﻿132 Dr. F. A. Lindemann on the 



The calculation of the variation of the electrical resistance 

 with the temperature cannot be attempted here. It depends 

 obviously upon the amplitude of the atomic vibrations and 

 upon the force acting upon the electrons whilst they are within 

 the sphere of repulsion. As, according to Debye, there are 

 vibrations of almost every frequency less than v m , and as all 

 their amplitudes may vary, it will certainly be very difficult 

 to take an average of all the probable forces acting upon the 

 electron space-lattice. We may take it, however, that there 

 exists a law of force kf{r) which entails a resistance propor- 

 tional to the square of the amplitude A, i. e. proportional to the 

 pi 



energy E as A 2 =— , if a is the quasi-elastic force holding 



the atoms in position. As has been shown, a is roughly 

 proportional to N, the number of electrons per cm. 3 *. 

 Therefore the resistance is a function of N and k, say 

 <£(N, £)E. The dimensions would seem to lead to the 



formula - = a t 23 , 12 E, p being the density of the electron 



space-lattice. As p, N and k are independent of the tem- 

 perature, the resistance is thus in accord with the experi- 

 mental facts. 



This proportionality of the resistance to the temperature 

 only holds good of course for pure metals. In alloys con- 

 sisting of metals which do not form mixed crystals, i. e. which 

 consist of an agglomeration of pure crystals, the resistance 

 might be expected to be the sum of the resistance of the 

 components and the temperature coefficient would be normal. 

 In other alloys the homogeneity of the space- lattice would 

 be disturbed and the resistance would be larger. The 

 temperature coefficient would probably be smaller, for the 

 heat-motion might in some cases render the passage of the 

 electrons more easy, as the interspersed atoms which are in 

 the way might be moved into a more favourable position. 

 Somewhat similar phenomena may be expected in a liquid 

 metal, whose conductivity should be considerably less than 

 it is in the solid state. 



Conduction of heat. — Debye has shown that a homo- 

 geneous space-lattice would have apparently infinite heat 

 conductivity f. This diminishes the less homogeneous the 

 space-lattice becomes. Debye's theory explains Eucken's 

 apparently paradoxical experimental results on heat con- 



* Verh. d. d. Phys. Ges. xiii. 24. pp. 1107 & 1117 (1911). 

 t ' Vortrage iiber die kinetisclie Theorie der Materie und Elektricitat r 

 (Teubner), 1914. 



