Remark. Should the proportional part corresponding to the daily variation of the sun's longitude and any given time be required, it may be taken from the first page of the Table, by esteeming the seconds of variation, in that page, as minutes, and then raising the signs of the corresponding proportional parts one grade higher than what are marked at the top of the said page: the seconds of variation will, of course, be taken out after the usual manner. Thus, Suppose that the daily variation of the sun's longitude be 57: 40%, and the Greenwich time 9 hours 50 minutes, to find the corresponding equation, or proportional part. Pro. part to 9:50 and 57:40 is 23.37.38.20 = 23:38" + Note. It is easy to perceive that the foregoing operations might have been much contracted, by taking out two or more of the proportional parts at once; but, lest doing so should appear anywise ambiguous to such as are not well acquainted with the method of taking out tabular numbers, it was deemed prudent to arrange the said operations according to their present extended form, so as to render them perfectly intelligible to every capacity. The present Table was computed agreeably to the established principles of the rule of proportion; viz., As one day, or 24 hours, is to the variation of the sun's right ascension, declination, &c. &c., in that time, so is any other portion of time to the corresponding proportional part of such variation. ... TABLE XVI, To reduce the Moon's Longitude, Latitude, Right Ascension, Declination, Semidiameter, and Horizontal Parallax, as given in the Nautical Almanac, to any given Meridian, and to any given Time under that Meridian. This Table is arranged in a manner so nearly similar to the preceding, that any explanation of its use may be considered almost unnecessary; the only difference being, that the proportional parts are computed to variation in 12 hours, instead of 24. By means of the present Table, the propor tional part corresponding to any variation of the moon's longitude, latitude, right ascension, &c. &c. &c., may be easily obtained, to the greatest degree of accuracy, as follows; viz. Turn the longitude of the ship or place into time (by Table I.), and add it to the apparent time at such ship or place, if it be west; but subtract it if east and the sum, or difference, will be the corresponding time at Greenwich. Take from pages V., VI., and VII. of the month, in the Nautical Almanac, the moon's longitude, latitude, right ascension, declination, semidiameter, and horizontal parallax, (or any one of these elements, according to circumstances,) for the noon and midnight immediately preceding and following the Greenwich time, and find their difference; which difference will express the variation of those elements in 12 hours. Enter the Table with the variation, thus found, at top, and the Greenwich time in the left-hand column; in the angle of meeting will be found the corresponding equation, or proportional part, which is always to be added to the moon's longitude and right ascension at the preceding noon or midnight, but to be applied by addition, or subtraction, to the moon's latitude, declination, semidiameter, and horizontal parallax, according as they are increasing or decreasing. And, since the Greenwich time and the variation in 12 hours will be very seldom found to correspond exactly; it is the sum, therefore, of the several equations making up those terms, that will, in general, express the required proportional part. Example. Required the moon's longitude, latitude, right ascension, declination, semidiameter, and horizontal parallax, August 2d, 1824, at 310", in longitude 60:30, west of the meridian of Greenwich? To find the Moon's Longitude : Moon's longitude at noon, August 2d, 1824, per Nautical Almanac, Propor. part to 7 0 and 6: 0: 0 = 0. 6. 0. 0 Propor. part to 7:12 and 6:31:59 is 3.55. 11. 24 +3:55:11 Moon's longitude, as required. To find the Moon's Latitude: Moon's latitude at noon, August 2d, 1824, per Nautical 7:21:11:38" Proportional part to 7:12 and 23:35 is 14. 9. 0-14: 9% Note.-In consequence of the unequal motion of the moon in 12 hours, (when her place is to be determined with astronomical precision,) the proportional part of the variation of her longitude and latitude, found as above, must be corrected by the equation of second difference contained in Table XVII.; and the same may be observed of her right ascension and declination, To find the Moon's Right Ascension: Moon's right ascension at noon, August 2d, 1824, per 223:33:36" = 0. 0.35. O Propor. part to 7:12 and 6:51:49 is 4. 7. 5.24 +4 7: 5% Moon's declination at noon, August 2d, 1824, per Nautical Almanac,'. 227:40:41* 20:57: 7" Propor. part to 7:12 and 1:23:43 is 50. 13.48 = +50:14" * When accuracy is required, the moon's right ascension and declination must be corrected by the equation of second difference, on account of the irregularities of her motion in 12 hours. To find the Moon's Semidiameter: Moon's semidiameter at noon, August 2d, 1824, per Nautical Moon's horizontal parallax at noon, August 2d, 1824, per Nautical Almanac, 15:33% 4" 15:29% Proportional part to 7:12 and 23" is 13.48 Moon's horizontal parallax, as required 14" 56:52" Remarks.-1. It is evident that, in the above operations, the greater part of the figures might have been dispensed with, by taking out two or more of the proportional parts at once; but since they were merely intended to simplify and render familiar the use of the Table, the whole of the proportional parts have been put down at length. 2. This Table was computed according to the rule of proportion; viz.:→→ As 12 hours are to the variation of the moon's longitude, latitude, right ascension, &c. &c. &c., in that interval, so is any other given portion of time to the corresponding proportional part of such variation. TABLE XVII. Equation of Second Difference. Since the moon's longitude and latitude, and also her right ascension and declination, require to be strictly determined on various astronomical occasions; particularly the two latter when the apparent time is to be D |