﻿13-i Dr. F. A. Lindemann on the 



metal at 3° to 1/2° Abs. In this region we cannot apply 

 Debye's formula for the conduction of heat. We can only 

 conclude from his reasoning that it must be large. Only an 

 exact theory could give some idea as to his " free path " /, 

 which he defined as the distance in which the energy of the 



elastic waves is diminished to -^ part. He finds the heat 



conductivity X = ^~-Z ? q being the velocity of sound , — » 



7 the specific heat. As has been or will be shown, p, /c, and 

 y depend upon N and D, / can only depend upon the 

 number of layers of atoms per cm. -^-v~ 1/3 or upon N and 

 probably T. Therefore X=/(N, D, T). Although we lack 

 an exact theory for the conductivity of a crystal at very low 

 temperatures, we can conclude from the measured con- 

 ductivity of the diamond that it does not vary with the 

 temperature. Therefore X reduces to ^r(N, D), and this 



theorv gives the law of Wiedemann-Franz, - = E const., 



if x = ^-(N, D)—<£(N, *)= w . A consideration of the 



. 1 



dimensions appears to lead to the equation X-^ N1 , 3 1/g 3/2 . 



If this be true, - = fjjm a^ - This assumption is of 



course simply introduced to show that the observed pro- 

 portionality of electric and heat conductivities is not incon- 

 sistent with the electron space-lattice hypothesis. The 

 suggested theory does not pretend to predict this law as 

 the old theory does ; but, on the other hand, it would not 

 seem to lead to the absolute contradictions for which the old 



theory is noted. Jf k is of the form Tfrs, - reduces to 



N . N °" 



, 1 „, 1 - )j)2 . Thus supposing, for instance, D to be equal for all 



metals, &^-N 2 would lead to the law of Wiedemann-Franz. 

 As in the case of the electrical conductivity, impurities should 

 produce inhomogeneity of the space-lattice and thereby 

 diminish the heat-conductivity. 



Specific heat. — At emphasized above, the question of tne 

 specific heat of the electrons has been the chief stumbling- 

 block of the old theory. The argument which leads to the 

 difficulty, namely, that as the electrons conduct heat so well 

 they must have a large heat-capacity, is sound only as long- 

 as the electrons behave like a gas. If they form a solid, 

 on the other hand, the converse is nearer the truth. 



There are analogies, as stated above, in the conduction of 



