406 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



netic field. Conversely, when a current flows through a conductor in a 

 magnetic field, temperature differences, as well as potential differences, 

 arise in the conductor. Altogether, there are twelve effects of this type: 

 four thermomagnetic effects in transverse fields, two thermomagnetic 

 effects in longitudinal fields, four galvanomagnetic effects in transverse 

 fields, and two galvanomagnetic effects in longitudinal fields. 



Of these various effects, the transverse galvanomagnetic effect in a 

 transverse field has been studied most extensively. This is commonly 

 known as the Hall effect. The relation between the electromotive force 

 and the variables of the system are given by the equation: 



_ RHi 

 D ' 



where H is the field intensity, i is the total current flowing, and D is the 

 thickness of the conducting sheet carrying the total current i. R, which 

 is the constant of the Hall effect, is a property of the conductor in ques- 

 tion. This constant varies greatly for different metals and may have 

 either positive or negative values. As a rule, the effect is greatest in 

 substances of relatively low conducting power. It is particularly marked 

 in bismuth. Here, however, as might be expected, the value of the coeffi- 

 cient depends upon the orientation of the crystal. Since the flow of 

 current in a conductor is influenced by an external magnetic field, it fol- 

 lows that the resistance of a conductor will be influenced by an external 

 field. 



At low temperatures, the influence of a magnetic field on the resist- 

 ance becomes marked, particularly for bismuth. K. Onnes 30 has shown 

 that at very low temperatures, where metals are normally in the supra- 

 conducting state, the curves connecting resistance and field strength are 

 similar to those connecting resistance and temperature. The action of 

 transverse and longitudinal fields differs little. For lead and tin the 

 critical value of the field strength at which the resistance rises abruptly 

 to measurable values lies between 500 and 700 G. It varies slightly with 

 temperature. 



The various galvanomagnetic and thermomagnetic effects would ap- 

 pear to be of great importance from a theoretical standpoint; for, if a 

 current is carried by charged particles, the observed effects must be due 

 to the reaction of the field on these particles. It might be expected that 

 the reaction of the field on the moving particles in a metallic conductor 

 would be similar to that observed in the case of the cathode rays. Actu- 

 ally, however, the observed effect in the case of most metallic conductors 



Ver8l. Akad f van Wetensch. Amsterdam 23, 493 (1914). See also J. Clay, Joe. cit. 



