COMSTOCK STUDIES IN ASTRONOMY 85 



where the coefficient C has the value 



C = tan <p + tan |p a ] 1 + (tan d 2 - tan g>) cot <J cos (2r -f U) I (12) 



If at the time of observation the southern star was near 

 the zenith, or Polaris was near elongation, or the collima- 

 tion constant, c, was very small, the bracketed factor may 

 be put equal to 1, giving 



C = tan <p + tan % p 2 



For a determination of azimuth we write equation (3) in 

 the form 



tan a = tan m cosec g> tan b cot g> 



and assuming the equation 



tan a' = tan m' cosec q> (13) 



find by subtraction 

 a = a' + b tan <p -\- c sec g> \ 1 cot d^ tan % p 2 cos (2r + C7) j- (14) 



If K and M denote respectively the reading of the azi- 

 muth circle corresponding to the star observations, and to 

 that position of the instrument in which the rotation axis 

 lies in the plane of the prime vertical (collimation axis in 

 the meridian), we have, obviously, 



M = K + a' + b tan cp + C'c (15) 



where C' is an abbreviation for the coefficient of c given in 

 the preceding equation. 



Since the collimation constant, c, changes sign when the 

 instrument is reversed, an observation of Polaris and a 

 southern star in each position of the instrument, W. and 

 E., will suffice for the determination of 4 T and c from the 

 observed times of transit, and also, if the instrument is 

 provided with an azimuth circle, for the determination of 

 M and c, from the circle readings. The agreement between 

 the two values of c thus determined furnishes a valuable 

 control upon the accuracy of the observations and their 

 reduction. 



In the preceding investigation the effect of flexure, ine- 



