In explaining the structure of a crystal, although the representation in the figure be such as to shew the decrease of the lamina, by rows of particles of such a size as to give a surface uneven, similar to a succession of steps, it is obvious, that if we substitute for this the delicate struc ture of nature, the number of lamina: may be so great, and the number of their cubical particles such, that the de pression or channel at their edges will be altogether imperceptible to our senses, and the surfaces will appear perfect planes.
Such is an example of the production of a secondary from a primitive form by a superposition of lamina, decreasing ac cording to a certain law. It is obvious that the laws of decrement may be vari ous, and accordingly the decrements sta ted by Hauy are of four different kinds : first, decrements on the edges, or paral lel to the sides of the primitive form, of which the above is an example. 2. De crements on the angles, that is, decre ments, of which the lines are parallel to the diagonals of the faces of the primi tive form. 3. Intermediate decrements, or those which are parallel to lines situ ated between the diagonals and edges of that form. 4. Mixed decrements, in which the number of ranges abstracted in breadth or in height give proportions, the two terms of which are beyond unity.
These four laws of decrement explain, by the modifications of which they are susceptible, all the varieties of form, un der which crystals are presented to us. These modifications are reduced to the following : 1. Sometimes the decrements take place on all the edges, or on all the angles. 2. Sometimes on certain edges or certain angles only. 3. Sometimes they are uniform by one, two, three ranges, or more. 4. Sometimes the law varies from one edge to another, or from one angle to another. 5. In some cases the decre ments on the edges correspond with the decrements on the angles. 6. Sometimes the same edge or the same angle under goes successively several laws of decre ments. And, lastly, there are cases, in which the secondary crystal has faces parallel to those of the primitive form, and which give rise to new modifications, from their combinations with the faces resulting from the decrements.
With such diversity of laws, the num ber of forms which may exist is immense, and far exceeds what have been observ ed. Confining the calculation to two of
the simplest laws, those which produce subtractions by one or two ranges, it is shewn that carbonate of lime is suscepti ble of 2044 different forms, a number 50 times greater than that of the forms al ready known ; and if decrements of three and four ranges be admitted into the combination, the calculation will give 8,388,604 possible forms of the same sub stance. And even this number may be much augmented, in consequence either of intermediate or mixed decrements be ing taken into account.
In concluding this sketch of Crystallo graphy, which we have extracted from the excellent " System of Chemistry" by Murray, we have also thought it proper, with him, to give the figures of the more usual forms of crystals, and their modifi cations, with the terms and definitions of Werner, instead of following Hauy in his minute, though valuable, It is necessary to premise, that the parts of which a crystal is conceived to be composed are, planes, edges, and an gles. Planes, according to the usual geo metrical definition, are surfaces lying evenly between their bounding lines : they are distinguished into lateral, which are considered as those parts of the sur face of the body which are of the great est extent, and which form its confines towards its smallest extent ; and extreme or terminal, which are those of smallest extent, and form the bounds of the body towards its largest extent. Edges are formed by the junction of two planes un der determinate angles ; they also are la teral, or those formed by the junction of two lateral planes; and terminal, formed by the junction of two terminal planes, or of a terminal with a lateral plane. Last ly, angles are formed by the junction of three or more planes in one point.
Werner admits even primary figures of crystals which are susceptible of nume rous modifications. These figures are the icosaedron, the dodecaedron, the hexae dron, which includes the cube and the rhomb, the prism, the pyramid, the ta ble, and the lens.
1st. The icosaedron, fig. 13, is a solid, consisting of twenty equilateral triangu lar planes, united under equal angles. 2c1. The dodecaedron, fim. 14, or solid, of twelve equal or pentagonal faces. 3d.