0.70 o.oo 0.8 1 -43 0.72 0.85 0.65 0.75 0.64 0.08 0.15 -33 330 0.78 O.O2 0.72 0.41 0.98 0.88 0.68 0.79 0.62 0.04 0.18 o-37 34 0.87 O.IO 0.64 -39 1.25 0.91 0.69 0.83 0.59 0.03 0.21 0.40 35 0.94 0.2O 0.54 -35 1.54 0.92 0.70 0.84 0.56 0.00 0.25 -43 360 0.99 0.34 0.45 0.32 1.83 0.91 0.70 0.84 -53 o.oo 0.28 0.46 [31] TABLE VI. For the Terms in SM to be Multiplied in t. Argument 10. I 2 3 -14.521 '4-455 '4-383 '4-37 .066 .072 .076 .081 45 46 47 48 -7.171 6-934 6.695 6.455 .23 7 .239 .240 .241 90 9' 92 93 + 3-9' 4.129 4-355 4-579 .228 .226 .224 .222 '35 136 '37 '38 + 11.729 11.835 11.936 12.035 .106 .101 .099 .oo5 4 14.226 .087 49 6.214 244 94 4.801 .221 '39 12.130 . \j\j*j .092 5 '4-'39 50 5.970 95 5.022 140 12.222 .092 .244 .219 .088 6 -14.047 .097 5' -5.726 .246 96 + 5.241 .2l6 141 + I2.3IO .o85 7 '3-95 .102 S 2 5-48o .247 97 5-457 .2l5 142 '2-395 .082 8 13.848 .107 53 5-233 .248 98 5-672 .212 '43 12.477 .078 9 10 '3.741 13.630 .III 54 55 4.985 4-736 .249 99 IOO 5.884 6.093 .209 '44 '45 '2-555 12.630 / .075 .117 .25o .208 .072 n '3-5'3 .122 56 4.486 25o IOI + 6.301 . 2o5 146 + 12.702 12 '3-39' .126 57 4.236 IO2 6.506 . 2O2 '47 12.769 ' J[ '3 13.265 58 3-986 .252 I0 3 6.708 .201 148 12.834 .061 '4 '3-'34 .i36 59 3.734 252 104 6.909 '49 12.895 '5 12.998 60 3482 I0 5 7.107 .19 150 12.952 .007 .141 .252 .I 9 5 .o54 16 '7 -12.857 12.712 .145 .i5o 61 62 3.230 2.977 .253 .253 1 06 107 + 7-302 7-495 .193 152 + 13.006 13.056 .o5o f\/.t\ 18 12.562 .i54 63 2.724 ,( 108 7.686 ,QQ '53 13.101 .U4-J '9 12.408 .i58 64 2.471 . 2 J \J .253 109 7-874 . X OO .i85 '54 '3-'45 .O4O 20 12.250 65 2.218 IIO 8.059 '55 13.185 .i63 .252 .i83 .o36 21 12.087 .167 66 f 1.966 .253 in + 8.242 .179 156 + 13.221 ,o32 22 23 2 4 11.920 11.750 11.576 .170 .174 .178 67 68 69 1.460 1.207 .253 .253 .253 I 12 "3 8.421 8.597 8.771 .176 .174 .171 '57 158 '59 13-253 13.281 '3-37 .028 .026 .022 25 11.398 70 0.954 "5 8.942 1 60 '3-329 .182 .252 .168 .019 26 n. 216 .186 7' 0.702 .250 116 + 9.110 .i65 161 + 13.348 .014 27 28 29 3 11.030 i '.84 1 10.648 10.452 .189 .193 .196 72 73 74 75 0.452 O.2OI + 0.049 0.298 .251 .25o .249 "7 118 "9 120 9.275 9.438 9.598 9-755 .i63 .160 '.i5 7 162 163 164 165 13.362 '3.372 '3-38o '3-384 .010 .008 .004 .199 .248 .154 .000 3' 10.253 .203 76 + 0.546 247 121 + 9.909 .i5o 1 66 + 13-384 ,oo3 32 33 34 10.050 9.844 9.636 .206 .208 .212 77 78 79 0-793 1.040 1.285 *-** / .247 .245 .245 122 I2 3 124 10.059 10.206 10.35' .147 .145 .141 167 168 169 '3-374 '3-364 .007 .010 .014 35 9-424 80 I.53O '25 10.492 170 '3-35 .2l5 .242 .i38 .017 36 37 - 9.209 8.992 .217 22O 81 82 + 1.772 2.OI4 .242 126 127 + 10.630 10.765 .i35 i3a 171 172 + '3-333 '3.3" .022 38 39 8.772 8.550 .222 .224 83 84 2.255 2-495 .240 .239 128 129 10.897 11.026 lw2 .129 .126 '73 '74 13.286 13.258 .028 .o3i 40 8.326 85 2-734 V Y 130 11.152 '75 13.227 .226 .236 .122 .035 42 43 44 8.100 7.871 7.640 7.406 .229 .231 .234 .235 86 87 88 89 + 2.970 3.206 3-439 3.670 .236 .233 .231 .23l 132 '33 '34 + 11.274 11.508 11.620 .119 .115 .112 .100 176 '77 178 '79 + 13.192 '3-'54 13.112 13.067 .o38 .042 .o45 .048 45 7.171 90 3.901 '35 11.729 ^7 1 80 13.019 [32] TABLE VI. CONCLUDED. For the Terms in &M to be Multiplied in t. Argument 10. Concluded. I 180 + 13.019 o52 225 + 7.536 .186 270 - 2.442 O/I 315 12.050 181 12.967 .o56 226 7.350 .188 271 2.683 .^41 .240 3 l6 12.207 .i54 182 183 12.91 I 12.852 .o5c) .062 227 228 7.162 6.972 .190 ,io3 272 273 2.923 3- l6 3 .240 .24o 317 318 12.361 12.51 1 .i5o .146 184 12.790 .066 229 6.779 .iq5 274 3-403 .241 319 12.657 .141 185 12.724 230 6.584 . . -y^ 275 3-644 320 12.798 .069 197 .240 .i38 1 86 187 + 12.655 12.583 .072 .076 231 232 + 6.387 6.188 .199 .202 2 7 6 277 3-884 4.122 .238 .238 321 322 12.936 13.070 ' * .i34 . i3o 188 12.507 .080 233 5.986 .203 278 4.360 .237 323 13.200 .125 189 12.427 .082 234 5.783 .2o5 279 4-597 .237 324 13-325 .120 190 12.345 235 5-578 280 4.834 * t-J 1 325 J 3445 .086 .207 .23 7 .116 191 + 12.259 OQO 236 + 5.371 281 5.071 ~1K 326 -13.561 192 12.169 .OO2 237 5.162 .211 282 5.306 . .4 3^ 163 4168 9 29 2900 47 74 2056 i5 119 3444 O 3 32 164 4158 I O I 2 30 2853 47 75 2072 16 1 20 3477 165 4146 31 2807 46 .f 76 2089 17 121 35io 33 32 1 66 4 J 3 2 14 ,4E 32 2761 46 77 2108 '9 122 3542 32 167 4117 1 J 33 2717 44 78 2127 19 I2 3 3574 3i 168 4100 n 34 2673 44 . T 79 2148 21 124 3605 3i 169 4081 '9 35 2630 4J 80 2170 22 125 3636 170 4061 2Q 36 2588 42 81 2193 23 126 3666 3o Ir. 171 0941 22 o / 37 2547 4i 82 2217 24 127 3696 oO 172 4015 ^4 nA 38 2507 4o 83 2242 25 128 3725 2 9 oft 173 3989 xu 39 2469 38 84 2268 26 I2 9 3753 2o fl 174 3962 27 9r 40 2431 38 85 2295 2 7 I 3 378i 2o '75 3933 29 4 1 2395 36 86 2323 28 I3 1 3808 27 1 76 393 3o 32 42 2360 35 87 235* 28 132 3835 2 7 177 3871 )/ 43 2326 34 88 2380 2 9 J33 3861 26 c 178 3837 04 9A 44 2294 32 89 2410 3o 134 3886 25 179 3801 ou 3- 45 2263 3i 90 2441 3i 135 39 11 25 1 80 37 6 4 J 7 [34] TABLE VII. CONTINUED. Perturbations of the Logarithm of the Radius Vector. Argument 1 . Concluded. Arg. Eq. D. Arg. Eq. D. Arg. t. * Eq. D. Arg. Eq. D. 1 80 3764 225 990 61 270 356 44 315 345 * 63 181 3725 X I 226 929 60 271 400 46 316 35*4 62 182 3684 41 227 869 272 446 i\\j 48 3^7 3576 183 3641 44 228 810 57 273 494 5o 3 l8 3636 58 184 3597 46 229 753 56 274 544 53 319 3 6 94 57 185 355i 230 697 275 597 320 375 1 47 54 55 54 1 86 3504 An 231 ,643 52 276 652 56 321 3805 53 187 3455 49 5i 232 59 1 5o 277 708 5o 322 3858 5o 188 344 52 233 54 1 49 278 767 jy 6 323 3908 JW 40 189 335.2 53 234 492 46 279 827 62 324 3957 **/ /A 190 3299 235 446 l\\J 280 889 325 4003 4U 55 45 64 44 191 3244 236 401 281 953 65 326 4047 192 3188 K.Q 237 359 / 1 282 1018 At 327 4090 * 193 3130 Do c 238 3^8 41 38 283 1085 07 AQ 328 4130 4o 194 3071 5 9 60 239 280 36 284 "53 uo 7 329 4167 36 95 3011 240 244 285 1223 33 4203 61 34 71 33 196 2950 241 210 286 1294 331 4236 197 2887 63 242 179 3i 287 1366 72 332 4267 3i 198 2824 63 65 243 150 29 26 288 H39 73 333 4295 28 26 199 2759 244 I2 4 289 1512 / 334 43 2I 200 2694 65 245 IOO 24 290 1587 75 335 4345 24 201 26*8 66 246 78 22 291 1663 76 A 336 4366 21 2O2 2561 67 247 59 J 9 rA 292 1739 76 337 4385 19 203 2494 67 248 43 IO 293 1816 77 338 4402 17 204 2426 68 f 249 29 14 294 1893 77 _Q 339 4416 14 205 2357 69 250 18 I I 295 1971 7 34 4428 12 2O6 2288 69 251 10 8 296 2049 78 _o H , 4437 9 207 2218 79 252 4 O 297 2127 78 342 4444 1 208 2148 70 253 i O 298 2205 _Q 343 4448 4 209 2078 70 254 i 299 2283 78 344 4450 2 210 2007 7 1 255 3 2 300 2361 7 345 4450 21 I 1936 7i 256 8 5 Q 301 2439 78 34 6 4448 2 212 1866 70 257 16 O 302 2516 77 347 4443 2I 3 1796 70 258 26 10 33 2593 77 348 443 6 7 2I 4 1725 7 1 259 39 1 304 2670 77 .A 349 4427 9 2I 5 1655 70 260 55 1 35 2746 7 350 4416 1 1 70 19 75 14 216 1585 6n 261 74 306 2821 351 440.2 217 1516 09 68 262 95 2 1 307 2896 7 352 4387 i5 218 1448 68 263 119 26 308 2969 7 3 353 4370 J 7 219 1380 68 264 1 45 39 3042 T 1 354 435 20 220 1312 265 29 310 7 1 355 4328 22 66 32 70 23 221 1246 66 266 206 3 11 3183 356 435 26 222 1 1 80 267 240 1A 312 3252 AQ 357 4279 22 3 1116 Ax 268 276 Ou 313 3320 uo 66 358 4252 2 7 22 4 1052 U 4 62 269 315 A\ 3H 3386 65 359 4224 3, 22 5 99 270 356 4* 3i5 345' 360 4193 [35] TABLE VII. CONTINUED. Perturbations of the Logarithm of the Radius Vector. Argument 2. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. 3644 23 45 1940 /Q 9 178 2O 135 3" i 3621 24 46 1892 40 48 91 158 18 136 33 20 ^ 3597 47 1844 Xn 92 140 18 '37 35 i n 3 3573 26 48 '795 49 48 93 122 16 138 369 V 2O 4 3547 26 49 1747 48 94 1 06 i5 139 389 20 5 3521 50 1699 95 9 1 140 409 27 48 14 20 6 3494 9-7 5' 1651 96 77 i3 141 429 7 34 6 7 J / 52 1603 48 97 64 142 449 2O 2O 8 3438 29 53 1555 48 98 53 ii H3 469 20 9 349 3o 54 1507 47 99 42 144 489 2O" 10 3379 55 1460 IOO 33 H5 509 3i 47 8 20 1 1 3348 56 1413 XT 101 25 146 529 12 3, 57 1366 4-7 102 18 7 H7 549 2O 13 3284 O ^ 33 58 3'9 46 103 12 4 148 568 2O H 3Z5 1 V 59 1273 104 8 149 588 15 3217 60 1227 4 105 4 150 607 '9 34 46 2 10 16 3183 61 1181 1 06 2 I r i 626 7 i? 3H8 3D 62 1 136 XX I0 7 O 2 1 5 2 645 19 18 3112 63 1092 44 XX 108 O 153 664 19 '9 375 3 7 64 1048 44 44 109 I 2 154 683 J 9 18 20 3038 7 65 1004 IIO 3 155 701 38 43 3 _ 18 21 3000 In 66 961 xl in 6 I 5 6 719 ifi 22 2961 J 9 67 918 40 I 12 10 4 157 737 1 O 23 2922 Xn 68 877 XI 11 3 15 K I 5 8 754 17 24 2882 40 / n 69 836 m /. i 114 20 3 159 771 ' 2842 4O 70 795 4^ 27 7 1 60 787 1 41 4o 8 16 26 2801 / w 71 755 116 35 161 803 16 27 2760 41 72 717 9Q 117 43 162 819 i5 28 2718 43 73 679 OO 38 118 53 10 163 834 i5 2 9 2675 x3 74 641 119 63 10 164 849 T X 3 2632 40 75 605 1 20 74 1 1 165 863 14 44 35 12 14 3 1 2588 44 76 570 35 121 86 12 1 66 /- 877 i3 32 2544 44 77 535 34 122 9.8 l3 167 890 i3 33 2500 A5 78 501 7o I2 3 in 168 93 I 2 34 2455 (t*j 45 79 469 O 32 124 125 i5 169 915 12 35 2410 80 437 I2 5 140. 170 927 46 3i i5 11 36 2364 81 406 126 155 .K 171 938 1 1 37 2318 /{. 82 37 6 I2 7 170 J J 172 949 38 2272 40 47 83 347 29 2T 128 1 8.6 17 173 960 10 39 2225 ' /.n 84 320 ' / 129 203 174 970 I O 40 2178 47 85 293 27 130 220 '7 1 7S 980 4 1 2131 47 /Q 86 268 25 I3 1 237 17 iR 176 989 9 42 2083 4o 87 243 n o I 3 2 255 1 o ,Q 177 998 9 43 2036 47 88 220 2o 133 273 1 O 178 1006 44 1988 4 89 199 21 134 292 J 9 i n 179 1014 i 45 1940 90 178 2 1 '35 311 '9 1 80 1021 i [36] TABLE VII. CONTINUED. Perturbations of the Logarithm of the Radius Vector. Argument 2. Concluded^ Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. 1 80 1021 225 1184 270 2275 _ 315 3744 18 181 1028 1 6 226 1103 9 271 2312 38 316 3762 18 182 1034 A 227 I 2O2 9 272 2350 38 3*7 3780 16 183 1040 U K. 228 1213 1 1 273 2388 38 318 379 6 184 1045 J 5 . 229 1224 11 274 2426 38 319 3811 i5 185 1050 230 IZ 35 275 2464 320 3826 5 12 38 14 186 1055 231 1247 276 2502 3o 321 3840 i3 187 1059 232 1260 1 277 2541 V 38 322 3853 188 1063 / 233 1274 14 278 2579 323 3865 1 2 189 1067 4 3 234 1288 i4 i5 279 2618 38 324 3876 1 1 190 1070 235 '33 280 2656 325 3886 1 3 16 38 9 191 1073 3 236 1319 - A 281 2694 38 326 3895 192 1076 2 237 1335 10 282 2732 38 327 393 193 1078 } 238 1352 D 283 2770 38 328 3910 7 194 1081 o 239 1370 IO 284 2808 38 329 3916 6 1083 240 1389 19 285 2846 330 3921 5 2 20 38 4 196 1085 2 241 1409 286 2884 331 3925 197 1087 242 1429 20 287 2921 7 332 3928 3 198 1089 2 243 1450 21 288 2958 7 333 393 2 199 1091 I 244 1472 22 23 289 2995 36 334 3932 2 200 1092 245 1495 290 3031 335 3932 o 2 23 36 2OI 1094 I 246 1518 24 291 3067 36 336 393 1 I 2O2 1095 247 1542 292 3^3 337 3930 i 203 1097 248 1567 25 293 3138 i/ 338 3928 2 204 1098 249 1593 nA 294 3172 04 o/ 339 3924 4 2O5 I 1 00 2 250 1619 20 295 3206 04 34 3920 4 206 IIOI i 251 1646 27 n o 296 3239 33 QT 341 ' 39'5 5 207 1103 2 252 1674 2o 297 3272 vd 342 399 6 208 1105 2 253 1703 29 298 334 32 343 3902 7 2O9 1107 2 254 1732 29 299 3336 3i 344 3894 210 1 109 2 255 1762 300 3367 345 3885 9 2 3o 3o 10 211 II II J 256 1792 fo 301 3397 3o 34 6 3875 i j 212 1114 j 257 1824 O 302 3427 347 3864 I T 2I 3 1117 o 258 1855 1 33 345 6 28 348 3852 I . I 2 2I 4 I 120 ij 259 1887 2 34 3484 28 349 3840 215 I 124 4 260 1920 35 35 12 35 3826 14 4 33 27 14 216 1128 261 '953 306 3539 35 1 3812 217 II 3 2 4 262 1987 34 35 37 3566 27 25 352 3796 1 218 I 137 263 2O22 TS 308 359 1 353 378o 1 219 1142 . 264 2057 O J 39 3615 24 2 354 3764 8 22O 1148 265 2092 3 310 3639 355 3746 lu 6 36 23 ID 221 1154 266 2128 311 3662 22 356 3727 * V 222 1 161 7 267 2164 312 3684 2 I 357 3708 19 22 3 1168 7 8 268 22OI 3 7 313 3705 2O 358 3688 2O 224 1 176 8 269 2238 7 3H 3725 359 3666 22 225 1184 270 2275 3^5 3744 . 360 3644 22 [37] TABLE VII. CONTINUED. Perturbations of the Logarithm of the Radius Vector. Argument 3. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. 1484 47 45 8l I 2 9 481 135 2433 53 I H37 * / 46 46 69 II 9 1 5 IO 3i I 3 6 2486 54 2 '39* 45 47 58 92 frH 3i 137 2540 53 3 1346 45 48 48 93 572 3i 138 2593 54 4 1301 44 49 39 9 o 94 603 33 2647 JiJ. 54 5 1257 5 30 7 95 636 140 2701 44 "J 34 54 6 1213 43 5 1 23 6 96 670 34 141 2755 54 7 1170 43 S 2 17 5 97 704 35 142 2809 8 1127 ^M 42 53 12 5 98 739 36 143 2863 54 9 1085 4i 54 7 3 99 775 36 144 2917 54 10 1044 55 4 IOO 8n 145 2971 4t 21 37 54 n 1003 56 2 2 101 848 38 146 3025 54 12 964 40 57 O 102 886 3o H7 379 /. 194 5366 OO o.-i . 239 6242 284 53" 3r> 329 394 J4 K, 195 5403 J 7 240 6241 I 285 5272 *9 33 3040 J4 87 2 4o 54 196 5440 or 241 6239 286 5232 33 1 2986 re 197 5475 65 242 6236 . 287 5192 40 332 2931 D3 K.K. 198 55" 36 K 243 6232 4 288 5'5' 4i 333 2876 55 e / 199 5546 o5 0. O. 244 6228 4 289 5109 42 /O 334 2822 54 ec 200 5579 OO 245 6222 290 5067 42 335 2767 DO 2OI 5612 33 o rt 246 6215 7 291 5024 43 /O, 336 2713 54 r / 2O2 5644 O2 "Jo 247 6208 7 292 4981 4-J / / 337 2659 04 c / 203 5676 O 2 3 n 248 6 1 99 9 293 4937 44 /* 338 2605 a4 c / 204 5706 ou 7n 2 49 6189 10 294 4892 4J /K. 339 2551 04 r / 205 5736 OO 250 6179 IO 295 4847 4J 340 2497 54 29 11 46 53 2O6 5765 On 251 6168 ,0 296 4801 X6 34i 2444 CO 207 5794 29 252 6155 IO ,0 297 4755 4U /A 342 2391 Do c . 208 5821 27 253 6142 IO 298 4709 40 XT 343 2337 54 CO 209 5848 27 26 254 6128 14 i^ 299 4662 47 /8 344 2284 JO fio 210 5874 255 6113 ID 300 4614 40 345 2232 J2 25 16 48 52 21 I 5899 OX 256 6097 ,A 301 4566 Xr 346 2180 52 212 59 2 3 ~4 o / 257 6081 1 U T Q 302 45'7 49 347 2128 <1 213 5947 ^4 2 2 258 6063 10 33 4468 49 /r\ 348 2076 02 ^T 214 5969 259 6044 !9 34 4419 49 *ir> 349 2024 33 . 215 599 1 22 260 6025 *9 35 4369 JO 35 '973 01 21 21 5o 5i 216 6012 261 6004 306 4319 'in 35i 1922 *;r> 2I 7 6032 20 262 5983 21 37 4269 JU /;, 352 1872 JO f\n 218 6051 : 9 ,Q 263 5961 22 nl 308 4218 >ji R, 353 1822 oo Ar^ 219 6069 1 O 264 5938 2J 39 4167 VI C 9 354 1772 DO 220 6086 J 7 265 5914 24 310 4115 J 6 355 1723 4t> 16 25 52 4o 221 6102 T A 266 5889 n^ 3 11 4063 9 356 1674 ^y yO 222 6118 1 U tS 267 5864 2 J 312 4011 v 53 357 1626 4 /Q 22 3 6i33 1 J it, 268 5837 27 3*3 3958 *;) 358 1578 40 224 6146 rvj ,-3 269 5810 27 01 34l 395 JO S-3 359 J 53i 47 225 6159 1 1 270 5783 2 7 3i5 3852 >JO 360 1484 47 [39] TABLE VII. CONTINUED. Perturbations of the Logarithm of the Radius Vector. Argument 4. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. 340 I O 45 5 OI 6 90 77 135 "5 Q i 35 IO 46 495 6 9 1 70 7 136 123 O Q 2 360 47 489 92 63 7 137 131 O Q 3 369 10 48 482 7 93 56 7 1 138 1 39 O 8 4 379 49 475 94 49 i 139 H7 5 388 9 5 468 95 43 140 155 o 9 8 6 8 6 397 5 1 460 Q 96 37 141 163 7 406 9 52 452 O 8 97 3 2 A 142 172 9 8 45 9 53 444 Q 98 27 J j H3 1 80 9 424 9 54 43 6 O 99 22 J 144 189 9 10 433 9 55 427 9 IOO 18 197 . 8 9 4 8 1 1 441 8 56 418 101 14 3 146 205 8 12 449 57 409 102 1 1 H7 213 13 457 58 399 IO 103 8 148 221 8 H 465 59 389 10 104 6 2 148 229 15 472 7 60 379 I O 105 4 2 150 2 37 16 479 7 61 369 IO 1 06 2 2 '5 1 245 8 17 485 6 62 359 IO I0 7 I I 152 252 1 18 491 6 63 348 1 1 108 O I 260 8 '9 497 6 64 338 10 109 154 267 7 20 503 6 65 327 1 1 I 10 o O '55 274 7 21 508 5 66 316 II in o 156 28l 7 22 5*3 5 67 305 1 1 112 I I 157 288 7 23 4 68 294 1 1 113 2 I 158 294 6 24 521 4 69 283 I I 114 4 2 300 6 25 525 4 70 272 I I "5 6 2 1 60 306 6 26 528 3 71 261 II 116 8 2 161 312 6 27 3 72 250 1 1 117 1 1 Q 162 317 5 28 534 73 240 IO 118 4 3 163 322 5 29 535 I 74 229 I I 119 18 4 164 327 5 30 536 i 75 218 I I 1 20 22 4 165 33 1 4 3' 537 I 76 207 II 121 26 4 A. 1 66 335 4 32 537 o 77 197 122 31 J 167 339 4 33 537 o 78 1 86 1 I 123 36 e 168 342 34 537 o 79 176 124 4 1 D 169 345 35 536 I 80 1 66 10 I2 5 46 170 348 2 10 6 3 36 534 81 156 126 52 171 35' 37 532 2 82 146 1 I2 7 58 172 353 2 38 53 2 83 136 IO 128 64 173 355 2 39 527 j 84 127 9 I2 9 70 '74 357 2 40 524 85 118 9 130 77 7 i75 358 I 4, 520 4 86 109 9 131 84 7 D 176 359 I 42 516 87 101 Q 132 92 O 177 359 O 43 51 1 88 93 O 133 99 7 Q 178 359 C 44 506 5 89 85 8 X 34 107 O 8 179 359 O 45 501 90 77 '35 "5 1 80 358 [40] TABLE VII. CONTINUED. Perturbations of the Logarithm of the Radius Vector. Argument 4. Concluded-. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. 1 80 358 225 209 270 245 Q 315 114 2 181 357 i 226 207 2 271 245 | 316 112 2 182 356 i 227 206 I 272 244 o 317 I IO I 183 355 i 228 205 I 273 244 I 3i8 IO9 I 184 354 i 229 204 I 274 243 J 3 J 9 108 j 185 352 2 230 203 I 275 242 320 107 2 I I O 1 86 35 Q 231 2O2 o 276 241 2 321 107 O 187 347 ij 232 202 277 239 322 107 188 344 3 233 2O2 278 238 I 2 323 107 O 189 34 1 3 234 2O2 O 279 236 2 324 108 1 190 338 2 35 2O2 o 280 234 325 109 3 2 I 191 335 236 2O2 I 281 232 3 326 no 2 192 33i 4 237 203 I 282 229 2 327 112 2 193 328 3 238 204 J 283 227 3 328 II 4 2 194 3H 4 239 205 J 284 224 3 329 116 3 195 320 4 240 2O6 285 221 33 119 I 3 3 196 316 241 207 2 286 21 8 3 33i 122 3 197 312 242 209 287 215 332 125 198 308 4 ^ 2 43 2IO 2 288 211 3 333 129 4 199 33 3 244 212 I 289 208 4 334 133 5 200 299 245 213 290 204 335 138 5 2 4 5 2OI 2 94 246 215 j 291 2OO 336 '43 2O2 290 4 K 247 216 2 292 196 x 337 148 20 3 285. J 248 218 I 293 I 9 2 4 338 54 204 281 4 249 219 2 294 188 339 I 60 20 5 276 250 221 295 184 4 34 1 66 206 272 4 251 223 2 2 296 1 80 4 34i 173 7 207 268 4 252 225 1 297 176 342 1 80 1 208 263 253 226 2 298 172 4 343 187 1 209 259 4 254 228 2 299 168 344 194 1 210 2 55 4 255 230 300 164 345 202 211 251 4 256 232 2 301 1 60 4 346 210 8 212 247 4 2 57 234 2 302 156 4 347 219 9 213 243 4 258 235 I 33 152 4 348 227 214 239 4 259 237 2 34 148 4 . 349 236 9 2I 5 235 4 260 238 I 305 144 4 35 245 9 216 232 3 Q 261 239 I 306 140 4 35 1 254 9 2I 7 229 _ ) 198 1841 21 2 43 2510 7 288 2396 12 333 ! 549 2J _ j 199 [ 1861 20 244 2517 7 289 2384 12 334 1526 2o nt 200 1881 2O 245 2524 7 290 2371 l3 335 53 20 2OI 1901 20 246 2530 6 291 2358 13 336 1480 23 202 1921 20 247 2536 6 292 2345 i3 337 1456 24 ol 203 1941 2O 248 2541 293 2331 14 338 H33 U 204 1961 20 249 2546 5 294 2317 14 339 1409 24 Q 205 1980 19 250 2551 295 2302 i5 34 1386 2J 2O6 1999 19 251 2555 4 296 2287 i5 34i 1363 23 ,,-J 207 2018 '9 252 2559 4 297 2272 i5 342 134 \J 208 2037 9 2 53 2562 3 298 2256 16 343 1316 24 ol 209 2056 19 T 254 2565 299 2240 16 344 1293 2j 23 2IO 2074 I o 255 2567 2 300 2224 16 345 1270 21 I 2092 18 18 256 2569 2 w o 301 2207 17 346 1247 23 23 212 21 IO 257 2571 302 2190 l l 347 1224 2I 3 2127 !? 258 3572 I 33 2173 17 348 1200 24 rt Q 2I 4 2144 17 259 2572 O 34 2155 ' 18 349 U77 2o nl 215 2161 17 260 2572 O 35 2137 18 350 1154 23 216 2178 17 261 2571 I 306 2119 18 35i 1131 23 j 217 2195 17 262 2570 I 307 2IOI 18 352 1108 23 t\ T 218 2211 16 263 2569 I 308 2O82 '9 353 1085 2o 219 2227 16 / 264 2567 2 39 2063 9 354 1063 22 nl 22O 2243 IO 265 2565 2 310 2044 J 9 355 1040 2o 221 2258 i5 266 2562 3 3U 2025 19 356 1018 22 _ -5 222 2273 i5 267 2559 3 312 2OO5 20 357 995 2o 223 2288 i5 268 2556 3 313 I98 5 20 358 973 22 224 Z33 i5 269 2552 4 3H 1965 20 359 95i 22 225 2317 U 270 2548 4 3i5 1945 20 360 929 22 [43] TABLE VII. CONTINUED. Perturbations of the Logarithm of the Radius Vector. Arguments 6 to 12, inclufive. Arg. 6. 7. 8. 9. 10. 11. 12. IO 20 3 40 230 231 227 218 207 i ~4 9 ii i5 46 52 57 61 65 6 5 4 4 3 79 62 46 32 20 17 16 14 12 9 354 328 299 266 231 26 29 33 35 36 9 16 21 26 30 7 5 5 4 3 420 392 360 323 283 28 32 37 4o 4i 4 27 15 7 2 i3 12 8 5 2 50' 60 70 192 174 155 18 19 20 68 70 70 2 Q II 4 i 7 3 i '95 1 60 125 35 35 32 33 37 4 1 4 4 3 242 201 161 4i 4o 38 I 6 I 5 8 80 90 135 "5 20 70 69 I 3 3 93 65 28 44 48 4 123 88 35 H 25 ii 21 3 5 24 4 3o i3 IOO no 1 20 94 75 57 19 18 16 66 63 59 3 4 5 8 17 28 9 ii 14 22 9 19 i3 1 52 57 63 5 6 58 34 16 24 18 ii 38 54 7 1 16 17 18 130 140 150 1 60 28 17 9 i3 ii 8 6 54 48 43 37 6 5 6 7 4 2 57 74 9' i5 17 17 18 2 I 7 19 i 12 18 70 76 82 87 6 6 5 4 5 i 4 15 4 3 ii 89 108 128 146 19 20 18 18 170 1 80 3 o 3 30 2 4 6 109 127 18 37 60 23 94 3 32 56 24 164 1 80 16 5 17 27 i 29 i3 190 200 o 3 ~3 6 '9 H 5 5 144 1 60 16 14 87 118 3i 33 95 93 2 3 -85 118 33 37 193 205 12 8 2IO 22O 9 8 ii 9 5 4 2 174 1 86 12 9 185 34 35 90 85 5 8 '55 '95 4o 4o 213 218 a 5 2 230 240 250 260 28 57 74 i3 16 17 20 3 i o o 2 I O 2 195 202 205 206 7 3 i ,3 220 255 288 319 35 33 3i 28 77 68 58 47 9 10 ii IO 235 275 3H 35^ 4o 3 9 37 33 220 219 214 206 I 5 8 n 270 94 2 203 347 37 384 195 20 2 5 22 ii 29 i3 280 290 114 134 20 20 4 7 3 4 198 189 9 ii 369 386 17 i3 26 17 9 8 413 43 6 23 18 182 1 66 16 17 3OO 310 154 19 18 1 1 16 5 6 I 7 8 164 14 i5 399 406 7 i 9 3 6 3 454 465 ii 5 149 I 3 I 18 19 : 32O 330 340 35 360 191 206 218 226 230 i5 12 8 4 22 28 34 40 46 6 6 6 6 149 132 "5 97 79 17 17 18 18 407 402 392 376 354 10 a 21 o o 2 5 9 o 2 3 4 470 467 458 442 420 9 16 22 112 92 74 56 40 20 18 18 16 [44] TABLE VII. CONTINUED. Perturbations of the Logarithm of the Radius Vector. Arguments 13 to 21, inclufive. Arg. 13. 14. 15. 16. 17. 18. 19. 20. 21. o 66 i5 45 14 218 7 23 16 13 9 1 3 16 44 13 10 20 5 1 38 i3 12 59 75 16 16 225 229 / 4 Q 39 56 17 8 5 94 94 o i 2O 24 44 42 15 18 3 40 26 16 10 Q 1 06 i5 229 228 I 73 89 16 3 3 93 9 1 2 27 31 40 38 21 23 5 8 O K 122 226 2 101 12 4 87 A 35 35 26 60 3 %j 3 136 i3 226 O I I IO 9 4 7 81 U 7 38 32 28 70 o I 49 227 2 114 10 74 40 28 2 9 80 o 3 161 1 2 229 3 114 o 13 67 7 42 25 30 90 3 170 9 232 no 16 58 9 44 21 31 6 7 4 7 9 100 9 8 177 236 3 103 18 49 g 46 17 32 IJO 17 IO 181 j 239 96 7 19 4 1 g 45 13 31 120 27 1 2 182 J 240 2 89 7 6 19 33 g 45 IO 31 I 3 140 39 53 14 i5 181 177 4 7 238 231 7 ii 83 79 4 18 17 25 18 7 6 43 7 4 3 28 150 68 i5 170 220 16 79 2 15 12 5 39 2 26 I 60 83 16 161 9 ii 204 23 81 6 13 7 3 37 I 24 170 99 i5 150 i3 181 26 87 7 n 4 3 33 22 I 80 114 137 155 94 10 i 30 O 19 i5 14 3o 8 i 190 129 i3 123 16 125 3o IO2 7 9 o o 26 o 17 2OO 142 12 107 16 95 3o 109 6 7 i 22 2 H 210 22O '54 164 IO g 9 1 76 i5 16 65 40 25 2 T "5 117 2 J 6 5 i 4 3 3 15 4 6 n 9 230 240 172 177 5 3 60 46 14 i3 19 6 i3 5 116 iii 5 ' IO 5 6 7 12 5 5 II 8 9 12 6 4 250 1 80 33 1 2 i 3 101 I 2 8 17 6 6 16 3 260 1 80 o 21 9 4 ii 89 16 10 23 6 4 1 9 2 270 177 12 15 73 15 2 9 2 23 I 6 7 19 17 8 280 171 8 5 34 23 56 17 37 O 27 O 290 163 10 I I 57 28 39 J 7 16 21 44 7 8 I 3 1 I 300 1 53 O 85 23 24 52 I 34 I 3IO 141 1 2 I I / 114 29 oR ii 1 2 26 60 o g 3 37 2 32O 330 127 112 i5 i5 5 12 4 7 142 1 68 40 26 21 3 o o 3 3 26 24 68 75 7 5 7 40 42 4 6 340 97 16 21 9 I i 189 3 g 21 82 5 9 43 8 35 360 81 66 i5 32 45 i3 206 218 12 n 23 12 17 13 87 4 13 16 44 44 IO 13 [45] TABLE VIL CONCLUDED. Perturbations of the Logarithm of the Radius Vector. Arguments 22 to 37, inclufive. Are 22. 23. 24. 25. 26. 27. ?8 W 30 31. 32. 33. 34. 35 36 37 12 22 26 35 6 7 8 10 7 1 1 5 6 3 o 3 10 15 25 29 3 7 5 8 10 I 9 12 6 7 3 i 4 20 17 28 31 24 9 3 7 10 2 10 '3 7 8 2 i 5 3 19 31 33 19 ii i 7 10 3 1 1 H 7 9 2 2 6 40 21 33 35 H 13 o 7 10 4 12 15 8 10 I 2 7 50 22 35 36 9 H 6 10 6 13 '5 9 10 I 3 8 60 2 4 37 36 6 16 5 9 8 '3 15 9 1 1 4 9 70 25 38 36 3 17 I 5 9 10 H 16 9 12 O 4 10 80 25 38 35 i '9 2 4 8 13 H '5 10 12 5 1 1 90 26 38 34 20 3 3 7 15 H '5 10 12 o 6 n IOO 26 37 32 21 5 3 7 '7 H '5 10 12 o 6 12 no 25 36 3 i 21 8 2 6 '9 H H 9 12 7 12 120 2 4 34 28 2 22 1 1 2 5 21 13 13 9 II o 7 12 I 3 2 3 32 2 5 5 21 H I 4 23 12 12 8 I I o 8 12 140 22 29 22 9 21 17 I 3 2 4 I I 10 8 10 I 8 12 150 20 26 1 9 *3 20 20 O 2 25 10 9 7 9 I 8 I I I 60 18 23 15 18 '9 2 3 I 26 9 8 6 8 2 8 10 170 16 20 12 2 3 18 26 O I 26 8 6 6 7 2 8 10 I 80 4 16 10 29 16 29 o 26 7 5 5 6 3 8 9 I9O ii 13 7 34 15 31 o O 25 5 4 4 5 3 7 8 200 9 10 5 40 '3 33 I 2 4 4 3 3 4 4 7 7 2IO 7 7 3 45 1 1 35 I o 23 3 2 3 3 4 6 6 22O 5 *5 i 50 9 36 I o 22 2 2 2 5 6 5 230 4 3 o 55 8 36 2 2O I I 2 5 5 4 240 2 i o 58 6 36 3 I 18 I I I 6 4 3 250 I o 61 5 35 3 I 16 I O 6 4 2 26o I o I 63 3 34 4 2 13 O O O 6 3 I 270 o 2 64 2 33 5 3 n o 6 2 I 280 o I 4 64 I 3i 5 3 9 o I o 6 2 O 290 I 2 6 63 I 28 6 4 7 o 2 I 6 I 3OO 2 4 8 62 25 6 5 5 I 3 I I 6 I o 3 IO 3 6 ii 59 I 22 7 6 3 2 4 2 I 6 O o 32O 4 9 H 55 I 19 7 7 2 3 6 2 2 5 33 6 12 17 5i 2 16 8 8 I 4 7 3 3 5 O I 340 8 15 21 46 3 '3 8 9 O 5 8 4 4 4 o 2 35 10 18 2 4 4' 4 10 8 9 O 6 10 4 5 4 2 360 12 22 26 35 6 7 8 10 o 7 n 5 6 3 o 3 \ [46] TABLE VIII. Terms in S log. r to be Multiplied by t. \ Argument 10. _____ I 2 - 41.88 45-H 48-38 3.26 3.24 45 46 47 -146.68 H7.7I 148.68 i.o3 0.97 9 9 1 92 14I.6l 140.52 139.40 1.09 1. 12 T T / 135 136 137 -68.96 66.95 64-94 2.O1 2.01 2.o3 3 51.60 3rirt .22 o T _ 48 149.60 0.92 n RA 93 138.26 I.I4 1.18 138 62.91 2.o5 4 54-79 o.IQ 49 1 50.46 u.ou 0.80 94 137.08 1 .2 1 139 60.86 2.04 5 57-95 j . I O 5 151.26 95 135.87 140 58.82 3.i4 0.75 1.24 2.06 6 7 8 61.09 64-19 67.27 3.IQ 3.o8 3.o4 5i 52 53 152.01 152.70 153.33 0.69 o.63 ' 0.57 96 97 98 -134-63 133-37 132.08 1.26 1.29 i.33 141 142 H3 -56.76 54-69 52.61 2.Q7 2.08 2.08 9 70.31 3.oi 54 153-9 o.5i 99 130-75 1.35 144 5-53 2.09 10 73-32 55 154.41 100 129.40 H5 48.44 2.97 o.45 i.38 2.Q9 1 1 - 76.29 2.g3 56 154.86 o.3o 101 128.02 1.41 146 -46.35 2. II 12 79.22 2.8o 57 155-25 ^"-'y o.34 IO2 I26.6l 1.43 H7 44.24 2. II 13 82.11 2.85 58 155-59 0.28 103 125.18 1.43 148 42.13 2.12 H 84.96 59 155.87 O.23 104 123--73 I Al H9 40.01 2.12 15 87.77 2.76 60 156.10 0.18 105 122.26 1.4 _ 1.49 150 37.89 2.13 16 - 9-53 61 156.28 1 06 -120.77 1 S I -35.76 2.13 17 93-25 2.72 62 156.40 O. I 2 O.o8 107 119.25 1 .32 152 33-63 2.14 18 19 95.92 98.53 2.67 2.61 63 64 156.48 156-51 o.o3 108 109 117.70 1 16.13 1 . 33 i.5 7 153 154 29-35 2.14 2.l5 20 101.10 2. 37 65 156.49 I 10 II4-54 9 155 27.20 _ r 2.52 0.07 1.61 2.13 21 103.62 o Xi 66 -156.42 O I 2 iii -112.93 1.63 156 -25.05 2.l5 22 106.09 2.47 2/ _ 67 156.30 I 12 1 1 1.30 157 22.90 2.16 23 108.50 41 2.35 68 156-13 0.17 O.22 H3 109.65 1.67 158 20.74 2.l5 24 110.85 ft 69 155.91 I 14 107.98 1 / 159 18.59 2.16 2 5 1 1 3.16 4.O 1 70 155.65 I 15 106.28 1.70 1 60 16.43 2.24 O.32 1.72 2.17 26 -115.40 7i -I55-33 o 35 116 104.56 I 73 161 14.26 2.16 27 28 29 117.59 H9.73 121.81 2.19 2.14 2.08 72 73 74 154.98 154.59 154-14 o.3g o.45 117 118 119 102.83 101.09 99-32 1.70 1-74 '77 162 163 164 12. IO 9.94 7.78 2.16 2.16 . 2.16 3 123.82 2.QI 1.95 75 153.65 0.49 o.53 1 20 97-53 1.79 i. 80 165 5.62 2.16 32 -125.77 127.66 1.89 i fio 76 77 -153.12 152.55 0.57 121 122 - 95-73 93-9i 1.82 166 167 346 2.16 2.l5 33 129.48 1 .02 78 15L93 O.O2 ^ AA I2 3 92.07 T RA 168 + 0.85 2.16 34 131.25 1.77 79 151.27 Q.OO 124 90.21 l .00 169 3.OI 2.17 3 t 5 132.96 i.65 80 150.58 0.69 O.73 125 88.35 1.88 170 5 .I8 2.l5 36 -134.61 t Kr. 81 -149-85 126 - 86.47 171 + 7-33 2.l5 37 136.20 I .09 82 149.08 0.77 OQn I2 7 84.57 i .90 172 9.48 2.l3 38 137-72 1.52 1.47 83 148.26 ,O2 o.85 128 82.67 i .90 1.92 J 73 ii. 61 2.14 39 i39-!9 ! I/ T 84 147-41 r> 88 I2 9 80.75 1 74 1 3-75 2.13 40 140.60 41 85 i4 6 -53 u.oo I 3 78.82 1.9 175 15.88 n w *> i.34 0.91 i. 9 5 2.1 j 42 -141.94 143.21 1.27 86 87 -145-62 H4.67 0.95 131 132 - 76.87 . 74.9i 1.96 176 177 + 18.01 20.14 2.13 2.l3 43 144.42 1. 21 - T A 88 143.68 0.99 133 72.94 1.97 I nR 178 22.27 2.12 44 145.58 1 . 10 89 142.67 1 .01 134 70.96 1 .90 179 24-39 2. II 45 146.68 I.IO 90 141.61 1 .06 135 68.96 2.00 180 26.50 [47] TABLE VIII. CONCLUDED. Terms in log. r to be Multiplied by t. Argument 1 0. Concluded. 1 80 + 26.50 225 + 107.89 T 3-7 270 + 140.70 3'5 + 92-36 181 28.60 2. IQ 226 109.26 1.07 271 140.64 O.OO 3'6 90.15 2.21 182 30.69 2.09 227 1 1 0.6 1 i.35 272 '4-53 O.I I 3'7 87.89 2.26 n 1 T 183 32.78 2.09 228 111.93 1.32 273 140.38 o. 1 5 318 85.58 2.JI 184 34.85 2.07 229 113-23 i.Jo 274 140.19 o. 19 3'9 83.21 2.36 185 36.92 2.07 230 114.50 1.27 275 139.96 O.23 320 80.80 2.41 2.06 1.24 0.27 2.45 186 + 38.98 2.o5 2 3 I + "5.74 1.22 276 + 139.69 O 32 321 + 78.35 2 5o 187 41.03 232 116.96 277 '39-37 322 75.85 188 43.06 2.o3 2.o3 233 118.16 1. 2O 1.16 278 139.01 o 4o 323 73-3' 2.54 189 190 45.09 47.11 2.02 234 235 119.32 120.46 1. 14 279 280 138.61 138.16 0.45 324 325 70.72 68.08 2.64 2.OO 1. 12 0.49 2.68 191 + 49- 11 236 + 121.58 281 + 137.67 326 + 65.40 192 193 51.11 53-'o 2.OO 1-99 237 238 122.67 '23.73 1.09 1. 06 i.o3 282 283 137.13 '36.55 o.58 062 327 328 62.68 59-92 2.72 2.76 fin 194 '95 55-07 57-03 1.97 1.96 2 39 240 124.76 125.76 1. 00 284 285 '35-93 135.26 0.67 329 330 57.12 54-27 2.OO 2.85 I.gS 0.97 0.72 2.88 196 197 + 58.98 60.91 1.93 241 242 + 126.73 127.68 0.95 286 287 + '34-54 133.77 0.77 r> Si 33' 332 + 5'.39 48.47 2.92 198 62.82 I. 9 I 243 128.59 0.91 0.88 288 132.96 U.Ol o.85 333 45-5' 2.96 199 6473 I.gl I 8r> 244 129.47 289 132.11 334 42.52 2.99 3.02 200 66.62 I.9 245 130.32 0. 290 131.21 0.90 335 39-50 1.87 0.82 0.95 3.06 2OI + 68.49 246 + 131.14- 291 + 130.26 336 + 36.44 2O2 70.35 i 8/ 247 0.79 292 129.26 i .00 337 33-35 3.09 Iff 203 72.19 i .04 1.82 248 132.69 O.7O 0.73 293 128.20 i .00 1. 10 338 30.24 O. I I 3.i5 204 74.01 1.81 249 '33.42 i 0.69 294 127.10 339 27.09 3.17 205 75.82 250 134.11 2 95 125.95 34 23.92 / 1.79 0.66 I.2O 3.19 2O6 + 77-6i 1.77 251 + '3477 o.63 296 + 124.75 1.24 34' + 20.73 3.21 207 79.38 252 '35-40 297 123.51 i.3o 342 17.52 3 23 208 81.14 In / 253 136.00 O.OO 298 122.21 343 14.29 209 2IO 82.88 84.60 74 1-72 254 255 136.56 137.09 o.53 299 300 120.86 1 19.46 1.40 344 345 1 1.04 I'll o. 2D 3.2 7 1.70 o.5o 1.45 3.29 211 + 86.30 1.68 2 5 6 + '37-59 0.46 301 + 118.01 i.Si 346 + 4.48 3.3i 212 87.98 1.65 257 138.05 302 1 16.50 i 55 347 1.17 213 89.63 1.64 258 138.46 0.39 303 114.95 1.61 348 2.14 3.3i 214 91.27 1.62 259 138.85 o.36 34 "3-34 i.65 349 5-45 3.3i 215 92.89 260 139.21 305 1 11.69 350 8.76 i. 60 0.32 1.71 3.32 216 + 94-49 i.58 261 + '39-53 n oft 306 + 109.98 35' 1 2.08 *3.o2 217 96.07 i.56 262 139.81 U. .0 37 108.23 1.81 352 15.40 3 33 218 97.63 263 140.05 o. 24 308 106.42 1.86 ' 353 '8-73 -j -5-3 219 99.17 264 140.26 0. 21 39 104.56 354 22.06 O. O J 7 3*3 22O 1 00.68 i 265 '40.43 0.17 310 102.66 i .90 355 25-39 O.OO 1.49 o.i3 1.96 3.3a 221 + 102.17 * /-. 266 + 140.56 3" + 100.70 356 28.71 222 223 103.64 105.08 '47 1-44 267 268 140.66 140.71 O. IO o.o5 312 3'3 98.69 96.63 2.OI 2.06 357 358 32.02 35.32 3.3o 224 106.49 1.41 i.4o 269 140.72 O.OI O.O2 3'4 94.52 2 . 1 1 2.l6 359 38.60 3.28 225 107.89 270 140.70 92.36 360 41.88 [48] TABLE IX. CONTINUED. Perturbations of the Co-ordinate . Argument 1. Argument 2. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. 281.4 o.3 1 80 277.6 2.2 213-5 2.7 1 80 124.1 0.7 5 283.2 0.4 185 265.3 2.6 5 199.4 2.9 I8 5 120.5 0.7 10 285.5 o.5 190 251.1 3.0 10 184.6 3.o 190 II7.O o. 7 15 288.5 0.6 195 235.1 3.3 '5 169.3 3.i '95 113.6 0.6 20 292.0 0.7 200 2 I 8.0 3.5 20 153-6 3.2 200 III.O 0.4 25 295.7 0.8 205 200.3 3.5 2 5 I37-7 3.2 205 109.6 O.I 3 299.6 0.8 2IO 182.6 3.5 30 I2I.8 3.i 2IO 109.6 0.2 35 33-4 0.7 215 165.4 3.3 35 106.2 3.i 215 III. 2 o.5 40 307.1 0.7 22O 149.1 3.1 40 91.0 3.o 22O II4.6 0.9 45 310.2 o.5 225 134-7 2.7 45 76.5 2.8 225 I 20. 1 i.3 5o 3 I2 -5 .0.4 230 122. 1 1.1 5o 63.0 2.5 230 127.4 1.6 55 313-8 0.2 235 II2.4 1-7 55 ,51.0 1.1 235 136.6 2.0 . 60 314.2 o.i 240 105.2 I.I 60 40-5 1.9 240 H7-3 2.3 65 3'3- 2 o.3 245 IOI.2 o.5 65 3'-9 1.5 245 159-4 2.5 70 3ii-3 o.5 250 IOO.3 O.I 70 25-3 I.I 250 172.5 2.7 75 308.3 0.7 255 102.7 0.8 75 21. 1 0.6 255 186.3 2.8 80 304-7 0.8 260 107.9 1.3 80 I9.O 0.2 260 2O0.6 2.8 85 300.6 0.8 265 II5.9 1.8 85 19.4 o3 265 214.8 2.8 90 296.5 0.8 270 I26.I 1.1 90 21.9 0.7 270 228.5 2.7 95 292.8 0.7 275 138.4 2.6 95 26.6 I.I 275 241.3 2.5 IOO 289.7 o.5 280 I52.I 2.8 IOO 33-2 i.5 280 253.2 1.1 105 287.4 0.4 285 166.6 2. 9 105 41.5 1.8 285 263.7 1.9 IIO 286.1 O.I 290 181.5 3.o no 50.9 2.0 290 272.5 1.6 "5 286.0 O.I 295 196.5 2.9 "5 61.3 2.1 295 279.4 1.2 120 287.0 o.3 30O 210.8 2-7 1 20 72.1 1.1 300 284.5 0.8 125 289.1 o.5 35 224.0 2.5 125 83.0 2.1 305 287.6 0.4 130 291.9 0.6 3IO 235.9 2.2 130 93-4 2.0 3IO 289.0 O.I 135 295.2 0.7 315 246.2 1-9 135 103.0 1.8 315 288.4 ol 140 298.5 0.6 320 254.9 1.6 140 ii 1.6 1.6 320 286.0 0.7 H5 301.4 o.5 325 261.8 1.2 H5 118.7 1.3 325 281.8 1.0 150 303.6 0.3 33 267.4 1.0 150 124.2 0.9 330 276.0 i.3 155 34-3 0.0 335 271.5 0.7 155 128.0 0.6 335 268.7 1.6 1 60 303-4 0.4 34 274.6 o.5 1 60 130.2 o.3 34 260.0 1.9 165 300.5 0.8 345 276.9 0.4 165 130.6 0.0 345 250.0 2.1 170 295-3 i.3 350 278.5 o.3 170 129.6 o.3 35 238.8 2.3 175 287.6 1.8 355 280.0 o.3 175 127.3 o.5 355 226.6 2.5 1 80 277.6 1.1 360 281.4 o.3 * 1 80 124.1 0.7 360 213.5 2. 7 *.* The Differences are calculated for i Degree, [49] TABLE IX. CONTINUED. Perturbations of the Co-ordinate . Argument 3. Argument 4. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. Arg. Eq. D. 9- 1 Q.I 1 80 433-3 I.O I 20. 1 5.3 1 80 74.3 0.7 5 5-6 0-7 185 437-6 0.7 5 93-i 5.3 185 74.1 o.5 10 1.6 0.4 190 440.4 0.4 10 67.2 4-9 190 79-o 1.4 15 0.5 O.I '95 441.6 O.I 15 43-9 4.4 195 87.9 2.1 20 0.9 ~o~3 200 44L3 0.2 20 23-4 3.5 200 100.4 2.6 2 5 3- 2 0.6 205 439- 1 0.6 25 9.1 2.2 205 114.0 2-7 30 7.0 0.9 210 435-4 0.9 3 1.2 Q.8 2IO 127.6 2.6 35 12.6 i.3 2I 5 430.0 1.2 35 0.6 0.6 215 139.7 2.1 40 19.7 1.6 22O 423-1 1.5 40 7-3 2.1 220 148.9 i.5 45 28.4 1.9 225 414.6 1.8 45 21.6 3.5 225 154.4 0.7 50 38.5 2.2 23O 405.0 2.1 5 42.7 4.8 230 155-5 0.2 55 50.2 2.4 235 393-5 2.4 55 70.0 6.0 235 152.1 I.I 60 63.0 2.7 240 381.0 2.6 60 102.3 6.9 240 144.7 1.8 65 77.2 2. 9 245 367.1 2. 9 65 138.6 7 .5 245 '3 4- 2.4 70 9 2 -3 3.i 250 352.3 3.1 70 177.1 7.8 250 121. 1 2-7 75 108.5 3.3 255 33 6 -4 3.3 75 2l6.2 7-7 255 107.3 2.7 80 125.5 3.5 260 3I9-7 3.4 80 254.3 7 .3 260 93-9 2.5 85 143.2 3.6 265 302.1 3.6 85 289.6 6.7 265 82.5 2.0 90 161.6 3. 7 270 284.0 3. 7 9 320.9 5. 7 270 74-3 1.2 95 180.4 3.8 275 265.4 3. 7 95 346.8 4.5 275 70.5 0.3 IOO 199.5 3.8 280 246.5 3.8 IOO 366.3 3.2 280 71-5 0.7 105 218.7 3.8 285 227.2 3. 9 105 378.6 i-7 285 77.5 i-7 no 237.9 3.8 290 207.9 3.8 IIO 383.1 O.I 290 88.3 2.6 "5 257.0 3.8 295 188.8 3.8 "5 379-6 T4 2 95 103.3 3.3 1 20 275.8 3. 7 3OO 169.8 3.8 120 368.6 2.9 300 121.4 3.8 125 294.2 3.6 305 151.2 3. 7 125 350.5 4.2 305 141.2 3. 9 130 312.0 3.5 310 133-2 3.5 130 326.5 5.3 310 160.9 3.8 !35 329.1 3.3 315 115.8 3.4 135 297.7 6.1 315 179.2 3.3 140 345-5 3.2 32O 99.3 3.2 140 265.5 6.6 320 194.3 2.6 H5 360.7 3.o 325 83-7 3.o 145 231.6 6.8 325 204.8 i.5 150 375-0 2-7 330 69.0 2.8 150 197.7 6.6 330 209.7 0.4 *55 388.1 2.5 335 55.6 2.6 '55 165.5 6.1 335 208.5 0.8 1 60 400.1 2.2 34 43-3 2.3 1 60 136.6 5.3 34 201.2 2.1 165 410.5 1.9 345 32.6 2.0 165 112. 2 4.3 345 187.6 3.2 170 419.6 i-7 35 23-2 i-7 170 93-4 3.i 350 168.8 4.2 75 4 2 7.3 1.4 355 15.4 1.4 , 175 80.7 1.9 355 145.8 4-9 180 433-3 I.O 360 9- 1 i.i 1 80 74-3 0.7 360 I 20. 1 5.3 ** The Differences are calculated for i Degree. [50] TABLE IX. CONTINUED. Perturbations of the Co-ordinate . Arguments 9 to 15, inekifive. Arg. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 64.8 3.8 13.6 3.5 5-5 2.1 17.0 5-2 1.8 2. 4 O.O 0.6 14 32.0 10 20 6 i.o 56.4 4.6 5.o I O.I 6-9 3.2 2.6 5-3 5.0 1.4 0.7 14.5 11.9 34 3-3 O.I 2.0 1.6 0.0 O.I 0.7 37.6 43.2 5.6 5.6 30 51.4 5.3 4-3 2. 1 4.6 0.3 94 4.8 2.8 1.2 I.O 0.0 0.0 48.3 5.i 40 46.1 5.5 2.2 4.2 0.0 7.2 7.6 3 o 0.8 2.0 0.3 O.O 53- 4.7 5 40.6 0.9 3-7 O.I 5.1 11.5 0.9 0.6 3.1 0.8 O.I 57-1 4.1 60 70 35- 29.6 5.4 5.3 0.2 -7 O.I 0.8 3-2 2.7 0.3 0.6 3-3 1.8 16.1 20.8 4-7 A 3 0.4 0.2 4.6 6.2 i-S 2.4 0.5 I.I 60.4 62.9 3.3 2.5 80 24-3 5.o I.I 2.2 1.2 0.8 25.1 |.*vJ 4-0 O.I 8.1 3-5 1.8 64.5 1.6 n f\ 90 19-3 2.6 1.8 2.0 0.2 29.1 O.O 9-9 4-7 2.7 65.1 u.u IOO 14.5 4.8 4-7 2.1 1-3 2-9 0.0 32.5 3.4 O.I ii. 8 5-9 3-8 64.7 0.4 I 10 10.4 4-1 i f\ 74 2.7 0. 9 4.0 O.2 35-2 2.7 o } O.2 13-6 74 4.9 63-3 1.4 120 6.9 O.O n n 10.6 3. 2 0.6 5-1 0.9 37-5 Z.\J 1.8 0.4 15.4 8-7 6.1 61.0 2.3 I 3 4.0 2-9 H-3 ' 7 0.3 6.3 2.1 39-3 1.6 0.7 17.1 IO.O 7-3 57-9 3.i 140 1.9 2.1 I.I 18.2 4.1 0.2 7-6 3-6 40.9 1.2 I.O 1 8.6 "3 8.6 53-9 4.0 / /I 150 0.8 o.3 22.3 4 ft 0.0 8-7 54 42.1 1.3 14 19.8 12.4 9-7 49-3 4.6 I 60 0.5 26.5 .2 4_ 0.0 9-9 7-5 434 I 2 1.8 20.7 13-5 10.8 *44.2 5.1 170 1.2 0.7 i 8 30.5 .0 O.O I I.O 9-9 44-6 I 2 2.2 214 14.4 u. 8 38.8 5.4 I 80 3.0 1 . O 344 3.9 O.I 11.9 12.4 45-8 2.6 21.8 15.0 12.6 33-2 5.6 3.o 3.5 1.2 5.6 190 6.0 4,, 37-9 3 0.4 12.6 14.9 47.0 3-0 21.8 15.4 ^3-3 27.6 2OO IO.O .0 / 8 41.1 .2 n . 0.7 13.3 17.5 48.0 I .O r Q 34 21.5 15.5 13.7 22. 5.6 210 14.8 4.0 5.5 43.7 2.O 2.1 I.O 13.7 2O.O 48.8 O.o 0.8 3-8 20.8 15.6 14.0 16.8 5.2 220 20.3 6.3 45.8 T 1.4 14.0 22.2 49.6 4.2 19.8 "5-3 14.0 12. 1 4-7 230 26.6 6.7 47.i I.O 0.6 1.9 13.9 24-3 50.1 O.2 4-5 18.7 14.8 '3-9 8.1 4.0 240 33.3 A n 47.7 2.4 13.7 26.1 5-3 o 4-7 17.2 14.1 1 3.5 4.8 3.3 250 40.0 0-7 47.6 O. I 2.9 134 2 7 .6 50.0 O.O 4.8 15.6 13.2 12.9 2.3 2.5 260 46.7 6.7 6.2 46-9 0.7 i.5 34 12.7 28.6 49.2 0. 4.9 13.7 12. 1 12.2 0.7 1.6 270 52.9 454 3-8 12.0 29.2 47-5 1 -1 5.0 11.9 IO.9 II.3 O.I 0.6 5.6 2.1 2.6 280 58.5 4m 43-3 4.2 II. I 29.4 44-9 4-9 IO.O 9-7 IO.2 0.5 0.4 290 63.2 1 40.6 2.7 3_ 4-6 IO.O 29.2 41.2 3.7 4.8 8.2 8.3 9.1 1.9 1.4 300 3IO 66.9 69.6 2. 7 374 33-7 .2 3.7 j n 5.0 5-3 8.9 7-7 28.5 27.3 36.5 4.7 5.4 6.0 4.6 4.3 6.4 4-7 6. 9 5-6 7.9 6.7 4.2 7-3 2.3 320 70.9 29.8 0.9 5-5 6-5 2 5 .8 25.1 A, T 4.0 3.2 4-3 5-5 "3 4.0 330 71.0 I .O 25.7 4.1 4.2 5.6 5-3 24.0 19.0 O. I 5.6 3.6 2.O 3-2 4-3 15.9 4.6 34 70.0 21.5 5-6 4- 1 21.9 1 3.4 3-2 I.I 2.1 3-2 21.0 5.i 35 67.8 2.2 17-5 4.0 5-6 3- 19.5 8-7 4-7 i *; 2.8 0.4 1.2 2.2 26.4 5.4 360 64.8 .Q 13.6 9 5-5 2.1 17.0 : 5-2 O.D 2.4 0.0 0.6 1.4 32.0 5.6 [51] TABLE IX. CONTINUED. Perturbations of the Co-ordinate . Arguments 16 to 29, inclufive. Arg. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. o O 1.9 7-3 21.5 n n O.I I.O o.o 10.5 3-3 4.2 0.2 15-6 o.o 5-5 2.4 IO 1.9 6.1 28.5 7.0 7-5 o.o 0.9 o.o 9-7 3-9 2.6 0.0 14.2 0.0 5.8 2O 1.9 4-7 36.0 7-9 0.0 0.7 0.0 8.8 4-5 '4 0.0 12.7 O.I 6.0 3-9 3 2.O 3.1 43-9 8.0 0.0 0.7 O.I 7-9 5.0 0.5 O.I II. 2 >3 6.1 4-7 40 2.1 1.6 51.9 7 8 o.o 0.6 O.I 6.9 5-5 0.0 0-3 9-5 0.5 6.2 5-5 5 2-3 0.6 59-7 /" 1 ") O.I 0.4 O.2 5-8 5-9 o.o 0.6 7.8 0.8 6.1 6-3 60 2-5 o.o 67.2 7-j 6.9 -3 0.4 0.3 4-8 6.2 0.4 I.O 6.2 i.i 5-9 7-2 70 2.7 O.2 74.1 0.5 O.2 0.4 3-8 6-5 I.I 1.5 4.8 1.4 5-6 7-9 80 2.8 0.8 80.0 A 8 0.7 0.2 0.5 2.8 6.7 2-3 2.1 3-4 1-7 5-3 8.4 90 2.9 1.9 84.8 **<-> 3.4 I.O O.I 0.6 1.9 6.8 3-8 2.8 2.2 2.1 4-9 8.9 IOO 2.9 3.1 88.2 '3 O.O 0.7 1.2 6.7 5-7 3-5 1.4 2-5 4-5 9-2 no 2.7 4-3 90.1 1.9 o.3 1.6 0.0 0.8 0.7 6.6 77 4-3 0.6 2.8 4.0 9-5 120 2.5 5-4 90.4 1.9 O.O 0.9 0.2 6-4 I O.O 5.0 0.2 3.1 3-5 9-6 130 2.2 6.1 89.1 '' 2.2 O.O .0 O.O 6.1 12.4 5.8 O.O 3.4 2.9 9-5 140 1.8 6-5 86.3 A 1 2-5 0.0 .1 O.O 5-7 14.8 6.5 0.2 3.7 2.4 9-3 150 1.4 6.5 82.1 4. A 5.5 2.7 O.I .1 O.I 5-2 17.1 0.6 3-9 8.9 160 I.O 6.3 76.6 6.5 3.0 O.I .2 0.4 4-7 19.4 7^6 1.3 4- 1 1.4 8.5 170 0.6 5-9 70.1 7m 3-2 O.I .2 0.9 4.1 21.6 8.0 2.2 4.2 I.O 7-9 1 80 0.3 5.3 62.9 2 3-3 0.2 .2 3-5 23.6 8.4 3-4 4-2 0.7 7-2 7.8 190 O.I 4.* 55-.I 3-4 -3 .2 2-3 2-9 25.2 8.6 4-8 4.2 0.4 6-5 200 0.0 4.2 47.2 7-9 3-4 0.5 .2 3-2 2.3 26.4 8.6 6-3 4.1 O.2 5-7 210 O.I 3-5 39-3 7-9 -i A 3-4 0.5 .1 4.1 1.8 27.3 8.5 7.9 3-9 O.I 4-9 22O 3 2.7 31.7 7-0 3-4 0.6 .1 5.1 1.3 27.8 8-3 9-6 3-7 O.O 4- 1 230 0.5 2.0 24.6 7- 1 A l 3-3 0.8 .O 6.2 0.9 27.8 8.0 I 1.2 3-4 O.I 3-3 240 0.7 1-3 18.2 O.4 5m 3.1 0.8 0.9 7.2 0.6 27.4 7-6 12.8 0.3 2.4 250 I.O 0. 7 12.7 .3 ' - 2.9 .0 0.8 8.3 0-3 26.7 H.2 2.8 0.6 1.7 260 1.3 0-3 8.0 4-7 O f. 2.7 .0 0.7 9.2 O.I 25.5 6-1 I 5 .6 2-5 0.9 1.2 2 7 1.6 0.3 4-4 o.o 2.4 .1 0.6 IO.I o.o 24.0 5.8 16.8 2.1 0.7 2.6 280 1.9 0.7 1.8 2.1 .2 0.5 10.8 O.I 22.1 5.1 17.6 1.7 1.7 0.4 290 2.1 1.6 0-3 1.5 1.8 .2 0.4 11.3 0.2 2O.I 4-3 18.4 1.4 2.2 O.I 300 2.2 2.8 O.I O.2 *5 .2 0-3 11.8 0.4 I 7 .8 3-6 18.8 I.I 2-7 0.0 310 2.2 4-3 0.9 2.0 1.2 .2 O.2 I2.O 0.7 154 2.8 19.0 0.8 3-3 O.I 320 2.2 5-7 2.9 3~ 0.9 .2 0.1 12. 1 I.I 13.0 2.1 18.8 0.5 3.8 0.3 33 2.1 6-9 6.1 .2 41 0.7 .1 O.I II.9 1.6 I0. 5 1-5 18.4 4-3 0.7 34 2.O 7-7 10.2 I 0.4 .1 O.O I 1.6 2.1 8.2 I.O 17.7 O.I 4.8 I.I 35 1.9 7.8 '5.5 A n O.2 .1 0.0 II. I 2.7 6.2 0.6 16.8 o.o 5-2 1.7 360 1.9 7-3 21.5 o.o O.I .O o.o I0. 5 3-3 4.2 0.2 15.6 o.o 5-5 2.4 TABLE X. Terms of the Co-ordinate to be Multiplied in t. Argument 10. " - i 2 3 4 5 + 21,10 19.47 17-83 16.18 14.51 12.84 1.63 1.64 1.65 1.67 1.67 45 46 47 48 49 50 -50.37 5 I - 6 3 52.86 54.06 55.25 56.41 1.26 1.23 1.20 I.I9 i. 6 90 9 1 92 93 94 95 82.65 82.82 82.97 83.09 83.20 83.28 0.17 o.i 5 O.I 2 O.II 0.08 135 I 3 6 137 138 139 140 -71.43 70.82 70.18 69.53 68.87 68.20 0.61 0.64 o.65 0.66 0.67 1.68 i.i3 0.06 0.68 6 + ii. 16 * A~ 5' -57-54 96 -83.34 141 -67.52 7 9-47 1.&9 52 58.66 1.12 97 83.39 o.oo 142 66.82 0.70 8 I'll 1.70 53 59-75 1.09 98 83.41 O.02 H3 66. i o 0.72 9 10 6.07 4-37 1.70 1.70 54 55 60.82 61.86 1.07 I.o4 99 IOO 8341 83.38 O.OO o.o3 144 H5 65.38 64.64 0.72 0.74 1.70 1. 01 0.04 0.75 1 1 12 '3 + 2.67 + 0.95 0.76 1.72 I.7I 56 57 62.87 63.86 64.83 0.99 0.97 101 102 103 -83.34 83.28 83.21 0.06 0.07 146 -63.89 63.14 62.38 0.75 0.76 H 15 2-47 4.18 I.7I I.7I 59 60 65.77 66.68 0.94 0.91 IO4 I0 5 83.11 82.99 0. 10 O.I 2 149 150 61.59 60.80 0.79 0.79 I.7I 0.80 0.14 0.80 16. - 5.89 7-59 1.70 61 62 -67.57 68.44 fmv\f 0.87 1 06 107 82.85 82.70 o.i 5 n .0 151 152 60.00 59.18 0.82 _ Q n 18 9.29 1.70 63 69.28 0.84 108 82.52 0. 10 58.36 O.o2 n O1 '9 10.99 1.70 / Q 64 70.09 0.81 109 82.32 O.20 '54 57-53 <>.' i n OS 20 12.67 I.OB 65 70.88 0.79 I IO 82.11 O.2I '55 56.68 O.D3 1.68 0.76 0.23 o.85 21 -H-35 66 -71.64 / 1 1 1 -81.88 156 -55.83 Qj 22 16.02 1.67 67 72.38 0.74 112 81.63 0.25 '57 54.96 0.87 Q 23 17.68 1.66 68 73.09 0.71 I 13 81.36 0.27 158 54.09 O.87 QQ 2 4 '9-34 1.66 69 73.78 0.69 114 8 1. 08 0.28 159 53-21 O.OO 25 20.98 1.64 70 74-44 0.66 115 80.78 o. 3o 1 60 52.32 0.&9 i.63 0.63 0.32 0.90 26 22.61 71 -75.07 116 80.46 _ 1 / 161 -51.42 27 24.22 1.61 72 75-68 0.61 117 80.12 0.34 _ -j e 162 50.52 O.9O 28 25.82 27.41 1.60 1.59 73 74 76.27 76.84 0.59 0.57 118 119 79-77 79.41 O.J5 o.36 _ 0_ 163 164 49.60 48.67 0.92 O.93 _ _1 3 28.98 1.57 75 77.38 o.54 120 79.02 0.09 165 47.74 0.94 i.55 Q.5l 0.40 O.94 3 1 -30-53 76 -77.89 121 -78.62 1 66 46.80 3 2 32.07 i.54 77 78.38 0.49 122 78.21 0.41 . -5 167 45.85 o. 9 5 33 33.6 1.53 78 78.85 0.47 I2 3 77.78 0.43 . r 168 44.89 0.96 34 35-n i.5i 79 79.30 0.45 124 77-33 0.45 ./ 169 43.92 0.97 35 36.60 1.49 80 79-72 0.42 I2 5 76.87 0.46 170 42.95 0.97 1.4*7 0.40 0.48 0.98 36 -38.07 * ** i 81 80.12 126 -76.39 171 -41.97 37 39-52 . 1.45 82 80.49 0.37 127 75.90 0.49 jr 172 40.99 0.98 38 40.95 1.43 83 80.84 o.35 128 75.39 O.DI '73 39-99 1.00 39 42.36 1.41 84 81.16 0.32 129 74.87 O.52 r . '74 38.99 1. 00 40 43-75 1.39 85 81.47 o.3i 130 74-33 0.94 '75 37.98 1. 01 4' -45.12 i.3 7 86 -81.75 0.28 '3' -73-77 o.56 F f 176 36.96 1.02 42 46.47 i. i") 87 82.01 0.26 I 3 2 73-2i 0.90 K.O 177 35-94 1.02 43 47.79 1.32 88 82.24 0.23 72.63 0.3 ' t 178 34.91 I.o3 44 49.09 i.3o 89 82.46 0.22 '34 72.04 0.99 179 33.88 i.o3 45 50.37 1.28 90 82.65 O.lg 71.43 0.61 1 80 32.84 1.04 [53] TABLE X. CONCLUDED. Terms of the Co-ordinate to be Multiplied in t. Argument 10. Concluded. 1 80 181 182 183 184 185 -32.84 31.80 30.75 29.69 28.63 27.57 1.04 i.o5 1. 06 1. 06 1. 06 22 5 226 227 228 22 9 23O + 16.94 18.04 19-13 20.23 21.32 22.41 1. 10 1.09 1. 10 1.09 1.09 270 271 2 7 2 273 ^74 275 + 59-51 6O.2O 60.86 6l.5I 62.15 62.77 0.69 0.66 o.65 0.64 0.62 315 316 317 318 319 320 + 69.21 68.81 68.38 67.92 67.42 66.90 0.40 0.43 0.46 o.5o 0.52 1.07 1. 08 0.60 o.56 1 86 26.50 I O7 231 + 23-49 1. 08 2 7 6 + 63.37 o.58 321 + 66.34 o.Sg 187 188 189 190 23.26 22.17 1 * u / 1.09 1. 08 1.09 232 233 234 235 2 +57 25.65 26.72 27.78 1. 08 1.07 1. 06 277 2 7 8 279 280 63-95 64.51 65.06 65-59 o.56 o.55 o.53 322 323 324 325 6575 65-13 64.48 63.79 0.62 o.65 0.69 1.09 1. 06 o.5i 0.72 191 21. 08 236 + 28.84 _ _y- 28l + 66.10 326 + 63.07 r 192 193 194 195 19.98 18.88 17.78 16.67 1. 10 1. 10 1. 10 I. II 237 238 239 240 29.89 30.93 31.96 33-00 I.O3 1.04 I.Q.3 i.o4 282 283 284 285 66.59 67.06 67-51 67-94 0.49 0.47 o.45 0.43 327 328 329 33 62.32 6i.53 60.72 59.87 0.73 0.79 0.81 o.85 I. II i.o3 0.41 0.88 196 197 -15.56 14.45 I. II 241 242 + 34-03 35-04 I.OI 286 287 + 68.35 68.73 o.38 rn 1A 332 + 58-99 58.08 0.91 198 199 I 3-34 12.22 I. II 1. 12 I. II 243 244 36.05 37.05 I .OI 1. 00 I.OO 288 289 69.09 69.42 O.oO o.33 0.32 333 334 57-1-3 56.16 0.97 I.OI 200 II. II 245 38.05 29O 69-74 335 55.15 1. 12 0.98 o.3o 1.04 2OI - 9-99 1. 12 246 + 39-03 0.98 2 9 I + 70.04 O 27 336 + 54-11 1.07 2O2 8.87 247 40.01 v * 7 292 70.31 \j. & 1 337 53-04 / 2O3 7-75 1. 12 1. 12 248 40.98 0.97 0.96 293 70.56 0.25 O.22 338 51-93 i . 1 1 204 6.63 249 41.94 294 70-78 339 50-79 i i f\ 205 5.50 25O 42.89 0.9 295 70.98 O.2O 340 49.63 1 . 1 U i.i3 0.94 0.17 I.I9 206 - 4.37 251 + 4*3.83 , 296 + 71-15 n T^i 34i + 48.44 1.22 207 3-24 1-1 252 44.76 0.9 297 71-3 U. 1 J 342 47.22 I 2A 208 2.1 I i.i 253 45.69 9 298 71.42 343 45.98 1 . 4^ 209 - 0.99 1. 1 2 254 46.60 O.QI O.QQ 299 7L51 0.09 O O7 344 44- 7 i 1.27 i.3o 2IO + 0.14 255 47.50 30O 71-58 345 43-4i i.i3 0.89 O.O4 i.33 21 I + 1.27 1. 12 256 + 48.39 0.87 3 OI + 71.62 O.O2 346 + 42.08 i.35 212 2I 3 2-39 3-52 1. 12 257 2 5 8 49.26 50.13 0.87 0.86 32 303 71-64 71.62 O.O2 O.O4 347 348 40-73 39.34 i.3g 1.41 214 4.64 259 50.99 o 8/! 34 71-58 O.O7 349 37-93 I /!3 215 5-77 I.I 260 51-83 \j,Ucl 305 71.51 35 36.50 1 .q*j i.i3 o.83 O.IO 1.45 216 + 6.90 I . I 2 26l + 52.66 0.82 306 + 71-41 0.12 35i + 35-05 I 47 217 8.02 262 5348 0.80 37 71.29 o.i 5 35 2 '33.58 l>4/ T /f\ 218 9.14 I . I 2 263 54.28 OQ 308 71.14 353 32.09 1.49 219 10.26 1. 1 2 1.12 264 55.06 '/ 0.78 309 70.95 0.22 354 30.58 1.54 220 11.38 265 55.84 w. /u 3 IO 70.73 355 29.04 1. 12 0.76 0.24 i.56 221 222 223 + 12.50 13.61 14.72 .1.11 I. II 266 267 268 + 56.60 57-35 58.08 0.75 0.73 3H 312 3U + 70-49 70.22 69.91 O.27 o.3i 0.34 356 357 358 + 27.48 25.91 24.33 i.5 7 i.58 224 225 15.83 16.94 I . I I I. II 269 2 7 58.80 59.5I O.72 0.71 3H 69-57 69.21 0.36 359 360 22.73 21.10 i.63 [54] TABLE XL The Mean Anomaly. Year. Mean Anomaly. t Months. Mean Motion. t H. M'n Motion. t 1850 324^6' 28".83 - -999 January . . . o o' o".oo + o.ooo i o o' 4 1*45 + o.ooo 1851 65 38 23 .51 o.ooo February. . 8 33 59-88 + 0.085 2 Q I 22 .90 + 0.000 18525 166 46 53 .02 I.OO2 March .... 16 18 15 .25 + 0.162 3 2 4.35 + 0.000 1853 267 38 47 .69 2.OOI April 24 52 15 .12 + 0.246 4 o 2 45 .81 + o.ooo I8C4. 8 3O 4.2 .37 3.OOI May 33 9 40 .17 +0.328 5 O 3 27 .26 + O.OOI JT i8cc " J T 'Jl IOQ 22 37 O4. . + 4*.ooo June j j y i / 4.1 4.3 4.O .04. J + 0.41 3 J 6 J 1 048 .71 + O.OO I U 5 5 l8>65 t^y * * j / f 210 3i 6.cc 5.002 July.., T \J T " T CO I C .OQ * 1 J + 0.406 7 T_ . i O 4 CO ,l6 + O.OO I I8 57 J O5 311 23 I .22 6.001 Auguft .... j j y 58 35 4.96 i TJ + 0.580 / 8 T J 0531 .61 + O.OO I 1858 52 14 55 .90 7.001 September 67 9 4 .84 + 0.665 9 o 613 .06 + O.OO I I8 59 153 6 50.57 + 8.000 Oftober... 75 26 29 .88 + 0.747 10 o 6 54.51 + 0.001 1 860 5 254 15 20 .08 9.002 November 84 o 29 .76 + 0.832 1 1 o 7 35 -97 + 0.001 1861 355 7 H.76 IO.OOI December 92 17 54 .80 +0.914 12 o 817 .42 + O.OO I 1862 95 59 9 -43 I 1. 00 1 '3 o 8 58 .87 + O.OO 2 1863 196 51 4 .10 + I2.00O '4 o 9 40 .32 + O.OO 2 18645 2 97 59 33 - 6l I3.O02 15 10 21 .77 + O.OO2 1865 38 51 28 .29 I4.0OI * 16 Oil 3 .22 + O.OO 2 1866 139 43 22 .96 15.001 17 o 1 1 44 .67 + O.OO2 1867 240 35 17 .63 + 16.000 18 12 26 .12 + 0.002 1868^ 1869 34 1 43 47 -M 82 35 41 .82 17.002 18.001 Days. M'n Anomaly. t *9 20 o 13 7 .58 o 13 49 .03 + 0.003 + 0.003 1870 183 27 36 .49 19.001 I oi6' 34".8 3 + 0.003 21 o 14 30 .48 + 0.003 1871 284 19 31 .17 + 20.000 2 o 33 9 .67 + 0.005 22 o 15 n .93 + 0.003 1872.2? 25 28 o .67 2I.OO2 3 o 49 44 .50 + 0.008 Z 3 o 15 53 -38 + 0.003 1873 126 19 55 .35 22.001 4 i 6 19 .34 + 0.0 1 I 24 o 16 34.83 +.0.003 1874 227 1 1 50 .02 23,001 5 I 22 54.17 + o.o 1 4 1875 328 3 44.70 + 24.0OO 6 i 39 29 .01 + 0.016 18765 69 12 14 .21 25.OO2 7 i 56 3 .84 + o.o 1 9 1877 170 4 8 .88 26.001 8 2 12 38 .68 + O.O22 1878 270 56 3 .55 27.001 9 2 29 13 .51 + 0.025 *.* In Bissextile Years, fub- 1879 i88o5 ii 47 58 .23 112 56 27 .74 + 28.0OO 29.0O2 10 ii 2 45 48 -35 3 2 23 .18 + O.O27 + 0.030 *F traft i from the date during the firft two months. 1881 213*48 22 .41 30.001 12 3 18 58 .02 + 0.032 1882 314 40 17 .09 31.001 13 3 35 32 -85 + 0.035 1883 55 32 ii .76 + 32.OOO H 3 S 2 7 - 6 9 + 0.038 18845 156 40 41 .27 33.002 15 4 8 42 .52 + 0.041 1885 257 32 35 -94 34-001 16 4 25 17 .36 + 0.043 1886 358 24 30 .62 35.001 I? 4 4 1 5 2 .19 + 0.046 1887 99 16 25 .29 + 36.000 18 4 58 27 .02 + 0.049 18885 200 24 54 .80 37.OO2 *9 5 15 i .86 + 0.052 1889 301 16 49 .47 38.001 20 5 31 36.69 + 0.055 1890 42 8 44.15 39.001 21 5 48 ii .53 + 0.058 1891 143 o 38 .82 + 4O.OOO 22 6 4 46 .36 + 0.o6o 18925 244 9 8 .33 41.002 2 3 6 21 21 .20 + 0.063 1893 345 i 3 -oi 42.001 2 4 6 37 56 .03 + 0.066 1894 85 52 57 .68 43.001 2 5 6 54 30.87 + 0.069 1895 1 86 44 52 .35 + 44.000 26 711 5 .70 + 0.071 18965 287 53 21 .86 45.002 27 7 27 40 .54 + 0.074 1897 28 45 16 .54 46.001 28 7 44 15 -37 + 0.077 1898 129 37 ii .21 47.001 29 8 o 50 .21 + O.O80 1899 230 29 5 .88 + 48.000 30 8 17 25 .04 + 0.082 1900 331 21 .56 49.00 I 31 8 33 59'-88 + 0.085 [55] TABLE XL CONCLUDED. The Mean Anomaly. MOTION. MOTION. n. In n Minutes. In n Seconds. w. In n Minutes. In n Seconds. i o o' o".6 9 o o' o".oi 31 o o' 2 1 ".4 1 o o' o". 3 6 z 1.38 o .02 32 22 .11 0-37 3 2 .07 o .03 33 22 .80 0.38 4 2 .76 o .05 34 23 -49 o-39 5 3-45 o .06 35 24 .18 o .40 6 4-H o .07 36 24.87 o .41 7 4.84 o .08 37 25 -56 0.43 8 5 -53 o .09 ' 38 26 .25 0.44 9 6.22 o .10 39 26 .94 0.45 10 6 .91 .11 40 27 -63 o .46 n 7 .60 o .13 4* 28 .32 0.47 12 8 .29 o .14 42 29 .01 o .48 13 8 .98 0.15 43 29 .70 0.49 H 9.67 o .16 44 30.40 0.51 15 10 .36 0.17 45 31 .09 0.52 16 n .05 o .18 46 31 -78 0.53 17 n .74 o .20 47 32 .47 0.54 18 12 .43 .21 48 33 -16 o-55 19 13 -'3 O .22 49 33.85 o .56 20 13 .82 o .23 50 34-54 0.57 21 14.51 o .24 5 1 35 . 2 3 0.59 22 15 .20 0.25 S 2 35 .92 o .60 23 15.89 o .26 53 36 .61 o .61 2 4 16.58 o .28 54 37.30 o .62 25 17 .27 o .29 55 37 -99 o .63 26 17 .96 o .30 56 38 .68 o .64 27 1 8 .65 o .31 57 39.38 0.66 28 19-34 o .32 58 40.07 o .67 29 20 .03 0.33 59 40.76 0.68 30 2O .72 0.34 60 41 .45 o .69 [56] TABLE XII. Equation of the" Centre. Argument: The Correfted MearT Anomaly, M.* M. D.I' M. D.I' M. D.I' o o' 10 20 3 40 5 o o' o".oo o 5 59 .61 o ii 59 .22 o 17 58 .81 o 23 58 .38 o 29 57 .92 35.961 35.961 35. 9 5 9 35.957 35.954 35. 9 5i 8 o' IO 20 3 40 50 445' 2 5"- 22 4 5 1 16 .17 4 57 6 .77 5 2 57 .00 5 8 46 .87 5 H 36.35 35.og5 35.060 35.023 34.987 34.948 34.911 1 6 o' 10 20 30 40 50 9i7'34"-79 9 23 i .32 9 28 27 .19 9 33 5 2 -41 9 39 16 .96 9 44 4 -84 32.653 32.587 32.522 32.455 32.388 32.320 I 10 20 30 35 57 -43 o 41 56 .89 o 47 56 .29 53 55 -65 35.946 35.940 35. 9 36 35.929 9 o IO 20 30 5 20 25 .46 5 26 14 .17 5 32 2 .49 5 37 5 -4 34.871 34.832 34-7QI 17 o 10 20 3 9 50 4 .04 9 55 26.56 10 o 48 .38 1069 .52 32.252 32.182 32.H4 32.044 40 50 o 59 54 .94 1 5 54-15 35.921 35.911 40 5 5 43 37 -9 5 49 24 .99 34.709 34.666 40 5 10 ii 29 .96 10 16 49 .70 31.974 31.903 2 i ii 53 .26 35. 9 o3 IO 5 55 ii -65 34.623 18 o 10 22 8 .73 3i.832 10 2O i 17 52 .29 i 2 3 5i - 2 3 35.894 35.884 10 20 6 o 57 .88 6 6 43 .66 34.578 34.535 IO 20 10 27 27 .05 10 32 44 .64 31.759 31.687 30 40 i 29 50 .07 i 35 4 8 -80 35.873 35.861 30 40 6 12 29 .01 6 1 8 13 .91 34.490 34.443 30 40 10 38 i .51 10 43 17 .65 3i.6i4 3i.54i 5 i 41 47 .41 35.848 50 6 2 3 58 -34 34.3 9 8 5 10 48 33 .06 31.467 3 i 47 45 -89 35.835 II 29 42 .32 34.35i 19 o i 53 47 -73 3i 3 3 IO i 53 44 - 2 4 35.820 IO 6 35 2 5 -83 34-3o2 10 10 59 i .66 3 3 20 i 59 4 2 -44 35.8o6 20 6 41 8 .85 34.255 20 ii 4 14 .83 3 i. 243 3 40 5 2 5 40 .50 211 38 .40 2 17 36 .13 35.790 35.773 35.757 30 40 5 6 46 51 .40 6 5 2 33 -46 6 58 15 .01 34.206 34.155 34.106 3 40 50 ii 9 27 .26 ii 14 38 .93 ii 19 49 .84 31.167 31.091 3i.oi4 4 10 20 30 2 23 33 .70 22931 .09 2 35 28 .29 2 41 25 .30 35.739 35.720 35.701 35.68i 12 O 10 20 30 7 3 56 .07 7 9 36 .61 715 1 6 .64 7 20 56 .15 34.o54 34.oo3 33. 9 5i 33.8oq 2O 10 20 3 ii 24 59 .98 ii 30 9 -35 ii 35 37 -93 1 1 40 25 .74 30.937 3o.858 30.781 40 2 47 22 .11 35.66i 40 7 26 35 .14 V" 33.845 40 ii 45 3 2 -77 3o.623 50 2 53 18 .72 35.63 9 5 7 3 2 i3 -59 33.791 5 ii 50 39 .00 3o.544 r o IO 2 59 15 .11 3 3 ii .28 35.617 35.594 13 o 10 7 37 5i -5 7 43 2 8 .87 33. 7 3 7 33.68i 21 10 ii 55 44-44 12 o 9 .08 3o.464 3o.384 20 3 13 7 -22 35.5 7 o 20 7 49 5 -68 33.626 2O 12 5 52 .92 3o.3o3 3 40 3 17 2 .92- 3 22 58 .38 35.546 35.521 30 40 7 54 4i -94 8 o 17 .63 33.56 9 33.5i2 3 40 12 10 55 .95 12 15 58 .l6 30.221 3o.i42 50 3 2g 53 -59 35.495 5 8 5 5 2 -75 33.454 5 12 20 59 .58 6 o 3 34 48 -54 35.468 14 o 8 ii 27 .29 33.396 22 o 12 26 .17 20.076 IO 20 3 3 4 43 -22 3 4 6 37 -63 3 5 2 3i -76 35.441 35.4i3 35.385 10 20 30 8 17 i .25 8 22 34 .62 8 28 7 .40 33.337 33.278 33.2i8 10 20 30 12 3 59 -93 12 35 58 .86 12 40 56 .96 77 / 29.893 29.8lO 20.728 40 3 5 8 25 .61 35.355 4 8 33 39.58 33.i58 40 12 45 54.24 7 / 29.641 50 4 4 19 .16 35.325 50 8 39 ii .16 33.097 5 12 50 50 .65 29. 558 7 o 4 10 12 .41 35.294 15 8 44 4 2 -13 33.o35 23 o 12 55 46.23 20 473 I 10 4 16 5 -35 35.263 IO 8 50 12 .48 32.973 10 13 o 40 .96 "V"H fv 29-388 20 4 2 i 57 -98 35.23i 20 8 55 42 .21 32.910 20 13 554-84 2g.3o3 3 4 2 7 5 - 2 9 35.198 3 9 i ii -31 32.847 30 13 10 27 .87 29.216 40 4 33 4 2 - 2 7 35.i65 40 9 6 .39 -78 32. 7 83 40 13 15 20 .03 5 4 39 33 -9 2 35.i3o 5 9127 .61 32.718 5 13 20 1 I .33 29.044 8 o 4 45 2 5 - 22 16 o 9 17 34-79 2 4 o T 3 2 5 i -77 *If M. is >i8o, take 360 M as Argument, and the fign of the Equation of the Centre negative. [571 TABLE XII. CONTINUED. Equation of the Centre. M. 24 o' 10 i 3 2 5 ' 1*77 13 29 51 -33 D.I' 28.956 28.869 M. 32 o' 10 17 3 25 .28 D.I' 24.427 24.327 M. 40 o' 10 i955'33"-i9 19 58 48 .02 D.I' 19.482 19.379 20 13 34 40 .02 28.781 20 17 7 28 .55 24.226 20 20 2 I .8l 19.274 30 13 39 27 .83 28.693 3 17 ii 30 .81 24.126 30 20 5 14.55 19.169 40 13 44 14.76 28.695 4 17 15 32 .07 24.025 4 20 8 26 .24 19.065 50 13 49 o .81 28.5i6 50 17 19 32 .32 23.925 50 20 II 36 .89 18.960 25 o 13 53 45 -97 28.427 33 o 17 23 31 .57 23.823 41 o 20 14 46 .49 18.855 10 20 13 58 30 .24 14 3 13 .61 28.337 28.247 10 20 17 27 29 .80 17 31 27 .03 23.723 23.621 10 20 20 17 55 -4 20 21 2 .54 18.750 18.645 30 14 7 56 .08 28.i58 30 17 35 23 .24 23.520 3 20 24 8 .99 18.540 40 14 12 37 .66 28.067 40 17 39 18 .44 23.418 40 20 27 14 .39 18.436 5 H 17 l8 -33 27.976 5 17 43 12 .62 2 3.3i 7 50 20 30 18 .75 i8.33o 26 o 14 21 58 .09 27.885 34 o '7 47 5 -79 23.215 42 o 20 33 22 .05 18.226 10 14 26 36 .94 27.793 10 7 5 57 -94 23.112 10 20 36 24 .31 18.120 20 14 31 14.87 27.702 20 17 54 49 .06 23.011 20 20 39 25 .51 18.016 30 40 50 14 35 51 .89 14 40 27 .99 1-4 45 3 .16 27.610 27.517 27.425 3 40 50 17 58 39 .17 18 2 28 .26 18 6 16 .32 22.909 22.806 22.704 30 4 5 20 42 25 .67 20 45 24 .7 8 2O 48 22 .84 17.911 17.806 17.701 27 o H 49 37 -4 1 27.332 35 o 18 10 3 .36 22.601 43 o 20 51 19 .85 17.596 10 14 54 10 .73 27.239 10 18 13 49 .37 22.498 10 20 54 15 .81 17.492 20 14 58 43 .12 27.145 20 18 '7 34-35 22.3g6 20 20 57 10 .73 17.387 30 15 3 H-57 27.052 3 1 8 21 1 8 .31 22.293 3 21 o 4 .60 17.282 4 5 15 7 45 .09 15 12 24 .67 26. 9 58 26.863 40 50 18 25 i .24 18 28 43 .13 22.189 22.087 40 5 21 2 57 .42 21 5 49 .20 17.178 17.073 28 o 10 15 16 43 .30 15 21 IO .98 26.768 26.674 36 o 10 1 8 32 24 .00 18 36 3 .83 2i. 9 83 21.880 44 o 10 21 8 39 -93 21 II 29 .6l 16.968 16.864 20 15 25 37 .72 26.578 20 i 8 39 42 .63 21.776 20 21 H 8 - 2 5 16.759 30 15 3 3 -5 26.483 3 1 8 43 20.39 21.673 3 21 17 5 - 8 4 16.655 40 15 34 z8 -33 26.387 40 1 8 46 57.12 21.569 40 21 19 52 .39 1 6.55o 50 15 38 52 .20 26.292 50 18 50 32 .81 21.466 50 21 22 37 .89 16.446 29 o 15 43 15 .12 26.195 37 o 18 54 7 .47 21.362 45 o 21 25 22 .35 16.341 10 20 15 47 37 -07 15 51 58 .06 26.099 26.oo3 10 20 1 8 57 41 .09 19 i 13 .67 21.258 2i.i54 IO 20 21 28 5 .76 21 30 48 .13 16.237 i6.i33 30 40 15 56 1 8 .09 16 o 37 .15 25.906 25.809 30 4 19 4 45 .21 19 8 15 .71 2i.o5o 20.946 30 4 21 33 29 .46 21 3 6 9 -75 16.029 15.925 50 16 4 55 .24 25.71 1 5 19 ii 45 .17 20.842 5 21 38 49 .00 i5.82o 30 o IO 16 9 12 .35 i 6 13 28 .49 25.6i4 38 o 10 1 9 '5 i3 -59 19 1 8 40 .97 20.738 2o.634 46 o 10 21 41 27 .20 21 44 4-3 6 15.716 i5.6i2 20 30 40 16 17 43 .64 16 21 57 .82 l6 26 II .02 25.4i8 25.320 25.221 20 3 40 19 22 7 .31 19 25 32 .60 19 28 56 .84 20.529 20.424 2O.32O 20 3 40 21 46 40 .48 21 49 15 .56 21 51 49 .60 i5.5o8 i5.4o4 i5.3oi 5 16 30 23 .23 25.123 50 19 32 20 .04 2Q.2I6 5 21 54 22 .6l 15.196 31 o 16 34 34.46 25.O24 39 19 35 42 .20 20.112 47 o 21 56 54.57 15.093 10 1 6 38 44 .70 24.924 10 19 39 3 -32 2O.OO7 10 21 59 25 .50 14.989 20 16 42 53 .94 24.826 20 19 42 23 .39 19.902 20 22 i 55 .39 14.887 30 4 50 16 47 2 .20 16 51 9 .47 16 55 15 .74 24.727 24.627 24.527 3 40 50 19 45 42 .41 19 49 o .38 19 52 17 .31 19.797 19.693 19.588 3 40 5 22 4 24 .26 22 6 52 .08 22 9 18 .87 s 14.782 14.679 14.575 32 o 16 59 21 .01 40 o 19 55 33 -19 _,. o 22 1 1 44 .02 [58] TABLE XII. CONTINUED. Equation of the Centre. M. D. i' M. D. i' M. D. i' 48 o' IO 20 3 22Il'44".62 22 14 9 .35 22 16 33 .04 22 18 55 .70 14-473 14.369 14.266 14.163 56 o' IO 20 3 ti A 8' -7 A" T-I 23 4 4 // 23 50 i .17 23 5i 3 6 -59 23 53 ii .04 9.640 9.542 9.446 ' 9.348 64 o' 10 20 3 24 48 30 .27 24 49 20 .76 24 50 10 .36 5.i38 5.o49 .4.960 4.871 40 5 49 o IO 22 21 17 .33 22 23 37 .92 22 25 57 .49 22 28 l6 .02 14.069 13.967 13.853 40 5 57 o 10 23 54 44 -52 23 56 17 .02 23 57 4 8 .5 6 23 59 19 .12 9.260 9. 1 54 9.066 8.960 40 50 65 o 10 24 50 59 .07 24 51 46 .88 24 5 2 33 -8i 2453 19.85 4.781 4.693 4.604 4.5i5 20 22 30 33 .53 1 3. 649 20 24 o 48 .72 8.864 20 24 54 5 .00 4.427 30 4 50 22 32 50 .02 22 35 5 -49 22 37 J 9 -94 i3.547 i3.445 1 3. 343 3 40 5 24 2 17 .36 24 3 45 .04 24 5 ii .75 8.768 8.671 8.676 3 40 50 24 54 49 .27 24 55 32 .66 24 56 15 .18 4.339 4.262 4.164 50 o 10 22 39 33 -37 22 4 1 45 -77 i3.24o 58 o 10 24 6 37 -5 1 24 8 2 .30 8.479 8.384 66 o 10 24 56 56 .82 24 57 37 -58 4.076 ^ nRn 20 22 43 57 -H i3.o36 20 24 9 26 .14 8.288 20 24 58 17 .47 J.9O9 3.901 3 4 22 46 7 .50 22 48 l6 .84 12.934 12.832 3 40 24 10 49 .02 24 12 10 .95 8.193 8.097 30 40 24 58 56 .48 24 59 34 .62 3.8i4 3.727 5 22 50 25 ,l6 5 24 13 31 .92 8.oo3 50 25 on .89 3f . 12.731 .641 51 o IO 22 52 32 .47 22 54 38 .76 12.629 12 527 59 o 10 24 H 5 1 -95 24 1 6 n .03 7.908 7.8i3 67 o 10 25 o 48 .30 25 i 23 .84 3.554 3.468 20 22 56 44 .03 12.426 20 24 17 29 .16 7.718 20 25 i 58.52 3.382 3 22 58 48 .29 12.325 30 24 1 8 46 .34 7.624 30 2 5 2 3 2 -34 3.296 40 23 o 5 1 -54 12.224 40 24 2O 2 .58 7.53o 40 2 5 3 5 -3 3.210 5 23 2 53 .78 12.123 5 24 21 17 .88 7-435 50 2 5 3 37 -40 3.125 52 o 23 4 55 - OI 12.022 60 o 24 22 32 .23 7-341 68 o 25 4 8 .65 3.o3g 10 23 6 55 .23 11.921 10 24 23 45 - 6 4 7.248 10 25 4 39 .04 2.064 20 23 8 54.44 1 1 .820 20 24 24 58 .12 7.164 20 25 5 8.58 *.y* yi * 2.869 3 23 10 52 .64 II.72O 3 24 26 9 .66 7.061 30 25 5 37 -27 2.784 40 23 12 49 .84 II.62O 40 24 27 20 .27 6.967 40 25 6 5 .11 2.700 5 23 14 46 .04 I l.Slg 5 24 28 29 .94 6.876 5 25 6 32 .11 / 2.6i5 53 o 23 16 41 .23 11.419 61 o 24 29 38 .69 6.782 69 o 25 6 58 .27 2.53i 10 23 18 35 .42 1I.32O 10 24 30 46 .51 6.689 IO 25 7 23 .58 2.447 20 23 20 28 .62 11.219 20 24 3 1 53 -4 6.696 20 25 7 48 .05 2.363 3 23 22 20 .8l 1 1. 1 20 3 2432 59 -36 6.5o4 30 25 8 ii .68 2.280 4 23 24 12 .01 11.020 40 2 4 34 4 -4 6.412 40 25 8 34.48 2.196 50 23 26 2 .21 IO.92O 5 2435 8.52 6.319 50 25 8 56 .44 2.II3 54 o 23 27 5 1 -4 1 10.821 62 o 24 36 n .71 6.228 70 o 25 9 17 -57 2.o3o IO 23 29 39 .62 10.721 10 2437 13 -99 6.i36 ' 10 . 25 9 37 -87 947 20 23 3 1 26 .83 10.623 20 2438 15 -35 6.044 20 25 9 57 -34 7^ / .864 3 23 33 13 .06 10.524 30 24 39 1 S -79 6.962 30 25 10 15 .98 .782 40 23 34 5 8 -3 10.425 40 2440 15 .31 5.862 40 25 10 33 .80 .699 5 23 3 6 4 2 .55 IO.327 5 2441 13 -93 5.772 50 2 5 I0 5 -79 .617 55 o 23 38 25 .82 10.228 63 o 24 42 ii .65 5.68o 71 o 25 1 1 6 .96 .5'35 10 23 40 8 .10 10.129 10 24 43 8 .45 5.58g 10 25 I I 22 .31 .453 20 23 4i 49 -39 io.o3i 20 24 44 4 -34 5.499 20 25 II 36 .84 .372 3 23 43 29 .70 9.933 3 24 44 59 -33 5.409 3 25 II 50 .56 .291 40 23 45 9 -03 9-836 . 40 24 45 53 .42 5.3i8 40 2 5 12 3 .47 200 50 23 4 6 47 -39 - _OQ 50 24 46 46 .60 50 25 12 15 .56 Q.^OO 5.229 .129 56 'o 23 48 24 .77 64 o 24 47 38 .89 72 o 25 12 26 .85 [59] TABLE XII. CONTINUED. Equation of the Centre. M. 72 o' 25i2'26".85 D.I' 1.047 M. 80 o' 25 6'i 3 '. 3 o D.I' 2.607 M. 88 o' 2 4 32'27". 5 8 D.I' 5.83o IO 20 25 12 37 .32 25 12 46 .99 0.967 0.886 IO 20 25 5 47 -23 25 5 20 .44 2.679 2.750 10 20 24 31 29 .28 24 3 3 .36 5.892 5.955 30 | 25 12 55 .85 0.806 3 25 4 52 .94 2.822 30 24 29 30 .81 6.018 40 25 13 3 -9 1 O.727 40 25 4 24.72 2.892 40 24 28 30 .63 6.080 5 25 13 ii .18 v " / * 1 O.646 5o 25 3 55 -80 2.962 50 24 27 29 .83 6.142 73 o 25 13 17 .64 O.567 81 o 25 3 26 .18 3.o33 89 o 24 26 28 .41 6.204 10 25 13 2 3 -31 w / 0.487 IO 25 2 55 .85 3.io4 10 2425 26.37 6.265 20 25 13 28 .18 ^ 1 0.408 20 25 2 24 .8l 3.174 20 24 24 23 .72 6.326 30 40 25 13 32 .26 2 5 13 35 -55 0.829 Q.25O 3 .4 25 i 53 .07 25 I 20 .63 3.244 3.3i3 30 40 24 23 20 .46 24 22 l6 .58 6.388 6.449 5 25 13 38 .05 O.I7I 50 25 o 47 .5 3.383 50 24 21 12 .09 6.5io 74 o 25 13 39 .76 rf. i 0.098 82 o 25 o 13 .67 3.453 90 o 24 20 6 .99 6.571 10 25 13 40 .69 0.014 IO t r\ 2459 39 -H T A c n i t~\ *? 3.522 10 *} rt 24 19 I .28 7 A I n C A Cifl 6.632 20 25 13 40 .83 0.064 4*\j 2 4 59 3 -9 2 3.591 zu Z 4 * 7 54 -9 6.692 30 25 13 40.19 0.142 3 24 58 28 .01 3.66o 30 24 1 6 48 .04 6. 7 5i 40 2 5 13 38.77 0.219 40 24 57 5' 1 -41 3.729 40 24 15 40 .53 6.812 5 2 5 *3 36.58 0.297 50 24 57 14.12 3.797 50 24 H 32 .41 6.871 75 o 25 13 33 .61 0.374 83 o 24 56 36.15 3.866 91 o 24 13 23 .70 6.932 IO 25 13 29.87 0.452 IO 2 4 55 57 -49 3.934 10 24 12 14 .38 6.991 20 25 3 25 .35 0.528 20 2455 18.15 4.00 1 20 24 1 1 4 .47 7.o5i 3 25 13 20 .07 o.6o5 3 2454 38 .14 4.069 30 24 9 53 -96 7.109 40 25 13 14 .02 0.682 40 24 53 57 .45 4.i37 40 24 8 42 .87 7.169 5 25 13 7 .20 0.759 50 24 53 1 6 .08 4.204 50 24 7 31 .18 7.227 76 o 25 12 59.6l 0.835 84 o 2452 34.04 4.272 92 o 24 6 1 8 .91 7.286 10 25 12 51 .26 0.911 IO 24 51 51 .32 4.338 10 24 5 6.05 s 7.345 20 25 12 42 .15 0.987 20 2451 7.94 4.406 20 24 3 52 .60 7-4o3 3 25 12 32 .28 .062 3 24 50 23 .88 4.472 3 24 2 38 .57 7.461 40 25 12 21 .66 .i37 40 2449 39 .16 4.538 40 24 i 23 .96 7.520 50 25 12 IO .29 ** / .213 50 2448 53 78 4.6o5 50 24 o 8 .76 7.577 77 o 25 II 58 .l6 .288 85 o 2448 7-73 4.671 93 o 23 58 52 -99 7.635 10 20 25 ii 45 .28 25 ii 31 .65 .363 .437 10 20 24 47 21 .02 2446 33 .65 4.737 4.802 10 20 23 57 36 .64 23 56 19 .72 7.692 7.750 30 25 ii 17 .28 .5l2 30 2445 45 - 6 3 4.868 30 2355 2.22 7.807 40 25 I I 2 .16 .586 40 24 44 56 .95 4.933 40 23 53 44 -'5 7.863 5 25 10 46 .30 .660 50 24 44 7 .62 4-999 50 23 52 25 .52 7.921 78 o 25 10 29 .70 .735 86 o 2443 i7 -63 5.o64 94 o 2351 6.31 7-977 10 25 10 12 .35 .808 10 24 42 26 .99 5.129 10 23 49 4 6 -54 8.o34 20 25 9 54.27 .882 20 2441 35 .70 5.i 9 3 20 23 48 26 .20 8.090 30 25 9 35 -45 .955 30 24 40 43 -77 5.258 3 23 47 5 -30 8.146 40 25 9 '5 -9 V 2.028 40 2439 5 1 -'9 5.322 40 23 45 43 -84 8.202 50 25 8 55 .62 2. IOI 50 2438 57 -97 5.386 50 23 44 21 .82 8.258 79 o 25 8 34 .61 2.174 87 o 2438 4.11 5.45o 95 o 23 42 59 -24 8.3i3 10 25 8 12 .87 2.247 10 2437 9.6-1 5.5i4 IO 23 4 1 3 6 - 11 8.36 9 20 25 7 5 .4o ~- / 2.32O 20 2436 14.47 5.578 20 23 40 12 .42 8.425 3 25 7 27 .20 2.391 30 2435 18 .69 / 5.641 30 23 38 48 -17 8.479 40 25 7 3 .29 2.464 40 24 34 22 .28 5.7o3 40 23 37 23 .38 8.535 5 25 6 38 .65 2.535 50 24 33 25 .25 v, i w 5.767 5 23 36 8 .03 8.589 80 o 25 6 13 .30 88 o 2432 27 .58 96 o 23 34 32 .H [60] TABLE XII. CONTINUED. Equation of the Centre. M. D.I' M. D. i' M. D. i' 96 o' IO 2 3 33 5 -70 8.644 8.698 104 o' 10 22I5' 3 6".26 22 13 45 .47 11.079 1 1.126 112 0' 10 2O 36 22 .15 13.170 13.2IO 20 2 3 31 38 .72 8.753 20 22 II 54 .21 11.174 20 20 34 io .05 i3.25o 3 40 23 30 ii .19 23 28 33 .12 8.807 8.860 3 40 22 10 2 .47 22 8 10 .27 1 1. 2 2O 11.266 30 4 20 31 57 .55 20 29 44 .66 13.289 13.329 50 '23 27 i 4 ..52 8.915 5 22 6 17 ,6l n.3i3 5 20 27 31 .37 13.369 97 o 23 25 45 .37 8.968 105 o 22 4 24 .48 11.359 113 o 20 25 17 .68 1 3.4o8 IO 20 30 23 24 15 .69 23 22 45 .47 23 21 14 .72 9.022 9.075 9.128 10 20 30 22 2 30 .89 22 O 36 .85 21 58 42.34 11.404 n.45i 11.496 IO 20 30 20 23 3 .60 20 20 49 .13 20 18 34 .26 i3.447 13.487 i3.526 40 2 3 19 43 -44 9.181 40 21 56 47 -38 11.542 40 20 1 6 19 .00 13.565 50 23 1 8 ii .63 9-234 50 21 54 5i -9 6 11.587 5 20 14 3 -35 i3.6o3 98 o 23 16 39 .29 9.287 1 06 o 21 52 56 .09 n.633 114. o 20 ii 47 .32 i3.642 10 23 15 6 .42 9.339 IO 21 50 59 .76 11.678 - io 20 9 30 .90 i3.68o 20 2 3 13 33 -03 9.392 20 21 49 2 .98 11.723 20 20 7 14 .10 13.719 3 23 ii 59 -ii 9-444 30 21 47 5 .75 11.768 30 20 4 56 .91 13.757 . 40 23 10 24 .67 9.496 40 21 45 8 .07 n.8i3 40 20 2 39 .34 13.795 5 2 3 8 49 .71 9.548 5 21 43 9 -94 11.857 50 2O O 21 .39 13.833 99 23 7 14.23 9.600 107 o 21 41 II .37 11.902 115 o 19 58 3 .06 13.871 10 23 5 38 .23 9.65i IO 21 39 12.35 11.946 10 19 55 44-35 13.909 20 3 23 4 i -72 23 2 24 .69 9 . 7 o3 9.754 20 30 21 37 12 .89 21 35 12 .99 11.990 I2.o34 20 30 19 53 25 .26 19 51 5 .80 13.946 13.984 ' 4 5 2 3 o 47 .15 22 59 9 .10 9-8o5 9 .856 40 50 21 33 12 .65 2131 II .87 12.078 12.122 40 50 19 48 45 .96 19 46 25 .76 14.020 i4-o58 lop o 22 57 3 -54 9.907 108 o 21 29 IO .65 12.166 116 o 19 44 5 -18 14.095 10 22 55 51 . 47 9-958 10 21 27 8 .99 12.209 IO 19 41 44 .23 I4.i32 20 22 54 II .89 10.008 20 21 25 6 .90 12.253 20 19 39 22 .91 14.169 30 22 52 31 .8l io.o58 30 21 23 4.37 12.295 30 19 37 i .22 i4-2o5 40 22 50 51 .23 10.109 40 21 21 I .42 12.338 40 19 34 39 -17 14.242 50 22 49 10 .14 io. 1 58 5 21 1 8 58 .04 12.382 50 19 32 26.75 14.279 IOI 22 47 28 .56 f 10.209 109 o 21 16 54 .22 12.424 117 o 19 29 53 .96 i4.3i5 10 22 45 46 -47 io.258 10 21 14 49 .98 12.467 10 19 27 30 .81 i4.35i 20 22 44 3 .89 io.3o8 20 21 12 45 .31 12.509 20 19 25 7 -3 14.387 30 22 42 2O .8l 10.357 30 21 IO 40 .22 i2.55i 30 19 22 43 .43 14.422 40 5 22 40 37 .24 22 38 53 .18 10.406 10.455 40 5 21 8 34.71 21 6 28 .78 12.593 12.636 4 50 19 20 19 .21 19 17 54 - 6 3 14-458 14.494 IO2 O 22 37 8 .63 io.5o4 IIO M 4 22 .42 12.678 118 o 19 15 29 .69 i4-53o 10 22 35 23 -59 10.553 10 21 215 .64 12.719 10 19 i-3 4-39 14.565 20 22 33 38 .06 10.602 20 21 o 8 .45 12.761 20 19 io 38 .74 14.601 3 22 31 52 .04 io.65o 30 20 58 .84 I2.8o3 30 19 8 12 .73 14-635 40 50 22 30 5 .54 22 28 l8 .55 10.699 10.747 40 50 20 55 52 .81 20 53 44-37 12.844 12.885 40 50 19 5 46 .38 19 3 19 .67 14.671 103 o IO 20 22 26 31 .08 22 24 43 .13 22 22 54 .71 10.795 10.842 10.890 III O 10 20 20 51 35 .52 20 49 26 .26 20 47 1 6 -59 12.926 12.967 i3.oo8 1 19 o 10 20 19 o 52 .62 18 58 25 .22 18 55 57 -47 14.740 I4-77 5 14.809 3 22 21 5 .8l /" 10.938 30 20 45 6 .51 i3.o48 3 18 53 29 .38 14.844 40 22 19 1 6 .43 10.985 4 20 42 56 .03 13.089 40 1851 o .94 14.878 50 22 17 26 .58 II.032 50 20 40 45 .14 13.129 50 18 48 32.16 14.912 104 o 22 15 36 .26 112 20 38 33 -85 120 1 8 46 3 .04 [61] TABLE XII. CONTINUED. Equation of the Centre. M. D. i' M. D. i' M. D. i' 120 O' i846' 3 '.04 128 o' I640'27*.22 136 o' i423' 56*.7o IO 20 3 40 50 '8 43 33 -57 18 41 3 .77 18 38 33 -63 18 36 3 .15 18 33 32 -34 14.947 14.980 i5.oi4 i5.o48 i5.o8i 10 20 3 40 5 16 37 42 .83 16 34 58 .16 16 32 13 .20 16 29 27 .97 1 6 26 42 .45 16.489 16.467 16.496 16.523 16.552 J 10 20 30 40 5 14 20 59 .97 14 1 8 3 .02 14 15 5 .83 14 12 8 .38 14 910 .77 17.673 17.695 17.719 17-745 17.765 121 10 18 31 i .20 18 28 29 .72 i5.i48 129 o 10 16 23 56 .66 16 21 10 .59 16.579 16.607 it\ M*S 137 o 10 14 612 .90 14 3 14 .80 17.787 17.810 20 3 40 5 18 25 57 .91 18 23 25 .77 18 20 53 .30 18 18 20 .50 i5.2i4 15.247 1 5. 280 20 3 40 5 16 18 24 .24 16 15 37 .62 16 12 50 .73 16 10 3 .56 1 U.UJ J 16.662 16.689 16.717 20 30 40 5 14 o 1 6 .48 '3 57 17 -94 13 54 19 .17 1351 20 .18 17.854 17.877 17.899 122 10 2O 30 40 5 18 15 47.38 18 13 13 .93 1 8 10 40 .15 1 8 8 6 .05 18 5 31 .63 18 2 56 .89 i5.3i2 15.345 15.378 i5.4io 15.442 15.474 i5.5o6 130 o 10 20 30 40 5 16 7 16 .12 16 4 28 .41 1 6 i 40 .43 15 58 52 .18 15 56 3 .67 1553 14 .89 16.744 16.771 16.798 16.825 i6.85i 16.878 16.904 138 o 10 20 30 40 50 13 48 20.97 '3 45 2I -54 13 42 21 .89 13 39 22 .02 13 36 21 .93 '3 33 21 .63 17.921 17.943 17.965 17.987 18.009 18.080 i8.o52 123 o 10 20 18 o 21 .83 7 57 4 6 -45 17 55 10 .76 15.538 15.569 i5.6oi 131 o 10 20 15 50 25 .85 ! 5 47 36.54 1 5 44 46 .97 16.931 16.957 16.988 139 o 10 20 13 30 21 .11 13 27 20 .38 13 2 4 I 9 .43 18.073 i8.o 9 5 30 40 5 7 S 2 34.75 17 49 58 .42 17 47 21 .78 i5.633 15.664 15.695 30 40 5 15 41 57 .14 !5 39 7 -05 15 36 16 .70 17.009 I7.o35 17.061 30 40 50 13 21 18 .28 13 18 16 .92 '3 15 15 -35 18.186 i8.i5 7 18.179 124 o 17 44 44.83 15.726 132 o 15 33 26 .09 17.087 140 o 13 12 13 .56 18.200 10 1742 7.57 15.758 IO 15 30 35 .22 17.112 10 13 9 ii .56 18.220 20 17 39 29 .99 15.788 20 15 27 44.10 17.188 20 13 6 9.36 18.241 30 17 36 52 .1 1 15.819 30 15 24 52 .72 17.163 3 13 3 6.95 18.261 40 17 33 13 .92 i5.85o 4-0 15 22 I .09 17.188 40 '3 o 4-34 18.281 50 17 3i 35 -42 i5.88i 50 15 19 9 .21 17.214 5 12 57 i .53 18.802 125 o 10 20 17 28 56 .61 17 26 17 .50 17 23 38 .09 15.911 1 5.941 15.971 133 o 10 20 15 1 6 17 .07 15 13 24 .68 15 10 32 .04 17.239 17.264 17.289 141 o 10 20 12 53 58 .51 12 50 55 .28 12 47 51 .86 18.323 18.842 18.861 30 17 20 58 .38 16.001 30 '5* 7 39 -'5 / TT 17.3l4 30 12 44 48 .25 18.382 40 17 18 18 .37 i6.o32 40 15 4 46 .01 17.338 40 12 41 44.43 18.402 50 17 15 38 .05 16.061 50 15 i 52 .63 17.363 50 12 38 40 .41 18.422 126 o 10 17 12 57 .44 17 10 16 .53 16.091 16.121 134 o 10 14 58 59 .00 1456 5.12 17.388 17.412 142 o 10 12 35 36.19 12 32 31 .78 18.441 18.461 20 3 17 7 35 -32 17 4 53 .82 16. i5o 16.179 20 30 1453 ii .00 14 50 16 .65 17.435 17.460 20 3 12 29 27 .17 12 26 22 .37 18.480 i8.5oo 40 50 17 212 .03 1 6 59 29 .94 16.209 i6.238 40 50 14 47 22 .05 14 44 27 .22 17.483 17.508 40 5 12 2 3 17 .37 12 20 12 .19 i8.5i8 18.538 127 o 10 20 3 16 56 47 .56 1654 4.89 16 51 21 .93 16 48 38 .68 16.267 16.296 16.325 i6.354 135 o 10 20 30 1441 32 .14 14 38 36 .82 1435 41 .27 14 32 45 .48 17.532 17.555 17.579 17.603 H3 o IO 20 30 12 17 6 .81 12 14 I .24 12 10 55 .48 12 7 49 -53 i8.55 7 18.576 18.595 18.614 40 16 45 55 .14 16.882- 40 14 29 49 .45 17.626 40 12 4 43 -39 18.682 50 16 43 ii .32 16.410 50 14 26 53 .19 n.64o 50 12 i 37.07 i8.65o 128 o 16 40 27 .22 136 o 14 23 56 .70 / ~*+y 144 o ii 58 30.57 [62] TABLE XII. CONTINUED. Equation of the Centre. M. D.I' M. D.l' M. D.I' 144 o' 10 1 158' 30^.57 ii 55 23 .88 18.669 18.688 152 o' 10 925' 58"45 9 22 43 .99 19.446 io.45o 1 60 o' 10 6 C 4 8' 2 ".52 6 44 42 .36 20.016 20.026 20 30 40 50 ii 52 1 7 .00 1 1 49 9 .94 I I 46 2 .70 1 1 42 55 .28 18.706 18.724 18.742 18.760 20 30 40 50 9 19 29 4.0 91614 .66 9 I2 59 -79 9 9 44 .78 19.474 19-487 19.501 20 3 40 50 6 41 22 .10 6 38 i .75 6 34 4i -3 6 31 20 .76 2o.o35 2o.o45 2o.o54 20 o63 145 o 10 20 30 40 ii 39 47 .68 ii 36 39 .90 ii 33 3i -94 ii 30 23 .80 ii 27 15 .49 18.778 18.796 18.814 i8.83i 18.848 153 o 10 20 30 40 9 6 29 .63 9 3 14.35 8 59 58 -94 8 5 6 43 -39 8 53 27 .71 19.528 19.541 19.555 19.568 19.581 161 o 10 20 30 40 6 28 o .13 6 24 39 .40 621 18 .58 6 17 57 .66 6 14 36 .66 20.073 20.082 20.092 20.100 2O.IIO 50 146 o 1 1 24 7 .01 II 20 58 .35 18.866 18.883 50 154 o 8 50 ii .90 8 46 55 .96 19.594 10.607 5 162 o 6 ii 15 .56 6 7 54.38 20.118 20.127 10 20 30 40 50 ii 17 49 .52 ii 14 40 .52 ii ii 31 .34 II 8 22 .00 II 512 .48 18.900 18.918 18.934 i8.g52 18.969 10 20 30 40 5 8 43 39 - 8 9 8 4 23 .69 8 37 7 .36 8 33 5 -9 1 8 3 34-33 19.620 19.633 19.645 ig.658 19.671 10 20 30 40 50 6 4 33 " 6 i ii .75 5 57 50 .30 5 54 28 .76 5 5i 7 .H 20. 1 36 20.145 20. 1 54 20.162 20.170 147 o 10 20 30 4 50 148 o 10 20 30 4 50 II 22 .79 10 58 52 .94 10 55 42 .92 10 52 32 .73 10 49 22 .38 10 46 ii .87 10 43 i .19 10 39 50.35 10 36 39 -35 10 33 28 .19 10 30 16 .87 10 27 5 .39 18.985 19.002 19.019 I9.o35 ig.oSi 19.068 19.084 19.100 19.116 ig.i32 19.148 19.163 155 o 10 20 30 40 50 156 o 10 20 30 40 5 8 27 17 .62 8 24 o .79 8 20 43 .84 8 17 26 .76 8149 .56 8 10 52 .24 8 7 34 .80 8417 .24 8 o 59 .56 7 57 4i -77 7 54 23 .86 751 5 .84 19.683 19.695 19.708 19.720 19.732 19.744 19.756 19.768 19.779 19.791 19.802 19.814 163 o 10 20 30 40 5 164 o 10 20 3 40 50 5 47 45 -44 5 44 23 .65 5 4i i .79 5 37 39 .84 5 34 17 .81 5 30 55 -70 5 27 33 .5i 5 24 1 1 .24 5 20 48 .89 5 17 26.47 5 H 3 -97 5 10 41 -39 20.179 20.186 2o.ig5 20.203 20.211 20.219 20.227 20.235 20.242 20.250 20.258 20.265 149 o 10 20 3 40 50 10 23 53 .76 10 20 41 .97 10 17 30 .02 10 14 17 .92 10 ii 5 .67 10 7 53 .26 19.179 19.195 19.210 19.225 19.241 157 o 10 20 30 40 50 7 47 47 .70 7 44 29 .44 7 41 ii .07 7 37 52.59 7 34 34 .0 7 3i 15 -30 19.826 19.837 19.848 19.859 19.870 19.881 165 o 10 20 30 40 50 5 7 i8.74 5 3 56 .02 5 o 33 .23 4 57 10-36 4 53 47 42 4 5 24 .42 20.272* 20.279 20.287 20.294 2o.3oo 2o.3o8 150 o 10 20 3 40 50 151 o 10 20 30 40 50 10 4 40 .70 10 i 27 .99 9 58 15 -13 9 55 2 .12 9 51 48 .96 9 4 8 35 -65 9 45 22 .20 9 42 8 .60 9 38 54-86 9 35 40 -97 9 33 26 .94 9 29 12 .76 19.271 19.286 19.301 19.316 ig.33i 19.345 19.360 19.374 19.389 19.403 19.418 19.431 158 o 10 20 30 4 50 159 o IO 20 3 40 5 7 27 56 .49 7 24 37 .57 7 21 18 .54 7 17 59 4 7 14 40 .16 7 ii 20 .81 7 8 i .36 7 4 41 .81 7 i 22 .15 658 2 .39 6 54 42 .53 6 51 22 .58 19.892 19.903 19.914 19.924 19.935 19.945 19.955 19.966 19.976 19.986 19.995 20.006 1 66 o 10 20 30 40 50 167 o 10 20 30 4 50 4 47 i -34 4 43 38 .19 4 40 14 .98 4 36 51 .70 4 33 28 .35 4 30 4 .94 4 26 41 .47 4 23 17 .93 4 19 54-33 4 16 30 .67 4 13 6 .95 4 9 43 -17 2o.3i5 20.321 20.328 20.335 20.341 20.347 20.354 2o.36o 20.366 20.372 20.378 20 384 152 o 9 25 58 .45 1 60 o 6 48 2 .52 168 o 4619 .33 [63] TABLE XII. CONCLUDED. Equation of the Centre. M. D.I' M. D.l' M. D.I' 168 o' 10 20 30 40 5 169 o IO 4 6' i 9 ". 3 3 4 2 55 .43 3 59 3i 47 3 5 6 7 46 3 5 2 43 -39 3 49 19 -26 3 45 55 -08 3 4 2 3 - 8 5 20.090 20.396 20.401 20.407 2o.4i3 20.418 20.423 20.428 172 o' 10 20 '' 3 40 5 173 o 10 2 41 6 .45 2 37 4 1 -36 2 34 l6 -23 2 30 51 .06 2 27 25 .86 2 24 O .62 2 20 35 .35 2o.5o5 2Q.5og 2o.5i3 20.517 2O. 520 20.524 20.527 2o.53o 176 o' 10 20 3 40 50 177 o 10 18 55 -58 15 29 .82 12 4 .04 8 38 .24 5 12 43 i i 46 .60 58 20 .76 20.575 20.576 20.578 2o.58o 2o.58i 20.583 20.584 20.585 20 30 40 5 170 o 10 20 3 4 5 171 o 10 20 30 40 50 172 o 339 6.57 3 35 42 .23 3 32 17 - 8 4 3 28 53 .41 3 25 28 .92 322 4.38 3 18 39 .80 3 15 15 -17 31150 .49 3 8 25 .77 35 * -oo 3 i 36 .19 25811 .34 2 54 46 44 2 51^21 .50 2 47 56 .52 2 44 31 .51 20.434 20.439 20.443 2C.449 20.454 20.458 20.463 20.468 20.472 20.477 20.481 20.485 20.490 20.494 20.498 20.501 20 30 40 50 174 o IO 20 30 40 50 175 o 10 20 30 40 50 176 o 2 17 10 .05 2 13 44.71 2 10 19 .34 2 6 53 .94 2 3 28 .51 203 .05 56 37 .56 53 12 .05 49 46 .5 1 46 20 .94 42 55 -35 39 2 9 -74 * 36 4 .10 32 3 8 44 29 12 .76 25 47 .06 I 22 21 .33 20.534 20.540 20.543 20.546 20.549 2o.55i 20.554 20.557 2o.55g 2o.56i 20.564 2o.566 20.568 20.570 20.573 20 30 40 50 178 o 10 20 . 30 40 50 179 o IO 20 3 40 50 r 80 o o 54 54.91 o 51 29 .04 o 48 3.16 o 44 37 .26 o 41 ii .36 37 45 45 34 19-53 o 30 53 .60 o 27 27 .66 o 24 i .71 o 20 35 .76 o 17 9 .81 o 13 43 - 8 5 o 10 17 .89 o 6 51 .93 o 3 25 .96 o o oo .00 20.587 20.588 20.590 20.5go 20.591 2o.5g2 20.593 2o.5g4 20.595 2o.5g5 20.595 20.596 20.596 20.596 20.597 20.596 ' [64] TABLE XIII. Logarithm of the Elliptical Radius Vector. Argument : The True Anomaly, v* t) U p V. i* V. _ V. ^, 0' 0.2597938 o.3 8 0' 0.2605536 32. 1 6 o' 0.2628260 63.3 10 0.2597941 i .0 10 0.2605856 32.6 IO 0.2628893 64.0 20 0.2597951 1.6 20 0.2606182 33.3 20 0.2629533 64.6 3 0.2597967 2.3 3 0.2606515 33.Q 30 0.2630179 65.2 40 0.2597990 3.0 40 0.2606854 34.6 4 0.2630831 65.9 50 0.2598020 3.6 50 0.2607200 35.2 5 0.2631490 66.5 I O 0.2598056 4.3 9 0.2607552 35.0 17 o 0.2632155 AT o 10 0.2598099 5.Q 10 0.2607911 36.5 10 0.2632827 u /* 67.8 20 0.2598149 5.6 20 0.2608276 }-, n 20 0.2633505 68.5 30 0.2598205 6.3 3 0.2608648 O7.2 37 3 0.2634190 60. i 4 0.2598268 6 o 40 0.2609027 o /.y 38.5 40 0.2634881 69.8 5 0.2598337 u.y 7.6 50 0.2609412 39.2 50 0.2635579 70.4 2 0.2598413 8.3 IO O 0.2609804 3n S 18 o 0.2636283 / v>t * IT IO 0.2598496 8 Q 10 0.2610202 09.0 /n ^ 10 0.2636994 71.1 1 T 1 2O 0.2598585 u.y 0.6 20 0.2610607 4*-*. J /i i 20 0.263771 1 71.7 T2 3 30 0.2598681 V' v IO.2 30 o.26nof8 41 * 1 4i.8 30 0.2638434 I**" 73.O 40 0.2598783 IO.O 40 0.261 1436 /o 4 0.2639164 73.6 5 0.2598892 wy ii. 5 50 0.2611861 4*2. J 43.1 50 0.2639900 74.3 3 o 0.2599007 12.2 II 0.2612292 /} O 19 o 0.2640643 /***^* *f / O IO 0.2599129 12 O 10 0.2612730 40.0 // / 10 0.2641392 74-9 75.6 20 0.2599258 *T*T i3.5 20 0.2613174 44.4 45.1 20 0.2642148 76.3 3 - 2 599393 14.2 3 0.2613625 45 7 30 0.264291 1 76.8 40 - 2 599535 14.8 40 0.2614082 **'-' / /.h A 40 0.2643679 77 5 5 0.2599683 i5.5 5 0.2614546 4J.4 47. Q 50 0.2644454 77. J 78.1 4 o 0.2599838 16.2 12 0.2615016 ** /* u X*T -7 20 o 0.2645235 / j 78.8 10 0.2600000 16.8 10 0.2615493 47.7 /Q x 10 0.2646023 20 0.2600168 17.5 20 0.2615977 40.4 20 0.2646817 79-4 80.0 3 40 0.2600343 0.2600525 * F*"* 18.2 1 8.8 30 40 0.2616467 0.2616963 49*O 49.6 5o,3 3 40 0.2647617 0.2648424 80.7 8i.3 5 0.2600713 19.5 50 0.2617466 5i.o 5 0.2649237 82.0 5 0.2600908 2O.I 13 o 0.2617976 'ii fi 21 0.2650057 82.6 IO 0.2601 109 20.8 IO 0.2618492 j i *\j 52 2 10 0.2650883 83.3 20 0.2601317 21.4 20 0.2619014 52 O 20 0.265 1716 83. 9 3 0.2601531 22.1 3 0.2619543 53.6 3 0.2652555 84.5 40 0.2601752 22.7 40 0.2620079 54.2 4 0.2653400 85.2 50 0.2601979 / 23.4 50 0.2620621 54.8 50 0.2654252 85.8 6 o 0.2602213 24.1 14 o 0.2621 169 55.5 22 O 0.26551 10 86.4 10 0.2602454 24.7 10 0.2621724 56.2 10 0.2655974 87 i 20 0.2602701 *-+ / 25.4 20 0.2622286 56.8 2O 0.2656845 07.1 8-T 7 3 0.2602955 26.O 3 0.2622854 IT / 3 0.2657722 07.7 QQ / 40 0.2603215 26.7 40 0.2623428 ^7.4 58.i 40 0.2658606 00.4 8o.O 50 0.2603482 f.\j. i 27.4 5 0.2624009 58.8 5 0.2659496 89.6 7 o 0.2603756 28.0 15 o 0.2624597 'in X 23 o 0.2660392 10 0.2604036 28.7 10 0.2625191 ^y.iv 60 I 10 0.2661295 90. \J 20 0.2604323 BVl / 29.3 20 0.2625792 20 0.2662204 90.9 3 0.2604616 3o.o 30 0.2626399 6l,4 30 0.2663119 9I5 40 0.2604916 3o.i 40 0.2627013 62.0 40 0.2664041 92.2 rO ft 5 0.2605223 ' / 3i.3 50 0.2627633 62 i 50 0.2664969 y ..0 r*3 / 8 o 0.2605536 16 o 0.2628260 \j&. I 24 o 0.2665903 9^*4 * If v. is > 1 80, take 1 80 v. as the Argument. [651 * TABLE XIII. CONTINUED. Logarithm of the Elliptical Radius Vector. V. 24 o' 0.2665903 p V. 32 o' 0.2718109 ? V. 40 o' 0.2784370 p IO 0.2666843 94.0 10 0.2719348 "* 10 0.2785895 rQ - 20 0.2666790 94.7 20 0.2720593 1 24-5 20 0.2787427 IOO. 3 30 4 0.2668743 0.2669702 95.9 rvA A 30 40 0.2721844 0.2723102 I 2 J. I 125.8 126.3 3 40 0.2788964 0.2790507 i53.7 1 54. 3 50 0.2670668 90.0 50 0.2724365 5 0.2792056 154.9 25 o 0.2671640 97.2 __ Q 33 o 0.2725635 127.0 41 o 0.2793610 i55.4 r r IO 0.2672618 97.0 rtft t\ 10 0.2726910 1 27.5 128.2 10 0.2795170 I JO.O llA A 20 0.2673603 QO, J 20 0.2728192 t 08 8 20 0.2796736 1 JO.O 30 0.2674594 99.1 30 0.2729480 I 2O. o 3 0.2798307 157.1 40 50 0.2675591 0.2676595 99-7 100.4 101 .0 40 5 0.2730774 0.2732074 129.4 i3o.o i3o.6 40 5 0.2799884 0.2801467 157.7 i58.3 1 58. 9 26 o 10 0.2677605 0.2678621 ioi. 6 IO2.3 34 o 10 0.2733380 0.2734692 l3l.2 i3i.8 42 o 10 0.2803056 0.2804650 1 5g. 4 20 0.2679644 102.9 20 0.2736010 i32.4 20 0.2806251 160. i 160.6 30 0.2680673 io3.5 3 0.2737334 i33.i 3 0.2807857 4 0.2681708 104.1 40 0.2738665 i33.6 40 0.2809469 lol . 2 5 0.2682749 104.8 5 0.2740001 5 0.281 1086 101.7 162.3 27 o 0.2683797 io5.4 35 o 0.2741343 i34.8 43 o 0.2812709 10 0.2684851 106.0 10 0.2742691 i35.4 10 0.2814338 I O2 .9 i63.4 20 0.268591 1 1 06. 6 20 0.2744045 i36.o 20 0.2815972 164 o 30 40 0.2686977 0.2688049 107.2 IO7.O 30 40 0.2745405 0.2746771 136.6 137.2 30 40 0.2815612 0.2819258 164.6 i65.i 50 0.2689128 /y 1 08. 5 50 0.2748143 137.8 5 0.2820909 165.7 28 o 0.2690213 109.1 36 o 0.2749521 i38.4 44 o 0.2822566 166.2 10 20 30 0.2691304 0.2692401 0.2693505 109.7 110.4 1 1 1.O 20 30 0.2750905 0.2752295 0.2753691 i3g.o 139.6 lAO. 2 IO 20 3 0.2824228 0.2825897 0.2827571 166.9 167.4 40 0.2694615 1 1 1 .6 4 0.2755093 I4O.8 40 0.2829250 167.9 5 0.2695731 112.2 5 0.2756501 I4I.4 5 0.2830935 1 60. i 29 o 10 0.2696853 0.2697982 II2.9 n3.5 37 o 10 0.2757915 0.2759334 I4I.9 142.6 45 o IO 0.2832626 0.2834322 V * 169.6 20 0.2699117 1 14. 1 20 0.2760760 143.2 20 0.2836024 1 70. 2 30 0.2700258 1 14.7 30 0.2762192 3 0.2837731 170.7 171.3 4 0.2701405 ii5.3 40 0.2763629 1 44. 3 40 0.2839444 5 0.2702558 116.0 5 0.2765072 144.9 5 0.2841 163 171.9 172.4 30 o 0.2703718 116.6 38 o 0.2766521 145.5 46 o 0.2842887 10 0.2704884 i n 2 IO 0.2767976 146.1 10 0.2844617 173.5 20 0.2706056 1 1 /. f. 117.7 20 0.2769437 146.7 20 0.2846352 I74.I 3 0.2707233 118.4 3 0.2770904 147.3 3 0.2848093 174.6 4 0.2708417 I IQ.Q 40 0.2772377 T XT o 40 0.2849839 175 2 50 0.2709607 II9.6 50 0.2773856 14 /.y 148.4 5 0.2851591 175.7 31 o 0.2710803 I 20. 2 39 o 0.277534 I49-O 47 o 0.2853348 I 76. 2 10 20 0.2712005 0.2713214 120.9 I2I.4 10 20 0.2776830 0.2778327 149-7 1 5o. 2 10 20 0.28551 10 0.2856878 176.8 30 0.2714428 I 22. 1 30 0.2779829 i5o.8 30 0.2858652 l "n n 4 0.2715649 122.7 40 0.2781337 1 5l .A 4 0.286043 l 1 / rv Tl8 A 5 0.2716876 123.3 5 0.2782851 5 0.2862215 1 70.4 179.0 32 o 0.2718109 40 o 0.2784370 48 o 0.2864005 [66] TABLE XIII. CONTINUED. Logarithm of the Elliptical Radius Vector. V. 48 o' IO 20 30 40 0.2864005 0.2865801 0.2867602 0.2869409 0.2871220 179.6 180.1 180.7 181.1 181.7 V. 56 o' 10 20 30 40 0.2956146 0.2958191 0.2960242 0.2962297 0.2964357 204.5 205.1 ao5.5 206.0 206.5 64 o' IO 20 30 40 0.3059716 0.3061986 0.3064261 0.3066540 0.3068823 227.0 227.5 227.9 228.3 228.8 50 0.2873037 i8a.3 50 0.2966422 207.0 50 0.3071111 229.2 49 10 0.2874860 0.2876688 182.8 i83.3 57 o IO 0.2968492 0.2970567 207.5 65 o 10 0.3073403 0.3075699 229.6 23o.i 20 0.2878521 i83.8 20 0.2972647 2Qo.O 208.4 20 0.3078000 23o.5 30 40 50 0.2880359 0.2882203 0.2884052 184.4 184.9 i85.5 30 40 50 0.2974731 0.2976821 0.2978915 209.0 209.4 30 40 50 0.3080306 0.3082615 0.3084929 23o.g 23i.4 a3i.8 ' 50 o 0.2885907 186.0 58 o 0.2981014 *2\Q A 66 o 0.3087247 232.2 IO 0.2887767 186.6 IO 0.2983118 10 0.3089569 232.6 20 3 0.2889633 0.2891503 187.0 187.6 20 30 0.2985227 0.2987340 2 10.9 211. 3 20 30 0.3091895 0.3094226 233.1 233.5 40 0.2893379 188.1 4 0.2989459 2II-9 40 0.3096561 233.9 5o 0.2895260 188.7 50 0.2991582 2 1 2.O 212.8 5 0.3098900 234.3 51 o 0.2897147 189.1 59 o 0.2993710 2i3.3 67 o 0.3101243 234.7- 10 0.2899038 189.7 IO 0.2995843 2i3.8 IO 0.3104590 mv^ I 235.1 20 0.2900935 1QO. 2 20 0.2997981 20 0.3105941 235.6 3 40 0.2902837 0.2904745 IQO.S IQ I 2 3 40 0.3000123 0.3002270 2 14* 2 214.7 3 40 0.3108297 0.3110657 236.o 236.4 50 0.2906657 191.8 50 0.3004422 2 1 0. 2 50 0.3113021 236.8 52 o 0.2908575 * 7 60 o 0.3006579 68 o 0.3115389 237. 2 10 0.2910499 IQ2.8 IO 0.3008740 2 IO. I 216.6 10 0.31 17761 237.6 20 0.2912427 * V ^ 193.3 20 0.3010906 20 0.3120137 238.o 30 0.2914360 In'} n 30 0.3013077 217.1 3 0.3122517 238.4 40 0.2916299 190.9 194.4 40 0.3015252 217.3 2 17. Q 40 0.3124901 238.8 5 ^0.2918243 194.9 50 0.3017431 218.5 5 0.3127289 239.2 53 o 0.2920192 m*) /. 61 o 0.3019616 218.0 69 o 0.3129681 10 0.2922146 1 y-'*4 195.9 10 0.3021805 219.4 10 0.3132077 24Q.O 20 3 0.2924105 0.2926069 196.4 JQ7 O 20 30 0.3023999 0.3026197 219.8 220.3 20 30 0.3 '34477 0.3136881 240.4 24O.8 40 0.2928039 V /" 197.5 40 0.3028400 22O.8 40 0.3139289 241.2 50 0.2930014 198.0 5 0.3030608 221.2 50 0.3141701 241.6 54 o 0.2931994 198.5 62 o 0.3032820 221 6 70 o 0.3144117 242.O IO 0.2933979 IO 0.3035036 IO o-3'4 6 537 20 0.2935969 I99.O 20 0.3037257 222.1 222 6 20 0.3148961 242.8 3 0.2937964 20O.O 3 o-30394 8 3 223.0 3 0.3151389 243.1 4 0.2939964 2OO.5 40 0.3041713 223.4 40 0.3153820 243.5 5 0.2941969 2OI.O 5 0-3043947* 224.O 50 0.3156255 243.9 55 0.2943979 201 .6 63 o 0.3046187 71 o 0.31 58694 o / / "3 10 0.2945995 2O2 O 10 0.3048431 224.8 10 0.3161137 ^44.O / / M 20 0.2948015 202.5 20 0.3050679 225.2 20 0.3163584 ^44.7 245.0 30 0.2950040 2o3.o 30 0.3052931 30 0.3166034 245 5 40 0.2952070 2o3.6 40 0.3055188 226.2 40 0.3168489 245.8 50 0.2954106 204.0 5 0.3057450 226.6 50 0.3170947 246.2 56 o 0.2956146 64 o 0.3059716 72 o 0.3173409 [67] TABLE XIII. CONTINUED. Logarithm of the Elliptical Radius Vector. V. 72 o' 0.3173409 d 80 o' 0.3295663 d V. 88 o' 0.3424646 O 10 20 0.3175875 0.3178344 246.0 246.9 o /_ o 1C 20 0.3298288 0.3300916 2O2. 3 262.8 10 20 0.342739* 0.3430*37 274.5 274.6 3 0.3180817 247-0 30 0.3303547 f 30 0.3432884 274.7 40 5 0.3183294 0.3*85774 247.7 248.0 4 50 0.3306181 0.3308818 263.7 40 5 0.3435633 0.3438385 274.9 275.2 248.4 264.0 275.4 73 o 10 0.3188258 0.3190746 248.8 81 o 10 0.3311458 0.3314101 264.3 89 o IO 0.3441139 0.3443895 275.6 20 0.3*93237 249.1 24Q.5 20 0.3316746 264.9 20 0.3446653 276.0 30 . 4 0.3195732 0.3198230 *"+7 249.8 250.2 30 40 0-33*9395 0.3322046 265.1 265.4 3 40 0-34494*3 0.3452174 276.1 276.3 5 0.3200732 5 0.3324700 _/ r f 5 0-3454937 25o.5 2OD.O 276.5 74 o 10 0.3203237 0.3205746 250.9 25l .2 82 o 10 0.3327356 0.3330015 265-9 266 2 90 o 10 0.3457702 0.3460469 276.7 20 0.3208258 20 0.3332677 266.4 20 0.3463237 27 - 30 0.3210774 V 30 0-333534* 266 7 3 0.3466007 277.0 40 0.32*3294 0.3215817 232. 252.3 252.6 40 50 0.3338008 0.3340678 267.0 267.2 40 50 0.3468779 0.347*552 277.2 277.3 277.5 75 0.3218343 83 o 0-334335 A * 91 o 0.3474327 10 0.3220873 *M 1 10 0.3346025 207.3 267.8 IO 0.3477104 277.7 20 0.3223406 253 20 0.3348703 268.O 20 0.3479882 277.8 278.0 30 40 50 0.3225943 0.3228483 0.3231026 254-0 254.3 254-7 3 40 50 o.3354o66 0.335675* 268.3 268.5 3 40 50 0.3482662 0.3485443 0.3488226 278.1 278.3 278.5 76 o 10 0.3233573 0.3236123 255. o 84 o 10 0.3359439 0.3362129 269.0 269.3 92 o 10 0.3491011 0-3493797 278.6 20 30 0.3238677 0.3241234 255.7 256.O 20 30 0.3364822 0.3367517 269.5 269.7 20 3 0.3496585 0-3499374 278.9 279.0 40 50 0.3243794 0.3246358 256.4 256.6 40 50 0.3370214 0.33729*4 270.0 270.3 40 50 0.3502164 0.3504956 279.2 279.3 77 o 0.3248924 257.0 85 o 0.3375617 270.5 93 o 0.3507749 279.5' 10 20 30 4 0.325*494 0.3254067 0.3256644 0.3259224 257.3 257-7 258.Q 258.2 IO 20 3 40 0.3378322 0.3381029 0.3383738 0-3386450 270.7 270.9 271.2 271.4 IO 20 3 40 0.3510544 0.35*334 0.3516137 0.35*8935 279.6 279.7 279.8 280.0 50 0.3261806 258.6 50 0.3389*64 * / * * 271.6 50 0.352I735 280.1 78 o 0.3264392 258.9 86 o 0.3391880 271 O 94 o 0.3524536 280.2 10 0.3266981 259.2 10 0-3394599 / * *y 272.1 IO 0.3527338 280.4 20 30 0.3269573 0.3272169 259.6 259.8 20 30 0.3397320 0.3400043 272.3 272.5 20 30 0.3530142 0.3532946 280.4 280.6 40 0.3274767 * 7 v 260. 2 40 0.3402768 272.7 40 0.3535752 280.7 50 0.3277369 260.4 50 0.3405495 273.0 50 0.3538559 280.8 79 o 10 0.3279973 0.3282581 260.8 261 o 87 o 10 0.3408224 0.3410956 273.2 273.4 95 o 10 0.354*367 0.3544*76 280.9 281.1 20 0.3285191 261.3 20 0.34*369 273.6 20 0.3546987 281.2 30 0.3287804 2OI *7 3 0.3416426 273.8 30 0-3549799 281.2 40 0.3290421 262.0 40 0.3419164 274.0 40 0.355261 1 281.3 50 0.3293041 262.2 50 0.3421904 274.2 50 0.3555424 281.5 80 o 0.3295663 88 o 0.3424646 96 o 0.3558239 [68] TABLE XIII. CONTINUED. Logarithm of the Elliptical Radius Vector. Argument : The True Anomaly, v. O a V. V. M V. w 96 o ; 0-3558239 oSi f\ 104 o' 0.3694030 oQI / 112 0' 0.3829324 o -. 10 0.3561055 tfOl.U oSr A IO 0.3696864 20O.4 18! 1 10 0.3832117 279-J 20 0.3563871 JO1 .U ,0, 20 0.3699697 2O-J.-J rQ"3 1 2O 0.3834908 279.1 3 0.3566689 ZO 1 .O 9 Q, Q 3 0.3702530 2OO.O 18"} o 30 0.3837698 279.0 018 8 40 0.3569507 4W 1 10 0-3577967 OZm L oSo i IO -37 I 3 8 59 2oo. 2 ofi"? 10 0.3848839 27O.O 018 o 20 0.3580788 V4| 1 282.3 20 0.3716690 2c5o. I oftl I 20 0.3851621 270*2 278.O 30 0.3583611 282.3 30 0.3719521 7uwt 1 r,0-} n 30 0.3854401 4 0.3586434 282.4 40 0.3722351 20pJ*U >} n 40 0.3857178 277.7 9T7 f^ 5 0.3589258 282.4 50 0.3725181 ^oo.u 283.0 50 0.3859954 271.0 277.5 98 o 0.3592082 282.5 1 06 o 0.3728011 114 o 0.3862729 II'* O-I1 3 10 -3 59497 282.6 10 0.3730840 2o2>9 282.8 10 0.3865502 277.3 20 30 4 50 0-3597733 0.3600560 0.3603387 0.3606215 282.7 282.7 282.8 282.8 20 30 40 50 0.3733668 0.3736496 -37393 2 3 0.3742150 282.8 282.7 282.7 282.6 20 30 40 50 0.3868272 0.3871041 0.3873808 0.3876573 277.0 276.9 276.7 276.5 276.3 99 o IO 20 0.3609043 0.3611872 0.3614701 282.9 282.9 282.9 107 o IO 20 0.3744976 0.3747801 0.3750626 282.5 282.5 282.4 115 o IO 20 0.3879336 0.3882097 0.3884856 276.1 275.9 O"r1 T 30 40 50 0.3617530 0.3620360 0.3623191 283.0 283.1 283.x 30 40 50 0-3753450 0.3756273 0.3759095 282.3 282.2 282.2 30 4 50 0.3887613 0.3890368 0.3893121 270.7 275.5 275.3 275.1 IOO O 10 20 30 0.3626022 0.3628853 0.3631685 -3 6 345 I 7 283.1 283.2 283.2 283.3 108 o IO 20 30 0.3761917 0.3764738 0.3767558 0-3770377 282.1 282.0 281.9 28l.8 116 o 10 20 30 0.3895872 0.3898621 0.3901367 0.3904111 274.9 274.6 274.4 O1/ O 40 50 0.3637350 0.3640183 283.3 283.3 40 50 0.3773195 0.3776012 281.7 28l.6 40 50 0.3906853 0-3909593 ^74. * 274.0 OT^ T IOI IO 0.3643016 0-364 5 8 49 283.3 283.4 109 o 10 0.3778828 0.3781643 281.5 28l.5 117 o 10 0.3912330 0.3915065 *7 0> 7 2 7 3.5 273.3 20 0.3648683 283.4 20 0.3784458 281.3 20 0.3917798 273.0 3 0.3651517 283.4 30 0.3787271 28l.2 30 0.3920528 272.8 40 5 0-365435 1 0.3657185 283.4 283.4 40 50 0.3790083 0.3792894 28I.J 28l.O 4. 50 0.3923256 0.3925981 272.5 OTT ^ IO2 0^3660019 283.4 110 0.3795704 280.8 118 o 0.3928704 Z 1 4. J 910 n IO 0.3662853 283.4 10 0.3798512 280.8 10 0.3931424 * / *>w 271.8 2O 3 40 5 0.3665687 0.3668522 0.3671357 0.3674191 283.5 283.5 283.4 283.5 20 30 40 5 0.3801320 0.3804126 0.3806932 0.3809736 280.6 280.6 280.4 280.2 20 3 40 50 0.3934142 0.3936857 0-393957 0.3942280 271.5 271.3 271.0 270.8 103 o 0.3677026 283.4 III 0.3812538 28c.I 119 o 0.3944988 Oln K 10 20 30 40 50 0.3679860 0.3682695 0.3685529 0.3688363 0.3691196 283.5 283.4 283.4 283.3 283.4 10 20 30 4 5 o-38i5339 0.3818139 0.3820937 0.3823734 0.3826530 28o.O 279.8 279.7 27 9 .6 2TO / 10 20 30 40 50 0-3947693 0-3950395 0-3953094 o-395579i 0.3958485 2 jiJ. J 270.2 269.9 ' 269.7 269.4 104 o 0.3694030 112 0.3829324 fir* 1 2O 0.3961176 269.1 [69] TABLE XIII. CONTINUED. Logarithm of the Elliptical Radius Vector. V. 120 0' IO 0.3961176 0.3963864 d M 268.8 V. 128 o' 10 0.4086450 0.4088967 d 251.7 V. 136 o' 10 0.4201901 0.4204178 6 227.7 20 3 0.3966549 0.3969231 268.2 oA& n. 20 30 0.4091479 0.4093987 sSi.3 25o.8 20 30 0.4206450 0.4208716 227.2 226.6 .! 40 So 0.3971911 0,3974588 JOO.O 267.7 40 50 0.4096491 0.4098990 249-9 40 5 0.4210977 0.4213231 226. 1 225.4 121 O 0.3977261 267.3 267.0 129 o 0.4101485 249.5 249.0 137 o 0.4215480 224.9 224.3 IO 0.3979931 o A/I 8 IO 0.4103975 10 0.4217723 nnl Q 20 30 0.3982599 0.3985263 2OO.O 266.4 20 3 0.4106461 0.4108943 248.2 9 /.I n 20 . 30 0.4219961 0.4222192 223. 223.1 n n n & 40 0.3987924 2 * 40 0.4111420 247.7 40 0.4224417 222.3 50 0.39905,82 / e c 50 0.4113893 _ ff Q 5 0.4226636 221.9 2OD.O 240.8 221.3 122 O 0.3993237 130 o 0.4116361 246.3 138 o 0.4228849 10 0.3995889 2 ' 2 10 0.41 18824 10 0.4231056 220.7 2O 0.3998537 V's 20 0.4121283 9X1 / 20 0.4233257 220. 1 30 4 50 0.4001 182 0.4003824 0.4006463 264.2 263.9 263.5 30 40 5 o-4 I2 3737 0.41 26186 0.4128630 44*J.l 244-9 244-4 244.0 30 40 50 0.4235452 0.4237641 0.4239824 219.5 218.9 218.3 217.6 123 o 0.4009098 263.2 131 o 0.4131070 243.5 139 o 0.4242000 fV 2 17.0 IO 0.401 1730 262.8 10 0.4133505 243.O 10 0.4244170 2O 0.4014358 262.5 20 0.4135935 242.5 20 0.4246335 n t K O 3 0.4016983 262 2 3 0.4138360 242.1 30 0.4248493 2 1 J.O 40 0.4019605 261.8 40 0.4140781 241.5 40 0.4250644 21 5. J 214.6 50 0.4022223 261.4 5 0.4143196 24I.I 50 0.4252790 2 1 3.Q 124 o 0.4024837 261 * I 132 o 0.4145607 240.5 140 o 0.4254929 2 1 3. 2 10 0.4027448 260.7 10 0.4148012 240.1 10 0.4257061 212.6 20 0.4030055 260 /I 20 0.4150413 239.5 20 0.4259187 30 0.4032659 260.0 3 0.4152808 23 9 .1 30 0.4261307 21 2.O 211. 4 40 0.4035259 25o.6 40 0.4155199 238.5 40 0.4263421 50 0.4037855 25o.3 50 0.4157584 238.1 50 0.4265528 210.7 210. 1 125 o 10 20 0.4040448 0.4043037 0.4045622 fcv v 258.9 258.5 258.1 133 o IO 20 0.4159965 0.4162340 0.4164710 23 7 .5 237.0 236.5 141 o IO 20 0.4267629 0.4269723 0.4271811 209.4 208.8 30 0.4048203 257.8 3 0.4167075 236.O 30 0.4273892 20 .1 40 0.4050781 257.4 40 0.4169435 ' 235.4 40 0.4275966 207.4 206.8 50 0.4053355 **' /** 257.0 5 0.4171789 234.9 5 0.4278034 2o6. 1 126 o 10 0.4055925 0.4058491 256.6 256. 2 134 o IO 0.4174138 0.4176482 234-4 233.8 142 o 10 0.4280095 0.428^149 2o5.4 20 0.4061053 255.8 20 0.4178820 233.3 20 0.4284197 20 / 30 0.406361 1 255.4 30 0.4181153 232.7 30 0.4286238 2o3.4 40 0.4066165 255.0 40 0.4183480 / 232.2 40 0.4288272 2O2. 7 50 0.4068715 254.6 50 0.4185802 23i.6 50 0.4290299 2O2.I 127 o 0.4071261 254.2 135 o 0.4188118 23l.I H3 o 0.4292320 201.3 10 0.4073803 253.8 10 0.4190429 23o.6 10 0.4294333 2OO.7 20 0.4076341 253.3 20 0.4192735 93r> n 20 0.4296340 / 20O.O 30 0.4078874 253. o 30 0-4195035 229 . 4 30 0.4298340 199.3 40 0.4081404 252.5 40 0.4197329 22g 40 0.4300333 198.6 50 0.4083929 252.1 50 0.4.100618 i 22 8 3 50 0.4302319 7 197.9 128 o 0.4086450 136 o 0.4201901 ' 144 o 0.4304298 [70] TABLE XIIL CONTINUED. Logarithm of the Elliptical Radius Vector. V. 144 o' 0.4304298 IQ1 1 V. 152 o' 0.4390569 160.6 V. I 60 0' 0.4457969 O T1 Q A 10 0.4306270 *V r* IO 0.4392175 T ^n T IO 0.4459155 1 I O.U 20 0.4308235 lr .K Q 20 0.4393772 1 J 9- 7 20 o.44 6 33 2 117.7 * t A O 3 0.4310193 1 Cy J. O 30 0-43953 61 i58.o 30 0.4461500 IIO.O _ _ e Q 40 0.4312144 i\ 4 0.4396941 40 0.4462658 113. _ _ jr _ 5 0.4314088 194'4 io3.6 5 0-43975 H 156.4 50 0.4463808 113. O 145 o 0.4316024 * 7 io3.o 153 o 0.4400078 i55.6 161 o 0.4464948 n3.i IO o-43 I 7954 IQ2 2 10 0.4401634 10 0.4466079 20 0.4319876 191.5 20 0.4403181 i53.9 20 0.4467201 112.2 III. 2 3 0.4321791 loo 8 30 0.4404720 i53.i 3 0.4468313 40 0.4323699 loo. i 40 0.4406251 l52.2 40 0.4469416 IIO.O 50 0.4325600 189.3 50 0.4407773 i5i.4 50 0.4470510 I09.4 108.4 146 o 0.4327493 188.6 154 o 0.4409287 i5o.5 162 o 0-447 * 594 107.5 10 0.4329379 187.8 10 0.4410792 lAo.l 10 0.4472669 1 06. 5 20 o.433 I2 57 187.1 20 0.4412289 4 v / 148.8 20 0.4473734 io5.6 3 o-4333 I2 8 / 186.3 3 0.4413777 148.0 - 30 0-447479 104.7 40 0-43 3499 * i85.6 40 0.4415257 40 0.4475837 io3 i 5 0.4336847 184.9 5 0.4416728 146.2 50 0.4476874 i\j*j. i 102.7 147 o 0.4338696 184.1 155 o 0.4418190 145.4 163 o 0.4477901 101.8 IO 0.4340537 i83.4 IO 0.4419644 144-5 10 0.4478919 IOQ.8 20 0.434237 1 182.6 20 0.4421089 143.6 20 0.4479927 99.9 30 o.4344'97 181.9 3 0.4422525 142.8 30 0.4480926 08.0 4 0.4346016 40 0.4423953 141.0 4 0.4481915 V v V 98.0 5 04347827 180.4 50 0.4425372 ** y 14i. i 50 0.4482895 7. 97.0 148 o 0.4349631 170.6 156 o 0.4426783 i4o.i 164 o 0.4483865 06. 1 10 0.4351427 17 178.8 10 0,4428184 139.3 10 0.4484826 7 9 5.i 20 0.4353215 178.0 20 0.4429577 i38.4 20 0.4485777 94. i 30 0-4354995 177.3 30 0.4430961 i37.6 30 0.4486718 o3 2 40 0.4356768 * / /- v 176.5 40 0.4432337 BkT J*W i36.6 40 0.4487650 y*-'.* 02. 2 50 0.4358533 175.8 50 0-443 3 73 135.8 50 0.4488572 7 91.3 149 o 0.4360291 174. Q 157 o 0.4435061 165 . o 0.4489485 QO. 3 10 0.4362040 /^**y 174.2 10 0.4436410 i34.o IO 0.4490388 80.3 20 0.4363782 * /*+ * n3.4 20 0-443775 i33.i 20 0.4491281 wvftv 88.4 30 0.4365516 1 /x^.if 172.6 30 0.4439081 l32.3 3 0,4492165 87.4 40 0.4367242 I7I.8 40 0.4440404 i3i.3 40 0.4493039 86.4 5 0.4368960 17I.I 50 0-4441 7 1 7 i3o.5 50 0.4493903 85.5 150 o 0.4370671 I7O.2 158 o 0.4443022 129.5 1 66 o 0.4494758 IO 0.4372373 10 -44443 I 7 128.7 10 0.4495602 83.5 20 0.4374068 168.6 20 0.4445604 20 0.4496437 82.5 3 0-4375754 167.8 3 0.4446881 126.8 3 0.4497262 81.6 40 0.4377432 I67.O 40 0.4448149 125.9 40 0.4498078 8o.5 50 0.4379102 166.3 50 0.4449408 I25.I 50 0.4498883 7O.6 151 o 0.4380765 i65.4 159 o 0.445065-9 124.1 167 o 0.4499679 /y* v 78.6 10 0.4382419 164.6 10 0.4451900 123.2 10 0.4500465 T7 A 20 0.4384065 i63.8 20 o-445 3 i 32 122.3 20 0.4501241 77.O 76.6 3 0-4385703 i63.o 30 -4454355 I2I.4 3 0.4502007 1*1 1 40 0-4387333 162.2 40 -44555 6 9 120.4 40 0.4502764 7 J -7 5 0.4388955 161.4 50 0.4456773 119.6 50 0.4503510 73.7 152 o 0.4390569 1 60 o 0.4457969 168 o 0.4504247 [71] TABLE XIII. CONCLUDED. Logarithm of the Elliptical Radius Vector. Argument : The True Anomaly, v. O o O V. M V. r. V. M 1 68 o' 10 20 30 4 50 0.4504247 0.4504973 0.4505690 0.4506397 0.4507094 0.4507781 7 2.6 71.7 70.7 69.7 68.7 172 o' IO 20 30 40 50 0.4518935 0.4519421 0.4519898 0.4520364 0.4520820 0.4521266 48.6 47.7 46.6 45.6 44.6 ft f. 176 o' 10 20 30 40 50 0.4527802 0.4528043 0.4528275 0.4528496 0.4528707 0.4528908- 24.1 23.2 22.1 21. 1 20.1 169 o 0.4508458 66 7 173 o 0.4521702 42 5 177 o 0.4529098 18 o 10 20 3 40 0.4509125 0.4509782 0.4510430 0.4511067 65.7 64.8 63.7 10 20 30 40 0.4522127 0.4522543 0.4522948 0.4523343 41.6 4o.5 3 9 .5 38 5 IO 20 30 4 0.4529278 0.4529448 0.4529607 0.4529756 17-0 1 5.9 14.9 50 0.4511694 61.7 50 0.4523728 3 7 .5 50 0.4529895 12.9 170 o IO 20 30 40 50 171 o 10 20 30 0.4512311 0.4512918 0-45 i 35 '5 0.4514102 0.4514680 0.4515247 0.4515804 0.4516351 0.4516888 0.4517415 60.7 59.7 58. 7 5 7 . 7 56.7 55.7 54-7 53.7 52.7 5i 7 174 o IO 20 30 40 50 175 o 10 20 30 0.4524103 0.4524468 0.4524822 0.4525166 0.4525499 0.4525823 0.4526136 0.4526440 0.4526733 0.4527016 36.5 35.4 34-4 33.3 32.4 3i.3 3o.4 29.3 28.3 2T 3 178 o 10 20 30 40 50 179 o IO 20 30 0.4530024 0.4530142 0.4530250 0.4530348 0.4530436 0.4530513 0.4530580 0.4530637 0.4530683 0.4530719 11. 8 10.8 9.8 8.8 7-7 6.7 5. 7 4.6 3.6 3 6 40 0.4517932 5o 6 40 0.4527288 4 0.4530745 50 0.4518438 49-7 50 0.4527550 25.2 50 0.4530761 o 5 172 o 0.4518935 176 o 0.4527802 1 80 o 0.4530766 If v is greater than 180, take 180 v as Argument. 172 I TABLE XIV. Auxiliary Quantities, for Computation of the Heliocentric Co-ordinates. (Referred to the Equator, and to the Mean Equinox at the beginning of the Year.) Year. A B. C. Log. a. Log. b. Log. c. 1850 3 I2l' l8".20 299 i '26^.50 3 2o55' 52^.99 9.9968336 9.9768259 9.5316651 1851 31 22 8 .59 299 2 14 .66 320 56 48 .05 9.9968326 9.9768218 9.5317063 1852 B 31 22 59 .12 299 3 2 .96 320 57 43 .27 9.9968315 9.9768177 9.53I7477 1853 31 23 49 -5 * 299 3 5i .12 320 58 38 .33 9.9968304 9.9768136 9.5317889 1854 31 24 39 - 8 9 299 4 39 .29 320 59 33 .39 9.9968294 9.9768094 9.5318302 1855 31 25 30 .28 2 99 5 27 .45 321 o 28 .45 9.9968283 9.9768053 9-5318714 1856 B 31 26 20 .81 299 6 15 .75 321 i 23 .64 9.9968272 9.9768011 9.5319128 1857 31 27 II .20 2 99 7 3 -9 1 321 2 18 .68 9.9968261 9-9767970 9.531954 1858 31 28 I .58 299 7 52 .08 321 3 13 .72 9.9968251 9.9767928 9.53I9953 1859 31 28 5' -97 299 8 40 .24 321 4 8 .75 9.9968240 9.9767887 9.5320365 1860 B 31 29 42 .50 299 9 28 .54 321 5 3 .92 9.9968229 9.9767846 9.5320778 1861 31 30 32 .89 299 10 16 .71 321 5 58 .94 9.9968218 9-9767805 9.5321190 1862 31 31 23 .29 299 ii 4 .88 321 6 53 .95 9.9968208 9.9767763 9.5321603 1863 31 32 13 .68 299 ii 53 -05 321 7 48 .96 9.9968197 9.9767722 9-5322015 1864^' 3^ 33 4-2i 299 12 41 .35 321 8 44 . 1 1 9.9968186 9.9767680 9.5322428 1865 3 33 54 -61 299 '3 2 9 -53 321 9 39 .10 9.9968175 9.9767639 9.5322840 1866 3 34 45 - OI 299 H 1 7 -7 321 10 34 .09 9.9968165 9.9767597 9-5323253 1867 31 35 35 -4 1 299 15 5 .87 321 ii 29 .08 9.9968154 9.9767556 9-5323665 1868 B 3i 36 25 .95 299 15 54.18 321 12 24 .20 9.9968143 9.9767514 9.5324078 1869 31 37 16.35 299 16 42 .36 321 13 19 .17 9.9968132 9-9767473 9.5324490 1870 31 38 6.75 299 17 30-53 321 14 14.14 9.9968122 9.9767431 9.5324903 1871 31 3 8 57 -16 299 1 8 1 8 .71 321 15 9 .10 9.99681 ii 9.9767390 9-5325315 1872 B 31 39 47 -7 299 19 7 .02 321 16 4 .20 9.9968100 9.9767348 9.5325728 1873 31 40 38 .10 299 19 55 .20 321 16 59 .14 9.9968089 9.9767306 9.5326140 1874 31 41 28 .50 299 20 43 .37 321 17 54.08 9.9968079 9.9767265 9.5326552 1875 31 42 1 8 .91 299 21 31 .55 321 1 8 49 .02 9.9968068 9.9767223 9.5326964 1876-6 3i 43 9-45 299 22 19 .86 321 19 44 .10 9.9968057 9.9767181 9-5327377 1877 31 43 59 -86 299 23 8 .04 321 20 39 .02 9.9968046 9.9767140 9.5327789 1878 31 44 50.26 299 23 56 .22 321 21 33 .93 9.9968036 9.9767098 9.5328201 1879 31 45 40.67 299 24 44 .40 321 22 28 .84 9.9968025 9.9767057 9.5328613 1880 B 31 46 31 .21 299 25 32 .71 321 23 2 3 .89 9.9968014 9.9767015 9.5329026 1881 31 47 21 .62 299 26 20 .90 321 24 18 .78 9.9968003 9.9766973 9-5329437 1882 31 48 12 .02 299 27 9 .08 321 25 13 .67 9.9967993 9.9766932 9.5329849 1883 3 1 49 - 2 .43 299 27 57 .27 321 26 8 .56 9.9967982 9.9766890 9.5330261 1884 /.' 3i 49 5 Z -98 299 28 45 .58 321 27 3 .58 9.9967971 9.9766848 9.5330674 1885 31 50 43 .38 299 29 33 .77 321 27 58 .45 9.9967960 9.9766806 9.5331085 1886 3 1 5 1 33 -79 299 30 21 .95 321 28 53 .32 9.9967950 9.9766765 9-533H97 1887 3152 24 .20 299 31 10 .14 321 29 48 .18 9.9967939 9.9766723 9-533I909 1888 B 3* 53 H-75 299 31 58 .46 321 30 43 .18 9.9967928 9.9766081 9.5332322 1889 3i 54 5 -15 299 32 4 6 - 6 5 321 31 38 .03 9.9967917 9.9766639 9-5332733 1890 3i 54 55 -5 6 299 33 34 -83 321 32 32 .87 9.9967907 9.9766598 9-5333H5 1891 3i 55 45 -97 299 34 23 .02 321 33 27 .72 9.9967896 9.9766556 9-5333557 1892 B 31 56 36.52 299 35 ii -34 321 34 22 .70 9.9967885 9.9766514 9-5333970 1893 31 57 26 .93 299 35 59 -53 321 35 17 -53 9.9967874 9.9766472 9-533438i 1894 3i S 8 17 -34 299 36 47 .72 321 36 12 .35 9.9967864 9.9766430 9-5334793 1895 3i 59 7 -75 2 99 37 35 -91 321 37 7 -17 9-9967853 9-9766388 9-5335205 1896 B 31 59 58 .30 299 38 24 .23 321 38 2 .13 9.9967842 9.9766346 9.5335618 1897 32 o 48 .71 299 39 I2 .42 321 38 56.93 9.9967831 9.9766304 9.5336029 1898 32 i 39 .12 299 40 o .61 321 39 5i -73 9.9967821 9.9766263 9-533644 1 1899 3 2 2 2 9 .54 299 40 48 .81 321 40 46 .52 9.9967810 9.9766221 9-5336852 1900 32 3 '9 -9 6 299 4 1 37 .00 321 4 1 4 -32 9-9967799 9.9766179 9-5337264 [73] TABLE XV. To find the Corrections of the three Co-ordinates a?, y, z from %. A X. A y. A z. I' 1850. 1900. 1850. 1900. 1850. 1900. 5000 + 7237 + 7296 + 19136 + 19217 56560 -56525 4900 7117 7175 18818 18897 55620 55585 4800 6996 7053 18500 18578 54679 54645 1 i 4700 6876 6932 18181 18258 53739 53705 1 20. 122. 4600 6756 6811 17863 17939 52799 52766 4500 6635 6689 17545 17619 51858 51826 i i I 4400 6515 6568 17227 17300 50918 50886 2 2 2 4300 6395 6447 16909 16980 49978 49946 3 4 4 4200 6275 6326 16590 16661 49038 49007 4 5 5 4100 6154 6204 16272 16341 48097 48067 5 6 6 4000 + 6034 + 6083 + 15954 + 16022 -47157 -47127 6 7 7 3900 59H 5962 15636 15702 46217 46187 7 8 8 3800 5793 5840 I53i8 15383 45276 45247 8 10 10 3700 5 6 73 5719 15000 15063 44336 44308 9 1 1 ii 3600 555 2 5598 14682 14744 43395 43368 10 12 12 3500 543 2 5476 H363 14424 42455 42428 20 24 24 3400 S3 12 - 5355 14045 14105 415*5 41488 30 3 6 37 3300 5191 5234 13727 13785 4574 40549 40 48 > 49 3200 5071 5"3 J3409 13466 39634 39609 50 6O 61 3100 495 4991 13091 13146 38693 38669 60 72 73 3000 + 4830 + 4870 + 12773 + 12827 -37753 -37729 70 O 84 S 8 5 2900 4710 4749 12455 12507 36813 36789 8. 96 _ o 98 2800 4589 4627 12137 12188 35872 35849 90' 108 I IO 2700 4469 4506 11818 11868 3493 2 349 10 2600 4349 4385 11500 11549 3399 1 3397 2500 4228 4263 11182 1 1229 3305 1 33030 2400 4108 4142 10864 10910 3211 1 32090 318. 320. 2300 3988 4021 10546 10590 31170 31150 22OO 3868 3900 10227 10271 30230 3021 1 i 3 3 2100 3747 3778 9909 995 i 29289 29271 2 6 2OOO + 3627 + 3657 + 959* + 9 6 32 -28349 -28331 3 10 IO 1900 3507 353 6 9273 9312 27409 27391 4 1 3 _ s 1 3 . . l8oo 3386 34*4 8955 8993 26468 26452 5 10 IO 1700 3266 3293 8637 8673 25528 25512 19 19 1600 3H 6 3I7 1 8319 8354 24588 24572 7 22 22 s 1500 3025 3050 8000 8034 23647 23632 8 25 20 I40O 2905 2927 7682 7715 22707 22693 9 29 2 9 1300 2 7J5 2807 7364 7395 21767 21753 10 3 2 S 3 Z s I20O 2665 2686 7046 7076 20827 20813 20 64 64 I I 00 2544 2564 6728 6756 19886 19874 30 95 96 o | IOOO + 2424 + 2443 + 6410 + 6437 -18945 -18934 4 127 120 . .~ 900 2304 2322 6092 6117 18005 17994 5 s !59 I DO 800 2183 22OO 5774 5798 17064 17054 DO 191 192 700 2063 2079 5455 5478 16124 16115 7 O^*. 223 224 600 1942 I 95 8 5*37 5'59 15184 15175 oo 254 r\ s 256 500 1822 1836 4819 4839 H243 H235 90 286 288 400 1702 1715 4501 4520 i33 3 i3 2 95 300 1581 '594 4183 4200 12363 12355 20O 1461 H73 3864 3881 11423 1 1416 100 34 I35 1 3546 35 61 10482 10476 O + 1220 + 1230 + 3228 + 3242 - 9542 - 9536 [74] TABLE XV. CON'CLUDED. To find the Corrections of the three Co-ordinates a?, y, z from e Ax. Ay. Az. c- 1850. 1900. 1850. 1900. 1850. 1900. o + I22O + 1230 + 3228 + 3242 - 9542 - 9536 + 100 I 1 00 1109 2910 2922 8602 8596 2OO 979 987 2592 2603 7661 7656 3OO 859 866 2274 2283 6721 6717 400 739 745 1956 1964 5780 5777 500 618 624 1637 1644 4840 4837 600 498 502 1319 1325 3900 3897 7OO 378 381 1 00 1 1005 2959 2957 800 258 260 683 686 2019 2018 9OO + 138 + 138 + 365 + 366 1078 1078 + 1000 + - 17 + 17 + 47 + 47 - 138 138 939- 941. I TOO 104 104 271 . 272 + 802 + 802 1200 224 226 589 592 1743 1742 i 9 9 1300 344 347 907 911 2683 2681 2 19 O 19 Q 1400 464 468 1225 1231 3624 3621 3 28 20 1500 584 589 J 543 1550 4564 4561 4 37 38 l6oO 705 711 1862 1870 554 5501 5 47 s- 47 1700 825 832 2180 2189 6445 6441 6 5 6 56 1 1800 945 95.3 2498 2509 7385 738o 7 66 66 1900 1066 1075 2816 2828 8326 8320 8 75 o - 75 + 2000 1186 1196 - 3^34 - 3H8 + 9266 + 9260 9 8 5 85 2100 1306 1317 3452 3467 10206 IO2OO TO 94 o o 94 * O Q 2200 1427 H39 3770 3787 11147 III4O 20 188 f\ 188 2300 1547 1560 4089 4107 12087 12079 30 282 _s 282 s 2400 1668 1681 4407 4426 13027 13019 40 376 s 376 2500 1788 1802 4725 4745 13967 *3959 5 s 469 _ s 470 - - 2600 1908 1924 5043 5065 14908 14899 60 563 - 565 - 2700 2029 2045 5361 5384 15848 15839 70 6 57 6 59 2800 2149 2166 5680 574 16788 16778 80 75i 753 2900 2270 2288 5998 6023 17729 17718 90 845 847 + 30OO -2390 2409 6316 - 6343 + 18669 + 18658 3100 2510 2530 6634 6662 19610 19598 3200 2631 2652 6952 6982 20551 20537 33 2751 2773 7270 7301 21491 2H77 3400 2871 2895 7588 7621 22431 22417 3500 2991 3016 7906 7940 23371 23356 3600 3112 3 J 37 8225 8260 24312 24296 3700 3232 3259 8543 8579 25252 25236 3800 3352 338o 8861 8899 26192 26176 3900 3473 3502 9179 9218 27133 27115 + 4000 -3593 -3623 - 9497 - 9538 + 28073 + 28055 4100 - 3713 3744 9815 9857 29013 28995 4200 3834 3866 10133 10177 29954 29935 4300 3954 3987 10452 10496 30994 30874 4400 4074 4108 10770 10816 31835 31814 4500 4194 4229 11088 11135 32775 32754 4600 43 i 5 435 i 11406 "455 33715 33694 4700 4435 4472 11724 11774 34656 34634 4800 4555 4593 12043 12094 35596 35573 4900 4676 4715 12361 12413 36537 36513 + 5000 4796 4836 12679 -12733 + 37477 +37454 [75] TABLE XVI. To be used for Calculating an Approximate Place, When only the first five Equations are taken into account. f. AJB. Ay. Ag. 5000 + 70 + 184 -543 4000 57 152 449 3000 45 1 20 355 2OOO 33 88 261 IOOO 21 56 167 O + 9 + 25 - 73 + 1000 - 3 - 7 + 21 2OOO H 39 "5 3OOO 27 7i 209 4OOO 39 103 303 50OO -5^ -134 + 397 (Units of the fifth decimal.) [76] TABLE XVII. To be used for Calculating an Approximate Place When only the First Five Equations are taken into account. M. V. Log. r. V. V. Log. r. V. V. Log. r. V. V. Log. r. 5 1850 32449' 5"-9 0.25992 "360 45 0.28339 315 90 0-3459 270 135 0.41894 22 1851 65 41 o . i - 2 5994359 46 0.28442 3H 91 0.34756 269 136 0.42032 22 1852 L 1 66 49 30 .! 2 0.25997 35 8 47 0-28547 3i3 92 0-34923 268 137 0.42168 22 1853 267 41 24 . 8 3 0.26003 357 48 0.28653 312 93 0.35091 267 138 0.42302 22 1854 8 33 19 .4 4 0.2601 1 356 49 0.28662 3ii 94 0.35259 266 139 jo-42433 22 1855 109 25 14 .1 5 0.26022 355 5 0.28872 31 95 0.35427 265 140 0.42562 22 1856 .Z? 2TO 22 Al 6 I8 57 1858 311 25 38 .3 C2 17 3? .O 6 7 0.26035354 0.2605 ! 353 5i 5 2 0.28985 0.29099 39 308 96 97 0.35596 0.35765 264 263 141 142 0.42689 21 0.42814121 5 185,9 j I J j ' I r 2 Q 27 6 8 0.26068 352 53 0.29215 37 98 0-35934 262 H3 0.42936 21 1860 E 1 5 j y . */ ' 254 17 57 .2 9 0.26089 35 ! 54 -29333 306 99 0.36104 261 144 0.4305621 1861 J I / j 1 355 9 5 1 - 8 10 0.261 1 1 35 55 0.29453 35 100 0.36273 260 H5 0-43I73 21 1862 , o _ 96 i 46 .5 ii 0.26136 349 56 0.29575 304 101 0.36443 259 146 jo. 43288 21 1863 _ Q s TJ 196 53 41 .2 12 0.26163 34 8 57 0.29698 33 IO2 0.36613 258 147 0.43400 21 I 864 JD * o a ~ 298 2 IO .7 13 0.26193 347 5 8 0.29823 302 I0 3 0.36783 257 148 0.43509 21 1065 i Q< 3 8 54 5 -4 H 0.26225 346 59 0.29950 301 104 0.36953 256 149 0.43616 21 1 OOO QjCjv 1 39 46 o .0 15 0.26259 345 60 0.30079 300 105 0.37123 255 150 0.43720(21 1 007 2 4 37 54 -7 1868 B 341 46 24 .2 16 0.26296 344 61 0.30209 299 106 0-37293 254 I5 1 0.43821 20 1869 82 38 18 .9 17 0.26335 343 62 0.30341 298 107 0.37463 253 152 0.43919 20 1870 * 183 30 13 .6 18 0.26376342 63 0.30475 297 108 0.37632 252 153 0.44014 2O 1871 284 22 8 .2 19 0.26419 34 1 64 0.30610 296 109 0.37801 251 154 0.44106 20 1872 B 2 5 30 37 - 8 20 0.26465 34 65 0.30747 295 no 0-37970 250 155 0.44195:20 1873 1874 1875 126 22 32 .4 227 14 27 .1 328 6 21 .8 21 22 0.26514 0.26564 339 33 8 66 67 0.30885 0.31025 294 293 I II I 12 0.38138 0.38306 249 248 156 I5 0.44281 20 0.4436420 1876 B 69 14 ci .3 23 0.26617 337 68 0.31 167 292 H3 0.38474 247 150 10.44443 20 1877 x T J J 170 6 46 .0 24 0.26672 33 b 69 0.31310 291 II 4 0.38640 246 159 0.44520 20 1878 270 58 40 .6 25 0.26729 335 70 0.31454 290 H5 0.38806 245 1 60 0-44593 2O 1879 1880 B O O * ii 5 35 -3 112 59 4 .8 26 27 0.26789 0.26851 334 333 7i 7 2 0.31600 0.31747 289 288 116 0.38972 117 -39i36 244 2 43 161 162 0.44663 19 0.4472919 I 00 J _ r> o 213 5 59 -5 28 0.26915 332 73 0.31896 287 118 0.39300 242 163 0.44792 19 1882 O O 31442 54.2 29 0.26982 331 74 0.32046 286 119 0.39463 241 164 0.44852 19 1883 * O O , T> 55 34 4 8 - 8 . _ x- r\ 3 0.27050 330 75 0.32197 285 120 0.39625 240 1 65 0.44908 19 1084 -D 1 50 43 is .3 * 88 5 257 35 13 .0 31 0.27121! 329 76 0-32349 284 121 0.39786 239 1 66 0.44961 '9 1886 358 27 7 .7 32 0.27194328 77 '0.32502 283 122 0.39945 238 167 0.45010119 1887 99 19 2 .4 33 0.27269 327 78 0.32657 282 123 0.40104 237 168 0.45056 19 1888 B 200 27 31 .9 34 0.27347326 79 0.32813 281 124 0.40261 236 169 0.45098119 1889 301 19 26 .6 35 0.27427325 80 0.32970 280 125 0.40418 235 170 '0.45136 i9< 1890 1891 1892 B I 8m 42 I I 21 .2 H3 3 15 -9 244 ii 45-4 36 0.27508:324 37 0.27592323 38 0.27678322 81 0.33128279 82 '0.33287:278 83 0.33447277 126 0.40573 127 0.40726 128 0.40878 234 233 232 171 0.45171 i8< 172 0.45202 i8i 173 0.4523018- I8 93 I8 94 I8 95 345 3 4 -i 8 5 55 34 - 8 i 86 47 29 .4 39 4 0.27766:321 0.27857320 84 8 5 0.33608 0.33769 276 275 129 ,0.41028 23 I 13 0-4H77 230 174 0.45254 i8( 175 0.4527418 1896 5287 55 5 8 -9 4i 0-27950319 86 o-3393i 274 131 0.41324 229 176 0.45291 18, .897 1898 28 47 53 .6 129 39 48 .3 42 ^.28044318 43 ,0.28140:317 87 0.34095 88 0.34260 273 272 132 ^0.41469 133 0.41613 228 227 177 '0.45 3041 1 8; 178 0.45313 18; 1899 23 3i 43 - 44 0.28239316 89 0.34425 271 134 0.41754 226 179 0.4531918 1900 3312337.6 45^0.28339315 90*5.34590270 135 o. 41894^25 180 o.4532i ! i8< [77 UNIVERSITY OF CALIFORNIA LIBRARY BERKELEY Return to desk from which borrowed. This book is DUE on the last date stamped below. MAY 1952 LD 21-95m-ll,'50 (2877sl6)476 UBEREL Y