The dimensions of the crater or funnel formed by the explosion depend on the amount of the charge ; its form may be considered as an irregular frustum of a cone, or paraboloid, and the mine is denomi nated one-lined, taco-lined, &c., according as the diameter of the crater at the surface of the ground is equal to once, twice, &c., the length of the line of least resistance. Every explosion of this kind necessarily produces a compression of the earth in all directions about the chamber to a certain extent; and the mines formed with high charges have been denominated globes of compression from this circumstance. A line drawn from the chamber to the circumference of the crater, on the ground, is considered as the radius of the globe of compression.
The last mentioned description of mine was first employed by Belidor for the purpose of destroying the galleries of the besieger at distances far greater than had before been considered practicable. When a very small, or at least, comparatively to its depth, a very small mine is exploded, no crater is produced, but it is evident that the earth about must be compressed, and galleries, &c., destroyed to a certain distance : the radius of this sphere of compression is termed the radius of rupture. When a crater is produced, the solid compressed will no longer be a spheroid, but an elipsoid, or nearly so, with its major axis passing through the centre of the charge, at right angles to the line of least resistance. With overcharged mines this radius of rupture is greatly increased : in fact it is found that with the ordinary or two-lined crater the radius of rupture, or semi-major axis of the ellipsoid, is P7 times the line of least resistance ; and the semi minor axis, or extent of compression downwards, is P3 times the line of least resistance. With a globe of compression producing a six-lined outer or maximum charged mine, these lines are and P4 times the line of least resistance. It will be seen that the lateral effect increases much more than the downward effect, as might be imagined. This great lateral effect was employed by Belidor for destroying the galleries of the besieger : such mines are, from the circumstances of the respective cases, perhaps more applicable by the besieger than the besieged.
The rules for determining the charges of mines are founded on the results of experiment, and it is evident that the charges must vary both with the nature of the soil and with the proposed figure of the mine, that is, with the ratio between the diameter of the crater and the length of the line of least resistance. When a mine of the kind called
lined is formed in common earth, the amount of the charge in pounds is considered as very nearly equal to one-tenth of the cube of the line of least, resistance in feet ; but for a three-lined and a four-lined mine it is supposed that the cube of this line should be multiplied by '21 and by respectively. It is said that Belidor, somewhere about the years 1753 to 1762, fired three charges of 3600 lbs., at a depth of 12 feet, all of which produced craters of 36 feet radius, or six-lined craters. In an experiment made at Potsdam, when a four-lined mine was formed in a sandy soil by the Prussian Major Le Febvre, the cube of the line of least resistance in feet was very nearly equal to the charge in pounds. According to the latest experiments of the French engineers, the charges of powder necessary to remove one cubic yard (English) of material are as follows :— Now the figure of the crater being supposed to be a paraboloid, of which the centre of the chamber is the focus—if a be the length of the line of least resistance in yards, and n a represent the radius of the crater at the surface of the ground, also if w= 3.1416, we shall have .
n27 (1+ + 1) 4 for the volume of the crater in cubic yards ; therefore, multiplying this volume by the numbers in the above table, we should have tho charge in pounds, which will hold good for mines up to three-lined craters.
The following rules, given by General Sir Charles Pasley, are very valuable, as deduced from experiment. L.L.R. meaning line of least resistance.
In order to determine the proper size of the chamber, or rather of the box, which is to contain the powder, it will be necessary to observe that one pound of gunpowder occupies, in volume, abou ' 30 cubic inches.
Experience has shown that the greater the charge of powder, the greater is the quantity of earth removed by the explosion. But this fact has its limits; for when the charge is considerable, since the whole of the powder does not take fire instantaneously, it will happen that the earth is partially displaced before the inflammation is complete so that fissures being formed in the ground, the force of the powder is spent in the air without producing any effect. Hence it may be con cluded that there is a certain charge of powder which will produce a maximum of effect; and it is supposed by Belidor that, in earth of mean tenacity, the greatest craters will have their diameters, at the surface of the ground, equal to about six times the length of the line of least resistance.