234 Da Brewster ow the laws of polarisation , 
On the general law of the tints for all crystals with one 
or more axes. 
When a crystal has one axis of double refraction, the 
tints are disposed on the surface of the sphere, in regular 
concentric circles around the real or resultant axes of the 
crystal; and the intensity of the tint at any point of the sphe- 
rical surface, is equal to Sin.*<p, <p being the distance of the 
point from the pole of the axis, and the maximum tint in 
the equator of double refraction being considered as unity. 
This value of the tint was deduced by M. Biot, from expe- 
riments on sulphate of lime, rock crystal, Iceland spar, and 
some specimens of mica, before he was acquainted with the 
discovery of the system of concentric rings; but it was 
obviously not entitled to any confidence as a general prin- 
ciple, not only from its having been deduced from such a 
small number of crystals, but from its not representing the 
phenomena in the very crystals from which it was deduced. 
In sulphate of lime, for example, Sin. 2 <p is every where erro- 
neous as the value of the tints. This error indeed is very small 
in particular azimuths when the distance of the tint from the 
pole, of what M. Biot calls the axis, exceeds 30°, but in other 
azimuths, such as that of 90°, the error is enormous, and in 
the great circle passing through the plane of the laminae, the 
phenomena have no connection whatever, with this law. 
M. Biot himself perceived the utter incompetency of the 
expression Sin.*<p to represent the phenomena in the vertical 
azimuths, and has expressed the aberrations which he ob- 
served in these directions by complicated empirical formulae. 
These formulae, however, though they represent M. Biot’s? 
