Royal Irish Academy. 493 
and the corresponding angle of incidence being given by the formula 
aie aay, 
5 Bria: , where «= 5 (M+). 
e+ Vf 2#2—1 M 
Since p + + cannot be less than 2, it is easy to see that, when 
i 
sint = 
there is a minimum, M+> cannot be less than 4, and therefore 
M cannot be less than 2 + 7 3, or 3°732. 
As an example, let M -+ = 6. Then, at a perpendicular in- 
cidence, one-half the incident light will be reflected. The minimum 
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 (Treatise on Light, Art. 594) 
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 (Comptes 
Rendus, tom. viii. p. 964), it follows from his theory that the most 
reflected 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 4, 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, vol. i. p. 2), 
two suppositions relative to the value of the refractive index presented 
themselves. Putting M for the modulus, and yx for the characteristic, 
I had to choose between the values M cos x and The latter 
cos 
value is that which I adopted; the former, which is M. Cauchy’s, 
was rejected because I saw that it would lead to the result above 
mentioned. 
Another result of M. Cauchy’s, which he has given twice in the 
Comptes Rendus (tom. ii. p. 428, and tom. vili. p. 965), requires to 
be noticed. When a polarized ray is reflected by a metal, the phase 
of its vibration is altered, and if the incidence be oblique, the 
change of phase is different, according as the light is polarized in 
the plane of incidence, or in the perpendicular plane. But when the 
ray is reflected at a perpendicular incidence, it is manifest that the 
change is a constant quantity, whatever be the plane of polarization. 
