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.[1]
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Stretched cords: A—first cord. B—second cord. C—third cord. D—triangle.
- ↑ It is interesting to note that the ratio of any length so obtained, to the whole length of the staff, is practically equal to the cosine of the angle represented by the corresponding gradation on the hemicycle; the gradations on the rod forming a fairly accurate table of cosines.
