47. 



ASTRONOMICAL OBSERVATIONS MADE AT THE OBSERVATORY OF 

 CAMBRIDGE, UNDER THE SUPERINTENDENCE OF PROFESSOR ADAMS. 



[Extracts from the Introduction to Vol. XXI. (1861 18C5).] 

 Corrections for Colhmation, Level, and Azimuth. 



UP to the end of 1863 the corrections for Colhmation, Level, and 

 Azimuth were applied in the usual way, hy the aid of Professor Challis's 

 calculating machine : thence forward, they were thrown into the form 



m + n cotan N.P.D. + c cosec N.P.D. 



where c denotes the collimation error, considered positive when the angle 

 between the line of sight and the eastern half of the axis is 

 less than a right angle ; 



i't, the elevation of the west end of the axis above the plane 

 of the equator ; 



and m, the deviation of the west end of the axis southward in the 

 plane of the equator. 



m, n, and c are expressed in seconds of time. 



It is easy to see that, if a and b denote the deviations of the axis 

 horizontally and vertically, or the azimuthal and level errors, expressed 

 in seconds of time, and < the latitude, 



m = asm<l> + bco8<f> = b sec (f> n tan <f>, 

 n= a cos (f> + b sin <, 

 consequently 



a = msin.(f> n cos (f> = b tan $ n sec </. 



