442 



CRYSTALLOGRAPHY. 



Theory. 



Tetrahe- 

 dron. 



Regular 

 six-sideil 

 prism. 



Rhomboi. 

 d3l dude, 

 cahedron. 



Triangular 

 dodecahe- 

 dron. 



is not always the case. In anxtase, for example, they 

 are long, and of course the solid angle at their summit 

 is composed of very acute plane angles meeting at a 

 point. The following species of minerals have this 

 primitive form : tinstone, zircon, molybdate of lead, 

 mellite, harmolome or cross-stone, and anatase. 



4. Octahedron composed of two pyramids termina- 

 ted by a rhomboidal base. They vary from each other 

 in the height of the pyramids, and the angles of the 

 rhomb constituting the common base of the pyramids. 

 Sulphur, carbonate of soda, realgar, and sphene. 



III. The regular tetrahedron is a figure bounded by 

 four equilateral and equiangular triangles ; or it may 

 be conceived as a three-sided pyramid terminated by 

 a triangular base. There are but few minerals which 

 have this figure for the primitive form of their crys- 

 tals. At present we recollect only grey copper ore, and 

 copper pyrites. 



IV. The regular six-sided prism is a prism compo- 

 sed of six equal rectangles, and terminated at each ex- 

 tremity by a regular hexagonal base. They differ from 

 each other in the height of the prism compared with 

 the diameter of the base. The following species of mi- 

 nerals have this primitive form : apatite, carbonate of 

 strontian, emerald, cinnabar, sidphuret of copper, pinite 

 and sommite. 



V. The rhomboidal dodecahedron is a solid bounded 

 by twelve equal rhombs. It is a beautiful, but not 

 very common primitive form. Every body must have 

 observed, that it is the shape which garnets usually 

 affect. We recollect no mineral species, except garnet 

 and blende, which have the rhomboidal dodecahedron 

 for the primitive form of their crystals. 



VI. The last primitive form is the triangular dode- 

 cahedron. It may be conceived to consist of two six- 

 sided pyramids applied base to base. The common 

 base, of course, is a regular hexagon. This is by no 

 means a common primitive form. Carbonate of barytes 

 and phosphate of lead are the only two species that we 

 recollect in which it occurs. In the first of these, the 

 pyramids arc long compared to the diameter of the 

 base ; in the second, they are short. 



From the preceding account of the primitive forms 

 of crystals, it is obvious that two of them, namely, the 

 parallelopiped and the octahedron, are by far the most 

 common, and include by far the greatest number of 

 primitive forms. The six-sided prism is likewise not 

 uncommon. But the other three primitive forms, 

 namely, the tetrahedron, the rhomboidal dodecahedron, 

 and the triangular dodecahedron, are comparatively in- 

 significant, occurring only each in about two species. 

 However, as these species happen to be very well mark- 

 ed and important, they could not be passed over with- 

 out impropriety. 



After we have obtained the primitive crystal of a mi- 

 neral by mechanical division, it very frequently hap- 

 pens that we can still continue the mechanical division, 

 either by cutting off slices parallel to the faces of the 

 primitive crystal, or in some other direction, when any 

 natural joints become evident. If we continue the me- 

 chanical division of calcareous spar by cutting off slices 

 parallel to the faces of the crystal, the only directions 

 that admit of mechanical division, it is obvious that 

 the figure of the substance will continue the same. It 

 will diminish in size; but will experience no other 

 change. Suppose, on the other hand, that we continue 

 to cut slices from a six-sided prism, by cuts parallel to 

 the faces of the prism, the consequence woul I be that 

 we would divide the whole prism into a number of trii 



angular prisms. This will be evident to the eye, by 

 inspecting Fig. 8. which represents the basis of a hex- 



Theory. 



agonal prism, divided into triangular prisms by such r^^ii 



Fig 8. 



continued divisions. 



Sometimes a parallelopiped admits of divisions in 

 other directions, besides those parallel to the faces. 

 Suppose the rhomboid AA'KH, Fig. 9. divisible both p; g% & 

 in the direction parallel to the six rhombs which con- 

 stitute its faces, and likewise in planes passing through 

 the oblique diagonal AO, the axis A' A and the edge 

 A'O comprehended between the diagonal and the axis, 

 the consequence of such a division would be, that the 

 rhomboid would be separated into six tetrahedrons, as 

 any person may satisfy himself by a little considera- 

 tion. These tetrahedrons are represented in the Figure 

 surrounding the original rhomboid ; and, to aid the 

 conception, the same letters are employed to denote 

 the same parts in the rhomboid, and in the tetrahe- 

 drons into which it is conceived to be divided. 



These examples of the ultimate changes which may 

 be produced upon the primitive crystals by mechanical 

 division, will be sufficient to give the reader an idea of 

 the subject. Hauy conceives, that, by these divisions, Integrant 

 we obtain the form of the integrant molecule, or of the molecule. 

 ultimate integrant atom of the mineral in question. 

 No proof can be advanced in proof of this conjecture, 

 except the impossibility of altering the form, how far 

 soever we carry on divisions, and the obvious conse- 

 quence, that, if these divisions be carried far enough, 

 we must at last reduce the crystal to its integrant par- 

 ticles. The subject is not of much importance, as far 

 as crystallography is concerned ; because the theory of 

 crystals is not in the least affected either by its truth 

 or its falsehood ; and no use whatever is made of the 

 integrant molecules in any part of the theory. We 

 must acknowledge, that the reasoning of the Abbe 

 Hauy appears to us plausible. It may therefore be 

 adopted, at least for the present, without any incon- 

 venience. 



That all minerals have integrant molecules of a de- 

 terminate shape, and that this shape never varies in 

 the same species, we conceive to be incontrovertible. 

 M. Delametherie, indeed, has endeavoured to prove, 

 that the integrant molecule varies in its form in the 

 same species ; but his arguments are founded entirely 

 upon the opinion of Berthollet, that substances are ca- 

 pable of uniting indefinitely in a great variety of pro- 

 portions, — an opinion entirely refuted by all the phe- 

 nomena of chemistry, and which no chemist can well 

 maintain, without refusing his assent to the best de- 

 monstrated truths in the science. We do not therefore 

 think it necessary to enter into any examination of the 

 arguments advanced by Delametherie in support of his 

 opinion, as they are arguments which no chemist can 

 admit, and which, of course, are not calculated to pro- 

 duce conviction. 



Hauy has found, that the integrant molecules of all 

 crystals, supposing them capable of being discovered 

 by mechanical division, may be reduced to three spe- 

 cies ; namely, the tetrahedron, the triangular prism, 

 and the parallelopiped. Now, it deserves attention, 

 that these are the three simplest conceivable solid bo-* 

 dies, being bounded respectively by four, five, and six 

 faces, — the smallest number of faces by which a solid 

 body can be bounded. It is needless to observe, that 

 each of these figures is capable of a good many varie- 

 ties, y alterations in the proportions, and the angles 

 of the respective faces. 



It may be worth while to give a few examples of the 



