It is a recognised axiom among military men that for such a scheme as the Germans had in view in France, the lowest superiority in numbers necessary is a proportion of four to three. Even that assumes equal training and equipment, and equal skill in leadership. The last factor, skill in leadership, which is in war the most difficult to estimate beforehand, is, at the same time, as this struggle has proved, tremendously important. In regard to it the odds were heavily against the Germans. The Battle of Ypres, it has become evident, was on their part a series of bad mistakes--mistakes which were not seen until too late. After the defeat at Reims Count von Moltke was removed from his place as Chief of the Staff and Baron von Falkenheyn appointed. The strategical scheme of Baron von Falkenheyn was sound and bold enough if Antwerp had not got into the way of it, and if, too, the tactical blunders of Ypres had not ruined its execution. Besides defects in leadership, the Germans had to face the striking comparative deficiency of their field artillery, and the fact that their gunnery had not turned out so practically sound as that of the French. It followed that to resume the offensive they must have a superiority of even more than four to three. They had begun with a superiority of two to one. Yet through the unexpected skill in their opponents' leadership they had been foiled and had had their initiative wrested from them. In view, however, of the demands of the campaign on the East, this necessary weight of numbers they could not on the West supply. One resource was to make it up by an appeal to the spirit of the army. That took the form of an unusually liberal distribution of rewards for individual valour.