The full historical truth, accurately stated, cannot be put into the formula, "The Prussians retreated northward in order to be able to join Wellington two days later at Waterloo." To state it so would be to read history backwards, and to presuppose in the Prussian staff a knowledge of the future. The true formula is rather as follows:--"The Prussians retired northward, and not eastward, because the incompleteness of their defeat permitted them to do so, and thus at once to avoid the waste of their Fourth Army Corps and to gain positions where they would be able, if necessity arose, to get news of what had happened to Wellington." In other words, to retreat northwards, though the decision to do so depended only upon considerations of the most general kind, was wise strategy, and the opportunity for that piece of strategy was seized; but the retreat northwards was not undertaken with the specific object of at once rejoining Wellington. It must further be pointed out that this retreat northwards, though it abandoned the fixed line of communications leading through Namur and Liège to Aix la Chapelle, would pick up in a very few miles another line of communications through Louvain, Maestricht, and Cologne. The Prussian commanders, in determining upon this northward march, were in no way risking their supply nor hazarding the existence of their army upon a great chance. They were taking advantage of one of two courses left open to them, and that one the wiser of the two. This retreat upon Wavre was conducted with a precision and an endurance most remarkable when we consider the fact that it took place just after a severe, though not a decisive, defeat. Of the eighty odd thousand Prussians engaged at Ligny, probably 12,000 had fallen, killed or wounded. When the Prussian centre broke, many units became totally disorganised; and, counting the prisoners and runaways who failed to rejoin the colours, we must accept as certainly not exaggerated the Prussian official report of a loss of 15,000.[13] In spite, I say, of this severe defeat, the order of the retreat was well maintained, and was rewarded by an exceptional rapidity. The First Corps marched along the westerly route that lay directly before them by Tilly and Mont St Guibert. They marched past Wavre itself, and bivouacked about midday of Saturday the 17th, round about the village of Bierges, on the other side of the river Dyle. The Second Corps followed the First, and ended its march on the southern side of Wavre, round about the village of St Anne. The Third Corps did not complete the retreat until the end of daylight upon the 17th, and then marched through Wavre, across the river to the north, and bivouacked around La Bavette. Finally, still later on the same evening, the Fourth Corps, that of Bulow, which had come to Ligny too late for the action, marching by the eastward lanes, through Sart and Corry, lay round Dion Le Mont.