FIGURE- OF CRYSTALS. 425 



fied on the solid angle at O of fig. 318, bj two planes 

 whose symbols are (D2 H3 Fi), and O 2 . If we pro- 

 duce the edge i d to a, so that i a is equal to twice 

 i d, and make i c zn 3 i k, it is evident that a b c 

 might be the position of the first plane upon an 

 enlarged primary form. And if we make i e =. 2 i b, 

 and if zz 2 i , d ef will represent the second plane 

 upon the same enlarged primary form. But the 

 edges of the two planes intersect each other at the 

 points g and h; and the line g h is consequently 

 the secondary edge at which the planes intersect 

 each other. Having found this intersecting line on 

 No. 1, as well as the positions of the intersections of 

 the primary with the secondary planes, we may pro- 

 ceed to construct the secondary figure, No. 2. To 

 do this, we should first draw a primary form in pen- 

 cil, similar and parallel to d i b k of No. 1, and taking 

 any point , in the edge i d, draw a c parallel to a c 

 No. 1. Take some point e in the edge i b, such that 

 the part exhibited of the plane d ef, should be pro- 

 portional in some measure to the part exhibited of 

 the plane a b c. 



This proportion must depend on circumstances, and 

 on the particular illustration our figure is intended to 

 afford. For we may evidently give any comparative 

 extension we please to the two planes, by taking one 

 of the points a or e, No. 2, nearer to d or b. 



Having fixed on the points a arid e, No. 2, we may 

 draw a g, g e, g h^ c h, parallel to the correspond- 

 ing linos of No. 1 ; and drawing 1 the lines at the back 

 of the figure parallel to those on the front, the 

 secondary form will be completed. 



In the future part of this section, the planes analo- 

 gous to a b c, and d e jf, will be termed directing 

 planes ; and their edges and intersecting lines, direct- 



ing lines. 



3 n 



