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.
An isolated wall, only two or three feet thick, may readily be demolished by exploding one or two casks of powder placed in contact with its base.

If the wall be five or six feet thick, the charges should be placed under the foundation.

For walls of still greater thickness it will be best to open a gallery to the centre of the wall, a foot or two above its base, and place the powder in chambers thus excavated.
Revetment walls may be overturned by placing the charges at the back of the wall, about one-third or one-quarter of the way up from the base.

If placed too near the base, a breach will be made in the wall without overturning it.
To demolish a bridge of masonry the powder should be lodged in chambers excavated in the centre of the piers.

When there is not time for excavating these chambers in the piers, a trench may be cut over the key of the arch, in which the powder is placed and exploded; or, the casks of powder may be suspended immediately under the arch, with the same results.