1912-13.] On the Electron Theory of Thermo-electricity. 169 
XVI. — On the Electron Theory of Thermo-electricity. By John 
M‘Whan, M.A., Ph.D., Assistant to the Professor of Mathematics 
in the University of Glasgow. Communicated by Professor 
A. Gray, F.R.S. 
(MS. received January 8, 1913. Read February 3, 1913.) 
The rdle played by the “ free ” (negative) electrons in metallic conductors 
as carriers of the electric current has formed the basis of theories developed 
by H. A. Lorentz,* * * § Sir J. J. Thomson,]- E. BieckeJ and others, regarding 
the thermo-electromotive force. In these theories the free electrons are 
considered collectively as an ideal gas permeating the metal and subject to 
the usual gas laws. The kinetic theory of gases is then applied to the 
problem of the motion of the atoms of the electronic “ gas/’ and expressions 
for the thermo-E.M.F. — differing in the various instances by a constant 
multiplier only — are deduced. The formulae so derived are not open to 
test as against experimental result, containing as they do the ratio of the 
electronic densities in the two metals forming the couple : they have been 
shown, in addition, to be inconsistent with some of the known facts. 
A new method of attack has been originated by Kruger, § and, inde- 
pendently, by Baedeker, || which admits of the application of thermodynamic 
processes in the electron theory. This method is based upon the researches 
of 0. W. Richardson into the emission of electrons from incandescent 
bodies, and it is the object of the present paper, starting from this point, 
to derive an expression for the thermo-E.M.F. differing in important respects 
from those found by Kruger and Baedeker, and probably approximating 
more nearly to the actual physical processes at a thermo-junction. It 
should, however, at once be stated that — as will be seen later — even this 
expression cannot pretend to account for all the known facts. 
The preliminary argument may be briefly summarised thus : — In- 
candescent bodies have been found — speaking generally — to emit negative 
electrons with great readiness, the saturation current of emission of electrons 
* Lorentz, Proc. Amsterdam , vii. 585 (1905), vii. 684 (1905) ; Arch. NSerl. (2) xx. 
336 (1905). 
t Thomson, Corpuscular Theory of Matter, p. 73. 
J Riecke, Wied. Ann., lxvi. 353, 545, and 1199 (1898) ; Ann. d. Phys. (4) ii. 835 (1900). 
§ Kruger, Phys. ZS., xi. 800 (1910). 
|| Baedeker, Phys. ZS., xi. 809 (1910) ; Elektrische Erscheinungen in metallischen 
Leitern, p. 91. 
