q$ 6 Dr. Brewster on the laws of polarisation , &c. 
This remark, however, is by no means an explanation of 
the fact. It is merely a different mode of expressing the 
fact, that the cubical and octohedral crystals have no double 
refraction; for the sphere is applicable to the optical action 
of air and all other fluids, whether aeriform or liquid, which 
have not the property of double refraction. 
The discovery of the remains of polarising axes in a great 
number of crystals of this class, completely proves that, 
like all other crystallized bodies, they actually possess the 
doubly refracting and polarising structure, but that this 
structure entirely vanishes in some specimens, by the equi- 
librium of the forces in every point of the crystal, and 
reappears in some specimens when that equilibrium is not 
complete. 
The principles of the resolution of polarising forces which 
we have already explained, indicate the manner in which this 
equilibrium is effected. Three equal and rectangular axes, 
either all of the negative, or all of the positive character, will 
produce a perfect equilibrium, or mutually destroy each other 
at every point of the crystal ; for since two equal positive 
axes are equivalent to one negative axis, of the same inten- 
sity as either of the two; and since this negative axis will be 
balanced by an equal positive axis coincident with it, it follows, 
that the three rectangular positive axes will be in equilibrio. 
In perfect crystals of this class where all the axes are equal, 
and their position exactly rectangular, the equilibrium of the 
forces is complete; but if the axes are not equal, or their 
position not accurately rectangular, the phenomena of one 
or more axes will be developed. If one axis, for example, is 
weaker than the other., then the result will be the appearance 
