capable of the disciplined and united action required by all real strategy, incapable even of forming the shield-wall and executing the feigned flight described by the contemporary chroniclers of the battle. While it is true that mediæval fighting was far more individualistic than that of ancient or modern armies and lacked also the flexible conditions which lie at the basis of modern tactics, there is the best of contemporary evidence for a certain amount of strategical movement at Hastings. On one point, however, the modern military critics have compelled us to modify our ideas of the battles of earlier times, namely, with respect to the numbers engaged. Against the constant tendency to magnify the size of the military forces, a tendency accentuated in the Middle Ages by the complete recklessness of chroniclers when dealing with large figures, modern criticism has pointed out the limitations of battle-space, transportation, and commissariat. The five millions with which Xerxes is said to have invaded Greece are a physical impossibility, for Delbrück has shown that, with this number moving under normal conditions, the rear-guard could not have crossed the Tigris when the first Persians reached Thermopylæ. Similarly the fifty or sixty thousand knights attributed to William the Conqueror shrink to one-tenth the number when brought to face with the official lists of English and Norman knights' fees. If William's army did not exceed five or six thousand, that of Harold could
