140 THE SOCIAL THEORY OF GEORG SIMMEL
determined by that common bond, but merely by the formal
 exigencies of the large group. This numerical subdivision
 of large groups is a schematic, formal, and mechanical
 type of social organization. It makes possible the
combination of smaller units into larger ones until social
differentiation and integration shall have given the large
group a unified organic structure instead of a mechanical
unity.
The numerically defined subgroup may have been
formed out of small organic circles, but its teleological
significance does not lie in its own structure, but in its external
 relationships to the large group. Such an organization
 makes it possible to maintain the character and the
structure of the parts independently of the growth of the
whole. The central administration deals only with elements
 of identical sociological quality, and an extension
of the group merely means a greater number of elements.
This type of social organization finds its most complete
expression in an army. Increase or decrease in size can be
obtained by simply adding or subtracting a number of
numerically fixed sociological forms. For that reason it
has always been used in a more or less pure form for all
warlike purposes. Nomadic peoples on a campaign of conquest
 have no other stable social content available as a
basis for organization and must resort to a formal principle
which will serve their purpose. The numerical principle is
the most advantageous one and infinitely superior to the
kinship organization in that it is less likely to lead to disruption
 through blood feuds. After the conquest, the numerical
 principle will often be projected into the administration
 of the conquered territory until a more factual or
organic principle can supplant it.
The advantages of such a subdivision on the numerical
principle hold, of course, for all magnitudes and are inde-