AND THE THEOEY OF A QUASI-LABILE ETHER. 239 



theory from the experiments of Dr. Hall, which show that the 

 operators expressing the relation between electromotive force and 

 current are not in general self -conjugate in this case. 



In the preceding comparison, we have considered only the limiting 

 cases of the two theories. With respect to the sense in which the 

 limiting case is admissible, the two theories do not stand on quite 

 the same footing. In the electric theory, or in any in which the 

 velocity of the missing wave is very great, if we are satisfied that 

 the compressibility is so small as to produce no appreciable results, 

 we may set it equal to zero in our mathematical theory, even if we 

 do not regard this as expressing the actual facts with absolute 

 accuracy. But the case is not so simple with an elastic theory in 

 which the forces resisting certain kinds of motion vanish, so far 

 at least as they are proportional to the strains. The first requisite 

 for any sort of optical theory is that the forces shall be proportional 

 to the displacements. This is easily obtained in general by supposing 

 the displacements very small. But if the resistance to one kind of 

 distortion vanishes, there will be a tendency for this kind of distortion 

 to appear at some places in an exaggerated form, and even to an 

 infinite degree, however small the displacements may be in other 

 parts of the field. In the case before us, if we suppose the velocity 

 of the missing wave to be absolutely zero, there will be infinite 

 condensations and rarefactions at a surface where ordinary waves 

 are reflected. That is, a certain volume of ether will be condensed 

 to a surface, and vice versa. This prevents any treatment of the 

 extreme case, which is at once simple and satisfactory. The difficulty 

 has been noticed by Sir William Thomson, who observes that it 

 may be avoided if we suppose the displacements infinitely small in 

 comparison with the wave-length of the wave of compression. This 

 implies a finite velocity for that wave. A similar difficulty would 

 probably be found to exist (in the extreme case) with regard to 

 the deformation of the ether by the molecules of ponderable matter, 

 as the ether oscillates among them. If the statical resistance to 

 irrotational motions is zero, it is not at all evident that the statical 

 forces evoked by the disturbance caused by the molecules would be 

 proportional to the motions. But this difficulty would be obviated by 

 the same hypothesis as the first. 



These circumstances render the elastic theory somewhat less con- 

 venient as a working hypothesis than the electric. They do not 

 necessarily involve any complication of the equations of optics. For 

 it may still be possible that this velocity of the missing wave is 

 so small that the quantities on which it depends may be set equal 

 to zero in the equations which represent the phenomena of optics. 



