From these remarks we must conclude--1st. That the very thin as well as the very deep formation is objectionable under ordinary circumstances, and can seldom be employed with safety. 2d. That the attack by battalions in columns by division is the best for carrying a position; the column should, however, be diminished in depth as much as possible, in order both to increase its own fire and to diminish its exposure to the fire of the enemy; moreover, it should be well covered by tirailleurs and supported by cavalry. 3d. That the mixed formation of the first line deployed and the second in columns of battalion by division is the best for defence. 4th. That either of the last two may be employed in the offensive or defensive, according to the nature of the ground, the character of the general, and the character and position of the troops. Squares are always good against cavalry. Troops should be habituated to all these formations, and accustomed to pass rapidly from one to another in the daytime or at night. None, however, but disciplined troops can do this: hence the great superiority of regulars on the field of battle, where skilful manoeuvres frequently effect more than the most undaunted courage. The arm next in importance on the battle-field is _cavalry_. The principal merit of this arm consists in its _velocity_ and _mobility_. Cavalry has little solidity, and cannot of itself defend any position against infantry; but in connection with the other arms, it is indispensable for beginning a battle, for completing a victory, and for reaping its full advantage by pursuing and destroying the beaten foe. There are four different modes of forming cavalry, the same as for infantry: 1st in deployed lines; 2d, a line of regiments in column of attack on the centre; 3d, the mixed formation; and 4th, the deep formation of several columns. 1st. The thin formation was deemed objectionable for infantry, on account of its liability to be penetrated by cavalry. The same objection does not hold so forcibly with respect to this latter arm; but full lines are deemed less advantageous than lines deployed checker-wise or in echelon. In either case the distance between the lines should be sufficient to prevent the second line from coming in contact with the first, in case the latter receives a slight check. This distance need not be so great in lines deployed checker-wise, as when they are full, or in echelon.