in two columns by
brigade, as is represented in Figure 32. These are less heavy than a
single column of grand-division by battalion, but are subject to nearly
the same objections.

All offensive operations on the field of battle require _mobility,
solidity_, and _impulsion_; while, on the other hand, all defensive
operations should combine _solidity_ with _the greatest possible amount
of fire_.

Troops in motion can make but little use of their fire-arms, whatever
may be their formation. If in very large masses, they move slower and
are more exposed; but the moral effect of these large moveable columns
is such, that they frequently carry positions without ever employing
their fire. The French columns usually succeeded against the Austrian
and Prussian infantry, but the English infantry could not so easily be
driven from their ground; hey also employed their fire to greater
advantage, as was shown at Talavera, Busaco, Fuente de Honore, Albuera
and Waterloo. The smaller columns and the mixed formation were always
most successful against such troops.

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, a