148 



There are occasions on which every consideration of this kind 

 must give way to a regard for the interests of science. 



To show that the principles of M. Cauchy contradict, in- 

 stead of explaining, the phenomenon of elliptic polarization, 

 let us take the axes of coordinates as before; and let us sup- 

 pose, for the sake of simplicity, and to avoid his tJiird ray, 

 that the normal displacements vanish. Then his fundamental 

 equations take the form 



cU 



I = S^-Ar, + SAA?, 



where /, g, h are quantities depending on the law of force 

 and the mutual distances of the molecules.* If, therefore. 



* 1 have not thought it necessary to transcribe the original equations of M. 

 Cauchy, which are rather long. He has presented them in different forms ; but the 

 system marked (16) at the end of § 1 of his Memoir on Dispersion, already quoted, 

 is the most convenient, and it is the one which I have here used. The directions 

 of the coordinates being arbilrary, I have supposed the axis of z to be perpendicu- 

 lar to the wave-plane. Then, on putting ? = 0, A ? = 0, in order to get rid of 

 the normal vibration, the last equation of the system becomes useless, and the other 

 two are reduced to the equations (2), given above ; the letters/, g, h, being writ- 

 ten in place of certain functions depending on the mutual actions of the molecules. 

 It will be proved, further on, that this simplification does not at all affect the argu- 

 ment. As the directions of x and y still remain arbitrary, I have made them pa- 

 rallel to the axes of the supposed elliptic vibration. 



It may be right to observe, for the sake of clearness, that, when the medium is 

 arranged symmetrically, it is always possible to take the directions of ^ and y such 

 that the two sums depending on the quantity A may disappear from the equations 

 (2), and then the vibrations are rectilinear. But when the arrangement is unsym- 

 metrical, this is no longer possible. 



The equations (2) are precisely the same as those which have been employed 

 by Mr. Tovey and by Professor Powell, the latter of whom, in his lately published 

 work, entitled, "A General and Elementary View of the Undulatory Theory, as ap- 

 plied to the Dispersion of Light, and other Subjects," has dwelt at great length on 

 the theory of elliptic polarization, which they have been supposed to afford, and 

 which he regards as a most important accession to the Science of Light. Professor 

 Powell has also made some communications on the subject to the British Asso- 



