This is far the most important point for the reader's consideration.
It may be said with justice that no one can understand this war who
has not grasped the conflict between these two fundamental conceptions
of armed bodies in action, and the manner in which (by the narrowest
and most fortunate margin!) events in the first phase of the war
justified the French as against the German school.

I must therefore beg the reader's leave to go somewhat thoroughly into
the matter, for it is the foundation of all that will follow when we
come to the narration of events and the story of the Western battle
which began in the retreat from the Sambre and ended in the Battle of
the Marne.

The first postulate in all military problems is that, other things
being equal, numbers are the decisive factor in war. This does not
mean that absolute superiority of numbers decides a campaign
necessarily in favour of the superior power. What it means is that _in
any particular field_, if armament and discipline are more or less
equal on the two sides, the one that has been able to mass the greater
number _in that field_ will have the victory. He will disperse or
capture his enemy, or at the least he will pin him and take away his
_initiative_--of which word "initiative" more later. Now, this field
in which one party has the superior numbers can only be a portion of
the whole area of operations. But if it is what is called the decisive
portion, then he who has superior numbers _in the decisive time and
place_ will win not only there but everywhere. His local victory
involves consequent success along the whole of his line.

For instance, supposing five men are acting against three. Five is