8 Proceedings of the Royal Society of Victoria. 



quantites with E'o, Co.S(^', etc., can now be obtained as 



follows: — 



From SP Fig. 2 cut off ST so that 



ST = wx.jTi^crG'i = x.fi'K.f^,^ 



d — 



then ST represents —n^^ixrp-nfi.^) 



that is, the e.ni.f. in the secondary due to variation of its leakage 

 flux. 



From IIP cut off RQ -= r^C^, then RQ represents the ohmic 

 drop in the secondary. 



Subtracting the vectors ST and RQ from RS (which represents 

 the total e.m.f. in the secondary), we get QT, which fully 

 represents E.2, the terminal e.m.f., and the angle PQT = ^ where 

 Cos<^ is the power factor of the load. 



If R be the external resistance or its equivalent in the 

 secondary circuit 

 so that R = Ra - ^2, and if 



then as d = — ^s — and t., = 



Ra /-2 



u 1 1 1 

 we have _l— • n\ 



QP_R.,-r2_ RQ' 

 Since Rp- " r7— i^^-^ 



E,^Cosc^ = E,'^'Cos<^' 



^ ^'Cosc^' ;/., El 

 or E.>= /irt r ~ -FT; (spe S 9). 



Again since PS = PT + TS 



RaCjtan <^' = R Cgtan (^ + wn^crx.f^,^ 



tan0' tan<^ 



-^=-^ + ^2 • (11.) 



By means of the relations I. and II. we can now transform 

 the formulae already obtained in B' and <^' to others in B and ^. 



11. Before doing so, however, it will be well to direct atten- 

 tion to the possil)le values of Ti, Xg, ^, B\ x-^^ Xj, and SinS, as when 

 these are considered the formulse admit of considerable simplifi- 

 cation through dropping terms of negligible value. 



