4 Proceedings of the Royal Society of Victoria. 



is represented by the vector RS equal in length to 2vn„'F and 

 behind F in phase by a right angle. 



For the present we will assume that the secondary current Cj 

 lags behind the internal secondary e.m.f. E'j or RS by an angle 

 <p'. This angle will depend on the load and its power factor, as 

 well as on the secondary magnetic leakage, and will subsequently 

 be expressed as a function of these quantities. 



From R draw RP making the angle SRP = <^'and drop SP 

 perpendicular to RP ; then the vector RP fully represents RaC^, 

 where R^is the total resistance or its equivalent in the secondary 

 circuit. 



4. From M draw MN parallel to RP and equal to n„C^, that is 

 TIT XT r\ E-P tVfliFCoSch' „,^ .F 



MN = «,,C,, = «2--- = «2 — i.g ^ = ^'Cos d) - 



Ro R2 o" 



where v = —^ — , 

 Ro 



then the vector NM represents n^^C^^ and as OM represents 

 «iCi + «2Co, we have 7i-^G^ fully represented by the vector ON. 

 As the angle OMN = ^ + 8 + </>' and OM = F/o- we iind that 



ONo,.„A=A-J, ',.^^,...C, - 

 where A"= 1 + 2^'Cos</.'Sin(S + </.') + e'-'Cos'cf>'. 



If the angle MON be called )^, we tine), by projecting the sides 

 of the triangle OMN on OR and on a line perpendicular to OR, 

 the relations 



A'Cos(x f 8) = Cos8 + ^'Cosc^'Sinc^' 



A 'Sin(x + 8) = SinS + ^'Cos- <^' 

 which will be useful. 



5. From O along ON cut ofi' a length OB that will re^Dresent 

 rjCj, where r^ is the resistance of the primary coil ; OB will 

 represent therefore the effective e.m.f. that produces current in 

 the primary coil, and will be the vector sum of (a) the impressed 

 e.m.f. El, (^) the e.m.f. 



'di _ 



due to variation of the main flux F, and (r) the e.m.f. 



