It requires much attention to conduct heads of battalion columns of both lines nearly parallel to their lateral ones, and perpendicularly, or diagonally to front or rear, according to the nature of the movement. To determine with precision, and in due time, their points in the new line, that wavering and uncertainty of march may be avoided. In great movements to allow the soldier every facility of motion without increasing the distances of divisions, and to require the most exact attention on entering the new line, and in forming. To avoid obstacles in the course of marching, but as soon as possible to re-enter the proper path of the column, while out of that path, the colors of that battalion column may be lowered, (as a mark for the neighboring column, not to be then entirely regulated by it) and again advanced when it regains its proper situation.

All the battalions of a second line, must at the completion of every change of position, find themselves placed in the same relative situation with respect to the first, as they were in before the commencement of the movement.

All changes of position of a first line are made according to one of the modes already prescribed: in general, in critical situations, they are made on a fixed flank, or central point, and by the echellon march of platoons or echellons of smaller sections than platoons, where ground and other circumstances require it; and the echellons may upon occasion be each marched in file, but keeping its position: but the movements of a second line being protected, more complicated, and embracing more ground, are made by the march of battalion columns regulated by a certain determined division of the line.

In all cases where a change of position is made on a flank or central point of the first line, the movement of its corresponding point of the second line determines the new relative situation of that second line.

Movements Parallel with a line of fire. Movements are said to be parallel with a line of fire, when one or more lines march either in the rear of troops engaged with an enemy, or in face of an enemy, who is advancing to attack. The greatest accuracy and order are required on both occasions, particularly on the latter; for if the second line, which is the line of support, does not preserve its perpendicular direction with respect to every leading point, and its relative parallelism and distance with the line engaged, according to circumstances, it will not only run the risk of becoming useless itself, but will in all probability endanger the line it covers, should any sudden necessity occur for a change of position.

PARALLELOGRAM, (Parallelogramme, Fr.) a plain figure bounded by four right lines, whereof the opposite are parallel one to the other. It likewise means an instrument composed of five rulers of brass or wood, with sliding sockets, to be set to any proportion, for the enlarging or diminishing any map or draught.

PARALYSER, Fr. To paralyse. A term frequently used by the French since the revolution, to express the bad effects of a factious spirit, &c. Un seul factieux quelque fois paralyse toute une administration: one factious man will sometimes render the designs of a whole administration abortive.

PARAMETER. See [Gunnery] and [Projectiles].

PARAPET, in fortification, an elevation of earth, designed for covering the soldiers from the enemy’s cannon, or small shot; its thickness is from 18 to 20 feet; its height 6 on the inside, and 4 or 5 on that side next the country: it is raised on the rampart, and has a slope called the superior talus, or glacis of the parapets, on which the troops lay their arms to fire over. The slope renders it easy for the soldiers to fire into the ditch. It has a banquette or two on the inside for the troops who defend it, to mount upon, for better discovering the country, the ditch, and counterscarp, to fire as they find occasion.

Parapet of the covert-way, is what covers that way from the sight of the enemy; which renders it the most dangerous place for the besiegers, because of the neighborhood of the faces, flanks, and curtains of the place.