466 The Theory of Aether and Electrons in the 



When the temperature of the metal is high, the ions 

 emitted are mainly negative; and it is found* that in these 

 circumstances, when the surrounding gas is rarefied, the satura- 

 tion-current is almost independent of the nature of the gas or 

 of its pressure. The leak of resinous electricity from a metallic 

 surface in a rarefied gas must therefore depend only on the 

 temperature and on the nature of the metal ; and it was shown 

 by 0. W. Richardsonf that the dependence on the temperature 

 may be expressed by an equation of the form 



b 



where i denotes the saturation-current per unit area of 

 surface (which is proportional to the number of ions emitted in 

 unit time), T denotes the absolute temperature, and A and b 

 are constants.! 



In order to account for these phenomena, Eichardson 

 adopted the hypothesis which had previously been proposed || 

 for the explanation of metallic conductivity ; namely, that 

 a metal is to be regarded as a sponge- like structure of 

 comparatively large fixed positive ions and molecules, in the 

 interstices of which negative electrons are in rapid motion. 

 Since the electrons do not all escape freely at the surface, he 

 postulated a superficial discontinuity of potential, sufficient to 

 restrain most of them. Thus, let N denote the number of free 

 electrons in unit volume of the metal ; then in a parallelepiped 

 whose height measured at right angles to the surface is dx, 

 and whose base is of unit area, the number of electrons whose 



* Cf. J. A. McClelland, Proe. Camb. Phil. Soc. x (1899), p. 241; xi (1901), 

 p. 296. On the results obtained when the gas is hydrogen, cf. H. A. Wilson, 

 Phil. Trans, ccii (1903), p. 243; ccviii (1908), p. 247; and 0. W. Richardson, 

 Phil. Trans, ccvii (1906), p. 1. 



fProc. Camb. Phil. Soc. xi (1902), p. 286; Phil. Trans, cci (1903), p. 497. 

 Cf. also H. A. Wilson, Phil. Trans, ccii (1903), p. 243. 



J The same law applies to the emission from other bodies, e.g. heated 

 alkaline earths, and to the emission of positive ions at any rate when a steady 

 state of emission has been reached in a gas which is at a definite pressure. 



Phil. Trans, cci (1903), p. 497. 



|| Cf. pp. 457 et sqq. 



