326 Sir J. J. Thomson on the Mobility of 



Variation of Q with the pressure. — Since & l5 k 2 , and X are 

 all inversely proportional to the pressure p, Q will be of the 

 form €~PP(P—y) m Q will therefore be very small until p 

 diminishes so as to be comparable with j3~* . At this stage it 

 will rapidly increase as the pressure diminishes, and there 

 will be be an appreciable number of ions crossing with a 

 mobility greater than k 2 , and thus possessing an abnormally 

 large mobility. Since j3 is proportional to d/X, the ab- 

 normality will set in at higher and higher pressures, as d is 

 diminished and X increased. The apparent mobility will 

 thus depend on the electric force, and also it will no longer 

 be inversely proportional to the pressure. ^ d 



Considered as a function of d. Q varies as e n H k i~K) and 

 thus diminishes exponentially with d. Since V" varies as 



6h where 6 is the absolute temperature, Q will vary as e~* ' n * 

 It is probable that the electron would more readily escape 

 from a molecule against which it struck when its kinetic 

 energy is large than when it is small, so that we should 

 expect n to depend upon 6 ; n and 6 increasing together. 



It will be seen from the preceding results that the mobility 

 of a negative particle, as measured by its average velocity 

 over a given distance when acted on by unit electric force, 

 is not a definite quantity ; some particles have one mobility, 

 others another, and particles can be found possessing any 

 given mobility, provided this is between /q and k 2 . When, 

 however, the conditions are such that dY/nXk^K is large, as 

 it will be unless the pressure is so low that n\ is com- 

 parable with d, the number of particles having mobilities 

 appreciably greater than k 2 is exceedingly small, so that in 

 this case the mobility of the negative particle is substantially 

 definite. 



The number of ions which have a mobility greater than 

 some given value K can easily be calculated as follows. If 

 the electron travels a distance at least equal to x before 

 uniting with a molecule to form a negative ion, the time 

 taken to traverse the distance d will not be greater than 



x d — x 



+ 



&jX k 2 X. 



The average speed will therefore not be less than 



^X 

 x/ki + (d— x)/k 2 ' 

 so that K the mobility will not be less than 



d 

 x/k 1 4-(d — x)/k 2 ' 



