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 

 laminar, 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 per- 

 fect 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 various, 

 and accordingly the decrements stated by 

 Hauy are of four different kinds : first, 

 decrements on the edges, or parallel to 

 the sides of the primitive form, of which 

 the above is an example. 2 Decrements 

 on the angles, that is, decrements, of 

 which the lines are parallel to the dia- 

 gonals of the faces of the primitive form. 

 3. Intermediate decrements, or those 

 which are parallel to lines situated be- 

 tween 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, 

 under which crystals are presented to 

 us. These modifications are reduced to 

 the following : 1. Sometimes the decre- 

 ments 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 ran- 

 ges, or more. 4. Sometimes the law va- 

 ries from one edge to another, or from 

 one angle to another. 5. In some cases 

 the decrements on the edges correspond 

 with tl decrements on the angles. 6. 

 Sometimes the same edge or the same 

 angle undergoes successively several laws 

 of decrements. 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 modifi- 



VOL. IV 



cations, 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 

 geometrical definition, are surfaces lying 

 evenly between their bounding lines: they 

 are distinguished into lateral, which are 

 considered as those parts of the surface 

 of the body which are of the greatest ex- 

 tent, and which form its confines towards 

 its smallest extent ; and extreme or ter- 

 minal, 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 under determi- 

 nate angles ; they also are lateral, or 

 those formed by the junction of two la- 

 teral planes ; and terminal, formed by the 

 junction of two terminal planes, or of a 

 terminal with a lateral plane. Lastly, 

 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 dodccaedron, the 

 hexaedron, which includes the cube and 

 the rhomb, the prism, the pyramid, the 

 table, and the lens. 



1st The icosaedron, fig. 13, is a solid, 

 consisting of twenty equilateral triangular 

 planes, united under equal angles. 2d. 

 The dodecaedron, fig. 14, or solid, of 

 twelve equal or pentagonal faces. 3d. 



