3d. The mixed system, or the combination of the two preceding, has sometimes been employed with success. Napoleon used this formation at Tagliamento, and the Russians at Eylau. Each regiment was composed of three battalions, the first being deployed in line, and the other two formed in columns of attack by division in rear of the two extremities, as shown in Fig. 30. It may in some cases be better to place the second and third battalions in line with the first, and on the two extremities of this battalion, in order to prolong the line of fire. The centre of the line of each regiment would be less strong, however, than when the two battalions by column are placed in rear of the other which is deployed. This mixed system of formation has many advocates, and in certain situations may be employed with great advantage. 4th. The deep order of heavy columns of several battalions is objectionable as an habitual formation for battle, inasmuch as it exposes large masses of men to the ravages of artillery, and diminishes the mobility and impulsion of an attack without adding greatly to its force. Macdonald led a column of this kind at the battle of Wagram with complete success, although he experienced enormous losses. But Ney's heavy columns of attack at Waterloo failed of success, and suffered terribly from the concentric fire of the enemy's batteries. Whenever deep columns are employed, Jomini recommends that the grand-division of twelve battalions should have one battalion on each flank, (Fig. 31,) marching by files, in order to protect its flanks from the enemy's attacks. Without this defence a column of twelve battalions deep becomes an inert mass, greatly exposed to be thrown into disorder or broken, as was the column of Fontenoy, and the Macedonian phalanx by Paulus Emillus. A grand-division is sometimes arranged 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.