292 Maxwell. 



all modern theories of dispersion. The earliest of these was 

 devised by Maxwell, who, in the Cambridge Mathematical Tripos 

 for 1869,* published the results of the following investigation : 



A model of a dispersive medium may be constituted by 

 embedding systems which represent the atoms of ponderable 

 matter in a medium which represents the aether. We may 

 picture each atomj- as composed of a single massive particle 

 supported symmetrically by springs from the interior face of 

 a massless spherical shell : if the shell be fixed, the particle 

 will be capable of executing vibrations about the centre of the 

 sphere, the effect of the springs being equivalent to a force on 

 the particle proportional to its distance from the centre. The 

 atoms thus constituted may be supposed to occupy small 

 spherical cavities in the aether, the outer shell of each atom 

 being in contact with the aether at all points and partaking 

 of its motion. An immense number of atoms is supposed to 

 exist in each unit volume of the dispersive medium, so that 

 the medium as a whole is fine-grained. 



Suppose that the potential energy of strain of free aether 

 per unit volume is 



where j denotes the displacement and E an elastic constant ; 

 so that the equation of wave-propagation in free aether is 



3*1 a 2 ,, 



''a? = K & 



where p denotes the aethereal density. 



Then if <r denote the mass of the atomic particles in unit 

 volume, (TJ + ) the total displacement of an atomic particle at 

 the place x at time t, and <rp 2 the attractive force, it is evident 

 that for the compound medium the kinetic energy per unit 

 volume is 



* Cambridge Calendar, 1869 ; republished by Lord Kayleigh, Phil. Mag. xlviii 

 (1899), p. 151. t This illustration is due to "W. Thomson. 



