EVOLUTIONS may be divided into two classes, the simple and the compound; simple evolutions are those which consist in simple movements, which do not alter the shape or figure of the battalion, but merely afford a more or less extended front or depth, keep it more or less closed to its flanks or centre, turn its aspect to flank or rear, or break it into divisions, subdivisions, sections, or files, in order that it may unfold itself, or defile and resume its proper front or order of battle. All the various ways of defiling, forming line, opening to right and left, closing or deploying, doubling the ranks or files, or changing front upon either of the flanks by conversion, are called simple evolution. Compound evolutions are those which change the shape and figure of battalions, break them into divisions or companies, separate the companies from the main body, and again replace or rejoin them; in a word which afford the means of presenting a front at every direction. Compound evolutions are practised either by repeating the same simple evolution several times, or by going through several simple evolutions, or moving in different modes with different parts of the same corps, which ultimately tend to the same object. The EVOLUTIONS _of the ancients_ were formed and executed with uncommon good sense and ability. Considering the depth and size of the Grecian phalanx, it is astonishing how the different parts could be rendered susceptible of the most intricate and varied evolutions. The Roman legion, though more favorable to such changes and conversions, from being more loose and detached, did not execute them upon more sound or better principles. EVOLUTION (_in geometry_) the equal _evolution_ of the periphery of a circle, or any other curve, is such a gradual approach of the circumference to rectitude, as that all its parts do meet together, and equally evolve or unbend; so that the same line becomes successively a less arch of a reciprocally greater circle, till at last they turn into a straight line. EVOLUTION _of powers_ (_in algebra_) extracting of roots from any given power, being the reverse of involution. EXAGON. See HEXAGON. EXAMINER. One who scrutinizes. EXCAVATION, the act of cutting or otherwise making hollows; also the cavity formed. In military matters, it is generally applied to the place from whence the earth or other substance has been taken by mining. EXAMPLE, any act or word which disposes to imitation. The example of a superior officer has considerable influence over the mind of an inferior; but in no instance does it appear more important than in the good and bad behaviour of a non-commissioned officer or corporal. These characters, therefore, should be particularly correct in their duties, tenacious of every principle of military honor, and remarkable for honesty. Old soldiers should likewise direct their attention to the strict observance of rules and regulations, as young recruits always look up to them for example.