which his force shall have the advantage. The advantage having
been gained and recognized (or an advantage existing and being
recognized), strategy insists on forcing a battle, for the reason
that _every contest weakens the loser more than it does the winner_.

This does not mean that it is always wise to engage a weaker force
that is temporarily separated from its main body. It is readily
understandable, for instance, that it would be unwise in two cases:

1. A case in which the weaker force were so little weaker, and
were part of a force so much larger than the total of the smaller
force, that the gain as between the two forces actually engaged
would not be great enough to compensate for the loss entailed.
For instance, a reference to Table I shows that an _A_ force of
1,000 engaging a _B_ force of 800 would have 569 left when _B_ was
reduced to zero. This is impressive: but if the _B_ force of 800
were part of a total _B_ force of 2,000, in other words if there
were an _A_ force of 1,200 near at hand, _B_ would have 569 left
with which to oppose 1,200, a proportion a little less advantageous
than the proportion he started with--1,000 to 2,000.

2. A case by which the _B_ force may have divided with the express
purpose of luring _A_ to attack; arrangements having been made
whereby the inferior _B_ force would simply hold the _A_ force
until the whole _B_ force could come to its assistance; arrangements
having been also made that this would be accomplished before the
detached part of _B_ should get very badly damaged.

Attention is invited to Table III, which is a continuation of Table
I. It represents what would happen if a force of 1,000 should fight
separately two forces, one of 800 and the other of 200. In column
1, _A_ is supposed to have engaged the 200 first, and so to have
become reduced to 970, and to engage 800 afterward. In column 2,
_A_ is supposed to have engaged 800 first, thereby becoming reduced
to 569, and then to engage the 200 force. The table indicates that
it makes no difference whether _A_ engages the stronger or the
weaker force first.

Column 3 shows that a force of 841, the part remaining after a
force of 1,000 had annihilated a force of 500, would have 653 left
after annihilating a second force of 500. Taken in connection with
columns 1 and 2, this indicates that it is easier to defeat two
separated _equal_ forces than two separated _unequal_ forces of the
same aggregate value; that the