166 
PHYSICS: E. H. HALL 
tain a current of 1000 amperes per square centimeter through copper 
will decide for or against the transition of an electron in one out of every 
10,000 atom-ion colHsions. 
With this revision of our conditions we find that the number of ions 
required to maintain a current of 1000 amperes per square centimeter 
is about 1 for every 170 atoms. This degree of ionization, at medium 
temperatures, does not seem improbable. At least, it cannot be ob- 
jected to on the ground that it would make the specific heat of the metal 
too large. 
2. Ohm^s Law. — The mere fact that so small a portion of all the atom- 
ion collisions need be decisively affected by the potential gradient in 
order to maintain large currents raises a very strong presumption in 
favor of the proposition that the number of cases so affected will be pro- 
portional to the steepness of this potential gradient. Wherever we find 
an effect which begins with the beginning of a certain kind of stress 
and is tested through only a small part of its possible range, the mag- 
nitude of the effect in question is found to be proportional to the mag- 
nitude of the producing stress. 
3. The Temperature Relation. — The theory of conduction which. we 
are considering does not, at present, seem capable of giving a satisfac- 
tory account of the relation between conductivity and temperature. 
It would make the conductivity increase, remain constant, or decrease, 
according to circumstances, with rise of temperature. But, even so, 
it is worth examining somewhat further; for in some fashion it may at 
least supplement whatever main theory of conduction shall be found 
to hold. 
In the following discussion certain assumptions are introduced which 
might require modification upon further study: 
A free electron striking an atom is supposed to rebound or to enter 
the atom driving out another electron. 
A free electron striking an ion is supposed always to unite with it 
to make an atom. 
A, the total increase of distance from centre to centre of neighboring 
atoms during the rise of temperature from absolute zero to T, is sup- 
posed to be proportional to T. 
L, the mean free path of a free electron between collisions, is sup- 
posed to be proportional to A and so to T. 
If c is the mean velocity of the free electrons, the mean time between 
collisions of an electron is proportional to T -^ c. 
Let n = the number of free electrons, or the number of ions, per unit 
volume of the metal. 
