136 
DR. BREWSTER ON THE LAWS OF 
low refractive power. I experienced great difficulty in this part of the inquiry, 
from the necessity of having plates without any crystalline structure. I tried 
gold leaf in a variety of ways ; but I found it almost impossible to obtain cor- 
rect results, on account of the light which was transmitted unchanged through 
its pores. 
By stretching a film of soapy water across a 
wire I obtained the following measure. 
Water. 
rectangular frame of copper 
Incidence. 
Inclination. 
Rotation. 
0 
CO 
. 54° 1 7' • • 
. . 9° 17' 
I next tried a thin plate of metalline glass of a 
Metalline Glass. 
very high refractive power. 
Incidence. 
Inclination. 
Rotation. 
0° . . 
. 45° 0' . . 
O 
o 
© 
20 . . 
. 45 42 . . 
0 42 
30 . . 
. 46 50 . . 
1 50 
40 . . 
o 
GO 
3 0 
55 . . 
. 51 12 . . 
6 12 
80 . . 
. 62 32 . . 
. . 17 32 
From a comparison of these results it is manifest that the rotation increases 
with the refractive power. 
In examining the effects produced at different angles of incidence, it becomes 
obvious that the rotation varies with the deviation of the refracted ray ; that is, 
with i — i' the difference of the angles of incidence and refraction. Hence from 
a consideration of the circumstances of the phenomena I have been led to 
express the inclination <p of the planes of polarization to the plane of refrac- 
tion by the formula, 
Cot <p = cos (i — «'), 
the rotation being = <p — 45°. 
This formula obviously gives a minimum at 0°, and a maximum at 90° ; 
and at intermediate points it represents the experiments so accurately, that 
when the rhomb of calcareous spar is set to the calculated angle of inclination, 
the extraordinary image is completely invisible, — a striking test of the correct- 
ness of the principle on which it is founded. 
The above expression is of course suited only to the case where the inclina- 
