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
