70 Proceedings of the Royal Society of Victoria. 



(c) If a represent the harmonically varying quantity nCos7vf, 

 then since 



■T, (nCos7Ci/)=.zvnCoslzvf + :^ j 



TT 



we "^ a or wia will represent — (;/Cosz£'/), and we may write 



dt 



IT 



d '2 



—az=we a = 2VLa. 

 at 



60. If o-/47r be the permeance of the magnetic circuit, closed 

 or open, and limited in section by the iron core where the latter 

 exists ; and if 8 be the angle of magnetic lag of the iron, then as 

 the flux density remains very nearly constant throughout the 

 range of operation of a transformer, we may without much error 

 consider o- and 8 as constants. 



The total number Nj of magnetic lines looped on the Wj turns 

 of the primary coil is the sum of three sets, namely, 



1. Those traversing the iron core, produced by the magnetising 

 ampere turns Jl^G■^-\- n.^Cj, and behind them in phase by the 

 angle 8. 



Hence these 



= (re («iCi + n.J^.^ 



2. Those produced by C^ and in phase with it that miss the 

 iron core. 



Let these 



3. Those produced by C.2 and in phase with it that miss the 

 iron core. 



Let these 



Hence 

 similarly 



where x^.^ and x-^.^ have similar significations with regard to the 

 secondary coil that x^^ and x^i have with regard to the primary. 



