72 Proceedings of the Royal Society of Victoria. 



Cos(S + <^) + a-i2Cos</) + ^ I {x^. - a-.>,)Sin8 + ^ + ^^ j 



tan/3= ^ " " ^fe^^ 



Sin(S + c^) + .^128111^ +^|l +(^i2 + X22)Cos8+ -2^-{-Xi^xA 



where it — /? is the angle that Cj is behind C^ in phase. 



62. Eliminating Cg from equations (I.) and (IV.) and putting 



X-^i X^i ~r •^22 "^12 ^^ -^) 



1 _ 



■^11^22 ^12"^21 ^'j 



T1T2 



— + — ^ = «, 



To T, 



we get 



«lJ^l_ Tl 



g ^2 +6'-^ +ir22 + — ^ 



'^ T2 



+ _L_ ^ ^ „^Ci 



e ^2 ^'+d)e +x.„ + — e 9 f 

 from which by § 59, b, we find that 



A ^iTi ' D ^ "^ 



where 



D^=l + 2.riiCosS + 2 — +V+ -, + 2^(xSin(^ + TCos<^ 



Tl Ti I 



+ (x-iiX + -)Sin(8 + <^) + (a;uT--)Cos(S + <^) + «Cos(S-<^) 

 — wSin(8 - ^) + r«ii;« + — jSint^-hTiCi] « — — ^Cos^ I 



also, if a be the angle that C, is behind E^ in phase, so that Cosa 

 is the power factor of the transformer, 



