The Electron Theory of Metallic Conduction. 287 



The planes in which the particles move relatively to the 

 ellipsoid are normal to the direction ('21, '22, *95) which 

 makes the angle 34° V with the axis of rotation. Each 

 particle goes twice round its ellipse relative to the shell, 

 while the latter makes three revolutions round the axis. 

 The motion relative to the ellipsoid is, of course, retrograde. 



Fig. 10. Ellipsoid (10 3 1) round axis (-33, '87, -37), 

 planes of motion normal to (*09, *27, *96) which is inclined 

 to the axis of rotation at angle 51° 42', one rotation relative 

 to the shell to three turns of the shell round the axis. 



Fig. 11. Ellipsoid (10 3 1) round axis ('22, «96, -17) 

 planes of motion normal to (*12, '56, '82) t angle between 

 these directions 45° 15', one relative rotation to four of the 

 shell round the axis. 



Figs. 12-1G. Ellipsoid (5 2 1) round axis ('33, '86, *38), 

 planes of motion normal to ("17, '53, '83), angle 34° 10', 

 one relative rotation to two of the shell. 



Fig. 12 shows the space-path for a particle on a central 

 section, fig. 13 on a section § way out towards the parallel 

 tangent plane, figs. 14 and 15 on sections '90 and "98 of the 

 way out respectively, and fig. 10 the limiting circular form. 



XXVII. On the Electron Theory of Metallic Conduction. — IV. 

 By G. H. Livens*. 



THE general theory of metallic conduction based on the 

 idea that it takes place by free electrons whose velocities 

 are prescribed by collision with the molecules, has been inter- 

 preted in its most general possible form by Drude and 

 Thomson and by Lorentz on rather different but apparently 

 fundamentally identical lines. According to Lorentz, the 

 whole problem turns on the determination of the law of 

 distribution of velocities, which in the absence of all external 

 forces is taken to be determined by the Maxwellian law of 

 equality of mean energies as in gas theory, and which in 

 their presence is presumed to depart but slightly from 

 this law. 



As Lorentz proves t, the most general law of distribution 

 of velocities consistent with the more fundamental basis of 

 the theory and determined by the specification of the number 

 of electrons per unit volume at the point (a, y, z) in the 

 metal and with their velocity components in the range 

 between (f, rj, f) and (f + tff, v + dv, %+dQ. depends on the 



* Communicated bv the Author. 



f Vide ' The Theory of Electrons,' pp. 266-271. 



