CALCITES OF NEW YORK 29 
= — 35 == 211.31 
The latter expression is the Bravais-Miller symbol for this particular 
plane. The scalenohedron of which the above plane constitutes one of the 
faces is shown, with the Bravais-Miller symbols of the faces in figure 16. It 
will be noted that the numbers which constitute the indexes of the initial 
face (2131) are repeated in different order (with respect to the first three) 
and with different sign for all the faces of the form. The form is designated 
by the indexes of that one of its planes which lies to the 
right in the front positive sextant, figure 14, the general 
expression for these indexes being (h k i 1). In the 
doemerewana)l ewe —— snake — alee SeriG) ly he 
general expression h k il is modified in special cases. For 
positive rhombohedrons where the initial face is parallel 
to the axis II and intercepts I and —III equally, k in the 
general expression becomes 0 (i. e. {) and h is equal to i. 
The general symbol then for a positive rhombohedron 
is (h o h 1) in which 4 equals the coefficient of R in the 
corresponding Naumann symbol. Similarly the general 
symbol for a negative rhombohedron is (o hh 1), 
Prismatic forms being parallel to the axis IV have for Fig. 16 
the fourth index 0, thus the symbol for the prism of the first order is 
(1010) and that for the prism of the second order (1120). In the case of 
pyramids of the second order where h equals k and i equals 2 h, the 
general expression becomes (h.h.2h.1) in which 2% equals the coefficient of 
P2 in the corresponding Naumann symbol. : 
Goldschmidt’s system of symbols. Goldschmidt in his Index der Krys- 
talljormen der Mineralien adopts three forms of symbols. Of these the first 
This relation which is dependent on a geometrical property of the hexagon is uni- 
versally true. It follows from the above that in the Bravais-Miller symbol for any 
hexagonal plane, the algebraic sum of the first and second indexes is equal to the third 
with the sign reversed. 
