294 NEW FORMUL^^- RELATIVE TO COMETS. 



which it may be proper here to insert. By means of the two expres- 

 sions 



{l"-l)P^{l^l)r _ {l"-l)t'-{l-l)t" . 



^'— tt"(Jf+t") .'"'— tt\t'-^t") ' 



which are deducible from the values of /', /", expressed by Maclaurin's 

 theorem ; I obtained in parts of radius, dl = — 2-232849; d^l z= 

 — 15*51 507. The similar values which depend on the geocentric 

 latitudes were d X = —2-498243, fl'Pl = —22-139036; and 

 adopting in this method the formulae : 



n 



= Qdl-\- 2 tan(L — /) 



sm;icos;i 



which may be found expressed differently in the Mecanique Celeste 

 and Theorie Analytique, &c. I obtained — or i = — 3-278562. 

 The three equations 



a;, = X; + p («a — ^ dl), 



y, = Y, + p{i(3+ adl), 



,. d%\ 



resulting from the diflferentiation of (1), and in which a = cos (/ — L), 

 |3 = sin (/ — L), y = tan 7,, then gave me the following values : 



a;, = X, — p (3-761473), 



y, = Y, + p (1-261091), 



z, = — p (3-965141); 



which are exceedingly different from (e), with regard to the coeffi- 

 cients of ? in the values of x, and y,. 



