The lake may have been chiefly filled by the Bahr Yûsuf and the flood waters inundating the Nile Valley, but, to fulfil the conditions of a six months’ flow-in and six months flow-out of the lake, under the new conditions supposed, and retaining a maximum lake-level of R.L. 22·50, the canal of supply would have to have its off-take from the Nile moved to a point about half-way between Beni Suef and Biba. Supposing the Bahr Yûsuf and the flood water of the Nile Valley filled this lake during the flood months and the Bahr Yûsuf ceased to flow with the end of the flood, the canal from between Beni Suef and Biba would have had to supply only about 10 million cubic metres a day to make good the loss by evaporation, if the lake-level was not to be allowed to fall below R.L. 22·50 till the return-flow to the Nile was required. But there is no reason to suppose this to have been a necessity. With a lowest level of 17·50 instead of 19·50, the problem of the lake as a relieving and supplementing reservoir to the Nile, with houses and cultivation above its highest levels, is much simplified, and a large margin is given between R.L. 20·50 and 22·50 for increasing the volumes given in my former calculations, to render the lake a more efficient safety-valve for excessive floods, and for moderating the fall of the Nile to low discharges by giving back to it a more abundant outflow. Accepting this view of the range of the lake-levels, we shall have to look upon the Magnûnah Canal and its branches as channels of return-flow to the Nile for the commencement of the period of outflow, which would afterwards cease to carry any discharge in summer, when the lake-level had fallen below about R.L. 19·00. For the remaining period of outflow the Kosheshah Escape branch from Abûsir-el-Malaq to the Nile and the branch to Memphis skirting the Libyan Hills, would have carried all the discharge returning to the Nile Valley. The peculiar isolated piece of Nile desert opposite Lahûn and the cultivated strip of land between it and the main desert, through which the Bahr Yûsuf flows into the Fayûm, seems to lend itself to the regulation of the entry and exit of the Nile waters. To control the entry of the waters a regulator A and cross bank _a b_ from the island desert across the Bahr Yûsuf to the main desert on the west could have been made. (See map, Plate XXI.) The excess water, excluded from the lake by regulation on A, would have found its way along the east of the patch of desert as it does to-day.