Solid Bodies through a Liquid. 335 



which show that the acceleration of k, under the influence of K, 

 follows simply the law of acceleration of a mass under the influ- 

 ence of a force. Again (for the motions of the solids), let 



f =f-«^-«^- &c, 77 =7?-^-^/c f - &c, . . . ; (12) 



and let -=-=-, &c. denote variations of Q on the hypothesis of f , 

 7} , . . . each constant. 



We have from (5), remembering that yy- &c. denote varia- 

 tions of T, on the hypothesis of f, i} 3 . . . k, k! } . . . constant, 



__d_Q/ dj [ dff \ m, 



or, by (7), 



]^_1Q ;/^,^ . +&c \ 



-*(^4 + ^ +&c ')" &c - + rff--- (13) 



Hence, by (1), 



-*(-f «f +*>*+3£-T... (U) 



Now remark that, according to the notation of (12), f , 7) , . . . 

 are the momentum-components of the solids due to their own 

 motion alone without cyclic motion of the liquid ; and therefore 

 eliminate f, rj, . . . by (12) from (14). Thus we find 



+ to. -*-g...-<«) 



