. 159. OF THE IMPERFECTIONS OF CRYSTALS. 



bohedral system ; if it be a pyramidal axis, the dodecahe- 

 dron will assume the appearance of a combination of the 

 pyramidal system ; and if it be a prismatic axis, it will have 

 the aspect of a combination of the prismatic system. The 

 same changes are sometimes met with in the digrammic 

 tetragonal-ieositetrahedron. It is also a case not unfre- 

 quently occurring, that single faces are enlarged in the 

 manner just described, of which the isosceles six-sided pyra- 

 mids of rhombohedral Quartz may be quoted as a remark- 

 able instance. 



It will not be amiss to mention here the following pre- 

 cautions, in order to avoid the errors into which such irregu- 

 larities might bad. First of all, those angles must be care- 

 fully examined, in which the faces of the forms intersect 

 eacli other. Suppose, for instance, a form, exhibiting the 

 aspect of a vertical oblique-angular four-sided prism, com- 

 bined with a horizontal one, which belongs to the long dia- 

 gonal of the former, but whose edges are all = 109 28' 16" 

 and 70 31' 44"; this form will be the octahedron. If in a 

 form representing a rhombohedral combination of R + n and 

 P + os, or in a pyramidal one of P + n and [P + co], all 

 the edges are = 120, this form will be the dodecahedron. 

 A form, which seems to be hemi-prismatic, and composed 

 of an oblique-angular four-sided prism, and half the num- 

 ber of the faces of a horizontal one, if the edges of combi- 

 nation prove to be equal to those of the prism, is not what 

 it appears, but it is a rhombohedron. If, on the contrary, 

 in a solid contained under six rhombic faces, those edges 

 which represent the terminal edges of the rhombohedron, 

 be not equal, the solid itself will not be a rhombohedron, 

 but a hemi-prismatic form of the description given above. 



In the second place, it is necessary to attend to those 

 forms which enter into combinations with the one, respect- 

 ing the determination of which there exists some uncer- 

 tainty. 



If in a right rectangular four-sided prism, instead of one 

 or more of its solid angles, we observe equilateral triangles, 

 the form will be the hexahedron ; if these triangles be iso- 



