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Rh mass of the mountains in order that the owners may lay out their plans, and that their workmen may not encroach on other people's possessions. The surveyor either measures the interval not yet wholly dug through, which lies between the mouth of a tunnel and a shaft to be sunk to that depth, or between the mouth of a shaft and the tunnel to be driven to that spot which lies under the shaft, or between both, if the tunnel is neither so long as to reach to the shaft, nor the shaft so deep as to reach to the tunnel; and thus on both sides work is still to be done. Or in some cases, within the tunnels and drifts, are to be fixed the boundaries of the meers, just as the Bergmeister has determined the boundaries of the same meers above ground. The history of surveying and surveying instruments, and in a subsidiary way their application to mine work, is a subject upon which there exists a most extensive literature. However, that portion of such history which relates to the period prior to Agricola represents a much less proportion of the whole than do the citations to this chapter in De Re Metallica, which is the first comprehensive discussion of the mining application. The history of such instruments is too extensive to be entered upon in a footnote, but there are some fundamental considerations which, if they had been present in the minds of historical students of this subject, would have considerably abridged the literature on it. First, there can be no doubt that measuring cords or rods and boundary stones existed almost from the first division of land. There is, therefore, no need to try to discover their origins. Second, the history of surveying and surveying instruments really begins with the invention of instruments for taking levels, or for the determination of angles with a view to geometrical calculation. The meagre facts bearing upon this subject do not warrant the endless expansion they have received by argument as to what was probable, in order to accomplish assumed methods of construction among the Ancients. For instance, the argument that in carrying the Grand Canal over watersheds with necessary reservoir supply, the Chinese must have had accurate levelling and surveying instruments before the Christian Era, and must have conceived in advance a completed work, does not hold water when any investigation will demonstrate that the canal grew by slow accretion from the lateral river systems, until it joined almost by accident. Much the same may be said about the preconception of engineering results in several other ancient works. There can be no certainty as to who first invented instruments of the order mentioned above; for instance, the invention of the dioptra has been ascribed to Hero, vide his work on the Dioptra. He has been assumed to have lived in the 1st or 2nd Century B.C. Recent investigations, however, have shown that he lived about 100 (, Encyc. Brit, 11th Ed.,, 378). As this instrument is mentioned by Vitruvius (50 – 0 B.C.) the myth that Hero was the inventor must also disappear. Incidentally Vitruvius (, 5) describes a levelling instrument called a chorobates, which was a frame levelled either by a groove of water or by plumb strings. Be the inventor of the dioptra who he may, Hero's work on that subject contains the first suggestion of mine surveys in the problems, where geometrical methods are elucidated for determining the depths required for the connection of shafts and tunnels. On the compass we give further notes on p. . It was probably an evolution of the 13th Century. As to the application of angle- and level-determining instruments to underground surveys, so far as we know there is no reference prior to Agricola, except that of Hero. Mr. Bennett Brough (Cantor Lecture, London, 1892) points out that the Nützliche Bergbüchlin (see Appendix) describes a mine compass, but there is not the slightest reference to its use for anything but surface direction of veins. Although map-making of a primitive sort requires no instruments, except legs, the oldest map in the world possesses unusual interest because it happens to be a map of a mining region. This well-known Turin papyrus dates from Seti I. (about 1300 B.C.), and it represents certain gold mines between the Nile and the Red Sea. The best discussion is by Chabas (Inscriptions des Mines d'Or, Chalons-sur-Saone, Paris, 1862, p. 30–36). Fragments of another papyrus, in the Turin Museum, are considered by Lieblein (Deux Papyras Hiératiques, Christiania, 1868) also to represent a mine of the time of Rameses I. If so, this one dates from about 1400 B.C. As to an actual map of underground workings (disregarding illustrations) we know of none until after Agricola's time. At his time maps were not made, as will be gathered from the text.

Each method of surveying depends on the measuring of triangles. A small triangle should be laid out, and from it calculations must be made regarding a larger one. Most particular care must be taken that we do not deviate at all from a correct measuring; for if, at the beginning, we are drawn