The case referred to by Dr. Carpenter of the heating apparatus in London University is also unsatisfactory. The water leaves the boiler at 120° and returns to it at 80°. The difference of specific gravity between the water leaving the boiler and the water returning to it is supposed to produce the circulation. It seems to me that this difference of specific gravity has nothing whatever to do with the matter. The cause of the circulation must be sought for in the boiler itself, and not in the pipes. The heat is applied to the bottom of the boiler, not to the top. What is the temperature of the molecules in contact with the bottom of the boiler directly over the fire, is a question which must be considered before we can arrive at a just determination of the causes which produce circulation in the pipes of a heating apparatus such as that to which Dr. Carpenter refers. But, in addition to this, as the heat is applied to the bottom of the boiler and not to the top, convection comes into play, a cause which, as we shall find, does not come into play in the theory of oceanic circulation at present under our consideration.
The Force exerted by Gravity.—Dr. Carpenter speaks of his doctrine of a general oceanic circulation sustained by difference of temperature alone, “as one of which physical geographers could not recognise the importance, so long as they remained under the dominant idea that the temperature of the deep sea is everywhere 39°.” And he affirms that “until it is clearly apprehended that sea-water becomes more and more dense as its temperature is reduced, the immense motive power of polar cold cannot be understood.” But in chap. vii. and also in the Phil. Mag. for October, 1870 and 1871, I proved that if we take 39° as the temperature of maximum density the force exerted by gravity tending to produce circulation is just as great as when we take 32°. The reason for this is that when we take 32° as the temperature of maximum density, although we have, it is true, a greater elevation of the ocean above the place of maximum density, yet this latter occurs at the poles; while on the other hand, when we take 39°, the difference of level is less—the place not being at the poles but in about lat. 56°. Now the shorter slope from the equator to lat. 56° is as steep as the larger one from the equator to the poles, and consequently gravity exerts as much force in the production of motion in the one case as in the other. Sir John Herschel, taking 39° as the temperature of maximum density, estimated the slope at 1/32nd of an inch per mile, whereas we, taking 32° as the actual temperature of maximum density of the polar seas and calculating from modern data, find that the slope is not one-half that amount, and that the force of gravity tending to produce circulation is much less than Herschel concluded it to be. The reason, therefore, why physical geographers did not adopt the theory that oceanic circulation is the result of difference of temperature could not possibly be the one assigned by Dr. Carpenter, viz., that they had under-estimated the force of gravity by taking 39° instead of 32° as the temperature of maximum density.
The Work performed by Gravity.—But in order clearly to understand this point, it will be better to treat the matter according to the third method, and consider not the mere force of gravity impelling the waters, but the amount of work which gravitation is capable of performing.
Let us then assume the correctness of my estimate, that the height of the surface of the ocean at the equator above that at the poles is 4 feet 6 inches, for in representing the mode in which difference of specific gravity produces circulation it is of no importance what we may fix upon as the amount of the slope. In order, therefore, to avoid fractions of a foot, I shall take the slope at 4 feet instead of 4½ feet, which it actually is. A pound of water in flowing down this slope from the equator to either of the poles will perform 4 foot-pounds of work; or, more properly speaking, gravitation will. Now it is evident that when this pound of water has reached the pole, it is at the bottom of the slope, and consequently cannot descend further. Gravity, therefore, cannot perform any more work upon it; as it can only do so while the thing acted upon continues to descend—that is, moves under the force exerted. But the water will not move under the influence of gravity unless it move downward; it being in this direction only that gravity acts on the water. “But,” says Dr. Carpenter, “the effect of surface-cold upon the water of the polar basin will be to reduce the temperature of its whole mass below the freezing-point of fresh water, the surface-stratum sinking as it is cooled in virtue of its diminished bulk and increased density, and being replaced by water not yet cooled to the same degree.”[71] By the cooling of the whole mass of polar water by cold and the heating of the water at the equator by the sun’s rays the polar column of water, as we have seen, is rendered denser than the equatorial one, and in order that the two may balance each other, the polar column is necessarily shorter than the equatorial by 4 feet; and thus it is that the slope of 4 feet is formed. It is perfectly true that the water which leaves the equator warm and light, becomes by the time it reaches the pole cold and dense. But unless it be denser than the underlying polar water it will not sink down through it.[72] We are not told, however, why it should be colder than the whole mass underneath, which, according to Dr. Carpenter, is cooled by polar cold. But that he does suppose it to sink to the bottom in consequence of its contraction by cold would appear from the following quotation:—
“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.
It would appear, however, that this is not what is meant after all. What Dr. Carpenter apparently means is this: when a quantity of water, say a layer one foot thick, flows down from the equator to the pole, the polar column becomes then heavier than the equatorial by the weight of this additional layer. A layer of water equal in quantity is therefore pressed away from the bottom of the column and flows off in the direction of the equator as an under current, the polar column at the same time sinking down one foot until equilibrium of the polar and equatorial columns is restored. Another foot of water now flows down upon the polar column and another foot of water is displaced from below, causing, of course, the column to descend an additional foot. The same process being continually repeated, a constant downward motion of the polar column is the result. Or, perhaps, to express the matter more accurately, owing to the constant flow of water from the equatorial regions down the slope, the weight of the polar column is kept always in excess of that of the equatorial; therefore the polar column in the effort to restore equilibrium is kept in a constant state of descent. Hence he terms it a “vertical” circulation. The following will show Dr. Carpenter’s theory in his own words:—
“The action of cold on the surface water of each polar area will be exerted as follows:—
“(a) In diminishing the height of the polar column as compared with that of the equatorial, so that a lowering of its level is produced, which can only be made good by a surface-flow from the latter towards the former.
“(b) In producing an excess in the downward pressure of the column when this inflow has restored its level, in virtue of the increase of specific gravity it has gained by its reduction in volume; whereby a portion of its heavy bottom-water is displaced laterally, causing a further reduction of level, which draws in a further supply of the warmer and lighter water flowing towards its surface.