410 
MR. J. H. JEANS ON THE DISTRIBUTION OF ^FOLECULAR ENERGY. 
Variation of y with Temperature. 
■ff 
§ 15. Thu.s our conclusion is tliat it is not permissible to count the degrees of 
freedom ; they must be weighted as well. We can write 
7=1 + 
3 + Art, 
where o, is the “ weight ” of the sth degree of freedom. So long as —is small, 
we may put «, = 0. AVhen this quantity is very great, either owing to the greatness 
of K or the absence of e„ we put a, = 1. For intermediate values of —^K, rvill 
be a proper fraction, the value of which depends not only on the temperature but 
also on the series of changes through which the gas has passed. 
As a consequence of this, it is clear that y may be expected to vary with the 
temperature, and that it is no loiiger restricted to having one of the values given by 
the formula 1 + 2/72. It would be going too far to expect any agreement with 
experiment at present, since we are considering a, purely arbitrary type of molecule 
such as certainly does not exist in nature. 
Case of a Diatomic Molecule. 
^6. As an illustration of the forenoino- theorv, we mav examine the case of a 
molecule which is composed of two atoms lield together by an attractive force. The 
atoms can execute internal vibrations olviup' rise to the emission of lio-ht : for these 
O O & ’ 
viljratlons we can suppose — ^/K to be very small, so that a = 0. The molecule can 
rotate about its axis of .symmetry, but we can suppose /3 to be zero, so that again 
a = 0. For the rotation about the two remaining axes ^ will be large, so that we 
may take a = 1. We can suppose that the oscillations of the atoms as a whole about 
their position of equilibrium are dissipated by radiation so that a = 0."^ 
This leads us to the value y = If, a value which it is impossible to arrive at by 
means of Boltzmaxn’s theorem when we are considering a molecule which is made up 
of two separable parts, but which is nevertheless known to be the true value for many 
diatomic gases, such as hydrogen, nitrogen, and oxygen. If the present theory in 
* Riidiation of this kind would give rise to definite lines in the spectrum of a frequency which might, 
and probably would, be r^ery different from the frequencies of the light vibrations given out by the 
internal vibrations of the atoms. In this connection it is of interest to remember that experiments with 
Hertzian vibrators have demonstrated the existence, in certain substances, of free periods of which the 
frequency is only about 1/1,000,000th of the frequency of the sodium lines. (P. Drude, ‘ Wied. Ann ,’ 
vol. 58, p. 1; vol. 59, p. 17 ; vol. 61, p. 131.) 
