184 On the Study of Transformers. 



If, then, we can neglect 2hy6, we have the law when 

 there is no leakage (9). But when 2Lyd cannot be 

 neglected, of course the effect of it is to make the secondary 

 voltage fall off more quickly as the load increases than would 

 be indicated by formula (9). This I find shown by such 

 actual experimental results on transformers as I have at 

 command. 



As I have already said, when we assume no magnetic 

 leakage, it is of no importance whether we assume that per- 

 meability is constant or not, or whether there is hysteresis or 

 not; the results given by (2) have been shown to be practi- 

 cally correct for such frequencies and amounts of iron &c. as 

 are usual in transformers. 



But if there is leakage y, and if yu and therefore L varies 

 from instant to instant during a cycle, it is certain that 

 y will alter in an inverse way. Making, then, the very 

 unnecessary assumption that there is hysteresis in a trans- 

 former, it is obvious that Ly will not vary very much during 

 a cycle, and the results of calculation will not be very dif- 

 ferent from what they are on the assumption that /n is con- 

 stant. I have elsewhere given reasons for assuming that there 

 is really no hysteresis in transformer working. 



Taking the sizes of iron and other dimensions of any 

 working transformer, and using them for calculating such 

 tables as I have given, it will be found that on calculating 

 the true power P given to the primary coil and comparing it 

 with W, if W is 



Effective Primary Volts x Effective Primary Current, 



P 



then ^ is nearly 1, even when the load is rather 



small, and may be said to be exactly 1 for ordinary and all 

 greater loads, if there is no magnetic leakage. But if there 



p 

 is magnetic leakage, ^ is, as before, much less than 1 for 



very small loads, getting greater with the load until for heavy 

 loads it reaches a maximum value, and for very heavy loads 

 diminishes again. But it is always less than 1, and is less 

 and less at its maximum value as the current departs further 

 from a simple sine function of the time. In Mr. Eliott's 

 two tables, 



P 



^ = cos e, 



and without magnetic leakage e is for nearly the whole 

 range of load — that is: — If there is no magnetic leakage, the 

 power given to the transformer is obtained by multiplying 



