﻿1046 Prof. Townsend and Mr. Bailey on the 



The increase of X with the electric force when the mean 

 velocity of agitation remains approximately constant at about 

 .20 x 10 7 cm. per sec. is clearly due to a large loss of energy 

 in collisions v\ itb velocities greater than the mean, and a 

 change in the distribution about the mean as Z and W 

 increase. 



As an illustration of what would take place under this 

 condition, it may be supposed that when the velocity of an 

 electron exceeds a value A, its velocity is reduced to B when 

 it collides with a molecule, and while its velocity of agitation 

 is again increased from B to A, under the action of the 

 electric force, the electron makes several collisions with 

 molecules in which there is very little loss of energy. 

 The distance z that the electron travels in the direction of 

 the electric force Z while the velocity of agitation rises from 

 B to A is 0=?n(A 2 -B 2 )/2eZ, and the total number N of 

 collisions with molecules while travelling the distance z is 

 approximately uz/lW. Hence N is inversely proportional 

 to the product ZW. .Each collision in which there is a large 

 loss of energy m(A. 2 — B 2 )/2 is therefore followed by a 

 large number N in which the loss is negligible, so that the 

 average loss is inversely proportional to N and therefore 

 directly proportional to ZW. Thus, although the mean 

 velocity of agitation remains constant, the mean loss of 

 energy in a collision increases with ZW. In this case the 

 velocities of agitation are distributed near the mean value u 

 when Z and W are small, but as Z and W increase, the 

 number of electrons with velocities near the mean diminishes 

 and the number near the limits increases. 



Another example of the effect of a change of distribution 

 of the velocities of agitation about the mean, occurs when 

 electrons move in pure hydrogen and in a mixture of argon 

 and hydrogen. In hydrogen the loss of energy per collision 

 is much greater for the larger velocities of agitation than 

 for the smaller. Thus an effect which increases the number 

 of electrons with velocities near the mean will reduce the 

 average loss of energy per collision. With a constant 

 force Z the velocity W in pure hydrogen is in many cases 

 reduced by about 20 per cent, by adding argon to the 

 hydrogen, while the mean velocity u of agitation remains 

 unchanged. The loss of energy in the collisions with the 

 argon may be neglected, so that in these cases the average 

 loss of energy in collisions with molecules of hydrogen is 

 proportional to ZW when the electrons are moving in pure 

 hydrogen, and to ZW x '8 when the electrons are moving in 

 the mixture, the reduction being due to a change in the 



