Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/302

calculated by considering the mechanical force required in order to increase the distance between the plates of a condenser, so as to enlarge the field comprised between them. The result is that tho energy per unit volume of the dielectric is εE′²/8π, where ε denotes the specific inductive capacity of the dielectric and E′ denotes the electric force, measured in terms of the electrostatic unit: if E denotes the electric force expressed in terms of the electrodynamic units used in the present investigation, we have E = cE′, where e denotes the constant which^[1] occurs in transformations of this kind. The energy is therefore εE²/8πc² per unit volume. Comparing this with the expression for the energy in terms of E and D, we have

$\mathbf {D} =\epsilon \mathbf {E} /4\pi c^{2}$,

and therefore the constant c₁ has the value cε^-1/2. Thus the result is obtained that the velocity of propagation of disturbances in Maxwell's medium is cε^-1/2, where ε denotes the specific inductive capacity and c denotes the velocity for which Kohlrausch and Weber had found^[2] the value 3·1 x 10¹⁰ cm./sec.

Now by this time the velocity of light was known, not only from the astronomical observations of aberration and of Jupiter's satellites, but also by direct terrestrial experiments. In 1849 Hippolyte Louis Fizeau^[3] had determined it by rotating a toothed wheel so rapidly that a beam of light transmitted through the gap between two teeth and reflected back from a mirror was eclipsed by one of the teeth on its return journey. Tho velocity of light was calculated from the dimensions and angular velocity of the wheel and the distance of the mirror; the result being 3·15 10¹⁰ cm./sec.^[4]

1. Cf. pp. 227, 259.
2. Cf. p. 260.
3. Comptes Rendis, xxix (1849), p. 90. A determination made by Cornu in 1874 was on this principle.
4. A different experimental method was employed in 1862 by Léon Foucault (Comptes Rendus, lv, pp. 501, 792); in this a ray from an origin O was reflected by a revolving mirror M to a fixed mirror, and so reflected back to M, and again to O. It is evident that the returning ray MO must be deviated by twice the angle through which M turns while the light passes from M to the fixed mirror and back. The value thus obtained by Foucault for the velocity of light was