eJ>JB 



= 0. 



398 Prof. L. Natanson on the 



which Lord Kelvin, Prof. Boltzmann,and other writers adopted 

 when endeavouring to find dynamical analogies for electro- 

 magnetic phenomena. The part of the energy, called T, 

 which depends on the quantities dAJdt, dAJdt, dkjdt, will 

 be then the electric energy 



T= a ^tf^<feK(E2+E* +E s); . . (4) 



the other U, connected with the collocation of the variables 

 A , A , A z themselves, will be 



V=^tifcvd !/ dzMKl + Vl + Kl)- • ■ (5) 



Supposing SA x , 8Ay, SA z to be variations as usual and 

 K, C, fi and dx dy dz not to be subject to variation, we shall 

 have 



f [K^ _ (*£« _ *5*) -4,rCF,+4,rCE 1 5A, 

 dxdydzl L dt V By ^z I " x \ 



[ +[.... ]SA y+ [....]8A s . j (6 ) 



This equation is readily transformed. First : 



££*Ifii.**K(£*A. + <§ 8 A,4 f W.) = j>T, (7) 



and 



- fWff & ^ G ( F » 8 A, + F y SA J+ F,8A,) = PW# r . (8) 



J 'o J h 



Then, from the well-known Maxwell-Helmholtz principle, 

 on the continuity of properties oil surfaces of separation 

 between different media, and from the equations (3), we 

 obtain 



-iJ>m***{(g.-$)M£-#>'. 



f (BA y aA,\BSA,_/aA I _ BA.N38A, 



\ fix B.y / Bi/ V ~dz ^x ) ~dz 



^ V "dz ~dx / ~$x V dy d? / ^ 

 = -| *dt8\J (9) 



> 



i 



I 



J 



