214 Hr. Brewster on the laws of polarisation, &c. 
In order to apply it however with the utmost simplicity, I 
have found it very convenient to consider every crystal as 
cut into a sphere, one of whose diameters is the axis of double 
refraction, and to suppose that the polarised ray passes 
through the centre of the sphere By this means we have 
no occasion to consider the refractive power of the crystal, 
or the difference of thickness arising from oblique transmis- 
sion ; for the polarised ray is always incident perpendicularly, 
and the thickness of the sphere is every where the same. If 
in this sphere, AB, fig. 3. is the axis of the system of rings, 
then P p may be called the diameter of no polarisation, or the ap- 
parent axi of double refraction and polarisation ; P a nd p the poles 
of no polarisation ; COD, the equator of maximum polarisation , 
and EF the isochromatic lines or curves of equal tint. Now, since 
the tint varies as the square of the sine of the angle which 
the transmitted ray forms with the axis Pp, it will be a maxi- 
mum in every point of the equator COD, and will be repre- 
sented by Sin 2 . 90°. Hence if be the angle which any other 
diameter EO forms with the axis, the tint at E, and at every 
point of the parallel EF, will be represented by Sin. a <p. By 
determining therefore experimentally the tint t, produced at 
any given thickness B, and at any inclination the maximum 
tint Th for that thickness, will be T — arid the tint for 
any other thickness b will be T = ~ x ---■ . It is obvious 
from these formulae,, that any given tint can be developed at 
any angle or distance from the axis, merely by varying the 
thickness of the crystal or the diameter of the sphere. 
If it should be required to find the tints corresponding to 
any angle of incidence upon the natural faces of the crystal. 
