It is not every crystallized substance, however, that admits of this mechanical analysis. But with regard to those that have hitherto refused it, Hauy has re marked, that their surface striated in a certain direction, or the relation subsist ing among the different secondary forms of the same substance, afford indications which lead to the determination, with at least much probability, of their primitive forms.
Such is the process, by which Hauy es tablishes what he names the " Primitive Form of Crystals," and which he defines, "A solid of a constant furrh, inserted symmetrically in all the crystals of the same species, and the faces of which ob serve the directions of the layers which compose these crystals." The primitive forms hitherto observed are reducible to six ; the parallelopipedon, which in cludes the cube ; the rhomb, and all the solids which are terminated by six faces parallel two and two ; the tetraedron ; the octaedron ; the regular hexaedral prism ; the dodecaedron, with equal and similar rhomboidal planes ; and the dode caedron with triangular planes.
carries the division of crystals still further, however, than the primitive forms. The solid which constitutes it is not the last term of the mechanical ana lysis ; it may always be still further sub divided parallel to its different, faces, and sometimes even in other directions. All the enveloping matter is equally divisible by sections parallel to the faces of the primitive forms : and the only limit to this possible division is that placed by the composition of the substance. The cal careous spar, to take it as an example, • may be reduced to a particle, beyond which the division cannot be carried, without resolving it into its elements, lime and carbonic acid ; or at least it may be reduced to a particle, beyond which, if its minuteness allowed us to operate upon it, it is demonstrable its figure would not change. To these last parti cles, the result of the mechanical ana lysis, Hauy gives the name of integrant particles, and their union constitutes the crystal. Their forms, so far as experi ment has been carried, are three : the tetraedron, the simplest of the pyramids ; the triangular prism, the simplest of prisms ; and the parallelopipedon, the simplest of solids, which have their faces parallel,. two and two. There is little doubt that it is between these that the at traction of cohesion is immediately ex erted.
The primitive forms, and the figures of the integrant particles, being determin ed, it remains to complete the theory of the structure of crystals, to skew by what arrangements the secondary forms, in other words, the actually existing crys tals, are produced.
The nucleus of the crystal is the sym metrical solid which constitutes its primi tive form, arising from the union of the integrant particles, either by their faces or their edges ; and the additional matter, which forms the crystal, consists of lay ers of these particles superadded to that nucleus, and arranged on its faces ; and to account for the formation of the crystal under a figure different from that of its primitive form, these layers, as they re cede from it, are supposed to decrease, in the space they occupy, from the regu lar abstraction of one or more ranges of the integrant particles. This decrease may take place in various modes ; and ac cording to these, different figures of crys tallization will be produced.
Thus, to take the simplest example, let us suppose the primitive form is a cube ; it is easy to conceive that on each of its six sides may be reared a series of decreasing layers, or laminx, composed entirely of cubical particles, each layer diminishing on each of its edges by one row of the minute cubes of which it consists. The laminx thus decreasing as they recede from the base on which they rest, until the apex consists of a single particle, it is obvious, that on each side of the cube a four-sided pyramid will be formed. Two of these are represented, (fig. 12.) A B C D, G B C G.
We shall thus have, then,- six four.' sided paramids, and of course 24 trian gles, such as A B C, B C E, C E G, &c. But since the decrease is uniform on all the sides, as from the line B C to A, and from the same line to E, it must also be uniform from A to E ; it is obvious, there fore, that the side A B C of the one py ramid will be found exactly in the same plane as the side B C E of the adjacent pyramid ; so that the entire surface of these will be the rhomb A B E C. The case must be tbe same with all the others. The 24 triangles will therefore be reduc-' ed to twelve rhombs, and the figure will be a dodecaedron, very remote from the primitive form. Now a crystal of this figure, and having. this primitive form, would be resolved into that form, merely' ' by cutting off the six solid angles, by sections, in the direction of the small diagonals of the sides, which go to the formation of these angles. We should thus successively uncover six squares, which will be the faces of the primitive cube.