COMSTOCK — STUDIES IS ASTRONOMY 97 



t = {a,- T,) - {a, - T,) 



sin Tt 2 sin^ I rr . , 



a = -: X = : ~ cot i p 



SHI p sin 1 



tan u = 



cos N = 



1 — a cos t 

 tan (p tan ^ (p — cc) cos M 



(13) 



I — a cos t 

 C ^ 2 cosec 2 <p cot N 



^T-\-C^ <P = (ct, - T.,)-\- {M + N) 



Since cos N= cos ( — N) the algebraic sign of Nis not de- 

 termined by the equations, but it is apparent from the 

 physical conditions of the problem that N must be positive 

 for a star west of the meridian and negative for a star east 

 of the meridian. The coefficient of ^ <p appears in equa- 

 tions (13) with changed sign in order that ^ ^ may repre- 

 sent a correction to the assumed latitude. In the use of 

 these formulae x may be computed with four place logar- 

 ithms, a and 31 with five place, and N with six or seven 

 jDlace tables. 



It will frequently happen that the observations of the 

 polar star and the southern star composing a pair will be 

 made at slightly different zenith distances, the slight 

 change in the zenith distance of the line of sight of the 

 telescope being indicated by an altered reading of the level 

 bubble. This alteration is most conveniently taken into 

 account by applying to the observed time, T., a correction 



r 7 /> ^^ ^ sec (p (&2 — ft,)r ,. .^ 



Level Corr. = — — ^ z = —. — f- • —^ ^-^ — (14) 



dz sill J-2 lo ^ ^ 



where h, and h^ are the level readings, r the value of a 

 level division in seconds of arc, and Ao the azimuth of the 

 star. The factor h. — &i is to be considered positive when 

 the bubble runs from its initial position toward the objec- 

 tive end of the telescope. 



The factor ^^^ '^ in the preceding equation may be re- 

 placed by an expression which is most conveniently treated 

 in connection with the thread intervals. 



