PRINCIPLES OF CRYSTALLOGRAPHY. 



247 



3. The cases given under the second and tliird rules are special cases 

 of a more general one; and, certainly, two given faces, [hJcl) and {pqr)^ 

 in which — 



fc _ g 



T r 



can alwaj^s be so represented that their symbols have the form (e u v) 

 and (.r wi"), because the three indices of a face may be multiplied by the 

 same number withont changing the symbol. 

 For the zone we have — 



euv euv 

 xuv xuv 



u . V — n . u ; V . X — e . V ; e . u — u . x 



o; V {x — e); u [e — x) 



or, if we divide the three zooe-indices by {x — e), [0 v «] ; a face, {r st)^ 

 lies in this zone, if — 



o.r-\-v.s — u.t = o 

 so — 



s _u 



i~v 



Let any two faces of a zone be represented by the symbols (xuv) and 

 {euv), or, generally, let them have two similarly-situated 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 _ ^ 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. 



