806 Mr. T. Carlton Sutton on the 



between v and (y + 8v), where 8v is small, and k and a are 

 constants to be determined later. 



(2) The same result is given directly in the case of the 

 form 



which is derived in the first place on the assumption that 

 action occurs when the velocity o£ collision lies between the 

 narrow limits v and (v + 8v). This can be written 



v 



where k'8v = k, and gives 



_ a 1 



k e o — T - 8v 



as the chance that a pair of colliding atoms has a relative 

 velocity of approach lying between v and (v + 8v). 



This is the same expression as that derived by Maxwell, 

 Clausius, and others for the " chance that a collision between 

 molecules should have a relative velocity lying between v 

 and (v + 8v)." Hence, results may be deduced from it cor- 

 responding, form by form, to results deduced from Maxwell's 

 expression. 



For instance, the chance that a particular molecule of a 

 homogeneous gas has a velocity of translation less than 

 (y + 8v) and greater than v is proportional to 



2 v2 



ex. 6 



where a is the mean velocity of translation of the molecules. 

 Hence, the chance that a particular atom has a velocity 

 (relative to the molecule as a whole) greater than v and less 

 than (v + 8v) may be written as 



K - \o^) ~ 



1 8v > 



a? 



where K and K7 are independent of a but may depend on v. 

 Again, the value of the chance is independent of the units 

 chosen, i. e. is of zero dimensions, whence K and K/ are 

 seen to be multiples of v 2 , and can be written Kjv 2 and K 2 v 2 , 

 where K x and K 2 are constants of zero dimension. 



