COMSTOCK — STUDIES IN ASTRONOMY 89 



ferentiate for himself equations (16), we reproduce here 

 the form in which Dollen expresses the differential coefli- 

 cients and the correction terms involving them: 



X + pX = to + Qk -i- RG+ DJ d 

 a' = pA' =-. jjA'o + Qk-^ RG 



where 7i, G and j s represent variations in the elements 

 with which x^ and N^ were computed, and Q, Q', 11, R', D 

 are differential coefficients having the following values: 



Q = pX + fi R = pu + r 



Q' = i/A R = Pit 



The values of /^. r, ^, m and D involve only the coordinates 

 of the stars and are given among the general constants for 

 each star of Dollen's list. 



The values of k, G and js are as follows: 



J ex = a. - (cx.,)^ g = -Ur^- (cri)o 



^ d 



} 



G - g + ^ a 

 (5o)o k = --j^i -(<S,)o ( 



where the subscript o denotes the tabular values of the co- 

 ordinates corresponding to x,>, AT,. These assumed values 

 are given as a part of the table of constants for each star, 

 and an ephemeris of g and log k precedes the table of con- 

 stants. 



The actual reduction of a set of observations by means of 

 these general constants will not often be made, but recourse 

 will be had to the General Ephemerides constructed from 

 them for 93 of the 180 stars. These ephemerides give at 

 intervals of ten days throughout the year the instantaneous 

 values of N and T, T = a^ 4- a-, and from them the observer 

 should construct a local ephemeris of the values of 6 and 

 a' for a few of the tabular dates near the epoch of his ob- 

 servations, using the relations 



e =: T-{-pX a' = pN 



Values of 9 and a' interpolated from the local ephemeris 

 will be immediately available for the reduction of observa- 

 tions in which the observed interval S — S' equals the 



