2 $6 Dr. Brewster on the laws of polarisation , &c. 
Malus concluded that arragonite and sulphate of barytes were 
crystals with one axis, whereas they have both two axes, 
and, by M. Biot's mode of observation, he concluded that 
sulphate of lime , arragonite , topaz, sulphate of barytes , sulphate 
of strontian, and feldspar,' had only one axis, whereas they 
have all two distinct axes of double refraction. 
The method of observation which I have always employed, 
consists in observing the system of coloured rings which are 
seen along the axes of crystals with one axis, and along 
the resultant axes of crystals with two axes. These rings 
I first discovered in mica and topaz, about the end of the 
year 1812, and early in 1813 I discovered in beryl and 
several other minerals with one axis, the system of rings 
peculiar to crystals of that class. Dr. Wollaston discovered 
the same system of rings in calcareous spar in 1814; and 
long after this discovery was made, M. Biot examined the 
phenomenon, and showed by measuring the diameters of the 
rings that in this crystal the variation of the tints was 
expressed by Sin.*<p. By similar measurements of the 
rings in zircon , ice, beryl, emerald, sapphire , ruby, rubellite , 
tourmaline, apatite, vesuvian, mellite, nepheline, muriate of lime, 
muriate of strontian , arseniate of copper, I have found that 
the expression Sin. *<p applies within the limits of the error 
of experiments to all these crystals, which, excepting 
hydrate of magnesia and quartz, are the only crystals known 
to have but one axis of double refraction. I therefore con- 
sider myself as entitled to set out with this formula, as an 
expression of the tints for all crystals with one axis, whether 
their action is of a positive or a negative character. 
In proceeding to explain the general law which 1 have 
discovered for determining the tints in crystals with any 
