HALL. — ELECTRIC CONDUCTION AND THERMOELECTRIC ACTION. 71 



This quantity, as a whole, must have a negative value, if it is to accord 

 with the experimentally known facts; but as to the signs of its separate 

 terms there may be some question. It seems plain that the first 

 term is negative and that the third term is positive. The second 

 term, if there were no evidence to the contrary, I should take as 

 positive, and at first I did so take it, believing that I had experimental 

 ground, as well as a priori ground, for this belief. The experimental 

 ground proved not to be good footing, and I am now inclined to 

 the opinion that this term is negative, for reasons which will pres- 

 ently appear. The fourth term evidently has the sign of its factor 

 (v — ^ p — |). Now according to my discussion of the Thomson effect 

 (see equations (15)— (21)) this factor is probably positive in many 

 metals, and, as the third term of a p is obviously positive, we reach the 

 conclusion that, in these metals at least, the negative value of the tem- 

 perature coefficient a p cannot be accounted for if the electric conduc- 

 tion within these metals is solely, or even mainly, by means of the 

 (B) electrons. We are thus led to attach especial importance to the 

 first term in the value of K, as given in equation (2), and to the first 

 two terms in the values of a p , as given in equation (3) . 



1 r)F 



In seeking further light on the term y? r-~, the sign of which 



has thus far been left in doubt, we naturally turn to such experiments 

 as show the effect of increased pressure on the electric conductivity of 

 metals. We have at command the data for calculating, in the case 

 of several metals, approximately what the temperature coefficient of 

 the conductivity would be if heating occurred with such increase of 

 pressure as to keep the volume of the metal constant. If we call this 

 coefficient a v , and if we assume that we can find an expression for it 

 by merely dropping from the value of a p the two terms which contain 

 the factor dS-hdT, we have 



o, = ^~+~-F 2 (5)(v-ip-i)T^^. (3a) 



In liquid mercury, according to the experiments of Barus, 8 the value 

 of a v is positive; but in the solid pure metals, so far as I know, it is 

 negative and, though numerically less 9 than a p , not very much less. 

 If, then, equation (3a) is a correct expression for a v , it appears that the 



1 dF i • 

 term j? -^j, is negative, since the second term, as we have seen, is 



probably positive. 



8 Bulletin of the U. S. Geol. Survey, No. 92 (1892), p. 75. 



9 See the Appendix to this paper for discussion of this matter. 



