Dr. Brewster on the laws of polarisation, &c. 261 
T, is counteracted at m in every part of the line MN, by the 
action of the axes at A, &c. perpendicular to the plate, the in- 
tensity of the perpendicular axis at the distance A m— D, will 
also be equal to T. Hence, in order to find the tint t produced 
by this perpendicular axis at any other distance A c—d, 
we have t = r -^- by the law for one axis; but as this tint 
is counteracted by the tint T produced at c by the axis in 
the plane of the laminee, we have the resulting tint or 
t =5 T — "jpr- •* Here the law is very simple, and the tints are 
all disposed in straight lines, in consequence of the angle of the 
forces being 180°, and the number of the axes infinite. This 
case is precisely the same as that of regular crystals when the 
tints are calculated in the plane COD, PI. xv. fig. 4, by means 
of two axes at O and A, the effect of the axis A is the same 
at every point in the line COD, and therefore the resulting 
tint, at any point, is the uniform tint produced by A (which 
is the same as the tint at O) minus the tint produced by the 
axis O alone. The law of the progression of the tints there- 
fore in rectangular plates of glass, is exactly the same as in 
crystals with two axes ; and we have the same difficulty in 
determining whether the axes are of the same or of opposite 
names. 
The similarity between the various phenomena of the real 
* This formula is the same as that which I had deduced long ago from experi- 
ment. M. Biot had also obtained from observation the very same expression of the 
tints, and about the same time. The formula which I have employed was more 
general than that of M. Biot, as I had found the term D to be a function of the 
breadth of the plate. My formula was therefore t ~ T — B being the breadth 
of the plate; or if T is the maximum tint given by the plate, we have t — T- — Tggqjl * 
See Edinburgh Transactions, Vol. VIII. Art. XVIII. 
