356 EEPORT — 1893. 



tion, has been given in 1883 by Prof. Willard Gibbs,^ under the title of 

 ' An Investigation of the Velocity of Plane Waves of Light, in which, 

 they are regarded as consisting of solenoidal electrical fluxes in an 

 indefinitely extended medium of uniform and very fine-grained structure.' 

 The principle on which his investigation is based is the very general 

 idea that the regular simple harmonic light- waves traversing the medium 

 excite secondary vibrations in its molecular electrical structure, which 

 is supposed very fine compared with the length of a wave. "When there 

 is absorption the phases of these excited vibrations will difi'er from that 

 of the exciting wave ; but even in this most general case the simple 

 harmonic electric flux with which we are alone concerned is at each 

 point completely specified by six quantities, the three components of the 

 flux itself, and the three components of its rate of change with the time. 

 In the same way, the electric force may be similarly specified by six co- 

 ordinates. Now the electric elasticity of the medium, as regards its 

 power of transmitting waves, is specified by the relation connecting 

 average force and average flux, this average referring to a region large 

 compared with molecular structures, but small compared with a wave- 

 length. The most general relation of this kind that can result from the 

 elimination of the molecular vibrations must be of the form of six Unear 

 equations connecting the quantities specifying the flux with the quanti- 

 ties specifying the force, the coefficients being functions of the wave- 

 length. If E denote the force and U the displacement, ' we may there- 

 fore write in vector notation 



where $ and ^ denote linear functions, 



' The optical properties of the media are determined by the forms 

 of these functions. But all forms of linear functions would not be con- 

 sistent with the principle of the conservation of energy. 



' In media which are more or less opaque, and which, therefore, absorb 

 energy, '"P must be of such a form that the function always makes an 

 acute angle (or none) with the independent variable. In perfectly 

 transparent media '^^ must vanish, unless the function is at right angles 

 to the independent variable. So far as is known, the last occurs only 

 when the medium is subject to magnetic influence. In perfectly trans- 

 parent media the principle of the conservation ef energy requires that 

 <P should be self-conjugate, i.e., that for three directions at right angles to 

 one another the function and independent variable should coincide in 

 direction. 



' In all isotropic media not subject to magnetic influence it is probable 

 that <I> and ^ reduce to numerical coefiicients, as is certainly the case with 

 <l> for transparent isotropic media.' ^ 



For the further examination of the content of this relation connecting^ 

 the two electric vectors we may express it in the symbolical form 



[flux] = [p] [force] + 2 , [force] 



> J. Willard Gibbs, ' On the General Equations of Monochromatic Light in 

 Media of every Degree of Transparency,' American Journal of Science, February, 

 1883. 



2 J. Willard Gibbs, loc. ait., p. 133 ; J. Larmor, Proc. Land. Math. Soc, xxiv. 1893, 

 where, however, some of the statements need correction. 



