﻿Applications of the Electron Theory of Matter. 595 



§ 2. JMectrical and 2 hernial Conductivity and the Law of 

 Force ivhich governs the collisions of Electrons in metals. 



Lorentz * has shown how to calculate the electric and 

 thermal conductivities of metals, without ignoring the 

 existence o£ Maxwell's law of distribution of velocity 

 among the electrons, on the assumption that the collisions 

 take place with hard immovable elastic spheres. This 

 assumption has been made, not because it is especially 

 likely to correspond with nature, but because it simplifies 

 the calculations. It appears, however, that this restriction 

 is not necessary, and that the same type of calculation may 

 be applied to the hypothesis that the collisions take place 

 with immovable point centres of force which act on the 

 electrons with a force equal to ~K/d s , where d is distance and 

 K is positive when the forces are repulsive. In what 

 follows I shall adopt Lorentz's notation as far as possible, 

 and merely indicate the way in which his calculation has to 

 be modified. 



Let n be the number of the centres of force in unit 

 volume, r = f, 77, f the velocity of an electron, f(£,% Qd^dwdt, 

 the number of electrons whose velocity components lie be- 

 tween £ and f + df, y and rj + drj, and f and J+dffi then the 

 number of electrons which leave the group f n £ in unit time 

 owing to deflexions through an angle between 26 and 2(6 + d6) 

 in an azimuth between ^ and ty + dyjr is f 



nrf& Vi Qd£d V dZbdbdf. . . . (1) 



Here the polar axis coincides with r'and b is the perpen- 

 dicular distance from the centre of force to the originally 

 straight path of the electron, and 



bdb 





where M x and M 2 are the masses of the particles. Since we 

 are supposing Mj/Ms to be very small, we can put 



(M. 1 + M 2 )/M 1 M c2 = m-\ 



where m is the mass of an electron. The relation between 

 6 and oc is- 



♦"-ft" -Mr) 



dx % 



* ' Theory of Electrons,' p. 267. 

 t Maxwell's Scientific Papers, vol. ii. p. 36. 

 2 11 2 



