40 



Sir J. Conroy. 



[Feb. 15, 



light be as r to 1. Then it will be easily seen that the theoretical 

 intensity for common light reflected first from the metal, and then 

 from the paper, as determined by the method of the paper, will be 

 (rJ 2 + I 2 )/(r + l) instead of £ (J 2 +I 3 ). The former exceeds the latter 

 by- 



0'— i)(J 2 — i 2 ) 



2(r+l) ' 



which is positive, since r is a little greater than 1, and J 2 is greater 

 than I 2 . This excess is very small, but as far as it goes it tends rather 

 to increase, on the whole, the difference between theory and observa- 

 tion, since the observed intensity nearly always falls short of the 

 calculated. 



The imperfection of the polish in the case of such soft metals as 

 silver and tin has, doubtless, much to do with it. But the polish of 

 the steel seems to have been practically perfect, and yet this metal 

 showed discrepancies, though not so great. 



But I think there are strong reasons for believing that the ordinarily 

 received formulae for metals can only give a more or less approximate 

 result. 



MacCullagh was the first to show that by substituting for the 

 refractive index in Fresnel's f ormulae a complex imaginary, and then 

 interpreting the formulae as Eresnel has done in a somewhat analo- 

 gous case, results were obtained agreeing, at any rate approximately, 

 with those deduced from, observation. Cauchy afterwards gave 

 formulae substantially the same, as they differ only in algebraic- 

 development, but made an important advance in the physical theory 

 by connecting the coefficient of V — 1 in the complex imaginary with 

 an intense absorbing action of the medium. 



But metals are not the only bodies to which the formulae of 

 Fresnel do not apply. More than fifty years ago Sir George Airy 

 showed that in the case of diamond a considerable quantity of light 

 polarised perpendicularly to the plane of incidence was reflected at 

 the angle which made the nearest approach to a polarising angle ; and 

 that on increasing the angle of incidence through the angle of 

 maximum polarisation there was a rapid retardation of phase. 

 Similar phenomena were afterwards observed in other transparent 

 substances of high refractive index, and more recently M. Jamin has 

 observed them in transparent substances in general with a few 

 exceptions . 



The effect increases on the whole with the refractive index of the 

 substance, but not in such a manner as to allow us to suppose that it 

 is a function of the refractive index. Hence two independent con- 

 stants are required to define for a given kind of homogeneous light 

 the optical character of a transparent substance. 



