Greek tactics developed the phalanx; Roman tactics, the legion; the tactics of the barbarians employed the square phalanx, wedge or lozenge. The mechanism of these various formations is explained in all elementary books. Polybius enters into a mechanical discussion when he contrasts the phalanx and the legion. (Book 18.) The Greeks were, in intellectual civilization, superior to the Romans, consequently their tactics ought to have been far more rational. But such was not the case. Greek tactics proceeded from mathematical reasoning; Roman tactics from a profound knowledge of man's heart. Naturally the Greeks did not neglect morale nor the Romans mechanics, [2] but their primary, considerations were diverse. What formation obtained the maximum effort from the Greek army? What methods caused the soldiers of a Roman army to fight most effectively? The first question admits of discussion. The Roman solved the second. The Roman was not essentially brave. He did not produce any warrior of the type of Alexander. It is acknowledged that the valorous impetuosity of the barbarians, Gauls, Cimbri, Teutons, made him tremble. But to the glorious courage of the Greeks, to the natural bravery of the Gauls he opposed a strict sense of duty, secured by a terrible discipline in the masses. It was inspired in the officers by a sentiment of the strongest patriotism. The discipline of the Greeks was secured by exercises and rewards; the discipline of the Romans was secured also by the fear of death. They put to death with the club; they decimated their cowardly or traitorous units. In order to conquer enemies that terrified his men, a Roman general heightened their morale, not by enthusiasm but by anger. He made the life of his soldiers miserable by excessive work and privations. He stretched the force of discipline to the point where, at a critical instant, it must break or expend itself on the enemy. Under similar circumstances, a Greek general caused Tyrtaeus to sing. [3] It would have been curious to see two such forces opposed. But discipline alone does not constitute superior tactics. Man in battle, I repeat, is a being in whom the instinct of self-preservation dominates, at certain moments, all other sentiments. Discipline has for its aim the domination of that instinct by a greater terror. But it cannot dominate it completely. I do not deny the glorious examples where discipline and devotion have elevated man above himself. But if these examples are glorious, it is because they are rare; if they are admired, it is because they are considered exceptions, and the exception proves the rule. The determination of that instant where man loses his reasoning power and becomes instinctive is the crowning achievement in the science of combat. In general, here was the strength of the Roman tactics. In particular cases such successful determination makes Hannibals and Caesars.