îîosearchos ou tho Distrilnition of the Mean Motions of the Asteroids. 45 



Or neglecting tlie quantities of higher orders we get 

 at 2 4 ^ 



where 



2V=-£l ^*'^' 



* s'x—î^p^e^'"^ cosd' 



If we put ^'=- in this equation, N(e^—e^) is always positive, and 

 hence 



Accordingly the revolution of Type 1 in its limiting case approaches 

 the position of contact, and the revolution of Type 2 recedes from 

 that position. 



55. The equation corresponding to (10) takes the form 



neglecting the quantities of higher orders. Now 



nJe{e'--e')dt= f , <^'-~^') dd' 

 J J sx—gco%o' 



According^ we can prove that 

 I e{e'-~e')dt>0 







as in the case of the second order. Hence 



/, dt 



