[ 210 ] 



XXX. On Crystallography. By M. Hauy. Translated 

 from the last Paris Edition of his Traite de Mineralogie. 



[Continued from p. 108.] 



JL)ecrf.ment s on thk Edges. — Let i^' (fig. 1 1, PI. 11.) 

 be a dodecahedron with rhombic planes. This sohd, which 

 is one of the six primitive forms of crystals, also presents 

 itself occasionally as a secondary form, and in this case it 

 has as a nucleus, sometimes a cube and sometimes an oc- 

 tahedron. Supposing the nucleus to be a cube : 



In order to extract this nucleus, it is sufficient succes- 

 sively to remove the six solid angles composed of four 

 planes, such as s, r, t, &c., by sections adapted to the di- 

 rection of the small diaaonals. These sections will displav 

 as many squares A E Ol, EO 0' E', I 0' T (fig. 12) Sec.', 

 which will be the faces of the cube. 



Let us conceive that each of these faces is subjected to a 

 series of decreasing laminae solely composed of cubic mole- 

 cules, and that every one of these laminae exceeds the suc- 

 ceeding one towards its four edges, by a quantity equal to 

 one course of these same molecules. Afterwards we shall 

 desiirnate the decreasing laminae which envelop the nucleus 

 by the name of lamirice of stiperposition. Now it iseasv to 

 conceive that the different series will produce six quadran- 

 gular pyrannds similar in some respects to the quandran- 

 gular sups of a column, which will rest on the faces of the 

 pube. Three of these pyramids are represented in fig. 13, 

 and hiive their summits \\\ s^ t, r. 



Now as there are six quadrangular pyramids, we shall 

 therefore have twenty-four triangles, such as O 5 1, O t I, Sec. 

 But because tlie decrement is uniform from s to f, and so 

 on with the rcsl, the triangles taken two and two are on 

 a levelj and form a thomb $ O t I. The surface of the solid 

 will therefore be composed of twelve equal and similar 

 rhombs, i. e. this solid will have the same form with that 

 %vhich is the subject of the problem. This structure takes 

 place, alihough imperfictly with respect to the crystals 

 called boracic spars, ar.d the effect of the decrement on 

 which it depends attains its limits in a substance the nature 

 ofvhichis not yet well determined, and which we shall 

 nvv.e particuls'ly explain hereafter. 



The dodecahedron now under consideration is repre- 

 sented by iig. 13, in such a way that the progress of the 

 decrement may be perceived by the eye. On examining the 

 figure attentively, v.e shall find that it has been traced on 



the 



I 



