L O N 



From the Nautical Almanack find the lime at Greenwich when the 

 moon AVHS at that distance. 



From the altitude of the sun or star, find the time at the place of ob- 

 servation. 



The difference of the times thus found, gives the difference of the 

 longitudes. 



Formula for deducing the true from the observed distance. 

 Conceive S, M to be the true places of the star and moon in two ver- 

 tical circles S Z, M Z forming at the zenith Z the /_ M Z S ; then since 

 both parallax and refraction take place entirely in the direction of ver- 

 tical circles, some point s above S, in the circle Z S, will be the apparent 

 place of the star, and m below M (since in the case of the moon the de- 

 pression by parallax is greater than the elevation by refraction) Avill be 

 the apparent place of the moon : let 



D (S M) be the true, d (s m} the apparent distance, 

 A, a (900 Z M, 90 Z S) the true altitudes, 

 H, A (90 Z m) 990 _ z s) the apparent altitudes, 

 cos. A. cos. a 



then if F = 



cos. H. cos. k * 



or if we make the fraction, on the right hand side of the equation = 

 sin. 8 0, we shall have 



sin.* = cos.2 i ( A + a) , cos.- 6. 



and sin. = cos. (A -f- ) . cos. 8. 



The true distance of the moon from the sun or star being thus found, 

 we are next to find the time at Greenwich corresponding to this true 

 distance. To do this, we must observe that the true distance is com- 

 puted in the Naut. Almanack for every three hours for the meridian of 

 Greenwich. Hence considering that distance as varying uniformly, the 

 time corresponding to any other distance may be thus computed. Look 

 into the Naut. Almanack, and take out two distances, one next greater, 

 and the other next less, than the true distance deduced from observa- 

 tion, and the difference D of these distances gives the access of the moou 

 to, or recess from, the sun or star in three hours ; then take the differ- 

 ence d between the moon's distance at the beginning of that interval, 

 and the true distance deduced from observation, and then say, D '. d '. ' 

 3 hours : the time the moon is acceding 1 to or receding- from the sun or 



