6 Proceedings of the Royal Society of Victoria. 



R., being the total resistance or its equivalent in the secondary- 

 circuit 



^ ^~Rr~R, 



It is worth noting that Tj, To, and 6' are of zero dimensions. 



7. Returning to the diagram Fig. 2, if we call the angle EOB 

 a, so that Cosa is the power factor of the transformer, we find by 

 projecting the figure OECB on ON and on a line perpendicular to 

 ON, that 



EjCosa = r,C, + K;/?iFSin(8 + x) -= r,Q,[\ + ""' ,Sin(S + x)] 



= riCi[l + A,(Sin8 + ^'Cos-<^')] 

 making use of the relations in ^ 4 and 5. 



EiSina = .TiTiriCi + 7e'«iFCos(S + x) = ^i^iixxT^ + ~,Cos(S + x)] 



= riCi[a-,Ti f ^,[0os8 + ^'Cos</,'Sin<^')] 

 whence, squaring and adding 



E^^ = r;^C;- \ 1 + x;\C- + % + ^ [Sin(8 + x) + ^-iTiCos(S + x)]\ 



n El A' 



or C\=-l ^ 



where D'^ = 1 + 2a-iCos8 + 2^ + 2 Vosc}>'{x,Sincf>' + 9^) + 



Ti T] ^ 



Dividing EiSina by E^Cosa 



, _Cos8 + ^'Cos<^'Sin<^'+A:iA'' 



Sin8 + ^'Cos-<^'+ A" 



The above relations enable us to determine practically ti and 8 

 for any closed-circuit transformer. For on open secondary $' = 0. 



A' = l. D'=l+.TiCosS + ^^=l (q.p.), 



as it will be shown later on that Xi is always a small fraction 

 and Ti a large number for a transformer of the type treated 

 in this section. Hence if Cq be the primai-y current on open 

 secondary 



