Measuring Power in Transformers. 191 



fractional portion of the field due to primary current which 

 escapes the secondary winding, or it is the fractional portion 

 of the field due to the secondary current which escapes the 

 primary winding. The reasoning is the same even if a small 

 difference be supposed to exist between the y of the first and 

 they of the second equation; that is, if M is not the same 

 in the two circuits. I submit that in the absence of any 

 prior definition of "leakage" this is simple and reasonable. 

 Dr. Sumpner's " leakage " is a very different thing. He 

 said, let I P = I 8 (1+^), then x is the magnetic leakage. 



Of course, on any reasonable assumption of alterations in 

 fjb, the permeability of iron, or on the most reasonable assump- 

 tion that /j, really is constant during a quickly-performed 

 cycle, Dr. Sumpner's x varies greatly during the cycle. I 

 cannot give a physical meaning to x. My "leakage" ydoes 

 not vary if //, is constant during a cycle, and I have given a 

 perfectly definite physical meaning to it. 



It may be well to add, here, why I think it reasonable to 

 assume fi constant during a cycle. 



1st. I have shown that if there is any leakage, the use of 

 equations (1) and (2) is quite unreasonable. 



2nd. If there is any leakage, it is impossible to treat the 

 subject mathematically unless some assumption is made con- 

 cerning JuL. 



3rd. It is quite certain that the law of variation of fi when 

 the cycle is very slowly performed must be quite different 

 from the law when the cycle is very quickly performed, as it 

 always is in practice. 



Ith. The analogies between magnetic stress and strain and 

 ordinary stress and strain in materials are well established. 

 Now every material exhibits strain hysteresis when slowly 

 loaded and unloaded, and exhibits no hysteresis whatever 

 when the loading and unloading are very quickly performed. 

 Even the most inelastic of materials will transmit a musical 

 note unchanged. Hence for years I have taught my students 

 to look upon magnetic hysteresis as very important when 

 cycles are slowly performed and as unimportant when cycles 

 are very quickly performed. Unless on this assumption, how 

 is it that there is so little heating of the iron of a transformer 

 by hysteresis even when transforming the largest amounts of 

 energy ; and such heating as there is must be partly due to 

 eddy currents. I therefore maintain that /x constant during 

 a cycle (and this means that my " leakage'-' is constant during 

 a cycle) is the only reasonable assumption that can be made 

 in the present state of our knowledge. 



But even if this reasonable assumption of no hysteresis and 



