BYSTEMS OF CRYSTALLIZATION. 



15 



diagonals a and b } drawn in a plane parallel to the base, are the 

 lateral axes, 



Fi^. 1 represents a cube. It has all its planes square (like 

 fig. 9), and all its plane and solid angles, right angles, and the 

 three axes consequently cross at right angles (or, in other 



10. 



11. 



X 



12. 



words, make rectangular intersections) and are equal. It is an 

 example under the first of the systems of crystallization, which 

 system, in allusion to the equality of the axes, is called the 

 Isometric system, from the Greek for equal and measure. 



Fig. 2 represents an erect or right square prism having all its 

 plane angles and solid angles rectangular. The base is square 

 or a tetragon, and consequently the lateral axes are equal and 

 rectangular in their intersections y but, unlike a cube, the verti- 

 cal axis is unequal to the lateral. There are hence, in the square 

 prism, axes of two kinds making rectangular intersections. The 

 system is hence called, in allusion to the two kinds of axes, the 

 Dimetric system, or, in allusion to the tetragonal base, the Te 

 tragonal system. 



Fig. 3 represents an erect or right rectangular prism, in 

 which, also, the plane angles and solid angles are rectangular. 

 The base is a rectangle (fig. 10), and consequently the lateral 

 axes, connecting the centres of the opposite lateral faces, are un- 

 equal and rectangular in their intersections ; and, at the same 

 time, each is unequal to the vertical. There are hence three 

 unlike axes making rectangular intersections; and in allusion 

 to the three unlike axes, the system is called the Trimetric sys- 

 tem. It is also named, in allusion to its including erect prisms 

 having a rhombic base, the Orthorhombic system, orthos, in 

 Greek, signifying straight or erect. 



This rhombic prism is represented in fig. 4. It has a rhom- 

 bic base, like fig. 11 ; the lateral axes connect the centres of the 

 opposite lateral edges ; and hence they cross at right angles and 

 are unequal, as in the rectangular prism. This right rhombic 

 prism is therefore one in system with the right rectangular 

 prism. 



Fig. 6 represents another rectangular prism, and fig. 6 



