268 Mr. W. T. David on Thermal 



during r is 



SV=T[>(E)-£(V)]<fc, 



and the average value of V over a time r is roughly 



Y=V 1+ SV/2, 



where V L is the vibratory energy possessed by the molecule 

 as it enters on its free-path, that is, immediately at the end 

 of collision. If the transference of energy daring collision 

 is exceedingly rapid (as it probably is in the case of the low- 

 frequency vibrations of carbonic acid gas and steam mole- 

 cules*) Vi will approach the value V . But if the rate of 

 transfer of energy is not sufficiently rapid to reduce V to V 

 at the end of a single collision, it will be obvious that the 

 greater the departure of V from V before collision the greater 

 will be the departure of Vj from V after collision. In 

 either case V will be appreciably different from Y (which 

 is proportional to the absolute temperature of the gas) if the 

 gain of vibratory energy, BY, during the free-path is 

 appreciable. 



From this theory it appears that at any given gas tempe- 

 rature the greater the gain of vibratory energy during the 

 ■free-path the greater will be the average vibratory energy of 

 the molecules, and therefore of the radiating power of the 

 gas ; and that, other things being the same, 



(i.) the greater the density of radiation energy in the 

 aether (which depends among other things upon the 

 transparency and volume — or virtual volume — of 

 the gas) the greater will be the radiating power of 

 the gas ; 

 and (ii.) the smaller the time of description of free-path 

 (or, in other words, the greater the density of the 

 gas) the nearer will the average vibratory energy of 

 the molecules approach a value which is proportional 

 to the absolute temperature of the gas. In a very 

 dense gas, therefore, as in the case of solids and 

 liquids, the radiation would depend on the tempe- 

 rature alone. 

 The radiating power of a gas which emits thermal radiation 

 thus appears to be a function of the absolute temperature of 

 the gas, the value of the density of radiation energy in the 

 aether, the rate at which the molecules emit radiation, the 

 time of description of free-path (inversely as the density 

 of the gas), and the rate of partitioning of energy during 



collisions. 



* Phil. Trans. A. vol. ccxi. (1911), footnote p. 409. 



