Log, a log. p sin 'log. A ; log. flog. p sin p' + log. cos D', log. blog. Glog. B. gr V · f. log. u log. G+ 9.4180; h=1— (a + b). = 3. With the values of p, q, u, v, &c., found for the requisite times, make the computation by Arts. 8, 9, &c., of the rule to Prob. XVI., using logarithms to four decimal figures, and natural numbers to three or four decimals. Then, for the times of beginning and end thus found, taken to the nearest hundredth of an hour, repeat the calculation, using logarithms to five or more decimal figures. When the eclipse is annular or total, the times of its beginning and ceasing to be so, are found in a similar manner, only using 7 instead of 1. Note.-The general quantities, whose values are found by the first article, serve not only for calculating the times of beginning, &c., of an clipse for any place at which it will be visible, but also for the calculations requisite to determine the longitude of a place, from the observed times of beginning and end at that place.* EXAMPLE. Let it be required to compute, for Philadelphia, the eclipse of May 15th, 1836. 1. For quantities independent of the place. By the Nautical Almanac, the time of new moon is May 15th, at 2hrs. 6.9m. Taking, therefore, T 15d. 2h., we find from the Nautical Almanac,† and from tables of sines, tangents, &c., the following quantities : π-T! D. h. 54' 17".12 3729 .00 54 24 .90 151 40 28 .1452 17 57 .14 54 16 .42 252 10 33 .90 52 20 25 .34 9 51 .44 54 24 .218.48 54 15 .73 352 40 42 .6252 22 53 .55 17 49 .0754 23 .53 54 15 .05 453 10 54 .30 52 25 21 .78+45 32 .52 54 22 .85 54 14 .73 *The values of p, q, u, v, &c., are found by the formulæ in Art. 75 of the Appendix. To find them by the formulæ in (App. 69), the values of a, d, and g, must first be computed (App. 68). For all important eclipses, these and the other general data are given in the Berlin Ephemeris. †The values of A, A′, D, D', 7, and f' may be obtained from the part of the Nautical Almanac given in Table LXV. The value of is given in a different x part of the Almanac. D. h. D 15 019° 1′24.70′′N. 119 11 33.01 219 21 36.10 319 31 33.96 419 41 26.60 π A D. D. h.log.sin D'log.cos D' log. A. | log. B. |—n' 15 09.511399.975827.1746 7.6391 19.51161 9.97579 7.1749 7.6390 29.511829.975777.17517.6390 P A — A D' b d g' 39.512049.97574 7.1753 7.6390 49.512259.97572 7.1755 7.6390| h.m 0 0 p A — A' . At time T 2. or Ohr. Ar. Co. log. sin 1.8016094 + 0.006960 p. 1.13301 30 0.89265 + 0.000093 - 0.41184 30 20 0.17140 30 0.06907 D' 18°56′ 35.90′′N. + 4'48.80" 15′ 49.90" 7.6632559 10": 18 57 46.28 23 49.82 15 49.88 7.6632491 +33 12.54 15 49.88 7.6632456 +42 30.07 15 49.87 |7.6632422 30+0.30956 30+ 0.55005 40+ 0.79056 π log. sin 8.2770142n D B log.cos 9.9756086 log. sin 8.27701n .24039 .24042 .24044 א" .24047 .24049 .24049 .24051 0.0542322n +b=+ D-D' log. 0.0542n d' log. sin 8.2770n с 5.9703 Making similar calculations for the other hours, finding the values of p and q for the half hours, by the last problem, and proceeding as directed in the rule, we obtain the following values. Diff +.24036 p' +4807 7.84263 π .4808 .4809 D' a + 0.088671 3480 q + 0.09215 g ι q. 0.09215 0.17903 + 0.291652 id=+ .000046 0.26584 +0.273210 0.35258 Ar. Co. log. sin 1.8017948 log. sin 8.1993348 9.4353665 9.4363961 0.43926 0.52587 Ar. Co. log. sin 1.8016094 log. sin 7.1461719 8.9477813 .4810 0.61241 0.69889 .4811 0.78530 'Ar. Co. log. sin 1.8016094 log.cos 9.9999996 log. tang 7.6632559 9.4648649 0.291606 0.56482 Diff. +.08688 .08681 .08674 . 08668 .08661 .08654 .08648 .08641 ľ +.1738 0.56481 0.01840 .1738 0.564810.01 .56486 .01844 .1735 .56490 .01848 .56494 .01852 .1733 .56497 .01855 .56500 .01858 .1730 .56502 .01860 .56504 .01862 .1727 .56505 .01863 Sidereal time at mean noon at Greenwich, Z H, at time T, (2hrs.) 44 11 0 A" 2′ 28′′.2 Making now the approximate calculation, the results obtained would be nearly the same as those found in the first example to Prob. XVI. We may, therefore, for finding the times of beginning and end more accurately, take T′ = 0.06h. for the beginning, and T' = 2.56h. for the end. Z Long. of Philada. Z, at time T, (6 .00095 = .0578 For Philadelphia. p=-1.10417;q=0.10258; p=0.4807; d=0.1738; H-73°17′0′′. log. p sin o' log. p sin o' .73522 Τ .0625 9.8053 log. A. 7.1746 6.9799 9.88517 log. sin 9.98125 n For the beginning. 83° 19′ 25′′.3 h. h. m. 0.06 0 3.6 9.86642 n log. sin 9.5114 9.4180 8.7958 n log. G. 9.3440 9.4180 8 9 25.3 52 20 25.3 h. m. sec. 3 22 57.98 2 0 16.71 5 33 17.69 83° 19′ 25′′.3 8.7620 b = .00096 h = 1 − (a + b) =.56290 9.80532 log. cos 9.97582 9.78114 9.88517 log.cos 9.45885 log. G. 9.34402 log. sin 9.51140 8.85542 log. G. 9.3440 log. B. 7.6391 6.9831 V p'u'.4229 P U d a = .00096 log. p cos. q' H N 60° 48′ 20′′ - .36895 .20615 .2363 W u ť .0382 .44887 .22373 130° 31' 11" .86478 .87242. T' h. h. m. sec. T' — t' + t = 0.06764 = 0 4 3.5 true time of beginning. h. - 2.56 p=.09793; q.53625; p=.4810; g.1731; H-35° 47′ 0′′. log. p sin o' ρ log. p sin ' ρ D' . 9.8053 log. A 7.1752 6.9805 log. 9.37346 Ar. Co. 0.37376 9.88517 log. sin 9.76695n 9.65212n log. cot 9.74722 9.31419n log. sin 9.5119 9.4180 8.5820n log. sin 9.94100 Ar. Co." 0.24957 log. cos 9.54030 For the end. h. m. sec. Beginning 7 3 23.5 A. M., Philad'a mean time. ،، (6 (6 End 2 If a more accurate computation of the time of greatest obscuration and of the quantity of the eclipse is desired, let T' the time before found, taken to the nearest hundredth of an hour, and find the values of p, q, u, v, &c., for this time. The computation may then be made by articles 8 and 10 of the rule to Prob. XVI., using logarithms to five decimal figures, and putting the value of g' found by the first part of the present rule, in stead of the number 2732. |
