354 On Crystallographj . 



ways conceive a plain figure like a section made in a solid. 

 Let t s z s', therefore, (fig. 43 A) be an assortment of small 

 squares, in wiiich the square BNDG, composed of 49 

 imperfect squares, represents the section of the nucleus*, 

 and liie. extreme squares/, p, i, B,J', c,s, c, h, &cc., thekind 

 of steps formed by the laminis of superposition. We 

 may conceive that the assortment has commenced by the 

 square BNDG, and that different piles of small squares 

 are afterwards applied on each of the sides of the central 

 square; for example, on the side B N : in the first place the 

 five squares comprehended belweenyand h, afterwards the 

 three squares contained between c and e, and then the 

 square s. This progress corresponds with what would take 

 place if the dodecahedron conu;nenced by a cube propor- 

 tioned to its volume, and which afterwards increased by an 

 addition of laminae continually decreasing. 



But on the other hand, we may imagine tliat the assort- 

 ment had been at first similar to that which we see (fig. 

 43 C), in which the square BNDG is only composed of 

 nine molecules, and bears on each of its sides only a single 

 square s, t, s' , %. If we refer, in imagination, this assort- 

 ment to the solid of which it is the section, we shall easily 

 judge that this solid had for its nucleus a cube composed 

 of 27 molecules, and of which each face, composed of nine 

 squares, carried on that of the middle a small cube, so that 

 the decrement by one range is already exhibited in this 

 initial dodecahedron. J 



. This assortment, by means of an application of new 1 

 squares, will become that of fig. 43 B, in which the central " 

 square BNDG is formed of 25 small squares, and carries 

 on each of its sides a pile of three squares, besides a ter- 

 minal square 5, i, ./, or %. Here we have already two la- 

 mince of superposition, instead of one onlv. Finally, by 

 an vdterior application, the assortment of fie. 43 B will be 

 changed into that of fig. 43 A, where wc see three laminae 

 of superposition. These diflTereiit transitions, of which we 

 are at liberty to continue the series as far as we please, will 

 give an idea of the manner in v^hich secondary crystals may 

 increase in volume by preserving their form ; from vvhidi 

 we may judge that the structure is combined with this 

 augmentation in volun)e ; so that the law (according to 

 which all the laininai applied on the nucleus when it has 



* This section is t'lat which would pass by tlie points «, i' ({ig. 11) of the 

 dodecahedron, and by the centres ot the ridges E O, A I, &e., of the nu- 

 cleus. Thus th.e point B (tig. 4.".) u regarded as .situated at an equal dis:aiic« 

 between the points E, O, (iig. 1 1,) and the point N, at equal distance be- 

 ■ twecH the points A, I, &c. 



attained 



