44 Proceedings of the Royal Society of Victoria. 



2/3, and at the outer surface of the coil the width is 2/3 + 7rD, if 

 we assume that the corners of the coil are quadrants of circles. 



Hence B = 2yS + ^D. 



[This allowance for the corners of the coil may be considered 

 rather large, but if so it is compensated by the fringing of the 

 lines crossing the windows, which has not been allowed for.] 



Adding an equal amount for the other uncovered side of the 

 coil, the flux across dz due to C^ is 



16B ^ zdz 



■X T2D' 



IT 



and it is looped on 



^^22 of ;/iCi, 

 so that the energy associated with it is 



Integrating this between the limits z = l\l'2 and s^O we get 



4B«,^Ci-^|i - 2A, + 4Vlog^|^|, where A,=^^ 



which is the energy of Cj due to its lines through the primary 

 coil. 



Again the energy of Cj due to the lines it sends through the 

 space occupied by the secondary coil is 



V^" 



=4B«/Ci'^ f 

 J K 



dy 



2D 



J -^ TT 



= 4B«/Cinogl:tl^^^:^i 



' ' * l + 2Ai 



where j/j^— . 

 K 



The sum of these two results being \i\l\Q,{- 

 Similarly, if ^2=^, i/.^= i=_ 



TTOn p., J/, 



