28 NEW YORK STATE MUSEUM 
Bravais-Miller system of symbols. The system of symbols adopted by 
Bravais after the method of Miller has several points of superiority over 
other systems. It provided an expression for every face of a form and is 
particularly adapted to the determining of zonal relations by means of 
zone equations. This system or some modification of it is now in almost 
universal use. 
4 The Bravais-Miller symbols are essen- 
\ é tially a system of indexes, or relative inter- 
cepts of the axes, expressed in numbers. As 
applied to the hexagonal system these 
indexes are four in number, the first three 
relating to the horizontal axes and the fourth 
to the vertical axis. Assume the hexagonal 
axes numbered as shown in figure 15 and 
consider their extremities as positive and 
negative as indicated. Any plane having the 
position relative to these axes indicated by 
the shaded plane would intercept the axes 
in the proportion: 
I et I IV 
Fig, 15 
This proportion expresses the position of the chosen plane in space 
with respect to the hexagonal axes, but inasmuch as it is somewhat cumber- 
some, particularly when the intercepts are fractional ratios, Miller takes 
the reciprocals of the terms of the proportion and reduces them to whole 
numbers, placing a minus sign over the intercept on a minus axis thus: 
‘Tn the first of the proportions, which is essentially the symbol as written by Weiss, 
the first term is 1. Calling the second term n, the third term will be represented by the 
2 n 
expression — 
nN 
=a and the general expression for any plane referred to hexagonal axes 
a 
ener 
n+1- 
MAV i OCMW ELLEN setin 
