For one day, sixteen miles and a half; for seventeen to twenty-five days, fifteen miles; for forty to fifty days, thirteen miles. These numbers are particularly selected, because they occurred in the course of the Work. The Reader will be pleased to observe, that the miles spoken of in the construction, are always those of sixty to a degree of a great circle. However tedious this investigation may appear to the generality of readers, it is absolutely necessary; as it is the hinge upon which the whole turns: and a neglect of attention to this particular subject, would warrant the Reader’s taking the whole for granted, without further examination. Mr. BEAUFOY having given, from the materials in his possession, so full an account of each road and country, nothing remains for me to do, but simply to describe, from the same materials, the mode of fixing the principal positions, in the Map. As the object of it is to exhibit the new matter only, care has been taken to exclude all that has already appeared, except what was absolutely necessary towards explaining the other: and as the borrowed particulars are distinguished from the rest, the Reader cannot be mistaken. The outline of the great body of Africa, together with the courses of the Nile, Gambia, Senegal, and Wad-drah, are copied from Mr. D’Anville. Fezzan (or rather its capital, Mourzouk) is given in the Itineraries at the distance of seventeen days and half from Mesurata. These, taken at fifteen miles per day, produce two hundred and sixty-two miles. The bearing is said to be South from Mourzouk; and this latter is placed according to D’Anville. Mourzouk, then, falls in latitude 27° 20′. Agadez, the next principal station, is, at a medium forty-one days from Mourzouk, on a South West course, or thereabouts: and these, at thirteen miles per day, produce four hundred and fifty-five miles; and place Agadez in latitude 20° 20′; and nearly in the meridian of Tripoli. Agadez is the Agadost of Edrisi. From Agadez to Cashna is seventeen days; which, at fifteen miles per day, give a distance of two hundred and fifty-five miles. The bearing is said to be South South West. Cashna, then, will stand in or about the latitude of 16° 20′ North, and about a degree and half West from Tripoli. D’Anville’s _Casseenah_ (undoubtedly meant for Cashna) is placed about thirty-seven miles to the North West of the position assumed in the accompanying Map; whence I consider mine as a near approximation, especially as the distance from Mesurata is upwards of nine hundred and seventy miles. Cashna may be regarded as the central kingdom of the great body of Africa; and as a part of the region named SOUDAN, of which at present but few particulars are known.