CRYSTALLOGRAPHY. Hauy has succeeded in developing the theory of crystals, so far as to shew, that in every crystallized substance, whatever may be the difference of figure which may arise from modifying circumstances, there is in all its crystals a primitive the nu cleus, as it were, of the crystal, invaria ble in each substance, and by various mo difications, which he points out, giving rise to the numerous secondary or actual ly existing forms.
The fact which led to these views is, that crystals can be mechanically divided only in certain directions, so as to afford smooth surfaces, a fact long known by those who work on the gems. Suppose we have a crystal of calcareous spar, a regular hexaedral prism, represented in plate crystallography, fig. 5 and 6, if we endeavour to divide it parallel to the edges which form the outlines of the basis of the prism, we shall find that three of these edges, taken alternately, are the upper extremity of the edges I f, d c, b rn, readily yield to this division by a knife struck in the proper direction ; but that the other three, those which are interme diate,/ d, c b, and m 1, cannot be divided in a similar manner : and if broken by a greater force, the fracture, instead of be ing polished like the others, is rugged and uneven. If we repeat the experi ments at the under extremity of the prism, we shall find here, also, that seg ments of three only of the edges can be detached ; but these edges, instead of be ing the corresponding one with those di visable at the upper extremity, that is, 1 f, c d, b m, are the intermediate ones f d, c d, b m, are the intermediate ones df, c b, and m I.
The six divisions compose so many trapeziums. Three of these are repre sented in fig. 6. namely, the two which cut off the edges, / f, c d, represented by the dotted lines p p, o o and a a, k k, and that which cuts off the inferior edge df, and which is marked by the dotted lines Each of these trapeziums will have a smoothness and lustre, from which it can be perceived that it coincides with one of the natural joinings, the assemblage of which form the prism. The prism can not be divided in any other directions than these. But if the division be con tinued parallel to the first segments, it necessarily happens, that on one hand the surfaces of the bases of the prism be come narrower, and that on the other hand the heights of the sides diminish : and at the point at which, continuing the section, the bases disappear, the prism will be changed into a dodecaedron, with pentagonal faces (fig. 7) ; six of which, o o i e,oIkii, &c. are the re mains of the sides of the prism, and the other six, EAIo 0, 0 A, K &c. are the immediate results of the mechanical divi sion.
In this, and the two succeeding figures, the hexaedral prism, which circumscribes the solid extracted from it in the division, is still represented, to shew better the progress of the operation.
Beyond this point, the planes at the extremity preserve their figure and di mensions, while the lateral planes conti nue to diminish in height, until the points o, k of the pentagon o Ikii coin ciding with tile points i, i, and also the other points similarly situated having a like coincidence, each pentagon is reduc ed to a simple triangle, as is represented in fig. 8.
Lastly, by continuing the section the triangles are made to disappear, so that there remains no vestige of the surface of the original prism ; but in place of it we have the obtuse rhomboid E A 1 0 (fig. 9), which is therefore the nucleus, or primitive form.
This discovery of the method of divid ing a crystal was made by Hauy, in examining a crystal of calcareous spar which had been detached from a group of which it formed a part. He observed that the fracture had happened at one of the edges of the base of the prism, and that its surface was perfectly smooth and regular. Attempting to detach a seg ment in a similar direction from the con tiguous edge, he could not succeed, but the one next to it was easily divided ; and proceeding in this manner, lie was able to effect the mechanical division of the crystal in the manner already explained. Struck with the important result of the experiment, he applied the same method to other crystalline forms of the same substance, and obtained from them the same result ; the crystal, whatever was its figure, being by this mechanical divi sion converted into a rhomb. Thus, in the dodecaedron, composed of two six sided pyramids joined by the base, the primitive form may be obtained at once by making is first section, on the edges E 0, 0 I, fig. 10; a second, on the edges I K, G K ; a third, on G H, E ; a fourth, on 0 1,1K; a fifth, on G K, G H; and lastly, a sixth, on E H, E 0 ; and the re sult is, that these edges become the same with the lateral edges of the primitive form, as may be perceived from mere in spection of fig. 11, which represents this primitive form described in the dodecae dron. He then applied it to other crys talline substances, and found, that from these also, by discovering the joints by which the lamina composing the' crys tals were united, a certain primitive form might be extracted. That of fluor spar is an octaedron ; and that of the heavy spar, a prism with rhomboidal bases ; of corun dum, a rhomboid somewhat acute ; of beryl, a hexaedral prism ; and of the elba iron-ore, a cube. Each of these forms is constant with regard to the species, and is that from which all the -forms of the varieties, often extremely numerous, are derived. The latter are denominated, by Hauy, secondary forms. Sometimes, though rarely, the primitive and secon dary forms are the same.