ME. J. H. JEANS ON THE DISTRIBUTION OF MOLECULAR ENERGY. 
427 
are in contact in any position, their potential has a constant value H. When two 
molecules are not very near, let us suppose that the transfer of energy between 
different r, s modes may be neglected, so that the main transfer of energy takes 
place through collisions.* 
At any collision, the r, s energy of the colliding molecules will be small, so that the 
amount by which the r, s energy is increased will depend only on the u and q 
energies of the colliding molecules; that is to say, on the average, on h. 
Thus if n collisions take place per unit time, the total transfer from the u, q modes 
of energy to any specified r, s mode may be taken to be Cn/h, where C is a constant 
for any particular r, s mode. 
The sum of such amounts must be equal to the amount radiated per unit time, 
and may therefore be supposed to he roughly proportional to the energies of the 
r, s modes. It follows that for a single molecule the r, s energy is proportional 
to n/NA. 
Now we may take for the number of collisions 
- ^/h ’ 
n ANe“^” 
m ~ ’ 
and if p be the density, the radiation will be proportional to e~^^, or, in terms of 
cn 
the temperature, to 
This example is of such a special nature that not much imjDortance can be attached 
to the actual result obtained. It is, however, of interest, as showing that it is at any 
rate possible for the radiation to increase very rapidly with the temperature. A 
comparison with the result of § 9, shows that the introduction of a field offeree has 
introduced a factor e~'r into the expression for the radiation, and a factor of this 
form figures in every formula for radiation, t 
The presence of the factor p multiplying the expression for the radiation, is an 
essential feature of the present theory.]; If the exponential factor changes very 
rapidly with the temperature, so that the point of incandescence is sharply defined, 
then this point will clearly be ahnost independent of p, and variations in radiation on 
* This assumption, although not stated explicitly in the investigation of Part 11., is implied in the 
assumptions made there. 
t Wien and Planck give for the radiation in the part of the spectrum between X and X + SX, the 
formula e~n cl'K. Lord Rayleigh, on theoretical grounds, suggests as an emendation ciTX”^ elk. 
(‘Phil. Mag.,’ June, 1900.) 
\ [Added March 19, 1901.—I was not aware, when writing this, that the presence of the factor p had 
been detected experimentally. See Liveing and Dewar, ‘ Roy. Soc. Proc.,’ 49, p. 217, or Kayser, ‘ Hand- 
buch der Spectroscopic’ (1900), L, p. 143.] 
where A is a constant. 
Hence 
3 I 2 
