202 Notes on some Points in the Theory of Light. 



a host of followers ; and even the extraordinary error, which it 

 is my more immediate object to expose, has been continually 

 gaining ground up to the very moment at which I write, and 

 has at last begun to be ranked among the elementary truths of 

 the undulatory theory of light. Notwithstanding my un- 

 willingness, therefore, to be at all concerned in such discus- 

 sions, I do not think myself at liberty to remain silent any 

 longer. 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 co-ordinates as before ; and let us sup- 

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

 that the normal displacements vanish. Then his fundamental 

 equations take the form 



r/ 2 



= S/A? + 



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

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



* I 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 co-ordinates being arbitrary, I have supposed the axis of z to be 

 perpendicular 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 written 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 argument. As the directions of x and y still remain arbitrary, I have 

 made them parallel 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 x and y such 

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

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

 metrical, this is no longer possible. 



