1889.] , Theories of Crystal Structure. 225 
sixty-five possible Sohncke systems of points.and that these may 
be grouped according to theirsymmetry into six classes, corres- 
ponding to the six crystallographic systems ; and further that 
there are within each class minor subdivisions, characterized 
by a partial symmetry corresponding to the hemihedral and 
tetartohedral forms of crystallographers. 
The theory of Sohncke contains within itself the essential 
features of a Bravais network of structural molecules, and also 
the auxiliary hypothesis regarding the arrangement of parts 
within the molecules which is required to account for merohe- 
drism. On close examination the arrangement of Sohncke 
proves to be a simple extension of that of Bravais. 
Each of Sohncke's arrangements may be regarded as de- 
rived from one of the parallelopipedal networks of Bravais if 
for every point of the latter be substituted a group of symmet- 
rically arranged satellites. It is not necessary that any particle 
in a group of these satellites should actually coincide with the 
point of the Bravais network from which the group is derived ; 
and the points of the Sohncke system do not themselves form 
a network ; it is only when all the points in each group of 
satellites are condensed into one centre that a Sohncke system 
coincides with a Bravais network. 
To any particle of one of the satellite groups corresponds in 
every other group a particle similarly situated with regard to 
the point from which the group has been derived. Every such 
point may be said to be homologous with the first. 
Each complete set of homologous points is itself a Bravais 
network in space, and consequently a Sohncke system may be 
regarded as a certain number of congruent networks interpen- 
etrating one another: the number 
of such networks, in general, being 
equal to the number of points which 
constitute each group of satellites. 
The relation of a Sohncke system 
to the network from which it is de- 
rived may be illustrated by a bees'- 
cell distribution of points in one 
