47] ASTRONOMICAL OBSERVATIONS MADE AT CAMBRIDGE. 375 



The collimation and level errors were found by observing the reflec- 

 tion of the wires in a trough of mercury, with a Bohnenberger's eye- 

 piece, before and after reversing the Instrument. The deviation of the 

 line of sight from the vertical, in one position of the Instrument, which 

 was assumed to be illumination West, being b + c, in the other position, 

 illumination East, it will be b c. The value of c thus obtained at any 

 reversal of the Instrument was, up to the end of 1863, in most cases 

 supposed constant till the next reversal and used for finding b by means 

 of intermediate observations of the reflection of the wires. Subsequently 

 mean values of c were generally taken. 



This method assumes that the position of the Y's is unaltered during 

 the process of reversal, a supposition which was by no means borne out 

 by the examination of the pivots in May, 18G4, and it was thought 

 better to adopt some mode of determining the errors independently for 

 each position of the Instrument. 



In default of Collimating Telescopes, a star near the pole, usually 

 Polaris, was observed both directly and by reflection at the same cul- 

 mination ; from the times of transit reduced to the centre wire and 

 corrected for irregularity of Pivots, the level error was easily found thus, 



if a be the star's Right Ascension, 8 its Declination, 



T the time of the direct observation, reduced to the centre wire 

 and corrected for irregularity of Pivots, 



T' the time of the reflected observation, 

 E the Clock correction, 



a, b, c the Azimuth and Level errors, and the Collimation error 

 of the centre wire, 



a=T+E+a 



cos 8 cos 8 cos 



= T' I E | ct ~ fr- , 



cos 8 cos 8 cos S ' 



whence T- T' + 2b = , 



cos o 



1 l /T/ T\ COS ^ 



and b = - ( 1 ./) .-. -,-, . 



2 v ' cos (< - 8) 



