1893.] the Electric and Luminiferous Medium. 451 



ing energy into the dielectric, that constitutes the mechanical forcive 

 acting on it. But we can go further than this ; the locality of this 

 transformation of energy, so far at any rate as regards the material 

 forcive, is the surface of the conductor ; and the gain of mechanical 

 energy by the conductor is therefore correctly located as an absorp- 

 tion of energy at its surface ; therefore the forcive acting on the con- 

 ductor is correctly determined as a surface traction, and not a bodily 

 forcive throughout its volume. One mode of representing the dis- 

 tribution of this surface traction, which, as we know, gives the correct 

 amount of work for every possible kind of virtual displacement of the 

 surface, is to consider it in the ordinary electrostatic manner as a 

 normal traction due to the action of the electric force on the electric 

 density at the surface ; we conclude that this distribution of traction 

 is the actual one. To recapitulate : if the dielectric did not transmit 

 disturbance so rapidly, the result of the commotion at the surface 

 produced by the motion of the conductor would be to continually 

 start wavelets which would travel into the dielectric, carrying energy 

 with them. But the very great velocity of propagation effectually 

 prevents the elastic quality of the medium from getting hold ; no 

 sensible wave is produced and no flow of energy occurs into the di- 

 electric. The distribution of pressure in the medium which would 

 be the accompaniment of the wave motion still persists, though it now 

 does no work in the dielectric; it is this pressure of the medium 

 against the conductor that is the cause of the mechanical forcive. 



The matter is precisely illustrated by the fundamental apergu of 

 Sir George Stokes with regard to the communication of vibrations to 

 the air or other gas. The rapid vibrations of a tuning-fork are com- 

 municated as sound waves, but much less completely to a mobile 

 medium like hydrogen than to air. The slow vibrations of a pen- 

 dulum are not communicated as sound waves at all ; the vibrating 

 body cannot get a hold on the elasticity of the medium, which retreats 

 before it, preserving the equilibrium condition appropriate to the con- 

 figuration at the instant ; there is a pressure between them, but this 

 is instantaneously equalised throughout the medium as it is produced, 

 without leading to any flow of vibrational energy. 



Now let us formally consider the dynamical system consisting of 

 the dielectric media alone, and having a boundary just inside the sur- 

 face of each conductor ; and let us contemplate motions of the con- 

 ductors so slow that the medium is always indefinitely near the state 

 of internal equilibrium or steady motion, that is conditioned at each 

 instant by the position and motion of the boundaries. The kinetic 

 energy T of the medium is the electrodynamic energy of the currents, 

 as given by Neumann's formula ; and the potential energy W is the 

 energy of the electrostatic distribution corresponding to the conforma- 

 tion at the instant ; in addition to these energies we shall have to 



