CRYSTALLOGRAPHY. 



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. 



In explaining the structure of a crystal, 

 although the representation in the figure 

 be such as to shew the decrease of the 

 laminae, 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 laminae 

 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 laminae, 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, details. 



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 

 tw.o 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. 

 2d. The dodecaedron, fi*. 14, or solid, of 

 twelve equal or pentagonal faces. 3d. 



