408 Mr. W. M. Hicks on some Effects of Dissociation 

 sions which impinge with a blow < c 



V m 1 m 2 \ / 



10. The foregoing expression enables us to find the mean 

 blow at any temperature, thus. The number of blows > c is 

 given by an expression of the form Xe -fAe2 ; hence the num- 

 ber of blows between c and c + Be 



= 2\fice-' xc2 Se ; 

 hence the mean blow 



r-2 



2\A c-e-^dc 

 No. of blows >0 



= — - = S x 2 e~ x2 dx = —p= I e~ x ' 2 dx = ^\/- ; 



hence, calling the mean blow 



4fju 4 w 1 + ?n 2 'mi + mj' 



or </ is proportional to the square "root of the temperature. We 

 may therefore express the number of blows > c in the form 



2NN 



\ WlW 2 / 



III. Case o/ a?2 Elementary Gas. 



11. We will now employ the foregoing formula to investi- 

 gate the effect of dissociation on an elementary gas whose 

 molecule is diatomic. We shall suppose the dissociation to 

 occur through a molecule receiving a blow > c ; also that if 

 two atoms come within a mean distance s 2 so that they would 

 impinge with a blow < c, they will combine into a molecule. 

 Let then x = number of molecules in unit of volume, 

 2y — number of free atoms in unit of volume, 

 so that 2(x + ij) = whole number of atoms present =N ; say. 

 Further, let m = mass of an atom ; 



s, s 1? s 2 be the mean effective distances between two mo- 

 lecules, a molecule and an atom, and two atoms. 



Then the number of collisions of molecules with a blow > c 



= 2x 2 s/^rs 2 \/~e~^ re ' 

 V m 



= half the number of molecules destroyed The number of 



