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



It appears, therefore, that in the elastic theory that part of 

 the potential energy which depends on the deformation ex- 

 pressed by the equations of wave-motion bears to the whole 

 potential energy the same ratio which the velocity of a group 

 of waves bears to the wave-velocity. In the electrical theory, 

 that part of the kinetic energy which depends on the motions 

 expressed by the equations of wave-motion bears to the whole 

 kinetic energy the same ratio. 



Returning to the consideration of equations (26) and (27), 

 we observe that in transparent bodies the last member of these 

 equations represents a quantity which is small compared with 

 unity, at least in the visible spectrum, and diminishes rapidly 

 as the wave-length increases. This is just what we should 

 expect of the first member of equation (27). But when we 

 pass to equation (26), which relates to the elastic theory, the 

 case is entirely different. The fact that the kinetic energy is 

 affected by the presence of the ponderable matter, and aflPected 

 differently in different directions, shows that the motion of the 

 sether is considerably modified. This implies a distortion 

 superposed upon the distortion represented by the equations of 

 wave-motion, and very much greater, since the body is very 

 fine-grained as measured by a wave-length. With any other 

 law of elasticity we should suppose that the energy of this 

 superposed distortion would enormously exceed that of the 

 regular distortion represented by the equations of wave- 

 motion. But it is the peculiarity of this new law of elasticity 

 that there is one kind of distortion of which the energy is 

 very small, and which is therefore peculiarly likely to occur. 

 Now if we can suppose the distortion caused by the ponder- 

 able molecules to be almost entirely of this kind, we may be 

 able to account for the smallness of its energy. We should 

 still expect the first member of (26) to increase with the wave- 

 length on account of the factor Z^, instead of diminishing, as 

 the last member of the equation shows that it does. We are 

 obliged to suppose that h, and therefore the type of the vibra- 

 tions, varies very rapidly with the wave-length, even in those 

 cases which appear farthest removed from anything like 

 selective absorption. 



The electrical theory furnishes a relation between the re- 

 fractive power of a body and its specific dielectric capacity, 

 which is commonly expressed by saying that the latter is equal 

 to the square of the index of refraction for waves of infinite 

 length. No objection can be made to this statement ; but the 

 great uncertainty in determining the index for waves of infi- 

 nite length by extrapolation prevents it from furnishing any 

 very rigorous test of the theory. Yet as the results of extra- 



