Solutions

The solution to (1) was two-fold: first the line of the tunnel had to be mapped over the surface of the hill, and then subsequently projected or extrapolated underground. Mapping and marking a straight line was done by setting up posts covering the 1,500m distance over the hill-top; the straightness of the line is maintained by positioning each new post exactly on the line projected by the align ment of the previous two. Beginning at the top of the hill, from which both the area of the spring and the general position of the city can be seen, it was not difficult to de fine this straight line: but projecting it underground was more complex. How was this done?

   If the mouth of the tunnel is taken as one point of reference, then at least one other clearly visible, external point of reference is needed, which can be perfectly aligned with the aperture from inside, as the tunnel progresses deeper, so as to maintain the correct and constant line of the tunnel. This second external point of reference must also be in absolute alignment with the posts which define the trajectory over the hilltop. This is relatively easy to do on flat land; but, in this case, the terrain drops steeply away at both ends of the tunnel. At the north end, a mark er could at least be fixed on the facing slope of the hillside visible across the valley; but at the south (city) end, this was not possible: the land simply dropped towards the sea on this side. So a shaft had to be dug straight down from one of the posts on the surface of the hill to the tunnel below, so as to provide a second point of reference within the tunnel. A beam of wood, hung on two ropes down the shaft from a similar beam perfectly aligned with the posts on the surface, provided a further, more exact point of reference for direction: so long as this hanging beam was aligned with a marker in the aperture of the tunnel, the workmen knew, as they looked back from their cutting face, that their direction of trajectory corresponded to the line of posts on the surface. It appears, in fact, that two such shafts were dug, perhaps for added verification.

   If both the groups that were digging were now ready to follow exactly the predetermined alignment on the surface, they would in theory meet—so long as they had begun at exactly the same level—problem (2)—and had continued to dig exactly horizontally. To ensure the same height above sea-level for the point of departure on opposite sides of the mountain, a series of posts was again necessary, this time following the contour of the hill from one side to the other, a distance of about 1,900–2,000m. The posts needed to be in the form of a ‘T’, with the bar at 90Β° to the vertical which was set into the ground and verified with a plumb line. The first two or three had to be checked by a water-level; thereafter, each new post had to be exactly at the height of the visual plane defined by the tops of the previous two. The rough nature of the terrain required that this operation had to be repeated hundreds of times. This meant that the compound margin for er ror was immense. Nothing other than stringent, almost superhuman, meticulousness on the part of the engineer can account for the fact that the difference in level between the two tunnel entrances, over such a distance, is actually no more than 4cm—equivalent to an error of about 1 part in 50,000.

   Beginning now to dig into the mountain at the two respective intersections of these two lines of posts—the horizontal and the vertical—guaranteed convergence if an absolute horizontality of cutting and straightness of direction were maintained (3). These were the least difficult requirements to fulfill. So long as, respectively, the exter nal marker on the hillside across the valley from the north entry, and the hanging beam(s) down the shaft(s) inside the south entry, were perfectly aligned with the marker visible against the daylight of each entrance, then each trajectory was running straight along the same imaginary line. To maintain horizontality, standing water or a water level (the ‘chorobates’) could possibly have been used, or, more likely, a type of hanging sighting-tube which was used in Mesopotamia, and consisted of a hollow copper pipe, about 40cm long, suspended horizontally, through which a sighting can be taken of a fixed marker to ensure equivalent level. A gentle gradient would eventually be required for the water; but Eupalinos had to construct the tunnel on a perfect horizontal. To cut it on a gradient ran the risk of the tunnel flooding and becoming unworkable, if a seam of flowing water were accidentally to be encountered during the digging.

   The last, and unpredictable, kind of problem (4) which he faced—areas of unstable rock, which threatened col lapse—does appear to have been encountered by Eupalinos, some way in from the north entrance. It was so bad that it forced him to deviate from a straight line in search of a more stable area to cut through. This had serious consequences for him, because it inevitably meant that the sightline from the cutting-face to the daylight at the entrance was lost for good, as soon as he deviated. There after, he was literally and metaphorically working in the dark. In correcting his initial deviation, once good rock was again found, he appears to have overcompensated and lost the correct alignment. There was always a risk that the two troops would miss and continue oblivious of one another; now the risk was even greater. To ensure that this did not happen, he devised a simple solution: the trajectory of both campaigns was turned slightly to the same (east) side, so that if the level of each tunnel re ally were identical, sooner or later they had to cross one another’s path; which they did. It is this manoeuvre that accounts for the irregularity of line in the middle of the tunnel. A passage was now open right through the heart of the mountain.

Samos Island is part of the Northern Aegean Island Group, Greece.

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