AND THEORY OF INTEGRATION. 31 



of a function of a, . . . h, which we may denote by a'. We 

 have then 



da '= d(b,...h) dr ^~ d(b*..K) dt > (85) 



dfa, ...r 2n ) d(r 2 , ...r 2n ) 



which may be integrated by quadratures. In this case we 

 may say that the principle of conservation of extension-in- 

 phase has supplied the * multiplier ' 



1 



d(b, ...h) (86) 



d(r z , . . . r zn ) 



for the integration of the equation 



dr, -r l dt = 0. (87) 



The system of arbitrary constants a', 5, ... h has evidently 

 the same properties which were noticed in regard to the 

 system a, 6', ... h. 



