168 
PHYSICS: E. H. HALL 
From equations (1), (2), (3) and (4) we get 
F = '^^{e^-^^-^^^-l), (5) 
As F is the number of ion heat-paths completed per unit volume per 
second, we assume that the conductivity is, other things being equal, 
proportional to F. Accordingly our question as to the dependence of 
# conductivity on temperature becomes a question as to the dependence 
of F on T. This in turn, since n, c and T are the only variables in the 
value of F, evidently involves the question of the dependence of c and 
n upon T. 
Types of collisions Contribution to 
Before After B P F 
1 1 0 
2 1 1 
1 0 1 
1 0 1 
2 0 2 
7=2 + 5 
FIG. 4 
It is by no means certain that the mean kinetic energy of the free 
electrons is equal to that of gas molecules at the same temperature. 
Thus Jeans^ says, ^'In this case owing to the small mass of the electron, 
the frequencies of the vibrations of the medium ['quasi-gas'] consti- 
tuted by the electrons are very high, so that the old laws of partition of 
energy will not give anything even approaching a good approximation 
to the truth." In a paper published in 1914 I reached the conclusion^ 
that, in a metal represented by a straight line on the thermo-electric 
diagram, the mean velocity of the free electrons may be proportional 
not to T', but to T, at least approximately. 
We shall here use, in turn, the two assumptions: 
c = yT^ (6) and c = yT (6'), y being a constant. 
