NEUMANN ON ESTIMATING THE INTENSITY OF LIGHT. 403 
which depends upon the relative intensities of the two beams. A 
measurement of the angle, or the azimuth of the resulting plane of 
polarization, thus enables us to estimate the relative intensity of 
the two rays. A second kind of reciprocal action of two rays of 
light consists in their interference, which is applied to photometric 
purposes in such a manner, that one ray is kept half an undula- 
tion behind the other, and this is diminished in intensity by the 
usual method until it completely destroys the other, whereby 
the equality of the two rays is very accurately ascertained, and 
hence, as the proportion in which one ray is diminished com- 
paratively to the other is known, the original relation of their 
intensities may be deduced. 
A ray of polarized light is allowed to fall upon a perfectly 
transparent medium; this I decompose into two others, one of 
which is polarized in a direction parallel to the plane of inci- 
dence, the other perpendicular to it; their amplitudes may be S$ 
and P. In this case the reflected ‘and refracted light are likewise 
polarized, and the amplitudes of the former in the two compo- 
nent beams, which are polarized in directions parallel and per- 
pendicular to the plane of incidence, may be R, and R,, but in 
the refracted light the intensities of the two component rays will 
be D,? and D,?. Supposing the medium to be completely trans- 
parent, we obtain the following proportion for the amplitudes 
SP, \R,: 
S?+ P?=R,? + R,? + D,? + D,”. 
Experiment has however shown, that R, and D, disappear at 
the same time as S, and that the same occurs with P and R,, 
D,, hence this proportion resolves itself into two others, 
Ss? = R?.+ D? 
eR ee ol be 
These two equations would be caer for ascertaining the four 
unknown quantities R,, R,, D,, D,, if the proportions of any 
two were known, as R, : R, or D, : D,. This proportion how- 
ever is obtained by observing the angle formed by the plane 
of polarization of the reflected and refracted light with the plane 
of incidence. Brewster made so many observations of this angle 
as to enable him to deduce the following two laws: 
R, _cos(¢+¢)P. Dy, _ ] P 
R,  cos(¢—9/)S° D, ~ cos (¢— 9/) S” 
in these $ represents the angle of incidence, and ¢! the angle of 
refraction. These, transferred to the above equations, give 
