During the cruise of the Challenger the specific gravity of the surface water was observed daily while at sea, and that of water from the bottom and intermediate depths as often as opportunity offered. These observations were almost entirely confined to the region between the parallels of 40° N. and 40° S. latitudes, which, including as it does the regions of the equatorial calms, of the trade winds, and to a certain extent of both the northern and southern westerly winds is decidedly the most interesting field for such investigations. Many valuable observations have been made by other observers, and I have availed myself more especially of the series of observations made by Lenz during Kotzebue's voyage to the Pacific and back. His observations were almost entirely confined to the surface water.