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144 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