328 Models of the Aether. 



mitting waves through a medium consisting of an incompressible 

 fluid in which small vortex-rings are closely packed together. 

 The wave-length of the disturbance was supposed large in com- 

 parison with the dimensions and mutual distances of the rings ; 

 and the translatory motion of the latter was supposed to be so 

 slow that very many waves can pass over any one before it has 

 much changed its position. Such a medium would probably 

 act as a fluid for larger motions. The vibration in the wave- 

 front might be either swinging oscillations of a ring about a 

 diameter, or transverse vibrations of the ring, or apertural 

 vibrations ; vibrations normal to the plane of the ring appear 

 to be impossible. Hicks determined in each case the velocity 

 of translation, in terms of the radius of the rings, the distance 

 of their planes, and their cyclic constant. 



The greatest advance in the vortex-sponge theory of the 

 aether was made in 1887, when W. Thomson* showed that the 

 equation of propagation of laminar disturbances in a vortex- 

 sponge is the same as the equation of propagation of luminous 

 vibrations in the aether. The demonstration, which in the 

 circumstances can scarcely be expected to be either very simple 

 or very rigorous, is as follows : 



Let (u, v, w) denote the components of velocity, and p the 

 pressure, at the point (x, y, z) in an incompressible fluid. Let 

 the initial motion be supposed to consist of a laminar motion 

 {/(?/), 0, Oj, superposed on a homogeneous, isotropic, and fine- 

 grained distribution (u' 0t v , w ) : so that at the origin of time 

 the velocity is {/ (y) + u' , v , w n \ : it is desired to find a 

 function / (y, t) such that at any time t the velocity shall 

 be \f(y, t) + u', v, w), where u', v, w, are quantities of which 

 every average taken over a sufficiently large space is zero. 



Substituting these values of the components of velocity in 

 the equation of motion 



du _ du du du dp 



dt dx ~ dy~ dz ~ dx' 



* Phil. Mug. xxiv (1887), p. 342 : Kelvin's Math, and Phys. Papers, iv, p. 308. 



