213 
Dr. Brewster on the laws of polarisation, &c. 
fig*, i.* Let the rhomboid ABCD be now cut into two plates, 
by any line MN, and let the rings, produced by each of the 
plates, be examined separately in the way already described: 
it will then be found that the squares of the diameters of the 
rings are in every case proportional to the numbers which 
represent the corresponding tints in Newton’s table ; and 
that the squares of the diameters of similar rings, as pro- 
duced by plates of different thicknesses, are reciprocally 
proportional to the square roots of these thicknesses. These 
two results, which were first obtained by M. Biot, lead to 
the general conclusion that the tints produced at different 
inclinations to the axis of the crystal, are to one another, as 
the square of the sine of the angle which the polarised ray 
forms with that axis. This l^w of the tints for crystals with 
one axis, was deduced by M. Biot from the action of rock 
crystal, as well as calcareous spar ; and also from the phe- 
nomena of certain specimens of mica which he supposes to 
have one axis. I have found it perfectly correct in all the 
other crystals contained in the table ; and it may therefore 
be considered as a general law, which we may apply with 
confidence in our future researches. 
* The system of coloured rings produced by one axis of double refraction, and the 
still more beautiful and complicated system produced by two axes, were discovered 
by me in the year 1813. I observed the former in beryl, emerald, ruby, 8c c. and the 
latter in topaz, mica, and a great variety of other minerals. Dr. Wollaston was the 
first who detected the circular system of rings in Iceland spar, and they were shown 
to me by that eminent philosopher in July 1814. In a letter dated Dec. 3, 1815, 
M. Biot announced to me, that he had then discovered the circular rings in Iceland 
spar, and it appears that the same observation was made by M. Seebeck, in Dec. 
1815; these dates, however, are nearly a year and a half posterior to that of Dr. 
Wollaston’s experiment. 
