64 
Proceedings of Eoyal Society of Edinburgh. [sess. 
possible faces normal to the common base and all intersecting in 
A. The base is therefore a possible zone plane, and A is a possible 
zone axis (see fig. 1.) 
An axis of symmetry of the nth order is crystallographically pos- 
.A 
i 
i 
Fig. 1. 
27 r 
sible only when cos — is rational. — Let A be a crystallographical 
axis of symmetry of the nth order. An edge OB normal to it 
iA 
(possible as shown above) necessitates n - 1 other edges crystallo- 
graphically identical with it and all making equal angles with their 
neighbours. Take two such neighbouring edges, OB and OB\ along 
with A, as axes of reference. The face 111 has equal parameters 
