58 PROFESSOR W. THOMSON ON THE POSSIBLE DENSITY OF THE 



Merely to commence the illumination of three cubic miles, requires an amount 

 of work equal to that of a horse-power for a minute ; the same amount of 

 energy exists in that space as long as light continues to traverse it ; and, if the 

 source of light be suddenly stopped, must be emitted from it before the illumi- 

 nation ceases.* The matter which possesses this energy is the luminiferous 

 medium. If, then, we knew the velocities of the vibratory motions, we might 

 ascertain the density of the luminiferous medium ; or, conversely, if we knew 

 the density of the medium, we might determine the average velocity of the mov- 

 ing particles. Without any such definite knowledge, we may assign a superior 

 limit to the velocities, and deduce an inferior limit to the quantity of matter, by 

 considering the nature of the motions which constitute waves of light. For it 

 appears certain that the amplitudes of the vibrations constituting radiant heat 

 and light must be but small fractions of the wave lengths, and that the greatest 

 velocities of the vibrating particles must be very small in comparison with the 

 velocity of propagation of the waves. Let us consider, for instance, plane polar- 

 ized light, and let the greatest velocity of vibration be denoted by v ; the distance 

 to which a particle vibrates on each side of its position of equilibrium, by A ; and 

 the wave length, by X. Then if V denote the velocity of propagation of light 

 or radiant heat, we have 



v =27r T' 



and therefore if A be a small fraction of \, v must also be a small fraction 

 (2 7T times as great) of V. The same relation holds for circularly polarized light, 

 since in the time during which a particle revolves once round in a circle of radius 

 A, the wave has been propagated over a space equal to X. Now the whole me- 

 chanical value of homogeneous plane polarized light in any infinitely small space 

 containing only particles sensibly in the same phase of vibration, which con- 

 sists entirely of potential energy at the instants when the particles are at rest at 

 the extremities of their excursions, partly of potential and partly of actual energy 

 when they are moving to or from their positions of equilibrium, and wholly of 

 actual energy when they are passing through these positions, is of constant 

 amount, and must therefore be at every instant equal to half the mass multiplied 

 by the square of the velocity the particles have in the last-mentioned case. But 

 the velocity of any particle passing through its position of equilibrium is the 

 greatest velocity of vibration, which has been denoted by v ; and, therefore, if $> 

 denote the quantity of vibrating matter contained in a certain space, a space of 

 unit volume for instance, the whole mechanical value of all the energy, both 



* Similarly we find 15000 horse-power for a minute as the amount of work required to generate 

 the energy existing in a cubic mile of light near the sun. 



