282 Notice of Delqfosse's Memoir on Crystallography. 



to which the optical and acoustic properties may be added, 

 ought to lead us to the determination of this molecular form. 



In the present case, the apparent anomaly leads us to adopt 

 the regular tetrahedron' as the molecule, and to conceive these 

 small solids arranged in rows, in such a manner that at one 

 of the angles of the resulting cube there is found a base, 

 while at the opposite angle a summit presents itself; from this 

 it will follow that the two opposite angles, which are geome- 

 trically identical, are found completely different in a physical 

 respect, and the law of symmetry will appear in all its force 

 in such a system, if, as nature presents it to us, one of the 

 angles is modified differently from the other. In this suppo- 

 sition of molecular forms and arrangement, the edges of the 

 cube are all geometrically and physically identical, since they 

 all correspond to the edges of the tetrahedron. This also takes 

 place with the modifications of boracite, for the twelve edges 

 of the cube are found to be modified in it at the same time 

 and in the same manner. 



If we study, comparatively, substances in which all the 

 angles of the cube are modified altogether and in the same 

 manner, for example fluor-spar, we will conclude that all the 

 parts are geometrically and physically identical, which leads 

 us to admit the cube itself as a molecule, since it is the only 

 solid that can fulfil this condition. 



Comparing the conclusions relating to fluor-spar with those 

 stated in reference to boracite, we at once perceive that na- 

 ture presents us with two kinds of cubes ; one sort, formed of 

 tetrahedrons, which possess the character of having fear of 

 their solid angles physically different from the four opposite 

 ones ; the other, formed of cubical molecules, or octahedrons, 

 in which all the angles are identical both in a physical and 

 geometrical sense. But besides these there is a third. 



The crystallization of pyrites, as well as that of grey cobalt, 

 is referable to the cube, but the modifications in these cases 

 present an inverse order of things from what takes place in 

 boracite. In the latter substance the solid angles are physi- 

 cally of two different sorts, and the edges are identical in 

 every respect. In the two others, every thing is the reverse 

 of this ; the angles are all identical, and the edges are not so. 



