368 On the Hall Effect and Allied Phenomena. 



In discussing the influence of temperature on the Hall 

 effect in the ferromagnetic metals, Mr. Livens states that, 

 " In these cases as the temperature is increased the Hall 

 effect coefficient increases, exactly parallel with the magnetic 

 permeability, until the critical temperature is reached, when 

 it decreases more rapidly to a value more akin to that found 

 in the simpler metals. This would appear to be almost con- 

 clusive evidence of the appropriateness of the explanation of 

 these irregularities suggested above." That there is a sudden 

 decrease both in the Hall effect and in the permeability at 

 the critical temperature cannot be questioned, but from this 

 fact it is not to be inferred that the coefficient of the Hall 

 effect and the permeability depend on the temperature in the 

 same way. The Hall effect seems to be a more complicated 

 function of the magnetic permeability than the statement 

 quoted above seems to indicate. 



Kundt has shown that the Hall electromotive force is 

 proportional to the intensity of magnetization for a particular 

 temperature. If E is the Hall electromotive force ; I, the 

 intensity of magnetization; Jc, the susceptibility; H, the 

 magnetizing force ; and A, a constant of proportionality, 



E=AxI=Ax£xH. 



For a given value of H the relation between the Hall electro- 

 motive force and the susceptibility is given by the equation 



E/& = A X constant. 



If the Hall effect and the permeability increase parallel to 

 each other, the ratio of the Hall electromotive force to the 

 susceptibility should be independent of the temperature, that 

 is A should be independent of the temperature. Experiments 

 have shown that A is a function of the temperature and that 

 it increases rather rapidly with the temperature. Hence the 

 Hall effect and the permeability depend in different ways on 

 the temperature, and the variation of the Hall effect with the 

 temperature cannot be entirely accounted for by the variation 

 of the permeability with the temperature. 



Very truly yours, 



Alpheus W. Smith. 



Ohio State University, 

 Columbus, O. 



