=Base-Lines=—The triangulation was commenced by measuring a base line[62] near Gebel Muelih by means of a 100-metre steel tape, which had been previously standardised at the Khedivial Observatory. A level tract having been selected, in such a position as to afford easy connection with points already triangulated from the Nile Valley, a line about two and a half kilometres long was ranged out, along which wooden pegs were driven flush with the ground at 100-metre intervals. The inequalities of the ground between the pegs were levelled off by tiny embankments and cuttings, so as to enable the tape to lie flat. On each peg was nailed a zinc plate having a millimetre scale running in the direction of the line. In measuring, the tape was laid on the ground, stretched to a constant tension by a spring balance at each end, in such manner that its end marks fell on the zinc scales, and readings were simultaneously taken on the scales at the two ends. Temperatures were taken in several places along the tape by mercurial thermometers. The operation of measurement was carried out in the early morning, so as to avoid any large difference of temperature between the ground and the air. The levels of the pegs were found by spirit levelling. After correction for the initial error of the tape, temperature, stretch, and inclination, the true length of the base-line reduced to sea-level was found, as the mean of two separate measurements at different tensions, to be 2,482·280 metres. The azimuth of the line was found by observations of _Polaris_ at elongation to be 30° 30′ 6″ E. of N. The geographical position of the west end of the line was found by triangulation-connexion with the Nile Valley by Mr. Villiers Stuart to be latitude 24° 53′ 36″·7 N., longitude 34° 4′ 17″·9 E. A second connexion to a base-line was made near Gebel Um Harba, where a base had been previously measured by Mr. Villiers Stuart in the course of his triangulation of the western part of the desert. In this case the connexion was not made to the actual base-line, but to another main line tied directly on to it. The data at this point of connexion from the two triangulations afforded a useful check on the accuracy of the work, and were as follows:— ------------------+------------------+----------------+------------ |From Mr. Stuart’s | From my |Difference. | triangulation. | triangulation. | +------------------+----------------+------------ Latitude N. | 23° 36′ 55″·0 | 23° 36′ 55″·6 | 0″·6 | | | Longitude E. | 34° 30′ 38″·1 | 34° 30′ 37″·6 | 0″·5 | | | Length of line | | | to Dagalai beacon| 13,170·2 metres. |13,167·9 metres.|2·3 metres. ------------------+------------------+----------------+------------