Experiments on Residual Ionization. 



403 



Langevin has carried out four of the remaining integrations 

 in such a way as to obtain the result 



Jim V 2/imJ Jo" 7 *' 



where <r is the radius of the sphere of action of the molecule 

 and 



-vs 



If now we let 6 (fig. 4 U) be the angle between g and the 

 normal to the sphere of action, then v the velocity normal to 

 this sphere is equal to g cos 6 and b = a sin (9. Making these 

 substitutions in the above integral, we obtain for the total 

 number of collisions perc.c. per second for which the relative 

 velocity normal to the sphere of action is less than a certain y, 



d_ 

 3 



Jim V 2hmJ Q \ cos 

 /r»r V -Ik 



ve-% hmv2 dv 





( ;,-!,k»tU-\ 



To obtain the number of collisions per c.c. per second for 

 which the relative velocity tangential to the sphere of 

 collision is greater than a certain u, put it=^sin0, and 

 b = <r sin 6 in the expression for v above. Then the number 

 of such collisions is 



km v 2km \ J sm 



/i 3 m 3 V 2Aw 

 = ?n 2 <7 2 \ / ^Le-V 1 " 1 "-. 



- cos A '"" 2 7/1 

 j^e'^sin-^edO 



2 E 2 



