Such an increase of the summer supply would probably have the effect of doubling the area under summer crops in the Delta, if it could be obtained now, but it is not clear how it could have been utilised without a barrage to raise the water-level, and without, as far as we know, any Sêfi (summer) canals.

It is not, however, imagined that in the days of Lake Mœris there was any such scientifically economical control of the Nile waters, as supposed in the foregoing calculations, but they are given to show what the possibilities of a lake under the conditions assumed would be. My aim has been to establish its utility, in answer to Linant’s argument against the developed Lake Qurûn theory, which consisted in a demonstration that this lake could have served no useful purpose, such as the historians credited it with.

Possibly the needs of navigation were a more important consideration in those days than summer irrigation, though not given the first place now. An increased volume supplied at low water to the shallowing water-routes would even for this object have been a gain.

The disappearance of all trace of the regulators is felt by some to be a difficulty in the way of the admission of their former existence, inasmuch as the ancients built on such a colossal scale. But the Labyrinth, which was built out of the reach of water, has disappeared, and its traces were only of late years identified in a mass of stone chips and trenches filled with sand, which underlay the foundations. Such being the fate of the Labyrinth, which must have surpassed the regulators as a structure of colossal dimensions, it is only natural to suppose that the stones forming the superstructure of the regulators should also have been removed for the same objects as the stones of the Labyrinth, and, if the materials of the floors were spared, it would only be on account of their situation being unfavourable to their removal. But, if spared, the action of running water would in time cause their disappearance, either by undermining them and burying them to depths below their original position, or by depositing a layer of mud above them. In the latter case they may still exist in a situation where some future excavation may chance to bring them to light again.

Hence I hold that, in the face of Strabo’s explicit statement that there were regulators at each end of the canal for controlling the inflow and outflow of the lake, the objection of want of evidence of the former existence of regulators is not sufficiently strong to be allowed to have much weight against the theory, that the submerged Fayûm, with the entry and exit of its waters kept under control by regulators, and its water-levels ranging between R.L. 22·50 and 19·50, was the Lake Mœris of Herodotus; the Arsinoïte Nome, in connection with it, consisting of the reclaimed high lands within the limits of the lake and along the borders of the lake itself and margins of the feeder canal. It is admitted, as a weak point in this theory, that unless the Arsinoïte Nome can be imagined as extending into the Nile Valley, the area of cultivable land comprised in the nome is very limited. Let us see how far such a conception of Lake Mœris is in accord with the testimony of the ancient records which relate to it.

Strabo remarks, that “the Lake Mœris, by its magnitude and depth, is able to receive the superabundance of water which flows into it at the time of the rise of the river, without overflowing the inhabited and cultivated parts of the province.” This could not be made to accord with M. Linant’s theory, and can only be understood by supposing that the high lands in the Fayûm were reclaimed, and that the flood waters filled the rest of the Fayûm without rising so high as to inundate them. At the same time the area of the lake must have been great to fit it, under this limitation, to receive a sufficient volume to moderate the Nile floods and to be able to return to the Nile a sufficiently large supply to supplement the low Nile discharge in an efficient manner. The figures representing the possible performances of the lake have been given.

Diodorus also says, “Accordingly the king dug a canal from the Nile to the basin 10 miles in length and 300 feet in breadth.” This would seem to show that the canal took off from the Nile immediately opposite Lahûn, for, if its mouth had been carried further south up the Nile, its length would have exceeded 10 miles. The breadth of 300 feet equals 91½ metres. This also agrees with the size of the inflow and outflow canals which would have been necessary to discharge the calculated volumes.

A canal with bed width 90 metres, depth 8 metres, and water surface slope ¹⁄₂₀₀₀₀, will discharge about 69½ million cubic metres per 24 hours, which agrees with the calculation for the inflow.

A canal with bed width of 90 metres, depth 6½ metres, and water surface slope of ¹⁄₂₅₀₀₀, would discharge 34 million cubic metres per 24 hours, which agrees with the calculations for the outflow.

Diodorus remarks also that “a little south of Memphis a canal was cut for a lake, brought down in length from the city 40 miles.” This is somewhat obscure, but may mean that a canal 40 miles in length was dug to connect Memphis with the lake. Supposing the canal that fed the lake from the Nile passed Abûsir-el-Malaq as already described, the canal to connect the lake and Memphis would have taken off from the feeder canal at or near Abûsir-el-Malaq. The distance from that point to the modern Bedreshên, the station at which tourists alight for viewing the ruins of Memphis, is 47 miles, and it is quite possible that what was known as Memphis extended several miles to the south, and that the canal was only 40 miles in length between Abûsir-el-Malaq and Memphis.