On the Possible Density of the Luminiferous Medium, §c. 37 



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 illumination ceases*. 

 The matter which possesses this energy is the luminiferous me- 

 dium. 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 moving 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 consti- 

 tute 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 velo- 

 cities of the vibrating particles must be very small in comparison 

 with the velocity of propagation of the waves. Let us consider, 

 for instance, plane-polarized 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 pro- 

 pagation of light or radiant heat, we have 



v~ 27r x' 



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

 small fraction {2ir 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 mechanical value of homogeneous plane-polarized light in 

 any infinitely small space containing only particles sensibly in 

 the same phase of vibration, which consists entirely of potential 

 energy at the instants when the particles are at rest at the extre- 

 mities of their excursions, partly of potential and partly of actual 

 energy when they are moving to or from their positions of equi- 

 librium, and wholly of actual energy when they are passing 

 through these positions, is of constant amount, and must there- 

 fore 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 p 1 note the 



* 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. 



