440 



CRYSTALLOGRAPHY. 



Thcorv. 



Theory of 

 the struc- 

 ture of 



crystals. 



Mauy*sme. 

 Ihod of 

 dissecting 

 carbonate 



t.f lime. 

 Plate 



cexxn. 



P'g- 1. 



Fig. 2. 



looked for degree of perfection. He lias formed a com- 

 plete theory of crystallography, and drawn up accord- 

 ing to it a system of mineralogy, which was published 

 in 1801. Though many unavoidable mistakes occur in 

 this work, which have been gradually corrected since, 

 and though many of his primitive forms are in fact hy- 

 pothetical, and may turn out erroneous, }ret the work 

 must be admitted to be altogether extraordinary, to 

 constitute an era in the science of mineralogy, and to 

 develope a theory not only highly curious in itself, but 

 exceedingly useful and important. 



We shall divide this article into three Chapters. In 

 the first we shall give such a popular view of the theory 

 of crystallization, as will, we flatter ourselves, be in- 

 telligible to all our readers. In the second Chapter, we 

 shall give the mathematical theory which is necessary 

 for all who wish to prosecute the subject farther, or 

 who would be able to judge of the accuracy of the la- 

 bours of Hauy, or indeed to understand them. In the 

 third Chapter, we shall give a table of the forms of the 

 crystals of all minerals, as far as the subject has been 

 hitherto investigated. 



Chap. I. 

 Theory of the Structure of Crystals. 



To give a general notion of the structure of crystals, 

 we shall describe Hauy's mechanical dissection of a six- 

 sided prism of calcareous spar, and the discovery of the 

 immitive nucleus, because it was the circumstance that 

 ed to the discovery of the theory of the structure of 

 crystals, such as we have it at present. While looking 

 over the cabinet of M. Defrance, a hexahedral prism 

 of carbonate of Lime broke off a group to which it was 

 attached. M. Defrance made him a present of it. This 

 crystal had a corner broken off from the base by which 

 it had been attached to the group. M. Hauy attempted 

 to detach similar corners from the other angles, and af- 

 ter some time succeeded in bringing to view its rhom- 

 boidal basis. This excited in him a movement of sur- 

 prise, and first suggested to him the theory of the struc- 

 ture of crystals. His method of proceeding in the dis- 

 section of this crystal, may be understood from the 

 following description. 



Take a regular six-sided prism of calcareous spar, 

 (Plate CCXXII. Fig. 1, and 2.) if you attempt to divide 

 it parallel to the edges of the base, you will find that 

 three of these edges, taken alternately in the upper 

 base ; for example, the edges If cd, bm, will admit of 

 this division, while the other three of them will not. 

 To succeed in the lower base, you must not make 

 choice of the edges If, c'd', b'm', which correspond 

 with the upper edges ; but the alternate edges d'f, b'c', 

 I'm'. Fig. 2. These six cuts will expose to view as many 

 trapeziums. Three of these are represented in Fig. 2 ; 

 namely, the two which come in place of the edges If, 

 ed, and which are marked by the dotted lines ppoo, 

 patch, and that which comes in place of the lower 

 edged' J", and which is marked by the dotted lines 

 nnii. 



Each of these trapeziums will have a polish and 

 lustre, from which it will be easy to perceive that they 

 coincide with the natural joints of the prism. You will 

 attempt in vain to divide the prism in any other direc- 

 tion ; but if you continue the division parallel to the 



Fig. X 



first cuts, it is obvious that the size of the bases will Theory, 

 continually dimmish, while the prism itself will con- '""■" ■"%"■'■ *" 

 tinually grow shorter. Just when the bases disappear f^JL., 

 altogether, the prism will be converted into a dodeca- 

 hedron, (Fig. S.) with pentagonal faces ; six of which, 

 as ooiOe, olkii, are the remains of the faces of the 

 prism, and the six others, E A I oo, od kii, are the re- 

 sult of the mechanical division. 



If we continue the dissection, the faces at the ends 

 will preserve their figure and size, while the lateral 

 faces will continually diminish in length, till at last the 

 points o, k of the pentagon olkii being confounded with 

 the points i, i, and the same thing happening with all 

 the other points similarly situated, each pentagon is 

 converted into a simple triangle, as we see in Fig. 4. 

 New slices taken off some make the triangles disappear, 

 so that no vestige of the original prism remains. Thus 

 we obtain the nucleus, or primitive form, (Fig. 5.) 

 which consists of an obtuse rhomboid, t the inclina- 

 tion of whose faces is 105°, and the plane angles of the 

 rhombs 101° 52' and 78° 8'. 



This example will suffice to give the reader some 

 notion of the manner of dissecting crystals, and of ob- 

 taining their primitive nucleus. There are a great 

 many other crystalline forms of carbonate of lime ; but 

 all of them, when properly dissected, give a rhomboidal 

 nucleus, precisely similar to that obtained^ from the 

 hexahedral prism in the preceding example. A very 

 common crystalline shape of this mineral is the dode- 

 cahedron, represented in Fig. 6. consisting of two six- 

 sided pyramids applied base to base. This is the crys- 

 tal, the nucleus of which was found by Bergman. No- 

 thing is easier than to detect the primitive crystal 

 here. We have only to make cuts parallel to the edges 

 EO, OI, and to the other edges, where the bases of 

 the two opposite pyramids unite. This will be evident 

 by inspecting Fig. 7- in which the primitive nucleus is 

 represented, and the same letters are employed, as in 

 Fig. 6. to denote the same parts of the dodecahe- 

 dron. 



It would be easy to multiply examples ; but we con- 

 ceive that the two preceding ones will suffice to giv© 

 our readers an idea of the way in which the primitive 

 nucleus may be detected, which is all that we have in 

 view at present. All crystals do not admit of this me- 

 chanical division ; but in them, what is called the cleav- 

 age, and which is in fact the direction of the natural 

 joints of the crystal, may frequently be detected. These, 

 assisted by the theory, as we shall see afterwards, are 

 generally sufficient to give us a pretty near approxima- 

 tion, at least, to the primitive form of these bodies. 



All the different primitive forms hitherto observed 

 may be reduced to six ; namely, 



1. The parallelopiped. 



2. The octahedron. 



3. The tetrahedron. 



4. The regular six-sided prism. 



5. The dodecahedron with rhomboidal faces, equal 

 and-similar. 



6. The dodecahedron, with triangular faces, consist- 

 ing of two six-sided pyramids applied base to base. 



I. The parallelopiped, as every body knows, is a so- 

 lid figure, bounded by six faces parallel to each other, 

 two and two. Thus, for example, a cube is a parallelo- 

 piped. From this definition, it is obvious that there 

 may be an infinite number of parallelopipeds, differing- 



Primitive 

 lorms. 



+ By a rhomboid, in this article, is always meant a figure bounded by sii equal rhombuses, parallel two and two. 



5 



