322 
DR. BREWSTER ON THE PHENOMENA AND LAWS 
and the rapidity of their changes. In order to investigate the nature of these 
variations, let us consider what will take place at 2, 4, 6, 8, and 10 reflexions 
from silver in the loops above and adjacent to 73° the maximum polarizing 
angle. The following are the numbers which regulate the phenomena. 
Fig. 6. 
No. of the 
Reflexions. 
Nature of the Reflexions. 
Limits of the Loops. 
Length of 
the Loops. 
Inclination of 
the Plane, or <p. 
a b 
. 2 . 
First of the series 
. 73 
— 90 0 . 
O t 
17 0 
O ! 
. 39 48 
cd 
. 4 . 
First of the series 
. 73 
— 82 30 . 
9 30 
. 37 22 
e f 
. 6 . 
Multiple of 3 . . 
• 73 
— 79 40 . 
6 40 
. 32 25 
" h 
O 
. 8 . 
Multiple of 2§ 
. 73 
— 78 8 . 
5 8 
. 27 53 
m n 
. 10 . 
Multiple of 2^ . 
. 73 
— 77 13 . 
4 13 
. 24 16 
This Table may be illustrated by the annexed diagram, where A B passes 
through the incidence of 90°, and C D through A g 3 
that of 73°, the points m, g, e , c, a corresponding A 
respectively with the incidences of 77° 13', 78° 8', II 
79° 40', and 82° 30', or those at which the ray is 
restored by 1 0, 8, 6, and 4 reflexions. The curvi- 
lineal spaces a b, c d, e f, g h, and m n, are the 
loops already referred to, whose breadths repre- 
sent the intensity of the extraordinary ray, which 
is a minimum at the nodes a , c, e,g, m, and b, d,f, 
//, ??, and reaches its maximum near the middle of the loops. 
If the image reflected from the silver is a circular disc of white light of a 
given magnitude, then by two reflexions at 73°, or at the point b the extraordi- 
nary image will be red above and blue below, when the principal section of the 
analysing prism is in the plane — 39° 48' ; but these colours will be very faint, 
as the disc occupies but a small part of the loop a b. The disc indeed may be 
made so small, that the extraordinary image will entirely disappear in this loop. 
In this case the ordinary image will be white, as all the reflected light will pass 
into it. At four reflexions the loop c d is little more than one half of a b, and 
consequently the light will vary much more rapidly from d to the maximum. 
When the analysing prism has its principal section in the plane —37° 22', the 
extraordinary image at c will be coloured with red light above and blue below; 
and when it is in the plane -f 31° 52', the extraordinary image at d will be 
-s — r 
FD 
