Models of the Aether. 3 1 7 



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. Leahyf to the case of two spheres pulsating in an 

 elastic 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 cross- 

 section, of the surfaces of tubes of small sectional area : 

 the tubes either forming closed curves, or extending inde- 

 finitely 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 b'w sin pt, where b denotes the radius of 

 the twist, and t 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 



* A theory of gravitation has heen hased by Korn on the assumption that 

 gravitating particles resemhle slightly compressible spheres immersed in an incom- 

 pressible perfect fluid : the spheres execute pulsations, whose intensity corresponds 

 to the mass of the gravitating particles, and thus forces of the Newtonian kind are 

 produced between them. Cf. Korn, Eine Theorie der Gravitation und der elect. 

 Etscheinungen, Berlin, 1898. 



t Trans. Camb. Phil. Soc. xiv (1884), p. 45. 



J Trans. Camb. Phil. Soc. xiv (1885), p. 188. 



