COM STOCK — STUDIES IN ASTRONOMY 77 



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

 tain from (i) with sufficient precision 



2a -{- A' -^ A" = {& -\- c") cosec z 

 and introducing these values into (J) we have 



(n' + n") r + lli = [A' - .4") tan z - (c' - c') sec z 



+ (c' + c") cos 5 Bin t cosec zsin i {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')tanz 



Q = (c '+ e") cos S sin t cosec z sin ^ {T — T ) 



we obtain from the equations 



sin z sin A = — cos 5 sin t 



sin z cos A =■ cos cp sin S — sin cp cos d cos t (7) 



reduced by means of the relations furnished by the as- 

 tronomical triangle, the equation 



P = cos 6 cos qsecz .2 sin i {T — T) 206265 



where q is the parallactic angle of the star. Introducing 

 Bessel's auxiliary ^into this equation, substituting in the 

 last term of {6} in place of cos 8 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 r= cot <p cos t 



■D r^ ri-<p1 if sin^{T—T") 



P = o.61o46 cos S — '— (8) 



L J sin z tan (N -\- 6) ^ ' 



§ = (c -f- c") sin A . sia i {T - T") 

 in' 4- n") r + 2/i = P -\- Q - {c' - c") sec z 

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

 the formulee, 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, tp, s, t, by means 

 of equations (7). 



Since /-^ changes sign when the instrument is reversed, a 



