XXVI. CORRECTIONS OF THE Lunar Method of finding the Longitude. THE By Mr. REUBEN BURROW. HE intent of the following remarks is to point out an error in the ufual Practice of making the Lunar Obfervations, and another in the Method of Computatian. It is well known that a little before and after the conjunction, the whole hemifphere of the Moon is vifible, and the enlightened crefcent seems to extend fome distance beyond the dusky part. Now, having determined the longitude of a place from the eclipfes of Jupiter's Satellites, I took feveral fets of diftances of the Moon's limb from a Star near the time of the conjunction, both from the bright and the dufky parts of the circumference, and having calculated the refults, I found that thofe taken from the dufky part were much nearer the truth than the others. The nature of the error evidently fhewed, that the ftar had really been at fome diftance from the limb when it appeared to be in contact with it; and, as the error was a confiderable part of a degree, I faw it would be of confequence to difcover the cause of it; which, however, was obvious enough from Newton's principles, and may be explained as follows. Let Let AD be the diameter of the moon, and A the center of a star in contact with the moon's limb: now, as the enlightened part of the moon evidently appears to extend beyond the dufky part, let the concentric circle BC reprefent the moon's limb thus apparently magnified, and fuppofe the ftar to be equally magnified; then with the center A, and the diftance DC, describe a circle, which confequently will touch the moon's apparent circumference inwardly now, as this laft is a confequence of fuppofing the center of the ftar to touch the circumference of the moon, exclusive of the deception, it follows, that the proper method of taking the distance, is to make the star appear to touch the moon inwardly. But all the writers on this fubje&t have particularly directed that the ftar be made to touch outwardly. Let B, therefore, be the point of contact, and a the center: the error then is Aa, or the fum of the apparent increase of the moon's radius and the apparent radius of the star: this quantity, it is evident, will make a confiderable error in the refult; and errors arifing from this fource are the more to be attended to, as they are not of a kind to be leffened by increafing the number of observations. The fame reasoning is applicable to the Sun and Moon, with very little alteration. The distance of the Moon from the Sun or a Star, at each three hours, is given in the Nautical Ephemeris; and the method of inferring the time for any intermediate distance, is by fimple proportion: this would be juft if the Moon's motion was uniform: but as this is not the cafe, the velocity should be taken into the account, as well as the fpace, in determining the time taken by the Moon to move any given diftance; and the proper measure of the velocity is fuch a quantity as has the fame ratio to the space defcribed, as three. hours have to the time that has been actually taken to move move the given distance: to find this quantity correctly, would require interpolation; but it will be fufficient in practice to find the time firft by the common method, and then to correct the interval for three hours to that time, by taking a proportional part of the fecond difference of the Moon's diftance at the beginning of each three hours; fuppofing the firft differences to answer to the middle of each interval. The laft correction, though not fo confiderable as the firft, will often bring the refult nearer to the truth by three, four, five, or fix miles, and fometimes more, which in geographical determinations is of confequence; and, by paying attention to those and fome other caufes of error, which fhall be pointed out hereafter, the refults in general will be much nearer to the truth than is ufually imagined. It is common to throw blame on the imperfections of the Lunar Tables, but it would be much more properly applied to bad inftruments and bad obfervers. CONTENTS CONTENTS OF THE FIRST VOLUME. I. On the Orthography of Afiatick Words III. A Royal Grant found at Mungir IV. An Infcription on a Pillar near Buddal IX. On the Gods of Greece, Italy, and India X. On a Cave with an Infcription near Gaya 309 332 XVIII. Page XVIII. On the Literature of the Hindus XIX. 1. A Royal Grant found at Tana XX. On the Vajracita or Pangolin XXI. Infcriptions on the Staff of Firuz Shah XXII. A Conversation with an Abyffinian XXIII. On the Indian Trial by Ordeal XXIV. The Second Anniversary Discourse XXV. Difcourfe III. On the Hindus XXVI. The Lunar Obfervations corrected APPENDIX: A Meteorological Journal. |