Besides the difficulty of depending upon the exact application of an order of battle arranged in advance, it often happens that battles begin without even the assailant having a well-defined object, although the collision may have been expected. This uncertainty results either from circumstances prior to the battle, from ignorance of the enemy's position and plans, or from the fact that a portion of the army may be still expected to arrive on the field. From these things many people have concluded that it is impossible to reduce to different systems the formations of orders of battle, or that the adoption of either of them can at all influence the result of an engagement,--an erroneous conclusion, in my opinion, even in the cases cited above. Indeed, in battles begun without any predetermined plan it is probable that at the opening of the engagement the armies will occupy lines nearly parallel and more or less strengthened upon some point; the party acting upon the defensive, not knowing in what quarter the storm will burst upon him, will hold a large part of his forces in reserve, to be used as occasion may require; the assailant must make similar efforts to have his forces well in hand; but as soon as the point of attack shall have been determined, the mass of his troops will be directed against the center or upon one wing of the enemy, or upon both at once. Whatever may be the resulting formation, it will always bear a resemblance to one of the figures previously exhibited. Even in unexpected engagements the same thing would happen,--which will, it is hoped, be a sufficient proof of the fact that this classification of the different systems or orders of battle is neither fanciful nor useless.