The main thing in an offensive battle is to seize upon the decisive point of the field.  This point is determined by the configuration of the ground, the position of the contending forces, the strategic object of the battle; or, by a combination of these.  For example, when one wing of the enemy rests on a height that commands the remainder of his line, this would seem the decisive point to be attacked, for its occupation would secure the greatest advantages; but this point may be so very difficult of access, or be so related to the strategic object as to render its attack out of the question.  Thus it was at the battle of Bautzen:  the left of the allies rested on the mountains of Bohemia, which were difficult of attack, but favorable for defence; moreover, their only line of retreat was on the right, which thus became the point of attack for the French, although the topographical and tactical key of the field was on the left.

III.  It frequently happens in modern warfare that battles result from the meeting of armies in motion, both parties acting on the offensive.  Indeed, an army that is occupying a defensive position may, on the approach of the enemy, advance to meet him while on the march.  Battles of this kind may partake of the mixed character of offensive and defensive actions, or they may be of the nature of a surprise to both armies.  To this class belong the battles of Rosbach, Eylau, Lutzen, Luzzara, Abensberg, &c.

Surprises were much more common in ancient than in modern times, for the noise of musketry and the roar of artillery, belonging to the posts or wings assailed, will prevent any general surprise of an army.  Moreover, the division into separate masses, or corps d’armee, will necessarily confine the surprise to a part, at most, of the forces employed.  Nevertheless, in the change given to military terms, a surprise may now mean only an unexpected combination of manoeuvres for an attack, rather than an actual falling upon troops unguarded or asleep.  In this sense Marengo, Lutzen, Eylau, &c. are numbered with surprises.  Benningsen’s attack on Murat at Zarantin in 1812 was a true surprise, resulting from the gross negligence and carelessness of the king of Naples.

An order of battle is the particular disposition given to the troops for a determined manoeuvre on the field of battle.  A line of battle is the general name applied to troops drawn up in their usual order of exercise, without any determined manoeuvre; it may apply to defensive positions, or to offensive operations, where no definitive object has been decided on.  Military writers lay down twelve orders of battle, viz.:  1st.  The simple parallel order; 2d.  The parallel order with a crotchet; 3d.  The parallel order reinforced on one or both wings; 4th.  The parallel order reinforced on the centre; 5th.  The simple oblique order; 6th.  The oblique order reinforced on the assailing wing; 7th.  The perpendicular order on one or both wings; 8th.  The concave order; 9th.  The convex order; 10th.  The order by echelon on one or both wings; 11th.  The order by echelon on the centre; 12th.  The combined orders of attack on the centre and one wing at the same time.