the Abht Hauy's Theories of Crystallography. 16*7 



and in consequence have supposed the whole of this theory 

 to be grounded on hypothesis. It would be equally errone- 

 ous to confound these sections of crystals with De ITsle's 

 truncations. The latter, indeed, warns his readers that, by 

 the word truncations, he wishes only to figure the appear- 

 ance of the crystal examined. They are not, therefore, real, 

 but only a means of warping the imagination to the exterior 

 form of the crystal, and are by their nature only descrip- 

 tive. The Abbe Hauy's sections are real, and are pointed 

 out to the observer by the interior structure of the crystals ; 

 they are experimental. 



2d, The plane smooth surfaces obtained by the above me- 

 thod are respectively parallel to. 3, 4, or 6 planes. The 

 mutual inclination of these planes to each other is con- 

 stant in crystals of the same substance, whatever may be 

 the exterior form of the crystal. Native antimony, phos- 

 phate of lead, and quartz, seem to show an appearance of 

 more than 6 planes, and the Abbe Haiiy leans to the opi- 

 nion of only 5 planes in some cases ; but as these are ex- 

 ceptions to the general rule, and would only tend to com- 

 plicate this statement, I shall take no further notice of 

 them. 



Let us suppose the smooth surfaces to be only parallel 

 to 3 planes, or, in other words, that the substance will 

 only split in three directions. In that case, the sections can 

 only produce a parallelopipedon, whose nature is determined 

 by the mutual inclinations of the planes to each other. If 

 the planes are perpendicular, it will be rectangular, &c. 



We next suppose the smooth surfaces to be parallel to 4 

 planes. Here a distinction arises, whether 3 of these 

 planes have a common intersection, or not ; and it must be 

 remembered that, if the 4 planes have a common intersec- 

 tion, no solid can be produced ; as they can neither bound 

 nor include a space. If, therefore, 3 of the 4 planes have a 

 common intersection, the splittings will produce either 

 1 hexaedral prism, or 3 parallelopipedons, which will be simi- 

 lar or dissimilar, according to the similarity or dissimilarity 

 of inclination of the planes, or 1 triangular prism. On the 

 contrary, if the 4 planes only intersect each other, two and 

 two, there will be produced either 1 octaedron, or 4 paral- 

 lelopipedons, or 1 tetraedron. 



Lastly, let us suppose the smooth surfaces to be parallel 

 to 6 planes ; then there arise an immense number of cases. 

 But we will for the present confine ourselves to the only 

 case that has hitherto been observed in nature, — where the 



N 2 intersection 



