KING PHILIP, it will be remembered, received his military education in the school of EPAMINONDAS, who, as is well known, revolutionised the Higher Thought of every Higher Command by the discovery and application of a single tactical fact--namely, that the chances of A being able to give B a stronger push than B can give him are _in direct ratio to the numerical superiority of A over B_. It follows, then, that, faced with a sufficient superiority, B _must_ retire, and _the initiative then rests with the side that possesses it_.
In pursuance of this tactical ideal EPAMINONDAS argued that the old method of winning battles, which was that A should exercise superior force against every point of B's line (or body), required that A should be bigger than B, buskin for buskin and brisket for brisket. 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. It should be noted, as a brilliant example of PHILIP'S staff work, that in the Macedonian Army, for the avoidance of confusion in the field, "phalanks" is now spelt "flanks."