368 ON THE MOTION OF 



< 5 ' &* — n 



Jl,lk, — "* y, — ^ B.mk, — a y, 



BJh.nl = %p£ = A ; Amknl = %^ = B, , 



omitting infinitesimals of the second order, and restoring At 

 and M, we obtain (34) 



*7 —3lOB l y ! , = o, 



r+Mo^'e = o, 



JP = o. 



By an examination of the values of the first and second differ- 

 entials of the indefinite integrals £,, »?„ £,, £ , ^ £ a given by 

 equations (10), it will readily be seen that, with the assistance 

 of the relations (4), (6), (8), the following expressions will be 

 verified (35) 



&l = d& — rb dR+ Z,dQ, 

 dn, = d n , — IdP-^- idH, 

 dl = dl — £f/Q+ n.dP; 



d% = d^ — dvM-hd&Q, 



d\, = 4-<(IP + <f,^, 

 d% = *£,— dfrdQ-i-dq.dP: 



equations analogous to those first obtained by Lagrange to de- 

 note the motions of rotation of a system of particles which 

 have at the same time individual motions of their own. In 

 the case of small oscillations the third and sixth of these equa- 



