266 Dr. Brewster on the laws of polarisation , &c. 
certain rate of variation in the density at which the polarising 
force will be proportional to the fourth power, or the varia- 
ble influence upon the tints to the square of the sine of the 
angle which the polarised ray forms with the axis. 
The preceding reasoning must not be considered as mere 
speculation, for such a crystal as that represented in fig. 14, 
may be actually constructed with plates of glass. Let ABCD, 
for example, represent in section, a circular plate of glass 
whose thickness is ML, and along whose axis MN, is seen 
the system of coloured rings shown in PI. xv. fig. 1. Then, if we 
conceive the plate bent back into the position a M be L d, we 
have the external spherical stratum of our elementary sphere; 
and in like manner we may conceive the interior strata to be 
formed by a succession of circular plates DEFC, See. bent 
into the spherical form dhcfKe. Now, since the tints of 
the circular plate ABCD vary as the squares of the distances 
from its axis ML, we may suppose that the same law still 
exists, after it, is bent into aMbchd. But the distances from 
the axis MN are now the sines of the angular distances from 
M ; and therefore, since the same is true of all the other 
spherical strata, of which the elementary sphere is composed, 
it follows that the tints produced by the transmission of 
polarised light, along any diameter of the sphere, are propor- 
tional to the square of the sine of the angle, which the ray 
forms with the axis of the crystal. In order to construct this 
sphere artificially, we have only to crystallize a series of 
hemispherical strata, and join them together at the line ah in 
the manner represented in the figure. This sphere, it will be 
readily seen, is totally different from a solid sphere of crys- 
tallized glass, which has no particular axis, but which gives. 
