NEW FORMULA RELATIVE TO COMETS. 293 



posed this axis to be directed to E, we shall find in terms of p before 

 used ; 



x, = — 0-008716 — p (4-263202),"] 



y,= + 1-014544 + p (2-452316), I (e) 



^, = — p (3-815140). J 



But if we also change p into p cos ^, so that p may denote the ray 

 CE, we shall get 



X, = —0-008716 — p (4-020544), 



y, = + 1-014544 + p (2-312732), 



^, = — p (3-597985). 



The accuracy of these results we believe to be very considerable. 

 Mr Pontecoulant's values in terms of p are the following : 



X, = — 0-008686 — p (4026273), y, = +1 -014545 + p (2-314020) ; 



2-, = — p (3-605632). (See Theorie Analytique, &c., vol. II., p. 70.) 



With the desire of making a comparison between the principal terms 

 of formulae (E), and the values (d) above given, I have subjected them 

 to computation. By taking the first expressions for E, E', E' and e", 

 the coefficients of the curtate distance p were as here given ; 



X, = X,~p (4-050920) — &c. 



y, = Y, + p (2-047392) + &o. 



2-, = — p(3-646140) — &c. 



so that the terms aflfected by K differ little from —p (-245653), 

 H- p (-345974), — p (-168997), and will in the destined use of (E) 

 not exceed the order of the intervals /', t'\ 



To the data of the example now considered, I have been induced to 

 apply the method of La Place; and with surprise I found results 



