derived from underground sources in the same rock—namely, the Nubian sandstone, which covers such vast areas in the Sudan and Egypt. I had thus four well-determined natural water-levels at the corners of a great quadrilateral whose sides averaged over 500 kilometres in length, and embraced more than 20 square degrees of the Earth’s surface. Now just as in solid geometry the levels of any three points determine the inclination of an oblique plane to the horizontal, so on the Earth any three levels will determine the inclination of a surface to the geoid (of course assuming both geoid and surface to have the same curvature). And on making the calculation, I found that I obtained practically the same degree and direction of inclination for the natural water-surface, whichever three of the four known points I utilized for the calculation. In other words, I found that if I took, say, the levels of Kufra, Abu Mungar, and Sheb, and deduced from them the inclination of the water- surface to the horizontal, I could _calculate_ the level of Merga pretty exactly. Extending the trial, I found that I could do the same with a fairly close approximation for the other wells in the Sheb neighbourhood, and also for wells in the oases of Dakhla and Kharga. The conclusion seemed irresistible that all the wells considered were fed from a continuous sheet of underground water; and it was evident that this water did not come from the Nile, firstly because of the high level of Merga, which is above that of the swamps of the Bahr el Ghazal and other western feeders of the White Nile, and secondly because of the direction of the downward slope of the underground static water-surface, which is from the south-west, instead of from the south as it would have been had the water been derived from the Nile in the Bahr el Ghazal region. The true source of the water must be somewhere more or less nearly on a line drawn south-west from Dakhla, for this is the direction of upward slope of the underground static water-surface; and if such a line be drawn on a map of Africa, it will be found to lead towards the Erdi and Ennedi region, on the borders of the Chad basin. It is in the highlands of Eastern Erdi and Ennedi, therefore, that we must look for the source of the artesian water of the Egyptian oases. What is known of this region from the recent explorations of Colonel Tilho lends good support to our conclusion.[17] It is a bare and rugged sandstone country, where, in spite of a rainfall which is by no means negligible, permanent water-sources are scanty, and where, in consequence, there must be a considerable absorption of moisture by the rocks; and it lies at so high an altitude as to give sufficient “head” for the absorbed water to percolate through the porous sandstones and thus to reach Egypt.