Mechanism of Molecular Action. 



The expression therefore becomes 



Sv. 



It follows that 



—3~e dv 



807 



is the chance that the velocity lies between (4- oo ) and (•— oo ),. 

 and necessarily has the value unity. On integration this 

 gives 



2 a? V K 2 3 ' 



The average velocity of the atoms, r, (relative in each 

 case to the velocity of the corresponding molecule as a 

 whole) is given by 



m 



9 r jit 



Jo a ° 



dv=v, 



i. e. Kx=K 2 2 . 



a. 



Whence T ^ 16 a. 



K 1= 



?' 



and 



K 2 = n? 



K x and K 2 have been shown to be constants of zero dimen- 

 sion ; hence v is seen to be proportional to a, i. e. to the 

 square root of the absolute temperature. 



Substituting these values of K x and K 2 , it is found that: — 

 The chance that the velocity of an atom in a molecule 

 (relative to the velocity of the molecule as a whole) is greater 

 than v and less than (v + $c) is 



IF ? e 8v > 



where v, the average velocity of such atoms, is propor- 

 tional to the square root of the absolute temperature. 



