In the three oblique systems the axes are partly or altogether obliquely inclined to one another, while their magnitudes are unequal. Fig. 11 is a crystal of the monoclinic system, and Fig. 12 of the triclinic system. The names of the different oblique systems indicate the mutual inclinations of the axes. Fig. 13 represents a crystal of the hexagonal system, which is allied in symmetry to the dimetric system; but there are four lines of symmetry, of which the three A A', B B', and C C, lying in the

same horizon, are equal in their mutual inclination and magnitude, while the fourth axis, D D', is at right angles to these but different in magnitude.

The reader will now have formed a tolerably correct idea of a crystal, and when it is borne in mind that crystallization is a widely diffused and essential property of matter, and also that the solution of this question has engaged some of the ablest minds of the century, the high purpose and importance of this investigation will perhaps become evident to him.

Now, the invariability of certain relations existing between the axes and the planes bounding crystal forms are geometrically similar, and are effects produced by causes similar, Fig. 13. to those which occasion the constancy of the slopes in heaps of the same material. In the heap of gravel considered above, the horizon was chosen as the reference plane—in the crystal the planes containing the lines of symmetry are selected as reference planes, whereby to gauge the inclination of the bounding surfaces. From our considerations of the heap of gravel, the reader will perceive the intimate connection between outward form and internal structure, and is in a measure prepared to follow deductions made from the one upon the other. Already in the remote infancy of mineralogy assumptions as to the internal structure of crystals were made to explain the axial relations alluded to. The assumption that the internal structure of a crystal is similar to, and in a measure identical with, the internal structure of a cannon-ball pile, is sufficient to