Part 13

_MINE._—The excavation formed by the blowing up of a mine is found by experiment to be nearly a paraboloid. It was formerly supposed that the diameter of the entonnoir, or excavation, was always equal to only double the line of least resistance; but experiments have proved, that the diameter of the excavation may be increased to six times the line of least resistance; and that the diameter of the globe of compression may be increased to eight times that line; this is called the _maximum_ of a mine, or the greatest effect that can be produced by a globe of compression. In any mine intended to produce an effect within this extent, the effects will be nearly as the charges.

The globes are to each other as the cubes of their radii. Their radii are the hypothenuses of rightangled triangles, of which the line of least resistance, and the semi-diameter of the excavation, are the other two sides. Therefore, to find the charge to produce any required diameter of the excavation, the following will be the rule, the radius being found as above:

As the cube of the radius of the globe of compression in the following table, (having the same line of least resistance as the required globe,)

Is to the cube of the radius of the required globe;

So is the charge corresponding in the following table,

To the charge required.

_Table for the Charges of Mines, according to Valiere._

+-------------+--------------++-------------+--------------+ | Line of | Charge for || Line of | Charge for | | Least | the Mine. || Least | the Mine. | | Resistance. | || Resistance. | | +-------------+--------------++-------------+--------------+ | Feet. | lbs. oz. || Feet. | lbs. oz. | | 1 | 0 2 || 21 | 868 3 | | 2 | 0 12 || 22 | 998 4 | | 3 | 2 8 || 23 | 1140 10 | | 4 | 6 — || 24 | 1296 — | | 5 | 11 11 || 25 | 1558 9 | | 6 | 20 4 || 26 | 1647 12 | | 7 | 32 2 || 27 | 1815 4 | | 8 | 48 — || 28 | 2058 — | | 9 | 68 5 || 29 | 2286 7 | | 10 | 93 12 || 30 | 2530 4 | | 11 | 124 12 || 31 | 2792 4 | | 12 | 162 — || 32 | 3072 — | | 13 | 205 15 || 33 | 3369 1 | | 14 | 257 4 || 34 | 3680 12 | | 15 | 316 4 || 35 | 4019 8 | | 16 | 384 — || 36 | 4374 — | | 17 | 460 9 || 37 | 4748 11 | | 18 | 546 12 || 38 | 5144 4 | | 19 | 643 — || 39 | 5561 2 | | 20 | 750 — || 40 | 6000 — | +-------------+--------------++-------------+--------------+

This table is calculated upon a supposition that the excavation of the mine is a paraboloid, having a base double the line of least resistance; and that 10 lbs. 10 oz of powder is sufficient for raising one cubic fathom of earth, by making the line of least resistance of the required globe only equal to the radius of the globe of compression.

The charges thus found by means of this table, being only for one nature of soil; _viz._ light earth and sand, (that for which the table is calculated) must be augmented according to the following table of Vauban’s, by one, four, five, seven, or nine elevenths of the charge found.

_Table of the Quantity of Powder required to raise a Cubic Fathom, according to the Soil._

1 Light earth, mixed with sand 11 pounds. 2 Common earth 12 3 Strong sand 15 4 Clay, or fat earth 16 5 Old and good Masonry 18 6 Rock 20

The following rule is however laid down by Belidor, and generally adopted, if it be intended that the mine shall produce its maximum or greatest effect: Multiply the line of least resistance, expressed in feet, by 300, the product will be the charge in pounds.

In making mines of any kind, the following remarks may be of service.

The best form for the chamber would be spherical; but from the difficulty of its construction, it is always made a cube, of one inch larger dimensions than the box to contain the powder.

The chamber must not be made in the prolongation of the branch of the mine, but at one side, and lower than the level of the branch, if the soil be dry; but higher if it be wet.

One cubic foot will contain 75 lbs. of powder; upon which principle the size of the case to contain the powder must be regulated. The auget is generally one inch square interior dimensions, and the end of it must reach the centre of the chamber; where the saucisson must be fastened, to prevent its being easily pulled out.

The branch of the mine to be sprung must be closed in the strongest manner by doors well secured by props, and must be stopped with earth or rubbish to a distance, taken in a straight line, equal to 1½ times the line of least resistance.

In proportioning the length of saucisson, in order that any number of mines may be fired at the same instant, a return of a right angle is generally reckoned equal to 4 inches in a right line.

The first step in making a mine, whether for attack or defence, is to sink a shaft to the depth of the bottom of the gallery, having two of its sides in the direction of the sides of the gallery. These shafts should be where the galleries are to cross each other, or in the centre of the length of gallery to be made. These shafts should never be further apart than 40 or 50 fathoms; for it is found, that the air is not fit for respiration in the larger galleries at a greater distance from the shaft than 25 fathoms; at 20 fathoms in those of medium dimensions; and at 15 in the smallest.

The rectangular frames used in sinking a shaft are commonly placed 4 feet asunder; and in the galleries they are only 3 feet. A gallery intended to be lined with masonry, must be 7 feet high, and 6 feet wide, in order that it may be, when finished, 6 feet high, and 3 feet wide.

Temporary galleries are only made 4½ feet high, and 2½ or 3 feet wide.

The branches, at the ends of which the chambers are to be placed, are only made 2½ or 3 feet high, and 2 feet, or 2 feet 3 inches wide.

The first of these is dug on the knees; the second sitting or lying.

The miners are divided into brigades of 4 each; and the rate of work for each brigade is 3 feet of the temporary gallery in 4 hours. The first brigade is relieved by a second, after having worked 4 hours, or laid one frame; which second brigade is again relieved by the first, at the expiration of the same time.

In the most easy ground to work, a miner may be heard to the distance of 14 or 15 fathoms under ground; and the noise made by fixing the frames of the galleries may often be heard as far as 20 or 25 fathoms. A drum braced, standing on the ground, with a few peas or other round substances on the head, will be very sensibly affected by an approaching miner.

It is of the most essential consequence to place the entrances to the countermines beyond the reach of any surprise from the enemy.

To prevent an enemy gaining possession of the galleries of the countermines, they should be well secured by strong doors, at every 15 fathoms. These should be musquet proof.

A glacis, properly countermined, and every advantage taken of it to retard the besiegers, may, with proper management, prolong a siege at least 2 months; and if the rest of the works are also countermined, and properly defended, they may add another month to the siege. Every system of countermines must depend upon the system of fortification to which they are to be adapted; the general principle for their regulation is, that the galleries should occupy situations, from which branches can be most readily run out under the most probable points of the besieger’s batteries and approaches. The general system of countermines commonly used in a place prepared beforehand, is as follows:—The principal or _magistral_ gallery runs all round the work, under the banquette of the covert way, and across the places of arms, having the entrances at the re-entering places of arms. Nearly parallel to this at 20, 25, or 30 fathoms distance is another gallery, called the _envellope_. These two galleries are connected by galleries of _communication_, under the gutters of the re-entering parts of the glacis, and under the ridges of the salient parts. From the envellope are run out about 15 or 16 fathoms, galleries, in directions parallel to the capitals of the works, and at 23 fathoms distance from each other. These are called _listeners_.

Sometimes, shafts are sunk from the ends of these listeners, and by connecting these shafts, a second envellope formed. Behind the escarps of the different works, galleries are likewise made, about the level of the bottom of the ditch; from whence branches may be run out into or under the foundations of the walls; and if the ditch be dry, galleries of communication may be made from these to the magistral gallery; and from which communications branches may be run out for chambers to annoy the besiegers in their passage of the ditch. The entrances to the escarpe galleries are by means of posterns, which descend from behind the interior slope of the rampart.

If a place be not countermined before hand, a great deal may be done, even after the investment of the place, to prolong the siege by countermines. In this case, the first thing to be done immediately that the place is invested, to sink a shaft in each of the places of arms of the covert way; one in each branch of the covert way, opposite that part of the bastion where the breach will most probably be made; and one in the flanked angle of each bastion. Those on the covert way will be on the banquette, and sunk to about 18 inches below the bottom of the ditch. Those in the bastions to about 12 feet below the bottom of the ditch. Thus prepared, the moment the side on which the attack is to be made can be ascertained, galleries must be carried on from these shafts on the side attacked along the capitals, in the form of tressles; or double T; and advanced as far into the country as the time will admit. Communication galleries may likewise be driven between these different works on the covert way, and from them to the work in the bastion; which will prevent the enemy gaining possession of their entrances. All these works may be carried on after the investment of the place; and be in sufficient forwardness by the time the enemy gains the third parallel.

The following rules are given by Vauban for fougasses, or small mines, having the diameter of the excavation equal to double the line of least resistance: The side of the chamber must be exactly a sixth part of the depth of the shaft. The side of the box to hold the powder exactly a ninth part of the depth of the shaft.

These remarks respecting mines are principally extracted from the General Essay on Fortification before mentioned, written in French, and published at Berlin, 1799.

_MORTARS._—_Weight and Dimensions of English Mortars._

+------------------+------------+---------+-----------+-------+ | | | | Powder | Range | | Nature. | Weight. | Length. | contained |at 45°.| | | | |in Chamber.| | | | | | [10] | | +------------------+------------+---------+-----------+-------+ | |ct. qr. lbs.| Ft. In. | lbs. oz. | Yds. | | Brass Sea S. |82 — 8 | 5 3 | 32 — | 4100 | | Iron |82 1 — | | 20 — | | | 13 --------------+------------+---------+-----------+-------+ | Brass Land. |25 — 10 | 3 7½ | 9 12 | 2100 | | Iron |36 2 12 | | 9 8 | | +------------------+------------+---------------------+-------+ | Brass Sea S. |33 — — | 4 8 | 12 8 | 3800 | | Iron |41 — — | | 10 — | | | 10 --------------+------------+---------+-----------+-------+ | Brass Land. |10 1 25 | 2 9 | 4 10 | 1900 | | Iron |16 — 6 | | 4 8 | | +------------------+------------+---------+-----------+-------+ | Brass Land. | 4 1 8 | 2 1¾ | 2 — | 1600 | | 8 Iron | 8 — 11 | | 2 4 | | +------------------+------------+---------+-----------+-------+ | 5½ Brass Land. | 1 — 20 | 1 4¼ | — 9 | 1200 | +------------------+------------+---------+-----------+-------+ | 4⅖ Brass Land. | — 3 11 | 1 1½ | — 4½ | 1000 | +------------------+------------+---------+-----------+-------+

[10] See the word _Chambers_, for Experiments on the best form.

_French Mortars, in their own Weights and Measures._

+------------------+------------+---------+-----------+-------+ | | lbs. | | | | |12 Inches | 2060 | | 3 7 | 2400 | |10 for long Ranges| 2000 | | 7 4 | 2800 | |10 ” short ” | 1560 | | 4 — | 2200 | | 8 ” ” ” | 595 | | 1 4¾ | 1160 | |Stone Mortars.[11]| 1100 | | 2 8 | | |12 inch } | 2750 | | 12 — | 2700 | |10 ” } Gomers | 2000 | | 6 8 | 2800 | | 8 ” } | 600 | | 2 — | 1400 | +------------------+------------+---------+-----------+-------+

[11] Stone Mortars should not be fired at a greater distance than 250 yards.

_Ranges with a 10 Inch Sea Mortar, at 21 Degrees, on a Horizontal Plane._

+-------------+-----------+---------+----------+-------+-------+ | Weight of | Weight of | Charge. |Elevation.|Flight.|Range. | | Mortar. | Shell. | | | | | +-------------+-----------+---------+----------+-------+-------+ |ct. qrs. lbs.| lbs. oz. | lbs. oz.| Deg. | Sec. |Yards. | |34 2 14 | 86 — | 5 8 | 21 | 14¾ | 2335 | | | 87 — | | | 16 | 2510 | +-------------+-----------+---------+----------+-------+-------+

_Ranges with Sea Service, Iron Mortars, at 45 Degrees, upon a Horizontal Plane. 1798_

+--------------------------++-------------------------+ | 13 Inch. || 10 Inch. | +---------+--------+-------++--------+--------+-------+ | Charge. | Flight.|Range. || Charge.| Flight.|Range. | +---------+--------+-------++--------+--------+-------+ |lbs. oz.| Sec. | Yards.||lbs. oz.| Sec. | Yards.| | 2 — | 13 | 690 || 1 — | 13 | 680 | | 4 — | 18 | 1400 || 2 — | 18 | 1340 | | 6 — | 21 | 1900 || 3 — | 21 | 1900 | | 8 — | 24½ | 2575 || 4 — | 24 | 2500 | | 10 — | 26½ | 2975 || 5 — | 26 | 2800 | | 12 — | 29 | 3500 || 6 — | 27 | 3200 | | 14 — | 29½ | 3860 || 7 — | 29 | 3500 | | 16 — | 30 | 3900 || 8 — | 30 | 3800 | | 18 — | 30½ | 4000 || 9 — | 30¼ | 3900 | | 20 — | 31 | 4200 || 9 8 | 30½ | 4000 | +---------+----------------++--------+--------+-------+

_Ranges with French Mortars, at 45 Degrees, in French Weights and Measures._

+---------------+---------------+----------------+---------------+ | 12 Inch. | 10 Inch, | 10 Inch, | 8 Inch. | | | long Ranges. | short Ranges. | | +--------+------+--------+------+---------+------+--------+------+ |Charge. |Range.| Charge.|Range.| Charge. |Range.| Charge.|Range.| +--------+------+--------+------+---------+------+--------+------+ |lbs. oz.|Yards.|lbs. oz.|Yards.|lbs. oz. |Yards.|lbs. oz.|Yards.| | 1 — | 388 | 1 — | 450 | 1 — | 658 | — 5 | 316 | | 1 8 | 632 | 2 — | 1080 | 1 8 | 964 | — 10 | 794 | | 2 — | 862 | 3 — | 1536 | 2 — | 1280 | — 15 | 1112 | | 2 8 | 954 | 4 — | 2070 | 2 8 | 1428 | 1 4 | 1280 | | 3 — | 1292 | 5 — | 2206 | 3 — | 1432 | | | | 3 8 | 1390 | 6 2½ | 2304 | 3 10¼ | 1920 | | | +--------+------+--------+------+---------+------+--------+------+

_Medium Ranges with Land Service Iron Mortars, at 45 Degrees. 1798._

+------------------------++------------------------+ | 13 Inch. || 10 Inch. | +--------+-------+-------++--------+-------+-------+ |Charge. |Flight.|Range. || Charge.|Flight.|Range. | +--------+-------+-------++--------+-------+-------+ |lbs. oz.| Sec. | Yards.||lbs. oz.| Sec. | Yards.| | — 14 | 6½ | 245 || — 8 | 6½ | 235 | | 1 — | 7½ | 318 || — 10 | 8 | 358 | | 1 4 | 8½ | 412 || — 12 | 9 | 464 | | 1 8 | 9½ | 523 || — 14 | 10 | 534 | | 1 12 | 10½ | 613 || 1 — | 10½ | 638 | | 2 — | 11 | 697 || 1 2 | 11½ | 749 | | 2 4 | 12½ | 840 || 1 4 | 13 | 873 | | 2 8 | 13 | 906 || 1 6 | 13½ | 956 | | 2 12 | 14 | 1054 || 1 8 | 14 | 1028 | | 3 — | 15 | 1132 || 1 10 | 15 | 1123 | | 3 4 | 16 | 1244 || 1 12 | 15 | 1226 | | 3 8 | 16½ | 1317 || 1 14 | 16 | 1325 | | 3 12 | 17 | 1424 || 2 — | 16½ | 1357 | | 4 — | 17 | 1490 || 2 2 | 17 | 1480 | | 4 4 | 17½ | 1580 || 2 4 | 17½ | 1532 | | 4 8 | 18½ | 1656 || 2 6 | 17½ | 1571 | | 4 12 | 19 | 1744 || 2 8 | 18½ | 1700 | | 5 — | 19½ | 1824 || 2 10 | 19 | 1780 | | 5 4 | 19½ | 1900 || 2 12 | 19½ | 1825 | | 5 8 | 20 | 1950 || 2 14 | 20 | 1880 | | 5 12 | 20½ | 2062 || 3 — | 20 | 1916 | | 6 — | 21 | 2095 || 4 — | 25 | 2485 | | 7 — | 24 | 2510 || 4 8 | 26 | 2536 | | 8 — | 25 | 2706 || | | | +------------------------++------------------------+ | 8 Inch. || 5½ Inch, Brass. | +--------+-------+-------++-------+--------+-------+ |Charge. |Flight.|Range. ||Charge.| Flight.|Range. | +--------+-------+-------++-------+--------+-------+ |lbs. oz.| Sec. | Yards.||oz. dr.| Sec. | Yards.| | — 5 | 6 | 225 || 1 8 | 5½ | 155 | | — 6 | 7½ | 328 || 1 12 | 6 | 198 | | — 7 | 8½ | 428 || 2 — | 6½ | 255 | | — 8 | 9½ | 474 || 2 4 | 7½ | 316 | | — 9 | 10 | 560 || 2 8 | 8 | 380 | | — 10 | 11 | 664 || 2 12 | 8½ | 426 | | — 11 | 12 | 762 || 3 — | 9½ | 470 | | — 12 | 12½ | 801 || 3 4 | 10 | 540 | | — 13 | 13½ | 859 || 3 8 | 10½ | 590 | | — 14 | 14 | 960 || 3 12 | 11 | 630 | | — 15 | 14½ | 1011 || 4 — | 11½ | 725 | | 1 0 | 14½ | 1115 || 4 4 | 12 | 746 | | 1 1 | 15 | 1156 || 4 8 | 12½ | 800 | | 1 2 | 16 | 1262 || 4 12 | 13½ | 910 | | 1 3 | 16½ | 1320 || 5 — | 13½ | 935 | | 1 4 | 17 | 1380 || 5 4 | 14 | 1016 | | 1 5 | 17½ | 1446 || 5 8 | — | — | | 1 6 | 18 | 1530 || 5 12 | — | — | | 1 7 | 18½ | 1600 || 6 — | 15 | 1175 | | 1 8 | 19 | 1660 || | | | | 1 9 | 19½ | 1720 || | | | +--------+-------+-------++-------+--------+-------+

_Medium Ranges with Brass Mortars, at 45 Degrees. 1780._

+----------------++----------------++----------------+ | 13 Inch.[12] || 10 Inch. || 8 Inch. | +--------+-------++--------+-------++--------+-------+ |Charge. | Range.||Charge. | Range.||Charge. | Range.| +--------+-------++--------+-------++--------+-------+ |lbs. oz.| Yards.||lbs. oz.| Yards.|| oz. dr.| Yards.| | 2 12 | 862 || 1 10 | 823 || 10 8 | 580 | | 2 14 | 939 || 1 11 | 852 || 11 — | 635 | | 3 — | 998 || 1 12 | 783 || 11 8 | 711 | | 3 2 | 1003 || 1 13 | 758 || 12 — | 708 | | 3 4 | 1090 || 1 14 | 823 || 12 8 | 701 | | 3 6 | 1139 || 1 15 | 888 || 13 — | 777 | | 3 8 | 1165 || 2 — | 892 || 13 8 | 825 | | 3 10 | 1209 || 2 1 | 940 || 14 — | 870 | | 3 12 | 1270 || 2 2 | 941 || 14 8 | 853 | | 3 14 | 1322 || 2 3 | 1041 || 15 — | 866 | | 4 — | 1309 || 2 4 | 1128 || 15 8 | 899 | | 4 2 | 1331 || 2 5 | 1103 || 16 — | 921 | | 4 4 | 1391 || 2 6 | 1221 || 16 8 | 987 | | 4 6 | 1363 || 2 7 | 1258 || 17 — | 987 | | 4 8 | 1324 || 2 8 | 1215 || 17 8 | 1062 | +--------+-------++--------+-------++--------+-------+

[12] For the Ranges with the 5½ inch Brass, see the _Iron Mortars_.

_Ranges with a 5½ inch Brass Mortar, at 15 Degrees._

+-------+-------+------------+---------+ |Charge.|Flight.|First Graze.|Rolled to| +-------+-------+------------+---------+ |oz. dr.| Sec. | Yards. | Yards. | | 2 8 | 3 | 209 | 303 | | 3 — | 3½ | 256 | 330 | | 3 8 | 4 | 375 | 443 | | 4 — | 4½ | 457 | 501 | | 4 8 | 5 | 530 | 600 | | 5 — | 5½ | 561 | 627 | | 5 8 | 6½ | 667 | 715 | | 6 — | 7 | 709 | 780 | +-------+-------+------------+---------+

_Medium Ranges with Land Service Iron Mortars, at 10 Degrees Elevation.—Powder in Cartridges._