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denoted by the clock. The fame meridian prefently arrives 

 at the ftar, whofe A. R. is in like manner expreffed by the 

 clock. The time elapfed between the obfervations would be 

 the true interval of their A. R's. fuppofing the moon to have 

 flood flill in her orbit — But the moon was increafing her A. R. 

 during the whole of the elapfed time ; and of courfe every 

 moment approaching nearer to the ftar, therefore when the 

 ftar paffed their difl-erence of A. R. was decreafed by the quan- 

 tity of A. R. gained by the moon during the interval of fy- 

 dereal time elapfed fince her own paffage. If then a given' 

 meridian fhould pafs the moon at 12H. and a ftar at 14HS. 

 their apparent difference of A. R. would be 2H. and their true 

 difference of A. R. at the moment of the pafTagc of the ftar 

 would be the apparent difference — the moon's increafe of A. R. 

 in 2H. If under another meridian the moon fhould pafs at 

 12H. i', and the ftar at 14H. then their apparent difference of 

 A. R. under that meridian would be iH. 59', — and their true 

 difference A. R. at the time of the ftar's paffage iH. 59' — the 

 moon's increafe of A. R. in iH. 59'. Therefore the adual 

 difference of thefe obferved differences of A. R. is not the true 

 quantity required, but mufl be Icffened by a quantity of A. R. 

 proportioned to the moon's rate in her orbit ; and the differ- 

 ence of the two fydereal intervals of 2H. and iH. 59'.; for let 

 us fuppofc the moon to increafe her A. R. at the regular rate 

 of 30' of a degree for an hour, and a meridian to pafs her 

 firft limb at 12H. and that the fame meridian applies to a ftar 



at 



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