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 »; the distance 
to which a particle vibrates on each side of its position of equilibrium, by A ; and 
the wave length, by A. Then if V denote the velocity of propagation of light 
or radiant heat, we have 
v A 
Vv = PH i7e x? 
and therefore if A be a small fraction of A, must also be a small fraction 
(2 or 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 A. 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 v7; 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. 
