On Measuring Power in Transformers. 185 



effective primary volts by effective primary amperes. But 

 when there is magnetic leakage, this rule is wrong. The 



P 



ratio of ^ , for example, in the second table is never greater 



than cos 20°. Such experimental results as are at my com- 

 mand confirm my view that 



Effective Primary Volts x Effective Primary Amperes 



give a result always greater than the true power, even for 

 very great loads; a result to be expected if there is con- 

 siderable ma one tic leakage. 



XXVI. Mr. Blakesley's Method of Measuring Poiver in 

 Transformers. By Prof. J. Perry, F.R.S* 



MR. BLAKESLEY'S method of measuring the power 

 given to the primary coil of a transformer becomes 

 more important the more it is studied. Mr. Blakesley proved 

 it to be correct if currents followed the simplest periodic law; if 

 there was no magnetic leakage; if magnetic permeability was 

 constant. Any person who has used Fourier's theorem knows 

 that if Mr. Blakesley's rule is right for a sine function, it 

 must be right for any periodic function whatsover; as any 

 periodic function may be expressed in sine functions, and 

 each of these enters into the equations as if it were alonef. 



* Cornmimicated by the Physical Society : read May 22, 1891. 



f This assertion was challenged in the discussion. Perhaps I ought 

 to have explained myself more fully. At the time I happened to be 

 working with Fourier's Series very much, and I lost siglit of the fact 

 that what was very evident to me might not be evident to others. 



If x — %^ (a { sin ikt-\-b t cos ikt), 



and y = 2°° ( a ; s , m &*+& cos ikt) , 



2 

 where & = — and r is the periodic time, then the average value of xy 



between the limits and r is 



and does not involve any term such as a f u r or h i (3 r ; that is, into the 

 expression for the average value each term of the Fourier's Series enters 

 just as if there were no other terms. Nearly all practical Electrical 

 Engineers are in the habit of ignoring calculations which assume that a 

 current is a sine function of the time ; they say that such calculations 

 are useless because the current never is a true sine function of the time. 

 I have here given one of many examples which might be given in 

 which a proposition concerning any periodic function need only be 

 proved for one of the Fourier terms of that function. And in all cases, 

 the result of the study of a sine function is at once applicable to any 

 periodic function whatsoever. 



