But since it is sufficient,
while "refusing" the rest of one's own body (or line), to bring an
overwhelming force to bear on the point of a person's jaw, in order to
discomfit him, so in a battle a numerically inferior A, by concentrating on
a vital point of numerically superior B, can gain a local numerical
superiority which will enable him to rout B utterly. (This is always
supposing that B is not doing the same thing himself on the other wing, in
which case each army would miss the other altogether--a condition of things
into which the military art does not care to follow them).
Hence the phalanx or "preponderating mass formation." The Macedonian
development of this depends (to reduce the matter to the simple algebraical
formula to which all military problems are susceptible) on the fact that if
_x_ equals the greatest efficiency of an army, and the rooted square of
stability to the _n_th rank equals the phalanx, then the rooted square of
stability to the _n_th rank equals _x_ minus the tangential curve of
velocity of mobility. This should be plain even to the amateur student of
tactics. Blending almost a military expert's appreciation of this cardinal
doctrine with his natural selfishness as a leader of cavalry, PHILIP has
given to this, the mobile arm, much of the striking power of the original
phalanx. This is now placed in the centre, its business being mainly to
force a salient in the enemy's line, the two resultant enclaves of which
can then be shattered (at their re-entrants) by the cavalry squadrons,
hurled forward on both phalanks.
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