Tlwory of Refraction in Gases. 471 



= const+ I ('Xq{- 1 )co^pf§dt 



= ir'^\ say, 



^vllere -^ and 6 are the angular coordinates. 

 In the undisturbed motion we have 



^=ucos{a)t — e^), 7] = ff eon {cot — €2) , ^=y cos {cot — e^), 



where 



f + V- + ^' = const. = co'~r- = 7^2(^2 _^ sin^df^) ; ' 



and hence, neglecting squares o£ Xq, we get 



ir^i^ + sin^^4,^) + eXjL+^)l4^ + 'tt^\ =const. = B 



\mi 7712/ L-f^—jr p'^-^'y^r^ J 



in the disturbed motion. 



In the undisturbed motion the usual Boltzmann-Maxwell 

 law o£ the distribution of velocities gives us 



e w"* CO dco, 



where co' is the mean value o£ co'. 



Xow in the disturbed motion E is independent of time ; 

 so that with the same restrictions as in the ordinary Boltz- 

 mann-Maxwell law we have 



—1 J .-o '"'^'[m.'^mj / pk sin pt ^Hcospt ), [ 



as a permanent distribution -law independent of time. 

 Although t is involved explicitly, -y-=0. 

 Neglecting squares of Xq, we may write this 



This law leadsj as we might expect, to periodic orientation 

 of the axes of the molecules. It appears to me that the 

 validity is not affected by the rapidity of the waves. The 

 above distribution having once obtained, continues to re- 

 present the distribution, since E is constant throughout the 



