186 Prof. J. Perry on Mr. Blakesley's Method of 



Prof. Ayrton and Mr. Taylor have proved the method to 

 be correct for currents of any periodic law, the permeability 

 varying in any way whatever. But they make the assump- 

 tion that there is no magnetic leakage. 



I believe that it was Dr. Hopkinson who, in his paper read 

 before the Royal Society on March 10th, 1887, first departed 

 from the old-fashioned way of treating mathematically the 

 equations concerning currents in neighbouring coils, and he 

 has been followed by everybody else who has written upon 

 that subject since. Some writers of eminence have given, and 

 incompletely, Hopkinson's investigation, evidently not having 

 seen his paper. In my opinion the usual method is somewhat 

 misleading. Assuming no eddy currents in the conducting 

 part of a transformer, the equations written in the old- 

 fashioned, and in what I venture to say is the only correct 

 way, become 



V = RC +LC + MC'") 



= R'C + MC+ L'C'J ' W 



Here V is the voltage at the terminals of the primary cir- 

 cuit, R its resistance, C its current, and L its coefficient of 

 self-induction. R' is the resistance of the whole secondary 

 circuit, in which we assume no independent electromotive 

 force; C is its current, L/ is its coefficient of self-induction, 

 and M is the mutual induction between the two circuits. 

 It may be well to state that, using amperes, volts, and ohms: — 

 If P and S are the numbers of windings of the primary and 

 secondary respectively; if a is the cross section of the iron 

 in square centimetres, X the average length of the complete 

 iron magnetic circuit, and /u, the permeability (being about 

 1500 in ordinary transformer working), we may take it that 



a/i 4tt 

 L=F X TO' 



L = b IlO' 



and if there were no magnetic leakage — that is, if all the 

 field due to a primary current through every single winding 

 of the primary passed through every single winding of the 

 secondary, then M= \/LV 7 or 



M-PS*£. 



But there is always some magnetic leakage, and it fills me 

 with astonishment that so many investigators should assume 

 that a little leakage makes no difference. 



