190 



Mr. William Galbraith, on some 



Differentiating equation (H) and 



— A^sin. 1 



12 COS. 2 w 



5 . ,, ^w 



=T-.A^ sin. 1 tan. CO. COS. ?« — —r- 

 12 2 COS. ^1(7 



since tan. + cos. = R2 = ]. 



But .— * = COS. therefore 

 sin. 



5 ^ . _. COS. i^; w X sin. Y Iw 



I X =77-. A^sm. I tan. w x — x — =— i 



12 sin. t^ cos.-^ w siu. wcos.w 



and since the sin. 2 ?f? = 2 sin. w cos. w, we have 



2 sin. I" X ^ w Sin. 2" X d w ,,^^ 



d X = o = — ' — s • • • (12) 



sm. 2 w sin. 2w ^ 



Taking ^ w = 1", substituting for sin. 2 w its value when 

 w = 23° 27 40", formula (12) will become 



d X = 0-0000132748a: (13) 



Log. of 0-0000132748 is 5-1230279 

 By this means the correction for the variation of w from 

 23° 27' 40" may be readily obtained, by adding this constant 

 logarithm and the log. oi dw in the given case to the sum of 

 the logs, under I, the sum will be the log. of the correc- 

 tion of X. 



Example 1 . Let «; = 23° 27 43"- 76, a = 60" a m? = + 

 3"-76, required the reduction to the solstice. 



I. II. III. 



Const, logs. . . . 9 8555770, 2-745874, 8-03287 



A = 60>" log. A2 = 3-55630-25, A^ = 7-112605, a ^ = 0-66891 



1= +43' l"-54 log. 3-4118795 

 2=— 0-72 C.L. 5123 



3=— 0-05 log. aw 0-575 



0-13 



9-858479 



8-70178 



2d = — 0"-72 3d=— 0"-05 



4= + 



x=-\- 43 0-90 4th: 



9-110 

 + 0"-13 



