Francesca Tronchin and I have been virtually shaking our heads at an item in the Guardian which includes a headlinish sort of thing:
The Romans built a 50km aqueduct from Uzès to Nîmes in France with an overall fall of about 17 metres and an average gradient of 1/3000. How did they determine the fall, and maintain the gradient during building?
In one word, the answer is probably . . . bamboo! A length of bamboo about 10-20cm diameter would make an accurate, jumbo-sized spirit level-come-theodolite.
Half-filled with water, it could be laid horizontally on trestles and used to lay out a levelling survey, all the way from Uzès to Nîmes. Using it like a telescope, they could use little buoys floating in the water at each end to sight a point a short way off. Stakes hammered into the ground would record the level at a given point, before the bamboo is moved to sight the next section.
Before doing this, the Romans would have had no way of knowing whether the planned route would be uphill or downhill. A team would have set out from both Uzès and Nîmes, each using a bamboo tube to sight a reasonably accurate contour along the sides of the valleys. When the teams met up they would see the elevation difference. Then the operation would be repeated, this time allowing a gradient deduced from the horizontal distance and the fall.
During the surveys the Romans would have spotted that an aqueduct at Pont du Gard would save a long detour. They knew the earth was a sphere, so the levelling operation (similar to those of the canal “navvies” in England during the 18th century) would need a correction to allow for the curvature of the earth to prevent the levelling measurement climbing slightly in both directions.
… first of all, bamboo didn’t exist in Europe at the time (tip o’ the pileus to FT for confirming that from her own research into exotic building materials and the referenceable item in Wikipedia). Second of all, the Roman surveyors (gromatici) actually had an instrument for such situations called a chorobates which Vitruvius describes in 8.5 of his de Architectura (via Lacus Curtius):
1. I shall now describe how water is to be conveyed to houses and cities, for which purpose levelling is necessary. This is performed either with the dioptra, the level (libra aquaria), or the chorobates. The latter instrument is however the best, inasmuch as the dioptra and level are often found to be incorrect. The chorobates is a rod about twenty feet in length, having two legs at its extremities of equal length and dimensions, and fastened to the ends of the rod at right angles with it; between the rod and the legs are cross pieces fastened with tenons, whereon vertical lines are correctly marked, through which correspondent plumb lines hang down from the rod. When the rod is set, these will coincide with the lines marked, and shew that the instrument stands level.
2. But if the wind obstructs the operation, and the lines are put in motion, so that one cannot judge by them, let a channel be cut on top of the rod five feet long, one inch wide, and half an inch high, and let water be poured into it; if the water touches each extremity of the channel equally, it is known to be level. When the chorobates is thus adjusted level, the declivity may be ascertained.
3. Perhaps some one who may have read the works of Archimedes will say that a true level cannot be obtained by means of water, because that author says, that water is not level, but takes the form of a spheroid, whose centre is the same as that of the earth.e Whether the water have a plane or spheroidal surface, the two ends of the channel on the rod right and left, when the rod is level, will nevertheless sustain an equal height of water. If it be inclined towards one side, that end which is highest will not suffer the water to reach to the edge of the channel on the rule. Hence it follows, that though water poured in may have a swelling and curve in the middle, yet its extremities to the right and left will be level. The figure of the chorobates will be given at the end of the book. If there be much fall, the water will be easily conducted, but if there be intervals of uneven ground, use must be made of substructions.