144 BOOK V. 
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 demon- 
strates 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 
