Theory of Cryjlallifathn. i6i 



of its fix folid angles correfponds to the centre of one of the 

 faces of the octaedrOn, which could not be the cafe on the 

 hypothefis of a decrement on the edges. From this relation 

 of pofition, added to the impofiibility of applying here the 

 theoretic calculus, I have concluded that the law of decre- 

 ments accomplices its end, in fuch cafes, by a progfefs differ- 

 ent from that which conducts to the forms before defcribed; 

 and my refearches, in regard to that point, have unfolded a 

 new order of facts which add much to the fecundity of cryf- 

 tallifation, and at the fame time to that of its theory* But 

 on this fubject it is neceffary to enter into a more particular 

 inveftigation. 



Let ABCD (fg- 27) be the fuperior or inferior furface 

 of a lamina compofed of fmall cubes, the bafes of which are 

 represented by the fquares that fub-divide the whole fquare. 

 If we confider the feries of cubes to which the fquares a, b, c t 

 d, e,f,g, b, i, belong, it is evident that all thefe cubes will be 

 On the diagonal drawn from A to C> and that they will form 

 One firing {Jig. 28), which will not differ from the firing of 

 the cubes a, n, q, r', s', f, u', z$ x'j, (Jig. 27) lying in the 

 direction of the edge A D ; except in this, that in the former 

 the cubes touch only by one of their edges, and in the lat- 

 ter by one of their faces. We fhall obferve at the fame 

 time, throughout the whole extent of the lamina, firings of 

 cubes parallel to the diagonal, one of which is pointed out by 

 the feries of letters q, v, k, u, x,y, z, another by that of the 

 letters n, t, I, m, p, 0, r, s, and fo of the reft. 



We may conceive then that the laminae of fuperpofitionj 

 inftead of projecting beyond each other one or more ranges 

 Of cubes-, in a direction parallel to the edge> project beyond 

 Pach other in a direction parallel to the diagonal ; and we 

 fhall conftruct in the like maimer around the cubic nucleus 

 folids of different figures, by placing, fucceffively, above 

 the different faces of this nucleus, lamina;, which may arife 

 in the form of pyramids, and which will experience the kind 

 of decrement juft defcribed. The faces of thefe folids will 

 Vol. I, M n©t 



