192 



From which the values of dp and dt may be obtained, t being the 

 time from periheUon. 



Let T = the time in the table of the Comet of 109 days when 

 anomaly = v 



A = change of anomaly in that Table in one day at time T 



. . (1) ■ 

 . . (2) 



• I P 



cos- ■^V = — 

 ^ r 



t = Tpi 



Then 



d» = AdT = (by equat. 2) 



/'dt 3tdp 



[P' ^P 

 by equat (1) log r + 2 log cos | » = log p 

 hence d log r = sin 1" dt tan ^ > + dp 



P 



I 



, ^ d log r 

 or (a;) —. — 177- 

 ^ ^ sm 1 



d » tan ^v + 



dp 



Let S, T, C, represent the Sun, Earth, and Comet 

 respectively, and P the projection of the Comet on 

 the plane of the earth's orbit. 



The processes to obtain the heliocentric longi- 

 tudes and latitudes, are 



sin STCxST 



sin SCT 



CST = 180°— SCT— STC 



sin CTP (geo. lat.) sin CST 



sin CSP Chel. lat.") = — orri/-. 



^ ^ sm olC 



^^„ cos CST 



cos TSP = . . . , 



cos hel. lat. 



Comets hel. long. = Earth's hel. long. + TSP 



Having thus obtained /3, fi' and tt, t' 



(a) 



(4) 



