A.—MATHEMATICS AND PHYSICS. 31 
Admitting that the intrinsic potentials exist, a straightforward 
~ ealculation shows that they are intimately connected with the magni- 
- tudes of the thermionic emission at a given temperature. The relation 
is, in fact, governed by the following equation: If A and B denote 
the saturation thermionic currents per unit area of the bodies A and 
B respectively, and V is the contact potential difference between them 
kT A 
at the absolute temperature T, then Norrie log B where & is the 
gas constant calculated for a single molecule (Boltzmann’s constant), 
and e is the electronic charge. 
I have recently, with the help of Mr. F. 8. Robertson, obtained 
a good deal of new information on this question from the experimental 
side. We have made measurements of the contact potential difference 
between heated filaments and a surrounding metallic cylinder, both 
under the high-vacuum and gas-free conditions which are now attain- 
able in such apparatus, and also when small known pressures of pure 
hydrogen are present. As is well known, both contact potentials and 
thermionic emission are very susceptible to minute traces of gas, but 
we find that under the best conditions as to freedom from gas there 
is a contact potential of the order of one volt between a pure tungsten 
filament and a thoriated filament. We also find that changes of a 
similar magnitude in the contact potential difference between a thoriated 
tungsten filament and a copper anode take place when the filament is 
heated. These changes are accompanied by simultaneous changes in 
the thermionic currents from the filament; and we find that the change 
in the contact potential calculated from change in the currents with the 
help of the foregoing equation is within about 20 per cent. of the 
measured value. Considering the experimental difficulties, this is a 
yery substantial agreement. Whilst the evidence is not yet as complete 
as I hope to make it, it goes a long way towards disproving the chemical 
view of the origin of contact potential difference. 
From what has been said you will realise that the connection between 
eontact potentials and thermionic emissions is a very close one. I 
would, however, like to spend a moment in developing it from another 
angle. To account for the facts of thermionic emission it is necessary 
to assume that the potential energy of an electron in the space just 
outside the emitter is greater than that inside by a definite amount, 
which we may call w. The existence of this w, which measures the 
work done when an electron escapes from the emitter, is required by 
the electron-atomic structure of matter and of electricity. Its value 
ean be deduced from the temperature variation of thermionic emission, 
and, more directly, from the latent heats absorbed or generated when 
electrons flow out of or into matter. These three methods give values 
of w which, allowing for the somewhat considerable experimental 
difficulties, are in fair agreement for any particular emitter. The data 
also show that in general different substances have different values of 
w. This being so, it is clear that when uncharged bodies are placed 
in contact the potential energies of the electrons in one will in general 
be different from those of the electrons in the other. If, as in the 
ease of the metals, the electrons are able to move freely they will 
