47] THE OBSERVATORY OF CAMBRIDGE. 377 



For convenience of calculation these quantities are given in Tables I, 

 II, III, at the end of this Introduction, for values of the hour angle 

 taken at intervals of 10 s and extending to a sufficient distance from the 

 meridian. 



When the star is not very near the pole, since 6 is very small, we 

 may write 



. sin" 6 for sin 2 - 

 4 2 



which gives 



correction = - : -7. sin A cos A sin 2 6. 

 2 sin 1 



But if E be the equatorial interval corresponding to the apparent 

 distance from the meridian of the point at which the bisection was 

 made, then 



sin A sin 6 = sin E ; 



. ., a sin 2 E 



therefore sin- 6 = -. - , 



sin- A 



and correction = - -j, cot A sin 2 E ; 



Zi S1H 1 



or, if E be expressed in seconds of time, 



sin 2 15" ., 



correction = - - -- .. h- cot A 

 2 sin 1 



= sin I" .& cot A. 



Zi 



In the Mural Circle, one equatorial interval of the wires =16'*6. 



Hence, if / be the number of intervals in the distance of the point 

 of bisection from the meridian, 



225 

 correction = - sin 1 " ( 1 6 6 )~ I" cot A 



a 



= [9"'] 7694] P cot A 

 = 0"'15037 2 cotA. 



In practice, the middle wire is always so nearly in the meridian 



that / may be taken to be the number of intervals in the distance of 

 the point of bisection from the middle wire. 



A. 48 



