474 



CRYSTALLOGRAPHY. 



Crystalline angle and radius could be expressed in rational nura- 

 For ms, DCT s, we would have a simple ratio between g and p. 



^~ v "—' But the logarithm of the sine of 81° 30' is 9,1697021, 

 which gives for the sine 14781, a number very near 

 15000. But radius being 100000, we see that the ratio 

 of 15 to 100, or 3 to 20, may be taken without sensible 

 error for the true one. We have then 2 p 1 : p- — g 1 : : 

 20 : 3, or 6p l =20p 2 — 20g 2 , and 10g*=7/?\ This 

 gives us g : p : : t/7 : y'lO. According to this hypothe- 

 sis, the smallest inclination of the faces of the rhom- 

 boid is 81° 23', a quantity which differs only by 7' 

 from observation. Hence the ratio ^/7 : \/10 is adopt- 

 ed as the true one. 



When all these methods fail, which is often the case, 

 the method adopted by Hauy is this. He supposes the 

 secondary crystals formed by a simple decrement; and 

 from this decrement, and the form of the secondary 

 crystal, the dimensions of the integrant molecules are 

 inferred. We shall not give an example of this me- 

 thod ; abundance will be found in the writings of 

 Hauy. 



We cannot avoid observing, that this is the weak part 

 of the Hauyan theory. Now that we are in possession 

 of accurate goniometers, it may be greatly improved, 

 and the calculus considerably facilitated. What Hauy 

 has been able to effect, considering the imperfect in- 

 struments in his possession, is really surprizing, and 

 does infinite honour both to his industry and sagacity. 

 But it is extremely probable that he is wrong in the 

 dimensions of a great many of the integrant molecules, 

 and of course that the form of the primitive crystal 

 which he assigns, is not perfectly correct. It would be 

 easy to give examples of this supposed inaccuracy ; but 

 the task would be invidious. Hauy is at present en- 

 gaged in printing a new edition of his work ; and, as 

 he is now in possession of much better instruments, we 

 may expect considerable ameliorations and improve- 

 ments. 



Chap. III. 



Of (he Crystalline Forms hitherto observed in the Mine- 

 ral Kingdom. 



'Crystalline This part of our task is attended with considerable 

 forms in the difficulty. The different crystals hitherto observed, are 

 miueral too numerous to put it in our power to give figures of 

 Jung om. jj ie w |j ] e ^ ant j we are afraid that bare description with- 

 out figures will scarcely be understood. We shall.adopt 

 a middle course. We shall describe particularly only 

 those crystals belonging to each species which we con- 

 sider as of most importance ; and we shall give figures 

 of those only which the young mineralogist ought to 

 make himself familiar with, before he undertakes the 

 general investigation of crystals. 



The number of crystals figured by Hauy in his Mi- 

 neralogy, amounts to about 564. But there would be 

 jae difficulty in more than doubling that number. Bour- 

 non has figured no fewer than 642 crystals of carbonate 

 ©f lime ; but a considerable number of these are mere- 

 ly simple modifications of the same crystalline form.. 

 Hauy has announced, that he will give, in hisnew edi- 

 tion, the figure of 150 varieties of carbonate of lime: 

 From this statement, the reader will perceive the great, 

 extent of the subject, and the consequent difficulties, 

 under which we mu3t labour. We shall not think it 

 necessary to notice every species of mineral, but only 

 the most important. 



We shall arrange our observations according to the 



primitive forms of the crystals, beginning with the pa- Crysialline 

 rallelopiped, which is the most important. Forms. 



I. Crystals whose primitive Form is the Paral- Parai 



LELOPIPED. 



LEL- 

 OP1PED. 



These may conveniently be arranged under ten dis- 

 tinct groups, according to the particular shape of the 

 parallelopiped. 



I. Primitive form a Cube. Cube. 



To this belong twelve species of minerals ; namely, 



1. Common salt. This species, as far as we have Common 

 seen it, exists only in three regular forms ; 1 . The cube ; salt - 



2. The regular octahedron, formed by a decrement of 

 one range upon each angle ; 3. The cubo- octahedron, 

 which is a cube with each of its angles wanting, and a 

 triangular face in their place. It is obviously die se- 

 cond form not completed. 



2. Borate of magnesia, or boracite. Two varieties of Boracite. 

 the crystals of this species have been observed. 1 . A 



cube with all its edges and four of its angles truncated. 

 This is produced by a decrement of one range upon all 

 the edges, and upon the alternate angles. 2. The same 

 figure as the preceding, with this addition, that the an- 

 gles left untouched in the first variety, have in this no 

 fewer than four small facets in their place. This is 

 produced by a farther decrement of two ranges upon 

 the alternate angles. 



3. Leucite, or amphigene. This mineral occurs usu- Leucite. 

 ally in lavas, and, as tar as we have seen, is always 

 crystallized in a form nearly spheroidal, having 24 tra- p la te 

 pezoidal faces. Some notion may be formed of it from ci;XXV. 

 inspecting Fig. 9- Fig. 9. 



4. Analcime, or cubizite. This mineral is common in Analcime. 

 greenstone, and occurs in Salisbury Craigs. We have 



only seen it crystallized in two forms; 1. A cube, with 

 each angle replaced by three facets, 2. A twenty-tour 

 sided figure, bounded by trapezoidal faces, equal and 

 similar. This figure is represented in Fig. 10. It is Fig. io. 

 produced by a decrement of two ranges upon all the 

 angles of the cubic nucleus. The first variety is pro- 

 duced by the same decrement, stopped short before it 

 had completed the trapezoidal faces. 



5. Aplome. This is a mineral usually crystallized Aplome. 

 in the rhomboidal dodecahedron. The figure of the 

 garnet is easily distinguished by its inferior specific 

 gravity and lustre. The figure is produced by a decre- 

 ment of one range on all the edges of the cubic nu- 

 cleus. 



6. Gakna, or mlpliuret of lead. The usual figure of G a | e n». 

 this species is the cube ; sometimes the octahedron ; fre- 

 quently the cubo-octahedron. The edges and angles 



of the octahedron are sometimes variously truncated. 



7. Pyrites, or mlphuret of iron. Of this there are i» vr ites. 

 three species ; but one of them, magnetic pyrites, may 



be omitted here. It occurs sometimes in cubes, but is 

 usually amorphous. Henee its crystalline forms are 

 still almost unknown. The other two species are, the 

 common pyrites, and the radiated pyrites. The first 

 has a cube for its primitive form, the second a right 

 quadrangular prism with a rhombic base, for its primi- 

 tive form. Hence it belongs to a subsequent group. 

 Pyrites occurs under such a variety of forms, that it 

 would be quite impossible to describe them all here. 

 The two species were long confounded, which occa- 

 sioned considerable confusion. Bournon pointed out, 

 long ago, the necessity of distinguishing different crvsj^ 

 2 



