Kew Method of determining the Longitude, 1 1 3 



Which agrees very nearly with the mean result (1^ 12*" 

 57*) of all the observations hitherto made in those places, 

 as given in the Con. des Terns for 1826. 



After Mr. Baily had nearly completed his paper, he re- 

 ceived from M. Nicolai, whom we have already mention- 

 ed, an indirect method of solving the problem, which 

 may sometimes be found convenient and is capable of con- 

 siderable accuracy. 



Let c and h denote the same quantities as before : let 



A=(/— t) + tVi ; — — ^)of the former formula : let 



^ '_ '^ \cos.d cos, 0/ 



X denoie the assumed difference of meridians and e the 

 error ; so that we may always have a:=x+e. Then will 

 the apparent time of the moon's culmination at the west- 

 ern observatory, be 



c=A-f(x+A)^^^^ nearly. 



s 



" Assume them as equal : and let a and b denote, as be- 

 fore, the true right ascension of the moon at those assum- 

 ed periods respectively. Then if 15 A =(a —^5) the value 

 of X has been assumed correctly, and the problem is solved. 

 But if not, call the difference, in this last equation, c?; 

 whence we shall have 



15A=(a—b)-\-d 

 and consequently d=^l5A—(a — b) 



" But d is evidently a function of the moon's difference 

 in right ascension ; and the time (e) in which it is describ- 

 ed (or the variation which it will cause in the value of x) 

 will depend on the relative motion of the moon, in right 

 ascension, in a true solar hour. Now, since e is generally 

 a very small quantity, the relative motion of the moon, du- 

 ring that short interval, may be deduced with sufficient 

 accuracy from the moon's motion in 24 hours as shown by 

 an ephemeris. Whence the value of e may be expreseed 

 by the following equation : 



€=—Xd 

 m 



where S may be taken, in all cases, equal to 24* 4'". 



VOL.IX— No. 1. 15 



