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



Of course, any self-induction in the outside part of the 

 secondary circuit will produce the same effect as a leakage in 

 the transformer itself. 



The interesting fact to which I wish to draw the atten- 

 tion of members of the Society is this, that however great 

 may be the magnetic leakage, Mr. Blakesley's method is still 

 correct if magnetic permeability is assumed constant during 

 a cycle. Multiplying equation (2) by C we have 



M LL'— M 2 • 



YC = KC 2 -rf, CC' + ^Vt^ CO. . . . (3) 



Integrating for the whole periodic time and dividing by 



that may be desired, the amplitudes and lags of the primary and secondary 

 currents, and indeed all other magnitudes involved. The graphic method 

 of working is evidently quite out of the question. 



My students have for several years made calculations of this kind, 

 obtaining tables of values for various frequencies and amounts of iron in 

 the transformer, and they are exceedingly instructive. Until such tables 

 are comnared with actual experimental results, it seems to me that 

 debates as to the effect of hysteresis consist merely of assertions having 

 no physical basis. 



For my present purpose I will give part of two tables calculated by 

 Mr. Eliott, one of my students. Taking the above values : — 



1st. If we assume that there is no magnetic leakage. In that case 

 M= VLL^l'S secohms. Using this value of M we get table I. 



2nd. If we assume that there is a little magnetic leakage, say one and 

 one third per cent., or that M=1'48 secohms. Using this value of M we 

 get Table II. 



Now it is perfectly certain that there is some magnetic leakage, always; 

 but it is rather difficult to say just how much there may be. I have 

 here assumed in taking M = 1'48 instead of T50 that 1£ per cent, of the 

 total induction due to the primary coils does not pass through the 

 secondary coils, and that 1^ per cent, of the total induction due to the 

 secondary coils does not pass through the primary coils. This number 

 has been taken at random. 



The meanings of the letters used at the heads of the various columns 

 are these : — 

 If V= 1000 sin -^t, 



. /2tt v 

 C = Asm (— f-ej, 



n , t , . /2ff , \ 



t =Asm ( — t— e ), 



, • /2tt A ~, 



\ ' = « Sill I— t — € )=p<^ > 



P= average power given to primary, 



P'= average power given out by secondary. 



Percentage efficiency ==100P'/P. 



Evidently V is the voltage at the terminals of the secondary circuit. 

 Angles of lag are given in degrees. 



