It will be observed that we have given no long account of the famous ‘Greek-fire,’ the one point in Byzantine military affairs which most authors condescend to notice. If we have neglected it, it is from a conviction that, although its importance in ‘poliorcetics’ and naval fighting was considerable, it was, after all, a minor engine of war, and not comparable as a cause of Byzantine success to the excellent strategical and tactical system on which we have dilated. Very much the same conclusion may be drawn from a study of the other purely mechanical devices which existed in the hands of the imperial generals. The old skill of the Roman engineer was preserved almost in its entirety, and the armouries of Constantinople were filled with machines, whose deadly efficacy inspired the ruder peoples of the West and East with a mysterious feeling of awe. The vinea and testudo, the catapult onager and balista, were as well known in the tenth century as in the first. They were undoubtedly employed, and employed with effect, at every siege. But no amount of technical skill in the use of military machines would have sufficed to account for the ascendancy enjoyed by the Byzantines over their warlike neighbours. The sources of that superiority are to be sought in the existence of science and discipline, of strategy and tactics, of a professional and yet national army, of an upper class at once educated and military. When the aristocracy became mere courtiers, when foreign mercenaries superseded the Isaurian bowman and the Anatolic cavalier, when the traditions of old Roman organization gave place to mere centralization, then no amount of the inherited mechanical skill of past ages could save the Byzantine empire from its fall. The rude vigour of the Western knight accomplished the task which Chosroes and Crumn, Moslemah and Sviatoslaf, had found too hard for them. But it was not the empire of Heraclius or John Zimisces, of Leo the Isaurian, or Leo the Armenian, that was subdued by the piratical Crusaders, it was only the diminished and disorganized realm of the miserable Alexius Angelus. IV. THE SUPREMACY OF FEUDAL CAVALRY. A.D. 1066-1346. [From the battle of Hastings to the battles of Morgarten and Cressy.] Between the last struggles of the infantry of the Anglo-Dane, and the rise of the pikemen and bowmen of the fourteenth century lies the period of the supremacy of the mail-clad feudal horseman. The epoch is, as far as strategy and tactics are concerned, one of almost complete stagnation: only in the single branch of ‘Poliorcetics’ does the art of war make any appreciable progress.