118 Astrondffiical and Nautical Collections. 



and therefore by substituting in this equation the fotmer value of 



sin.2 ^ Z, we get 



A,, , sin.-^A + d'xsin.-i^A >^rf' Xcos.5xcos.il/ X 2 



COS. oM = COS. a ^ =r-=7 =i 



COS. S' X COS. M' y. R 



or COS. S31 =r cos. d — sin. | . A + d' X sin. J A — d' X 60s. M 

 2.cos.»S^ 



X sec. iVr X 



R^ . cos. >S" 



^r V. sin. SM:=:y. sin. c? -f- sin. 4 A + <i' X sin. i A — rf' X coft. M 



X sec. M' X ^•^"^•'^ , which is the same as the Rule. * 

 R-^ . cos. 6' 



Example. 

 Let the apparent distance of the moon from a star be 51'^ 2§' 35" ; 

 the apparent altitude of the star 24° 48' ; that of the moon 12° 30'; 

 and the hor. parallax 56' 15". Required the true distance. 



o / // 

 A =: 51 28 35 



d' c= 12 18 



63 46 35 

 39 10 35 



1. sin. J A + d' = 31 53 17-5 = 9-722S51 



1. sin. J 'a -^ d' = 19 35 17 5 == 9-5^537§ 



i. cosin. M = 13 20 42 = 9-988112 



1. secant M' ==: 12 30 = 0-010418 



the constant logarithm 0-301 149 



N = 353109 . . ¥547909 

 V. s. d = 19882 



V. s. . . 372991 51° 10' 13" = true dist. 



it. Catalogue of the Stars in a Southern Constellation^ denominated 

 the Comet o/*Excke. By Mr. Charles Rumker. 



The positions are deduced from Mr. Rumker's own observations. 

 The elements of Aberration and Nutation are obtained according to 

 the method of Zach, Tables Nouvelles. 



• The logarithm 0-301 150 isthe logairthm of the constant dUantitt 2 x ^^^,. 



COS. 5 



