106 
PHYSICS: E. H. HALL 
Proc. N. A. S. 
Evidently any number given in column VI should be smaller than the 
corresponding number given in column VII; and this is the case; but, 
for aluminium, copper, gold, and magnesium the ratio approaches one- 
half, and for silver it is greater than one-half. This is a larger value of 
the ratio than seems probable; that is, one might expect for these metals, 
if the values of column VI are true, greater departures from the law of 
Dulong and Petit than they really show. It is to be remembered, how- 
ever, that the values of 7, upon which the numbers given in column VI 
depend, are based on the assumption that the mean free path of the free 
electrons within a metal is in all cases ten times the centre to centre dis- 
tance of adjacent atoms. If we assume longer paths, we get correspond- 
ingly smaller values in columns I and VI . According to Compton and Ross 1 1 
a photo-electrically excited electron can move in gold about twenty times 
the centre to centre distance of the atoms. 
In view of the fact that the known specific heats of metals are in some 
cases smaller and in some cases larger than the law of Dulong and Petit 
requires, one may allow himself considerable latitude in dealing with the 
distribution of heat energy among the various degrees of freedom of the 
atoms. It is perhaps worth while to note that the numbers given in 
column VI would be larger if calculated for a temperature above 0° C, 
as this fact suggests at least an explanation of the general increase in the 
specific heats of metals with rise of temperature. More exact knowledge 
than we now have concerning the rate of this increase is greatly to be de- 
sired. 
Doubtless my theory of heat conduction will be criticized as failing to 
deal in any general way with the Wiedemann-Franz law. This law is by 
no means exact. According to Jager and Diesselhorst the ratio (0 k) 
varies, at 18°C, from 6.36 X 10 10 in aluminium to 9.64 X 10 10 in bismuth, 
while the temperature coefficient of this ratio varies from 0.15% in bismuth 
to 0.46% in platinum and palladium. In dealing theoretically with the 
relations of thermal to electrical conductivity we may proceed in either 
of two ways. We may seek for such a mechanism of conduction and such 
a general formula as will give the W.-F. law and then undertake to show 
why the individual metals depart from it, or we may proceed at first without 
any regard to this law but finally treat each metal in such a way as to 
explain its more or less approximate conformity with the law. The latter 
is the method I have followed. 
I do not claim complete success in this undertaking. Some 01 the 
expedients I have adopted — for example, the values of 5 which I have 
assumed — are open to doubt. It may be that the mechanism which I 
have imagined and described, convection of heat by means of a circulatory 
electric current, can account for only a part, perhaps a small part, of the 
