HALL AND CAMPBELL. — MAGNETIC EFFECTS IN SOFT IRON. 643 



as such ; 2(1, tlie fact that it was much easier to measure current- 

 strengtii than potential-gradient, in the longitudinal direction, in metal 

 sheets of uneven thickness and uncertain quality such as were often 

 used in the early days of the Hall effect. 



It is true that before long it began to be seen that metals of high 

 resistance had, as a rule, high values of ^7^^, and this fact raised the 

 question whether high transverse potential-gradient might not go nat- 

 urally with high longitudinal potential-gradient as such. But it was 

 found that, in non-magnetic metals at least, rise of temperature, in- 

 creasing the resistance and the longitudinal potential-gradient, did not 

 as a rule, if ever, increase^ the Hall effect proportionally. Accord- 

 ingly, there has seemed to be no sufficient reason for recasting the 

 definition of c^e by introducing the potential-gradient instead of the 

 longitudinal current-strength. 



But the formula of Moreau suggests, or perhaps is suggested, by such 

 a change of view as this recasting of ^ T^ would imply. To prove this 

 statement an argument leading to this formula will now be given. 



We will treat the matter first in its qualitative aspect ; and we will 

 take the case of our soft iron, in order to be the more definite. Figure 1, 

 which is correct for this iron, shows a -f Hall effect, the equipotential 

 lines being rotated in the direction of the Amperian current of the 

 field. Such a rotation establishes a transverse potential-gradient, the 

 lower edge of the plate attaining thus the higher potential. 



Turning now to Figure 3 and remembering that in iron the Thomson- 

 effect coefficient, s, is negative, so that heat is absorbed by an electrical 

 current when it flows (in the ordinary conventional sense) from high 

 temperature to low temperature in iron, we see that in the present case 

 we must, in order that an electrical current may not flow along the 

 plate, have the cold end of the plate at a higher potential than the hot 

 end ; that is, we have, under the conditions of Figure 3, a potential- 

 gradient opposite in direction to the temperature-gradient and opposite 

 to the potential-gradient along the plate in Figure 1. Accordingly, 

 our magnetic field, rotating the equipotential lines of this stat'iG 

 Thomson-effect potential-gradient, would make in our iron the upper 

 edge of the plate electrically positive as compared with the low^er edge, 

 thus giving what we call a negative Nernst effect. The Nernst effect 

 in our iron is negative, according to our convention as to signs, and the 



' " The temperature-coefficient of the Hall effect in gold, zinc, platinum, 

 silver and aluminum has . . . been determined and it has been found that 

 with the exception of aluminum there is in each of these cases a decrease in 

 the effect as the temperature is raised from — 190° to about 22°." Dr. Alpheua 

 W. Smith, Physical Review, Jan., 1910. 



