I 204 ] 



according to the rate fhe moved at, at the time of the mid-inter- 

 val of the obfervations. 



To explain this, let us fuppofe the moon, by an equable 

 motion, to have changed her A. R. in 12H. by 6®, and on 

 that day under a different meridian her diiference of A. R. 

 from the fame ftar with which fhe had been compared at a 

 former meridian was found to be encreafed by i^, then 6°: 

 12H. : : i'^ : 2H. the longitude required. Now on another day 

 let us fuppofe the moon to have gained as before 6^ A. R. in 

 12H. but at the following rates for each hour of the 12H. 



Should the moon's A. R. be compared with the fame ftar at the 

 fame places on this day at the beginning of the 12 hours fhe 

 will be found to have adually gained in the interval of the 

 paffages of the 2 meridians 1°. o'. 11". and the proportion un- 

 equated would be 6° : 12H. : : \°. d. 11" : 2H. o'. 22". and fhould 

 the obfervations happen near the end of the 12H. the moon 

 would be found to have gained in the fame interval only 

 59'. 49". of A. R. and the unequated proportion would run thus, 

 6^ : 12H. : : 59'. 49' : iH. 59. 38 ; whence it is evident that the 

 longitude deduced from thefe obfervations would be in one cafe 

 22' too great, and in the other 22" lefs than the truth: This 



fource 



