This paper was commenced by the author more than twenty years since, with a view to the geological bearing of the subject, but was for some years unavoidably interrupted. It has now been brought down to 1868, the date of the 'Lightning’ expedition, when the subject was taken up by Dr. Carpenter, by whom it has since been so ardently and ably carried on. Nevertheless, as Dr. Carpenter’s work relates almost solely to recent investigations, the author considers that there is yet considerable interest attached to the work of the earlier observers from 1750 to 1868, though he feels that much of it is necessarily superseded by the great and more exact work subsequent to 1868. He is aware that the older observations have also not been deemed reliable on account of the error caused by pressure on the thermometers at depths; but this is far from applying to the whole of them, as that error was taken into account so early as 1836, if not before, and a large number of these observations are equally reliable with the more recent ones, while the greater part of the others admit of corrections which render them sufficiently available. In 1830, Gehler gave a list of 226 observations, and D’Urville, in 1833, tabulated 421 experiments according to depths. The present paper contains a record of about 1300 observations, which are arranged according to the degrees of latitude:—1st, for the northern hemisphere; 2nd, the southern hemisphere; 3rd, inland seas. They are all reduced to common scales of thermometer, measure of depth, and meridian. Their position is given on a map of the world, and the bathymetrical isotherms from the Poles to the Equator, based on the correct and corrected observations, are given in a series of ten sections. The author does not claim for these observations the exact value, or the unity and completeness of plan, of the more recent ones, while, as compared with them, the depths at which they were made are on the whole very limited; still they include a few at great depths; and as they extend over much ground that has not been covered by the expeditions of the ‘Lightning,’ 'Porcupine,’ and 'Challenger,’ he trusts that these Tables may be of some use as complemental to these later researches, and as bringing together and reducing to a common standard, observations scattered through a large number of works and memoirs. At the same time, the author would observe that he thinks it due to our many distinguished foreign colleagues who have been engaged in the inquiry, and whose work seems but little known, that the results of their researches should be understood in this country. Their conclusions, which are in close agreement with those formed, entirely in dependency, upon recent and better data by Dr. Carpenter, acquire, from this concordance, additional force and value. The author was not at all aware himself, in the earlier part of the inquiry, how much had been done, and often found himself framing hypotheses which, on further examination, he found had been long before anticipated by others.