CONTEMPORARY ADVANCES IN PHYSICS 673 



and this is the number of electron-paths which extend unintercepted 

 through the distance x measured from the plane x = 0. Out of these, 

 the number which are terminated between the planes x and x -\- dx'is 

 this: 



— dQ = N<jQdx = N(xQoexp(— Nax)dx (5) 



and this is the number of electron-paths which, measured from the 

 plane :c = to their termini, have lengths between x and x -f- dx. 

 Multiply it by x, and you have the sum of the lengths of all these paths. 

 Integrate this product xNaQdx from x = to x = <» , and one has 

 the total length of the unintercepted paths of all the Qo electrons; 

 divide the integral by Qo, and one has their mean length /, the "mean 

 free path for interception": 



I = fNax.expi- N(Tx)dx = (Na)-', (6) 



and this is the reason for giving the name "mean free path" to the 

 reciprocal of Na. As for the reciprocal of Nia, it is the value of mean 

 free path at zero Centigrade and one millimetre pressure; it may be 



denoted by /i : 



h = {N,a)-\ (7) 



Though everywhere along this train of reasoning the paths were 

 supposed to be measured from the plane x = where I said that the 

 corpuscles entered the gas, the result is not restricted. No matter 

 where the plane, from which the paths are measured (so long as it lies 

 in the gas), the mean of their lengths from that plane to their various 

 terminations has the same value {A^(r)~^. It follows that if these 

 so-called "interceptions" are elastic collisions, from which the electrons 

 rebound with practically the same value of speed as they had before- 

 hand, the mean-free-path from one collision to the next should likewise 

 be equal to {N(t)~^. But this is a deduction which we can hardly hope 

 to check by simple experiments on a beam of electrons, since after its 

 first collision a corpuscle quits the beam. Of course, if the "intercep- 

 tions" are adhesions of electrons to molecules, there is no sense in 

 making this extension. 



Something must now be said about the relation between these " mean 

 free paths" of electrons, and the quantity called the "mean free path of 

 the molecules of the gas." Even if c were equal to the gas-kinetic cross- 

 section o-Q — even if the molecules behaved towards one another as elastic 

 spheres of radius o-o/VtF, and towards electrons as elastic spheres of the 

 same radius o-o/Vtt — the mean free path of a molecule between collisions 

 with its mates would not be the same as the mean free path of an elec- 

 tron between collisions with molecules. For, conceiving an electron 



