512 NOTES TO BOOK IX. 



points of reflection were dry, the light was not circularly 

 polarized ; when two points were wet, the light was cir- 

 cularly polarized ; and when all four were wet, it was 

 not circularly polarized. 



(OA.) p. 501. In the Report on Physical Optics, 

 (Brit. Ass. Reports ] 834,) by Prof. Lloyd, the progress of 

 the mathematical theory after FresneFs labours is stated 

 more distinctly than I have stated it, to the following 

 effect. Ampere, in 1828, proved FresueFs mathematical 

 results directly, which Fresnel had only proved indirectly, 

 and derived from his proof Fresnel's beautiful geometri- 

 cal construction. Prof. MacCullagh not long after gave 

 a concise demonstration of the same theorem, and of the 

 other principal points of FresneFs theory. He represents 

 the elastic force by means of an ellipsoid whose axes are 

 inversely proportional to those of FresneFs generating 

 ellipsoid, and deduces Fresnel's construction geometrically. 

 In the third Supplement to his Essay on the Tlieory of 

 Systems of Rays, (Trans. R. I. Acad. vol. xvn.) Sir W. 

 Hamilton has presented that portion of FresneFs theory 

 which relates to the fundamental problem of the determi- 

 nation of the velocity and polarization of a plane wave, in 

 a very elegant and analytical form. This he does by means 

 of what he calls the characteristic function of the optical 

 system to which the problem belongs. From this func- 

 tion is deduced the surface of wave-slowness of the medium; 

 and by means of this surface, the direction of the rays 

 refracted into the medium. From this construction also 

 Sir W. Hamilton was led to the anticipation of conical 

 refraction, mentioned in the text. 



The investigations of MM. Cauchy and Lame refer 

 to the laws by which the particles of the ether act upon 



