Theory of Befract'wn in Gases, 469 



we shall thus be concerned with the mean rotational 

 eneroy ; and this, there is considerable reason to believe, 

 is proportional to the absolute temperature. We have to 

 note, however, that the two particles can remain in the 

 above state only as long as the pressure between the particles 

 does not vanish. As soon as the angular velocity attains the 

 value n given by 



,n„n, ^^^fXl 



J7li + »l2 



the particles must separate. For higher values ol: the 

 rotational energy we shall have elliptic or even hyperbolic 

 or parabolic orbits. 



In the gas a molecule may by collision attain a value of 

 rotational energy which is too great for the particles to 

 remain in contact. We must therefore have a small pro- 

 portion of dissociated molecules on average — small, because 

 o£ the comparatively high values of rotational energy 

 required. 



Further, the period of any elliptic orbits must be longer 



277 . 



than the period ^. The period thus defined is quite 



independent of temperature, and it seems to m©> ought to 

 be identified with a spectral line, there being considerable 

 evidence that luminosity in a gas is always associated with 

 ionization. 



We have now to calculate the efi'ect of electrical waves on 

 the motion of the molecule. 



Let the coordinates of the centre of nii be a^i, i/i, z^ ; 

 and ,j ^, J, iTi^ be x^^ 2/2? ^2 > 



and let r be the distance betw^een their centres. 



Further, let the incident plane waves be represented by 

 Electrical force, X = XoCOS {pt — kz)^ 

 Magnetic force, M = - Xq cos (^9^ — /jj), ^ 



We shall suppose the motion to be only slightly disturbed 

 from what it would be in the absence of weaves. The 

 linear velocities of the c.G. of the molecule are small com- 

 pared with Vq, and r is small compared with the wave- 

 length. Xeglecting squares of these ratios^ the equations 

 of motion are 



