Hall Effect and Allied Phenomena. 201 



excluded in a strictly analytical theory, except in so far as in 

 such cases where the average aspect of the irregularities may 

 be conveniently determined and expressed. Nevertheless, 

 the general compatibility or otherwise of the results of an 

 ideal theory based on the hypothesis of a suitable average may 

 provide some indication of the validity of the general theory; 

 and in this way only is the theory proposed in my paper to 

 be used. 



The same point may be further emphasised by reference 

 to Mr. Smith's second difficulty. In reviewing the influence 

 of temperature on the Hall effect in the ferromagnetic metals, 

 I stated that as the temperature increases the Hall effect 

 increases exactly parallel with the magnetic permeability, 

 until the critical temperature is reached, when it decreases 

 rapidly to a value more akin to that found in the simpler 

 metals. I conclude that this is evidence for the explanation 

 of the irregularities of these metals by the assumption of 

 strong local magnetic fields proportional to the polarization. 

 My use of the words (i exactly parallel " was perhaps un- 

 fortunate, as 1 did not intend to imply that the constant of 

 proportionality was independent of the temperature, or in 

 other words that the magnetization and Hall effect depend 

 on the temperature in the same way. The phenomena of 

 magnetization and conduction are fundamentally distinct, 

 and the average influence of the strong local molecular fields, 

 which now seem to be generally regarded as surrounding 

 the molecules of most substances, will in all probability be 

 very different in the two cases. The proportionality of the 

 strength of the local field with the polarization has been found 

 to provide a generally sufficient explanation in most cases of 

 the irregularities of the phenomena concerned • but it is to 

 be remembered that it is an averaged field that is operative, 

 and the type of average may be very different in the separate 

 cases or at different temperatures, so that the mode of 

 dependence of the various phenomena on the temperature 

 need not necessarily be the same. This implies that the 

 constant A in Mr. Smith's equation may quite consistently 

 be a function of the temperature, without in any way affecting 

 the general conclusions drawn in my theoretical paper. 



Very truly yours, 

 The University, Gr. H. LlVENS. 



Sheffield. 

 Mav 26th, 1916. 



