Theory ef CryJlalliZat'wt. 4$ 



cubes equal to thofe of the nucleus, the number of thefe 

 laminte will be found incomparably greater than in the pre- 

 ceding hypothecs ; at the fame time the cavities (cannelures) 

 which they will form, by the alternate fallying and re-enter- 

 ing of their edges, will be fcarcely fenfib'e ; and we may 

 even fuppofe the compofing cubes fo fmall that thefe cavities 

 will become imperceptible to our fenfes, and that the faces 

 of the pyramids will appear perfectly fmooth. 



. Now DCBE (jig. 12) being the pyramid refting on 

 the face ABCD (fig.l), and CBOG (fg. 12) the py- 

 ramid applied on the neighbouring face BCGH, {Jig. 7), if 

 we confuler that every thing is uniform from Eto O (f.g. 12) 

 in the manner in which the edges of the laminae of fuperpofi- 

 tion mutually project beyond each other, it will readily be 

 conceived that the face C EB of the firft pyramid ought 

 to be found exactly in the fame plane as .the face C O B of 

 the adjacent pyramid, fo that the aflemblage of thefe two 

 faces will form a rhombus E C O B. But for the fix py- 

 ramids we had twenty-four triangles, fimilar to CEB, 

 which, confequenlly, will be reduced to twelve rhombufes, 

 from which will refult a dodecaedron fimilar to that repre- 

 * fented (f.g' 5 and 6) ; and thus the problem is refolved. 

 The cube, before it arrives at the form of the dodecae- 

 dron, paries through a multitude of intermediate modifica- 

 tions, one of which is reprefentedy^. 13. It may be there 

 feen that the fquares p a e o, k l q it, m n t s, &c. correfpond 

 to the fquares A B C D, D C G F, C B H G, &c. {fig. 6) 

 and form the fuperior bafes of as many pyramids, incomplete 

 for want of the laminae by which they ought to be termi- 

 nated. The rhombufes EDL^ ; E C O B, &c. (fig. c), 

 by a necefi'ary confequence are reduced to fimple hexagons 

 a e C / k D, e B n m C, Sac. (fig, 13) and the furface of 

 the fecondary cryftal is compofed of twelve of thofe hexa- 

 gons and fix fquares. This is the cafe with the boracic 

 fpar, allowance being made for fome facets which take the 



place 



