402 



Mr. K. H. Kino-d 



on on some 



4 ions per c.c. per second at 17° C, they will produce 2 at 

 130° C, and 6 at' -20° C. It should be noted that the 

 above formula only includes the " negative ,} condition for 

 an ionizing collision, i. e. the normal velocity must be below 

 a certain value. A factor representing the " positive " con- 

 dition should also be introduced, i. e. the tangential velocity 

 must be greater than a certain value. To do this we may 

 proceed as follows : — 



The expression for the total number of collisions per c.c. 

 per second is obtained by Boltzmann as follows. We assume 

 the presence of two kinds of molecules of masses m and m 1 

 respectively; n and n l are the numbers of each kind per c.c,; 

 dco and da>i represent the products of the velocity components 

 for each kind; and/, /i, represent for the two kinds of mole- 

 cules the values of the function 



nj\ 



It 



a collision 



■hmc- 



The conditions of 

 molecule mj can be . 

 b and a defined as follows (fig. 4a): — 



Fia*. 4 a. 



between a molecule in and a 

 characterized bv the two parameters 



Fio\ 4 b. 



M x is the centre of the molecule of mass m { . The molecule 

 of mass m moves with a relative velocity g parallel to MiGr. 

 and the projection of the centre of this molecule on the plane 

 P drawn through M x perpendicular to M X G lies at M. The 

 line MtQ represents the intersection of the ^ planes P 

 and GrM x X. Then MiM = 6, and the angle MMiQ^a. The 

 number of collisions per c.c. per second is then 

 v = f //i gb dco da) 1 db da ; 



or integrating for a from to 27r, 



v= 2 ir f b db j gffi dco dw^ 



