Note 30 — Chapter XXVIII · A VERY FEW REMARKS WITH REFERENCE TO THE DELUGE.

“I return Sir John Herschel’s letter on deep-sea sounding. Anything from him is sure to be interesting and instructive; but there is a circumstance unnoticed in his communication which might obstruct the descent of a sounding apparatus to very great depth.

“Mr. Perkins found that at a depth of only 3,000 feet, sea-water was compressed ¹⁄₂₇th of its bulk at the surface. (Lib^y. of Useful Knowledge, vol. 1. Art. Hydrostatics.) Hydrostatic pressure has usually been estimated from depth alone, assuming that the density of the fluid was uniform; such, however, cannot be the case in an elastic fluid like water, for at great depths, being in a compressed state, it is more dense than at the surface.

“In estimating the amount of hydrostatic pressure at great depths, we should know the vertical height of the column and mean density of the fluid; and since density increases with depth, by reason of superincumbent pressure, the water at great depths must be enormously compressed, and, consequently, in a very dense state. Let us now inquire how increasing density (from compression alone) might affect an apparatus sent down by a weight, in order to reach the bottom, presuming that the solids composing the float and sinker were incompressible, and retained their form and magnitude during the operation.

“Let bees’-wax be a float, and cast-iron a sinker, and let each, for illustration, be one cubic foot in dimensions. Let it be possible that at some depth water may be compressed into one-fourth of its bulk at the surface, and still retain the properties of a fluid; let it also be granted that a solid will swim if specifically lighter than the contiguous fluid, and sink if heavier than an equal volume of the fluid. The specific gravity of bees’-wax is stated to be 964; that of cast iron, 7248; and that of sea-water at the surface, 1028: hence the buoyancy of wax immersed in sea-water at the surface, may be called 64, and the tendency of cast-iron to sink, from the same surface, 6220. Deducting 64, we have 6156 as the whole tendency of the mass (wax attached to iron) to sink from the surface. Let us now suppose that the machine has attained a depth where the water is compressed into a four-fold density, represented by 4112 for a cubic foot; and we have 3148 for the tendency of the wax to float, but only 3136 for the tendency of the iron to sink: and the inclination to ascend rather than descend, might be represented by 12. Thus we see that an apparatus may not be certain of arriving at the bottom of an ocean: as in an opposite manner, a balloon may not reach the highest regions of the atmosphere. Either machine could only attain a position where there would be no tendency either to descend or ascend.

“William Walker.”

Plymouth, 24th Feb. 1837.