356 ON PHYSICAL DATA 



when (a-' -.r)=(a' -a) we shall have ^"^^ ^ ^ = 

 .-. C = (m «> m') |^+-j^l |(«' - «) - "ilog- (*»' - «) 



a' — a ^ 



Hence, we have 



This is the square of the velocity with which the 

 particles approach or recede from each other 

 according as m is greater or less than Wi. 



Again, let the law of force, f{<x) =711+^207 + 

 n-j x'^ + W4 ^* + &c. &c. be taken. 



Then the roots of the equation 



n^^- n.iX -V n^oc^ -^ &c. = will deter- 

 mine so many points where equilibrium will take 



