the Molecular Velocities in Gases. 67 



if we put 



4 



Therefore the law of the velocities is 



a! — 



< f ) ( :c )= Y^ e ~ hr2 ' 



The maximum of this expression corresponds to x = h / . It 

 seems as if the velocities for certain groups might become in- 

 definitely great; but this is only apparent. Indeed, let //. be 

 the proportion of the molecules whose velocity exceeds nh! ', 

 n being a number containing several units, we shall have, on 

 changing x into h'y, 



P= \ <t>(z)dx=a'\ fer^dy, 

 or on partial integration 



£ 



*- n 



r x i 



y e-?ydy <| -^ydyi 



consequently 



For n = 10 or x > 8h, about, this view of jjl only commences 

 at the 43rd decimal; and the theory, established for numerous 

 groups, cannot be extended to some singular cases in which 

 only one or two molecules, perhaps, would be concerned. The 

 high velocities can only be brought about by a series of col- 

 lisions favourably arranged by chance. It is quite otherwise 

 with very low velocities, which a single collision can produce. 



The proportion p! of the velocities below a certain value of 



C x . x 



x is fi'= \ cj)(x)dx; and if jy is small, the exponential can be 



Jo _ . . 



replaced by unity, which gives 





«. 



For example, the proportion of the velocities below 



about 0-00075. 



10 



