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XVIII. An Ejlfay on the Method of determining the Difference 

 of Longitude between Places at Land, from the obferved 

 Tranfits of the Moon over their Meridians ; with a De~ 

 monjlration and Example. Bj> Mr. Gavin Lowis *. 



Ea eft methodorum rimpliclffimarum ratio atque natura, uc poftremas in 

 thentem veniant, et niil oblUaatiore animo, ne veniant tjuidem. 



BoscoviCK, 



jfXLTHOUGH the nlethod of determining the difference 

 of longitude at fea from the Umar obfervatiuns has been ac- 

 curately laid down bv Dr. Mafkelyne and other able nautical 

 aftronomers, it has, however, happened that feveral writers 

 on longitude and agronomy have, in the courfe of the lalt 

 twenty years, given rules for finding the difference of longi- 

 tude at land from the moon's tranfits, either fo erroneous or 

 imperfect, that the adoption thereof might do a ferious injury 

 both to navigation and geography: they have given exam- 

 ples, but no demonftrations ; or at leaft. fuch obfcure and im- 

 perfe6l ones, as prove that they had not a clear conception 

 of the matter. 



It is for thefe reafons that the following demonftration of 

 a rule both eafy and accurate for finding the difference of 

 longitude, is now propofed. The data are the obferved in- 

 creafe of the moon's right afccnfion in pafling from the firft 

 to the fecond meridian, and the increafe of the fun's tmd 

 moon's right afcenfion in twelve hours apparent time, which 

 may be had from the Nautical Almanac. 



DEMONSTRATION. 



Let the circle ABC reprefent the equator, P its pole, and 

 APD the firft meridian, as that of Greenwich. Suppofe that 

 the centres of the fun, the moon, and a fixed ftar are on that 

 meridian at the fame moment of time as reprefented at A, 

 and that they move from thence to the weftward with their 

 refpeftive velocities, the earth being confidered as at red. 

 Then, after twelve hours apparent time, the fun will be atD, 

 the oppofite point to A, or i8o' diftant from it; but the fixed 

 liar, moving in appearance over a greater fpace than iSo" in 

 twelve hours apparent time, will be at E; while the moon, 

 with a motion apparently flower than the fun and the ftar, 

 will appear after tweht hours at the point B, or on a meri- 

 dian B P. But ED is the djftance of the fun from the ftac 



^ C onjmunicatfd by tlie Author. 



Vol. XV. No. 58. H after 



March 1803. 



