1. CHAPTER II.--The proportion of cavalry to infantry in Grouchy’s force was large (more than one to five), but not excessive. He was given a task in which cavalry must play the chief part. At the close of such a battle as Ligny, the infantry on both sides must be more or less exhausted, and it becomes the duty of the cavalry to pursue the retreating enemy. Cavalry alone, however, will effect little, if the enemy takes to rear-guard positions; it must be supported or accompanied by artillery and infantry. It must be remembered that, of the two sides, the vanquished are the more exhausted, and the greater the enemy’s anxiety to draw his troops clear of pursuit, the closer that pursuit must be. The French cavalry at Ligny, except Milhaud’s Cuirassiers, had had little to do. The proportion of cavalry to infantry in an army cannot be laid down by any hard-and-fast rule. Prince Kraft wrote after 1870: “The duties of the cavalry are so comprehensive and so important, especially at the first moment of a war, that we cannot have too many cavalry ready for service.” But he was speaking of Germany. Continental armies require a far larger number of cavalry than our own; and not only for the reason that their other arms are so much more numerous than ours. The advance of modern armies is covered by a most numerous cavalry, sent out, as were the German cavalry in 1870, miles ahead, as a screen, and for the purpose of reconnaissance, or to harass the enemy’s concentration and cut his communications. 2. _The French Corps in 1815._--The French Corps in the 1815 Campaign were more independent than the Prussian Corps--that is to say, each corps, except Lobau’s, was provided with sufficient cavalry and artillery to enable it to act by itself. Each corps had a Light Cavalry Division; but in Grouchy’s force, the Cavalry Division (Domon’s) belonging to Vandamme’s Corps, with its horse battery, had been detached to the left wing. Gérard’s Corps had its complete parts, but the Seventh Cavalry Division attached to it numbered only 758 men; little more than a modern regiment. The Reserve Cavalry Division, under Jacquinot, also attached to Gérard’s Corps, numbered 1608 men, so that the two together would only make a modern brigade. In artillery, the corps, for those days, were well provided; and each corps also had its own engineers, from 140 to 200 strong.