146 On a Dynamical 1'heory of 



and the laws of propagation are linked together as parts of the 

 same system."* This step has since been made, and these anti- 

 cipations have been realised. In the present Paper I propose to 

 supply the link between the two sets of laws by means of a very 

 simple theory, depending on certain special assumptions, and 

 employing the usual methods of analytical dynamics. 



In this theory, the two kinds of laws, being traced from a 

 common origin, are at once connected with each other and 

 severally explained ; and it may be observed, that the explana- 

 tion of each, as well as the source of their connexion, is now 

 made known for the first time. For though the laws of crys- 

 talline propagation have attracted much attention during the 

 period which has elapsed since they were discovered by Fresnel,f 

 they have hitherto resisted every attempt that has been made to 

 account for them by dynamical reasonings ; and the laws of re- 

 flexion, when recently discovered, were apparently still more 

 difficult to reach by such considerations. Nothing can be easier, 

 however, than the process by which both systems of laws are 

 now deduced from the same principles. 



The assumptions on which the theory rests are these : First, 

 that the density of the luminiferous ether is a constant quantity ; 

 in which it is implied that this density is unchanged either by 

 the motions which produce light or by the presence of material 

 particles, so that it is the same within all bodies as in free 

 space, and remains the same during the most intense vibrations. 

 Second, that the vibrations in a plane- wave are rectilinear, and 

 that, while the plane of the wave moves parallel to itself, the 

 vibrations continue parallel to a fixed right line, the direction of 

 this right line and the direction of a normal to the wave being 

 functions of each other. This supposition holds in all known 

 crystals, except quartz, in which the vibrations are elliptical. 



Concerning the peculiar constitution of the ether we know 



* Ibid, p. 53, note. (Supra, p. 112.) The note here referred to was added 

 some time after the Paper itself was read. 



f These laws were published in his Memoir on Double Refraction Memoires 

 de V Institut, torn. vii. p. 45. 



