14 Proceedings of the Royal Society of Victoria. 

 =^ 1 —Sin (p( .r^SinS— — ^ ]\ 7—. + terms of lower orders, 



^ T ^ SlllS 



where in the second term we take ti^^t^^t. 



Hence at maximum efficiency, when the load is non-inductive 

 (^ = 0)the copper and the iron losses of a closed-circuit trans- 

 former are very approximately equal, and differ by a small 

 amount given by the above formula when the load is inductive. 



17. To determine the value of {B^ say) for which the copper 

 losses are z times the iron loss ; we have (see § 14) 



A' ^^CosV 



— + ^ = 2M'-*Sin8 



from which, after substituting for A and M their values given 

 in § 12, ^j, can in general be determined. 



For practical purposes 0^ will be given to a high order of 

 accuracy by 



where i = — | — 



18. In § 13 it has been shown that the output 



P,=^ 



'''^'l + 2xiCos8 + ^^+2^Cos0{XSin0 + TCos0 



^^Cos>(X'^ + 'P) 

 where X.=Xi + Xi and T= -|- — 



Let P„= 1 ^ 



SinS 



r,r,)l+2x,Cos8 + 2 



Iron loss on open secondary 



= sIHs ' (""' § "> 



Power absorbed on open secondary 



Power factor of transformer on open secondary ^^'"'' 



and take y=z:f^-^ 



■^ PqCos^ 



so that y is proportional to the output ; 

 also let 



XSin(/i + TCos^=/ 



XCos0-TSin0 = ^ 



