42 



MINERALOGY 



when e"d"V" will represent one of the dome faces ; the remain- 

 ing three are projected in a similar way. Figure 63 represents this 

 combination without the construction lines. 



Example II. Let it be required to draw (113) = 3a:3a:aof the 

 isometric system. Draw the axial cross and extend them in each 

 case to 3 a, Fig. 64 ; in the isometric system all the axes are inter- 

 changeable, and where one axis is cut by planes at 1 and 3 the other 

 axes must be cut by two planes also; there will be three planes in 

 each octant ; connect 3 a, a", 3 a', the three lines will be the inter- 

 section of the face 3 a : a : 3 a with the three axial planes separating 



the octants ; likewise connect 

 3 a', a, and 3 a" ; 3 a", 3 a, a'. 

 The intersections of these 

 three planes are 3 ac, 3 a"ad, 

 3a'b; those portions of the 

 intersections which represent 

 crystal edges are drawn in 

 full lines. The portion of 

 the crystal represented is 

 that contained in one octant 

 or one eighth of the whole 

 form. All edges in the three 

 remaining octants in front 

 of the plane of projection are 

 obtained by the same method 

 of projection. Those in the four octants behind the plane of pro- 

 jection, where the form is symmetrical in respect to a center, may 

 be conveniently drawn as in Fig. 65. If from any point c a line 

 be drawn to the center o and extended beyond the center an 

 equal distance as co, c will be the point behind the plane of 

 projection corresponding to c in front, likewise all other points 

 may be located by drawing lines through the center o and the 

 faces represented by connecting these points. 



Spherical or stereographical projection. In the spherical pro- 

 jection the crystal to be represented is placed at the center of a 

 sphere so that the intersection of the crystallographical axes coin- 

 cides with the center. The plane of projection passes through the 

 center of the sphere at right angles to the c axis, and intersects 

 the sphere in a great circle, the equator ; the c axis when extended 

 will intersect the sphere of projection at the north and south poles. 

 The eye is situated at the south pole to view the faces located in 



-b 



