CALCITES OF NEW YORK 35 
Turning again for a concrete example to figure 19, the indexes of the 
face 3142 which lies in the zone [1011.1120] when multiplied by the zone 
symbol [111] give the equation 
Cree alse) (aah) ——() 
—o + 1 +2—0 
The same relation may be verified for any face in the zone [1011.1120]. 
Applying this principle to the faces 4132, 2131, and 2461 in figure 19, it 
will be found that these three planes are also in zone, a fact not at first 
apparent from the figure. Thus: 
AAU Cyaan | 
(1—4) 2—2) (8—2)=[306] 
and 
(4x— 3) + (—1x0)+(2x6)=— 12 + 12=0 
This principle is highly useful in the study of crystal forms inasmuch as 
the forms occurring in zones show marked tendency to enter into crystal 
combination with each other. 
The indexes of a face occurring in two zones are obtained by cross 
multiplying the zone symbols of both zones. Taking again for a concrete 
example figure 19, the face 0221 lies in the zone [2131.2311] and also in the 
zone [2461.1120]. Its indexes can therefore be verified by cross multiplying 
the zone symbols of these two zones. 
Ot Tae seal 2) 51 D2] 
S x XX Xe 
We ea tO SRe 
DAs (EARP 
1) Bae Bye 
DS OS OS 
Te Pee 1-2 
On Gr 3 
Or dividing this ratio by — 3 and supplying the third term, 0221. 
