the Motion of Electrons in Gases. 889 



1/W is ?(/W, and the number of collisions with molecules is 

 k/IW, so that the average loss of energy of the electron due 

 to a collision is (ZelW)ju. Hence the proportion of the total 

 energy (-mu 2 )/2 which is lost in a collision is 



2Z*ZW v . ■•, , 2 W 2 



— =- , which reduces to A Q1 g x — =- . 



Thus when u is ten times W, between two and three 

 per cent, of the energy of the electron is lost in a collision. 

 It will be noticed that the mean free path I does not enter 

 into the final calculation, so that the result is independent of 

 the linear dimensions which maybe attributed to a molecule. 



The loss of energy of the electron although comparatively 

 small, is very much greater than the loss that would be 

 sustained by a small sphere moving with the velocity u in 

 colliding with a large sphere, if both spheres were perfectly 

 elastic. The energy lost by the electron appears as an 

 increase of the internal energy of the molecule such as a 

 vibration set up in some of the constituent electrons. Were 

 it not for this effect the velocities of agitation u would have 

 attained very much higher values than those observed, and 

 the velocities "W would have been less, since W is inversely 

 proportional to u. 



The effect produced by a small degree of inelasticity in 

 the collisions between spheres has been investigated by 

 Pidduck *. If /= ■£(!+/*), [m being the coefficient of resti- 

 tution as in collisions between inelastic spheres, the formula 

 for the value of/ in terms of k and W which is applied by 

 Pidduck to the case of the motion of electrons may be 

 written in the form 



W^ Jc-1 m 

 • /_i i? + k ' M' 

 where m is ths mass of an electron, and M the mass of a 

 molecule of the gas. 



The values of f for the different velocities of impact u are 

 given in Tables IV., V., VI., and VII. It will be noticed 

 that / decreases as u increases, which indicates that the 

 greater the velocity of impact the larger the proportion of 

 the energy of the electron which is converted into internal 

 molecular energy. 



14. It is of interest to consider the mode in which an 

 electron may lose its energy in colliding with a molecule 

 from the point of view of the quantum theory of radiation. 

 According to this theory a molecule can absorb energy from 



* F. B. Pidduck, Proc. Lond. Math. Soc. vol. xv. pp. 87 -127(1915 L6). 

 Phil. Mag. S. G. Vol. 12. No. 252. Dec. 1921. 3 N 



