discovery of a remarkable theorem relating to the vibrations of a strained solid[1] has given a new impulse to the study of the elastic theory of light. Let us first consider the facts to which a correct theory must conform.
It is generally admitted that the phenomena of light consist in motions (of the type which we call wave-motions) of something which exists both in space void of ponderable matter, and in the spaces between the molecules of bodies, perhaps also in the molecules themselves. The kinematics of these motions is pretty well understood; the question at issue is whether it agrees with the dynamics of elastic solids or with the dynamics of electricity.
In the case of a simple harmonic wave-motion, which alone we need consider, the wave-velocity () is the quotient of the wave-length () by the period of vibration (). These quantities can be determined with extreme accuracy. In media which are sensibly homogeneous but not isotropic the wave-velocity for any constant value of the period, is a quadratic function of the direction cosines of a certain line, viz., the normal to the so-called "plane of polarization." The physical characteristics of this line have been a matter of dispute. Fresnel considered it to be the direction of displacement. Others have maintained that it is the common perpendicular to the wave-normal and the displacement. Others again would define it as that component of the displacement which is perpendicular to the wave-normal. This of course would differ from Fresnel's view only in case the displacements are not perpendicular to the wave-normal, and would in that case be a necessary modification of his view. Although this dispute has been one of the most celebrated in physics, it seems to be at length substantially settled, most directly by experiments upon the scattering of light by small particles, which seems to show decisively that in isotropic media at least the displacements are normal to the "plane of polarization," and also, with hardly less cogency, by the diflSculty of accounting for the intensities of reflected and refracted light on any other
- ↑ Sir Wm. Thomson has shown that if an elastic incompressible solid in which the potential energy of any homogeneous strain is proportional to the sum of the squares of the reciprocals of the principal elongations minus three is subjected to any homogeaeons strain by forces applied to its surface, the transmission of plane waves of distortion, superposed on this homogeneous strain, will follow exactly Fresnel's law (including the direction of displacement), the three principal velocities being proportional to the reciprocals of the principal elongations. It must be a surprise to mathematicians and physicists to learn that a theorem of such simplicity and beauty has been waiting to be discovered in a field which has been so carefully gleaned. See page 116 of the current volume (xxv) of the Philosophical Magazine.
