I will briefly state the order, and reasons for the order, in which I have arranged the different parts into which this paper is divided. I have described the “Fayûm of To-day” first, as a conception of its condition in the past must of necessity be founded on a knowledge of its condition in the present. Next I give the statements made by the ancient travellers, as it is upon them that the ideas, of what Lake Mœris was, are based. I then proceed to try and dispose of theories which I consider erroneous, so as to clear the way for a more correct view; or at least to expose some of the errors of statement which might mislead others into accepting or forming wrong notions on the subject. Next I give the views that I have adopted, and point out what support they have from others, and discuss M. Linant’s objections to the views favoured. Then I have endeavoured to sketch the history of the Fayûm— (1) Before it became Lake Mœris. (2) As Lake Mœris. (3) While it was undergoing the process of being transformed from Lake Mœris to what it is to-day. And lastly, I have added a few remarks about the possible future of the Wadi Raiân, and the effect upon the Fayûm of a more abundant supply of water in consequence of the construction of storage reservoirs now under consideration. I have made use of all previous writings on the subject that I could lay hands on. Mr. Cope Whitehouse kindly lent me his papers and showed me where to get others. Mr. Flinders Petrie has also given me what information I applied to him for. The maps and levelling of the Fayûm, made under the direction of Lieut.-Col. J. C. Ross, C.M.G., late Inspector-General of Irrigation in Egypt, have naturally been invaluable aids to the study of the subject. Sir Colin Scott-Moncrieff, late Under-Secretary of State for Public Works, Egypt, has also given me his views on some points raised in this paper, and I have taken advantage of them. Miss M. Brodrick has most kindly assisted me in the correction of the proofs, and in other matters connected with the publication of this paper. Ali Bey Borhan, Chief Engineer of the Fayûm, and Monsieur A. Pini, in charge of works, have assisted me by collecting information and obtaining levels that were wanting. Finally, I wish to lay claim to no originality in the views adopted. What I have aimed at in this paper is to work those views out, and to go more thoroughly into them than has hitherto been done, thereby making a contribution to the discussion of an unsolved problem, interesting alike to Engineers, Archæologists, and Classical Scholars. As the metrical system is in use in Egypt, all dimensions and quantities are given throughout this paper in metres and cubic metres, and distances in kilometres. 1 metre = 3·2809 feet. 1 square metre = 10·7643 square feet. 1 cubic metre = 35·3166 cubic feet. = 220·097 gallons. 8 kilometres = 5 miles (approximately).