AND THE THEORY OF A QUASI-LABILE ETHER. 243 



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 affected differently in different directions, shows that the motion 

 of the ether is considerably modified. This implies a distortion super- 

 posed 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 ponderable 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 I 2 , 

 instead of diminishing, as the last member of the equation shows that 

 it does. We are obliged to suppose that 6, and therefore the type of 

 the vibrations, 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 refractive 

 power of a body and its specific dielectric capacity, which is com- 

 monly 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 infinite length by extrapolation prevents it 

 from furnishing any very rigorous test of the theory. Yet, as the 

 results of extrapolation in some cases agree strikingly with the 

 specific dielectric capacity, although in other cases they are quite 

 different, the correspondence is generally regarded as corroborative, in 

 some degree, of the theory. But the relation between refractive power 



