374 Ohservat 'ions on the vcduc of the cipher, 8fc, [Oct. 



etl by {d t), tlierefore (a -f- d t) is tho difference of 

 lin-ht ascensions or the moan time of (ransit. 



s 



Hence t = a -\~ d t 

 t — (It ~ a 



^ l-c/ 



In the case of the Moon the vahie of (/) thus (Irduc- 

 ed is only approximate, if further accuracy is required 

 we must repeat the operation and compute the difference 

 of the right ascensions of the Moon and the mean Sun, 

 and should this difference be equsl to (t) it will be the 

 exact time of culmination 



Let c represent the difference of A. R*. of the Moon& Sun 

 Mhe correction to be applied to t 

 m the Moon's hourly variation of A. R. 

 {€) being the hour angle of mean Sun and o the dif- 

 ference of right ascensions, 



I — t~h the hour angle of the Moon. 

 Now in one hour of mean solar time a meridian would 

 revolve Ih. Om. 9,86s. from west to east, in that time 

 the Mocn moves m seconds in the same direction, there- 

 fore the Moon at one hour's interval either before oi' 

 after the transit will be distant from the meridian by 

 (1 — 0—9,96 — m) hence the time of the Moon describ- 

 ing A will be, as (1^0— 9,86— : 1 : \ h f 



Therefore ^' = ^ 



i— 0—9,86— m 

 and ? 4- = T the true time of transit 

 Having nov7 determined the meantime of the Moon's 

 transit, the next step to find the time of rising and set- 

 ting will be, to compute the true declination of the Moon 

 at the instant of rising and setting : from the declination and 

 latitude of the place to determine the semidiurnal arc, 

 and then to find the time when the Moon's angle from 

 the meridian is equal to this quantity. This would at the 

 first sight appear to be easily effected, but a moments 

 reflection will present the intricacy of the operation ; 



