240 Prof. J. W. Gribbs^s Comparison of the Electric Theory 



The presence of ponderable matter disturbs the motions of 

 the aether, and renders them too complicated for us to follow 

 in detail. Nor is this necessary ; for the quantities which 

 occur in the equations of optics represent average values, 

 taken over spaces large enough to smooth out the irregu- 

 larities due to the ponderable particles, although very small 

 as measured by a wave-length*. Now the general principles 

 of harmonic motion f show that, to maintain in any element 

 of volume the motion represented by 



(£=5l^^'^V^ (4) 



^l being a complex vector-constant, will require a force from 

 outside represented by a complex linear vector-function of @; 

 that is, the three components of the force will be complex 

 linear functions of the three components of (J. We shall 

 represent this force by 



B^^dxdydz, (5) 



where '^ represents a complex linear vector-function J. 



If we now equate the force required to maintain the motion 

 in any element to that exerted upon the element by the sur- 

 rounding sether, we have the equation 



^g= -curl curl g 5 (6) 



which expresses the general law for the motion of monochro- 

 matic light within any sensibly homogeneous medium, and 

 may be regarded as implicitly including the conditions rela- 

 ting to the boundary of two such media, which are necessary 

 for determining the intensities of reflected and refracted 

 light. 



'& 



* This is in no respect different from what is always tacitly understood 

 in the theory of sound, where the displacements, velocities, and densities 

 considered are always such average values. But in the theory of light it 

 is desirable to have the fact clearly in mind, on account of the two inter- 

 penetrating media (imponderable and ponderable), the laws of light not 

 being in all respects the same as they would be for a single homogeneous 

 medium. 



t See Lord Rayleigh's * Theory of Sound,' vol. i. chapters iv., v. 



X It amounts essentially to the same thing, Avhether we regard the 

 force as a linear vector- function of (5 or of ii, since these differ only by 



477" 



the constant factor y- ^^^ there are some advantages in expressing 



the force as a function of @, because the greater part of the force, in the 

 most important cases, is required to overcome the inertia of the sether, 

 and is thus more immediately connected with(5. 



