246 



PEINCIPLES OF CRYSTALLOGRAPHY. 



Fiq.ll. 



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

 we draw the diameter C D and a perpeudicnlar to it, E F, and it is clear 

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



be 90° distant from every point of the 

 zone, and therefore also from E, while 

 the pole of the zone E F is one of the 

 points C or D, we draw the straight line 

 C E r and C P^), so that tjie arc r j) = 90°, 

 and thus find the pole jp of the zone 

 OED. 



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 

 while iu 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 pinacoids — 



100 100 

 010 010 



0.0— O.ljO.l — 1. 0;1.1 — 0.0 

 1 



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

 zone, so must — 



/i . + /v . 4- Z . 1 = 

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

 [0 01]ishTco. 

 2. Zone passing through a pinacoid and any face : 



hlcl liTvl 



100 100 



lc.o—l.O)l.l—h.o; h.o—lc.l 

 I Tc 



If a third face, xy;:, lies in the zone [o iZ], so must — 

 X .o-\- y .l—1c .z = 



or — 



yl=:Tcz^ ^ = 



2/_^' 



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. 



