Mr. J. J. E. Durack on Lenard Rays. 43 



When an ion approaches the molecule there will be an 

 attraction between them owing to the induced charge on the 

 molecule. If the mass o£ the ion is small compared with that 

 of the molecule the force will be directed to the centre of the 

 molecule, and at a distance r is equal to 



F= 



2,,3 



e\i 



2r 2 -a 2 



{r 2 -ci 2 y 



where a is the radius of the molecule, and e is the charge on 

 the ion. The potential at the point r is therefore 



S T J!f-a?_ 



2r 2 (r 2 -a 2 )' 



Let an ion be projected from an infinite distance with 

 a velocity which is large in comparison with the velocity of 

 translation of the molecules ; let p be the perpendicular 

 from the centre of the molecule to the direction of the 

 initial velocity. 



Let r = the length of the apse, 

 ?/= the velocity at the apse. 



Then : „ , ro e 2 a* 



2 ~ 2 2f*(i*-o*)' 



where m is the mass of the ion. 

 Also vp — v'r ; 



hence , 2 , v 2 p 2 e 2 a 3 



m 



2 r* 2r 2 (r 2 -a 2 ) 



or o o . e*a 3 1 



mv' 



p 2 = r 2 + 



Let pi be the value of p for which a collision just occurs, 

 i. e. when p = Pi the ion is drawn inside the sphere of action 

 by the attracting forces. Also let r x be the radius of the sphere 

 of action, N the number of molecules in 1 c.c. of the gas. 



We have the mean free path of the ion 



11 v 2 



but 9 9 , <? 2 a 3 1 



•* ' r ; 2 -a 2 



