The problems, though they concern a variety of subjects, are very much interwoven with each other, and they are mostly alike in that the first difficulty in any attempt to solve them has always been the incompleteness of our geographical knowledge concerning the Libyan Desert as a whole. If we possessed a series of detailed contour-maps covering the whole of the desert, most of the problems would be in a fair way of solution. But the surveys which would be necessary for such a result are impracticable at present, mainly on the score of expense. Some fifteen years ago I essayed the construction of a contoured map of the Libyan Desert, in connection with the International “Million” map of the world. But I had to give up the task, finding that there were vast areas without a single observation for altitude, while such altitude- data as did exist were open to errors of a magnitude intolerable for even a preliminary contouring of the areas with which they were concerned. The attempt however was not without its value, because it drew attention to the great lack of reliable levels in the Libyan Desert, and to the necessity of remedying this defect before even an approximately true picture of the general relief could be obtained. In the interval which has elapsed since my former attempt, a great deal of surveying has been carried out in the Libyan Desert, and in most of this work special attention has been paid to the matter of levels. Two long chains of triangulation have been run westward from the Nile to Siwa Oasis, one _viâ_ the Wadi Natrun and the other _viâ_ Baharia Oasis; another chain has been completed along the coast westward from Alexandria to Sollum, and a triangulation is now being carried out which will eventually connect the oases of Kharga and Dakhla with the Nile Valley. Small local triangulations have also been made in certain areas, such as Dakhla Oasis and in the neighbourhood of Owenat. In all these triangulations vertical as well as horizontal angles have been observed, so that reliable trigonometric altitudes are now available for almost all the points occupied or sighted. In the southern and central parts of the desert, we are still dependent on barometric levels; but the old determinations have mostly been replaced by later and better ones; and the use of motor-car transport, by facilitating exploratory journeys in hitherto untrodden regions, has permitted of a large number of additional determinations being made in tracts where no previous observations of any kind existed.[1]