Now 



and 



Also 



Eesearches on the Distribution of the Mean Motions of the Asteroids. 37 



Me- - è')dt = f-^-^^i^-Jl- dd 

 7 ^ ./ s'ex-p, cos d 



s'ex—p^ cos d = s'{^s'é--\-x)rj-\--^:r::^{Ç>s'é- — x,rj- + 



Hence 



e^(e--ê-) 2êH5è''îy + 



s'C^s'e' + x)\ 2 3s'è- + S êy 

 neglecting rf. Accordingly we can write 



Since x is positive in this case the coefficients P and Q are finite 

 and positive. The double sign Avill be taken the same as that of 

 ■f}. Now 



■I« <^* 



dd 

 and the sign of jy is the same as that of -tt throughout. Hence 





