the sun's), is to 24 hours, so is the approximate time of transit to the apparent time of the planet's transit over the meridian of Greenwich. Note. If the terms be reduced to seconds, the operation may be easily performed by logarithms. Example 1. Required the apparent time that the planet Mars will pass the meridian of Greenwich, March 16th, 1825 ? Planet's right ascension at noon of the given day = Approx. time of the planet's transit over the mer. of Greenw.=1 5 29'.7 Planet's right ascension at noon, March 16th,= 0:49"30: Note. The sum is taken because the planet's motion is retrograde. = As 24 ho.+629:24 6*29, in secs. 86789 Log.ar.comp.=5.061535 Is to 24 hours, in seconds= 86400 Log. = .. 4.936514 So is the approximate time of transit = 15" 29.7, in seconds = 3929.7 Log. 3.594359 3912. 1 Log. 3.592408 Example 2. To the apparent time of the planet's transit 1512. 1, in seconds = Required the apparent time that the planet Venus will pass the meridian of Greenwich, Sept. 23d, 1825 ? Planet's right ascension at noon of the given day = Sun's right ascension at that noon = Approx. time of the planet's tr. over the mer. of Greenw. 21:3410'.3 Difference of motion 0 1 4'.2 Note. The difference is taken because the planet's motion is progressive. As 24-14'.2=23:58 55'. 8, in secs.=86335. 8 Log.ar.co.=5.063809 Is to 24 hours, in seconds = So is the approx. time of 86400. Log. = . 4.936514 Given the Apparent Time of a Planet's Transit over the Meridian of Greenwich, to find the Apparent Time of Transit over any other Meridian. RULE. Take, from page IV. of the month in the Nautical Almanac, the apparent times of the planet's transits over the meridian of Greenwich on the days nearest preceding and following the given day, and find the interval. between those times; find, also, the difference of transit in that interval: then say, As the interval between the times of transit is to the difference of transit, so is the longitude, in time, to a correction; which, being added to the computed apparent time of transit, if the longitude be west and the planet's transit increasing, or subtracted if decreasing, the sum or difference will be the apparent time of transit over the meridian of the given place; but, if the longitude be east, a contrary process is to be observed; that is, the correction is to be subtracted from the approximate time of transit, if the transit be increasing, but to be added thereto if decreasing. Note. If the first and third terms of the proportion be esteemed as minutes and seconds, the operation may be performed by proportional logarithms. Example 1. Required the apparent time that the planet Mars will pass the meridian of a place 145:30: west of Greenwich, March 16th, 1825, the computed apparent time of transit at Greenwich being 1512'.1 ? As the interval=5:23:55"=14355"=22355 P. log. ar.co.=9.9028 Required the apparent time that the planet Venus will pass the meridian of a place 175:40. east of Greenwich, Sept. 23d, 1825, the computed apparent time of transit at Greenwich being 21:358'.1? PROBLEM XII. To find the Apparent Time of a Star's Transit, or Passage over the Meridian of any known Place. Since the plane of the meridian of any given place may be conceived to be extended to the sphere of the fixed stars, therefore, when the diurnal motion of the earth round its axis brings the plane of that meridian to any particular star, such star is then said to transit, or pass over the meridian of that place. This observation is applicable to all other celestial objects. The apparent time of transit of a known fixed star is to be computed by the following RULE. Reduce the right ascension of the star, as given in Table XLIV., to the given day; from which (increased by 24 hours if necessary,) subtract the sun's right ascension at noon of that day, as given in the Nautical Almanac, and the remainder will be the approximate time of transit. Turn the longitude of the given meridian or place into time, by Problem I., page 296, and add it to the approximate time of transit if the longitude be west, but subtract it if east; and the sum, or difference, will be the corresponding time at Greenwich; and let it be noted whether that time precedes or follows the noon of the given day. Find, in the Nautical Almanac, the variation of the sun's right ascension between the noons preceding and following the Greenwich time; then, To the proportional logarithm of this variation, add the proportional logarithm of the difference between the Greenwich time and the noon of the given day (esteeming the hours as minutes, and the minutes as seconds), and the constant logarithm 9. 1249*; the sum of these three logarithms, abating 10 in the index, will be the proportional logarithm of a correction, which, being added to the approximate time of transit if the Greenwich time precedes the noon of the given day, or subtracted therefrom if it follows that noon, the sum or difference will be the apparent time of the star's transit over the given meridian. Example 1. At what time on the 2d of January, 1825, will the star Rigel transit, or come to the meridian of a place 165:30: east of Greenwich? * This is the arithmetical complement of the proportional logarithm of 24 hours, esteemed as minutes. Right ascension of Rigel, reduced to the given day, Variation of right ascension 4*25! Diff. of Gr. time from noon = 47.36 Prop. log. At what time on the 2d of January, 1825, will the star Markab transit, or come to the meridian of a place 140:40: west of Greenwich? Right ascension of Markab, reduced to the given day,=. 22:56" 3! Sun's right ascension at noon of the given day = Approximate time of transit = Longitude 140:40: west, in time = Greenwich time = which, of course, is past the noon of the given day. 18.51.44 4.4 19: 9.22.40 13:26:59: 18:41 44 3d, = Variation of right ascension in 24 hours = * If 12 hours, diminished by half the variation of the sun's right ascension, be added to the apparent time of transit, thus found, the sum, abating 24 hours if necessary, will give the apparent time of transit below the pole. |