3 
derived from the experiments of Sir David Brewster. But, 
in the absence of a real theory, it is important that we 
should be able to represent the phenomena by means of em- 
pirical formule ; and, accordingly, the author has endea- 
voured to obtain such formule by a method analogous to 
that which Fresnel employed in the case of total reflexion 
at the surface of a rarer medium, and which, as is well 
known, depends on a peculiar interpretation of the sign 
7 —1. For the case of metallic reflexion, the author as- 
sumes that the velocity of propagation in the metal, or the 
reciprocal of the refractive index, is of the form 
m(cos x + 7 —1sinx); 
without attaching to this form any physical signification, 
but using it rather as a means of introducing two constants 
(for there must be two constants, m and x, for each metal) 
into Fresnel’s formule for ordinary reflexion, which contain 
only one constant, namely, the refractive index. 
Then if i be the angle of incidence on the metal, and @’ the 
angle of refraction, we have 
sini’ = m(cosy + / —1sin) sini, (1) 
and therefore we may put 
cosi’= m' (cos x’— ¥ — sin’) cosé, (2) 
if m'! cos*i= 1—2m? cos2y sini + m' sin “2, (3) 
2 = 
ite tan2y’= m* sin2y sin ~% (4) 
1—m*cos2x sin * ” 
Now, first, if the incident light be polarized in the plane 
of reflexion, and if the preceding values of sin?,cosz, be 
substituted in Fresnel’s expression 
sin(¢—2’) 
sin(i+i)’ 
for the amplitude of the reflected vibration, the result may 
be reduced to the form it 
a(cosé— ¥ —Isin8), (5) 
B2 
