in Algebra, the unfolding or opening of a curve, and making it describe an evolvent.—The word evolutio is formed of the preposition ἐξ “out;” and volvo, “I roll, or wind;” q. d. an unwinding, or unravelling.

The equable evolution of the periphery of a circle, or other curve, is such a gradual approach of the circumference to rectitude, as that its parts do all concur and equally evolve or unbend; so that the same line becomes successively a less arc of a reciprocally greater circle; till at last they change into a straight line. In the Phil. Trans. No. 260, a new quadratrix to the circle is found by this means, being the curve described by the equable evolution of its periphery.

is also used for the extraction of roots out of powers; in which sense it stands opposed to involution. See Algebra.

in the art of war, the motion made by a body of troops, when they are obliged to change their form and disposition, in order to preserve a post or occupy another, to attack an enemy with more advantage, or to be in a condition of defending themselves the better.

It consists in doublings, counter-marches, conversions, &c. A battalion doubles the ranks, when attacked in front or rear, to prevent its being flanked or surrounded; for then a battalion fights with a larger front. The files are doubled, either to accommodate themselves to the necessity of a narrow ground, or to resist an enemy that attacks them in flank. But if the ground will allow it, conversion is much preferable; because, after conversion, the battalion is in its first form, and opposes the file-leaders, which are generally the best men, to the enemy; and likewise, because doubling the files in a new or not well-disciplined regiment, they may happen to fall into disorder. See Doubling.