16 



MINERALOGY ' 



-b 



FIG. 20. Crystallographical Axes. 



crystallographical axes are chosen so as to pass through the crystal 

 parallel to the edges formed by the intersection of three faces, 



simply related and occurring the 

 more often on the individual crys- 

 tals. By this method the axes are 

 so placed as to be parallel to rows of 

 molecules in the point-system. This 

 will be understood by a considera- 

 tion of Fig. 6, page 5. ' 



In referring to the axes, the verti- 

 cal axis is always denoted by the 

 letter c, Fig. 20. The axis running 

 from right to left in the plane of the paper is denoted by the let- 

 ter b ; the axis running back and front through the paper is the a 

 axis. If in any case the axes are equal and interchangeable, the 

 equal axes are designated by 

 the same letter, as a. If planes 

 are passed through the origin, 

 so that each plane shall con- 

 tain two axes, Fig. 21, there 

 will be three such axial planes, 

 or principal sections, intersect- 

 ing at a common point o, 

 which will divide space dis- 

 tributed around o into eight 

 octants, in any one of which 

 it will be possible for a crystal face to occur. Each octant is 

 distinguished by measuring in a + or direction on the axes 

 from the origin o, as indicated in Fig. 20. The upper, front right 

 octant will be + a, + b, + c ; the lower, back, left octant will 

 be a, b, c ; the minus sign is the only one written. When 

 the angle between the axes are not right angles, they are distin- 

 guished as in Fig. 21, aob = a, aoc = P, boc = y. 



Crystal systems. When referred to their crystallographical 

 axes, crystals fall into six systems, here defined in terms of their 

 axes. 



I. Isometric. Includes all those crystals which may be re- 

 ferred to three equal and interchangeable axes at right angles. 

 All three axes are designated by the letter a. 



II. Tetragonal. Includes all those crystals which may be 

 referred to three axes, all at right angles, two of which, the lateral 



FIG. 21. Axial Planes and Angles. 



