PEINCIPLES OF CRYSTALLOGRAPHY. 249 



This results also from the zone-equation — 

 11 1 111 

 001 001 



1.1-0.1; 1.0-1.1; 1.0-0.,1 

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



l.j? — 1 . y -{■ . z = () orx — y 

 as condition of the tautozonality of a face, w y z, with 01 and 111; the 

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

 In the same way the position of d, in the zones h dc and « j; ^7, 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 — 



fc_l_0^-, 

 I 1 

 and therefore the symbol (0 1 1). 



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

 h Z, and by the zone h pf, asl 1, because — 



- = ■"- = - = 1 

 I ~ 1 ~ ~ 



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

 1c h o and dfn; for the last we have — 

 Oil Oil 

 10 1 10 1 



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

 or [111]; also as condition — 



h.l + k.l — 0.1 = or h=— 1c 

 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 hie lis the symbol of q — 



the last — 



hi 1 n T i\ 



ll^ = \=\ = lov{hhh) 



which, when contracted, is 1 T 1. 



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

 which reason — 



]c ^ -_1 ^ ^ _ 1 

 I 1 ~0 

 e has thus the symbol (Oil). 



There remains s in the zones m p se and d sfntohe determined ; the 

 first zone gives — 



^ = -=1 



1c~ 1 1 



