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fource of error therefore fhould be correded before the propor- 

 tion is Hated, by altering the firft term in conformity to the 

 moon's adual rate during the interval between the obfcrva- 

 tions. Thus in the firft analogy the deviation in 2 hours from 

 the mean rate of 30" per hour is + ii"; this multiplied by 6 

 gives i' 6", which added according to its fign to the firft term 

 of the proportion would make it 6°. i'. 6'', and the proportion 

 would ftand thus, 6°. i. 6 : 12H: : i. o. 11" : 2H. the ground 

 and necefllty of this corredion are evident, and when it is not 

 apphed the irregularity of the moon's rate being given, the quan-i 

 tity of error will be greater or lefs in proportion as the obferva- 

 tions were made at a part of the 12H. more or lefs diftant" 

 from the hour of the mean rate. Had thefe fuppofed obferva- 

 tions been made betw'een the 5th or 7th hours the longitude 

 would have come out true without any corredion of the rate' 

 whatfoever. 



Having premifed thus much on the nature and grounds of 

 this corrcdion, I fhal! proceed to a fhort explanation of the" 

 readieft method of making it under every pofllble change of ' 

 of the moon's rate with due accuracy and precifion. 



M. de la Lande, in his Aftronomy, liv. 7. article 152T, obferves 

 that when the longitudes or A- R's of the moon are ftridly 

 calculated from 12H. to 12H. as they are given in the Nautical 

 Almanacs and other Ephemerides, you may thence deduce the 

 horary motion for any part of this period to a great degree of 



precifion ; 



