How did the Romans work out the slope/gradient of their aqueducts?
Many writers declare themselves to be baffled at how the Romans could build aqueducts with very gradual slopes. The aqueduct that goes from Uzes to Nimes over the Pont du Gard has a difference in height from start to finish of about 10m. Yet the length is 15km. That is a slope of less than 1 in 1000.
The Romans did have a device, the chorobates, that could set a level surface. It was a table with a slot in it that was filled with water in it. But this would not have been accurate enough to layout an aqueduct with such a small slope. The problem with this is that even if the accuracy was one part in 10,000, each reading would introduce an error. Since the range over which it could manage this error would be far smaller than the length of the aqueduct the number of readings would be so large that the sum of the errors could make the results useless.
The problem would seem to be that there is an assumption that until one can survey the path of the aqueduct one cannot make it. But this has to be wrong.
The solution to this problem is to use the aqueduct itself to set the slope of the aqueduct.
Before the building starts there is one survey that is needed. It is to determine that the height of the source of the water is sufficiently above the point where the water will be delivered to make it worth starting the aqueduct. This does not have to be very accurate.
Suppose we are confident that the difference in height is, allowing for errors, sufficient. Then we can start building the aqueduct. It will be seen, from the method proposed, that we have to start at the source end. We can build further away but only to a limited height because we are not sure what the final height will be at any other points – yet..
The way it is done is that a length, say, about 1km, is built at the level of the source. The bottom of the trough is nominally flat. This length It is blocked off at its “lower” end, ie at “A” and is allowed to fill with water. It does not have to be filled to its full working depth but enough to clearly cover the bottom of it.
The long line here represents the bottom of the trough of the aqueduct.
At this stage two depth markers are fitted to mark the level of the water, ie, markers w and x.
A new block is fitted at “B”. The depth markers “W” and “X” are untouched.
Meanwhile the next kilometre of aqueduct has been built to the same height less about 10mm. This is blocked off at the low end at “C”. The block, “A”, at the low end of the first kilometre is removed. A new depth marker, “Y” is fitted near marker “X” but about 10mm lower.
Water is allowed to fill the second kilometre. This time though it is only allowed to fill to, say, 10mm below the level before. A depth marker, “Z” is fitted to the lower end of the second kilometre at the new depth, ie 10mm below the depth at the low end of the last kilometre.
This is repeated till the far end of the aqueduct has been built.
This method will have not problems with an aqueduct that follows a very irregular path.
In practice it would seem likely that many more depth markers would be used so the bottom of each 1km section would be flat.
The height when the aqueduct reaches it destination is unpredictable. But any height above the minimum required can be seen to be a bonus.