was detached would be thereby weakened; furthermore, the
information might have been incorrect--it might have been originated
and given out by the enemy, in the hope that it would cause such a
diversion of force.

Every operation in war entails a risk more or less great; and if
no risks were to be taken, it would be better not to go to war.
It is true that some wars have been undertaken in which the
preponderance of force was so great that there was very little
doubt of the actual outcome, and very little risk taken by one of
the two parties. Such wars, however, have been very few; and they
were hardly wars in the usual sense, any more than the beating of
a little boy by a big boy could properly be called a "fight."

Reference may again be made here to Table I on next page, which
shows the way in which fights between unequal forces proceed, and
the advantage of fighting the separated parts of an enemy rather
than the united force. We can see this clearly if we note that, if
two forces each aggregating 1,000 were in each other's vicinity,
and if the entire force _A_ was able to engage half of _B_, or
500, it would whip half of _B_, and have 841 remaining, with which
to engage the other half (500) of _B_. Reference to the end of
the third period in this table shows also that if a force of 789
engages a force of 523, it will have 569 left, after the other
has been reduced to zero. So, a force of 1,000 that engages two
forces of 500 separately, will have more than 500 left, after the
others have both been reduced to zero: whereas, if it engages both,
when they are united, both sides will be gradually reduced to zero,
remaining equal all the time.

TABLE I
----------------------------------------------------------------------------
| |Col.|Col.|Col.|Col.|Col.|Col.|Col.|Col.|Col.|Col.|
| | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|----------------------------------------------------------------------------|
|Value of offensive power A|1000|1000|1000|1000|1000|1000|1000|1000|1000|1000|
| at beginning B|1000| 900| 800| 700| 600| 500| 400| 300| 200| 100|
|Damage done in 1st A| 100| 100| 100| 100| 100| 100| 100| 100| 100| 100|
| period B| 100| 90| 80| 70| 60| 50| 40| 30| 20| 10|
|Value of offensive power A| 900| 910| 920| 930| 940| 950| 960| 970| 980| 990|
| at end of 1st period B| 900|