PRINCIPLES OF CRYSTALLOGRAPHY. 249 



This results also from the zone-equatiou — 

 111 111 



00 1 001 



1.1-0.1; 1.0-1.1; 1.0-0.1 

 which gives [1 1 0] as the zone-equation, or — 



1 . X —1 .y + . s=^0 OTX =.y 

 as condition of the tautozonality of a face, xy z^ with 01 and 111; the 

 symbol of m h Jc o becomes changed under these circumstances into (1 1 0). 

 In the same way the position of d, in the zones h dc and ap d, is deter- 

 mined. The first zone gives, as condition, the first index as equal to 0, it is 

 thus oh I; the second gives the equation of the second and third index — 



I 1 ""0 

 and therefore the symbol (0 1 1). 



Finally, the face/ is determined in the same way by the zone afc, as 

 h I, and by the zone h pf, as 10 1, because — 



h = ^ -^1 = 1 

 I ~1 "~0~ 



Thus it is to be kept in view that the quotient- may have any rational 



value which is first fixed by the two faces. 



For the face oi we have the zone b m a n, by which we get the symbol 

 Jc h o and dfn; for the last w^e have — 

 011011 

 10 1 10 1 



1 . 1-0.1; 1. 1-0. 1; 0.0-1 . 1 



or [111]; also as condition — 



A . 1 -f /v . 1 - . 1 = or /t = - A: 

 This condition is satisfied by ll and T 1 0, of which the first is the 

 symbol for the face in front, and the last for the opposite one behind. 



For the determination of q we have the zones cqn and d pf q; the 

 first gives, when li Jc I is the symbol of q — 



Jl 1 -, /7 T 7\ 



-=^^=-=- lor{JiJil) 

 the last — 



l^ = \=\ = lov{JihJi) 



which, when contracted, is 1 T 1. 



The face e lies in the zone b d c e, wherefore Ji = o ; and in a q e, for 

 ■which reason — 



Jt ^ -J. ^ _ _ . 

 I 1 



e has thus the symbol (0 1 1). 



There remains s in the zones m p s e and d sfn to be determined ; the 

 first zone gives — 



/i ^ 1 ^ 1 

 A;~ 1 ~ 1 



