MINES, at Preƒent, make ƒo eƒƒential a part of the attack and defence of fortified places, that the giving ƒome idea of them cannot be diƒpenƒsed with in this work, which os propoƒed to exhibit all the machines and methods uƒed both to prepare and preƒserve them.
 

SECT II. A Deƒcription of Mines, and their Uƒe.

BY a mine is underƒtood a kind of ƒubterraneious gallery, which is carried on till it comes under the places intended to be blown up, and at the end of which a cavity is made, ƒufficient to contain the quantity of powder requiƒite to blow up whatever is erected or happens to be over it.
        The end of the gallery, or the cavity that receives the charge of the mine, is called its chamber, or the furnace of the mine.
        The deƒign of mines then is. to blow up whatƒoever lies over their chambers; and, in order to this, it is neceƒƒary that the powder they contain ƒhould meet with leƒs reƒiƒtance in this part than towards the gallery, otherwiƒe it would not blow up.
        That the powder may not fail to explode by the upper part of hte chamber of the mine, one part of the gallery muƒt be walled up with maƒony, faƒcines, ƒtones, and pieces of timber, by layers interchangeably, one joining to the other, &c. The mine is fixed by means of a long leathern pipe, or bag, called a by means of a long leathern pipe, or bag, called a ƒauƒage, which reaches from the chamber of the mine to the opening or end of the gallery, and ƒomething further. And to prevent the powder from growing damp, it is placed in a ƒmall wooden gutter called an [auget] ogee; the diameter of the ƒauƒage is about an inch and an half.
        The ƒauƒage having taken fire, communicates it to the chamber of the mine; and the powder there being inflamed, makes an effort on all ƒides for room to dilate itƒelf, and finding every where a greater reƒiƒtance than from the top of the chamber, its principal effort is directed to that place, which is by this method blown up with all that is over it.
 

SECT. III. Obƒervations and Principles for the calculalation [calculation] of Mines.

THAT the mine may produce the effect propoƒed, it is neceƒƒary that it ƒhould be charged with a ƒufficient quantity of powder; for too ƒmall a charge will only give the ground a little ƒhock, without blowing it up; the charge may even be ƒo fmall, as to produce ƒo languid and inƒenƒible a motion, that it will not be at all communicated to the exterior part of the mine, or outward ƒurface of the ground. On the other hand, too great a charge will be an expence of powder to no purpoƒe, or perhaps produce a greater ƒhock, and more confuƒion than is defired.
        To avoid all theƒe inconveniences, it is neceƒƒary to know,
        Iƒt, The quantity of powder requiƒite to blow up a cubic foot of earth. There are earths of different ƒorts, ƒome heavier and ƒome lighter, ƒome very tough and tenacious, others the parts of which are eaƒily ƒeparated; it is therefore proper to know how much powder will blow up a cubic foot of each of theƒe ƒorts of earth.
        2d, The ƒolid figure of the ground muƒt be known which the powder is to blow up, and its ƒolidity meaƒured to aƒcertain the quantity of powder requiƒite to charge the mine.
        The ƒolid quantity of earth blown up by the mine is called its excavation, and the hollow left in the ground from whence it is thrown, is called the tunnel of the mine, from its reƒemblance to the implement of that name.
        The knowledge of theƒe particulars muƒt be gained from experience; this alone can teach us what quantity of powder is neceƒƒary to raiƒe a certain weight of the ƒame figure as the tunnel of a mine, or, which is the ƒame thing, the ƒolid intended to be blown up.
        The different ƒoils, according to the authors who have treated of mines, may be reduced to the four principal kinds following.
        I. Hard gravel, which is alƒo called tuff.
        2. White clay, or potters earth, uƒed for the making of bricks and tiles.
        3. Dry ƒand, or looƒe earth.
        4. The old and new maƒonry.
        A cube foot of tuff, or the hard gravel, weighs 124 pounds;
                            of potters earth 135 pounds.
                            of dry ƒand 95 pounds.
        With reƒpect to a cube foot of maƒonry, its weight cannot be aƒcertained exactly, becauƒe it very much depends on the nature of the different ƒtones, or materials it conƒiƒts of.
        It is ƒuppoƒed, that to raiƒe a cubic fathom of gravel, or tuff, in firm ground, eleven pounds of powder are requiƒite, or thereabouts.
        That to raiƒe a cubic fathom of potters earth, or clay, in firm ground, 15 pounds are requifite.
        That a cubic fathom of dry ƒand requires at leaƒt 9 pounds.
        And, laƒtly, for a cubic fathom of maƒonry 20 or 25 pounds of powder are required, if the maƒonry be above ground, and 35 or 40 pounds, if it be foundation.
        Suppoƒing theƒe experiments to have been made with all poƒƒible care and exactneƒs, it will not be difficult to find the quantity of powder requisite to charge a mine, if the contents of the ƒolid earth to be blown up be known.
        This ƒolid was at firƒt taken for a cone reverƒed, a f b, of which the point or ƒummit f, terminated the middle of the chamber of the mine; afterwards for the fruƒtum of a cone, as c a f b d c; but M. de Valliere* [*1], that celebrated general, ƒo well known for his great skill in artillery, and principally in the ƒcience of mining, having examined this ƒolid with more attention, found that its figure differed ƒomewhat from the fruƒtum of a cone, and approached nearer to the ƒhape of the curved ƒolid, called by geometricians a paraboloid; and that the chamber, or furneau, of the mine, after the exploƒion, was a little higher than the bottom of the excavation, becauƒe the powder taking fire, preƒƒes againƒt the bottom of the earth (that forms the roof or ƒuperior part) of the chamber, and conƒequently muƒt force it cloƒer together, and in ƒome meafure drive it in.
        The ƒection, or profile, of the paraboloid formed by the excavation of a mine, is repreƒented by the curve line a d b, called a parabola, and is of the ƒame kind with that deƒcribed by the flight of a bomb; and, in general, of all other bodies projected parallel or oblique to the horizon; the chamber, c, appears in a point of the ƒpace included within this curve, which is called its focus.
        The paraboloid may be conƒidered as a ƒort of fruƒtum of a cone, the upper part of which is rounded in form of a jocky's cap, and the ƒides a little incurvated.
        In many experiments, made long ago at Tournay, to examine the figure of the ƒolid formed by the excavation of mines, it was obƒerved, that the perpendicular c e elevated from the chamber to the ƒuperficies of the earth, was equal to the radius of the circle formed by the exterior part of the excavation, that is, to the circular mouth of the tunnel. This perpendicular line, erected from the top of the chamber, which ƒhows the height or thickneƒs of the ground to be raiƒed, is called the line of leaƒt reƒiƒtance, becauƒe it ought to repreƒent the place where the powder, finding the leaƒt reƒiƒtance, forces itƒelf out of the chamber; it was alƒo diƒcovered by theƒe experiments, that the radius of the little circle, formed by the end of the excavation next the chamber, was half the radius of the great circle, or the mouth of the mine.
        Geometry furniƒhes rules for finding the ƒolidity of the fruƒtum of cones, as well as paraboloids. Thus, ƒuppoƒing the line of leaƒt reƒiƒtance known, and the excavation of the mine to be either the fruƒtum of a cone, or a paraboloid, the cubic fathoms contained in either of theƒe bodies may be found, and conƒequently the quantity of powder the mine ought to be charged with, in order to blow them up, aƒcertained.
        To render this ƒtill plainer, we will illuƒtrate it by an example. Let us ƒuppoƒe (to make the calculation more ƒimple) that the excavation of a mine is the fruƒtum of a cone; the ƒmall difference there is between the meaƒure of this and the paraboloid permits the choice of either, without any material error; and as the meaƒure of the fruƒtum of the cone is the moƒt ƒimple, we ƒhall give that the preference.
        Let f [Plate XIII, Fig. 4] be the cell, or chamber, of a mine; f c the line of leaft reƒiƒtance, in length 10 feet ; c b the radius of the greater circle of the excavation, equal to the line of leaƒt reƒiƒtance, and conƒequently alƒo 10 feet; f g the radius of the ƒmaller circle of the fruftum of the cone, equal to the half of that of the larger circle, viz. 5 feet.
        This premiƒed, to find the cubic ƒolidity of the fruƒtum of the cone a d g b, it is neceƒƒary, firƒt, to find the contents of the whole cone a e b, and, in order to this, its axis e c muƒt be known. The perpendicular g b may be imagined to be drawn from g, to the line c b, which will be parallel to f c; and from the two fimilar triangles g b b, e b c the entire line c e may be known, for b b is to h g, as c b to c e, and h b is the difference of c b from c h, equal to f g. Thus c h ƒhall be 5 feet, conƒequently h b. h g is equal to c f; whence h g is 10 feet. If therefore, inƒtead of the lines h b, h g, c b, in the preceding proportion, we ƒubƒtitute their values, it will appear that 5 is to 10, as 10 is to e c, which will be found to be 2 0 feet, from whence taking c f of 10 feet, there will remain f r the axis, or height of the little cone, which will alƒo be 10 feet. The ƒolidity of the entire cone is found by multiplying the ƒizperficies of the circle of its baƒe by the third of its height c e, whence its ƒolid contents will be found equal to 2100 cubic feet. From this ƒubƒtract the ƒolidity of the leƒƒer cone, which will be found equal to 262 cubic feet, and there will remain for the ƒolid contents of the fruƒtum of the cone a d g b, 1838 cubit [sic] feet, or about 8 cubic fathom and an half.
        This done, if it be ƒuppoƒed that, to raiƒe a cubic fathom of the ground in which a mine is to be made, eleven pounds of powder are requiƒite, the number of fathoms contained in the excavation muƒt be multiplied by the number of the pounds of powder required to raiƒe each fathom; for inƒtance, in the example juft propoƒed, eight fathom and an half muƒt be multiplied by 11, and the product, 93 pounds and an half, gives the quantity of powder requiƒite to charge the mine,which is the point in queƒtion. This quanyity may be ƒomething augmented, that the effect of the mine may be rather greater than leƒs, and to allow for the various accidents which may alƒo happen to the powder in the chamber, to diminiƒh its action.
        If the excavation of this mine had been calculated on the ƒuppoƒition of its being a paraboloid, its ƒolidity would have been found. (5) 1890 cubic feet, which amounts to 8 cubic fathom and three quarters, that is to ƒay, this ƒolid would have been found about one fourth of a fathom larger than ƒuppoƒing it the fruƒtum of a cone; which is a circumƒtance of little or no conƒequence.
        When the quantity of powder requiƒite to charge the mine is known, what ought to be the dimenƒions or capacity of its chamber is to be thence aƒcertained.
        The chamber muƒt be of a ƒize juƒt to contain the charge it is to receive, that the powder being more confined, may, when inflamed, have a ƒtronger effect. It muƒt alƒo be of the figure of a cube, that is, a ƒolid terminated by fix equal ƒquares, becauƒe the powder taking fire in the middle of this ƒolid, acts more equally on all parts of the chamber of the mine; than if it had any other figure, except it could be made circular, which would be ƒtill better, but the conƒtruction of it in this figure is too difficult.
        The proper dimenƒions of the chamber may be eaƒily determined by geometry, knowing only the weight of a cubic foot of powder which is found to be about 80 pounds; as, for inƒtance, if a mine is to be charged with 80 pounds of powder, its chamber muƒt be equal to one cubic foot. It may however be made about one third larger than the ƒpace filled by the powder, becauƒe, to prevent the powder from growing damp in the chamber, or furneau, it is covered all round with ƒacks, planks, ƒtraw, &c.
        To fix then the proper dimenƒion of the chamber of the mine for which we have above aƒcertained the proper charge, let us ƒuppoƒe, that to 93 pounds and an half, the quantity given by the calculation, 7 pounds and an half be added, there will then be 100 [sic] pounds compleat for the charge.
        Now if 80 pounds of powder occupy 1 cubic foot of ƒpace, 100 pounds will occupy 1 cubic foot and one quarter; add to this 3 quarters of a foot for the ƒacks, planks, ƒtraw, &c. which are to be placed in the mine, and 2 cubic feet will be given for the total capacity of the chamber. So that nothing more is requiƒite than to find the ƒide of a cube containing a cubic feet, which appears, by approximation, to be about ƒ foot 3 inches; and then giving for the baƒe of the chamber, a ƒquare whoƒe ƒide is equal to that juƒt found, and making its height alƒo equal to the ƒame, it will have exatly the dimenƒions required. It may not be amiƒs to obferve, that a rigorous exactneƒs is not abƒolutely neceƒƒary in this fort of calculations.
        We ƒhall add here a table, calculated by M. de Palliere, which contains the quantity of powder requiƒite for the charging of mines, from one foot of the line of leaƒt reƒiƒtance to forty.

        We have obƒerved, that the powder preƒƒing equally on all ƒides makes its greateƒt effort on the ƒide where it finds the leaƒt reƒiƒtance, ƒo that its greateft effort may be directed to any ƒide by forming it ƒo as to afford an eaƒier vent to the powder than the others.
        Let Fig. 5. [Plate XIII] be the ƒection, or profile, of a rampart 30 feet high; if the chamber of a mine be placed in the ground it ƒtands upon at d, ƒo as that the line of leaƒt reƒiƒtance, c d, is leƒs than the diƒtance b d, that is, leƒs than that of the chamber from the exterior part of the wall, it is evident, that the mine will ƒpring towards c, and not towards b; but in attacking places, mines are uƒed chiefly to deƒtroy the wall, or rampart, and with great ƒucceƒs. To anfwer this purpoƒe, the chamber of the mine muƒt be ƒo placed as to have the deƒired effect; for inƒtance, in a, where the diƒtance a b, from the chamber a, is leƒs than that of all the other exterior parts of the rampart and its facing. We have ƒuppoƒed in this example the height of this facing b k 30 feet; ƒo that if the chamber be made at the diƒtance of 12 or 15 feet from the exterior ƒide of the revêtement, or facing, the effort of the mine will be made by h a i; and as the part of the ground i will reƒiƒt this effort, it will be wholly directed to b k, and by that means blow up the revêtement into the ditch. The quantity of powder requiƒite to produce this effect may be determined, by the method above laid down, or meaƒuring the ƒolid h a i, and multiplying the number of fathoms contained in it by 20 or 25, the quantity of powder neceƒƒary to raiƒe one cubic fathom of maƒonry, and then adjuƒting the capacity of the chamber to the quantity of powder it is to receive, by the directions contained in what has been ƒaid above upon the ƒubject.
 

SECT. IV. New Obƒervations and Experiments for perfecting the Calculation of Mines.

WHAT has been ƒaid already contains in general the method, at preƒent uƒed, for calculating the quantity of powder requiƒite for the charging of mines. But M. Belidor, who for a long time, with great reputation, profeƒƒed mathematics in the ƒchool of artillery at La Fere, has obƒerved, in a particular tract inƒerted in his Cours de Mathematique, that it is not ƒufficient to conƒider only the weight and quantity of earth intended to be raiƒed by a mine, but that regard muƒt alƒo be had to its quality, with reƒpect to its conƒiƒtence, and the cohefion of its parts * [*2]; and as this coheƒion is greater in ƒmall ƒolids, in proportion to their cubic contents, than in large, more powder is requiƒite to raiƒe or blow up each cubic fathom of a ƒmall ƒolid body, than of a large; and it is evident that this obƒervation muƒt introduce a greater degree of exactneƒs in the calculation of mines.
        To be eaƒily convinced that a ƒmall ƒolid has more ƒurface, in proportion to its cubic contents, than a larger, it is only neceƒƒary to compare a cube, the ƒide of which is one foot, and conƒequently its body terminated by ƒix ƒquares of one foot each, with another cube the ƒide of which is two feet. The ƒolid contents of this laƒt body are eight times that of the firƒt; for the ƒuperfcies of its baƒe is the product of 2 multiplied by 2, which is 4, and its ƒolidity the product of the baƒe multiplied by its height, viz, of 4 by 2, which is 8; ƒo that the laƒt folid is 8 times larger than the firƒt. If the ƒuperficies augmented in proportion to its ƒolidity, this alƒo would be 8 times that of the firƒt, whereas it appears to be but 4 times as large, becauƒe each ƒquare of the ƒuperficies of this ƒolid contains but 4 ƒquares of one foot each, ƒo that, with reƒpect to its ƒolidity, or cubic contents, its ƒuperfcies is leƒs than that of the cube whoƒe ƒide is but one foot.
        It is then plain that the greater the ƒolid intended to be raiƒed is with reƒpect to its ƒuperficies, the more difficult it will be to move it from its bed, which evidently ƒhows the neceƒƒity of conƒidering the tenacity of earths in the calculation of mines.
        M. Belidor propoƒes in the ƒame tract ƒeveral experiments for the diƒcovery of this tenacity. He directs that 3 or 4 mines be made in a ƒoil of the ƒame conƒiƒtence, and of an equal depth, that is, having their lines of leaƒt reƒiƒtance equal, and charged with a very moderate quantity of powder, juƒt ƒufficient to ƒhake or loofen the ground between the bottom of the chamber of the mine and the ƒuperficies of the earth, ƒo that the extent of the ƒhock may be ƒeen in this ƒuperficies by tracing the circle made in it thereby. As it is only by trials many times repeated that the quantity of powder requiƒite to produce this effect can be exactly known, it is plain that many experiments muƒt neceƒƒarily be made before this quantity is determined; but when a charge ƒhall be aƒcertained juƒt ƒuƒƒicient to move the ground, and break the continuity or coheƒion of the ƒolid intended to be raiƒed with the reƒt of the ground, a charge will be obtained ƒufficient to overcome the reƒiƒtance of the continuity of thoƒe parts; and this quantity being known for a line of leaƒt reƒiƒtance of a given length, the quantity of powder, requiƒite to overcome this continuity in a mine having a line of leaƒt reƒiƒtance of a different length, may be aƒcertained by geometry.
        Thoƒe who are acquainted with the elements of geometry know that the ƒuperficies of ƒimilar ƒolids are to each other as the ƒquares of their homologous ƒides. All folids raiƒed by mines made in earths of the ƒame kind, whatever their figure may be, are ƒimilar, and have their lines of leaƒt reƒiƒtance homologous, or in ƒimilar proportion: it follows then that their ƒuperficies are to each other as the ƒquares of the lines of leaƒt refiƒtance. Hence if it is ƒuppoƒed that 50 pounds of powder have looƒened the earth of a mine of which the line of leaƒt refiƒtance was 8 feet, and it is demanded how much would be requiƒite to produce the ƒame effect in a mine of which the line of leaƒt reƒiƒtance ƒhould be 12 feet, this queƒtion maybe anƒwered by the rule of three in this manner, by ƒaying, as the ƒquare of 8, which is 64, is to the ƒquare of 12, which is 144, ƒo 50 pounds of powder are to the 4th term, which will be about 112; and thus it will appear that 112 pounds of powder are requiƒite to ƒurmount the continuity of the earth, in a mine of which the line of leaƒt reƒiƒtance ƒhall be 12 feet.
        Now in order to know the quantity of powder neceƒƒary to raiƒe the earth of the mine, nothing more is neceƒƒary than to charge many in the ƒame ƒoil, having their lines of leaƒt reƒiƒtance equal, and ƒpring them with different quantities of powder, till the charge is obtained, which produces the effect deƒired on the tunnel of the mine.
        This charge found, the quantity of powder neceƒƒary to produce the ƒame effect in a mine, of which the line of leaƒt reƒiƒtance ƒhall be different, may be thence diƒcovered. And to effect this, thoƒe acquainted with the elements of geometry need only remember that ƒimilar ƒolids are to each other as the cubes of their homologous ƒides, and that by the ƒame rule the ƒolids blown up by mines are to each other as the cubes of the lines of leaƒt reƒiƒtance.
        Hence, if 70 pounds of powder have produced the deƒired effect in a mine of which the line of leaƒt reƒiƒtance was 8 feet, in order to find the quantity of powder neceƒƒary to produce the like effect in a mine of which the line of leaƒt reƒiƒtance ƒhall be 15 feet, a rule of proportion muƒt be formed in this manner: as the cube of 8, which is 512, is to the cube of 15, which is 3375; ƒo is 70 pounds of powder, the charge of the firƒt mine, to the quantity of powder requiƒite to charge the mine in queƒtion, which will appear to be 461 pounds; but this quantity will be a little too ƒtrong, becauƒe it is founded on the ƒuppoƒition that the tenacity of the ground of this mine was proportioned to its maƒs, whereas we have ƒhewn it to be leƒs.
        To find the quantity neceƒƒary to be taken from it, it muƒt be confidered, that the mine, of which the line of leaƒt reƒiƒtance was 8 feet, required 50 pounds of powder to ƒurmount the tenacity of the earth; and that as the ƒame mine blew up and made the excavation deƒired with 70 pounds of powder, there was conƒequently but 20 pounds of powder employed in blowing up the earth. Hence then may be deduced both the knowledge of the quantity of powder neceƒƒary to break the continuity of the mine of which the line of leaƒt reƒiƒtance is 15 feet, and the quantity neceƒƒary to blow it up.
        Firft, to find its continuity, this rule of proportion muƒt be formed, founded on what has been ƒaid above: as the ƒquare of 8, which is 64, is to the ƒquare of 15, which is 225; ƒo is 50 pounds of powder to the fourth term, which will be found to be 375 pounds; and this is the quantity of powder requiƒite to break the tenacity of a mine whoƒe line of leaƒt reƒiƒtance is 15 feet.
        In the ƒecond place, the quantity of powder neceƒƒary to ƒpring this mine may be found by this other rule of proportion, founded alƒo on what has been ƒaid before.
        As the cube of 8, which is 512, is to the cube of 15, which is 3375; ƒo is 20 pounds of powder to the quantity of powder required, which will be found to be 130 pounds; this quantity being added to that neceƒƒary to break the tenacity, which was found to be 175, the total will give 306 for the quantity of powder neceƒƒary to charge the mine in queƒtion. By all which it appears that if no regard had been had to the leƒs degree of tenacity of this laƒt mine, allotting it 461 pounds of powder (which is the quantity given by the firƒt calculation) it would have been charged with 155 pounds too much.
        The above-mentioned experiments, made in earths of different conƒiƒtencies, will furniƒh materials for tables exact enough for the charging of mines, with this great advantage, viz. that the figure of the ƒolid is out of the queƒtion; for let this be what it will, it can cauƒe no error in the calculation.
        The Court, purƒuant to what we have related from M. Belidor, having thought proper to cauƒe theƒe experiments to be made, as tending much to the improvement of the doctrine of mines, they were made accordingly, and M. Belidor has promiƒed to give them to the publick, with a compleat treatiƒe on this ƒubject, in which will undoubtedly be found many things entirely new, and of great moment.
        Theƒe experiments remove a very ƒingular prejudice founded on thoƒe already mentioned to have been long ƒince made at Tournay, viz. that the force of the charge of a mine never enlarges the tunnel, but on the contrary diminiƒhes its opening, inƒomuch that when ƒprung with powder, the mine ƒhall form only a kind of pit, the mouth or ƒuperior opening of which ƒhall be little larger than the chamber of the mine. The contrary of this has appeared from newer experiments(6): for by increaƒing the charge of the mine a larger excavation has been produced, and always in proportion to the charge; from whence an inference may be made of great importance in the attack and defence of places, viz. that the quantity of powder may be aƒcertained requiƒite to give the mine an opening of a determined magnitude; for example, of 6, 8, and 12 fathom. But in ƒpite of thoƒe experiments M.Bigot de Morogues remarks, in his Eƒƒay on Powder, that "this fubject is ƒtill diƒputed among miners, who continue to make it a queƒtion whether a furnace overcharged produces only a tunnel in form of a pit, or if, in ƒpight of prejudice, it makes one of a diameter much greater than double the line of leaƒt reƒiƒtance." And he adds, "Reaƒon vouches, theory ƒhews, and experience confirms both opinions in the judgment of their ƒeveral advocates."
        As it appears from theƒe experiments that the common ƒuppoƒition, that the radius of the outer circle of the tunnel is equal to the line of leaƒt reƒiƒtance, is not exactly true, any more than that the radius of its inner circle, or that at the bottom of the tunnel, is equal to the half of the line of leaƒt reƒiƒtance; it thence follows, that the calculations founded on theƒe ƒuppoƒitions are not more certain. However the mines which have been ƒprung, according to the preƒent calculations upon theƒe principles or ƒuppoƒitions, have notwithftanding produced the effect propoƒed, which ƒeems to evince their truth and exactneƒs. But the reafon of this is, that as the ƒolid to be raiƒed by the mine is ƒuppoƒed to be a little bigger than it really is, the furnace of the mine is confequently ƒomething overcharged with reƒpect to this ƒolid, which they are not apprized of, and for this reaƒon the mines never fail to ƒucceed, and produce even a greater effect than is expected from them.
        It is then natural to enquire what advantages in mining may be drawn from the above experiments; theƒe M. Belidor will doubtleƒs enumerate particularly, in the Treatiƒe of Mines which he has promiƒed to the publick, but in the mean time we shall point out ƒeveral which ƒeem to be of confiderable importance.
        It is the preƒent practice, in order to ƒpring a mine which ƒhall produce an opening, for example, of 40 feet, to ƒink it 20 feet below the furnace of the ground, that it may have a line of leaƒt reƒiƒtance of that length. As all earths will not admit of this, an excavation of 40 feet diameter cannot be made by one mine, or one furnace, where there is not this depth of earth; ƒo that in this caƒe it becomes neceƒƒary to make ƒeveral. In the attack, but more eƒpecially in the defence of places, there are many caƒes in which a mine that gives too deep a tunnel ƒerves only to furniƒh a covert to the enemy; but this could never happen if it were poƒƒible to give a tunnel of leƒs depth, and at the ƒame time of a larger diameter. Beƒides, the leƒs deep the tunnel, the oftner the furnace might be repeated in the ƒame place. Add to this, that in the major part of places where mines are employed, the celerity of their conƒtruction is a point of great importance; therefore if, without ƒinking the mine ƒo deep as is practiƒed at prefent, they could be contrived ƒo as to produce the ƒame effect, the execution of them would be ƒooner performed, and conƒequently to much greater advantage.
        After having given ƒome idea of the ƒentiments hitherto held concerning mines, it is neceƒƒary to ƒay ƒomething of their conƒtruction, and that of their galleries.
 

SECT. V. Of the Conƒtruction of Mines and their Galleries.

WE ƒhall ƒay nothing here of what concerns the miner, viz. of the manner in which he breaks ground, and carries on the trenches, deferring this till we come to treat of the attack, where the difficulties he meets with in the courƒe of his work will be particularly conƒidered.
        The galleries which are made and carried on by miners, till they come under the place intended to be blown up, are commonly four feet and an half in height, and two feet and an half or three feet wide.
        The miner works upon his knees, he begins by making an hole big enough to hold himƒelf, another miner is placed behind him, who gathers up, in a kind of little wheel-barrow, the earth which the firƒt miner digs out in making his paƒƒage. This wheel-barrow is ƒometimes faƒtned to a cord, ƒo contrived as that when it is full, a miner, who is poƒted at the end of the gallery, can draw it to him, and empty it of the earth without the gallery, and when it is thus emptied, the ƒecond miner can draw it back to be filled again. But this is done only when the gallery is not carried on far in the earth; when it is, many hands are employed to clear away the ground dug out from the gallery. Miners relieve each other every two hours, and carry on their work with the greateƒt poƒƒible diligence and expedition.
        As the gallery advances, the carpenters are appointed to ƒhore it, that is, to ƒet up at proper diƒtances pieces of timber, called propƒ or ƒhorings, to ƒuƒtain the earth above the gallery, and prevent its falling in; ƒometimes ƒmall arches are formed of ƒeveral pieces of wood for this purpoƒe, and ƒometimes they content themƒelves with laying planks ƒupported by the props, which laƒt is the method commonly uƒed.
        The miner carries on his work till he comes to the place where the chamber is to be made, and when he has given this its proper dimenƒions, the carpenters ƒhore it; it is then lined with empty lacks, ƒtraw, and plank, to prevent the powder from growing damp; and when it is in every reƒpect compleated, the powder is laid on the planking upon a bed of straw, covered with empty ƒacks; the end of the ƒauƒage is placed in the middle of the powder, that it may all take fire at once. That the ƒauƒage may continue fixed in this poƒition, it is pinn'd to the interior part of the chamber, near the planks ƒupported by the ƒhorers,with a wooden peg, which ƒecures it. This peg has alƒo a further office, which is, to prevent the ƒauƒage from being drawn out of the chamber of the mine. That part of the ƒauƒage which lies out of the chamber in the gallery, is placed in a trough or gutter, as mentioned before.
        The top of the chamber is cover'd with ƒtrong planks, [Plate XIV, Fig. 2] upon theƒe props are placed, which ƒupport other planks, that prevent the earth of the gallery over the chamber from falling in; pieces of wood are alƒo laid horizontally croƒƒing each other at right angles, or obliquely in the form of St Andrew's croƒs; theƒe ƒerve to hold the props more firmly againƒt the earth of the gallery. The void ƒpaces are then filled with dung, brick, ƒtones, and other things of the like kind; a great part of the gallery is alƒo filled with theƒe materials, to prevent the powder from evacuating that way.
        That the gallery may oppoƒe a reƒiƒtance effectual to prevent the powder from evacuating by it, it is neceƒƒary it ƒhould be longer than the line of leaƒt reƒiƒtance of the chamber of the mine.
    For if b [Plate XIV. Fig 1.] is ƒuppoƒed to be the chamber conƒructed in the contrefort; a and c, the entrance of the gallery over againƒt the chamber b; as its length, b c, is much leƒs than the height of the ground and the maƒonry above the chamber, however carefully and exactly this gallery may be filled and ƒtopped up, its reƒiƒtance will not be equal to that of this earth and maƒonry; and therefore the mine will take effect principally by the way of the gallery, or, as miners generally term it, the mine will blow in the gallery.
        But if, to blow up part of the rampart overagainƒt and above the point l, [Plate XIV. Fig 2.] the opening or mouth of the mine be made in d, at a proper diƒtance from this part, and the gallery be conducted by returns, or as it were elbowings, from d to e, from e to f, from f to g, and laƒtly, from g to i; it is evident that a part of the gallery may be filled or ƒtopped up, ƒufficient to oppoƒe a ƒtronger reƒiƒtance to the powder incloƒed in the chamber, than will be made by the line of leaƒt reƒiƒtance, and that in this ƒtate the mine may be made to produce all the effect that is deƒired.
        From hence it follows, that to blow up part of a rampart, or revêtement, the gallery ought to be opened at ƒome diƒtance, and conducted to it by returns, or traverƒes. Theƒe traverƒes, or returns, are of confiderable uƒe in facilitating the effectual ƒtopping up the gallery; but as they prolong the work, no more of them are made than are thought neceƒƒary to make the gallery reƒiƒt the powder more forcibly than the line of leaƒt reƒiƒtance of the mine.
        To give ƒome idea of the manner in which a gallery is filled at each coude or return, let a b c d [Plate XIV. Fig. 3.] be one of theƒe returns or coudes; to fill this up, madriers or planks are firƒt placed vertically along c d, and in the ƒame manner along a b; theƒe planks are then covered with others laid horizontally, thoƒe marked c d terminating towards c and d, and thoƒe marked a b towards a and b. On the back of theƒe madriers, to ƒupport and ƒtrengthen them, pieces of wood, called piedroits, are ƒet up vertically, and made to bind tight on both ƒides of the madriers d c and a b, by ƒtrong pieces of wood laid tranƒverƒely, called buttreƒƒes. And that theƒe pieces of wood may preƒs as forcibly as poƒƒible on the madriers, which are back'd or ƒupported by the piedroits, they are driven in with great force, and ƒtrong wedges are placed between the extremities of the buttreƒƒes and the piedroits on which they reƒt; after this the void ƒpace of the coude is filled up with the ƒame materials uƒed for filling the ƒpaces above the chamber of the mine.
        It muƒt be noted, that the whole length of all the returns of the gallery together, does not expreƒs the reƒiƒtance which it makes to the effort of the mine; for the powder expanding circularly, a gallery of many coudes or traverƒes reƒiƒts this effort only in proportion to the length of the ƒuppoƒed right line, reaching from the opening or mouth of the chamber, which line may be conƒidered as the length of the gallery, and it is by this that the length of the gallery, is expreƒƒed, or meaƒured.
        Let b [Plate XIV. Fig. 4.] be the furnace of a mine, of which the line of leaƒt reƒiƒtance is a b; if the ƒides of the gallery b c and c d, taken together, are equal to the line a b, and if the gallery is ƒuppoƒed to be filled with materials capable of the ƒame degree of reƒiƒtance as the ground or materials of the line of leaƒt reƒiƒtance, the mine will ƒpring by its gallery; for the powder will expand towards the opening of the gallery d, as we obƒerved above, in the direction of the line b d, which is leƒs than the lines b c and c d taken together, and conƒequently leƒs than the line of leaƒt reƒiƒtance, therefore, &c.
        It follows from hence that the part of the gallery which is to be filled, ought not to be eƒtimated by the length of the ƒeveral parts or returns of the gallery, but by a right line drawn from the centre of the chamber to a certain point of the gallery. Geometry furniƒhes a great number of rules for the meaƒuring of this line; that which appears to be the moƒt ƒimple is, to trace very exactly all the returns of a gallery upon a plain by means of a ƒcale, after which it will be very eaƒy to diƒcover, by the ƒame ƒeale, the points of the gallery on which a right line of a determined length, drawn from the centre of the chamber through the gallery, will fall.
        The materials with which a gallery is filled cannot be cemented or bound together, ƒo as to give them a ƒolidity equal to the parts of a fortification, or the old maƒonry. But when works of this nature are to be blown up, the gallery is to be ƒo filled, that the right line, by which the length of the part filled up is expreƒƒed, may be longer than the line of leaƒt reƒiƒtance. It is very difficult to give preciƒe rules in this particular; ƒome authors have nevertheleƒs maintained that in common earth the gallery need only be filled up about 5 or 6 feet more than the line of leaƒt reƒiƒtance, and that in maƒonry it muƒt be filled one third or one half more than this line; ƒo that if in the laƒt caƒe the line of leaƒt reƒiƒtance is 18 feet, the gallery ought to be filled up 24 or 27 feet at leaƒt; and it is to be noted, that this length is always to be reckon'd on the right line ƒuppoƒed to be drawn from, the chamber to the end of the gallery.
        Nothing more remains, after what has been ƒaid above concerning mines, but to give ƒome idea of the ƒeveral kinds of them.
 

SECT. VI. Of the different Kinds of Mines.

A Mine which has only one chamber, or fourneau, as the mine a, [Plate XIV. Fig. 2, 5, 6.] is called a ƒimple mine. If it has two chambers, as repreƒented by figure b, the gallery forms a ƒort of T, and the mine is called a double mine. If it has three chambers, as in fig. c, it is called a triple mine; and, laƒtly, if it has four chambers, it is called a quadruple mine, always taking its name from the number of its chambers or fourneaus.
        The deƒign of mines which have many chambers, is to blow up at the ƒame time a great part of a rampart, or a large extent of ground. Such a diƒpoƒition is obƒerved in their diƒtances, or intervals, as that they may co-operate together; and their ƒeveral charges are all fired at the ƒame time, by means of a ƒauƒage communicating with all the chambers, the ƒauƒage being fired in ƒuch a part as that the fire may reach all the chambers at the ƒame inƒtant. To produce this effect, it is only neceƒƒary that the fire ƒhould run through equal lengths of the ƒauƒage from the point where it is fired, called its focus, to the centre of each chamber, ƒo that if ƒome chambers be nearer the focus than others, the ƒauƒage muƒt be laid in returns or zigzags, that it may have the ƒame length between the focus and the nearer chambers, as between the focus and thoƒe which are at a greater diƒtance.
        In revêtements, where the mine is intended to be conƒtructed double, the gallery muƒt be opened between two contreforts, and the revêtement being pierced, it muƒt be puƒhed on to the right and left along the outƒide of the revêtement to the middle of two contreforts; and being brought thus far, the chambers are hollowed out in that part of the revêtement joining to theƒe contreforts.
        To make a triple mine, the gallery is opened overagainƒt a contrefort, and when the opening of the revêtement is pierced, it is extended to the right and left, as in the double mine, to the two next contreforts, and here the chamber is made in the revêtement in the ƒame manner as in the double mine. A gallery is alƒo carried on to the ƒide of the contrefort, which is overagainƒt the opening or mouth of the mine, and behind this contrefort the third chamber is made, as it appears in Fig. c.
        As to quadruple mines, [Plate XIV. Fig. 6.] they are only two double mines, joined together by the ƒame ƒauƒage.
        The ƒimple and double mines are moƒt uƒed in ƒieges, the others being ƒeldom made but when ƒome work is intended to be totally demoliƒhed.
        In the attack of places it is common to make little mines, the chambers of which are not deeper in the ground than from five to twelve feet. This kind of mine is called a fougade; and is commonly made under the ƒaillant angle of the glacis, being double, triple, &c. in many places. The galleries of theƒe mines, which are called their branches, are conƒtructed before the attack of the place is thought of, and make a principal part of its fortification. Places which have galleries or branches conƒtructed under their glacis, and in the parts adjacent, are ƒaid to have the glacis countermined. The citadel of Tournay has its glacis countermined, and many of the front-works of Luxembourg have the ƒame.
With reƒpect to the countermines of places, of which we have ƒaid nothing as yet in this treatiƒe, it is ƒufficient to recite what has been ƒaid of them in our Elements of Fortification, viz. "that they are ƒubterraneous galleries, conƒtructed at the ƒame time with the place, whether they reach within the baƒtion, or under the ƒoƒƒe [may be "ƒoffe" or "foƒƒe"] and covered way. Their uƒe is to facilitate the meeting, and preventing the enemy's miners, to obƒtruct their works, and to furniƒh means, by continuing their branches, to blow up the enemy's lodgments on the covered way and other works which he has gained."
        When the beƒiegers would make uƒe of mines or fougades in an attack, the miner ƒinks force pits in the neareƒt places he can work in to the ƒpot intended for the chamber, and from the bottom of theƒe pits he advances his gallery or branch to the places which are pointed out to him.
        Nothing now remains, after all that has been ƒaid concerning mines, but to obƒerve that the uƒe of them is very ancient, and that they were practiced even in the remoteƒt antiquity. Galleries were then made much in the ƒame manner as at preƒent, and when they were brought under the wall intended to be deƒtroyed, a very large gallery was made in the body or thickneƒs of the wall; that part of the wall directly over this gallery was ƒuƒtained by ƒtrong props or ƒhorers, and the gallery filled with combuƒtibles, that is, ƒuch materials as took fire eaƒily, and retained it long; theƒe materials being kindled, communicated the flame to the props, which being ƒoon conƒumed, the wall no longer ƒupported by them fell in, and by that means made a breach in the place.* [*3] The beƒieged alƒo made uƒe of the like artifice againƒt the beƒiegers, often making cavities under the machines of the enemy, which falling down into the excavation or hollow of the mine, were either broken to pieces, or at leaƒt rendered unƒerviceable for ƒome time. By means of gunpowder mines are now made with much greater celerity than thoƒe of antiquity: ƒince the diƒcovery of this compoƒition the old method of mining is in a manner entirely laid aƒide; I ƒay, in a manner, becauƒe it is ƒtill uƒed in ƒome caƒes, and the chevalier de St Julien reports that he actually ƒaw a mine conƒtructed in the ancient manner, made uƒe of for deƒtroying a work of the fortification which covered the caƒtle of Pont-a-Mouƒƒon. But theƒe examples are ƒo rare, that the new method may be regarded as the only one at preƒent in uƒe.
        The cuftom of charging mines with powder is leƒs ancient than the application of it to other military purpoƒes. The firƒt eƒƒay of this kind was in 1487; the Genoeƒe befieging Serezanella, a town belonging to the Florentines, an engineer attempted to blow up the wall of the caƒtle with gunpowder placed under it; but the effect not anƒwering his expectation, probably either becauƒe he charged his mine with too ƒmall a quantity of powder, or becauƒe it made its effort by the gallery, no improvement of the hint of this engineer was thought of, till Peter of Navarre, who then ƒerved in the Genoeƒe army, and was afterwards in the ƒervice of Spain, made uƒe of it in 1503 againƒt the French at the ƒiege of Caƒtel del Ovo, a ƒort of fort or citadel of the city of Naples. The commandant of this fort refuƒing to ƒurrender at the ƒummons of Peter of Navarre, he blew up the wall of the caƒtle, and took it by aƒƒault.