216 Notes on some Points in the Theory of Light. 

 there is a minimum, ^f+ cannot be less than 4, and therefore 



M cannot be less than 2 + A/3, or 3*732. 



As an example, let M + = 6. Then, at a perpendicular 



incidence, one-half the incident Ifght will be reflected. The 

 minirilum will be when i = 65 36', and at this angle only -^ of 

 the incident light will be reflected. The value here assumed 

 for the refractive index is that which Sir J. Herschel* assigns 

 to mercury ; but if my ideas be correct, it is far too low for that 

 metal. 



The only person who supposes that the refractive index of a 

 metal is not a large number is M. Cauchy, It has always 

 been held as a maxim in optics, that the higher the reflective 

 power of any substance, the higher also is its refractive index. 

 But M. Cauchy completely reverses this maxim ; for, as I have 

 elsewhere shown,f it follows from his theory that the most re- 

 flective metals are the least refractive, and even that the index 

 of refraction, which for transparent bodies is always greater 

 than unity, may for metals descend far below unity. Thus, 

 according to his formula, the index of refraction for pure silver 

 is the fraction 5, so that the dense body of the silver actually 

 plays the part of a very rare medium with respect to a vacuum. 

 It appears to me that such a result as this is quite sufficient to 

 overturn the theory from which it is derived. The formulas, 

 however, which he gives for the intensity of the reflected light, 

 are identical with the empirical expressions which I had given 

 long before, and are at least approximately true. 



In framing my own empirical theory,^ two suppositions re- 

 lative to the value of the refractive index presented themselves. 



Putting M for the modulus, and x % or the characteristic) I had to 



M 



choose between the values M cos Y and -. The latter value 



cos x 



is that which I adopted ; the former, which is M. Cauchy's, was 



* Treatise on Light, Art. 594. 



t Comptes Rendus, torn. viii. p. 964 ; vid. note at the end of this volume. 



^ See Proceedings, VOL. r. p. 2 (supra, p. 58). 



