COMSTOCK STUDIES IN ASTRONOMY 87 



table is given by Dollen with log x, when x is expressed in 

 seconds of time, as argument. When x is expressed in arc 

 values of 6 may be taken from any logarithmic table by 

 means of the relation 



6 = i (log tan x log sin x) 



If d(U) denote the value of 6 corresponding to log U 

 when Uis expressed in seconds of time we may, by the 

 introduction of the divisor, 15 sin Y , obtain in seconds of 

 time and arc, respectively, 



U = [4.13833 - 26 (U)l cot S tan S sin t 

 L J 1 cot 6\ tan d 3 cos t 



r n < 17 ) 



(- m'} = I 4.13833 -f 6 (ra')J cot d tan q> sin (t -f- U") 



log a' == log (15 cosec q> ) + log m' -\- 2 6 (m') 26 (a') 



In equations (16) the quantities h, I, C, C' are analogous 

 to the transit factors A, B, C used for the reduction of me- 

 ridian observations, and (7,0" may be tabulated for a given 

 latitude and assumed constant for a period of several years. 

 The quantities U and m' must be computed anew for each 

 observation, and a' must also be computed in case the azi- 

 muth is required. To diminish the labor of this computa- 

 tion Dollen tabulates for a selected list of 180 stars certain 

 General Constants, through which these computations are 

 considerably shortened. 



With assumed values of the coordinates of the stars and 

 an assumed interval S 8' 4 m put 



TT i 206*265 __ 



U = x -\ cot d sin (t-}- U) = N Q 



10 



We shall then have 



- (U+ m'} = x + p N = t a' = p' N 



where p and p' are functions of the latitude which differ 

 from tan <p and 15 sec 9 by terms of the kind above repre- 

 sented by 6, 



log p = log tan g> + 6 ( N tan <p) 

 logp' = log (15 sec cp) + 3 6 (N tan q>) 2 6 (.Vsec (p) 



