252 Prof. J. W. Gibbs's Comparison of the Electric Theory 



1/a, which is the square of the index of refraction for an 

 infinite wave-length, would be identical with the second 

 member of (33). 



Another similarity between the electrical and optical pro- 

 perties of bodies consists in the relation between conductivity 

 and opacity. Bodies in which electrical fluxes are attended 

 with absorption of energy absorb likewise the energy of the 

 motions which constitute light. This is strikingly true of the 

 metals. But the analogy does not stop here. To fix our 

 ideas, let us consider the case of an isotropic body and circu- 

 larly polarized light, which is geometrically the simplest case, 

 although its analytical expression is not so simple as that of 

 plane-polarized light. The displacement at any point may be 

 symbolized by the rotation of a point in a circle. The external 

 force necessary to maintain the displacement ^ is represented 

 by n~^%. In transparent bodies, for which n~^ is a positive 

 number, the force is radial and in the direction of the displace- 

 ment, being principally employed in counterbalancing the 

 dielectric elasticity, which tends to diminish the displacement. 

 In a conductor n~^ becomes complex, which indicates a com- 

 ponent of the force in the direction of %, that is, tangential to 

 the circle. This is only the analytical expression of the fact 

 above mentioned. But there is another optical peculiarity 

 of metals, which has caused much remark, viz. that the real 

 part of 11^ (and therefore of n~^) is negative, i. e. the radial 

 component of the force is directed towards the centre. This 

 inwardly directed force, which evidently opposes the electro- 

 dynamic induction of the irregular part of the motion, is 

 small compared with the outward force which is found in 

 transparent bodies, but increases rapidly as the period di- 

 minishes. We may say, therefore, that metals exhibit a 

 second optical peculiarity — that the di electrical elasticity is 

 not prominent as in transparent bodies. This is like the 

 electrical behaviour of the metals, in which we do not observe 

 any elastic resistance to the motion of electricity. We see, 

 therefore, that the complex indices of metals, both in the real 

 and imaginary part of their inverse squares, exhibit properties 

 corresponding to the electrical behaviour of the metals. 



The case is quite different in the elastic theory. Here the 

 force from outside necessary to maintain in any element of 

 volume the displacement ^ is represented by n^i^. In trans- 

 parent bodies, therefore, it is directed toward the centre. In 

 metals, there is a component in the direction of the motion ^, 

 while the radial part of the force changes its direction and is 

 often many times greater than the opposite force in transpa- 

 rent bodies. This indicates that in metals the displacement of 



