Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/337

 opposite in sign, to those which act between two magnets oriented along the directions of oscillation.

The results obtained by Bjerknes were extended by A. H. Leahy to the case of two spheres pulsating in an clastic medium; the wave-length of the disturbance being supposed large in comparison with the distance between the spheres. For this system Bjerknes' results are reversed, the law being now that of attraction in the case of unlike phases, and of repulsion in the case of like phases: the intensity is as before proportional to the inverse square of the distance.

The same author afterwards discussed the oscillations which may be produced in an elastic medium by the displacement, in the direction of the tangent to the crosssection, of the surfaces of tubes of small sectional area: the tubes either forming closed curves, or extending indefinitely in both directions. The direction and circumstances of the motion are in general analogous to ordinary vortex-motions in an incompressible fluid; and it was shown by Leahy that, if the period of the oscillation be such that the waves produced are long compared with ordinary finite distances, the displacement due to the tangential disturbances is proportional to the velocity due to vortex-rings of the same form as the tubular surfaces. One of these "oscillatory twists," as the tubular surfaces may be called, produces a displacement which is analogous to the magnetic force due to a current flowing in a curve coincident with the tube; the strength of the current being proportional to b2ω sin pt, where b denotes the radius of the twist, and ω sin pt its angular displacement. If the field of vibration is explored by a rectilineal twist of the same period as that of the vibration, the twist will experience a force