Vol. 7, 1921 
PHYSICS: E. H. HALL 
65 
by means of equation (10), from the values of (kf -f- k) and X, for 0° C, 
given in my already printed paper on the Thomson Effect and Thermal 
Conduction. Comparison of these two columns shows that the calculated 
values are three or four times as great as the observed values, but this 
disparity, before any adjustments have been attempted, is not discouraging. 
Column V gives the observed values for 100° C, while VI gives those 
found by means of equation (10) from the values of (k f -4- k) and X, 
for 100° C, given in the paper just mentioned. Here again the calcu- 
lated values are some-fold larger than the observed values. 
Columns III and VII, which are to be compared with I and V, re- 
spectively, are obtained from columns II and VI, respectively, merely 
by using new values of (kf -r- k) and X, for bismuth, these new values 
serving quite as well as the former ones, on the whole, for the Thomson 
effect and the thermal conductivity of bismuth. 
Columns IV and VIII, which are to be compared with I and V, respec- 
tively, are obtained from III an 1 VII, respectively, by using new values 
of (kf -J- k) and X for each of the other metals than bismuth, due regard 
being paid to the Thomson effect and the thermal conductivity in the se- 
lection of these new values. 
The agreement between columns I and IV is as good as need be. The 
agreement between columns V and VIII is not so good, the values in V 
being in every case the larger, as column IX shows. A new readjustment 
in the case of bismuth, making [(kf -r- &)X]ioo for this metal about 14% 
greater than the last re-adjustment left it, would reduce most of the differ- 
ences shown in column IX to a negligible size. But such a re-adjustment 
cannot be made without introducing disagreements at other points. The 
disparities between columns V and VIII, together with equally serious 
disparities, at 100° C, between thermal conductivities given by my for- 
mulae and those found by other means, must stand for the present. 
A plausible explanation of these discrepancies, where they are not to 
be acounted for by mere imperfection of experimental data, may be found 
in the crudity of my assumption that the number, n, of free electrons per 
cu. cm. of a metal, can be expressed by the formula 
n = zT q 
where z and q are constants. In making this assumption I did not ex- 
pect it to hold for so great a range of temperature as that between 0° 
and 100° C. In fact, I was greatly surprised to find, a year or so ago, 
that I could make the jump from 0° to 100° with any measure of success. 
It is interesting to inquire how the theory of the Peltier effect set forth 
in this paper can deal with Bridgman's observations on the magnitude 
and sign of this effect between compressed and uncompressed pieces of 
the same metal. Testing twenty metals, including two alloys, he measured 
the heat absorbed by unit quantity of ' 'positive electricity in passing from 
uncompressed metal to [the same] metal compressed" or, as I prefer to 
