47] THE OBSERVATORY OF CAMBRIDGE. 385 



In cases in which each comparison with a Star is complete in itself, 

 the differences of R.A. and N.P.D. are placed opposite to the name of 

 the Star, and the coefficients of Parallax opposite to that of the Comet ; 

 but in the cases in which the observations are made with the clock 

 going, and each bisection of the Comet is compared with the result 

 obtained from combining the two bisections of the Star which immediately 

 precede and follow it, the differences of R.A. and N.P.D. are placed 

 opposite to the Comet and the coefficients of Parallax opposite to the 

 Star, and usually in the line above the former quantities. 



These coefficients represent respectively 



Comet's Parallax in R. A. X A 

 and Comet's Parallax in N.P.D. x A, 



where A is the distance of the Comet from the Earth, considering the 

 Earth's mean distance from the Sun to be unity. 



Hence, to find the Parallax in R.A. and in N.P.D. respectively, these 

 coefficients must be divided by A. 



If PZ'C be the spherical triangle formed by the pole, the geocentric 

 zenith and the apparent place of the Comet, and if Z'Q' be a perpen- 

 dicular from Z' upon PC, then the values of these coefficients will be as 

 follows : 



-n T) / r\ cc. P 77 cos 4> sm ^ P 77 " sm Z'Q 



For R.A. Coefficient ="- --.-* = ^-, 



1 5 sm 8 15 sin o 



For N.P.D. Coefficient = - g* f sin (8 -P?) = _ p7r cos Z 'Q> sin (S - PC?'), 



COS -ity 



where TT denotes the Sun's mean equatorial horizontal parallax, 



p the distance of the point of observation from the Earth's centre, 

 considering the equatorial radius to be unity, 



<f>' the reduced or geocentric latitude, 

 h the hour angle, 

 and 8 the N.P.D. of the Comet or Planet. 



The quantities PQ' and Z'Q' are given by the equations 

 tan PQ' cot $' cos h, 



sin Z'Q' = cos <' sin h, or cos Z'Q' = -- jffs 



OOo JL \^ 



A. 49 



