of Mineral Species of the Trimetric System. 39 
guide (except sometimes in hemihedral forms); but here it is 
uot needed, as the basal plane is fixed from the nature of the 
prism. The principle holds true for topaz and many trimetric 
species. In the rhombic octahedron of sulphur, in which either 
axis might be made the vertical, the apical angles, in which the 
true vertical axis terminates, are at once distinguished in modified 
crystals, by the cluster of planes about them. But the ambiguous 
cases are numerous, and this criterion, like others, is not an un- 
failing reliance. 
en we may succeed in fixing upon the vertical axis ina 
Species, and also the unit vertical prism, it is often difficult to 
determine which planes about the base should be taken as the 
unit domes or octahedron; and often there is a choice between 
two or three planes equal in lustre and size; and consequently 
it may be altogether doubtful whether the vertical axis equals la, 
24, or 3a. Crystallographers may take whichever is most con- 
venient without any important objection. But when looking to 
_ 6. Values and Relations of the Angles of Forms.—In the se- 
Nes of prisms in each axial direction, the vertical, macrodiagonal, 
and brachydiagonal, the planes, as is well known, have simple 
axial ratios, and the more common ratios are 1: LAB 
If but a single prism occur in either direction, it is easy to caleu- 
late the values of the angles of other prisms having the above 
Mentioned relations. This gives a series of angles. If, then, 
two species correspond nearly with one another in one element of 
Principle that can be laid down; or it may be halved in the same 
way. But we may with certainty determine whether forms are 
