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 z= I {log tan x — log sin x) 



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

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

 introduction of the divisor, 15 sin 1", obtain in seconds of 

 time and arc, respectively, 



cos t 



r .^^~\ cot S, tan <5, sin t 



U= 14.13833 - 2(jL") hj ' . '. . 



L J 1 — dot d ^ tan 2 cui 



(— m') = r4. 13833 + d (m') J cot 8^ tan cp sin [t + U 



(17) 



log a' = log (15 cosec <p ) + Zogr m' + 2 6 im') -26 {a') 

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

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

 ridian observations, and C,C' 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 «' 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 — *S" = 4''' pnt 



- u = .To H — Y5~ ^°^ 1 ^'" (t-\-U) = Ao 



"We shall then have 



- {U+m) = a^o +P ^^0 = ^0 «■ == P' ^\ 



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

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

 sented by 6, 



log 2^ = log tan cp -\- 6 {IS tan q>) 

 Jog p = loj (15 sec cp) -\- '6 6 {N'tan cp) — 1 6 {N sec cp) 



