Vol. 7, 1921 
PHYSICS: E. H. HALL 
99 
whether it is capable of accounting for the whole or any considerable 
part of thermal conduction in metals. 
At the junction of two metals, on the other hand, the conditions of 
equilibrium permit no cyclic or circulatory motion of the electrons. 
In a later paper 2 I introduced the following assumptions: That n, 
the number of free electrons per cu. cm. of the metal, is expressed by the 
equation 
n = zT Q , (1) 
where T is absolute temperature while z and q are constants. 
That (k f -s- k), the ratio of free-electron conductivity to total conduc- 
tivity, is given by the equation 
(k f -f- k) = C + C x t + C 2 t\ (2) 
where t is temperature on the ordinary centigrade scale and C, Ci, C2, 
are constants. 
That the heat of ionization, in ergs, per electron is 
X' = \;.+ 2.6RT, (3) 
where X/ is a constant 3 and R is the gas-constant for a single molecule. 
In a still later paper 4 1 rejected (3) and put in its place 
X' = X; + sRT, (30 
where 5 is a constant never less than 2.5. This change involved the 
revision of all the tables of numerical values contained in the paper in 
which equation (3) was used. 
Equations (1), (2) and (3') introduced for each metal seven charac- 
teristic constants, z, q, C, Ci, C 2 , \ c and s, but z may for the most part 
be left out of consideration, as the definite numerical value of n is needed 
only incidentally 5 in what follows. 
To determine the six other constants for any metal we need six equa- 
tions. Let us suppose that we know for each metal the value of the 
Thomson effect, <r, the value of the heat conductivity at 0° C, and at 
100° C, 0ioo. 
My expression for a is in the form 
a = K + {K! + K*)T, (4) 
in which K, Ki and K 2 are determined functions of q, C, G, etc. Bridgman's 
experiments give me the values of K, K\ and K 2 , for many metals, and 
so from the Thomson effect I get three equations, which are too long to 
be given here. 
My expression for thermal conductivity is 
0=5(~< + sr)^(s + 9-1.5), (5) 
in which k a , the "associated-electron" conductivity, is (k—kf). With 
the known values of 0 O and 0i O o I get two more equations involving the 
six characteristic quantities to be determined for each metal. 
