RECENT STATISTICAL THEORIES IIS 



If so, then it must diminish with rising temperature. It would seem 

 reasonable enough for n to increase with rise of temperature, for 

 presumably the free electrons arise from ionization of the atoms, and 

 ionization is promoted by heat ; but for n to decrease would seem very 

 odd, notwithstanding Waterman's successes in accounting for some 

 of the data by such a theory. 



Part of the burden, then, must be cast on the mean free path — 

 indeed the whole of it, if we adopt the new statistics so that v is held 

 constant, and suppose in addition that n does not vary with tempera- 

 ture. But the elastic-sphere conception cannot stand the strain. 

 It gives for the mean free path a value independent of temperature,^^ 

 except insofar as the metal dilates with increase of heat. This is 

 pretty nearly checkmate. 



If however we might suppose that an electron may sometimes go 

 clear through an atom without being reflected or deflected, and that 

 the chance of such a piercing is relatively smaller and the chance of 

 a rebounding relatively greater, the more violently the atom is vi- 

 brating — then by this theory the mean free path would diminish as 

 the temperature rises, which is what is desired. This is an idea 

 proposed long since by Wien. 



The new idea is in result the same. The probability of the re- 

 bounding, or let me say of the scattering of an electron by an atom, 

 is supposed to increase with the vigor of the vibrations of the latter. 

 But for this a new reason is advanced: the reason, that while vibrating 

 the atom is most of the time away from its equilibrium-place in the 

 crystal lattice, and its relations with its companions are distorted. 

 The probability of scattering is made to depend not only on the 

 presence of the atom somewhere along the path down which the 

 electron is rushing, but also on the relative positions of all the other 

 atoms in the crystal. 



To make such an assumption is, in efl^ect, to compromise between 

 the corpuscle-theory and the wave-theory. For what is the evidence 

 from which it is inferred that a beam of light falling upon a grating, 

 say, or a beam of X-rays falling upon a crystal, are undulatory? 

 Essentially this: the way in which the beam is scattered or diffracted 

 by the regular array of rulings on the grating or atom-groups in the 

 crystal is different — greatly and strikingly different — from the way 

 in which we know that it would be scattered by a single ruling, or 

 suspect with good reason that it would be scattered by a single atom- 

 ic The value l/NirR^ familiar in the kinetic theory of gases, N standing for the 

 number of fixed spheres per unit volume, R for the sum of the radii of a hxed and 

 a moving sphere. 



47 



