The form of the crater caused by an explosion in ordinary soils is assumed to be a truncated cone, the diameter, _c d_, (Fig. 53,) of the lower circle being one-half the diameter, _a b_, of the upper circle. This form has never been ascertained to be exactly correct, but the theoretical results deduced from a mathematical discussion of this figure have been fully verified in practice. The radius, _p b_, of the upper circle is termed the _crater radius_; the line _o p_, drawn from the centre of the charge perpendicular to the surface where the explosion takes place, is termed the _line of least resistance_; the line _o b_, drawn from the centre of the powder to any point in the circumference of the upper circle, is termed the _radius of explosion_. When the crater radius is equal to the line of least resistance, the mine is termed _common_; when this radius is greater than the line of least resistance, the mine is termed _overcharged_; and when the radius is less, _undercharged_. A mine of small dimensions, formed by sinking a shaft in the ground, is termed a _fougasse_. The term _camouflet_ is applied to a mine used to suffocate the enemy's miner, without producing an explosion. Small mines made in rock or masonry, merely for the purpose of excavation, without any considerable external explosion, are called _blasts_. From experiments made on common mines, whose line of least resistance did not exceed fifteen feet, it has been ascertained that the tenacity of the earth is completely destroyed around the crater to a distance equal to the crater radius, and that empty galleries would be broken in at once and a half that distance. It has also been proved by experiment, that the crater radius in overcharged mines may be increased to six times the line of least resistance, but not much beyond this; that within this limit the diameter of the crater increases nearly in the ratio of the square roots of the charge; and that empty galleries may be destroyed by overcharged mines at the distance of four times the line of least resistance. By means of the deductions of physico-mathematical theory, and the results of experiments, rules have been determined by which the miner can calculate, with much accuracy, the charge necessary to produce a required result in any given soil. In the earlier stages of the history of this art, mines were only used to open breaches and demolish masses of masonry; but in later times they have been employed as important elements in the attack and defence of places.