CHAPTER X.

EXAMINATION OF THE GRAVITATION THEORY OF OCEANIC CIRCULATION.—DR. CARPENTER’S THEORY.—OBJECTIONS CONSIDERED.

_Modus Operandi_ of the Matter.—Polar Cold considered by Dr. Carpenter the _Primum Mobile_.—Supposed Influence of Heat derived from the Earth’s Crust.—Circulation without Difference of Level.—A Confusion of Ideas in Reference to the supposed Agency of Polar Cold.—M. Dubuat’s Experiments.—A Begging of the Question at Issue.—Pressure as a Cause of Circulation.

In the foregoing chapter, the substance of which appeared in the Phil. Mag. for October, 1871, I have represented the manner in which difference of specific gravity produces circulation. But Dr. Carpenter appears to think that there are some important points which I have overlooked. These I shall now proceed to consider in detail.

“Mr. Croll’s whole manner of treating the subject,” he says, “is so different from that which it appears to me to require, and he has so completely misapprehended my own view of the question, that I feel it requisite to present this in fuller detail in order that physicists and mathematicians, having both sides fully before them, may judge between us” (§ 26).[76]

He then refers to a point so obvious as hardly to require consideration, viz., the effect which results when the surface of the entire area of a lake or pond of water is cooled. The whole of the surface-film, being chilled at the same time, sinks through the subjacent water, and a new film from the warmer layer immediately beneath the surface rises into its place. This being cooled in its turn, sinks, and so on. He next considers what takes place when only a portion of the surface of the pond is cooled, and shows that in this case the surface-film which descends is replaced not from beneath, but by an inflow from the neighbouring area.

“That such must be the case,” says Dr. Carpenter, “appears to me so self-evident that I am surprised that any person conversant with the principles of physical science should hesitate in admitting it, still more that he should explicitly deny it. But since others may feel the same difficulty as Mr. Croll, it may be worth while for me to present the case in a form of yet more elementary simplicity” (§ 29).

Then, in order to show the mode in which the general oceanic circulation takes place, he supposes two cylindrical vessels, W and C, of equal size, to be filled with sea-water. Cylinder W represents the equatorial column, and the water contained in it has its temperature maintained at 60°; whilst the water in the other cylinder C, representing the polar column, has its temperature maintained at 30° by means of the constant application of cold at the top. Free communication is maintained between the two cylinders at top and bottom; and the water in the cold cylinder being, in virtue of its low temperature, denser than the water in the warm cylinder, the two columns are therefore not in static equilibrium. The cold, and hence heavier column tends to produce an outflow of water from its bottom to the bottom of the warm column, which outflow is replaced by an inflow from the top of the warm column to the top of the cold column. In fact, we have just a simple repetition of what he has given over and over again in his various memoirs on the subject. But why so repeatedly enter into the _modus operandi_ of the matter? Who feels any difficulty in understanding how the circulation is produced?

_Polar Cold considered by Dr. Carpenter the Primum Mobile._—It is evident that Dr. Carpenter believes that he has found in polar _cold_ an agency the potency of which, in producing a general oceanic circulation, has been overlooked by physicists; and it is with the view of developing his ideas on this subject that he has entered so fully and so frequently into the exposition of his theory. “If I have myself done anything,” he says, “to strengthen the doctrine, it has been by showing that polar cold, rather than equatorial heat, is the _primum mobile_ of this circulation.”[77]

The influence of the sun in heating the waters of the inter-tropical seas is, in Dr. Carpenter’s manner of viewing the problem, of no great importance. The efficient cause of motion he considers resides in _cold_ rather than in _heat_. In fact, he even goes the length of maintaining that, as a power in the production of the general interchange of equatorial and polar water, the effect of polar cold is so much superior to that of inter-tropical heat, that the influence of the latter may be _practically disregarded_.

“Suppose two basins of ocean-water,” he says, “connected by a strait to be placed under such different climatic conditions that the surface of one is exposed to the heating influence of tropical sunshine, whilst the surface of the other is subjected to the extreme cold of the sunless polar winter. The effect of the surface-heat upon the water of the tropical basin will be for the most part limited (as I shall presently show) to its uppermost stratum, and may here be _practically disregarded_.”[78]

Dr. Carpenter’s idea regarding the efficiency of cold in producing motion seems to me to be not only opposed to the generally received views on the subject, but wholly irreconcilable with the ordinary principles of mechanics. In fact, there are so many points on which Dr. Carpenter’s theory of a “General _Vertical_ Oceanic Circulation” differs from the generally received views on the subject of circulation by means of difference of specific gravity, that I have thought it advisable to enter somewhat minutely into the consideration of the mechanics of that theory, the more so as he has so repeatedly asserted that eminent physicists agree with what he has advanced on the subject.

According to the generally received theory, the circulation is due to the _difference of density_ between the sea in equatorial and polar regions. The real efficient cause is gravity; but gravity cannot act when there is no difference of specific gravity. If the sea were of equal density from the poles to the equator, gravity could exercise no influence in the production of circulation; and the influence which it does possess is in proportion to the difference of density. But the difference of density between equatorial and polar waters is in turn due not absolutely either to polar cold or to tropical heat, but to both—or, in other words, to the _difference_ of temperature between the polar and equatorial seas. This difference, in the very nature of things, must be as much the result of equatorial heat as of polar cold. If the sea in equatorial regions were not being heated by the sun as rapidly as the sea in polar regions is being cooled, the difference of temperature between them, and consequently the difference of density, would be diminishing, and in course of time would disappear altogether. As has already been shown, it is a necessary consequence that the water flowing from equatorial to polar regions must be compensated by an equal amount flowing from polar to equatorial regions. Now, if the water flowing from polar to equatorial regions were not being heated as rapidly as the water flowing from equatorial to polar regions is being cooled, the equatorial seas would gradually become colder and colder until no sensible difference of temperature existed between them and the polar oceans. In fact, _equality of the two rates_ is necessary to the very existence of such a general circulation as that advocated by Dr. Carpenter. If he admits that the general interchange of equatorial and polar water advocated by him is caused by the difference of density between the water at the equator and the poles, resulting from difference of temperature, then he must admit also that this difference of density is just as much due to the heating of the equatorial water by the sun as it is to the cooling of the polar water by radiation and other means—or, in other words, that it is as much due to equatorial heat as to polar cold. And if so, it cannot be true that polar cold rather than equatorial heat is the “_primum mobile_” of this circulation; and far less can it be true that the heating of the equatorial water by the sun is of so little importance that it may be “practically disregarded.”

_Supposed Influence of Heat derived from the Earth’s Crust._—There is, according to Dr. Carpenter, another agent concerned in the production of the general oceanic circulation, viz., the heat derived by the bottom of the ocean from the crust of the earth.[79] We have no reason to believe that the quantity of internal heat coming through the earth’s crust is greater in one part of the globe than in another; nor have we any grounds for concluding that the bottom of inter-tropical seas receives more heat from the earth’s crust than the bottom of those in polar regions. But if the polar seas receive as much heat from this source as the seas within the tropics, then the difference of density between the two cannot possibly be due to heat received from the earth’s crust; and this being so, it is mechanically impossible that internal heat can be a cause in the production of the general oceanic circulation.

_Circulation without Difference of Level._—There is another part of the theory which appears to me irreconcilable with mechanics. It is maintained that this general circulation takes place without any difference of level between the equator and the poles. Referring to the case of the two cylinders W and C, which represent the equatorial and polar columns respectively, Dr. Carpenter says:—

“The force which will thus lift up the entire column of water in W is that which causes the descent of the entire column in C, namely, the excess of gravity constantly acting in C,—the levels of the two columns, and consequently their heights, being maintained at a _constant equality_ by the free passage of surface-water from W to C.”

“The whole of Mr. Croll’s discussion of this question, however,” he continues, “proceeds upon the assumption that the levels of the polar and equatorial columns are _not kept at an_ _equality_, &c.” (§ 30.) And again, “Now, so far from asserting (as Captain Maury has done) that the trifling difference of level arising from inequality of temperature is adequate to the production of ocean-currents, I simply affirm that as fast as the level is disturbed by change of temperature it will be restored by gravity.” (§ 23.)[80]

In order to understand more clearly how the circulation under consideration cannot take place without a difference of level, let W E (Fig. 3) represent the equatorial column, and C P the polar column. The equatorial column is warmer than the polar column because it receives _more_ heat from the sun than the latter; and the polar is colder than the equatorial column because it receives _less_. The difference in the density of the two columns results from their difference of temperature; and the difference of temperature results in turn from the difference in the quantity of heat received from the sun by each. Or, to express the matter in other words, the difference of density (and consequently the circulation under consideration) is due to the excess of heat received from the sun by the equatorial over that received by the polar column; so that to leave out of account the super-heating of the inter-tropical waters by the sun is to leave out of account the very thing of all others that is absolutely essential to the existence of the circulation. The water being assumed to be the same in both columns and differing only as regards temperature, and the equatorial column possessing more heat than the polar, and being therefore less dense than the latter, it follows, in order that the two columns may be in static equilibrium, that the surface of the equatorial column must stand at a higher level than that of the polar. This produces the slope W C from the equator to the pole. The extent of the slope will of course depend upon the extent of the difference of their temperatures. But, as was shown on a former occasion,[81] it is impossible that static equilibrium can ever be fully obtained, because the slope occasioned by the elevation of the equatorial column above the polar produces what we may be allowed to call a _molecular_ disturbance of equilibrium. The surface of the ocean, or the molecules of water lying on the slope, are not in a position of equilibrium, but tend, in virtue of gravity, to roll down the slope in the direction of the polar column C. It will be observed that the more we gain of static equilibrium of the entire ocean the greater is the slope, and consequently the greater is the disturbance of molecular equilibrium; and, _vice versâ_, the more molecular equilibrium is restored by the reduction of the slope, the greater is the disturbance of static equilibrium. _It is therefore absolutely impossible that both conditions of equilibrium can be fulfilled at the same time so long as a difference of temperature exists between the two columns._ And this conclusion holds true even though we should assume water to be a perfect fluid absolutely devoid of viscosity. It follows, therefore, that a general oceanic circulation without a difference of level is a _mechanical impossibility_.

In a case of actual circulation due to difference of gravity, there is always a constant disturbance of both _static_ and molecular equilibrium. Column C is always higher and column W always lower than it ought to be were the two in equilibrium; but they never can be at the same level.

It is quite conceivable, of course, that the two conditions of equilibrium may be fulfilled alternately. We can conceive column C remaining stationary till the water flowing from column W has restored the level. And after the level is restored we can conceive the polar column C sinking and the equatorial column W rising till the two perfectly balance each other. Such a mode of circulation, consisting of an alternate surface-flow and vertical descent and ascent of the columns, though conceivable, is in reality impossible in nature; for there are no means by which the polar column C could be supported from sinking till the level had been restored. But Dr. Carpenter does not assume that the general oceanic circulation takes place in this intermitting manner; according to him, the circulation is _constant_. He asserts that there is a “_continual_ transference of water from the bottom of C to the bottom of W, and from the top of W to the top of C, with a _constant_ descending movement in C and a _constant_ ascending movement in W” (§ 29). But such a condition of things is irreconcilable with the idea of “the levels of the two columns, and consequently their heights, being maintained at a _constant_ equality” (§ 29).

Although Dr. Carpenter does not admit the existence of a permanent difference of level between the equator and the pole, he nevertheless speaks of a depression of level in the polar basin resulting from the contraction by cooling of the water flowing into it. This reduction of level induces an inflow of water from the surrounding area; “and since what is drawn away,” to quote his own words, “is supplied from a yet greater distance, the continued cooling of the surface-stratum in the polar basin will cause a ‘set’ of waters towards it, to be propagated backwards through the whole intervening ocean in communication with it until it reaches the tropical area.” The slope produced between the polar basin and the surrounding area, if sufficiently great, will enable the water in the surrounding area to flow polewards; but unless this slope extend to the equator, it will not enable the tropical waters also to flow polewards. One of two things necessarily follows: either the slope extends from the equator to the pole, or water can flow from the equator to the pole without a slope. If Dr. Carpenter maintains the former, he contradicts himself; and if he adopts the latter, he contradicts an obvious principle of mechanics.

_A Confusion of Ideas in Reference to the supposed Agency of Polar Cold._—It seems to me that Dr. Carpenter has been somewhat misled by a slight confusion of ideas in reference to the supposed agency of polar cold. This is brought out forcibly in the following passage from his memoir in the Proceedings of the Royal Geographical Society, vol. xv.

“Mr. Croll, in arguing against the doctrine of a general oceanic circulation sustained by difference of temperature, and _justly maintaining_ that such a circulation cannot be produced by the application of heat at the surface, has entirely ignored the agency of cold.”

It is here supposed that there are two agents at work in the production of the general oceanic circulation. The one agent is _heat_, acting at the equatorial regions; and the other agent is _cold_, acting at the polar regions. It is supposed that the agency of cold is far more powerful than that of heat. In fact so trifling is the agency of equatorial heat in comparison with that of polar cold that it may be “practically disregarded”—left out of account altogether,—polar cold being the _primum mobile_ of the circulation. It is supposed also that I have considered the efficiency of one of the agents, viz., heat, and found it totally inadequate to produce the circulation in question; and it is admitted also that my conclusions are perfectly correct. But then I am supposed to have left out of account the other agent, viz., polar cold, the only agent possessing real potency. Had I taken into account polar cold, it is supposed that I should have found at once a cause perfectly adequate to produce the required effect.

This is a fair statement of Dr. Carpenter’s views on the subject; I am unable, at least, to attach any other meaning to his words. And I have no doubt they are also the views which have been adopted by those who have accepted his theory.

It must be sufficiently evident from what has already been stated, that the notion of there being two separate agents at work producing circulation, namely heat and cold, the one of which is assumed to have much more potency than the other, is not only opposed to the views entertained by physicists, but is also wholly irreconcilable with the ordinary principles of mechanics. But more than this, if we analyze the subject a little so as to remove some of the confusion of ideas which besets it, we shall find that these views are irreconcilable with even Dr. Carpenter’s own explanation of the cause of the general oceanic circulation.

_Cold_ is not a something positive imparted to the polar waters giving them motion, and of which the tropical waters are deprived. If, dipping one hand into a basin filled with tropical water at 80° and the other into one filled with polar water at 32°, we refer to our _sensations_, we call the water in the one _hot_ and that in the other _cold_; but so far as the water itself is concerned heat and cold simply mean difference in the amounts of heat possessed. Both the polar and the tropical water possess a certain amount of energy in the form of heat, only the polar water does not possess so much of it as the tropical.

How, then, according to Dr. Carpenter, does polar cold impart motion to the water? The warm water flowing in upon the polar column becomes chilled by cold, but it is not cooled below that of the water underneath; for, according to Dr. Carpenter, the ocean in polar regions is as cold and as dense underneath as at the surface. The cooled surface-water does not sink through the water underneath, like the surface-water of a pond chilled during a frosty night. “The descending motion in column C will not consist,” he says, “in a successional descent of surface-films from above downwards, but it will be a downward movement of the _entire mass_, as if water in a tall jar were being drawn off through an orifice at the bottom” (§ 29). There is a downward motion of the entire column, producing an outflow of water at the bottom towards the equatorial column W, which outflow is compensated by an inflow from the top of the equatorial column to the top of the polar column C. But what causes column C to descend? The cause of the descent is its excess of weight over that of column W. Column C descends and column W ascends, for the same reason that in a balance the heavy scale descends and the light scale rises. Column C descends not simply because it is cold, but because it is _colder_ than column W. Column C descends not simply because in consequence of being cold it is dense and therefore heavy, but because in consequence of being cold it is _denser_ and therefore _heavier_ than column W. It might be as cold as frozen mercury and as heavy as lead; but it would not on that account descend unless it were heavier than column W. The descent of column C and ascent of column W, and consequently the general oceanic circulation, results, therefore, according to Dr. Carpenter’s explanation, from the _difference_ in the weights of the two columns; and the difference in the weights of the two columns results from their _difference_ of density; and the difference of density of the two columns in turn results from their _difference_ of temperature. But it has already been proved that the difference of temperature between the polar and equatorial columns depends wholly on the difference in the amount of heat received by each from the sun. The equatorial column W possesses more heat than the polar column C, solely because it receives more heat from the sun than column C. Consequently Dr. Carpenter’s statement that the circulation is produced by polar cold rather than by equatorial heat, is just as much in contradiction to his own theory as it is to the principles of mechanics. Again, his admission that the general oceanic circulation “cannot be produced by the application of heat to the surface,” is virtually a giving up the whole point in debate; for according to his gravitation theory, and every form of that theory, the circulation results from _difference_ of temperature between equatorial and polar seas; but this difference, as we have seen, is entirely owing to the difference in the amount of heat received from the sun at these two places. The heat received, however, is “surface-heat;” for it is at the surface that the ocean receives all its heat from the sun; and consequently if surface-heat cannot produce the effect required, nothing else can.

_M. Dubuat’s Experiments._—Referring to the experiments of M. Dubuat adduced by me to show that water would not run down a slope of 1 in 1,820,000,[82] he says, “Now the experiments of M. Dubuat had reference, not to the slow restoration of level produced by the motion of water on itself, but to the sensible movement of water flowing over solid surfaces and retarded by its friction against them” (§ 22). Dr. Carpenter’s meaning, I presume, is that if the incline consist of any solid substance, water will not flow down it; but if it be made of _water_ itself, _water_ will flow down it. But in M. Dubuat’s experiments it was only the molecules in actual _contact_ with the solid incline that could possibly be retarded by friction against it. The molecules not in contact with the solid incline evidently rested upon an _incline of water_, and were at perfect liberty to roll down that incline if they chose; but they did not do so; and consequently M. Dubuat’s experiment proved that water will not flow over itself on an incline of 1 in 1,000,000.

_A Begging of the Question at Issue._—“It is to be remembered,” says Dr. Carpenter, “that, however small the original amount of movement may be, a _momentum_ tending to its continuance _must_ be generated from the instant of its commencement; so that if the initiating force be in constant action, there will be a _progressive acceleration_ of its rate, until the increase of resistance equalises the tendency to further acceleration. Now, if it be admitted that the propagation of the disturbance of equilibrium from one column to another is simply _retarded_, _not_ prevented, by the viscosity of the liquid, I cannot see how the conclusion can be resisted, that the constantly maintained difference of gravity between the polar and equatorial columns really acts as a _vis viva_ in maintaining a circulation between them” (§ 35).

If it be true, as Dr. Carpenter asserts, that in the case of the general oceanic circulation advocated by him “viscosity” simply _retards_ motion, but does not _prevent_ it, I certainly agree with him “that the constantly maintained difference of gravity between the polar and equatorial columns really acts as a _vis viva_ in maintaining a circulation between them.” But to assert that it merely retards, but does not prevent, motion, is simply _begging the question at issue_. It is an established principle that if the _force_ resisting motion be greater than the force tending to produce it, then no motion can take place and no work can be performed. The experiments of M. Dubuat prove that the _force_ of the molecular resistance of water to motion is _greater_ than the _force_ derived from a slope of 1 in 1,000,000; and therefore it is simply begging the question at issue to assert that it is _less_. The experiments of MM. Barlow, Rainey, and others, to which he alludes, are scarcely worthy of consideration in relation to the present question, because we know nothing whatever regarding the actual amount of force producing motion of the water in these experiments, further than that it must have been enormously greater than that derived from a slope of 1 in 1,000,000.

_Supposed Argument from the Tides._—Dr. Carpenter advances Mr. Ferrel’s argument in regard to the tides. The power of the moon to disturb the earth’s water, he asserts, is, according to Herschel, only 1/11,400,000th part of gravity, and that of the sun not over 1/25,736,400th part of gravity; yet the moon’s attractive force, even when counteracted by the sun, will produce a rise of the ocean. But as the disturbance of gravity produced by difference of temperature is far greater than the above, it ought to produce circulation.

It is here supposed that the force exerted by gravity on the ocean, resulting from difference of temperature, tending to produce the general oceanic circulation, is much greater than the force exerted on the ocean by the moon in the production of the tides. But if we examine the subject we shall find that the opposite is the case. The attraction of the moon tending to lift the waters of the ocean acts directly on every molecule from the surface to the bottom; but the force of gravity tending to produce the circulation in question acts directly on only a portion of the ocean. Gravity can exercise no direct force in impelling the underflow from the polar to the equatorial regions, nor in raising the water to the surface when it reaches the equatorial regions. Gravity can exercise no direct influence in pulling the water horizontally along the earth’s surface, nor in raising it up to the surface. The pull of gravity is always _downwards_, never _horizontally_ nor upwards. Gravity will tend to pull the surface-water from the equator to the poles because here we have _descent_. Gravity will tend to sink the polar column because here also we have _descent_. But these are the only parts of the circuit where gravity has any tendency to produce motion. Motion in the other parts of the circuit, viz., along the bottom of the ocean from the poles to the equator and in raising the equatorial column, is produced by the _pressure_ of the polar column; and consequently it is only _indirectly_ that gravity may be said to produce motion in those parts. It is true that on certain portions of the ocean the force of gravity tending to produce motion is greater than the force of the moon’s attraction, tending to produce the tides; but this portion of the ocean is of inconsiderable extent. The total force of gravity acting on the entire ocean tending to produce circulation is in reality prodigiously less than the total force of the moon tending to produce the tides.

It is no doubt a somewhat difficult problem to determine accurately the total amount of force exercised by gravity on the ocean; but for our present purpose this is not necessary. All that we require at present is a very rough estimate indeed. And this can be attained by very simple considerations. Suppose we assume the mean depth of the sea to be, say, three miles. The mean depth may yet be found to be somewhat less than this, or it may be found to be somewhat greater; a slight mistake, however, in regard to the mass of the ocean will not materially affect our conclusions. Taking the depth at 3 miles, the force or direct pull of gravity on the entire waters of the ocean tending to the production of the general circulation will not amount to more than 1/24,000,000,000th that of gravity, or only about 1/2,100th that of the attraction of the moon in the production of the tides. Let it be observed that I am referring to the force or pull of gravity, and not to hydrostatic pressure.

The moon, by raising the waters of the ocean, will produce a slope of 2 feet in a quadrant; and because the raised water sinks and the level is restored, Mr. Ferrel concludes that a similar slope of 2 feet produced by difference of temperature will therefore be sufficient to produce motion and restore level. But it is overlooked that the restoration of level in the case of the tides is as truly the work of the moon as the disturbance of that level is. For the water raised by the attraction of the moon at one time is again, six hours afterwards, pulled down by the moon when the earth has turned round a quadrant.

No doubt the earth’s gravity alone would in course of time restore the level; but this does not follow as a logical consequence from Mr. Ferrel’s premises. If we suppose a slope to be produced in the ocean by the moon and the moon’s attraction withdrawn so as to allow the water to sink to its original level, the raised side will be the heaviest and the depressed side the lightest; consequently the raised side will tend to sink and the depressed side will tend to rise, in order that the ocean may regain its static equilibrium. But when a difference of level is produced by difference of temperature, the raised side is always the lightest and the depressed side is always the heaviest; consequently the very effort which the ocean makes to maintain its equilibrium tends to prevent the level being restored. The moon produces the tides chiefly by means of a simple yielding of the entire ocean considered as a mass; whereas in the case of a general oceanic circulation the level is restored by a _flow_ of water at or near the surface. Consequently the amount of friction and molecular resistance to be overcome in the restoration of level in the latter case is much greater than in the former. The moon, as the researches of Sir William Thomson show, will produce a tide in a globe composed of a substance where no currents or general flow of the materials could possibly take place.

_Pressure as a Cause of Circulation._—We shall now briefly refer to the influence of pressure (the indirect effects of gravity) in the production of the circulation under consideration. That which causes the polar column C to descend and the equatorial column W to ascend, as has repeatedly been remarked, is the difference in the weight of the two columns. The efficient cause in the production of the movement is, properly speaking, gravity; _cold_ at the poles and _heat_ at the equator, or, what is the same thing, the _excess_ of heat received by the equator over that received by the poles is what maintains the difference of temperature between the two columns, and consequently is that also which maintains the difference of weight between them. In other words, difference of temperature is the cause which maintains the _state of disturbed equilibrium_. But the efficient cause of the circulation in question is gravity. Gravity, however, could not act without this state of disturbed equilibrium; and difference of temperature may therefore be called, in relation to the circulation, a necessary _condition_, while gravity may be termed the _cause_. Gravity sinks column C _directly_, but it raises column W _indirectly_ by means of pressure. The same holds true in regard to the motion of the bottom-waters from C to W, which is likewise due to pressure. The pressure of the excess of the weight of column C over that of column W impels the bottom-water equatorwards and lifts the equatorial column. But on this point I need not dwell, as I have in the preceding chapter entered into a full discussion as to how this takes place.

We come now to the most important part of the inquiry, viz., how is the surface-water impelled from the equator to the poles? Is pressure from behind the impelling force here as in the case of the bottom-water of the ocean? It seems to me that, in attempting to account for the surface-flow from the equator to the poles, Dr. Carpenter’s theory signally fails. The force to which he appeals appears to be wholly inadequate to produce the required effect.

The experiments of M. Dubuat, as already noticed, prove that, any slope which can possibly result from the difference of temperature between the equator and the poles is wholly insufficient to enable gravity to move the waters; but it does not necessarily prove that the _pressure_ resulting from the raised water at the equator may not be sufficient to produce motion. This point will be better understood from the following figure, where, as before, P C represents the polar column and E W the equatorial column.

It will be observed that the water in that wedge-shaped portion W C W′ forming the incline cannot be in a state of static equilibrium. A molecule of water at O, for example, will be pressed more in the direction of C than in the direction of W′, and the amount of this excess of pressure towards C will depend upon the height of W above the line C W′. It is evident that the pressure tending to move the molecule at O towards C will be far greater than the direct pull of gravity tending to draw a molecule at O′ lying on the surface of the incline towards C. The experiments of M. Dubuat prove that the direct force of gravity will not move the molecule at O′—that is, cause it to roll down the incline W C; but they do not prove that it may not yield to pressure from above, or that the pressure of the column W W′ will not move the molecule at O. The pressure is caused by gravity, and cannot, of course, enable gravity to perform more work than what is derived from the energy of gravity; it will enable gravity, however, to overcome resistance, which it could not do by direct action. But whether the pressure resulting from the greater height of the water at the equator due to its higher temperature be actually sufficient to produce displacement of the water is a question which I am wholly unable to answer.

If we suppose 4 feet 6 inches to be the height of the equatorial surface above the polar required to make the two columns balance each other, the actual difference of level between the two columns will certainly not be more than one-half that amount, because, if a circulation exist, the weight of the polar column must always be in excess of that of the equatorial. But this excess can only be obtained at the expense of the surface-slope, as has already been shown at length. The surface-slope probably will not be more than 2 feet or 2 feet 6 inches. Suppose the ocean to be of equal density from the poles to the equator, and that by some means or other the surface of the ocean at the equator is raised, say, 2 feet above that of the poles, then there can be little doubt that in such a case the water would soon regain its level; for the ocean at the equator being heavier than at the poles by the weight of a layer 2 feet in thickness, it would sink at the former place and rise at the latter until equilibrium was restored, producing, of course, a very slight displacement of the bottom-waters towards the poles. It will be observed, however, that restoration of level in this case takes place by a simple yielding, as it were, of the entire mass of the ocean without displacement of the molecules of the water over each other to any great extent. In the case of a slope produced by difference of temperature, however, the raised portion of the ocean is not heavier but lighter than the depressed portion, and consequently has no tendency to sink. Any movement which the ocean as a mass makes in order to regain equilibrium tends, as we have seen, rather to increase the difference of level than to reduce it. Restoration of level can only be produced by the forces which are in operation in the wedge-shaped mass W C W′, constituting the slope itself. But it will be observed by a glance at the Figure that, in order to the restoration of level, a large portion of the water W W′ at the equator will require to flow to C, the pole.

According to the general _vertical_ oceanic circulation theory, pressure from behind is not one of the forces employed in the production of the flow from the equator to the poles. This is evident; for there can be no pressure from behind acting on the water if there be no slope existing between the equator and the poles. Dr. Carpenter not only denies the actual existence of a slope, but denies the necessity for its existence. But to deny the existence of a slope is to deny the existence of pressure, and to deny the necessity for a slope is to deny the necessity for pressure. That in Dr. Carpenter’s theory the surface-water is supposed to be _drawn_ from the equator to the poles, and not _pressed_ forward by a force from behind, is further evident from the fact that he maintains that the force employed is not _vis a tergo_ but _vis a fronte_.[83]