296 On Crystallography . 



of fig. 3S, it is evident that we must direct the (renchanr 

 planes parallel lo the ridges rs, t n,p g, &c., (figs. 14 and 

 38), in such a nianner that they become equally inclined 

 on the faces with which ihey form a junction. These planes 

 would pas'? at the same time on the equilateral triangles 

 pst, snp', &c., and we should have the nucleus, when 

 the whole would meet at the places of the centres of the 

 equilateral triangles. 



Hence it follows that the nucleus of which the ridges 

 01, OE, he, (fig. 15), were displayed on tho dodeca- 

 hedron,- is on the contrary entirely engaged in the icosa- 

 hedron (fig. 3S), excepting by its solid angles, which are 

 points only, and are confounded, as we have said, with the 

 centres of the equilateral triangles. This being granted, iu 

 order to form a precise idea of the structure of the icosa- 

 hedron, we must conceive that the laminae, which at first 

 adhere on the nucleus to a certain term, decrease solely by 

 their angles, as if the secondary solid should be sim- 

 ply an octahedron. Beyond this term the decrement on 

 the angles always continuing, a new one takes place which 

 is combined with it, and which being relative to the dode- 

 cahedron produces the twelve isoscele triangles. In this 

 way we may conceive how the nucleus is c'ompletely in- 

 closed in the dodecahedron, with the reserve of solid angles, 

 because the first laminae of superposition, which decrease 

 on their angles only, would continue to envelop this nu- 

 cleus by the portions of their edges to which the decrement 

 did not extend. It is sometimes necessary thus to suppose 

 differcntepochsat different decrements, which concur in the 

 production of a compound secondary form, when we wish to 

 give a detailed account of the mechanism of the structure. 



According to this detail, the distance between the centres 

 of two adjacent equilateral triangles, such ^s p t s, q t s\ 

 (fig. 38), ought to be equal to the corresponding ridge O I 

 of the nucleus (fig. 15), which is plainly to be seen by 

 simple inspection of the two figures. 



The result which we have developed takes place with 

 respect to one variety of sulphuretted iron. Naturalists, at 

 a period when the laws of structure were little understood, 

 were led to make a kind of geometrv of crystallization 

 which operated in our maimer, confounding its icosahedron 

 and dodecahedron with those which are caUed regular, and 

 the first of which is terminated by twenty cqudateral tri- 

 angles, and the other by twelve pentagons, which have all 

 their sides equal. But theory proves that neither the one 

 nor the other is possible in mineralogy. Thus, from the 



five 



