34 NEW YORK STATE MUSEUM 
The Bravais symbols (h kil) and (h’ k’ 7 V) of the two faces from 
which the indexes i and i’ are omitted are written twice over one another 
as represented thus: 
Votan Iced daw, = ike | 1 
K AK eka 
Wik Vv W el 
The four end indexes are struck out and the remaining indexes are 
multiplied and subtracted as follows: 
Joy A a hI = ih 
I tot, = Ig) 7 
hk’—kh’—=w 
The resulting numbers [u v w] inclosed in brackets gives the symbol for 
the zone axis. The above operation of cross multiplication 1s much simpli- 
fied by reading the products from left to right downward for the first term 
and from right to left downward for the second term of each equation. 
Strict attention should be paid to signs the results being algebraic products, 
sums and differences. Referring for a concrete example to figure 19 the 
zone symbol for the zone containing the faces 1011 and 1120 is 
LtO tL O) i 
XC XGEOXG 
Lik Olt) o 
O= 1) d= 0) SC. =0)e =m 
Also the zone symbol for the zone containing 2461 and 4261 is 
Aa Nl | 1 
(=4-9) 442) \G4= 16) —|6- 6) 2) 
or dividing this ratio through by 6, [112]. 
It has been demonstrated! that the algebraic sum of the (h k 1) indexes 
of any face ina given zone multiplied by the corresponding indexes [u v w] 
of the zone symbol is equal to 0; 
It Gl Fede Wok ll ww¥==0 
1 Miller, W. H. A Treatise on Crystallography. London 1839. p. 10. 
