Light and the Theory of a Quasi-labile Lther. 143 



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

 nite wave-length, would be identical with the second member 

 of (33). 



Another similarity between the electrical and optical proper- 

 ties 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 circularly po- 

 larized light, which is geometrically the simplest case, although 

 its analytical expression is not so simple as that of plane- po- 

 larized light. The displacement at any point may be symbolized 

 by the rotation of a point in a circle. The external force nec- 

 essary to maintain the displacement % is represented by n~ 2 $. 

 In transparent bodies, for which n~"" is a positive number, the 

 force is radial and in the direction of the displacement, being 

 principally employed in counterbalancing the dielectric elas- 

 ticity, which tends to diminish the displacement. In a con- 

 ductor n~ 2 becomes complex, which indicates a component of 



the force in the direction of ^, that is, tangential to the circle. 

 This is only the analytical expression of the • fact above men- 

 tioned. But there is another optical peculiarity of metals, 

 which has caused much remark, viz : that the real part of ri* 

 (and therefore of n~ 2 ) is negative, i. e., the radial component 

 of the force is directed towards the center. This inwardly 

 directed force, which evidently opposes the electrodynamic in- 

 duction 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 diminishes. We may say, 

 therefore, that metals exhibit a second optical peculiarity, — - 

 that the dielectric elasticity is not prominent as in transparent 

 hodies. This is like the electrical behavior 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 the imaginary part of their in- 

 verse squares, exhibit properties corresponding to the electri- 

 cal behavior 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 (5 is represented by n 2 Q$.. In trans- 

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



metals, there is a component in the direction of the motion (S, 

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

 often many times greater than the opposite force in transpar- 



