48 Proceedings of the Royal Society of Victoria. 



Adding I. and II. we get the energy of Co, due to the leakage 

 lines it sends across one window. The other window contributes 

 an equal amount, hence, 



or 



L',= -3^ »^\t^+ -^^^., ^ ^,j. (III.) 



«iC, r , 2) 



(I?) The mutual energy of C.^ and Cj, due to the C.j lines through 

 the even spaces being looped on Cj, can be read off from Fig. 7, 

 and is 



J 



J^ n,n.j:^,G'^b,. (IV.) 



The mutual energy of C.^ and Ci, due to the C.^ lines through 

 the odd spaces being looped on Cj is 



= j^ ;/i;/,C,c/-^ b,. (V.) 



[This will be seen by considering circuit 3, 3'. The flux round 

 it is "ifipi, and it completely encircles the two odd C, sections 1 

 and 1', and partially the Cj windings in 3 and 3'. But in § 44, 

 III., it was shown that the mutual energy due to a uniform flux 

 encircling a uniformly distributed current occupying the same 

 space, was the same as if the whole flux encircled half the 

 current ; hence, in this case, the energy contributed by 3 and 3' 

 is the same as if the flux 'i/.^b^ encircled one only of them com- 

 pletely, so that altogether the flux ?>fj'i encircles ?>n-^C-^lj oi the 

 current Cj.] 



Adding IV. and V., and doubling the sum to allow for the 

 other window, 



or M',,=M.,., \^tzlb,+ -^Izi/., j (VI.) 



(c) In a similar manner, by aid of the ]\I.M.F. diagram for 

 Cj also given in Fig. 7, or from symmetry we And that 



