PEINCIPLES OF CRYSTADLOGKAPHY. 



247 



3. The cases giveu under the secoDd and third rules are special cases 

 of a more general one; and, certainly, two given faces, (Jilil) and {pqr), 

 in which — 



fc _ 5 I 



T r 



can always be so represented that their symbols have the form [e u v) 

 and {.V uv), because the three indices of a face may be multiplied by the 

 same number without changing the symbol. 

 For the zone we have — 



euv e u V 

 xuv xuv 



u . V — V . ?( 

 o; 



V . X — e . V ; e . u — u 



V (x — e) ; u {e — x) 



or, if we divide the three zone-indices by [x — c), [0 v u] ; a face, (r s t), 

 o.r-\-v.s — u.t^=o 



lies in this zone, if 



so- 



Let any two faces of a zone be represented by the symbols {x u v) and 

 {euv), or, generally, let them have two similarly-sitaated indices in both 

 faces with like relations, all the faces of this zone will be represented in 

 the form {puv). 



That the second law comes also under this head is clear, because the 

 relation _ is indeterminate, and therefore can answer to every value. 



As an example of development by zones, we have chosen the crystal 

 represented in Fig. 12. Because we assume that there are no measure- 



ments, but only the data of the zones, we shall presume, in the projec- 

 tion, (Fig. 13,) that it is triclinic. In this projection we record the faces 

 in the order in which they are to be determined. 



