BarLtow—A Mechanical Cause of Homogeneity of Crystals. 613 
The number of different groups obtainable by twofold substi- 
tution given under the two heads A and B as before, is as 
under :— 
NuMBER OF GROUPS DERIVABLE. 
Description of group of similar similarly iN B 
situated ball-centres before 
substitution is made. 
Balls sub-| No. of |/Balls sub-| No. of 
stituted | Enantio- || stituted | Enantio- 
alike. morphs. || different. | morphs. 
Six-Ball Groups. 
| 6a, Class 9, the six similar ball centres lie 
at the angles of a regular hexagon, 3 — 3 — 
64, Class 10, the six similar ball centresilie 
at the angles of a regular hexagon (an 
enantiomorph), 3 — 3 — 
6c, Class 11, the six efratlle ball’ AST TRE lie 
at the angles of a regular hexagon, 3 — 5 — 
6d, Class 12, at the alternate corners of a 
right regular hexagonal prism, 4 1 pair 5 2 pairs 
6e, Class 13, at the corners of a triangular 
right prism, 4 1 pair 5 2 pairs 
6f, also Class 13, two and two in the sides 
of an equilateral triangle equidistant 
from the angles, ° 4 — 5 = 
6g, Class 15, form a trigonal 6- -point-group 
which has no plane of symmetry (an 
enantiomorph), 4 — 5 — 
6h, Class 17, at the angles of a regular 
hexagon, . 3 — 5 2 pairs 
6i, Class 18, at the angles of a regular 
hexagon (an enantiomorph), . 3 — 5 — 
67, Class 28, at the corners of a regular 
octahedron, 2 — 2 — 
6%, Class 29, at the corners of a regular 
octahedron (an enantiomorph), y) — 2 — 
67, Class 30, at the corners of a regular M 
octahedron, 2 — 3 1 pair 
6m, Class 31, at the corners of a regular 
octahedron, 2 — 3 — 
6x, Class 32, at the corners of a regular 
octahedron (an enantiomorph), 2 — 3 _— 
6p, Class 12, at the angles of a regular 
hexagon, me 4 1 pair 6 3 pairs 
6q, Class 14, at alternate angles of a regular 
right- -hexagonal prism, 5 , | 2 pairs 10 5 pairs 
67, Class 16, at the corners of a triangular 
prism, 5 2 pairs 10 5 pairs 
6s, Class 19, two and ‘two in the sides of an 
equilateral triangle equidistant from 
the angles, ‘ : 7 - : 
Nn 
1 pair 10 5 pairs 
1 The centres lie in planes of symmetry. 2 The centres lie on digonal axes. 
