OF ELLIPTIC POLARIZATION. 
323 
similarly coloured : The colours will be much brighter than in the case of 
two reflexions, and consequently the extraordinary image will not vanish. The 
consequence of this is, that the ordinary image is not white as before, but 
yellow, because a considerable portion of red and blue light are left in the ex- 
traordinary image. 
As the number of reflexions increase, and the loops ef,gh, &c. diminish, the 
disc will occupy a greater proportion of the whole loop, and the red and blue 
colours with which it is crossed grow brighter and brighter, and come closer 
and closer to their line of junction in the middle of the disc. Hence a greater 
quantity of red and blue light is left out of the ordinary image, which on this 
account becomes yellower and yellower, and at last of a greenish hue. 
In order to determine the position of the principal section of the analysing 
prism, when the extraordinary image is a minimum for any angle of incidence 
«, and any number of reflexions, let X — the inclinations of the plane of 
polarization of the restored ray at the nodes a, b ; m, n = the inclinations or 
values of <p in the formula tan <p — ^ ^ suited to the angles of incidence 
at the nodes ; x = the inclination <p suited to the incidence os. 
Now it is obvious that at the one node, the position of the principal section 
of the analysing prism, when the extraordinary image is a minimum, is + 
and that it gradually changes to 0° and then passes to — thus undergoing a 
change equal to while the inclination <p varies by a quantity equal to 
m — n. Hence calling I the inclination of the principal section to the plane 
+ 4 1 at the angle of incidence os, we have m — n : %|/ + x — m — x '• I- 
Hence 1 = 4' + % (^) 
When x — n, I = 
When * = Tn ^, | and I = t+*. 
2 5 m — n 2 2 
When the nodes of the loop are on different sides of the maximum polarizing 
angle, which happens only in the middle loop of 3, 5, 7, &c. reflexions, then 
m and n have opposite signs, and consequently their difference is m + n , and, 
( Tfl — x\ 
■ 2 ). 
It is impossible to determine the relative intensities of the ordinary and ex- 
