Rule XII. To take out the moon's declination and right ascension. The moon's declination and right ascension are recorded in the Nautical Almanac for the beginning of every hour of mean time at Greenwich. To find them for any other time we may proceed as follows: First. To find the moon's declination for any given time. 1. Get a Greenwich date. 2. Take out of the Nautical Almanac the moon's declination for two consecutive hours between which the Greenwich date lies, and take the difference. 3. Add together the logistic logarithm of minutes in Greenwich date and proportional logarithm of difference, the sum will be the proportional logarithm of correction, which take from the table and apply it to the declination for the hour of Greenwich date, adding or subtracting according as the declination is seen to be increasing or decreasing. The result is the declination required. Second. To take out the moon's right ascension. Proceed in a similar manner to that pointed out above for finding the moon's declination. EXAMPLES. January 24, 1852, at 5h 10m P.M. mean time, in long. 60° 10′ W., find the moon's right ascension and declination. (45.) June 2, 1852, at 2h 30m P.M. mean time, in long. 53° 15′ W., find the moon's right ascension and declination. Ans., Right ascen. 17h 11m 53s Declination. 21° 15' 54" S. (46.) Sept. 7, 1852, at 4h 15m A.M. mean time, in long. 56° 30′ E., find the moon's right ascension and declination. Ans., Right ascen. 5h 5m 178 (47.) July 10, 1853, at 9h 30m A.M. mean time, in long. 44° 20′ W., find the moon's right ascension and declination. Ans., Right ascen. 10h 36m 348 Declination 14° 14' 32" N. To take out the right ascension of the mean sun (called in the Nautical Almanac sidereal time). The right ascension of the mean sun, or the sidereal time at mean noon, is given in the Nautical Almanac for every day at mean noon. To find it for any other time we may proceed as in the rule for finding the right ascension of the apparent or true sun; but as the motion of the mean sun is uniform throughout the year (the motion in every 24 hours being 3m 568-555), the change in any given number of hours, minutes, and seconds is more easily found by means of a table. This table is given in the Nautical Almanac, and may be sought for in the Index under the title of "Time Equivalents, table of.” EXAMPLE. July 23, 1853, at 2h 42m P.M. in long. 80° 42′ E., required the right ascension of the mean sun. Find the right ascension of mean sun (called in the Nautical Almanac sidereal time) in the following examples: (48.) March 2, 1853, at 10h 42m P.M. mean time in long. 48° 10′ W. Elements from Nautical Almanac and answers. Sidereal time March 2, at noon, 22h 40m 44s.9. Ans. 22h 43m 25.0 To take out the lunar distances for any given time at Greenwich. 1. Get a Greenwich date. 2. Find two consecutive distances in the Nautical Almanac at times between which the Greenwich date lies. Take the difference of the distances. To the proportional logarithm of the excess of the Greenwich date above the first of the times taken from the Nautical Almanac add proportional logarithm of difference of distances; the sum will be the proportional logarithm of an arc; which are being applied to the distance at first time with its proper sign will be the distance required. EXAMPLE. September 24, at 6h 10m P.M. mean time nearly, in long. 60° 15′ W., required the distance of Aldebaran from the Dist. of Aldebaran at 6h 10m P.M. 19 31 31 Required the distance of the moon from certain stars in the following examples : (51.) Jan. 24, at 4h 30m P.M. mean time nearly, in long. 30° 30′ E., required the distance of Regulus from the moon. Ans., 69° 33' 6". (52.) May 20, at 6h 20m A.M. mean time nearly, in long. 40° 0' E., required the distance of a Pegasi from the moon. Ans., 56° 59' 7". (53.) June 10, at 9h 40m P.M. mean time nearly, in long. 32° 45′ W., required the distance of a Aquile from the Ans., 70° 32′ 35′′. moon. (54.) July 2, at 7h 20m A.M. mean time nearly, in long. 30° 0' E., required the distance of Jupiter from the moon. Ans., 54° 16' 52′′. (55.) Sept. 19, at 10h 30m A.M. mean time nearly, in long. 63° 15′ E., required the distance of Aldebaran from the moon. Ans., 72° 0′ 51′′. (56.) Dec. 15, at 2h 0m P.M. mean time nearly, in long. 19° 40′ E., required the distance of Pollux from the moon. Ans., 58° 56' 47". In the rule for finding the longitude by lunar observations, we have to ascertain the true distance of the moon from some heavenly body at the time of observation. If the heavenly body is one whose distance is recorded in the Nautical Almanac for every three hours, we may find the mean time at Greenwich corresponding to the true distance computed for the time of observation as follows: Rule XV. To find the time at Greenwich corresponding to a given distance of a heavenly body from the moon. 1. Under the given distance put down the two computed distances of the same heavenly body found in the Nautical Almanac between which the given true distance lies. 2. Take the difference between the first and second, and also between the second and the third. 3. From the proportional logarithm of the first difference subtract the proportional logarithm of the second difference, the sum is the proportional logarithm of the additional time to be added to the hours of the distance first taken out of the Nautical Almanac; the result is the mean time at Greenwich corresponding to the given distance. |