Electrons with Molecules of a Gas. 507 



3. When considering the velocities of electrons in air 

 under an electric Force, both the motion of agitation and the 

 motion in the direction of the electric force must he taken 

 into consideration; for even when the forces are sufficiently 

 large to produce appreciable numbers of additional electrons 

 by collisions, the mean velocity of agitation may be greater 

 than the mean velocity in the direction of the electric force. 

 Let W be the mean final velocity of a stream of electrons in 

 the direction of the electric force Z in a gas at pressure p, 

 it the mean final velocity of agitation. The velocities W 

 and a have been found for air over large ranges of forces and 

 pressures, and the values obtained are in good agreement 

 with the general kinetic theory. Thus the quantities W and 

 it have been found to depend on the ratio Z/p, and since u 

 increases with the force the velocity Wis not proportional to 

 the force. The experiments are comparatively simple as they 

 only involve the determination of the distribution of electrons 

 in a stream moving under an electric force, and the deflexion 

 of the stream by a magnetic force of small intensity. If the 

 motion of agitation were in thermal equilibrium with the 

 molecules of the gas the lateral diffusion of the stream of 

 electrons would follow certain simple laws, but in practice 

 the lateral diffusion is found to be abnormally large owing 

 to the increased velocity of agitation, and the factor k by 

 which the energv of agitation exceeds the normal value corre- 

 sponding to thermal equilibrium is easily obtained from the 

 experiments. The normal mean velocity of agitation v of 

 electrons in equilibrium with molecules of a gas at 15° 0. is 

 approximately 1*14 X 10' cm. per second, so that the actmd 

 mean velocity of agitation when the electrons are moving in 

 an electric field is l'14xl0 7 x V h. The following table * 

 gives the values of W X 10~ G and ux 10- 6 /l*14 = 10 Vk for 

 electrons moving in dry air, obtained from experiments in 

 which the forces ranged from 2 to 20 volts per centimetre, 

 and the pressures from "25 to 18 5 millimetres. 



Zip 2 -f> 12 5 10 20 50 100 



YVxiO - ''' -5 9 1*25 1-75 3 5-2 90 173 27 



»X10" 6 16 2-1 Si 47 02 07 75 101 127 



1-14 



- xlO- 17 lo-l 5 8 b-8 54 4-4 39 36 39 38 



calculated. ^ 



* J. S. Townseml & 11. T. Tizard, Proc. Roy. -Sue. lxxxviii. p. 336 

 (1913). 



