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one or more of thefe flars under your own meridian. Having 

 obtained correfponding obfervations from fome fettled obferva- 

 tory, find the diiFerence of the differences of A. R. of the 

 moon's limb from the fame flar, under each meridian ; take 

 from the ephemeris her incrcafe of A. R. for the 12H. including 

 the obfervations, and fay : As this quantity of A. R : 12H : : the 

 apparent difference of the obferved differences of A. R. to the 

 eflimate difference of longitude. This eftimate difference will 

 always be exa<5l enough to enable you from tables or by cal- 

 culation to find the corredions to which the obfervations and 

 the lunar rate muft neceffarily be fubjeded, to deduce from 

 them the true difference of longitude between the refpec- 

 tive places of obfervation. To elucidate the nature and grounds 

 of thefe feveral corredions, I fhall premife fome general confi- 

 derations on the obfervation of the difference of A. R. of the 

 moon's enlightened limb from a ftar, and of the equation of 

 the moon's increafe of A. R. in 12H. as given in the ephe- 

 meris. 



As this is acknowledged to be one of the moft certain and 

 convenient obfervations for determining the longitudes of places, 

 the redudion that is required to give it its due accuracy 

 feems deferving of a more diffufive explanation than as far 

 as I can find has been hitherto beftowed on it by any of 

 the writers on pradical aftronomy. Mr. Vince, in his late 

 treatife, mentions this method, as having been recommended 

 by Dr. Ma{l<^elyne in the year 1769; and reports the fuccefs- 



ful 



