3 1 6 Models of the Aether. 



Thomson, moreover, investigated* the ponderomotive forces 

 which act between two solid bodies immersed in a fluid, when 

 one of the bodies is constrained to perform small oscillations. 

 If, for example, a small sphere immersed in an incompressible 

 fluid is compelled to oscillate along the line which joins its 

 centre to that of a much larger sphere, which is free, the free 

 sphere will be attracted if it is denser than the fluid ; while 

 if it is less dense than the fluid, it will be repelled or attracted 

 according as the ratio of its distance from the vibrator to its 

 radius is greater or less than a certain quantity depending on 

 the ratio of its density to the density of the fluid. Systems 

 of this kind were afterwards extensively investigated by 

 C. A. Bjerknes.f Bjerknes showed that two spheres which 

 are immersed in an incompressible fluid, and which pulsate 

 (i.e., change in volume) regularly, exert on each other (by the 

 mediation of the fluid) an attraction, determined by the inverse 

 square law, if the pulsations are concordant ; and exert on 

 each other a repulsion, determined likewise by the inverse 

 square law, if the phases of the pulsations differ by half a 

 period. It is necessary to suppose that the medium is incom- 

 pressible, so that all pulsations are propagated instantaneously : 

 otherwise attractions would change to repulsions and vice versa 

 at distances greater than a quarter wave-length.^ If the 

 spheres, instead of pulsating, oscillate to and fro in straight 

 lines about their mean positions, the forces between them are 

 proportional in magnitude and the same in direction, but 



mutual distance I than when sinks of the same strengths are at infinite distance 

 apart by an amount lirpmm'/l. Since, in the case of the tubes, the quantities m 

 correspond to the fluxes of fluid, this expression corresponds to the Lagrangian 

 form of the kinetic energy ; and therefore the force tending to increase the coordi- 

 nate x of one of the sinks is (3/9#) (4ny> ww'/Z). "Whence it is seen that the like ends 

 of two tubes attract, and the unlike ends repel, according to the inverse square la\\ r . 



* Phil. Mag. xli (1870), p. 427. 



t Repertorium d. Mathematik von Konisberger und Zeuner (1876), p. 268. 

 Gottinger Nachrichten, 1876, p. 245. Comptes Rendus, Ixxxiv (1877), p. 1377. 

 Cf. Nature, xxiv (1881), p. 360. 



J On the mathematical theory of the force between two pulsating spheres in 

 a fluid, cf. W. M. Hicks, Proc. Camb. Phil. Soc. iii (1879), p. 276 ; iv (1880), 

 p. 29. 



