PROCEEDINGS 
OF THE 
NATIONAL ACADEMY OF SCIENCES 
Volume 5 JUNE 15. 1919 Number 6 
THE THERMO-ELECTRIC EQUATION P = TdV/dT ONCE MORE 
By Edwin H. Hall 
Jefferson Physical Laboratory, Harvard University 
Communicated, March 27, 1919 
At the Philadelphia meeting of the Academy in November, 1917, I ques- 
tioned the validity of this equation as commonly understood, P being taken 
as the ordinary Peltier effect and V the Volta effect between any two metals. 
But I did not make my point of objection entirely clear and wish now to try 
again; for the matter is important. 
It appears that Kelvin, who derived this equation from a course of theo- 
retical reasoning, did not regard P as necessarily the Peltier effect only, be- 
lieving that it might include some other, hitherto unknown, reversible heat 
effect accompanying movement of electric charge from one metal to another. 
0. W. Richardson, arriving at the same equation by a different course of reason- 
ing, held P to be simply the Peltier effect. My colleague Professor Bridgman, 
repeating with some modifications of his own the argument of Kelvin and 
also that of Richardson, came at first to a conclusion sustaining that of 
Richardson, and submitted his unpublished paper to me for criticism. 
I maintained that Kelvin's broader interpretation of the P was probably 
the correct one and ventured the suggestion that ionization and re-association 
within the metals according to the mass-law of equilibrium between free 
electrons and metal ions, furnished the reversible heat effect, additional to the 
ordinary Peltier effect, that Kelvin saw the need of. Bridgman felt, however, 
that I had not disposed of Richardson's argument, and accordingly I wish 
now to revise, but not to withdraw, my criticism. 
The passage which I quoted from p. 28 of his Emission of Electricity from 
Hot Bodies ended with the equation 
dS = ^[d(nv(f>) +pdv], 
in which dS is change of entropy of the system and "(p is the change in the 
energy of the system which accompanies the transference of each electron 
197 
