312 
PHYSICS: E. H. HALL 
Proc. N. a. S. 
20. Evidently it is possible, by taking for each metal an arbitrary 
value of X, to make the ratio of at 0° C. to ka at 100° C. agree with the 
observed ratio of total conductivity at 0° C. to total conductivity at 100° C, 
but this would be a rather fantastic performance. Attempts to account 
exactly, at present, by means of the theory of conduction presented in 
this paper, for the details of observed fact in the relationship of conduc- 
tivity to temperature would be the opposite of convincing. The value 
1.6 for % serves very well for many metals. 
21. I cannot in this paper reproduce the discussion by which I have 
sought to test the quantitative adequacy of the theory here presented. 
This discussion involves necessarily considerable additional conjecture and 
is not yet to be regarded as conclusive, b^t it is distinctly encouraging, 
provided it is allowable to use for certain factors values of an order of mag- 
nitude indicated below : 
Moment of inertia of an atom, 10"^^ gm., cm.,^ 
Time of orientation process, 5000 times the period of "characteristic" 
heat vibrations. 
Life-time of an ion, at 0° C, twice the orientation time. 
n, the number of free electrons or of ions, per cu. cm., in general accord with 
the data given in my Summary,"^ though I am now inclined to take, at 
0° C, the mean path of a "free electron" within a metal as perhaps fifty 
times the centre to centre distance of the atoms, instead of ten times, and 
so get a correspondingly smaller number for n, one of the quantities vary- 
ing inversely as the other. 
Under these conditions the mean kinetic energy of rotary motion of an 
atom (see (5)) comes out about 10 ~^ times the energy of translatory 
vibration. 
Behavior of the Free Electrons in Conduction 
22. According to the data given in any Summary, free-electron conduc- 
tivity bears to total conductivity about the same ratio at 100° C. as at 0° C, 
that is, in most metals the free-electron conductivity, kf, is roughly in- 
versely proportional to the absolute temperature. 
23. Various writers give us the formula 
■ n\ ce"^ 
kf = , 
^ kRT 
though they may differ in the value assigned to the constant k. If we take 
as approximately true, the proposition that kfT is a constant, we have 
