246 



PEINCIPLES OF CRYSTALLOGRAPHY. 



now, C,D are the points of section of the zone with the main circle, 

 we draw the diameter O D and a perpendicular to it, E F, and it is clear 

 that the pole sought for must lie in the zone E F. Since, now, it must 



Fnj.lh 



be 90° distant from every point of the 

 zone, and therefore also from R, while 

 the pole of the zone E F is one of the 

 lioints or D, we draw the straight line 

 C E r and Pjp, so that the arc r i^ = 90°, 

 and thus find the pole p of the zone 

 CRD. 



Thus, all the expedients are given which 

 are necessary for the construction and 

 use of the projection ; in general, the sim- 

 plest of these are sufficient, especially 

 c while in this method of projection we do 



not aim at the greatest exactitude attainable, but only a presentable 



representation of the arrangement of the faces. 



As a close of this section we shall give some special modes of the 

 laws of zones, and an example of a complete development of them. 

 1. Zone passing through two i)inacoids — 



100 100 

 010 010 



0.0 — 0.1 5 0.1 — 1.0; 1.1 — 0.0 

 1 



[0 1] is the symbol of the third pinacoid. If a face, Ji 1c I, lies in this 

 zone, so must — 



/i . + A: . 4- L 1 = 

 also, I = 1, the general symbol of a face lying in the zone 10 0.010==- 

 [0 1] is k h 0. 

 2. Zone passing through a pinacoid and any face : 



U h I lilil 



100 100 



k.o—l.o',l.l—h.o', h.o—Jc.l 

 o I % 



If a third face, J??y-, lies in the zone [o fk], so must — 

 X .0 + y .l—1c .z = 



7 7 y Tc 

 yl = lcz^ - = r 



or 



If. therefore, a zone passes through a pinacoid, the relation of those two 

 indices, which, in the symbol of the pinacoid, are o, is constant for all the 

 faces of this zone. 



