Theory of Cryjlallifatim. 1 65 



lamina preceding the lamina A' G' L K.'(fig. 32), while there 

 are fix which follow it as far as the cube z {Jig. 38) inclufive- 

 ly, the triangle LZQ. {Jig. 39), compofed of the fum of 

 the edges of thefe latter laminae, will have a much greater 

 height than the inferior triangle LCQ, as expreffed in (he 

 figure. 



The furface of the fecondary folid will be formed then of 

 34 quadrilaterals, difpofed three and three around each folid 

 ano-le of the nucleus. But in conlequence of the decrement 

 bv one range, the three quadrilaterals which belong to each' 

 folid angle, fuch as C {fg. 29), will be in the fame plane, 

 and will form an equilateral triangle Z I N (Jig. 40). The 

 twenty-four quadrilaterals then will produce eight equilateral 

 triangles, one of which is reprefented jig. 41, in fuch a 

 manner as to fliew, on a fimple view, the affortment of 

 the cubes that concur to form it ; and the fecondary folid 

 will be a regular octaedron. Figure 42 {hews this octaedron 

 in which the cubic nucleus is inclofed, fo that each of its 

 folid angles C, D, F, G, &c. eorrefponds to the centre of one 

 of the triangles I Z N, I P N, PIS, S I Z, &c. of the 

 octaedron. It may be readily feen, that to extract this nu- 

 cleus, it would be neceflary to divide the octaedron in its 

 eight folid angles, by feitions parallel to the oppofite edges. 

 For example, the fection made in the angle Z ought to be 

 parallel to the edges IS, IN, TN, TS; and hence will re- 

 fult a fquare which will itfelf be fituated parallel to the 

 fuperior bafe ABCDof the nucleus, and which will be 

 confounded with that bafe when the fections have made the 

 faces of the octaedron to difappear entirely. 



This ftru&ure is that of the octaedral fulphure of lead 

 (galena), and the muriate of foda (common fait) of the fame 

 form. 



I call decrements on the angles, thofe which take place in 



a direction parallel to the diagonals, as in the example juft 



mentioned. This denomination will fupply us with the 



means of exprefling in a precifc manner the refult of each 



M 3 decrement, 



