more than three; and if the forces bear upon each other equally, the
five will defeat the three. But if the five are so badly handled that
they get arranged in groups of two, two, and one, and if the three are
so well handled that they strike swiftly at the first isolated two and
defeat them, thus bringing up the next isolated two, who are in their
turn defeated, the three will, at the end of the struggle, have only
one to deal with, and the five will have been beaten by the three
because, although five is larger than three, yet _in the decisive time
and place_ the three never have more than two against them. It may be
broadly laid down that the whole art of strategics consists for the
man with superior numbers in bringing all his numbers to bear, and for
the man with inferior numbers in attempting by his cunning to compel
his larger opponent to fight in separated portions, and to be defeated
in detail.

As in every art, the developments of these elementary first principles
become, with variations of time and place, indefinitely numerous and
various. Upon their variety depends all the interest of military
history. And there is one method in particular whereby the lesser
number may hope to pin and destroy the power of the greater upon which
the French tradition relied, and the value of which modern German
criticism refused.

Before going into that, however, we must appreciate the mental
qualities which led to the acceptance of the theory upon the one side
and its denial upon the other.

The fundamental contrast between the modern German military temper and
the age-long traditions of the French service consists in this: That
the German theory is based upon a presumption of superiority, moral,