-- Note. The difference is taken between the transits on the given day and the day preceding, because the longitude is west, and the times of transit decreasing; this being the converse of the above example with respect to longitude and the motion of the transits.-Now, 6.30 Interval between the transits = 23:53:30: Prop. log. ar. comp. 9. 1230 .1.4424 .1.2829 -2:33: Prop. logarithm Correction = Mn. time of tran. on given day= 0:20 39: at the given meridian. Remark.-The correction is subtractive, because the longitude is west, and the times of transit decreasing; had they been increasing, the correction would be additive to the meridian passage at Greenwich on the given day. The young navigator must bear in mind, that in west longitude when the times of transit are increasing, a planet will not come to the meridian of any place until after it has passed the meridian of Greenwich; but, when the times are decreasing, it will come to the meridian of such given place before its transit at Greenwich.-Again, in east longitude, when the times of transit are increasing, a planet will come to the meridian of any given place before it passes the meridian of Greenwich; but, when the times are decreasing, it will not come to the meridian of such place until after it has passed the meridian of Greenwich. This observation will conduce to the elucidation of Article 3, page 517 of the Nautical Almanac for 1836. PROBLEM XIV. To Reduce the Sun's Right Ascension and Declination; the Equation of Time, and the Sun's Longitude, as given in the Nautical Almanac, to any given Mean Time under a known Meridian. RULE. Let the given mean time at ship or place be always reckoned from the preceding noon; to which apply the longitude in time (reduced by Problem I., page 341,) by addition if it be west, or subtraction if east; the sum, or difference, will be the corresponding mean time at Greenwich, subject to the conditions in Problem III., page 342. Take, from page II. or III. of the month in the Nautical Almanac, the sun's right ascension and declination, the equation of time, or longitude, as the case may be, for the mean noons 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 (reckoning the hours as minutes, and the minutes as seconds), and the constant log. 9. 1249:* the sum of these three logs. rejecting 10 from the index, will be the proportional log. of a correction, which is always to be added to the sun's longitude, or right ascension, at the mean noon preceding the Greenwich time; but to be applied by addition or subtraction to the sun's declination, or the equation of time at that noon, according as these elements may be in-. creasing or decreasing. Example. Required the sun's right ascension, and declination, the equation of time, and the sun's longitude, January 1st, 1836, at 3*40′′ mean time, in longitude 35:40:45" west of the meridian of Greenwich? *The arith. comp, of the prop. log. of 24 hours, esteemed as minutes. To Reduce the Sun's Declination at Mean Noon to a given Meridian; commonly called, "Correcting the Declination." RULE. If the equation of time be marked additive, in page I. (not page II.) of the month in the Ephemeris, it will express the approximate mean time of the sun's transit over the meridian of the ship past the apparent noon of the given day; but, if it be marked subtractive, 24 hours minus the equation will be the approximate mean time of the sun's transit past the apparent noon of the preceding day. To the approximate mean time of transit, thus found, apply the longitude, in time, by addition if west, or by subtraction if east; and the sum, or difference, will be the approximate mean time at Greenwich; with which, and the difference of declination for the mean noons immediately preceding and following it, proceed as in the second of the above operations. Example. Required the sun's declination at mean noon, March 26th, 1836, at a ship in longitude 173:45 west, and also at another ship in longitude 167:15 east of the meridian of Greenwich? Since the equation of time (viz. 5:44: taken to the nearest second) is marked additive; therefore the mean time of noon on the given day is 05:44; now, the west longitude, in time, viz. 11:35", being added to that, shows the Greenwich time at the western meridian to be 11:40" 44, past noon of the given day.-And, the east longitude, in time, viz. 11'9", being subtracted from 0544 (increased by 24 hours) shows the Greenwich time at the eastern meridian to be 12:56:44: past noon of the preceding day. To Correct for the Ship at the Western Meridian. . Correction of declination = Sun's corrected declination = 11:40:44 +11:26 Prop. log. 1. 1973 north. 2:31:33 north. To Correct for the Eastern Meridian. Difference of declination in 24 hours 23:32" Prop. log. = 1.1432 9.1249 Sun's declination at noon, March 25th = 1:56:35% north. Sun's corrected declination = 2: 9:17 north. Note. In strictness, the equation of time at Greenwich ought to be reduced to the given meridian :- but, since the greatest diurnal difference in that element never exceeds 30 seconds; which, at the utmost extent of longitude, would only affect the Greenwich time to the value of 15 seconds; and since a difference of this value cannot affect the sun's declination, (even at the time of the equinoxes, when its diurnal variation is the greatest,) more than the small fraction 0:25, or the fourth part of a second; therefore, for the above purpose, the reduction of the equation of time may be dispensed with. - Remark. The young navigator must bear in mind that the sun's right ascension, and declination, and, also, the equation of time are always to be taken from page II. of the month in the Nautical Almanac : the elements, of the same denominations, in page I. of the month, and which are adapted to "Apparent Time," are entirely for the use of astronomers, and not for the purposes of navigating a ship over the boundless ocean. Note.-The sun's right ascension is given in the Ephemeris to hundredths of a second, and his declination to tenths of a second; and the equation of time to hundredths of a second :-but, since, for practical purposes at sea, the nearest second in either of these elements will be sufficiently near the truth; if, therefore, the decimals in the right ascension, and in the equation of time be 50 or under, reject them; but if they be more than 50, increase the seconds in the right ascension, and equation of time by unity or 1. In like manner, should the decimal in the declination be 5, or under, reject it; but, if it be more than 5, increase the seconds of declination by unity or 1; as in the preceding example. PROBLEM XV. To Reduce the Moon's Semidiameter; Horizontal Parallax ; Longitude, and Latitude, as given in the Nautical Almanac, to any given Mean Time under a known Meridian. Let the given mean time at ship or place be always reckoned from the preceding noon; to which, apply the longitude, in time (reduced by Problem I., page 341), by addition, if it be west; but by subtraction if east; the sum, or difference, will be the corresponding mean time at Greenwich; with reference to the conditions in Problem III., page 342; noting whether it be past noon or midnight. Take from pages III. and IV. of the month in the Nautical Almanac, the moon's semidiameter, horizontal parallax, longitude, and latitude for the noon and midnight immediately preceding and following the Greenwich time; and find the 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 log. 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, at the noon or midnight preceding the Greenwich time; but to be applied by addition or subtraction to her latitude, semidiameter, or horizontal This is the arithmetical complement of the proportional log. of 12 hours, esteemed as minutes. |