Researches on the Distribution of the Mean Motions of the Asteroids. H 





The elements £ and w may be eliminated by these relations, viz. 



(8) 





14. The first two equations give 



de _ s'(e,£) + (s—s')(e,w) da 

 dt "" s'{a,£) dt 



01' 



2e 



de 

 It 



s'a dt à n s' dt 



whence 



2s' 



de _ 2 Hq dx 



de . 



Expanding the coefficient of e -^ in terms of e\ and n, in terms of 

 x^ and integrating we get 



(9) 



— : — -e-——-x+ Const. 

 s—s o 



in which x^ and e*, and higher powers are neglected. 



15. From the three equations of (8), we get 

 d^^lB^ da_ W^ de_^lB^ dd_ ^^f„,^}^-_ik_^d± 



, +^1 



dt ^a dt le dt Id dt 



= S7l()X 



Id (a,e) dt 



But 



cZa _ _ 2 n„ dx 

 dt 3 11 dt 



