“Until it is clearly apprehended that sea-water becomes more and more dense as its temperature is reduced, and that it consequently continues to sink until it freezes, the immense motor power of polar cold cannot be apprehended. But when this has been clearly recognised, it is seen that the application of _cold at the surface_ is precisely equivalent as a moving power to that application of _heat at the bottom_ by which the circulation of water is sustained in every heating apparatus that makes use of it” (§ 25).
The application of cold at the surface is thus held to be equivalent as a motor power to the application of heat at the bottom. But heat applied to the bottom of a vessel produces circulation by _convection_. It makes the molecules at the bottom expand, and they, in consequence of buoyancy, rise _through_ the water in the vessel. Consequently if the action of cold at the surface in polar regions is equivalent to that of heat, the cold must contract the molecules at the surface and make them sink _through_ the mass of polar water beneath. But assuming this to be the meaning in the passage just quoted, how much colder is the surface water than the water beneath? Let us suppose the difference to be one degree. How much work, then, will gravity perform upon this one pound of water which is one degree colder than the mass beneath supposed to be at 32°? The force with which the pound of water will sink will not be proportional to its weight, but to the difference of weight between it and a similar bulk of the water through which it sinks. The difference between the weight of a pound of water at 31° and an equal volume of water at 32° is 1/29,000th of a pound. Now this pound of water in sinking to a depth of 10,000 feet, which is about the depth at which a polar temperature is found at the equator, would perform only one-third of a foot-pound of work. And supposing it were three degrees colder than the water beneath, it would in sinking perform only one foot-pound. This would give us only 4 + 1 = 5 foot-pounds as the total amount that could be performed by gravitation on the pound of water from the time that it left the equator till it returned to the point from which it started. The amount of work performed in descending the slope from the equator to the pole and in sinking to a depth of 10,000 feet or so through the polar water assumed to be warmer than the surface water, comprehends the total amount of work that gravitation can possibly perform; so that the amount of force gained by such a supposition over and above that derived from the slope is trifling.