Gravitational Matter through Infinite Space. 163 



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 moving particles. 



§ 3. 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. 



§ 4. Let us consider, for instance, homogeneous 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 propagation of 

 light or radiant heat, we have 



v _ A 

 V = 2,r x ; 



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

 small fraction (2tt 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 an 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 extremities of their excursions, partly of potential 

 and partly of kinetic energy when they are moving to or from 

 their positions of equilibrium, and wholly of kinetic 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 which 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. This we have denoted by v ; 

 and, therefore, if p 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 kinetic 

 and potential, of the disturbance within that space at any time 

 is ipr 2 . The mechanical energy of circularly polarized light 



M2 



