The observed azimuths, unlike the observed latitudes, were more accurate than the results of triangulation, repetition having shown them to be reliable within 2″ or 3″, an error of which magnitude would soon be surpassed in the process of continuing a chain of azimuths with the unadjusted values of the angles of the triangles, which were the only values possible to be used in the field. On arriving at an azimuth station, therefore, a fresh chain of azimuths was begun from the results of the observation, and continued to the next station where astronomical observations were undertaken. The accumulated azimuth error was, however, never found to exceed 10″ in any chain, a quantity which could not sensibly affect the computed positions of points for plotting on the maps. =Connexion with the Sudan Surveys.=—At the south end of the area, connexion was made to a number of points triangulated by the Sudan Surveys, but as the Sudan triangulation was commenced as an independent piece of work from an observed latitude and a telegraphically determined longitude, the connexion affords no check on the accuracy of the triangulations. The difference found between my positions and those of the Sudan Surveys was practically constant for all the Sudan points connected, and amounted to 3″·5 in latitude and 26″ in longitude[70]; these figures represent the errors in the assumed latitude and longitude of the starting point of the Sudan Surveys, and will be employed as corrections to the Sudan positions now that a complete chain of triangulation connects Berber with the Mediterranean.