APPLICABLE TO MATHEMATICS, &C. 355 



where the bodies will remain at rest, if they are 

 placed there when they are not in a state of 

 motion. 



Since, f(.r) n x'^ + Wi x + n2, is the law of force 

 of each ray : substitute this value in equations 

 (2) and (3) and we shall have for the equations 

 of motion — 



U-^ = (m.m^)^ (s^^^ \--(^^) 



&-^l^^ = (^-'"^')f (^ri^y 1--(11) 



These equations may be written 



drx _ (mwm') ^ », n.^ } no\ 



df ~ M i ■*■ x'-x ^" {x'-xfl •••V^"'/ 



d^x^ _ (m 0) m') C "i . ^2 ? / 1 q\ 



Add equations (12) and (13), and we shall have 



~de^'' ''^-l M + M' n ^'-^ (^'-^n 



Multiply by 2 ^^ and integrate 



