Statistical mechanics 63 



But according to (72) is 



or 



U' = a^ + r.'R,,,, 



F2 = a2 + a*i?,,„, 

 which values, substituted in (140), give 



(143) a..^ = Io>jjj{- + i?o2o + -^^002) ^^j.dUdVdW. 

 From the general theorem given above we gather that 



"200 ~ — 4:1 , 



(144) . «020 = + 2/, 



and that all other coefficients aiju vanish. 



Consequently we have in this case rigorously: 



(145) V200 ^ I ( 4i?(,„o 200 "I" 2-Booo 020 QQ2) , 



where only the expression (136) for the 5-coefficients are to be substituted, to 

 complete the computation of V200 ■ 



46. If the law of Newton is valid, the circumstances are more complicated. 

 The quantity I is now no longer a constant. We know, however, that it depends 



only on = V + F^^ + W,' . 



To avoid the many indices we write 



-t-OO 



a 



with 



^fffi-^U'+^' + ^(^) ^'J'< dUdVdW, 



— CO 



4) = i e 



Consider first «„qq. I propose to show that this coefficient vanishes. We have 

 + «, 



«000 = (//'(- 2 ?7^+ W^)I{ü)^dUdVdW. 



— 00 



But we evidently have: 



/// liil)^ dU dVdW- III V 7(ß) ^dUdVdW = 



= fjlW'I{Ü)^dUdrdW = 

 = dUdVdW. 



