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



Similarly 



J ^^ /6-x l-3 /3\ (A-l)(;t-3) l-8-5 /3\- 



' 2 2 2A\^y 2-4 2-4-6U/ 



J h-l 1-3 / 3 y (A-l)(;t-3) 1-3-5/3 



2 2 2-4\4y'^ 



1-3 /^-3 1-3-5 / 3 



2-4 



1-3-5 / 3 \ Qi-'d){h-b) l-3-5-7 /^3 Y 

 2-4-6\4/"'" 2-4 2-4-ü-8\4y 



These series stop at a finite number of terms when h is odd, and 

 continue infinitely when h is even. If we put 



(10) «, = 27,— ^7, + ^^Js a,=I, ß,=I, 



we get finally 



(11) 







The numerical values of «„ «o, and ^i, for /(î=1, 2, o are computed 

 as follows : — 



8. If we put h=2 in (11), as it seems most natural, -4r is 



Lda ~\ i- at A 



-57- J to e^ Hence the effect must be very 



small for the bodies whose orbits have small eccentricities. Or in 

 other Avords if the effect be appreciable in the motion of asteroids 

 which have small eccentricities in general, it must be remarkably 

 great for the motion of the comets. This appears to be almost 

 fatal to our assumption, supposing the resistance still to exist, 

 because the effect of the resistance on the cometary motion, 

 whatever may be its law, is known to be very small if it exists 

 at all. 



But tliere is an answer to this objection. The comet, as far 

 as we know, is not a single body rigidly bound like a planet. It 



