200 Mr. Gr. H. Livens on the 



and this procedure would secure the analytically necessary 

 localization of the fields, which is essential to the mathematical 

 developments of either form of the theory, and it removes 

 the origin of the discrepancy between the two estimates of 

 the magnetic energy in the field. It would thus justify a 

 further simplification of the problem by restricting it to 

 stationary or quasi-stationary motions, and secure full 

 confirmation for the generality of the procedure adopted by 

 Larmor. 



The University, Sheffield, 

 April 15th, 1916. 



XX. On the Hall Effect and Allied Phenomena. 



To the Editors of the Philosophical Magazine. 

 Gentlemen, — 



IN the April number of your Magazine, in a short review 

 of my paper on the " Electron Theory of the Hall 

 Effect and Allied Phenomena," Mr. A. W. Smith directs 

 attention to two points in my work which may have given 

 rise to some misunderstanding. In reviewing the apparent 

 discrepancies in the sign of the four effects I stated, what 

 appeared to be a general rule, that the relative signs of the 

 four phenomena concerned are always the same. This 

 statement was based on the only evidence I had access to 

 when compiling the paper in question ; but I am not yet 

 inclined to modify it to any extent. On page 110 of 

 Baedeker's " Die elektrischen Erscheinungen in metallischen 

 Leitern," a table of the four coefficients for twelve metals is 

 compiled from the work of Zahn. Of these twelve all but 

 silver, copper, and antimony conform to the rule. To this 

 list Mr. Smith adds four more substances of which three are 

 irregular. There is therefore, on the whole, still a balance 

 of 10 to 6 in favour of my original statement. 



However, apart from statistics, I quite agree with Mr. Smith 

 that the rule in all its simplicity cannot possibly be infallible ; 

 but this is only what we might expect. The necessity for 

 simplicity of the physical hypotheses required in the analysis 

 of a mathematical theory puts that theory quite out of keeping 

 with the actual facts, which are concerned in the present 

 instance with substances whose composition is known to be 

 extremely complex and irregular. The constitutional irre- 

 gularities of matter are in no way susceptible of exact 

 mathematical specification, and have therefore always to be 



