176 TRANSACTIONS OF THE [aPR. 1,. 
laws for reflection which apply to the boundary surface between 
platinum and air are, of course, the laws to apply to the deter- 
mination of the amounts of polarization which ought to be 
caused by a single refraction at this boundary. 
The application of Fresnel’s laws of vitreous reflection requires, 
as has be seen, the determination of but one constant, the index 
of refraction, or the ratio of the velocities of propagation of light 
in the two media. Cauchy extended these laws so as to cover 
the case of metallic reflection by introducing another constant 
which he calls the co-efficient of extinction. The constant cor- 
responding to the index of refraction is, as in the case of trans- 
parent bodies, the tangent of the angle of maximum polariza- 
tion. The co-efficient of extinction is a constant depending upon 
the opacity of the body, and is found from the ratio between the 
amplitudes, after reflection, of two equal beams polarized re- 
spectively perpendicular and parallel to the plane of incidence, 
and reflected at the angle of maximum polarization. This ratio 
is evidently the tangent of the azimuth of re-established plane 
polarization, when the incident beam is polarized ina plane mak- 
ing an angle of 45° with the plane of incidence, plane polariza- 
tion being re-established after reflection by means of a quarter- 
wave plate or a Babinet compensator. 
This angle may be determined by experiment. Thus the two 
constants of metallic reflection are, 1, the angle of maximum 
polarization, and 2, the azimuth of re-established plane polari- 
zation at this angle. According to the theory of Cauchy, these 
two constants being known, the intensity of a beam reflected at 
any angle may be calculated. 
The complete explanation of Cauchy’ s theory and the deduc- 
tion of Cauchy’s formule were given by Hisenlohrin 1858. (see. 
Pogg. Ann. 104, p. 368). 
The final forms of the formule given by piceutoun are 
= tam (fA) KP tana gd 
in which K®? is the intensity of the reflected beam when the in- 
cident beam is polarized in the plane of incidence, A’? the 
intensity when the incident beam is polarized in the plane per- 
pendicular to the plane of incidence, and f and g are variables. 
given by the equations 
0 
cot f=cos (e + u) sin (2 arctan — a ) ] ie 
cos a 
cot g=cos (e — wu) sin (2 arctan — 6 -) 
