ELASTIC AND ELECTRICAL THEORIES OF LIGHT. 229 



the different coefficients in the function varying separately, because 

 G D and / D will not in general be similar functions.* If we consider a 

 constant direction of displacement while the period varies, G D and 

 / D will only vary so far as the type of the motion varies, i.e., so far 

 as the manner in which the flux distributes itself among the 

 ponderable molecules and intermolecular spaces, and the extent to 

 which the molecules take part in the motion are changed. There 

 are cases in which these vary rapidly with the period, viz., cases 

 of selective absorption and abnormal dispersion. But we may fairly 

 expect that there will be many cases in which the character of the 

 motion in these respects will not vary much with the period. 



r* f 



-^ and ^M will then be sensibly constant and we have an approximate 



expression for the general law of dispersion, which agrees remarkably 

 well with experiment.! 



If we now return to the equation of energies obtained from the 

 elastic theory, we see at once that it does not suggest any such 

 relation as experiment has indicated, either between the wave- velocity 

 and the direction of displacement, or between the wave-velocity and 

 the period. It remains to be seen whether it can be brought to 

 agree with experiment by any hypothesis not too violent. 



In order that V 2 may be a quadratic function of any set of 

 direction-cosines, it is necessary that A D and 6 D shall be independent 

 of the direction of the displacement, in other words, in the case of 

 a crystal like Iceland spar, that the direct action of the ponderable 

 molecules upon the ether, shall affect both the kinetic and the 

 potential energy in the same way, whether the displacement take 

 place in the direction of the optic axis or at right angles to it. 

 This is contrary to everything which we should expect. If, never- 

 theless, we make this supposition, 1 it remains to consider B ND . This 

 must be a quadratic function of a certain direction, which is almost 

 certainly that of the displacement. If the medium is free from 

 external stress (other than hydrostatic), B ND , as we have seen, is 

 symmetrical with respect to the wave-normal and the direction 

 of displacement, and a quadratic function of the direction-cosines 

 of each. The only single direction of which it can be a function is 

 the common perpendicular to these two directions. If the wave- 

 normal and the displacement are perpendicular, the direction- cosines 



*But G D ,/ D , and V 2 , considered as functions of the direction of displacement, are all 

 subject to any law of symmetry which may belong to the structure of the body 

 considered. The resulting optical characteristics of the different crystallographic 

 systems are given on pages 192-194. 



t This will appear most distinctly if we consider that V divided by the velocity of 

 light in vacuo gives the reciprocal of the index of refraction, and p multiplied by the 

 same quantity gives the wave-length in vacuo. 



