119 
of Edinburgh, Session 1884-85. 
These other faces are pyramid faces. Each pyramid face lies between, 
and in the same zone with, a prism face and a basal face. It may, 
therefore, he represented by the symbol 
1 
as +—U,, 
P 
where s and t are the symbols of the prism face and the basal face 
respectively, a and b are small whole numbers, and p is the ratio of 
the length of a line parallel to the axis after, to the length of the 
line before deformation. We may put 
b 
— = ft, 
a 5 
when this becomes, for the tetragonal system 
(hk 0) + -in (001), 
which is 
( hh j) 
the Miller symbol for a pyramid face in this system, with the ratio 
of the parameter of z to that of x or y , expressed by p. In the 
hexagonal system the symbol 
takes the form 
1 
+ — nt 
P 
(hkl) + — w (111), where h + k + l — 0 . 
We may leave p understood, as it is constant for the same substance 
and same temperature, and write this in the contracted form 
(hkl, ft). This gives 
h + 
7 , "ft 7 I ft 
k + — , l + — , 
P P 
as the coefficients of x, y , and z in the equation of the face referred 
to the rectangular axes of the regular system. These axes are, of 
course, not crystallographic axes of the hexagonal system, but some 
advantages arise from their use. They are rectangular, and there- 
fore the ordinary formulae of solid geometry can be used ; the 
symbol of the general form (hkl, n), where hk and l are free to 
change places and change sign together, and n changes sign indepen- 
dently, gives a clear oversight of all the faces of the holohedral 
form, and enables us to derive from the symbol the various kinds of 
hemihedry. 
