Surveying Triangle
Stretched cords: A—First cord. B—Second cord. C—Third cord. D—Triangle. [Pg 139] 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.

Surveying Triangles
Stretched cords: A—First. B—Second. B—Third. C—Fourth. C—Fifth. D—Quadrangle. [Pg 140] 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.

Compass
Compass. A, B, C, D, E, F, G are the seven waxed circles. [Pg 142] Orbis
A, B, C, D, E—Five waxed circles of the orbis. F—Opening of same. G—Screw. H—Perforated iron. [Pg 142A] Miner using level
A—Standing plummet level. B—Tongue. C—Level and tongue. [Pg 143] 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. Plummet cord and weight
Indicator of a suspended plummet level. [Pg 146] 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. Compass
A—Needle of the instrument. B—Its tongue. C, D, E—Holes in the tongue. [Pg 147] 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.