Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/364

It may, however, be remarked that this view of the origin of mass is not altogether consistent with the principle that the electron is an indivisible entity. For the so-called self-induction of the spherical electron is really the mutual induction of the convection-currents produced by the elements of electric charge which are distributed over its surface; and the calculation of this quantity presupposes the divisibility of the total charge into elements capable of acting severally in all respects as ordinary electric charges; a property which appears scarcely consistent with the supposed fundamental nature of the electron.

After the first attempt of J. J. Thomson to determine the field produced by a moving electrified sphere, the mathematical development of Maxwell's theory proceeded rapidly. The problems which admit of solution in terms of known functions are naturally those in which the conducting surfaces involved have simple geometrical forms—planes, spheres, and cylinders.^[1]

A result which was obtained by Horace Lamb,^[2] when investigating electrical motions in a spherical conductor, led to interesting consequences. Lamb found that if a spherical conductor is placed in a rapidly alternating held, the induced currents are almost entirely confined to a superficial layer; and his result was shortly afterwards generalized by Oliver Heaviside,^[3] who showed that whatever be the form of a conductor rapidly alternating currents do not penetrate far into its substance.^[4] The reason for this may be readily understood: it is virtually an application of the principle^[5] that a perfect conductor is impenetrable to magnetic lines of force. No perfect conductor is known to exist; but^[6] if the alternations of magnetic force to which a good conductor such as copper is exposed are very

1. Cf., e.g., c. Niven, Phil. Trans. clxxii (1881), p. 307; H. Lamb. Phil. Trans. clxxiv (1883), p. 519; J.J. Thomson, Proc. Lond. Math. Soc. xv (1884), p. 197: H. A. Rowland, Phil. Mag. xvii (1884), p. 413; J. Thomson, Proc. Lond. Math. Soc. xvii (1886), p. 310; xix (1888), p. 520; and many investigations of Oliver Heaviside, collected in his Electrical Papers.
2. Loc. cit.
3. Electrician, Jan. 1885.
4. The mathematical theory was given by Lord Rayleigh, Phil. Mag. xxi. (1886), p. 381. Cf. Maxwell's Treatise, § 689.
5. Cf. p. 313.
6. As was first remarked by Lord Rayleigh, Phil. Mag. xiii (1882), p. 314.