I(i2 



and the corresponding angle of incidence being given by tlie 

 formula 





sine = /- — -, where t 



=^G'+D- 



Since /n -\ — cannot be less than H, it is easy to see that, when 

 there is a niinimum, m H — cannot be less than 4, and there- 



M 



fore M cannot be less than 2 + Vs, or 3.732. 



As an example, let m + - = 6. Then, at a perpendicu- 

 lar incidence, one-half the incident light will be reflected. 

 The minimum will be when i=:65°36', and at this angle 

 only j^ of the incident light will be reflected. The value 

 here assumed for the refractive index is that which Sir J. 

 Herschel {Treatise on Liyht, Art. oOl), 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 (Comples Rendus, tom. viii. p. 964), it 

 follows from his theory that the most reflective 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 for- 

 mula, the index of refraction for pure silver is the fraction \, 

 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 (see Proceedings, 



