COMPAEISON OF THE ELECTEIC THEORY OF LIGHT, ETC. 233 



but its position in that plane is different, being perpendicular to the 

 ray instead of to the wave-normal.* 



It is the object of this paper to compare this new theory with 

 the electric theory of light. In the limiting cases, that is, when we 

 regard the velocity of the missing wave in the elastic theory as zero, 

 and in the electric theory as infinite, we shall find a remarkable 

 correspondence between the two theories, the motions of monochromatic 

 light within isotropic or aeolotropic media of any degree of trans- 

 parency or opacity, and at the boundary between two such media, 

 being represented by equations absolutely identical, except that the 

 symbols which denote displacement in one theory denote force in 

 the other, and vice versdJ In order to exhibit this correspondence 

 completely and clearly, it is necessary that the fundamental principles 

 of the two theories should be treated with the same generality, and, 

 so far as possible, by the same method. The immediate consequences 

 of the new theory will therefore be deduced with the same generality 

 and essentially by the same method which has been used with 

 reference to the electric theory in a former volume of this Journal 

 [page 211 of this volume]. 



The elastic properties of the ether, according to the new theory, 

 in its limiting case, may be very simply expressed by means of a 

 vector operator, for which we shall use Maxwell's designation. The 

 curl of a vector is defined to be another vector so derived from the 

 first that if u, v, w be the rectangular components of the first, and 

 u', v', w', those of its curl, 



,_^dv , _du dw ,_dvdu 



dy dz' ~ dz dx ' "~ dx dy ' 



where x, y, z are rectangular coordinates. With this understanding, 

 if the displacement of the ether is represented by the vector (, the 

 force exerted upon any element by the surrounding ether will be 



B curl curl (5 dx dy dz, (2) 



where B is a scalar (the so-called rigidity of the ether) having the 

 same constant value throughout all space, whether ponderable matter 

 is present or not. 



Where there is no ponderable matter, this force must be equated to 

 the reaction of the inertia of the ether. This gives, with omission of 

 the common factor dx dy dz, 



A(g=-B curl curl(g, (3) 



where A denotes the density of the ether. 



*Sir William Thomson, loc. citat. R. T. Glazebrook, Phil. Mag., December, 1888. 



t In giving us a new interpretation of the equations of the electric theory, the author 

 of the new theory has in fact enriched the mathematical theory of physics with some- 

 thing which may be compared to the celebrated principle of duality in geometry. 



