OF ELLIPTIC POLARIZATION. 
319 
maximum at intermediate points. These points of maximum intensity do not 
bisect the loops, or are not equidistant from the minima 1, 2, &c. ; but such is 
their relation to them, that the maximum for n reflexions is the minimum for 
2 n reflexions corresponding to the same angle. Thus the maximum for one 
reflexion, viz. 73°, is the minimum for two reflexions ; and the maxima for 
two reflexions, viz. 82° 30' and 63° 43', are the minima for four reflexions. 
The maximum may be found directly by computing the angle of incidence, 
which corresponds to a phase intermediate between the two minima, within 
which the maximum lies. 
Having thus determined the various points of the quadrant, at which elliptic 
polarization is produced, and at which it is destroyed, after any number of 
reflexions ; and also the position of the plane of the restored ray, I shall proceed 
to investigate the cause of those brilliant complementary colours which accom- 
pany these phenomena. 
As all transparent bodies have different values of their maximum polarizing 
angle, appropriate to the index of refraction for each colour of the spectrum, 
it is reasonable to suppose that as elliptic polarization is effected at the maxi- 
mum polarizing angle, this angle would vary for the differently coloured rays. 
That this is the case may be easily proved by observing the angles of restora- 
tion for homogeneous light after two reflexions. In silver the difference of 
the angles for red and blue light is about 5° in the sun’s rays ; so that calling 
7 3° the maximum polarizing angle for the mean yellow ray, the angle will be 
70 ^° for blue, and 7H° for red light. Hence if we examine a pencil of white 
light twice reflected at 70 ^-°, and place the principal section of the analysing 
prism in the plane —39° 48 f , the blue rays will disappear and the red will 
remain visible. In like manner, at an angle of 73° 30' the red will disappear, 
and the complementary blue will be visible ; while at an angle of 73° the yellow 
will disappear and red and blue will be seen together, one on each side of the 
place where the yellow has vanished. At angles of incidence greater than 7^\° 
and less than 70 ^°, and also at intermediate angles, the blue or the red wil 
still predominate in the pencil, the blue being in excess at all angles greater 
than 73°, and the red in excess at all angles less than 73°. Such are precisely 
the phenomena which take place, as will appear from the following Table. 
2 T 
MDCCCXXX. 
