156 

 Hence : 



^ = ^ I . . . Idt^ ...dt„.z (20) 



where the integration is extended over the volume of one period cell. 

 Written as a function of the q : 





d{t^ . . . cltn) 



d{q, ...qn) 



(20a) 



During the integration ever}^ q moves up and down once between 

 its limits. 



We use this to calculate — — (comp. formula 16): 



da 



dHrn _ ^i^/m d\/Fl 



da I \ ^ da 



By means of the relation : 



I. . .Idqi . .. dqi-x dqi^i . . . dq„ . F''« = i^'"» 

 it can easily be verified that form. (21) reduces to : 



. m 



=^ — ^ cijl>" . 2 I dqi-- — (22) 



da I ^ ^a 



Now from form. (10), (12), (14) and (19) we have 



where : 



1 



ƒƒ*■ 



dr\z. 







This series converges uniformly and can be integrated term by term. If we 

 now put: Tj — uj^ .t + const. ^ and calculate the form: 



z =■ Lim 



. - \dt. 



it is found — as none of the factors rwi^ + Sw^' is equal to zero — to reduce to 



1 



= ..=JJ*. 



dr^. z. 



