Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/338

 at right angles to the plane containing the twist and the direction of the displacement which would exist if the twist were removed; if the displacement of the medium be represented by F sin pt, and the angular displacement of the twist by ω sin pt, the magnitude of the force is proportional to the vector-product of F (in the direction of the displacement) and ω (in the direction of the axis of the twist).

A model of magnetic action may evidently be constructed on the basis of these results. A bar-magnet must be regarded as vibrating tangentially, the direction of vibration being parallel to the axis of the body. A cylindrical body carrying a current will have its surface also vibrating tangentially; but in this case the direction of vibration will be perpendicular to the axis of the cylinder. A statically electrified body, on the other hand, may, as follows from the same author's earlier work, be regarded as analogous to a body whose surface vibrates in the normal direction.

We have now discussed models in which the magnetic force is represented as the velocity in a liquid, and others in which it is represented as the displacement in an elastic solid. Some years before the date of Leahy's memoir, George Francis FitzGerald (b. 1851, d. 1901) had instituted a comparison between magnetic force and the velocity in a quasi-elastic solid of the type first devised by MacCullagh. An analogy is at once evident when it is noticed that the electromagnetic equation

is satisfied identically by the values

where e denotes, any vector; and that, on substituting these values in the other electromagnetic equation,