(54? 



■A 



Bowditch on the elements of the orbit of 



i 



by the usual rules of trigonometry, compute the three points 



■ 



of the assumed plane correspondin 



the three ob 



of 



as a 



the comet. Through these three points and about the suu 

 focus describe a parabola ; compute the area included by the ra^ 

 dii vectores drawn from the sun to these points, and the curve ; 

 and let the area described between the first and second observations 

 be D, that between the second and third E ; also T the time in 

 which the whole area D + E would be described by the comet ac- 



D 



G. 



cording to the rules of the parabolic motion ; lastly put ^ 



Proceed in the same manner with the second operation, using 

 K + P instead of K, and let the quantities D, E, T, G, become 

 respectively f?, e, #, ^ ; and in like manner for the third operation, 

 let those quantities become respectively S, e, t, y. 



Now by comparing the first and second operations we find that 

 an increase of P in the longitude of the node has changed the quan- 

 tities T, G, into tfg, by which means they have been increased re- 



spectively by t 



%g 



G; and as this increase was owing to the 



variation P in the longitude if the node, it is evident that if that vari- 



ation had been m times as great, or equal to m P, the increments 

 of T and G, would have b6en m.{t- — T), m,(g — G) respective- 

 ly ; these quantities being always supposed to be small. 



In like manner by comparing the first and third operations we 

 find that an increase of Q in the inclination of the orbit I, changes 



y — G ; consequently an increment of w Q in tlie inclination would 



T, G, intoT, 7, by which means they increase respectively r 



produce increments in the values of T, 



represented by 



n. (t 



r 



T), w. (y — G) respectively. 



Now by adding to T and G the increments corresponding to 

 ?nP,M Q, we shall have their values corresponding to the lone;!- 



^' 



