Part 102

+----------++-------------+---------- Line of least|Charge for||Line of least|Charge for Resistance. | the Mine.|| Resistance. | the Mine. -------------+----------++-------------+---------- 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 |2053 -- 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 resistance; and that 10 lbs. 10 oz. of powder is sufficient for raising one cubic fathom of earth. By the rule above given may be found the charge for any mine, that shall only shake the ground, without making any excavation, 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 9 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 1¹⁄₂ 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 4¹⁄₂ feet high, and 2¹⁄₂ or 3 feet wide.

The branches, at the ends of which the chambers are to be placed, are only made 2¹⁄₂ 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 squads of 4 each; and the rate of the work for each squad is 3 feet of the temporary gallery in 4 hours. The first squad is relieved by a second, after having worked 4 hours, or laid one frame; which second squad 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 before hand, 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 end 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 escarp 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, is 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 trefles, 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.

_Counter_-MINES, are those made by the besieged, whereas mines are generally made by the besiegers. Both mines and counter-mines are made in the same manner, and for the like purposes, viz. to blow up their enemies and their works; only the principal galleries and mines of the besieged, are usually made before the town is besieged, and frequently at the same time the fortification is built, to save expence.

_Eventer la_ MINE, _Fr._ to spring a mine. When used figuratively, this expression signifies to discover a plot, or make it known. It is likewise used to express the failure of any expedition or undertaking.

_Definitions of_ MINES. A mine is a subterraneous cavity made according to the rules of art, in which a certain quantity of powder is lodged, which by its explosion blows up the earth above it.

It has been found by experiments, that the figure produced by the explosion is a _paraboloid_, and that the centre of the powder, or charge, occupies the _focus_.

The place where the powder is lodged is called the _chamber_ of the mine, or _fourneau_.

The passage leading to the powder is called the _gallery_.

The line drawn from the centre of the chamber, perpendicular to the nearest surface of the ground, is called the line of least resistance.

The pit or hole, made by springing the mine, is called the _excavation_.

The fire is communicated to the mines by a pipe or hose, made of coarse cloth, whose diameter is about one and a half inch, called a _saucisson_, (for the filling of which near half a pound of powder is allowed to every foot) extending from the chamber to the entrance of the gallery, to the end of which is fixed a match, that the miner who sets fire to it may have time to retire, before it reaches the chamber.

To prevent the powder from contracting any dampness, the saucisson is laid in a small trough, called an _auget_ made of boards, three and a half inch broad, joined together, lengthwise, with straw in it, and round the saucisson, with a wooden cover nailed upon it.

_Foyer_, _Fr._ _Focus_ or _centre of the chamber_, some authors call the end of the saucisson that comes within the work, and which is to be set fire to, the foyer, or focus: but by most people, this is generally understood to be the centre of the chamber.

_Galleries and chambers of_ MINES. Galleries made within the fortification, before the place is attacked, and from which several branches are carried to different places, are generally 4 or 4¹⁄₂ feet wide, and 5 or 5¹⁄₂ feet high. The earth is supported from falling in by arches and walls, as they are to remain for a considerable time; but when mines are made to be used in a short time, then the galleries are but 3 or 3¹⁄₂ feet wide, and 5 feet high, and the earth is supported by wooden frames or props.

The gallery being carried on to the place where the powder is to be lodged, the miners make the chamber. This is generally of a cubical form, large enough to hold the wooden box, which contains the powder necessary for the charge: the box is lined with straw and sand-bags, to prevent the powder from contracting dampness.

The chamber is sunk something lower than the gallery, if the soil permits; but where water is to be apprehended, it must be made higher than the gallery; otherwise the besieged will let in the water, and spoil the mine.

_Quantities of powder to charge_, MINES. Before any calculation can be made of the proper charge for a mine, the density and tenacity of the soil in which it is to be made, must be ascertained, either by experiment, or otherwise; for, in soils of the same density, that which has the greatest tenacity, will require the greatest force to separate its parts. The density is determined by weighing a cubic foot (or any certain quantity) of the soil; but the tenacity can only be determined by making a mine. The following table contains experiments in 6 different soils, which may be of some assistance to form a judgment of the nature of the soil, when an actual experiment cannot be had.

+-------------------------------+--------+-------------+ | |Density.| Tenacity. | | +--------+-------------+ | | Weight |Quantity of | | | of |power to | | | 1 cubic|raise 1 cubic| | Nature of the soil. | foot. |fathom. | +-------------------------------+--------+-------------+ |1. Loose earth or sand | 95 pds.| 8 pds. | +-------------------------------+--------+-------------+ |2. Common light soil |124 | 10 | +-------------------------------+--------+-------------+ |3. Loam, or strong soil |127 | 12¹⁄₄ | +-------------------------------+--------+-------------+ |4. Potter’s clay, or stiff soil|135 | 13¹⁄₂ | +-------------------------------+--------+-------------+ |5. Clay, mixed with stones |160 | 16 | +-------------------------------+--------+-------------+ |6. Masonry |205 | 21¹⁄₂ | +-------------------------------+--------+-------------+

All the requisites in mining may be determined by the following problems, which admit of 4 cases; for any 3 of the articles below being given, the 4th may thence be found.

1. The nature of the soil,

2. The diameter of the excavation,

3. The line of least resistance,

4. The charge.

PROBLEM. I.

Given the nature of the soil, the diameter of the excavation, and the line of least resistance, to find the charge.

RULES.

1. To the square of the diameter of the excavation, add the square of double the line of least resistance, and reserve the said sum.

2. Multiply the square root of the reserved sum by double the line of least resistance, and subtract the product from the same sum.

3. Multiply half the remainder by the line of least resistance, and 1.57 times the product, will give the solidity of the excavation.

4. The charge will then be determined from the nature of the soil, as in the following example.

_Example_ I.

It is required to make a mine in the second sort of soil, mentioned in the foregoing experiments, which shall have a line of least resistance of 10 feet, and the diameter of its excavation 20 feet; what will be the proper charge?

The nature of this soil, by the table, requires 10 pounds of powder to 216 cubic feet.

_Calculation._

1. The diameter of the excavation is 20, and its square 400 Double the line of least resistance is 20, and its square 400 --- Therefore the sum to be reserved is 800

2. The square root of 800 is 28.3 Double the line of least resistance is 20 566 --- Which leaves the remainder 234 --- 3. Half the remainder is 117 Which multiplied by the line of least resistance, 10 --- Gives the product 1170 Which multiplied by 1.57 ------ Gives the solidity of the excavation feet 1836.9

feet. lb. feet. lb. 4. If 216 : 10 ∷ 1836.9 : 85 which is the charge required.

_By Logarithms._

1. Diam. of excavation is = 20 1.301030 Diameter squared is 2.602060 400 Double the line of least resistance is = 20 and its square 400 --- The sum to be reserved is 2.903090 800 -------- 2. Square root of sum is 28.3 1.451545 Double the line of least resistance is = 20 1.301030 -------- Product to be subtracted is 2.752575 566 -------- --- Remainder is 2.369216 234 Line of least resist. = 10 1.000000 10 pounds of powder 1.000000 To 216 cubic feet, _compl. arith._ 7.665546 To which add the _const. log._ 9.894870 -------- And the sum is the logarithm charge required 1.929632 = 85 lb.

_Problem_ II.

Given the nature of the soil, the line of least resistance, and the charge, to find the diameter of the excavation.

RULES.

1. Find the solidity of the earth to be raised, by a proportion from the nature of the soil, and multiply it by 1.27.--Divide the product by the line of least resistance, and to the quotient add the square of the line of least resistance: reserve the sum.

2. Multiply the square root of the sum reserved by twice the line of least resistance, and add the product to the said sum, and from the result subtract 3 times the square of the line of least resistance; so will the square root of the remainder be the diameter of the required excavation.

_Example_ I.

Let a mine be charged with 100 pounds of powder in a soil which requires 11 pounds of powder to raise 216 cubic feet, and let its line of least resistance be 10 feet: what will be the diameter of the excavation?

By the nature of the soil 11lb. : 216 feet ∷ 100lb. : 1964 feet, which is the solidity of the earth to be raised.

1. Therefore multiply 1964 By 1.27 ------- The product is 2494.28 ------- Which divided by the line of least resistance, 10, is 249.428

To which add the square of the line of least resistance 100.000 ------- And the sum to be reserved is 349.428

2. The square root of 349.428 is 18.7, which multiplied by twice the line of least resistance, 20, gives 374. ------- This added to the sum reserved gives 723.428

From which subtract 3 times the square of least resistance 300. ------- And there will remain 423.428

The square root of which is, 20.5 feet, being the required diameter of the excavation.

_By Logarithms._

Numb. Logar. Numb. Cubic feet = 216 2.334454 Powder 11lb. _co. ar._ 8.958607 Charge = 100 2.000000 Line of least resist. 10 _co. ar._ 9.000000 Constant logarithm 0.103804 -------- 2.396865 249.4 ----- To which add the square of line of least resistance 100.0 ----- Sum to be reserved is 2.543323 349.4 -------- Half of which logar. 1.271661 Twice line of least resistance, 20, 1.301030 -------- Product to be added is 2.572691 373.8 ----- The result is 723.2

From which subtract thrice the square of the line of least resistance 300.0 ----- And there remains 2.626546 423.2

Half of which logar. is 1.313273 20.57 feet, the diameter of the excavation required.

_Loading and stopping of_ MINES. The gallery and chamber being ready to be loaded, a strong box of wood is made of the size and figure of the chamber, being about ¹⁄₃d or ¹⁄₄th bigger than is required for containing the necessary quantity of powder: against the sides and bottom of the box is put some straw; and this straw is covered over with empty sand bags, to prevent the powder from contracting any dampness: a hole is made in the side next the gallery, near the bottom for the saucisson to pass through, which is fixed to the middle of the bottom, by means of a wooden peg, to prevent its loosening from the powder: or that, if the enemy should get to the entrance, he may not be able to tear it out. This done, the powder is brought in sand bags, and thrown loose in the box, and covered also with straw and sand bags; upon this is put the cover of the box, pressed down very tight with strong props; and, to render them more secure, planks are also put above them, against the earth, and wedged in as fast as possible.

This done the vacant space between the props are filled up with stones and dung, and rammed in the strongest manner: the least neglect in this work will considerably alter the effect of the mine.

Then the auget is laid from the chamber to the entrance of the gallery, with some straw at the bottom; and the saucisson laid in it, with straw over it: lastly, it must be shut with a wooden cover nailed upon it. Great care must be taken, in stopping up the gallery, not to press too hard upon the auget, for fear of spoiling the saucisson, which may hinder the powder from taking fire, and so prevent the mine from springing. The gallery is stopped up with stones, earth, and dung, well rammed, 6 or 7 feet further from the chamber than the length of the line of least resistance.