i6o Theory of CrjJiaU'tfationt 



by pointing out the pofition of the rhomboidal nucleus in- 

 clofed in the regular hexaedral prifm of the calcareous fpar, 

 was uot fufficient to conducl immediately to a determination 

 of the laws of thofe decrements which produce fecondary 

 cryftals. It was necelTary to pafs through intermediate fteps 

 more fimple than tlie fciiilt of thefe laws in regard to the 

 prifm in queftioft. I {hall now proceed to give an idea of 

 thefe kill remits, which depend on laws of decrements \. 

 Tines or departure are hot parallel to the edges of the primi- 

 tive form, but to the diagonals of its faces. 



fo a fuM the imagination in coficeivirig the method winch 

 1 have followed to inveftigate thefe new decrements, 1 fliall 

 remark, that the fame fubrlances which exhibit the dodecae- 

 dron with pentagonal planes originating from the cube 

 i y and zo), and which might even alllime the form ol 

 ihe dodceaeuron wh >fe planes are rhomb' . 5 and 6), 



are found abb under that of the regular o&aedrori. But it 

 appears, on the firft - ighl be poilible to bring 



the itruchire of this, oftaedron to a decferncht on the edges 

 of a cube; for, if we confine ourfclves fo malce the laminae 

 of fuperpo'ftiioh decrcafe' only on the edges of the two oppb- 

 Ete faces of this cube, for exampre, ori tbbfc of the ibperior 

 bale A B C D {Jig. 6), and of the inferior bafe, we flialf 

 have in gencrai'two pyramids applied ori thefe bafes; and 

 if wc fuppofe farther thai the faces of thefe pyramids are 

 extended until they meet, which is nothing elfe than conti- 

 nuing the efFecl of the law of decrements in the fpace fitu- 

 ated between the bafes of the cub/:, we {hall arrive at an oc- 

 laedrpn, the angles of which will vary according as the iaw r 

 (hall dvie mine a greater or fmallcr number of ranges fub- 

 tracled. But thebry demoriurates that there is rib' 1 , 

 however complicated it may be fuppofed, which h capable" 

 ftf giving equilateral triangles as the faces of this oelaedron. 



On the other hand, if wc divide a regular octaedron, ori- 

 ginating from a cube, we {hall perceive that the cubic nu- 

 • Lens is Gtirated in this o6taedioa in fuch a manner thai qach 



of 



