Applications of the Problem.

§ 1. The morphologic properties of crystals, that is to say, their outer forms and their structural planes, whether the latter are of cleavage, of twinning, of enclosures, or of alteration, are among their most important properties. They are, in fact, the only ones by which we can recognize complete pseudomorphs. They are also of great help to the petrographer in determining minerals, for the habits of minerals are so constant and the important planes so few that we may often pretty surely recognize them, either from external forms, or from cleavage, etc. Yet our assurance is often not so great but that we should welcome tests of the correctness of our assumptions, which would give them objective as well as subjective validity.

I wish to show how such tests may be applied; and I shall illustrate the more general cases by applications to one . . .

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