88 Mr. Whewell on calculating 
crystal is represented by a symbol indicative of the laws 
from which it results ; the symbol, by varying the indices 
only, may be made to represent any law whatever: and by 
means of these indices, and of the primary angles of the 
substance, we obtain a general formula, expressing the 
dihedral angle contained between any one plane resulting from 
crystalline laws, and any other. In the same manner we can 
find the angle contained between any two edges of the derived 
crystal. Conversely, knowing the plane or dihedral angles 
of any crystal, and its primary form, we can by a direct and 
general process deduce the laws of decrement according to 
which it is constituted. The same formula are capable of 
being applied to the investigation of a great variety of pro- 
perties of crystals of various kinds, as will be shown in the 
sequel. We shall begin with the consideration of the rhom- 
boid, and the figures deduced from it ; and we shall after- 
wards proceed to other primary forms. 
§ 1 . The Rhomboid. 
2. Let there be a rhomboid, A a, Fig. i . divided into a num- 
ber of small equal rhomboids by planes parallel to its faces. 
Let any one of the points of division of each of its three upper 
edges be taken, as P, Q, R ; and let a plane pass through these 
three points P, Q,R. Let the small rhomboids which are above 
this plane be removed, so as to leave a uniform assemblage 
of cavities. Then, the remaining surface P Q R, being com- 
posed of the trihedral angles of small rhomboids, if we. sup- 
pose the small rhomboids to become smaller than the least 
distinguishable magnitude, the surface P Q R will appear a 
plane. And if we suppose these rhomboids to represent the 
