224 ELASTIC AND ELECTRICAL THEORIES OF LIGHT. 



discovery of a remarkable theorem relating to the vibrations of a 

 strained solid * 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 some- 

 thing 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 (V) is the quotient of the wave-length (I) 

 by the period of. vibration (p). These quantities can be determined 

 with extreme accuracy. In media which are sensibly homogeneous 

 but not isotropic the wave-velocity V, 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 difficulty of accounting 

 for the intensities of reflected and refracted light on any other 



* Sir Wra. 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 homogeneous 

 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. 



