24 CONSERVATION OF EXTENSION-IN-PHASE 

 Fk 



F=l 



But since F is a homogeneous quadratic function of the 

 differences 



we have identically 



F=k 



rt 



d(pi -Pi) . . . d(q n - Q n ) 

 kF=k 



rwy&i 



F=l 



-Pj...d(<!.-Q 1 ). 



That is U=k n U l} (61) 



whence dU= U 1 nk n ~ l dk. (62) 



But if k varies, equations (58) and (59) give 



F=k-\-dk 



dU = I . . . I dpi . . . dq n (63) 



F=k 



F=k+dk 



F=k 



Since the factor Oe~ F has the constant value Ce~ k in the 

 last multiple integral, we have 



dR = C e~ k d U = C Ui n e~ k k n ~ l dk, (65) 



n e -k (\ + & + + . . . + N + const. (66) 



We may determine the constant of integration by the condition 

 that R vanishes with k. This gives 



