Notice of DelafosSe's Memoir on Crystallography. 283 



In fact, these edges are modified in a different manner, and 

 in such a way as those may be which represent the three di- 

 mensions of a right rectangular prism. The cube of the 

 pyrites cannot therefore be formed either of the small ordi- 

 nary cubes, which would render all the parts of it identical 

 each to each, or of small tetrahedrons, which would render the 

 edges identical by forming two kinds of solid angles. This 

 kind of cube is necessarily formed of small solids of which the 

 three dimensions are different, whether we admit geometrical 

 differences, or suppose that physical or chemical differences 

 exist. The molecule which must be admitted in this species 

 is the limit of the cube and of the right prism, as the solid which 

 would result from the replacing of the superior edges of a 

 rhombohedron in which the plane angles should be of 60° and 

 120°, would be found to be the limit of the cube and the 

 rhombohedron. It may be conceived that at these limits 

 the forms will have properties analogous to those of the allied 

 solids, and that then they differ from each other in respect to 

 symmetry. 



Thus, then, we have three kinds of very distinct cubes in 

 the substances which crystallize in the cubical system, or, if 

 the expression be preferred, three systems of cubical crystal- 

 lization. We may even see the possibility of a fourth and of a 

 fifthfor the limit of the cube and the rhombohedron,|of the cube 

 and of the square prism, &c. All the other crystalline systems 

 at present admitted appear to present analogous circum- 

 stances, and M. Delafosse points out many substances which 

 ought particularly to attract attention in this light. But, in 

 his present memoir, he only considers the rhombohedral sys- 

 tem by treating of the beryl, quartz, and tourmaline, referring 

 for comparison to the carbonate of lime. 



All these bodies, as is known, may be referred theoretically 

 either to the rhombohedron, or to the prism with regular hexa- 

 gonal bases, or finally to the dirhombohedron (bipyramidal 

 dodecahedron) ; but when we take into consideration the pe- 

 culiarities they present, and that, instead of imagining in some 

 of them constant anomalies, — an expression unquestionably 

 very singular — we see nothing but positive facts, to which we 



