set up in Molecules hy ColUsions. 285 



fraction of a second, but the figures we have obtained show 

 that under the actual conditions it is quite possible for the 

 energy to remain appreciably constant throughout unthinkable 



age: 



§ 10. We now discuss the vil)ratious set up in A by the 

 rotation and small vibrations of molecule B. If the molecule 

 is rotating with angular velocity (», and vibrating with fre- 

 quency q, there will be terms in the force exerted by this 

 molecule of frequencies ^ 



«^j '2, ']±'''^' ? + ^<^ (IS) 



Any one of these frequencies, say y./, will give rise to a 

 term in Y (equation 8) of the form 



Yo cos/»7 + Wq i'mp'f, 



where Yq, Wq vary with the time as slowly as did the 

 former Y. The corresponding part of X + iY may, from 

 equation (8), be written in the form 



Each term can be treated in the same manner as before, 

 and can be shown to be small, except when p is very nearly 

 equal to p' ; i. e. when p is very nearly equal to one of the 

 values given in (18) . 



Now CO varies from molecule to molecule, the most pro- 

 bable value being of the order of 10^^ f- It therefore appears 

 that p — (o,p + q — co, kc. will be very small only for a very 

 small fraction of the molecules, and obviously even when 

 this is so, the vibration set up will be very small. Thus 

 perceptible vibrations in A will in general only be excited 

 by vibrations of the same period in B, /. e. when 2J = q. Phy- 

 sically speaking the mechanism of the transfer of energy is 

 found in the "absorption"''' of light-waves. It seems un- 

 necessary to bring forward calculations to show that this is 

 small. 



§ 11. If E is the mean-energy of translation of the mole- 

 cules of a gas, F that of a single vibration, the equation 

 expressing the rate of change in F is 



^=_eF + (i)(E)F+ rXE), . . . (19) 

 at 



^-here — eF represents dissipation into the^ cether, <^(E)F 

 represents the amount regained by "absorption/' and /(E) 

 is the o-ain to F through collisions, which we have been 



* " The Mechanism of Radiation," Phil. Mag. 'Qj ii. p. 24:2. 

 t L. c. p. 424. 



