16 CRYSTALLOGRAPHY. 



another rhombic prism ; but, unlike figs. 3 and 4, the prisms are 

 inclined backward, and are therefore oblique prisms. The lat- 

 eral axes (a, b) are at right angles to one another and unequal, 

 as in the preceding system ; but the vertical axis is inclined to 

 the plane of the lateral axes. It is inclined, however, to only 

 one of the lateral axes, it being. at right angles to the other, 

 Hence, of the three angles of axial intersection, two are rec- 

 tangular, namely a on b, and c on b, while one is oblique, ihat is 

 c (the vertical axis) on a. In allusion to this fact, there oeing 

 only one oblique angle, this system is called the Monoclinic sys- 

 tem, from the Greek for one and inclined. 



Fig. 7 represents an oblique prism with a rhomboidal base 

 (like fig. 12). The three axes are unequal and the three axial 

 intersections are all oblique. The system is called the Triclinic 

 system, from the Greek for three and inclined. 



Fig. 8 represents a six-sided prism, with the sides equal, and 

 the base a regular hexagon. The lateral axes are here three in 

 number. They intersect at angles of 60° ; and this is so, 

 whether these lateral axes be lines joining the centres of oppo- 

 site lateral planes, or of opposite lateral edges, as a trial will 

 show. The vertical axis is at right angles to the plane of the 

 three lateral axes, inasmuch as the prism is erect or right. The 

 base of the prism being a regular hexagon, the system is called 

 the Hexagonal system. 



The systems of crystallization are therefore : 



I. The Isometric system : the three axes rectangular in in- 

 tersections ; equal. 



II. The Dimetric or Tetragonal system : the three axes 

 rectangular in intersections; the two lateral axes equal, and 

 unequal to the vertical. 



III. The Trimetrio or Orthorhombic system : the three axes 

 rectangular in intersections, and unequal. 



IV. The Monoclinic system : only one oblique inclination 

 out of the three made by the intersecting axes ; the three axes 

 unequal. 



V. The Triclinic system : all the three axes obliquely inclined 

 to one another, and unequal. 



VI. The Hexagonal system : the vertical axis at right angles 

 to the lateral ; the lateral three in number, and intersecting at 

 angles of 60°. 



These six systems of crystallization are based on mathemati- 

 cal distinctions, and the recognition of them is of great value 

 in the study and description of crystals. Yet these distinctions 

 are often of feeble importance, since they sometimes separata 



