EXPLOSIONS OF COAL-GAS AND AIR. 409 



single wave-length of 3'Gyu ; this at high temperatures (1800 C. abs. to 2400 C. abs.) 

 varies approximately as the square of the absolute temperatxire. 



These experiments suggest among other things that the radiation from thicknesses 

 of gas containing the same number of radiating molecules does not depend solely on the 

 temperature of the gas, even after correcting the observed values of the radiation for 

 absorption (see, e.y., Tables XVI. and XXI.). The following theoretical explanation 

 of this is suggested. A molecule as it describes its free path loses energy owing to 

 the emission of radiation and gains energy owing to the absorption of energy from 

 the ether, and the vibratory energy of the molecule will increase or decrease according 

 as the absorption is greater or less than the emission. During collision with another 

 molecule there will be a transference of energy between the vibratory energy and the 

 rotational and translational energies, which, as Mr. JEANS has shown, will be very 

 rapid if the duration of collision* is comparable with the periods of vibration of the 

 molecule. In the case of CO and steam at high temperatures the duration of 

 collision between the molecules is probably short in comparison with the periods of 

 their low frequency vibrations,* and the vibratory energy of the molecules will 

 therefore tend to take up during collision a value such that the energy in each of the 

 vibratory degrees of freedom equals that in each of the rotational and translational 

 degrees. During collision therefore the vibratory energy of the molecules will tend 

 to take up a value which is proportional to the absolute temperature, but during the 

 free-path there may be considerable departure from this value if the energy density 

 in the ether is above or below a certain value and the time of description of free-path 

 is not very short. From this theory it appears that at any given temperature the 

 greater the gain of vibratory energy during the free-path the greater will be the 



average vibratory energy of the molecule ; and that, other flung* being the same, 







* According to JEANS ("Dynamical Theory of "Gases," Camb. Univ. Press, 1904, Chap. IX.), transfer 

 of energy from the translational to the vibrational degrees of freedom, and riff rerxA, can go on at an 

 appreciable rate only when the duration of collisions between the molecules is comparable with the periods 

 of vibration of the molecule. It appears from experiment that the degrees of freedom possessing high- 

 frequency vibrations (which absorption spectra show to be very numerous) are not excited during 

 molecular collisions (at any rate at temperatures which can be commanded in the laboratory), presumably 

 because the duration of collision is not short enough. But in the case of COj we know from PASCHEN'.S 

 experiments on the emission of infra-red radiation from the heated gas that at 150 C. the transfer of 

 energy from the translational to those vibrational degrees of freedom possessing frequencies corresponding 

 to radiation of wave-length 2'8/i and 4 - 4/i goes on sufficiently rapidly to compensate for the loss of 

 energy by radiation. The duration of collision is dependent on the velocity with which the molecules 

 approach each other ; the higher the velocity the less time they remain in contact on collision. The mean 

 velocity is approximately proportional to the square root of the absolute temperature, and if at 150 C. 

 the duration of collision is short enough to excite the vibrations (infra-red, 2'8/i, 4'4/x, and 14- 1/x) in CO. 

 molecules, certainly at the high temperatures reached in explosions the duration of collisions will be short 

 enough to allow transfer of energy between the vibrational and translational to go on with extreme 

 rapidity. The same thing applies to the steam molecules, for they also emit infra-red radiation at quite 

 moderate temperatures. 



VOL. CCXI. A. 3 G 



