of the Hall Effect and Allied Phenomena. 545 



hypotheses to render an absolutely full account of the whole 

 set of the phenomena *. 



According to our theory each of the effects should have 

 the same sign (apart from variations of s from one metal to 

 another) in ail metals, viz. those which they have in bismuth 

 or copper. It appears, however, and not infrequently, that 

 the opposite sign is obtained in many cases and that there is 

 no definite regularity in the occurrence of either sign. It 

 is, however, of importance to notice in this connexion that 

 the signs of all the effects are found to be reversed if one of 

 them is, or in other words, the effects always have the same 

 relative direction. This observation is important as implying 

 that the cause of the reversal is common to them all. Now, 

 this occurrence of tlie opposite sign in all the phenomena to 

 that predicted by the theory is capable of a very simple 

 explanation, which although perhaps of an apparently 

 tentative and uncertain character, is nevertheless supported 

 by several independent classes of observation. It is to be 

 remembered that the effective magnetic field for the pheno- 

 menon is not the simple continuation of the magnetic field 

 examined from outside the metal but is the field at a point 

 right inside the metal where the above "internal" field will 

 in general be augmented by the addition of a purely local 

 field due to the polarization in the immediately surrounding 

 molecules or molecular groups. It is thus assumed to be 

 probable that in the regions accessible to the freely moving- 

 electrons this local part, which will on the average bo pro- 

 portional to the intensity of the magnetization, may com- 

 pletely reverse the sign of the total effective field. If this 

 explanation were a valid one we should, of course, expect 

 to find that in the strongly magnetic materials the local part 

 of the field would greatly preponderate over the external 

 field, and might in fact be taken simply as the effective field 

 itself. This is, as a matter of fact, exactly what is found to 

 be the case ; for it is found that if magnetization is substi- 

 tuted for magnetic force in the expression of the effects in 

 the ferromagnetic metals, then the coefficients at once 

 assume normal values, and remain reasonably constant as the 

 field is varied. 



The assumption of this local field would also provide an 

 effective explanation of the behaviour of the phenomena in 

 metals of more complex structure ; such as bismuth. In 

 fact, the local field is essentially constitutional in character 

 and would thus probably be different in different directions. 



• For detailed information respecting the experimental work, see 

 Baedeker, Die vlektrische Erscheinungen in met alii sch en Leitern, Oh. iv. 



Phil. Map. S. 6. Vol. 30. No. 178. Oct. 1915. 2 N 



