228 The American Naturalist. [April, 
In its most general form, then, the theory may now be ex- 
A crystal consists of a finite number of interpenetrating 
Sohncke systems which are derived from the same Bravais net- 
work. The constituent Sohncke systems are in general not 
interchangeable, and the structural elements of one are not 
necessarily the same as those of another. 
Or, since each Sohncke system consists itself of a set of in- 
terpenetrating networks, the theory may be thus expressed — 
A crystal consists of a finite number of parallel interpenetra- 
ting congruent networks : the particles of any one network are 
parallel and interchangeable; these networks group themselves 
into a number of Sohncke systems in each of which the parti- 
cles are interchangeable but not necessarily parallel. 
The number of kinds of particles which constitute the crys- 
tal may therefore be equal to the number of Sohncke systems 
involved in its construction. 
The structural units are no longer, as they were in the 
theory of Bravais, necessarily identical, but may represent at- 
omatic groups of different nature. 
The system in Fig. 2 consists of two sets of particles, A B 
and O; and, if a large enough number of these be taken, any 
portion of the system {i. c. any crystal constructed in this man- 
ner) consists of the particles united in the proportion of two 
of the first group to one of the second. Such an arrangement, 
then, may represent the structure of a compound, O A.,. 
"When, for example, a salt in crystaUizing takes up so- 
called water of crystallization which is only retained so long as 
the crystalline state endures, the chemical molecule salt-f 
water cannot be said to exist except in the imagination, for the 
presence of such a molecule cannot be proved. To obtain an 
easily intelligible example, without, however, pronouncing any 
opinion as to whether it may be realized, imagine the centred 
hexagons in the figure to be constructed in such a way that 
each corner consists of the triple molecule 3 H^O, and each 
centre consists of the molecule R. The chemical formula would 
then be R -f- 6H,0, and yet a molecule of this constitution 
