PROBLEM II. To reduce the Moon's Longitude, Latitude, Right Ascension, Declination, Semi-diameter and Horizontal Parallax, as given in the Nautical Almanac, to any given Meridian, and to any given time under that Meridian. RULE. To the apparent time at ship, or place, (reckoned from the preceding noon or midnight,) add the longitude, in time, if it be west, but subtract it if east, and the sum, or difference, will be the Greenwich time past that noon or midnight, according as it may be. Take from page V. VI. or VII. of the month in the Nautical Almanac, the moon's longitude, latitude, right ascension, declination, semidiameter, or horizontal parallax for the noon and midnight immediately preceding and following the Greenwich time, and find their difference; then, To the proportional log. of this difference, add the proportional log. of the Greenwich time past the preceding noon or midnight, (reckoning the hours as minutes, and the minutes as seconds,) and the constant logarithm 8.8239; the sum of these three logs., abating 10 in the index, will be the proportional log. of a correction which is always to be added to the moon's longitude or right ascension at the noon or midnight preceding the Greenwich time; but to be applied by addition or subtraction to her latitude, declination, semidiameter or horizontal parallax, at that noon or midnight, according as it may be increasing or decreasing. Note. Since the difference of the moon's longitude and right ascension, in 12 hours, will always exceed the limits of the Table, and also the difference of her declination in that interval, at times; if, therefore, the one half or one third of such difference be taken, and the correction, resulting therefrom, multiplied by 2 or 3, the required correction will be obtained. Example. Required the moon's longitude, latitude, right ascension, declination, semidiameter and horizontal parallax, Aug. 2d, 1824, at 3:10" past noon, in longitude 60:30 west of the meridian of Greenwich? The arithmetical complement of the proportional log, of 12 hours esteemed as minutes. To find the Moon's Longitude. Diff. in 12 hours 6:31:59% +3=2:10:393", prop. log. 7:12" = prop. log. = .1391 = 1.3979 Constant log. Moon's long, at noon, Aug. 2, 1824. =7:17:16:27 To find the Moon's Right Ascension: Diff. in 12 hours = 6:51′49′′ +32:17:163", prop. log. Constant log. 7:12 prop. log. = .1177 = 1.3979 = 8.8239 One third the corr. of the moon's rt. asc. 1:22:22" p. log, 0.3395 Moon's rt. asc. at noon, Aug. 2, 1824,223.33.36. Note.-The correction, or proportional part of the moon's motion, found as above, must be corrected by the equation of second difference contained in Table XVII., as explained in pages 33 and 34. Moon's semidiameter at noon, Aug. 2, 1824,15433" Corr. of moon's horiz. paral.. Moon's horiz. paral. at noon, Aug, 2, 1824, 57, 6: Note. The moon's semidiameter, thus found, must be augmented by the correction contained in Table IV., as explained in page 10. PROBLEM III. To reduce the Right Ascension and Declination of a Planet, as given in the Nautical Almanac, to any given time under a known Meridian, RULE. Turn the longitude into time, and add it to the apparent time at ship or place if it be west, but subtract it if east ; and the sum, or difference, will be the corresponding time at Greenwich. From page IV. of the month in the Nautical Almanac, take out the pla net's right ascension and declination for the nearest days preceding and following the Greenwich time, and find the difference; find, also, the difference between the Greenwich time and the nearest preceding day; then, To the proportional log. of this difference, add the proportional log. of the difference of right ascension, or declination, and the constant log. 9.9031*; the sum of these three logs., rejecting 10 from the index, will be the proportional log. of a correction, which being applied by addition, or subtraction, to the right ascension, or declination, (on the nearest day preceding the Greenwich time,) according as it may be increasing or decreasing, the sum, or difference, will be the correct right ascension or declination at the given time and place. Example. Required the right ascension of the planet Venus, July 3, 1824, at 10:20 apparent time, at a place 75:30: west of the meridian of Green which are to be ésteemed as minutes and seconds :-hence, The arithmetical complement of the proportional log. of 144 hours (6 days,) esteemed as minutes; and, hence taken as 2 hours and 24 minutes. |