EMISSION OF ELECTRONS FROM HOT BODIES 39
in which

M is the molecular weight of the gas, h is Planck's constant,
N is the number of molecules in one gram molecule of a gas
(Avogadro's number), v± and vz are the volumes which would
be occupied by one gram molecule of the gas under the con-
centration which it has at the points I and 2 respectively.
The respective numbers of molecules per c.c. at these points
therefore are

n, = / and n9 =

It is clear that the right-hand side of (23) when considered
as a function of T, n^ and n% will in general be quite compli-
cated. It simplifies very considerably, however, when the
quantities ^ and ;r2 are either both very small or both very
large, or when one of them is very small and the other very
large. It will be seen from (24) and (25) that when C is small
x is large, and vice versa, and that the value of x is completely
determined by that of C. The quantities N, £, and h entering
into C are universal constants; so that the value of C is de-
termined by that of the product MTzA It is evidently greater
the greater the molecular weight of the gas, the higher the
temperature and the lower the concentration. We infer from
this that the behaviour of (23) appropriate to small values of
C will at a given temperature occur at much smaller concentra-
tions for an atmosphere of electrons than for an atmosphere of
an ordinary gas, on account of the smallness of the mass of
an electron compared with that of an atom.

When CL and C2 are both large, and hence ^ and #2 are
both small, (23) reduces, after making use of (24) and (25), to

Wl - w, - £T log ^ -'AT log -2 . . (26)

^2 nl

This agrees with (22), since w% - wx is equal to $ for this case.
Thus (22) is seen to be a limit approached by (2.3) for highity Lectures," p. 29 (New York, 1913). way of escape from most, if not all, of