EXAMPLE II. When it is 21h.26 at Greenwich, on the 3d of June, what hour is it at a place in 120° East longitude 2 Time at Greenwich - 21h.26' Longitude 120°, in time = 8. – East. Time in longitude 120° E. = 5. 26, on June 4th. EXAMPLE III. When it is 13". 56' at Greenwich, on the 12th of August, find what hour it is at a place in longitude 97°.45'West. - Time at Greenwich 13h. 56' Longitude 97°45', in time=6. 31 W. Time in longitude 97°45' W. =7. 25, on the 12th of EXAMPLE IV. When it is 9h.20 at Greenwich, on the 2d of May, what hour is it at a place in longitude 160° West? Time at Greenwich - - - -24h.-33b. 20' Longitude 160°, in time - - - - = 10.40 W. Time in longitude 160° W. - - =22.40, on the 1st of May, or 40 minutes past 10 in the morning on the 30th of April. PRACTICAL ExAMPLES. 1. When may an emersion of the first satellite of Jupiter be observed at Bombay, in longitude 72°.54'30"E, which, by the Nautical Almanac, happens at Greenwich on the fourteenth of January 1822, at 6h.23/.33". Answer. 11b. 15'.11". 2. What is the expected time of the beginning of the Lunar eclipse, which happens on August 2d, 1822, at 10*.51'.40" at Greenwich, in longitude 76°49'.30" West? Answer, 5.44'.22". PROBLEM V. (B) Toreduce the declination of the sun, as given in the Nautical Almanac, to any other meridian, and to any given time of the day. RULE. The corresponding time at Greenwich being ascertained (Z. 266.), find the change of the sun's declination in 24 hours from the Nautical Almanac: Then, 24 hours : this change:: the time from noon at Greenwich : the variation of the sun's declination in that time. This variation must be added to the sun's declination at noon", or subtracted from it, according as the declination is increasing or decreasing. NoTE. By a similar process the change of the sun's longitude, or of right ascension, may be determined for any given time, or at any given place; and also the declination of a planet. EXAMPLE I. Required the sun's declination at noon, on the 12th of October 1822, at Glasgow, longitude 4°.15' W. First, 4°.15'-17minutes, the time by which the clocks at Glasgow are slower than at Greenwich; hence when it is noon at Glasgow, it is Oh'17' at Greenwich. Then 24h : 22.34":: 17' : 16" the increase of the sun's declination in 17 minutes of time; consequently when it is noon at 'Glasgow, the sun's declination is (7°.17.34"--16"=)7°.17.50" South. ExAMPLE II. What is the sun's right ascension, June 5th 1822, at 13h.48'. in longitude 63°.10'E.” Time at the given place - - - 13h. 48'. Longitude 63°. 10, in time - - = 4. 12.40" E. - Time at Greenwich - - - - 9. 35. 20 G)'s right ascension at noon June 5th, Naut. Alm. is 4.51%. 21.7 Increase of right ascension in 24 hours - - 4s. 6".9 * The sun's longitude, right ascension in time, and declination are given, in the IId page of the Nautical Almanac, for every day in the year, at noon, calculated for the meridian of Grecnwich. 1. Required the sun's declination on the 25th of August 1822, at 8.20, in longitude 48° West. The declination at Greenwich, at noon, (by the Nautical Almanac) being 10°.53'.35" N. and on the 26th, 10°.32'.50" N. Answer. 10°.43'.37". N. 2. Required the sun's right ascension at noon, on the 25th of May 1822, in longitude 124° East. The right ascension at Greenwich (Naut. Alm.) being 4".6'. 31", and on the 24th of May, 48.2.29". Answer. 4".5'.29". 3. Required the sun's declination January 24th, 1822, at 18h.40' in longitude 132° East. The declination at Greenwich, at noon, (Naut. Alm.) being 19°.16.13" South, and on the 25th, 19°.1'.38" S. Answer. 19°.10.14" S. 4. Required the sun's right ascension on the 16th January 1822, at 18.48, in longitude 68° West. The right ascension at Greenwich, at noon, (Naut. Alm.) being 19.51'.80", and on the 17th, 195,55'47". Answer. 19%. 54.2". PROBLEM WI, (C) To reduce the declination of the moon, as given in the Nautical Almanac, to any other meridian, ana to any given time of the day. RULE. Find the time at Greenwich corresponding to the time at the given place. (Z. 266.) Take the change of the moon's declination in 12 hours from the Nautical Almanac. Then, 12 hours : this change:: the time at Greenwich : the variation of the moon's declination in that time. This variation must be added to the moon's declination (at noon or midnight) if the declination be increasing, or subtracted if the declination be decreasing. NoTE. By a similar process the change of the moon's right ascension", semidiameter, and horizontal parallax may be ascertained for any given time, or at any given place. * The moon's age and time of passage over the meridian of Greenwich are Longitude 119.45° West, in time - - = O 47 W. Time at Greenwich - - - = 16*.32, or 4".32 past midnight. D's semi-dia. at midnight, 26th, – 15.57"; hor. paral. - - =58'.32” ) 's semi-dia. at noon, - 27th, = 15.59"; hor, paral. - - =58'.41’’ Increase in 12 hours, - - = 0.2"; increase in 12 hours - O'. 9” 12h : 2"::4h.32! : - - oon 12h : 9"::4*.32 : 3” 4 EXAMPLE I. 1. Required the moon's declination March 17th 1822, at 7".22' in longitude 57° W. The moon's declination at noon (Naut. Alm.) at Greenwich, being 26°.12' S, and at midnight 24°.58’S. Required the moon's semidiameter and horizontal parallax on the 26th of January 1822, in longitude 11°.45' West, at 15h.45' apparent time. The semidiameter, at Greenwich, at midnight, (Naut. Alm.) being 16.1" and at noon on the 27th, 16.3", also the horizontal parallax at the same time 58.32", and 58.41". Time at the given place - 15h.45' D's semi-dia at midnight = 15'.57". ||hor par. at midnight - = 58' 32" X’s ditto in long. 11°.45'W. = 15.57".7||hor-par..in long. 11°.45°W. =58.35”.4 Hence they's semi-diameter at 15h.45' in long. 11°.45' W, is 15.57”.7, and the horizontal parallax is 58'.35".4. given in the VIth page of the Nautical Almanac; and her latitude, longitude, right ascension, declination, semidiameter, and horizontal parallax, are given for moon and midnight at Greenwich in pages Vth, VIth, and VIIth, foreach month. * If the time at Greenwich had exceeded 12 hours, the moon's declination must have been taken out for midnight and the noon of the next day; and the variation applied to the midnight declination. PRACTICAL ExAMPLES. 1. Required the moon's declination on the 11th of January, 1822, at 17h,47 in longitude 162° West? The moon's declination at noon at Greenwich (Naut. Alm.) on the 12th of January, being 1°.19 N. and at midnight 19.35 S. Answer. The time at Greenwich is 45.35' on the 12th of January, and the moon's declination is 0°.13' North. 2. Required the moon’s semidiameter and horizontal parallax on the 19th of May, 1822, in longitude 38°40' E. at 11”. 15' apparent time. The moon's semidiameter at Greenwich (Naut. Alm.) at noon and midnight being 16.38" and 16.41’’; and the horizontal parallax at the same time 61'.3" and 61.13". Answer. The time at Greenwich is 8b. 40.20", D's semidiameter= 16.40" and horizontal parallax = 61.10". 3. Required the moon's declination on the 13th of May, 1822, at 19 in longitude 67° East. The moon's declination at Greenwich (Naut. Alm.) at midnight being 15°.5' S. and at noon on the 14th 12°.27° S. Answer. The time at Greenwich is 14".32', D's declination l 4°.32' S. 4. What is the moon's declination on July 19th, 1822, at 4".49 in longitude 114° East 2 The moon's declination at Greenwich (Naut. Alm.) at midnight on July 18th being 21°.12'N, and on July the 19th at noon 18°.51° N. Answer. The time at Greenwich is 21h. 13 July 18th, and the moon's declination 19°.24' N. PROBLEM VII. (D) To find the time of a star's culminating, or coming to the meridian of Greenwich. RULE. Subtract the right ascension of the sun for the given day from the right ascension of the star, and the remainder will be the time of the star's culminating nearly.—If the sun's right ascension exceed the star's, add 24 hours to the star's before you subtract. . . - - Take the increase of the sun’s right ascension in 24 hours, and add it to 24 hours. Then, This sum is to 24 hours as the star's right ascension diminished by the sun's, is to the time of the star's culminating. NotE. If the time of culminating be required for any other T |