Delta Rays from Gases. 85 



The total number o£ such rays produced is, o£ course, again n. 

 If f (V) is the fraction of these rays so emitted from the 

 molecules that they cannot reach the negative electrode when 

 the difference of potential between that electrode and the 

 place where they are produced is V, then it is easy to show 

 that this part of the current is 



v J 



,)dY. 



v J 



Hence we shall have 



//«=N/(V ) + »(l-2 M /V )+|^/'(V)rfV. . . . . (1) 



3. Now let us consider how this equation will be modified 

 when the pressure of the gas is not so low that the effects of 

 collisions between electrons and molecules are wholly negligible. 

 Valuable information as to the results of such collisions is pro- 

 vided by the recent work of Franck and Hertz *. They show 

 that, when the gas is hydrogen or helium, the number of colli- 

 sions made by an electron in travelling through the gas can be 

 determined from the mean free path of an electron calculated 

 from the data of the dynamical theory of gases ; and also 

 that, as a result of the collision, the electron is usually 

 reflected with a very small loss of energy. Their experi- 

 ments have not yet been extended to gases, such as oxygen, 

 which possess a marked " affinity for electrons/' but they 

 think it probable that the number of collisions in this case is 

 again calculable from the gas theory free path, while the 

 electron is not reflected but adheres to the molecule with 

 which it collides. 



When an electron adheres to a molecule it becomes an ion 

 very similar to the positive ions which carry the part of the 

 current (2). In all the cases which we shall consider this 

 part of the current is very nearly saturated, and hence we 

 may suppose that every electron which adheres to a molecule 

 arrives ultimately at the oppositely charged electrode, whether 

 it would or would not have done so if the collision had not 

 occurred. Assuming that the proportion of electrons which 

 can travel a distance x without collision is e~ , where \ is 

 the free path of an electron and is taken to be independent of 

 its velocity within the limits considered, we find in place of (1) 



i/e = N[l - e k { 1 -/(V„) ft + n(l - 2 M /V ) 



+f r°[i-<r^{i-/(V)}]<iV . . (■>) 



v oJo 

 * J. Francl< & (i. Hertz, DmUch. Phyn. (in. xv. 9, p. 878 (1913). 



