COMET OF 18S9-1896-1903 271 



the perturbations, their appHcation, and the derivation of new 

 osculating elements at several epochs during the interval under 

 discussion. 



The differential variations of the quantities with respect to the 

 time, with the exception of iV, were put in the ordinary standard 

 form : 



u ={Tr:R)R-\- {n:S)S+ (tt : JJ')M' 



while that of N' was put into the form : 



■iN , „ , dv , ., , de 



to -=[N:v)u--,+ {N:e) 



u- 



dt -^''■■^'"' d^^ '''■''"' dr 



in which formulas, R, S and JV are the component disturbing 

 forces and the quantities (tz'.R), etc., are the differential coeffi- 

 cients of the elements. From the numerical values of the above 

 variations, as computed for equidistant intervals of time, the 

 total change in the elements from one period to another, may 

 be found by simple mechanical quadrature. 



The component disturbing forces, R, S and IV were com- 

 puted by the usual formulas, as given in Oppolzer, but were 

 expressed in radians and in units of the sixth decimal place. 



The formulas for the differential coefficients of the elements 

 are as follows, where (o is the number of days interval between 

 computations and the quantities in brackets are logarithms : 



(?■ : IV) r= r cos it [9.31442] 

 ,„ ,,,^ '' sin 21 ^ 



(^■■^^)=^inT [9-31442] 

 (-^) = -^' [9.31442] 



^ sin 7' 

 (Tr:5) = (/+r)— [9-31442] 



( TT : ;F) ^= r sin ii tan \i [9.31442] 

 {y : R) rr= yiu7ue sin v 



P 

 ( 1' : 6" ) = 31'aw - 



(<■ : A') ^p sin v 



