. 159. OF THE IMPERFECTIONS OF CRYSTALS. 



sists in reducing the homologous faces to their regular size 

 and figure, which is effected by giving them an equal dis- 

 tance from the centre of the form, and by adding, if neces- 

 sary, those faces which do not appear at all in the combina- 

 tion ; provided the observation of one or more of the same 

 simple form entitles us to suppose this form to be one be- 

 longing to the combination. In thus completing irregu- 

 larly limited compound forms, it will always be necessary 

 to reflect on the possibility of the forms possessing a hemi- 

 rhombohedral, a hemi-pyramidal, a semi-tessular, &c. cha- 

 racter. If, for instance, in a hexahedron four of the solid 

 angles are replaced by equilateral triangles corresponding 

 to the faces of the tetrahedron, we are not entitled to sup- 

 pose that the four remaining solid angles too should be 

 truncated, because in this case it is the tetrahedron, and 

 not the octahedron, which is contained in the combination ; 

 but if only one more of the remaining solid angles be re- 

 placed by a triangle of the same description, then we are 

 fully entitled to add the rest of the faces required for the 

 production of the octahedron, or perhaps of two tetrahedrons? 

 since either the octahedron or two tetrahedrons are really 

 contained in the combination. 



Sometimes the combinations, like the simple forms, are 

 elongated or depressed in the direction of one of their axes ; 

 and they assume the aspect of such forms as belong to the 

 system to which the lengthened or shortened axes refer. 

 Examples of this kind occur very frequently in the combi- 

 nations of the hexahedron and the octahedron of hexahedral 

 Lead-glance. The crystals are sometimes elongated in the 

 direction of a prismatic axis, or depressed in the direction 

 of a rhombohedral one. The latter assume the appearance 

 of a rhombohedral combination, while the former possess the 

 aspect of a combination of the prismatic system. The most 

 common form of rhombohedral Quartz is a combination of an 

 isosceles six-sided pyramid P with the regular six-sided 

 prism P + os (Vol. II. Fig. 145., abstraction being made of 

 the faces s and s"). Very often this combination appears flat- 

 tened in the direction of a prismatic axis, and then it takes 



