Notice of Delafosse' s Memoir on Crystallography . 28l 



happily rejected by the exact|sciences, that the exception con- 

 firms the rule, no farther progress has been made. M. Delafosse 

 has now come to a conclusion diametrically the opposite to 

 this. There is no anomaty, he affirms, in the law of sym- 

 metry. That law remains, in this case, in full force, and it 

 is the identity of the parts which is not complete. There is 

 indeed a perfect geometrical, although there is not a physical 

 identity, and thence result the differences we witness ; or ra- 

 ther these differences ought to make us modify the notions 

 hitherto entertained respecting the internal structure of crys- 

 tals, which have been considered only on their purely geome- 

 trical relations. 



It is in this point of view that M. Delafosse has given a 

 general exposition of the rationale of the various changes 

 which it has appeared to him are necessary to be made on 

 the crystallographic theory of Hai'iy. He has applied his prin- 

 ciples to divers natural substances, boracite, common pyrites, 

 tourmaline, quartz, and beryl. We shall give a comprehensive 

 idea of his observations and conclusions. 



Boracite and common pyrites are referable geometrically to 

 the cube, like many other substances, but they present at the 

 same time certain peculiarities which distinguish them. In 

 boracite there are only four solid angles in the cube which are 

 modified altogether in the same manner, and as the eight solid 

 angles of a cube are geometrically identical, it has been con- 

 cluded, from the time of Haiiy to the present day, that we 

 had here an exception to the law of symmetry. M. Dela- 

 fosse, reasoning otherwise, has come to the conclusion, that 

 if the solid angles of this substance are geometrically identi- 

 cal, they are not so physically ; which means that the geome- 

 trical cube of boracite is not composed molecularly in the 

 same manner as the cube met with in many other substances. 

 One can imagine, in fact, that a cube may be composed, geo- 

 metrically speaking, in a multitude of different ways, for ex- 

 ample, of small cubes, small tetrahedrons, minute rectangular 

 prisms, &c. If the crystals were always simple, we could 

 never perceive these differences, at least by observing the 

 external form alone ; but the modifications they present, and 



