XXV. On determining the depth of the sea without the use of the sounding-line

It occurred to me some years ago that the inferior density of sea-water as compared with solid rock, such as that composing the crust of our earth, might be taken advantage of to devise a method of determining the depth of sea below a vessel. If an instrument could be constructed which, when suspended on board ship, would indicate extremely slight variations in the total attraction of the earth, those indications might be referable to the depth of sea, and a scale be obtained whose divisions would give the depth in fathoms, or other units, without having recourse to the laborious process of sounding by means of the sounding-line.Terrestrial Attraction : Newton.—Our knowledge regarding terrestrial attraction dates from Newton, who proved that “the attraction of a spherical shell on an external particle is the same as if the mass of the shell were collected at the centre,” and that the earth might be considered as consisting of an aggregate of such shells. Bearing in view, however, the fact of the earth’s rotation he proved its ellipticity, and that partly in consequence of that form, and partly on account of the centrifugal force engendered by its rotation, the total attraction of the earth in reference to a point on its surface must vary with latitude. He determined the ratio of increase on the supposition that the earth is homogeneous, and showed that it varies as the square of the sine of the latitude. It is actually represented by the formulag =g' (1 + ·005133 sin2 λ), in whichg signifies gravitation at a place in latitude λ, andg' = 32·088 gravitation at the Equator.