142 
DR. BREWSTER ON THE LAWS OF 
lion and reflexion, it becomes a point of great importance to compare the re- 
sults which they furnish. Calling R the reflected light, these formulae become 
But these two quantities are exactly equal, and hence we obtain the important 
general law, that, — At the first surface of all bodies, and at all angles of inci- 
dence, the quantity of light polarized by refraction is equal to the quantity 
polarized by reflection. I have said ‘ of all bodies’, because the law is equally 
applicable to the surfaces of crystallized and metallic bodies, though the action 
of their first surface is masked or modified by other causes. 
It is obvious from the formula that there must be some angle of incidence 
where R = 1 — R, that is, where the reflected is equal to the transmitted 
light. When this takes place, we have sin 2 <p — cos 2 <p', that is, 
The reflected is equal to the transmitted light, when the inclination of the 
planes of polarization of the reflected pencil to the plane of reflection, is the 
complement of the inclination of the planes of polarization of the refracted 
pencil to the same plane ; — or if we refer the inclination of the planes to the 
two rectangular planes into which the planes of polarization are brought, — 
The reflected will be equal to the transmitted light when the inclination of the 
planes of polarization of the reflected pencil to the plane of reflection, is equal 
to the inclination of the plane of polarization of the refracted pencil to a plane 
perpendicular to the plane of reflection. 
In order to show the connection between the phenomena of the reflected 
and those of the transmitted light, I have given the following Table, which 
shows the inclination of the planes of polarization of the reflected and the re- 
fracted pencil, and the quantities of light reflected, transmitted, and polarized, 
at all angles of incidence upon glass, m being equal to 1.525, and the incident 
light = 1000. 
