174 
Proceedings of the Royal Society of Edinburgh. [Sess. 
effects to the absolute temperature can only be derived on the assumption 
that is constant or negligibly small. For neither of these assumptions 
is there any sufficient justification. The equation of Kruger leads to no 
better a conclusion when the same process is employed. 
There still remains the possibility of examination of equations (1) or (4) 
by comparison with Avenarius’s empirical law for the thermo-electromotive 
force. This may be attempted in the following wa} r . 
If the conception of electronic-vapour-pressure is to have any physical 
significance whatever, it is certain that that pressure will determine the 
rate of evaporation of electrons out of the metal — i.e. the negative thermionic 
current, — and that, conversely, the vapour-pressure must be a one-valued 
function of the thermionic current. 
If n be the number of electrons leaving the metal per second and per 
;sq. cm. of surface, ne=j gives the saturation current. But if 0 be the 
absolute temperature, m the mass of an electron (molecule of electronic 
vapour), and v the root mean square of all the electronic velocities (in the 
usual significance of the kinetic gas theory), then for the vapour-pressure 
pcc mnv. 
Again, from the kinetic theory, v 2 cc 0, so that, substituting for n 
p=^ e Je, ( 7 ) 
where k is a constant, gives the relation between p and j. 
Thomson, Wilson, and Richardson have, however, arrived at the expres- 
sion * for the thermionic current — 
j = a6 i e~ b ^ i ( 8 ) 
from different theories, a, b being constants, so that we may write for the 
electronic-vapour-pressure 
p = a6e-& e , (9) 
an expression in which a, /3 will vary in general, if at all, only with the 
physical nature of the body from which the emission is taking place. 
For uniform absolute temperature 0, this gives 
a B e-fel 9 
a a e~M e 
log 0 = log 
/?a-/?b 
6 ’ 
* See, for example, J. J. Thomson, Gondn. of Elect, through Gases , § 93 (1903) ; H. A. 
Wilson, Elect. Props, of Flames and Incandescent Solids, p. 14 (1912) ; 0. W. Richardson 
Phil. Trans., cci. 516 (1903), Phys. ZS ., v. 6 (1904). 
