1863.] of a Solid Body about a Fixed Point, 63 



or 



or 



then 



and 



J 



These, then, are the integrals of the equations of motion when no exter- 

 nal forces are acting. The next step is to determine the variations of the 

 arbitrary constants, due to the action of disturbing forces, when, as in the 

 case of nature, those forces are small. With a view to this, it will be con 

 venient to change the arbitrary constants into the following, 



whence 



(0 - 0,)^^ = (S + 0)m'- (S + e,)n' ; 

 also, for brevity, let 



«M^«^+/)=x. §^^=*A 



Then the equations of motion become 



JPi= ^qZ:q am{lnt-^f). 



