OF CENTRAL CANADA PART I. 9 



be readily shown by the Law of Symmetry. This law, for instance, 

 exacts one of three things, of which the most important is to this 

 effect, viz., that if an edge or angle of a crystal be modified in any 

 way, all the similar edges or angles in the crystal must be modified in 

 a similar manner. Now the cube has twelve similar edges and eight 

 similar angles. Consequently, if one edge or one angle be truncated, 

 or, to use a term more in conformity with the actual operations of 

 Nature, if one of these be suppressed during the formation of the 

 crystal, the other edges (or angles) must be suppressed also ; and if 

 the new planes, which thus arise, be extended until they meet, the 

 rhombic dodecahedron on the one hand, and the regular octahedron 

 on the other, will result.* These forms, moreover, as well as their 

 intermediate oscillations, frequently occur in the same substancee : 

 red oxide of copper may be cited as an example. But between the 

 cube, a square prism, a regular hexagonal prism, and a rhombic 

 prism, no relations of this kind exist. Neither are these solids 

 related physicially : their optical, thermal, and other physical charac- 

 ters are equally distinct. By considerations of this sort, therefore, 

 we are able to establish six (or really seven) distinct Crystal Systems. 

 These (named chiefly in accordance with the relations of their axes, 

 or certain right lines assumed to pass through the centre of each 

 crystal, and terminate in opposite planes, edges, or angles) are 

 enumerated in the annexed tabular view : 



Crystal-axes of one i^ gih ( TM Regular or hopolar System (including the 

 Refraction sinale \ cube, rhombic dodecahedron, octahedron, &c., 



on ' 81ngle [ with their various combinations. ) 



Crystal-axes of two lengths. 

 Refraction, double, with 

 one neutral line or optical 



axis 



The Tetragonal System (including square-based 

 prisms and pyramids with their various com- 

 binations. ) 



The Hexagonal System (including regular hexa- 

 gonal prisms and pyramids, rhombohedrons, 

 &c., with their combinations.) 



* The Law of Symmetry, in its exact acception, may be thus expressed : 



(1.) If an edge or angle of a crystal be modified, all the similar edges or angles will exhibit 

 a similar modification. 



Or (2.) One-half or one-mth of the corresponding angles or edges, in alternate positions, will 

 be equally modified. Example. Cube and Tetrahedron (Boracite ; Arseniate of Iron.) 



Or (3.) All the similar edges or angles will be modified by one-half or one-mth the normal or 

 regular number of planes. Example. Cube and Pentagonal Dodecahedron (Iron Pyrites, 

 Cobaltine.) 



Conditions 2 and 3 produce hemihedrons or part-forms. 



