Voiv. 6, 1920 
PHYSICS: E. H. HALL 
141 
= part of specific electric conductivity due to associated electrons. 
kf = part of specific electric conductivity due to free electrons. 
k = ka + kf = total electric conductivity. 
e = the electron charge in electro-mag. measure = 1.6 X 10 
X = the latent heat of ionization per (1 e) electrons, in ergs. 
X' = the latent heat of ionization per electron, in ergs. 
Hypothesis (A) is, that the mere mechanical tendency of the free elec- 
trons is toward uniformity of pressure throughout the unequally heated 
metal. 
Hypothesis (B), alternative with (A), is that the mechanical tendency 
of the free electrons is toward the state of equilibrium produced by thermal 
effusion ; that is, 
^ ^ = constant. (4) 
Let C of figure (1) be the cold end and H the hot end of a metal bar 
forming part of a circuit in which an electric current is maintained by 
thermo-electric action, the resistance of some part of the circuit being so 
great that the conditions existing in CH are very little different from 
those of equilibrium. In this case the Joule heat generated in CH can 
be neglected in comparison with the Thomson heat there generated or 
absorbed. 
Contrary to custom, the direction of the stream of electrons through^the 
metal will, in this paper, be taken as the direction of the current, and 
accordingly a, the Thomson heat at any temperature T, will be defined 
as the heat absorbed by the electromagnetic unit quantity of electricity, 
(1 ^) electrons, in going through the metal from a place of temperature 
(r — 0.5) degree to a place of (T + 0.5) degree. This definition will 
make a negative for copper and positive for iron. The value of a will be 
expressed in ergs. 
C 
dT 
Fig. 1 
When the unit quantity of electricity, (1 -^ ^) electrons, {m ^) gm., 
goes through the slice dl of the bar CH, from the isothermal surface T 
to the isothermal surface T -\- dT, the fraction {kf k) of it consists 
of free electrons and the part {ka -^ k) of associated electrons. We have 
now to take note of the changes of energy, of various kinds, undergone 
by these two parts of the current. We shall list the various forms of energy 
here considered under five general heads: (1) bulk potential energy, or 
pv potential energy, to which the free electrons only are subject; (2) 
kinetic energy of the electrons, which we shall regard as negligible in the 
associated electrons and equal to that of monatomic gas molecules in the 
free electrons; (3) electric-charge potential energy, the P energy, to which 
both the free and associated electrons are alike subject; (4) the Pf potential 
