58 Proceedings of the Royal Society of Victoria. 



lying between the cylinders whose radii are r+^-2 and r-^d.^-^-Zf^, 

 and let r-\-i?.^ + ^i=rQ. 



The flux density due to Ci at all points on the cylinder of 

 radius fg — z is 



iirnjCi z 



where A' is the length of the windings parallel to the core, and 

 the flux in the Cj space between the cylinders of radii r^ — z and 



^0 — (2 + <2^0) is 



= -^ fMr.-z)dz, 

 and it is looped on that part 



that lies without it, hence it contributes energy ^E where 



Integrating between s^O and z^bi 



A' 



'(t-B 



~' A' i 3 ■*"12)' 

 as rQ^:.r-\-o-^-\-b.,. 



The current Cj also sends through the space occupied by coil 

 2 a uniform flux 



=^.|(.+AJ^-^} 



which is looped on all of Jifii and therefore contributes energy 

 to the amount 



'\rb.^\, 



A' 



so that the energy of Cj due to those lines that it produces and 

 that do not traverse the core is 



t it is also ^^L^Ci"^ 

 nee 



