92 
DR. BREWSTER ON THE DOUBLE REFRACTION PRODUCED 
cules is greater than along A and B, the compression which it produces will 
exceed the dilatation arising from A and B, and we shall have an axis of com- 
pression along C, or an axis of positive double refraction as in quartz and di- 
optase*. The same observations are applicable to minerals that crystallize in 
the pyramidal form. 
When the three axes A, B, C are all equal, the three rectangular compres- 
sions, produced by the aggregation of the molecules, will destroy one another 
at every point of the molecule, and the body which they compose will have no 
double refraction, and cleavages of equal facility. Hence all crystals in which 
it is known by cleavage that the particles cohere with equal force in three rect- 
angular directions have actually no double refraction. 
If the three attractive axes A, B, C are all unequal, the difference of density 
which they produce in the molecules will be related to two axes of double re- 
fraction, the strongest of which will be negative or positive according as the 
compression along C is less or greater than the dilatation produced along C 
by the united compressions of A and B. Hence all crystals belonging to the 
prismatic system, in which we are informed by cleavage that the particles co- 
here with unequal forces in three directions, have invariably two, or, as we have 
al ready explained, three unequal axes of double refraction, of which the strong- 
est is sometimes positive and sometimes negative. 
We have supposed the elementary molecules of bodies to be spherical when 
existing singly, or beyond the sphere of their mutual action ; but although 
their form must, in the case of doubly refracting crystals, be changed into 
oblate, prolate or compound spheroids, yet the deviation of these spheroids 
from the sphere may be so small, that the forms of the bodies which they com- 
pose may be regarded as arising from the union of spherical molecules. It is 
more probable, however, that the form of the molecules suffers a considerable 
change, and we may consider that change as determining the exact primitive 
form of the crystal and the inclination of its planes. 
The circumstance of almost all rhombohedral crystals having negative 
' Since this paper was written, I have seen the very valuable researches of M. Savart on the 
structure of crystallized bodies as developed by sonorous vibrations. The curious result of his ex- 
periments, that the axis of calcareous spar, a negative axis of double refraction, is the axis of least 
elasticity, while the axis of quartz, an axis of positive double refraction, is the axis of greatest elasti- 
city, harmonizes in a remarkable manner with the above views. 
