456 



ELEMENTARY ACTIONS. 



For a closed circuit, the first term of the second member is null ; 

 we get then 



~ hii'ds' , 



Since from experiment this component must be null, we get 



0, or k= . 

 2 



With this value of , the elementary action becomes 

 (i3) 



or 



ii'ds'ds I 3 



cos e - - cos 6 cos | , 



7.--'7,r^ 3'awfrl 

 ^hu 'ds'\ -T---T . 



[_r 2 2 r 3 J 



471. DETERMINATION OF THE CONSTANT A The components 

 of the action of the current parallel to the other axes are then 



ydx $xydr 



r* 2 r* 



zdx 3 xzdr 



~^~~2~^ 



di)'= \d^ = hu'ds'\ 

 d= \d^ Z - = hu'ds'{ 



Integration by parts gives 



xydr / i xy\ i Cxdy +ydx 

 " = V~3^/ 3J ^~ 



The former term of the second member being null for a closed 

 circuit, we have lastly 



hii'ds' C 



- J: 



ydx - xdy 



hii'ds' Czdx-xdz 



