47] THE OBSERVATORY OF CAMBRIDGE. 383 



Correction for Refraction. 



The seventh and eighth columns contain the excess of the Comet's 

 refraction above that of the Star, in Right Ascension and North Polar 

 Distance respectively. 



If the Transits of the two objects be observed across a wire placed 

 accurately in the apparent circle of declination, which is usually the case 

 in these observations, we shall have 



Excess of Comet's refraction in R.A. in seconds of time 



= AS x k sec j (8' - PQ) cos (28' - PQ) cosec 2 8', 



1 



Excess of Comet's refraction in N.P.D. = AS x k sec 2 (8' PQ). 



Where the symbols have the following significations : 



AS is the excess of the Comet's N.P.D. in seconds of arc, 



PZM being the spherical triangle formed by the pole, the zenith and 

 the middle point between the true places of the Comet and the Star, 

 ZQ is the perpendicular from Z upon PM. 



8' is the N.P.D. of the point M, or the mean of the N.P.D. of the 

 two bodies. 



k is a quantity depending on the zenith distance of M, and on the 

 state of the barometer and thermometer. 



PQ and ZQ are found from the hour angle (h) by means of the 

 equations 



tan PQ = cot < cos h 



cos (f> cos h sin <f> 



. n ^ - n ;=. , 



sin PQ cos PQ 



where < is the latitude of the Observatory. 



Also , the zenith distance of M, is given by the equation 



cos = cos ZQ cos (8' PQ). 



These formulae are equivalent to those of Bessel in his Untersuchungen, 

 Band i. p. 168, PQ being the quantity there denoted by N, and ZQ 

 being the complement of n. 



