MR. J. H. JEANS ON THE DISTRIBUTION OF MOLECULAR ENERGY. 
429 
abnormally high values, and this may result in the phenomena of phosphorescence, 
chemi-luminescence, &c. To take a definite instance, sujopose that corresponds to 
a vibration in the molecule of frequency y). If a ray of light passes through the 
substance, those components of this wave of which the frequency is nearly equal to p 
will supply energy to the mode of the molecules, and this energy will be distributed 
from the mode to the other modes, and so through the substance. Thus the result 
is a heating of the substance, and an absorption band in the spectrum of the light 
transmitted through it. The illustration might be varied by supposing that energy 
could not easily distribute itself from to all the other temperatures, but that it 
passed freely to a second temperature Tj. In this case the temperature Tj might 
conceivably attain to such a high value as to emit its own spectrum, and so set up 
fluorescence or calorescence. 
The spectrum of the .gas in any condition whatever will be arrived at by the 
superposition of the various spectra of the subsidiary temperatures, and the state 
of the gas as regards the emission of radiation will be completely specified by the 
values of the various subsidiary temperatures. 
Thermodynamics. 
§ 32. At temperatures at which the gas is dark, we may take 
'^1 = "^2 = • • • — 
Thus at these temperatures we are cftily concerned with the princij)al temperature, 
and the total energy of the gas is proportional to this temperature. If n degrees 
of freedom correspond to this temperature, the ratio of the specific heats will be 
1 + 2/n, 
both specific heats being constant as regards the temperature. The view which we 
have put forward does not clash with the ordinary thermodynamics as regards 
dark gases. 
When the subsidiary temperatures begin to have appreciable values the case is 
different. The total internal energy is now given by 
W = C {nT + S/CiTil, 
where C is a constant, and is the number of modes of energy of which the 
subsidiary temperature is r^. The specific heat at constant volume is given by 
Cl = c^W/cZT = C {n + S/oki//(T)}, 
and therefore depends on both the temperature and density. 
