11 



To find n, differentiate, on the same hypothesis, 



COS. z. = COS. a. COS. X) 4- sin. a. sin D. cos. P. 



and substituting for A its value just obtained we deduce 



_ f- gin. P m sift. P ,_. 



" "■ ~ tang. D ~~ tang. S sin. JD. ^ ' 



or where S is not known 



e sin. P + m. cos. P — m 



n = — 



tang. D. tang, a 



or, 



e sin. P m. sin. (D — ^) cos. P. 

 ~ tang. Z> sin. D sin. ^ 



When this correction is applied to the AR instead of the hour 

 angle, its sign must be changed. 



We obtain e by the declaration level, m by observing the distance 

 of the meridian mark from the apparent meridian = n' for 



m = — in' X sin. 2 a. 



By the use of these corrections, I can venture to say, that the 

 Armagh Equatorial gives results which are not unworthy of the 

 present improved state of astronomy. The only error which re- 

 mains is produced by slight variations of the supports of the declina- 

 tion level, connected with the extensive movements to which it is ex- 

 posed. This however is scarcely ever 5", and I hope to be able to 

 counteract it. Should I succeed, 1 shall from time to time lay such 

 of my results as are likely to be useful before the Academy. 



T, R. ROBINSON, 



Armagh, Januarif 4, 1825. 



c9 



