42 Proceedings of the Royal Society of Victoria. 



(neglecting the reluctance of the iron). 



This flux encircles all of n-^Ci and the energy associated with 

 it is 



SO that the total energy of Cj due to the leakage lines it produces 

 and that cross the window is 



The other window contributes an equal amount, hence as the 

 sum is also equal to i-L'iC'^, 



L': 



.i-Mr.^io. 



^,+ 



121^ 



Similarly, • 



(II.) 



The latter of the two fluxes already considered is partially 

 looped on w^Cj and the inutual energy of Cj and C.^ due to this 

 can easily be found as follows. 



The flux through 2(3'dy where j=OE, Fig. 5, is 



and it is looped on the portion 



— r- y or ;/.,U., 

 so that the mutual energy is 



Integrating from y=o to y^=b.2 we find that the mutual energy 

 of C2 and the leakage lines due to C^ is 



Thus we see that the mutual energy of the uniform Cj flux 

 that goes through the C^ coil, and fi.^j^^i is 



=\ . flux . «A- (III-) 



or is the same as if all the flux through the space were looped on 

 half the total current in the space, a result that will be made 

 use of in § 45, b. 



