Chapter XI: Book V (2)

Each method of surveying depends on the measuring of triangles. A small triangle should be laid out, and from it calculations must be made regarding a larger one. Most particular care must be taken that we do not deviate at all from a correct measuring; for if, at the beginning, we are drawn by carelessness into a slight error, this at the end will produce great errors. Now these triangles are of many shapes, since shafts differ among themselves and are not all sunk by one and the same method into the depths of the earth, nor do the slopes of all mountains come down to the valley or plain in the same manner. For if a shaft is vertical, there is a triangle with a right angle, which the Greeks call [Greek: orthogonion] and this, according to the inequalities of the mountain slope, has either two equal sides or three unequal sides. The Greeks call the former [Greek: trigonon isoskeles] the latter [Greek: skalenon] for a right angle triangle cannot have three equal sides. If a shaft is inclined and sunk in the same vein in which the tunnel is driven, a triangle is likewise made with a right angle, and this again, according to the various inequalities of the mountain slope, has either two equal or three unequal sides. But if a shaft is inclined and is sunk in one vein, and a tunnel is driven in another vein, then a triangle comes into existence which has either an obtuse angle or all acute angles. The former the Greeks call [Greek: amblygonion], the latter [Greek: oxygonion]. That triangle which has an obtuse angle cannot have three equal sides, but in accordance with the different mountain slopes has either two equal sides or three unequal sides. That triangle which has all acute angles in accordance with the different mountain slopes has either three equal sides, which the Greeks call [Greek: trigonon isopleuron] or two equal sides or three unequal sides.

The surveyor, as I said, employs his art when the owners of the mines desire to know how many fathoms of the intervening ground require to be dug; when a tunnel is being driven toward a shaft and does not yet reach it; or when the shaft has not yet been sunk to the depth of the bottom of the tunnel which is under it; or when neither the tunnel reaches to that point, nor has the shaft been sunk to it. It is of importance that miners should know how many fathoms remain from the tunnel to the shaft, or from the shaft to the tunnel, in order to calculate the expenditure; and in order that the owners of a metal-bearing mine may hasten the sinking of a shaft and the excavation of the metal, before the tunnel reaches that point and the tunnel owners excavate part of the metal by any right of their own; and on the other hand, it is important that the owners of a tunnel may similarly hasten their driving before a shaft can be sunk to the depth of a tunnel, so that they may excavate the metal to which they will have a right.

The surveyor, first of all, if the beams of the shaft-house do not give him the opportunity, sets a pair of forked posts by the sides of the shaft in such a manner that a pole may be laid across them. Next, from the pole he lets down into the shaft a cord with a weight attached to it. Then he stretches a second cord, attached to the upper end of the first cord, right down along the slope of the mountain to the bottom of the mouth of the tunnel, and fixes it to the ground. Next, from the same pole not far from the first cord, he lets down a third cord, similarly weighted, so that it may intersect the second cord, which descends obliquely. Then, starting from that point where the third cord cuts the second cord which descends obliquely to the mouth of the tunnel, he measures the second cord upward to where it reaches the end of the first cord, and makes a note of this first side of the minor triangle[17]. Afterward, starting again from that point where the third cord intersects the second cord, he measures the straight space which lies between that point and the opposite point on the first cord, and in that way forms the minor triangle, and he notes this second side of the minor triangle in the same way as before. Then, if it is necessary, from the angle formed by the first cord and the second side of the minor triangle, he measures upward to the end of the first cord and also makes a note of this third side of the minor triangle. The third side of the minor triangle, if the shaft is vertical or inclined and is sunk on the same vein in which the tunnel is driven, will necessarily be the same length as the third cord above the point where it intersects the second cord; and so, as often as the first side of the minor triangle is contained in the length of the whole cord which descends obliquely, so many times the length of the second side of the minor triangle indicates the distance between the mouth of the tunnel and the point to which the shaft must be sunk; and similarly, so many times the length of the third side of the minor triangle gives the distance between the mouth of the shaft and the bottom of the tunnel.

When there is a level bench on the mountain slope, the surveyor first measures across this with a measuring-rod; then at the edges of this bench he sets up forked posts, and applies the principle of the triangle to the two sloping parts of the mountain; and to the fathoms which are the length of that part of the tunnel determined by the triangles, he adds the number of fathoms which are the width of the bench. But if sometimes the mountain side stands up, so that a cord cannot run down from the shaft to the mouth of the tunnel, or, on the other hand, cannot run up from the mouth of the tunnel to the shaft, and, therefore, one cannot connect them in a straight line, the surveyor, in order to fix an accurate triangle, measures the mountain; and going downward he substitutes for the first part of the cord a pole one fathom long, and for the second part a pole half a fathom long. Going upward, on the contrary, for the first part of the cord he substitutes a pole half a fathom long, and for the next part, one a whole fathom long; then where he requires to fix his triangle he adds a straight line to these angles.

To make this system of measuring clear and more explicit, I will proceed by describing each separate kind of triangle. When a shaft is vertical or inclined, and is sunk in the same vein on which the tunnel is driven, there is created, as I said, a triangle containing a right angle. Now if the minor triangle has the two sides equal, which, in accordance with the numbering used by surveyors, are the second and third sides, then the second and third sides of the major triangle will be equal; and so also the intervening distances will be equal which lie between the mouth of the tunnel and the bottom of the shaft, and which lie between the mouth of the shaft and the bottom of the tunnel. For example, if the first side of the minor triangle is seven feet long and the second and likewise the third sides are five feet, and the length shown by the cord for the side of the major triangle is 101 times seven feet, that is 117 fathoms and five feet, then the intervening space, of course, whether the whole of it has been already driven through or has yet to be driven, will be one hundred times five feet, which makes eighty-three fathoms and two feet. Anyone with this example of proportions will be able to construct the major and minor triangles in the same way as I have done, if there be the necessary upright posts and cross-beams. When a shaft is vertical the triangle is absolutely upright; when it is inclined and is sunk on the same vein in which the tunnel is driven, it is inclined toward one side. Therefore, if a tunnel has been driven into the mountain for sixty fathoms, there remains a space of ground to be penetrated twenty-three fathoms and two feet long; for five feet of the second side of the major triangle, which lies above the mouth of the shaft and corresponds with the first side of the minor triangle, must not be added. Therefore, if the shaft has been sunk in the middle of the head meer, a tunnel sixty fathoms long will reach to the boundary of the meer only when the tunnel has been extended a further two fathoms and two feet; but if the shaft is located in the middle of an ordinary meer, then the boundary will be reached when the tunnel has been driven a further length of nine fathoms and two feet. Since a tunnel, for every one hundred fathoms of length, rises in grade one fathom, or at all events, ought to rise as it proceeds toward the shaft, one more fathom must always be taken from the depth allowed to the shaft, and one added to the length allowed to the tunnel. Proportionately, because a tunnel fifty fathoms long is raised half a fathom, this amount must be taken from the depth of the shaft and added to the length of the tunnel. In the same way if a tunnel is one hundred or fifty fathoms shorter or longer, the same proportion also must be taken from the depth of the one and added to the length of the other. For this reason, in the case mentioned above, half a fathom and a little more must be added to the distance to be driven through, so that there remain twenty-three fathoms, five feet, two palms, one and a half digits and a fifth of a digit; that is, if even the minutest proportions are carried out; and surveyors do not neglect these without good cause. Similarly, if the shaft is seventy fathoms deep, in order that it may reach to the bottom of the tunnel, it still must be sunk a further depth of thirteen fathoms and two feet, or rather twelve fathoms and a half, one foot, two digits, and four-fifths of half a digit. And in this instance five feet must be deducted from the reckoning, because these five feet complete the third side of the minor triangle, which is above the mouth of the shaft, and from its depth there must be deducted half a fathom, two palms, one and a half digits and the fifth part of half a digit. But if the tunnel has been driven to a point where it is under the shaft, then to reach the roof of the tunnel the shaft must still be sunk a depth of eleven fathoms, two and a half feet, one palm, two digits, and four-fifths of half a digit.

If a minor triangle is produced of the kind having three unequal sides, then the sides of the greater triangle cannot be equal; that is, if the first side of the minor triangle is eight feet long, the second six feet long, and the third five feet long, and the cord along the side of the greater triangle, not to go too far from the example just given, is one hundred and one times eight feet, that is, one hundred and thirty-four fathoms and four feet, the distance which lies between the mouth of the tunnel and the bottom of the shaft will occupy one hundred times six feet in length, that is, one hundred fathoms. The distance between the mouth of the shaft and the bottom of the tunnel is one hundred times five feet, that is, eighty-three fathoms and two feet. And so, if the tunnel is eighty-five fathoms long, the remainder to be driven into the mountain is fifteen fathoms long, and here, too, a correction in measurement must be taken from the depth of the shaft and added to the length of the tunnel; what this is precisely, I will pursue no further, since everyone having a small knowledge of arithmetic can work it out. If the shaft is sixty-seven fathoms deep, in order that it may reach the bottom of the tunnel, the further distance required to be sunk amounts to sixteen fathoms and two feet.

The surveyor employs this same method in measuring the mountain, whether the shaft and tunnel are on one and the same vein, whether the vein is vertical or inclined, or whether the shaft is on the principal vein and the tunnel on a transverse vein descending vertically to the depths of the earth; in the latter case the excavation is to be made where the transverse vein cuts the vertical vein. If the principal vein descends on an incline and the cross-vein descends vertically, then a minor triangle is created having one obtuse angle or all three angles acute. If the minor triangle has one angle obtuse and the two sides which are the second and third are equal, then the second and third sides of the major triangle will be equal, so that if the first side of the minor triangle is nine feet, the second, and likewise the third, will be five feet. Then the first side of the major triangle will be one hundred and one times nine feet, or one hundred and fifty-one and one-half fathoms, and each of the other sides of the major triangle will be one hundred times five feet, that is, eighty-three fathoms and two feet. But when the first shaft is inclined, generally speaking, it is not deep; but there are usually several, all inclined, and one always following the other. Therefore, if a tunnel is seventy-seven fathoms long, it will reach to the middle of the bottom of a shaft when six fathoms and two feet further have been sunk. But if all such inclined shafts are seventy-six fathoms deep, in order that the last one may reach the bottom of the tunnel, a depth of seven fathoms and two feet remains to be sunk.

If a minor triangle is made which has an obtuse angle and three unequal sides, then again the sides of the large triangle cannot be equal. For example, if the first side of the minor triangle is six feet long, the second three feet, and the third four feet, and the cord along the side of the greater triangle one hundred and one times six feet, that is, one hundred and one fathoms, the distance between the mouth of the tunnel and the bottom of the last shaft will be a length one hundred times three feet, or fifty fathoms; but the depth that lies between the mouth of the first shaft and the bottom of the tunnel is one hundred times four feet, or sixty-six fathoms and four feet. Therefore, if a tunnel is forty-four fathoms long, the remaining distance to be driven is six fathoms. If the shafts are fifty-eight fathoms deep, the newest will touch the bottom of the tunnel when eight fathoms and four feet have been sunk.

If a minor triangle is produced which has all its angles acute and its three sides equal, then necessarily the second and third sides of the minor triangle will be equal, and likewise the sides of the major triangle frequently referred to will be equal. Thus if each side of the minor triangle is six feet long, and the cord measurement for the side of the major triangle is one hundred and one times six feet, that is, one hundred and one fathoms, then both the distances to be dug will be one hundred fathoms. And thus if the tunnel is ninety fathoms long, it will reach the middle of the bottom of the last shaft when ten fathoms further have been driven. If the shafts are ninety-five fathoms deep, the last will reach the bottom of the tunnel when it is sunk a further depth of five fathoms.

If a triangle is made which has all its angles acute, but only two sides equal, namely, the first and third, then the second and third sides are not equal; therefore the distances to be dug cannot be equal. For example, if the first side of the minor triangle is six feet long, and the second is four feet, and the third is six feet, and the cord measurement for the side of the major triangle is one hundred and one times six feet, that is, one hundred and one fathoms, then the distance between the mouth of the tunnel and the bottom of the last shaft will be sixty-six fathoms and four feet. But the distance from the mouth of the first shaft to the bottom of the tunnel is one hundred fathoms. So if the tunnel is sixty fathoms long, the remaining distance to be driven into the mountain is six fathoms and four feet. If the shaft is ninety-seven fathoms deep, the last one will reach the bottom of the tunnel when a further depth of three fathoms has been sunk.

If a minor triangle is produced which has all its angles acute, but its three sides unequal, then again the distances to be dug cannot be equal. For example, if the first side of the minor triangle is seven feet long, the second side is four feet, and the third side is six feet, and the cord measurement for the side of the major triangle is one hundred and one times seven feet or one hundred and seventeen fathoms and four feet, the distance between the mouth of the tunnel and the bottom of the last shaft will be four hundred feet or sixty-six fathoms, and the depth between the mouth of the first shaft and the bottom of the tunnel will be one hundred fathoms. Therefore, if a tunnel is fifty fathoms long, it will reach the middle of the bottom of the newest shaft when it has been driven sixteen fathoms and four feet further. But if the shafts are then ninety-two fathoms deep, the last shaft will reach the bottom of the tunnel when it has been sunk a further eight fathoms.

This is the method of the surveyor in measuring the mountain, if the principal vein descends inclined into the depths of the earth or the transverse vein is vertical. But if they are both inclined, the surveyor uses the same method, or he measures the slope of the mountain separately from the slope of the shaft. Next, if a transverse vein in which a tunnel is driven does not cut the principal vein in that spot where the shaft is sunk, then it is necessary for the starting point of the survey to be in the other shaft in which the transverse vein cuts the principal vein. But if there be no shaft on that spot where the outcrop of the transverse vein cuts the outcrop of the principal vein, then the surface of the ground which lies between the shafts must be measured, or that between the shaft and the place where the outcrop of the one vein intersects the outcrop of the other.

Some surveyors, although they use three cords, nevertheless ascertain only the length of a tunnel by that method of measuring, and determine the depth of a shaft by another method; that is, by the method by which cords are re-stretched on a level part of the mountain or in a valley, or in flat fields, and are measured again. Some, however, do not employ this method in surveying the depth of a shaft and the length of a tunnel, but use only two cords, a graduated hemicycle[18] and a rod half a fathom long. They suspend in the shaft one cord, fastened from the upper pole and weighted, just as the others do. Fastened to the upper end of this cord, they stretch another right down the slope of the mountain to the bottom of the mouth of the tunnel and fix it to the ground. Then to the upper part of this second cord they apply on its lower side the broad part of a hemicycle. This consists of half a circle, the outer margin of which is covered with wax, and within this are six semi-circular lines. From the waxed margin through the first semi-circular line, and reaching to the second, there proceed straight lines converging toward the centre of the hemicycle; these mark the middles of intervening spaces lying between other straight lines which extend to the fourth semi-circular line. But all lines whatsoever, from the waxed margin up to the fourth line, whether they go beyond it or not, correspond with the graduated lines which mark the minor spaces of a rod. Those which go beyond the fourth line correspond with the lines marking the major spaces on the rod, and those which proceed further, mark the middle of the intervening space which lies between the others. The straight lines, which run from the fifth to the sixth semi-circular line, show nothing further. Nor does the line which measures the half, show anything when it has already passed from the sixth straight line to the base of the hemicycle. When the hemicycle is applied to the cord, if its tongue indicates the sixth straight line which lies between the second and third semi-circular lines, the surveyor counts on the rod six lines which separate the minor spaces, and if the length of this portion of the rod be taken from the second cord, as many times as the cord itself is half-fathoms long, the remaining length of cord shows the distance the tunnel must be driven to reach under the shaft. But if he sees that the tongue has gone so far that it marks the sixth line between the fourth and fifth semi-circular lines, he counts six lines which separate the major spaces on the rod; and this entire space is deducted from the length of the second cord, as many times as the number of whole fathoms which the cord contains; and then, in like manner, the remaining length of cord shows us the distance the tunnel must be driven to reach under the shaft.[19]

Both these surveyors, as well as the others, in the first place make use of the haulage rope. These they measure by means of others made of linden bark, because the latter do not stretch at all, while the former become very slack. These cords they stretch on the surveyor's field, the first one to represent the parts of mountain slopes which descend obliquely. Then the second cord, which represents the length of the tunnel to be driven to reach the shaft, they place straight, in such a direction that one end of it can touch the lower end of the first cord; then they similarly lay the third cord straight, and in such a direction that its upper end may touch the upper end of the first cord, and its lower end the other extremity of the second cord, and thus a triangle is formed. This third cord is measured by the instrument with the index, to determine its relation to the perpendicular; and the length of this cord shows the depth of the shaft.

Some surveyors, to make their system of measuring the depth of a shaft more certain, use five stretched cords: the first one descending obliquely; two, that is to say the second and third, for ascertaining the length of the tunnel; two for the depth of the shaft; in which way they form a quadrangle divided into two equal triangles, and this tends to greater accuracy.

These systems of measuring the depth of a shaft and the length of a tunnel, are accurate when the vein and also the shaft or shafts go down to the tunnel vertically or inclined, in an uninterrupted course. The same is true when a tunnel runs straight on to a shaft. But when each of them bends now in this, now in that direction, if they have not been completely driven and sunk, no living man is clever enough to judge how far they are deflected from a straight course. But if the whole of either one of the two has been excavated its full distance, then we can estimate more easily the length of one, or the depth of the other; and so the location of the tunnel, which is below a newly-started shaft, is determined by a method of surveying which I will describe. First of all a tripod is fixed at the mouth of the tunnel, and likewise at the mouth of the shaft which has been started, or at the place where the shaft will be started. The tripod is made of three stakes fixed to the ground, a small rectangular board being placed upon the stakes and fixed to them, and on this is set a compass. Then from the lower tripod a weighted cord is let down perpendicularly to the earth, close to which cord a stake is fixed in the ground. To this stake another cord is tied and drawn straight into the tunnel to a point as far as it can go without being bent by the hangingwall or the footwall of the vein. Next, from the cord which hangs from the lower tripod, a third cord likewise fixed is brought straight up the sloping side of the mountain to the stake of the upper tripod, and fastened to it. In order that the measuring of the depth of the shaft may be more certain, the third cord should touch one and the same side of the cord hanging from the lower tripod which is touched by the second cord--the one which is drawn into the tunnel. All this having been correctly carried out, the surveyor, when at length the cord which has been drawn straight into the tunnel is about to be bent by the hangingwall or footwall, places a plank in the bottom of the tunnel and on it sets the orbis, an instrument which has an indicator peculiar to itself. This instrument, although it also has waxed circles, differs from the other, which I have described in the third book. But by both these instruments, as well as by a rule and a square, he determines whether the stretched cords reach straight to the extreme end of the tunnel, or whether they sometimes reach straight, and are sometimes bent by the footwall or hangingwall. Each instrument is divided into parts, but the compass into twenty-four parts, the orbis into sixteen parts; for first of all it is divided into four principal parts, and then each of these is again divided into four. Both have waxed circles, but the compass has seven circles, and the orbis only five circles. These waxed circles the surveyor marks, whichever instrument he uses, and by the succession of these same marks he notes any change in the direction in which the cord extends. The orbis has an opening running from its outer edge as far as the centre, into which opening he puts an iron screw, to which he binds the second cord, and by screwing it into the plank, fixes it so that the orbis may be immovable. He takes care to prevent the second cord, and afterward the others which are put up, from being pulled off the screw, by employing a heavy iron, into an opening of which he fixes the head of the screw. In the case of the compass, since it has no opening, he merely places it by the side of the screw. That the instrument does not incline forward or backward, and in that way the measurement become a greater length than it should be, he sets upon the instrument a standing plummet level, the tongue of which, if the instrument is level, indicates no numbers, but the point from which the numbers start.

When the surveyor has carefully observed each separate angle of the tunnel and has measured such parts as he ought to measure, then he lays them out in the same way on the surveyor's field[20] in the open air, and again no less carefully observes each separate angle and measures them. First of all, to each angle, according as the calculation of his triangle and his art require it, he lays out a straight cord as a line. Then he stretches a cord at such an angle as represents the slope of the mountain, so that its lower end may reach the end of the straight cord; then he stretches a third cord similarly straight and at such an angle, that with its upper end it may reach the upper end of the second cord, and with its lower end the last end of the first cord. The length of the third cord shows the depth of the shaft, as I said before, and at the same time that point on the tunnel to which the shaft will reach when it has been sunk.

If one or more shafts reach the tunnel through intermediate drifts and shafts, the surveyor, starting from the nearest which is open to the air, measures in a shorter time the depth of the shaft which requires to be sunk, than if he starts from the mouth of the tunnel. First of all he measures that space on the surface which lies between the shaft which has been sunk and the one which requires to be sunk. Then he measures the incline of all the shafts which it is necessary to measure, and the length of all the drifts with which they are in any way connected to the tunnel. Lastly, he measures part of the tunnel; and when all this is properly done, he demonstrates the depth of the shaft and the point in the tunnel to which the shaft will reach. But sometimes a very deep straight shaft requires to be sunk at the same place where there is a previous inclined shaft, and to the same depth, in order that loads may be raised and drawn straight up by machines. Those machines on the surface are turned by horses; those inside the earth, by the same means, and also by water-power. And so, if it becomes necessary to sink such a shaft, the surveyor first of all fixes an iron screw in the upper part of the old shaft, and from the screw he lets down a cord as far as the first angle, where again he fixes a screw, and again lets down the cord as far as the second angle; this he repeats again and again until the cord reaches to the bottom of the shaft. Then to each angle of the cord he applies a hemicycle, and marks the waxed semi-circle according to the lines which the tongue indicates, and designates it by a number, in case it should be moved; then he measures the separate parts of the cord with another cord made of linden bark. Afterward, when he has come back out of the shaft, he goes away and transfers the markings from the waxed semi-circle of the hemicycle to an orbis similarly waxed. Lastly, the cords are stretched on the surveyor's field, and he measures the angles, as the system of measuring by triangles requires, and ascertains which part of the footwall and which part of the hangingwall rock must be cut away in order that the shaft may descend straight. But if the surveyor is required to show the owners of the mine, the spot in a drift or a tunnel in which a shaft needs to be raised from the bottom upward, that it should cut through more quickly, he begins measuring from the bottom of the drift or tunnel, at a point beyond the spot at which the bottom of the shaft will arrive, when it has been sunk. When he has measured the part of the drift or tunnel up to the first shaft which connects with an upper drift, he measures the incline of this shaft by applying a hemicycle or orbis to the cord. Then in a like manner he measures the upper drift and the incline shaft which is sunk therein toward which a raise is being dug, then again all the cords are stretched in the surveyor's field, the last cord in such a way that it reaches the first, and then he measures them. From this measurement is known in what part of the drift or tunnel the raise should be made, and how many fathoms of vein remain to be broken through in order that the shaft may be connected.

I have described the first reason for surveying; I will now describe another. When one vein comes near another, and their owners are different persons who have late come into possession, whether they drive a tunnel or a drift, or sink a shaft, they may encroach, or seem to encroach, without any lawful right, upon the boundaries of the older owners, for which reason the latter very often seek redress, or take legal proceedings. The surveyor either himself settles the dispute between the owners, or by his art gives evidence to the judges for making their decision, that one shall not encroach on the mine of the other. Thus, first of all he measures the mines of each party with a basket rope and cords of linden bark; and having applied to the cords an orbis or a compass, he notes the directions in which they extend. Then he stretches the cords on the surveyor's field; and starting from that point whose owners are in possession of the old meer toward the other, whether it is in the hanging or footwall of the vein, he stretches a cross-cord in a straight line, according to the sixth division of the compass, that is, at a right angle to the vein, for a distance of three and a half fathoms, and assigns to the older owners that which belongs to them. But if both ends of one vein are being dug out in two tunnels, or drifts from opposite directions, the surveyor first of all considers the lower tunnel or drift and afterward the upper one, and judges how much each of them has risen little by little. On each side strong men take in their hands a stretched cord and hold it so that there is no point where it is not strained tight; on each side the surveyor supports the cord with a rod half a fathom long, and stays the rod at the end with a short stick as often as he thinks it necessary. But some fasten cords to the rods to make them steadier. The surveyor attaches a suspended plummet level to the middle of the cord to enable him to calculate more accurately on both sides, and from this he ascertains whether one tunnel has risen more than another, or in like manner one drift more than another. Afterward he measures the incline of the shafts on both sides, so that he can estimate their position on each side. Then he easily sees how many fathoms remain in the space which must be broken through. But the grade of each tunnel, as I said, should rise one fathom in the distance of one hundred fathoms.

The Swiss surveyors, when they wish to measure tunnels driven into the highest mountains, also use a rod half a fathom long, but composed of three parts, which screw together, so that they may be shortened. They use a cord made of linden bark to which are fastened slips of paper showing the number of fathoms. They also employ an instrument peculiar to them, which has a needle; but in place of the waxed circles they carry in their hands a chart on which they inscribe the readings of the instrument. The instrument is placed on the back part of the rod so that the tongue, and the extended cord which runs through the three holes in the tongue, demonstrates the direction, and they note the number of fathoms. The tongue shows whether the cord inclines forward or backward. The tongue does not hang, as in the case of the suspended plummet level, but is fixed to the instrument in a half-lying position. They measure the tunnels for the purpose of knowing how many fathoms they have been increased in elevation; how many fathoms the lower is distant from the upper one; how many fathoms of interval is not yet pierced between the miners who on opposite sides are digging on the same vein, or cross-stringers, or two veins which are approaching one another.

But I return to our mines. If the surveyor desires to fix the boundaries of the meer within the tunnels or drifts, and mark to them with a sign cut in the rock, in the same way that the _Bergmeister_ has marked these boundaries above ground, he first of all ascertains, by measuring in the manner which I have explained above, which part of the tunnel or drift lies beneath the surface boundary mark, stretching the cords along the drifts to a point beyond that spot in the rock where he judges the mark should be cut. Then, after the same cords have been laid out on the surveyor's field, he starts from that upper cord at a point which shows the boundary mark, and stretches another cross-cord straight downward according to the sixth division of the compass--that is at a right angle. Then that part of the lowest cord which lies beyond the part to which the cross-cord runs being removed, it shows at what point the boundary mark should be cut into the rock of the tunnel or drift. The cutting is made in the presence of the two Jurors and the manager and the foreman of each mine. For as the _Bergmeister_ in the presence of these same persons sets the boundary stones on the surface, so the surveyor cuts in the rock a sign which for this reason is called the boundary rock. If he fixes the boundary mark of a meer in which a shaft has recently begun to be sunk on a vein, first of all he measures and notes the incline of that shaft by the compass or by another way with the applied cords; then he measures all the drifts up to that one in whose rock the boundary mark has to be cut. Of these drifts he measures each angle; then the cords, being laid out on the surveyor's field, in a similar way he stretches a cross-cord, as I said, and cuts the sign on the rock. But if the underground boundary rock has to be cut in a drift which lies beneath the first drift, the surveyor starts from the mark in the first drift, notes the different angles, one by one, takes his measurements, and in the lower drift stretches a cord beyond that place where he judges the mark ought to be cut; and then, as I said before, lays out the cords on the surveyor's field. Even if a vein runs differently in the lower drift from the upper one, in which the first boundary mark has been cut in the rock, still, in the lower drift the mark must be cut in the rock vertically beneath. For if he cuts the lower mark obliquely from the upper one some part of the possession of one mine is taken away to its detriment, and given to the other. Moreover, if it happens that the underground boundary mark requires to be cut in an angle, the surveyor, starting from that angle, measures one fathom toward the front of the mine and another fathom toward the back, and from these measurements forms a triangle, and dividing its middle by a cross-cord, makes his cutting for the boundary mark.

Lastly, the surveyor sometimes, in order to make more certain, finds the boundary of the meers in those places where many old boundary marks are cut in the rock. Then, starting from a stake fixed on the surface, he first of all measures to the nearest mine; then he measures one shaft after another; then he fixes a stake on the surveyors' field, and making a beginning from it stretches the same cords in the same way and measures them, and again fixes in the ground a stake which for him will signify the end of his measuring. Afterward he again measures underground from that spot at which he left off, as many shafts and drifts as he can remember. Then he returns to the surveyor's field, and starting again from the second stake, makes his measurements; and he does this as far as the drift in which the boundary mark must be cut in the rock. Finally, commencing from the stake first fixed in the ground, he stretches a cross-cord in a straight line to the last stake, and this shows the length of the lowest drift. The point where they touch, he judges to be the place where the underground boundary mark should be cut.

END OF BOOK V.

FOOTNOTES:

[1] It has been suggested that we should adopt throughout this volume the mechanical and mining terms used in English mines at Agricola's time. We believe, however, that but a little inquiry would illustrate the undesirability of this course as a whole. Where there is choice in modern miner's nomenclature between an old and a modern term, we have leaned toward age, if it be a term generally understood. But except where the subject described has itself become obsolete, we have revived no obsolete terms. In substantiation of this view, we append a few examples of terms which served the English miner well for centuries, some of which are still extant in some local communities, yet we believe they would carry as little meaning to the average reader as would the reproduction of the Latin terms coined by Agricola.

Rake = A perpendicular vein.
Woughs = Walls of the vein.
Shakes = Cracks in the walls.
Flookan = Gouge.
Bryle = Outcrop.
Hade = Incline or underlay of the vein.
Dawling = Impoverishment of the vein.
Rither = A "horse" in a vein.
Twitches = "Pinching" of a vein.
Slough = Drainage tunnel.
Sole = Lowest drift.
Stool = Face of a drift or stope.
Winds }
Turn } = Winze.
Dippas}
Grove = Shaft.
Dutins = Set of timber.
Stemple = Post or stull.
Laths = Lagging.

As examples of the author's coinage and adaptations of terms in this book we may cite:--

_Fossa latens_ = Drift.
_Fossa latens transversa_ = Crosscut.
_Tectum_ = Hangingwall.
_Fundamentum_ = Footwall.
_Tigna per intervalla posita_ = Wall plate.
_Arbores dissectae_ = Lagging.
_Formae_ = Hitches.

We have adopted the term "tunnel" for openings by way of outlet to the mine. The word in this narrow sense is as old as "adit," a term less expressive and not so generally used in the English-speaking mining world. We have for the same reason adopted the word "drift" instead of the term "level" so generally used in America, because that term always leads to confusion in discussion of mine surveys. We may mention, however, that the term "level" is a heritage from the Derbyshire mines, and is of an equally respectable age as "drift."

[2] See note on p. 46-47. The _canales_, as here used, were the openings in the earth, in which minerals were deposited.

[3] This statement, as will appear by the description later on, refers to the depth of winzes or to the distance between drifts, that is "the lift." We have not, however, been justified in using the term "winze," because some of these were openings to the surface. As showing the considerable depth of shafts in Agricola's time, we may quote the following from _Bermannus_ (p. 442): "The depths of our shafts forced us to invent hauling machines suitable for them. There are some of them larger and more ingenious than this one, for use in deep shafts, as, for instance, those in my native town of Geyer, but more especially at Schneeberg, where the shaft of the mine from which so much treasure was taken in our memory has reached the depth of about 200 fathoms (feet?), wherefore the necessity of this kind of machinery. _Naevius_: What an enormous depth! Have you reached the Inferno? _Bermannus_: Oh, at Kuttenberg there are shafts more than 500 fathoms (feet?) deep. _Naevius_: And not yet reached the Kingdom of Pluto?" It is impossible to accept these as fathoms, as this would in the last case represent 3,000 feet vertically. The expression used, however, for fathoms is _passus_, presumably the Roman measure equal to 58.1 inches.

[4] _Cavernos_. The Glossary gives _drusen_, our word _drusy_ having had this origin.

[5] _Purum_,--"pure." _Interpretatio_ gives the German as _gedigen_,--"native."

[6] _Rudis_,--"Crude." By this expression the author really means ores very rich in any designated metal. In many cases it serves to indicate the minerals of a given metal, as distinguished from the metal itself. Our system of mineralogy obviously does not afford an acceptable equivalent. Agricola (_De Nat. Foss._, p. 360) says: "I find it necessary to call each genus (of the metallic minerals) by the name of its own metal, and to this I add a word which differentiates it from the pure (_puro_) metal, whether the latter has been mined or smelted; so I speak of _rudis_ gold, silver, quicksilver, copper, tin, bismuth, lead, or iron. This is not because I am unaware that Varro called silver _rudis_ which had not yet been refined and stamped, but because a word which will distinguish the one from the other is not to be found."

[7] The reasons for retaining the Latin weights are given in the Appendix on Weights and Measures. A _centumpondium_ weighs 70.6 lbs. avoirdupois, an _uncia_ 412.2 Troy grains, therefore, this value is equal to 72 ounces 18 pennyweights per short ton.

[8] Agricola mentions many minerals in _De Re Metallica_, but without such description as would make possible a hazard at their identity. From his _De Natura Fossilium_, however, and from other mineralogies of the 16th Century, some can be fully identified and others surmised. While we consider it desirable to set out the probable composition of these minerals, on account of the space required, the reasons upon which our opinion has been based cannot be given in detail, as that would require extensive quotations. In a general way, we have throughout the text studiously evaded the use of modern mineralogical terms--unless the term used to-day is of Agricola's age--and have adopted either old English terms of pre-chemistry times or more loose terms used by common miners. Obviously modern mineralogic terms imply a precision of knowledge not existing at that period. It must not be assumed that the following is by any means a complete list of the minerals described by Agricola, but they include most of those referred to in this chapter. His system of mineralogy we have set out in note 4, p. 1, and it requires no further comment here. The grouping given below is simply for convenience and does not follow Agricola's method. Where possible, we tabulate in columns the Latin term used in _De Re Metallica_; the German equivalent given by the Author in either the _Interpretatio_ or the Glossary; our view of the probable modern equivalent based on investigation of his other works and other ancient mineralogies, and lastly the terms we have adopted in the text. The German spelling is that given in the original. As an indication of Agricola's position as a mineralogist, we mark with an asterisk the minerals which were first specifically described by him. We also give some notes on matters of importance bearing on the nomenclature used in _De Re Metallica_. Historical notes on the chief metals will be found elsewhere, generally with the discussion of smelting methods. We should not omit to express our indebtedness to Dana's great "System of Mineralogy," in the matter of correlation of many old and modern minerals.

GOLD MINERALS. Agricola apparently believed that there were various gold minerals, green, yellow, purple, black, etc. There is nothing, however, in his works that permits of any attempt to identify them, and his classification seems to rest on gangue colours.

SILVER MINERALS.

_Argentum purum in _Gedigen silber_ -- *Native silver
venis reperitur_

_Argentum rude_ _Gedigen silber -- _Rudis_ silver, or
ertz_ pure silver
minerals

_Argentum rude _Glas ertz_ Argentite *Silver glance
plumbei coloris_ (Ag_{2}S)

_Argentum rude _Rot gold ertz_ Pyrargyrite *Red silver
rubrum_ (Ag_{3}SbS_{3})

_Argentum rude _Durchsichtig Proustite *Ruby silver
rubrum rod gulden (Ag_{3}AsS_{3})
translucidum_ ertz_

_Argentum rude _Weis rod gulden -- White silver
album_ ertz: Dan es
ist frisch wie
offtmals rod
gulden ertz
pfleget zusein_

_Argentum rude _Gedigen Part Bromyrite Liver-coloured
jecoris leberfarbig (Ag Br) silver
colore_ ertz_

_Argentum rude _Gedigen -- Yellow silver
luteum_ geelertz_

_Argentum rude _Gedigen graw } { *Grey silver
cineraceum_ ertz_ } Part Cerargurite {
} (Ag Cl) (Horn {
_Argentum rude _Gedigen } Silver) Part { *Black silver
nigrum_ schwartz ertz_ } Stephanite {
} (Ag_{5}SbS_{4}) {
_Argentum rude _Gedigen braun } { *Purple silver
purpureum_ ertz_ } {

The last six may be in part also alteration products from all silver minerals.

The reasons for indefiniteness in determination usually lie in the failure of ancient authors to give sufficient or characteristic descriptions. In many cases Agricola is sufficiently definite as to assure certainty, as the following description of what we consider to be silver glance, from _De Natura Fossilium_ (p. 360), will indicate: "Lead-coloured _rudis_ silver is called by the Germans from the word glass (_glasertz_), not from lead. Indeed, it has the colour of the latter or of galena (_plumbago_), but not of glass, nor is it transparent like glass, which one might indeed expect had the name been correctly derived. This mineral is occasionally so like galena in colour, although it is darker, that one who is not experienced in minerals is unable to distinguish between the two at sight, but in substance they differ greatly from one another. Nature has made this kind of silver out of a little earth and much silver. Whereas galena consists of stone and lead containing some silver. But the distinction between them can be easily determined, for galena may be ground to powder in a mortar with a pestle, but this treatment flattens out this kind of _rudis_ silver. Also galena, when struck by a mallet or bitten or hacked with a knife, splits and breaks to pieces; whereas this silver is malleable under the hammer, may be dented by the teeth, and cut with a knife."

COPPER MINERALS.

_Aes purum _Gedigen kupfer_ Native copper Native copper
fossile_

_Aes rude _Kupferglas ertz_ Chalcocite *Copper glance
plumbei (Cu_{2}S)
coloris_

_Chalcitis_ _Rodt atrament_ A decomposed _Chalcitis_ (see
copper or notes on p. 573)
iron sulphide

_Pyrites aurei } _Geelkis oder { Part chalcopyrite Copper pyrites
colore_ } kupferkis_ { (Cu Fe S) part
} { bornite
_Pyrites aerosus_ } { (Cu_{3}FeS_{3})

_Caeruleum_ _Berglasur_ Azurite Azure

_Chrysocolla_ _Berggruen und { Part chrysocolla Chrysocolla (see
schifergruen_ { Part Malachite note 7, p. 560)

_Molochites_ _Molochit_ Malachite Malachite

_Lapis aerarius_ _Kupfer ertz_ -- Copper ore

_Aes caldarium } _Lebeter kupfer_ { When used for
rubrum fuscum_ } { an ore, is *Ruby copper ore
or } { probably
_Aes sui coloris_ } _Rotkupfer_ { cuprite

_Aes nigrum_ _Schwartz kupfer_ Probably CuO from *Black copper
oxidation of
other minerals

In addition to the above the Author uses the following, which were in the main artificial products:

_Aerugo_ _Gruenspan oder Verdigris Verdigris
Spanschgruen_

_Aes luteum_ _Gelfarkupfer_ } Impure blister { Unrefined copper
} copper { (see note 16,
} { p. 511)
_Aes caldarium_ _Lebeterkupfer_ } {

_Aeris flos_ _Kupferbraun_ } Cupric oxide { Copper flower
} scales {
} {
_Aeris squama_ _Kupferhammer- } { Copper scale (see
schlag_ } { note 9, p. 233)

_Atramentum _Blaw kupfer Chalcanthite Native blue
sutorium wasser_ vitriol (see
caeruleum_ or note on p. 572)
_chalcanthum_

Blue and green copper minerals were distinguished by all the ancient mineralogists. Theophrastus, Dioscorides, Pliny, etc., all give sufficient detail to identify their _cyanus_ and _caeruleum_ partly with modern azurite, and their _chrysocolla_ partly with the modern mineral of the same name. However, these terms were also used for vegetable pigments, as well as for the pigments made from the minerals. The Greek origin of _chrysocolla_ (_chrysos_, gold and _kolla_, solder) may be blamed with another and distinct line of confusion, in that this term has been applied to soldering materials, from Greek down to modern times, some of the ancient mineralogists even asserting that the copper mineral _chrysocolla_ was used for this purpose. Agricola uses _chrysocolla_ for borax, but is careful to state in every case (see note xx., p. x): "_Chrysocolla_ made from _nitrum_," or "_Chrysocolla_ which the Moors call Borax." Dioscorides and Pliny mention substances which were evidently copper sulphides, but no description occurs prior to Agricola that permits a hazard as to different species.

LEAD MINERALS.

_Plumbarius lapis_ _Glantz_ Galena Galena