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)[1] had instituted a comparison between magnetic force and the velocity in a quasi-elastic solid of the type first devised by MacCullagh.[2] 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,
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