220 Royal Society. 



to be exactly equal to the sum of the vires viva of the reflected and 

 refracted rays. But if it be partly expended on the medium and 

 partly upon the emergent rays, the vis viva of the incident ray ought 

 to exceed the vires viva of the reflected and refracted rays by a certain 

 quantity. The object of his present investigation was to take into 

 account the effect of such supposed excess, in the hope of arriving at 

 some explanation of the Stokcsian phaenomena. The remarkable re- 

 sult he has obtained, that every loss of vis viva will be accompanied 

 with a diminution of the refractive index, is quite in the direction of 

 Professor Stokes's own idea of M a change of refrangibility," but 

 throws no light on the change of period. This the author is inclined 

 to think is due to an action of the nature of harmonic resonance, and 

 from some calculations which he has made, he thinks it probable 

 that the light produced in the Stokesian experiments may be due to 

 resonant vibrations which are about a major or minor third lower in 

 pitch than those of the invisible rays producing them. 



The mode of procedure which appeared to the author most likely 

 to lead to a successful result, was to assume, in the first instance, 

 the hypothesis that the vis viva is expended solely on the reflected 

 and refracted rays, and afterwards to modify, if possible, the steps 

 of the process so as to adapt them to the hypothesis that a portion 

 of it is expended on the medium. In adopting the more simple hy- 

 pothesis, he was much struck by the formulae at which he arrived ; 

 for not only did the general law of refraction spring out most unex- 

 pectedly, but the very same expressions for the intensity of the re- 

 flected rays, which were first discovered by Fresnel, and subsequently 

 verified by the experiments of Brewster and Arago, were an imme- 

 diate consequence of the formula?. His results however differ in 

 some particulars from those of Fresnel. In the first place, the index 

 of refraction is not the simple quotient of the velocities of undula- 

 tion, but of those velocities each multiplied by the density of the 

 aether in the corresponding medium. In the second place, the vibra- 

 tions of the aethereal particles are performed in the plane of polar- 

 ization, and not perpendicular to that plane, as Fresnel supposed. 

 Further, the expressions for the intensities of the refracted rays 

 differ slightly in other respects from those of Fresnel, as given in 

 Airy's Tracts. 



The author states that he confines his attention to an isotropical 

 singly refracting medium, though he thinks, if he had more time at 

 his disposal, he could extend the theory to doubly refracting crystals. 

 A very simple integration gives him a general expression for the vis 

 viva of an elementary cycloidal wave, in terms of the amplitude and 

 the constants of the periodical function. By help of this he obtains 

 two equations of vis viva ; one for a wave whose vibrations are in 

 the planes of incidence, and the other for a wave whose vibrations 

 are perpendicular to that plane, both vibrations being transverse to 

 the axis of the ray. By the principle of superposition these two 

 equations will hold true simultaneously when the above waves are 

 regarded as the components of one and the same wave. He obtains 

 three other equations between the amplitudes from the simple con- 



