The _Belgica_ had the advantage of navigating a region in which no previous bathymetric researches had been made, and her soundings have a special value (although their actual number was not great) because they were not taken at random. On the voyage from Staten Island to the South Shetlands, a line of soundings was run nearly from north to south, giving a transverse section of the “antarctic channel” which separates the Andes from one of the projecting angles of Murray’s hypothetical antarctic continent. In another place also, beyond the antarctic circle, and to the west of Alexander I. Land, we were able to obtain a series of soundings, some before entering the ice, the others on account of the drift of the vessel when imprisoned in the pack. The soundings on our way southward are given in the Table as Nos. 1–9, and those taken between 70° and 107° west as Nos. 10–56, while the results are represented chartographically in the two maps. [Illustration: SOUNDINGS IN THE PACK (Soundings in fathoms)] The first map shows the probable arrangement of the depths to the south of Cape Horn and in the antarctic regions. Soundings Nos. 1, 2, and 3 prove that south of Staten Island the continental shelf is very narrow, and terminates seaward in an abrupt slope, the greatest depth sounded (2209 fathoms) lying, in fact, very near the island. To the east, on the contrary, the continental shelf extends to a great distance as Burdwood Bank. Between the southern versant of the Andes and the mountain system forming the framework of the antarctic lands visited by the expedition, there lies a deep, flat-bottomed depression, the floor of which rises gently towards the south, and not far from the South Shetlands an abrupt slope leads up to the rocky shallows near Livingstone Island. The last sounding taken gave a depth of 2625 fathoms in 56° 28′ south and 84° 46′ west, proving that the depth increases towards the Pacific Ocean. As, on the contrary, the Sandwich group, South Georgia, and Shag Rocks lie to the east, it seems probable that this great basin (called Barker Basin on the chart in the _Challenger_ Reports) does not extend to the east of these islands. In a note on the interest which attaches to the geological exploration of the lands in the far south, which I published in December, 1895,[3] I suggested that “Grahamland is connected with Patagonia by a submarine ridge, which forms a great arc extending between Cape Horn and the South Shetland Islands, and that the tertiary chain of the Andes reappears in Grahamland.” I maintain this hypothesis, which demands for its satisfactory demonstration not only the geological study of the land, but also and chiefly a detailed bathymetrical map. The first step to this end has now been made.