RECIPROCAL ACTION OF TWO SHELLS. 335 



which gives finally 



(32 ) 





352. To determine the relative energy of the system, let us 

 suppose that the shell S' moves away, and that during the time dt 

 the distance r of two elements varies by dtor 2>Jr--dt. The 



Ql Of 



corresponding elementary work of the force d^ is equal to 

 d^ dt t so that the total work ^ 2 T relative to the element ds 

 for the time dt is 



Integrating by parts, we have 



rv^^v? rv^v^i _ ryray; d , 



} It ^to' ^ [_ to to J J to to'to 



The first term of the second member is zero for the closed 

 surface C', which gives 



to 



The elementary work relative to the actions of the two circuits 

 in the time dt is therefore 



to 



This work being symmetrical in reference to the edges C and 

 C', we have also 



to 



