382 ASTRONOMICAL OBSERVATIONS MADE AT [47 





n = -. -.. p {sin </>' cos 8' cos <!>' sin 8' cos (6 a')}, 

 sin 1 



cos x sn x 



Also let &l be the correction of the assumed longitude in seconds of 



time ; 



AT 7 the correction of T in seconds of time ; 

 Aa, AS, &c. the corrections of a, 8, &c. in seconds of arc ; 



7 7Sl 



- and -T- , the changes of a and 8 in a second of time, 

 dt at 



estimated in seconds of arc ; 



sin TT , , sin cr , . , , . 



//!+/>) and . ^(l+s), the sines ot the true horizontal 

 sin 1 sin 1 



equatorial parallax and semi -diameter, each divided by sin 1". 



Calculate the following quantities : 



(a) = cos 8 [cos x + sm X sm 8' sin (a a')], 

 (8) = sin x cos x sin 8 sin (a a'), 



m = p sin TT cos ^>' [cos ^ cos (# a') + sin x sin 8' sin (0 a')], 

 (a')=m-(a), 



(8') = p sin 7T sin ^ [sin <' sin 8' + cos <j>' cos 8' cos (0 a')] sin x, 

 (T) = (/)- (1-00274) 15m, 



') = p sin TT [sin ^ cos <j>' cos 8' + sin x sm <^' sin 8' cos (6 a') 



cos x sin (f)' sin (6 a')], 





sn cr 



, , _ 



"srnT 7 ' 



Then the final equation of condition will be 

 J^,->SH) Aa+(8) AS + (a') Aa'+(8') A8' + (r) AT+(/) A/ + (f ) Ac/.' 



