Let A B and C D represent two armies drawn up against each other in three lines of battle, on opposite sides of a stream, E F. The commander of the army A B, finding he cannot cross and drive the enemy from their works, determines, by a flank march to the left, to go around them, crossing at the point E. In order to effect this he must send his trains off by the road I K L to some interior line, and then slowly unfold his masses upon the single road K E H. By the time the head of his column is at H the rear has not perhaps left K, and thus the whole length of his army is exposed on its side to an attack by the enemy, which may sever it into two unsupporting portions. It will be perceived that to accomplish such marches with security, they must be made in secret as far as possible, until a portion of the marching force reaches the rear of the enemy; the column must be kept compact, and great vigilance must be exercised. In his progress from the Rapidan to the James, General Grant made three movements of this character with entire success, each time putting our forces so far in the rear of the rebels that they were compelled to hasten their own retreat instead of delaying to avail themselves of the opportunity for attacking. Besides the topography of the country, various circumstances influence the manner in which a march is conducted--particularly the position of the enemy. When following a retreating foe, the cavalry is sent in the advance, supported by some infantry and horse artillery, to harass the rear guard, and, if practicable, delay the retreat until the main army can come up. This was the case in the peninsula campaign, from Yorktown to the Chickahominy. Again, the exact position of the enemy may not be known, or he may have large bodies in different places, so that his intentions cannot be surmised. It is then necessary to scatter the army so as to cover a number of threatened points, care being exercised to have all the different bodies within supporting distances, and to be on guard against a sudden concentration of the enemy between them. This was the case in the campaign which ended so gloriously at Gettysburg. The rebels were then threatening both Harrisburg and Baltimore, and the two extremities of our army were over thirty miles apart, so as to be concentrated either on the right, left, or centre, as events might determine. It happened that a collision was brought on at Gettysburg, and both armies immediately concentrated there. The corps on the right of our army was obliged to march about thirty-two miles, performing the distance in about eighteen or nineteen hours, and arriving in time to participate in the second day's battle. As much skill is evinced by a commander in preliminary manoeuvring marches and the assignment of positions to the different portions of his army as in the direction of a battle. Napoleon gained many of his victories through the effects of such manoeuvres.