Prof. Thomson, On the theory of the motion, etc. 375 



On the theory of the motion of charged Ions through a Gas. 

 By Sir J. J. Thomson, Cavendish Professor of Experimental 

 Physics. 



[Head 8 November 1909.] 



In the usual method of calculating the velocity of a charged 



ion through a gas, the expression for the velocity is obtained 



on the assumption that the ion after each encounter with a 

 molecule of the gas starts afresh and is as likely to move in any 

 one direction as the opposite. The momentum communicated to 

 the ion by the electric field in the interval before a collision 

 is assumed to be transferred to the molecule of the gas during 

 that collision, from which it follows that the maximum velocity 

 communicated to an ion by the electric field is that imparted 

 to it in the short interval between two collisions. It seems clear 

 however that the time during which the velocity is acquired 

 by the ion is the average time during which the ion continues 

 to move in one direction and not the time between two collisions, 

 and the time taken for an ion to have its motion reversed by its 

 collision with the other molecules may be much greater than the 

 time between two collisions. This will certainly be the case if 

 the mass of the ion is considerably greater than that of the 

 molecules against which it strikes. For let us suppose that the 

 average kinetic energy of the ion is equal to that of the molecules. 

 Let m be the mass of the ion, u its velocity, M and v the corre- 

 sponding quantities for the molecules, then since 



mu- = M'o^, 



'm 



__v _ li 



I TTl 



thus the momentum of the ion will be / -rv times the momentum 



of the molecule against which it strikes and so the ion will have 



1 / in 

 to collide with at least -^ . ^r molecules before its motion is re- 

 ^\J M 



versed. From this it would appear that the quantity \ which 



appears in the expression for the mobility of the ion should be, 



not the ordinary free path, which depends only on the size of the 



ions and molecules and not upon their masses, but that free path 



I fVYL 



multiplied by some fraction of / -^ ; if we call Xo the ordinary 



free path, the expression for the mobility would be 



e \o Im 

 ^ mu s/ M' 

 where p is o. numerical coefficient which we have not determined. 



