I40 
PHYSICS: E. H. HALL 
Proc. N. a. S. 
find that, among eighteen metals examined by Bridgman under high pres- 
sures, thirteen showed plus effects only, none showed minus effects only, 
but five showed mixed effects, minus at 0° C. and plus at 100° C. 
3a. According to the theory under discussion the Thomson effect 
should disappear if {kf -^ ^a) became zero. Accordingly increase of pres- 
sure, causing a decrease of this ratio, should diminish the Thomson effect. 
Among eighteen metals examined by Bridgman under pressure, nine 
showed a decrease throughout the whole range of observation, one showed 
an increase through the whole range of observation, one showed zero 
change everywhere, the other seven showed mixed effects. 
The following may be taken as a summary of the second paper : 
1. Thermal conduction in a metal may be due to the convective action 
of a circulating electric current, free electrons moving down the tempera- 
ture gradient and associated electrons moving up, with ionization at the 
hot end of the metal, involving absorption of heat, and re-association at 
the cold end, involving the emission of heat. 
2. A quantitative test of this thesis, made necessarily with various 
assumptions, indicated ionizing potentials of the same order of magnitude 
as those observed in the ionization of metal vapors ; but it seemed doubtful 
whether values so large as those here indicated are consistent with the 
magnitudes of the Thomson effect. It is to be noted that ionization within 
the solid body of a metal may well require less energy than ionization of 
the vapor. 
It seemed desirable to study the Thomson effect more fully from the 
standpoint of dual electric conduction before proceeding farther with 
the theory of thermal conduction. The results of an examination of the 
Thomson effect are now ready for publication. 
THE THOMSON EFFECT 
In what follows : 
n = the no. of free electrons per cu. cm. of a metal. 
V = the no. of cu. cm. of metal containing 1 gm. of free electrons. 
m = mass of electron, and G = no. of electrons in 1 gm. of electrons. 
Then nv = G = 1 m. (1) 
p = press, of free electrons, in dynes per sq. cm. of cross-section of the: 
metal. 
R = the gas constant for one molecule, or for one electron, = 1.37 X 
Then p = nRT, (2) 
and, for 1 gm. of free electrons, pv = nvRT = RT -r- m. (3) 
P = electro-mag. pot. due to purely electric forces within the metal. 
Pa = electro-mag. pot. due to differential attraction of the unequally 
heated metal for the associated electrons. 
Pf = corres. pot. due to differential attraction of the metal for the free- 
electrons. 
