Jstronomkal and Nautical Cclleclions. 



375 



§.70. 



In this method we have occasion for the solution of the pro- 

 blem, to determine, from the given position of the orbit with re- 

 spect to the ecliptic, and the geocentric longitude and latitude 

 of the comet, the heliocentric distance from the node, and the 

 distance of the comet from the sun. Newton takes this solu- 

 tion for granted : Gregory Euler, and SxRUYKhave entered 

 into the particulars of it; and Lexell, in a separate essay ; 

 and Professor Nordmark in an occasional Programma, have 

 endeavoured to simplify and accommodate to practice the for- 

 mulas subservient to it. And yet it seems to be possible to ob- 

 tain a more convenient practical solution than has hitherto been 

 made public. It has been usual to employ for the purpose plane 

 trigonometry only ; but the problem evidently belongs to sphe- 

 tical trigonometry, since it depends on the relative situation of 

 two planes, the first determined by the centres of the sun, the 

 earth, a*id the comet ; the second, or the orbit of the comet, by 

 the nodes and inclination appropriate to it. 



§.71. 



Now let E A gj T L be the ecliptic, ^ the node, here the 

 descending node, I J2 N the orbit as seen from the sun, 

 T the earth's place, and C the observed geocentric place of 

 the comet. The great circle T K C G being drawn through 

 the place of the comet, its heliocentric place will be K, R 



