Star's dec. on given day is 22:37:33", or 22:38 north, Sun's right ascension at noon of the given day is. Approximate time of star's transit Correction from Tab. XV., ans. to 7 13:18:, and 4:24", the vár. of the sun's right ascension . Apparent time of star's transit, or passage over the meridian 7:11:58: Time, in Tab. L. ans. to lat. 50: N., and dec. = 8' 3. 8 3 0: 30: Semi-diurnal arch, or time of half the star's Example 2. At what times will the star Sirius rise and set January 1st, 1824, in lat. 40:30 north, and long. 120 degrees, west of the meridian of Greenwich? Star's dec. on given day is 16:28:53 or 16:29 and its right ascension. Sun's right ascension at noon of the given day is Approximate time of the star's transit Corr. from Table XV., ans. to 11:53 25%, and 4'24", the var. of the sun's right ascension . Corr. from ditto, ans. to long. 120: west, and 4:24" the var. of the sun's right ascension south, 2.11 1.28 11:49 46: Appar. time of star's transit over the given meridian. + 2, nearly. 6:59, K Remark. The approximate times of the rising and setting of a fixed star may be readily reduced to the respective apparent times by the rule given for those of the sun, in page 126; omitting, however, the first part, or that which relates to the reduction of declination: and, since the fixed stars have no sensible parallax, the words "horizontal parallax" are, also, to be omitted; thus : To reduce the approximate times of rising and setting, as found in the last example, to the respective apparent times, the dip of the horizon being assumed at 6:30% Lat. of place of observ. 40:30. Nat. sine 6494 Horiz. refrac. 33+ dip of horiz. 6:30" 39'30" Prop. log.=0.6587 Constant log. = Correction=. 1.1761 3:44" Prop. log. 1.6833 Now, this correction being subtracted from the approximate time of rising, and added to that of setting, shows the former to be 6:45*2!, and the latter 16:54:30: PROBLEM III. Given the Latitude of a Place, and the Declination of a Planet, to find the Times of its Rising and Setting. RULE. Take, from page IV, of the month in the Nautical Almanac, the times of the planet's transits for the days nearest preceding and following the given day, and find their difference; then say, as 6 days are to this difference, so is the interval between the given day and the nearest preceding day, to a correction; which, being applied by addition or subtraction to the time of transit on the nearest preceding day, according as it is increasing or decreasing, the sum or difference will be the approximate time of transit. Find the interval between the times of transit on the days nearest preceding and following the given day; and then say, as the interval between the times of transit is to the difference of transit in that interval, so is the longitude, in time, to a correction; which, being added to the approximate time of transit if the longitude be west and the transit increasing, or subtracted if decreasing, the sum or difference will be the apparent time of the planet's 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 it be decreasing. To the apparent time of transit, thus found, apply the longitude, in time, by addition or subtraction, according as it is west or east ; and the sum or difference will be the corresponding time at Greenwich. To this time, let the planet's declination be reduced by Problem III., page 83; or as thus: Take, from the Nautical Almanac, the planet's declination for the days nearest preceding and following the Greenwich time, and find the difference; find, also, the difference between the Greenwich time and the nearest preceding day then say, as 6 days are to the difference of declination, so is the difference between the Greenwich time and the nearest preceding day, to a correction; which, being applied to the declination on the nearest preceding day, by addition or subtraction, according as it may be increasing or decreasing, the sum or difference will be the planet's correct declination at the time of its transit over the given meridian. Now, With the planet's declination and the latitude of the given place, enter Table L., and find the corresponding semidiurnal arch by Problem II., page 128; and, thence, the approximate times of rising and setting, in the same manner as if it were a fixed star that was under consideration. Example 1. At what times will the planet Jupiter rise and set, January 4th, 1824, in latitude 36: north, and longitude 135 west of the meridian of Greenwich? In strictness the semidiurnal arch ought to be corrected by adding thereto, or subtracting therefrom, the proportional part corresponding to it and the daily variation of transit, according as the transit may be increasing or decreasing. Time of preced. trans. Jan. 1, is 11:38" nearest prec. day 1st, trans. 11:38 0: Time of follow. trans. Jan.7, is 11. 8 given day 4th 3 to As interval between times of trans. 52330": diff. of transit 30" :: longitude in time 9 to. Apparent time of transit over given merid. Jan. 4th, 1824 = Corresponding time at Greenwich = 20 21 7: 23:17. N.; near. prec.1 0 00: dec. 23° 17′ 0′′N. 23.20 N.;Gr. tim. 4. 20. 21.7 = Jupiter's dec. reduced to his app. time of transit over the given meridian = Time, in Table L., ans. to lat. 36: north, and dec. 239 N. 2 × 19: Tabular difference to 30 of dec. 2'; now, 30: Semidiur. arch, or time of half planet's contin. above the hor. Approximate time of Jupiter's rising at the given meridian = Approximate time of Jupiter's setting at ditto. Example 2. 4: 7:51: At what times will the planet Mars rise and set, January 16th, 1824, in latitude 40 north, and longitude 140: east of the meridian of Greenwich? Time of preced. trans. 13th, is 16:54"; near.prec.day 13th,trans. 16:54" 0: Time of follow. trans. 19th, is 16, 34; given day As 6 is to 020", so is Approximate time of transit on the given day = 16th Interval between the times of transit = 5:23:40′′ As interval between times of transit = 52340:: diff. of 20" 920, to Apparent time of trans. over given merid. Jan. 16th, 1824 Corresponding time at Greenwich = + 1.18 Dec. of Mars, Jan. 13, is 0:37:S.; near. prec. 13 0 0 0:dec.0:37: 0:S. 19, is 1. 11 S.; Gr. time=16. 7.25.18 Ditto As 6 is to 0:34, so is 372518: to +18.45 Dec. of Mars reduced to his apparent time of transit over the given meridian = Semidiurnal arch in Table L., answering to lat. 40° N. and dec. 0:55:45 S., is 6'2"48; sub. from 12 leaves.. 5:57"12: Apparent time of the planet's transit over the given meridian=16.45. 18 Approximate time of rising of the planet Mars = Approximate time of setting of ditto 10:48 6: 22:42:30: Remark. The approximate times of a planet's rising and setting may be reduced to the respective apparent times, by the rule in page 126, for reducing those of the sun; omitting, however, the first part, or that which relates to the reduction of declination, and reading planet's instead of sun's horizontal parallax: this, it is presumed, does not require to be illustrated by an example. |