Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/486

When the temperature of the metal is high, the ions emitted are mainly negative; and it is found^[1] that in these circumstances, when the surrounding gas is rarefied, the saturation-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. Richardson^[2] that the dependence on the temperature may be expressed by an equation of the form

$i=AT^{\frac {1}{2}}e^{-{\frac {b}{T}}}$,

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.^[3]

In order to account for these phenomena, Richardson^[4]adopted the hypothesis which had previously been proposed^[5] 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

1. Cf. J. A. McClelland, Proc, Cumb. Phil. Soc. < (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. 217; and O. W. Richardson, Phil. Trans. ccvii (1906), p. 1.
2. Proc. Camb. Phil. Soc. xi (1902), p. 286; Phil. Trans. cci (1903), p. 497. Cf. also H. A. Wilson, Phil. Trans. ccii (1903), p. 243.
3. 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.
4. Phil. Trans. cci (1903), p. 197.
5. Cf. pp. 467 et sqq.