1889.] Theories of Crystal Structure. 227 
points which have been proposed to account for the geometri- 
cal and physical properties of crystals, may be included in the 
theory of Sohncke after this has received the simple extension 
which is now added by its author. 
In Bravais's network all the particles or structural elements 
were supposed to be identical, and in Sohncke's theory also 
there is nothing in their geometrical character to distinguish 
one particle from another. 
In Fig. 2, the hexagonal series of dots may, as was said 
above, be regarded as composed of a pair of triangular webs, 
A and B ; now these, although identical in other respects, are 
not parallel, for the distribution of the system round any point 
of A is not the same as that round any point of B until it has 
been rotated through an angle of 60^^. 
It is possible, however, to conceive similar interpenetrating 
networks which differ not only in their orientation but even in 
the character of their particles. The centre of each hexagon, 
for example, may be occupied by a particle of different nature 
from A and B to form a new web, O. The three webs are pre- 
cisely similar in one respect, since their meshes are equal equi- 
lateral triangles ; moreover, if the position of the points alone 
be taken into account, the whole system would form a Bravais 
web, i. e., if the particles of O were identical with those of A and 
B. If, however, as is here supposed, the set O consists of par- 
ticles different in character from A and B, the distribution round 
any point of o is totally distinct from that round any point 
of A or B. The points o are geometrically different from the 
points A B. The web A is interchangeable with B, but o is in- 
terchangeable with neither The interpenetrating networks are 
no longer to be regarded as consisting necessarily of identical 
particles, if an explanation is to be given of all the geometri- 
cal forms existing in nature. 
The above figure represents a Sohncke system, A B, of par- 
ticles of one sort interpenetrated by a Bravais web, o, of 
another sort; but there is no reason why two or more different 
Sohncke systems, no one of which is identical with a Bravais 
network, may not interpenetrate to form a crystal structure. 
