of the Hall Effect and Allied Phenomena, 547 



hardly surprising, seeing that any such action by the magnetic 

 field is an essentially excluded factor in the main hypothesis 

 on which the present type of theory is based. According to 

 this assumption, whatever action the molecules may exert 

 on the electrons during a collision, it is presumed that 

 this action has on the average no reference to direction in 

 the metal, so that any fields of the type of the magnetic 

 fields in question, which act on the electrons in a transverse 

 manner, cannot affect their aggregate motion parallel to the 

 direction of the field. If we drop this assumption of isotropy 

 the theory at once becomes much more complicated, although 

 it is possible to predict the type of result which might be 

 expected from it. The one constant of the above theory 

 which depends essentially on the character of the collisions 

 and constitution of the molecules is l m , and mathematically 

 speaking the assumption of isotropy merely implies that l m 

 is not a function of direction in the metal. In all cases, 

 however, and more particularly when the metal is magnetic, 

 the assumption of isotropy under the action of a magnetic 

 field is hardly justifiable, and we ought therefore to assume 

 that l m is then modified so as to be a function of direction in 

 the metal with reference to the magnetic force, the coefficients 

 being in general even functions of the magnetic force 

 intensity in the external field. This explanation would of 

 course not only account for the magnetic effect on the 

 longitudinal conductivity, but would also modify the trans- 

 verse effect of the same type which has been effectively 

 explained on the above theory, and probably in such a 

 manner as to account for the irregular behaviour of this 

 particular effect. 



There is of course an additional modifying action of a 

 similar type to that already considered, which might also in 

 certain cases provide an effective explanation of the effect of 

 the magnetic field on the electrical conductivity. Let us first 

 consider the ordinary problem of conduction. According to 

 the ordinary theory, if the electric force in the external field 

 is E the current density at any point in the metal is 



o-E, 



a being the usually accepted expression for the conductivity. 

 This result, however, neglects entirely the presence of the 

 electrons bound in the metallic atoms ; we know, however, 

 from independent evidence that such electrons do exist and 

 the application of an electric field will displace them relative 

 to the atom, so that each atom will become polarized, with, 

 however, also a residual charge in some cases. But then the 



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