472 Mr. G. W. Walker on the 



free path of a molecule ; and, as can be proved, the multiple 

 product o£ the differentials of coordinates and velocities is 

 also constant. The only point which we must take account 

 o£ is that the time over which we observe the effects produced 

 should be large compared with the time it takes for a 

 disturbance from this state to subside. 



We have now to find the sum of ^ for all the molecules. 



;i/2 r^eXA 1 ) -o . .^ 



^ ^ L T^(0^ J92_^2 J 



since the sum of the other terms vanishes on summation for 

 all the molecules. 



x^lso ... 



Hence, neglecting squares of Xo, we find that 



1 6 ^' d-^^ 



We are at liberty to integrate from up to the critical 

 value 12 at which the molecule splits up. 

 We have 



XT i^' • 



JNow --7^ IS a comparatively large number, and hence 



€ ^' is practically zero, co^ is thus the mean value of (o^, 

 and is proportional to the absolute temperature. 

 Hence we get 



t^ = Xop ,mpt ^^-^^ V-- 



(l-e i^') 



We are now in a position to calculate the contribution to 

 refraction. 



I 



