COMSTOCK STUDIES IN ASTRONOMY 77 



For the coefficient of the last term in equation (5) we ob- 

 tain from (it) with sufficient precision 



2a -\- A' -\- A* = (c + c") cosec z 

 and introducing these values into (5) we have 



(ri + w") r -f 2/? = (X A") tan z (c' c") sec z 



-\- (c' + c") cos S sin t cosec z sin % (T T") (6) 



If the star is near the meridian or is observed near the 

 collimation axis of the instrument, the last term in this ex- 

 pression will be very small and may frequently be neg- 

 lected. Putting 



P = (A' A") tan z 



Q = (c -f c") cos d sin t cosec z sin (T T) 



we obtain from the equations 



sin z sin A = cos sin t 



sin z cos A =. cos q> sin S sin q> cos $ cos t (7) 



reduced by means of the relations furnished by the as- 

 tronomical triangle, the equation 



P = cos d cos q sec z . 2 sin | (T - T") 206265 



where q is the parallactic angle of the star. Introducing 

 Bessel's auxiliary JVinto this equation, substituting in the 

 last term of (6) in place of cos 3 sin t cosec z its equivalent, 

 sin A, and collecting in a form convenient for computation 

 the equations necessary for the reduction of a series of ob- 

 servations, we have the following: 

 tan N cot (p cos t 



P = [-5.615161 cosS Sin \ (T - T "^ (8) 



L J sin z tan (N -{- d) 



Q = (c' + c") sin A .sin $ (T - T") 

 ( n ' 4. n ") T -f 2/5 = P + Q (c' c") sec z 



The zenith distance and azimuth of the star, z and A of 

 the formulae, may either be derived from the instrument 

 at the time of observation, or may be computed from the 

 latitude and the co-ordinates of the star, <?, s, t, by means 

 of equations (7). 



Since ft changes sign when the instrument is reversed, a 



