«C0 On Crystallography . 



Vion of tlie diagonals, like the rows one of which is de- 

 signated by a, b, c, d, e,f,. &<;.; the other by n, t, I, my 

 p, 0, r, s ; a third by q, v, k, ti, x, y, z, &c. See fig. 22, 

 whicli represents separately one of these ranges or rows. 



The molceules of the ranges parallel to the edsres touch 

 by one of their faces,, and the ranges themselves are simply 

 in juxta-position. The molecules of the ranges parallel to 

 the diagonals touch by one ridge only, and the rows are as 

 if dovetailed into each other. Now it seems to be well as- 

 certained that the lamince piled up on the faces of a cubical 

 or other nucleus, also decrease successively in several cases 

 bv subtraction of these ranges parallel to ihe diagonals. 



Here the faces produced in virtue of the decrement are 

 no longer simply striated, as in decrements on the edges, 

 but are full of points, which being all on a level, and es- 

 caping the eye from their minuteness, present only the 

 aspect of a plain surface. 



Now if we imagine that the laminae which are placed 

 over each other, issuing from the faces of a cube, decrease 

 by a single row on all the angles of these same faces, this* 

 decrenieut will produce the regular octahedron, the mecha- 

 nical division of which we have explained. 



In order the better to comprehend this result, we shall 

 here again adopt the synthetical method, and run over the 

 series of lauiina?. of superposition, by indicating the auxiliary 

 variations, which they undergo, and which assist the eflect 

 of the decrement, to which every thing inay be referred. 



Let AEOi (lig. 23 A, PI. IV) be the'superior base of 

 the nucleus subdivided into SI sntall squares, or facets of 

 molecules. What we are about to say relative to this base 

 may equallv be applied to the five other faces of the cube. 



Fig. 23 B represents the first lamina of superposition, 

 which should be placed above AEOI (fig. 23 A), in such 

 a manner that the point e' answers to the point e, the point 

 a' to the point a, the point o' to the point o, and the point 

 t' to the point i. We see in the first place by this arrange- 

 ment, that the squares Ec, An, O o, I i, (iig. A) remain 

 empty ; which is the initial effect of the law of decrement 

 alluded to. We see moreover that the edo;esOV, PN, 

 L C, FG, (fig. B) exceed by one row the edges E A, EO, 

 01, I A, (fig. A) as this is necessary that the nucleus mav 

 be enveloped towards the' satne edges, and that the solid 

 may increase as usual in the parts to which the decrement 

 does not extend. 



The superior face of the second lamina will be similar 

 toBKHD, (fig. 23 C) and it will be necessary to pla>;e 



this 



