Chapter VI
EXAMINATION OF THE GRAVITATION THEORY OF OCEANIC CIRCULATION.—LIEUT. MAURY’S THEORY.
Introduction.—Ocean-currents, according to Maury, due to Difference of Specific Gravity.—Difference of Specific Gravity resulting from Difference of Temperature.—Difference of Specific Gravity resulting from Difference of Saltness.—Maury’s two Causes neutralize each other.—How, according to him, Difference in Saltness acts as a Cause.
Introduction.—Few subjects have excited more interest and attention than the cause of ocean circulation; and yet few are in a more imperfect and unsatisfactory condition, nor is there any question regarding which a greater diversity of opinion has prevailed. Our incomplete acquaintance with the facts relating to the currents of the ocean and the modes of circulation actually in operation, is no doubt one reason for this state of things. But doubtless the principal cause of such diversity of opinion lies in the fact that the question is one which properly belongs to the domain of physics and mechanics, while as yet no physicist of note (if we except Dr. Colding, of Copenhagen) has given, as far as I know, any special attention to the subject. It is true that in works of meteorology and physical geography reference is continually made to such eminent physicists as Herschel, Pouillet, Buff, and others; but when we turn to the writings of these authors we find merely a few remarks expressive of their opinions on the subject, and no special discussion or investigation of the matter, nor anything which could warrant us in concluding that such investigations have ever been made. At present the question cannot be decided by a reference to authorities.
The various theories on the subject may be classed under two divisions; the first of these attributes the motion of the water to the impulse of the wind, and the second to the force of gravity resulting from difference of density. But even amongst those who adopt the former theory, it is generally held that the winds are not the sole cause, but that, to a certain extent at least, difference of specific gravity contributes to produce motion of the waters. This is a very natural conclusion; and in the present state of physical geography on this subject one can hardly be expected to hold any other view.
The supporters of the latter theory may be subdivided into two classes. The first of these (of which Maury may be regarded as the representative) attributes the Gulf-stream, and other sensible currents of the ocean, to difference of specific gravity. The other class (at present the more popular of the two, and of which Dr. Carpenter may be considered the representative) denies altogether that such currents can be produced by difference of specific gravity,[53] and affirms that there is a general movement of the upper portion of the ocean from the equator to the poles, and a counter-movement of the under portion from the poles to the equator. This movement is attributed to difference of specific gravity between equatorial and polar water, resulting from difference of temperature.
The widespread popularity of the gravitation theory is no doubt, to a great extent, owing to the very great prominence given to it by Lieut. Maury in his interesting and popular work, “The Physical Geography of the Sea.” Another cause which must have favoured the reception of this theory is the ease with which it is perceived how, according to it, circulation of the waters of the ocean is supposed to follow. One has no difficulty, for example, in perceiving that if the inter-tropical waters of the ocean are expanded by heat, and the waters around the poles contracted by cold, the surface of the ocean will stand at a higher level at the equator than at the poles. Equilibrium being thus disturbed, the water at the equator will tend to flow towards the poles as a surface current, and the water at the poles towards the equator as an under current. This, at first sight, looks well, especially to those who take but a superficial view of the matter.
We shall examine this theory at some length, for two reasons: 1, because it lies at the root of a great deal of the confusion and misconception which have prevailed in regard to the whole subject of ocean-currents: 2, because, if the theory is correct, it militates strongly against the physical theory of secular changes of climate advanced in this volume. We have already seen (Chapter IV.) that when the eccentricity of the earth’s orbit reaches a high value, a combination of physical circumstances tends to lower the temperature of the hemisphere which has its winter solstice in aphelion, and to raise the temperature of the opposite hemisphere, whose winter solstice will, of course, be in perihelion. The direct result of this state of things, as was shown, is to strengthen the force of the trade-winds on the cold hemisphere, and to weaken their strength on the warm hemisphere: and this, in turn, we also saw, tends to impel the warm water of the inter-tropical region on to the warm hemisphere, and to prevent it, in a very large degree, from passing into the cold hemisphere. This deflection of the ocean-currents tends to an enormous extent to increase the difference of temperature previously existing between the two hemispheres. In other words, the warm and equable condition of the one hemisphere, and the cold and glacial condition of the other, are, to a great extent, due to this deflection of ocean-currents. But if the theory be correct which attributes the motion of ocean-currents to a difference in density between the sea in inter-tropical and polar regions, then it follows that these currents (other things being equal) ought to be stronger on the cold hemisphere than on the warm, because there is a greater difference of temperature and, consequently, a greater difference of density, between the polar seas of the cold hemisphere and the equatorial seas, than between the polar seas of the warm hemisphere and the equatorial seas. And this being the case, notwithstanding the influence of the trade-winds of the cold hemisphere blowing over upon the warm, the currents will, in all probability, be stronger on the cold hemisphere than on the warm. In other words, the influence of the powerful trade-winds of the cold hemisphere to transfer the warm water of the equator to the warm hemisphere will probably be more than counterbalanced by the tendency of the warm and buoyant waters of the equator to flow towards the dense and cold waters around the pole of the cold hemisphere. But if ocean-currents are due not to difference in specific gravity, but to the influence of the winds, then it is evident that the waters at the equator will be impelled, not into the cold hemisphere, but into the warm.
For this reason I have been the more anxious to prove that inter-tropical heat is conveyed to temperate and polar regions by ocean-currents, and not by means of any general movement of the ocean resulting from difference of gravity. I shall therefore on this account enter more fully into this part of the subject than I otherwise would have done. Irrespective of all this, however, the important nature of the whole question, and the very general interest it excites, warrant a full consideration of the subject.
I shall consider first that form of the gravitation theory advocated by Maury in his work on the “Physical Geography of the Sea,” which attributes the motion of the Gulf-stream and other sensible currents of the ocean to differences of specific gravity. One reason which has induced me to select Maury’s work is, that it not only contains a much fuller discussion on the cause of the motion of ocean-currents than is to be found anywhere else, but also that it has probably passed through a greater number of editions than any other book of a scientific character in the English language in the same length of time.
Examination of Lieut. Maury’s Gravitation Theory.—Although Lieut. Maury has expounded his views on the cause of ocean-currents at great length in the various editions of his work, yet it is somewhat difficult to discover what they really are. This arises chiefly from the generally confused and sometimes contradictory nature of his hydrodynamical conceptions. After a repeated perusal of several editions of his book, the following, I trust, will be found to be a pretty accurate representation of his theory:—
Ocean-currents, according to Maury, due to Difference of Specific Gravity.—Although Maury alludes to a number of causes which, he thinks, tend to produce currents, yet he deems their influence so small that, practically, all currents may be referred to difference of specific gravity.
“If we except,” he says, “the tides, and the partial currents of the sea, such as those that may be created by the wind, we may lay it down as a rule that all the currents of the ocean owe their origin to the differences of specific gravity between sea-water at one place and sea-water at another; for wherever there is such a difference, whether it be owing to difference of temperature or to difference of saltness, &c., it is a difference that disturbs equilibrium, and currents are the consequence” (§ 467)[54]. To the same effect see §§ 896, 37, 512, 520, and 537.
Notwithstanding the fact that he is continually referring to difference of specific gravity as the great cause of currents, it is difficult to understand in what way he conceives this difference to act as a cause.
Difference of specific gravity between the waters of the ocean at one place and another can give rise to currents only through the influence of the earth’s gravity. All currents resulting from difference of specific gravity can be ultimately resolved into the general principle that the molecules that are specifically heavier descend and displace those that are specifically lighter. If, for example, the ocean at the equator be expanded by heat or by any other cause, it will be forced by the denser waters in temperate and polar regions to rise so that its surface shall stand at a higher level than the surface of the ocean in these regions. The surface of the ocean will become an inclined plane, sloping from the equator to the poles. Hydro-statically, the ocean, considered as a mass, will then be in a state of equilibrium; but the individual molecules will not be in equilibrium. The molecules at the surface in this case may be regarded as lying on an inclined plane sloping from the equator down to the poles, and as these molecules are at liberty to move they will not remain at rest, but will descend the incline towards the poles. When the waters at the equator are expanded, or the waters at the poles contracted, gravitation makes, as it were, a twofold effort to restore equilibrium. It in the first place sinks the waters at the poles, and raises the waters at the equator, in order that the two masses may balance each other; but this very effort of gravitation to restore equilibrium to the mass destroys the equilibrium of the molecules by disturbing the level of the ocean. It then, in the second place, endeavours to restore equilibrium to the molecules by pulling the lighter surface water at the equator down the incline towards the poles. This tends not only to restore the level of the ocean, but to bring the lighter water to occupy the surface and the denser water the bottom of the ocean; and when this is done, complete equilibrium is restored, both to the mass of the ocean and to its individual molecules, and all further motion ceases. But if heat be constantly applied to the waters of the equatorial regions, and cold to those of the polar regions, and a permanent disturbance of equilibrium maintained, then the continual effort of gravitation to restore equilibrium will give rise to a constant current. In this case, the heat and the cold (the agents which disturb the equilibrium of the ocean) may be regarded as causes of the current, inasmuch as without them the current would not exist; but the real efficient cause, that which impels the water forward, is the force of gravity. But the force of gravity, as has already been noticed, cannot produce motion (perform work) unless the thing acted upon descend. Descent is implied in the very conception of a current produced by difference of specific gravity.
But Maury speaks as if difference of specific gravity could give rise to a current without any descent.
“It is not necessary,” he says, “to associate with oceanic currents the idea that they must of necessity, as on land, run from a higher to a lower level. So far from this being the case, some currents of the sea actually run up hill, while others run on a level. The Gulf-stream is of the first class” (§ 403). “The top of the Gulf-stream runs on a level with the ocean; therefore we know it is not a descending current” (§ 18). And in § 9 he says that between the Straits of Florida and Cape Hatteras the waters of the Gulf-stream “are actually forced up an inclined plane, whose submarine ascent is not less than 10 inches to the mile.” To the same effect see §§ 25, 59.
It is perfectly true that “it is not necessary to associate with ocean-currents the idea that they must of necessity, as on land, run from a higher to a lower level.” But the reason of this is that ocean-currents do not, like the currents on land, owe their motion to the force of gravitation. If ocean-currents result from difference of specific gravity between the waters in tropical and polar regions, as Maury maintains, then it is necessary to assume that they are descending currents. Whatever be the cause which may give rise to a difference of specific gravity, the motion which results from this difference is due wholly to the force of gravity; but gravity can produce no motion unless the water descend.
This fact must be particularly borne in mind while we are considering Maury’s theory that currents are the result of difference of specific gravity.
Ocean-currents, then, according to that writer, owe their existence to the difference of specific gravity between the waters of inter-tropical and polar regions. This difference of specific gravity he attributes to two causes—(1) to difference as to temperature, (2) to difference as to saltness. There are one or two causes of a minor nature affecting the specific gravity of the sea, to which he alludes; but these two determine the general result. Let us begin with the consideration of the first of these two causes, viz.:—
Difference of Specific Gravity resulting from Difference of Temperature.—Maury explains his views on this point by means of an illustration. “Let us now suppose,” he says, “that all the water within the tropics, to the depth of one hundred fathoms, suddenly becomes oil. The aqueous equilibrium of the planet would thereby be disturbed, and a general system of currents and counter currents would be immediately commenced—the oil, in an unbroken sheet on the surface, running toward the poles, and the water, in an under current, toward the equator. The oil is supposed, as it reaches the polar basin, to be reconverted into water, and the water to become oil as it crosses Cancer and Capricorn, rising to the surface in inter-tropical regions, and returning as before” (§ 20). “Now,” he says (§ 22), “do not the cold waters of the north, and the warm waters of the Gulf, made specifically lighter by tropical heat, and which we see actually preserving such a system of counter currents, hold, at least in some degree, the relation of the supposed water and oil?”
In § 24 he calculates that at the Narrows of Bemini the difference in weight between the volume of the Gulf-water that crosses a section of the stream in one second, and an equal volume of water at the ocean temperature of the latitude, supposing the two volumes to be equally salt, is fifteen millions of pounds. Consequently the force per second operating to propel the waters of the Gulf towards the pole would in this case, he concludes, be the “equilibrating tendency due to fifteen millions of pounds of water in the latitude of Bemini.” In §§ 511 and 512 he states that the effect of expanding the waters at the torrid zone by heat, and of contracting the waters at the frigid zone by cold, is to produce a set of surface-currents of warm and light water from the equator towards the poles, and another set of under currents of cooler and heavy water from the poles towards the equator. (See also to the same effect §§ 513, 514, 896.)
There can be no doubt that his conclusion is that the waters in inter-tropical regions are expanded by heat, while those in polar regions are contracted by cold, and that this tends to produce a surface current from the equator to the poles, and an under current from the poles to the equator.
“We shall now consider his second great cause of ocean currents, viz.:—
Difference of Specific Gravity resulting from Difference in Degree of Saltness.—Maury maintains, and that correctly, that saltness increases the density of water—that, other things being equal, the saltest water is the densest. He suggests “that one of the purposes which, in the grand design, it was probably intended to accomplish by having the sea salt and not fresh, was to impart to its waters the forces and powers necessary to make their circulation complete” (§ 495).
Now it is perfectly obvious that if difference in saltness is to co-operate with difference in temperature in the production of ocean-currents, the saltest waters, and consequently the densest, must be in the polar regions, and the waters least salt, and consequently lightest, must be in equatorial and inter-tropical regions. Were the saltest waters at the equator, and the freshest at the poles, it would tend to neutralize the effect due to heat, and, instead of producing a current, would simply tend to prevent the existence of the currents which otherwise would result from difference of temperature.
A very considerable portion of his work, however, is devoted to proving that the waters of equatorial and inter-tropical regions are salter and heavier than those of the polar regions; and yet, notwithstanding this, he endeavours to show that this difference in respect to saltness between the waters of the equatorial and the polar regions is one of the chief causes, if not the chief cause, of ocean-currents. In fact, it is for this special end that so much labour is bestowed in proving that the saltest water is in the equatorial and inter-tropical regions, and the freshest in the polar.
“In the present state of our knowledge,” he says, “concerning this wonderful phenomenon (for the Gulf-stream is one of the most marvellous things in the ocean) we can do little more than conjecture. But we have two causes in operation which we may safely assume are among those concerned in producing the Gulf-stream. One of these is the increased saltness of its water after the trade-winds have been supplied with vapour from it, be it much or little; and the other is the diminished quantum of salt which the Baltic and the Northern Seas contain” (§ 37). “Now here we have, on one side, the Caribbean Sea and Gulf of Mexico, with their waters of brine; on the other, the great Polar Basin, the Baltic, and the North Sea, the two latter with waters that are but little more than brackish. In one set of these sea-basins the water is heavy, in the other it is light. Between them the ocean intervenes; but water is bound to seek and to maintain its level; and here, therefore, we unmask one of the agents concerned in causing the Gulf-stream” (§ 38). To the same effect see §§ 52, 522, 523, 524, 525, 526, 528, 530, 554, 556.
Lieut. Maury’s two causes neutralize each other. Here we have two theories put forth regarding the cause of ocean-currents, the one in direct opposition to the other. According to the one theory, ocean-currents exist because the waters of equatorial regions, in consequence of their higher temperature, are less dense than the waters of the polar regions; but according to the other theory, ocean-currents exist because the waters of equatorial regions, in consequence of their greater saltness, are more dense than the waters of the polar regions. If the one cause be assigned as a reason why ocean-currents exist, then the other can be equally assigned as a reason why they should not exist. According to both theories it is the difference of density between the equatorial and polar waters that gives rise to currents; but while the one theory maintains that the equatorial waters are lighter than the polar, the other holds that they are heavier. Either the one theory or the other may be true, or neither; but it is logically impossible that both of them can. Let it be observed that it is not two currents, the one contrary to the other, with which we have at present to do; it is not temperature producing currents in one direction, and saltness producing currents in the contrary direction. We have two theories regarding the origin of currents, the one diametrically opposed to the other. The tendency of the one cause assigned is to prevent the action of the other. If temperature is allowed to act, it will make the inter-tropical waters lighter than the polar, and then, according to theory, a current will result. But if we bring saltness into play (the other cause) it will do the reverse: it will increase the density of the inter-tropical waters and diminish the density of the polar; and so far as it acts it will diminish the currents produced by temperature, because it will diminish the difference of specific gravity between the inter-tropical and polar regions which had been previously caused by temperature. And when the effects of saltness are as powerful as those of temperature, the difference of specific gravity produced by temperature will be completely effaced, or, in other words, the waters of the equatorial and polar seas will be of the same density, and consequently no current will exist. And so long as the two causes continue in action, no current can arise, unless the energy of the one cause should happen to exceed that of the other; and even then a current will only exist to the extent by which the strength of the one exceeds that of the other.
The contrary nature of the two theories will be better seen by considering the way in which it is supposed that difference in saltness is produced and acts as a cause.
If there is a constant current resulting from the difference in saltness between the equatorial and polar waters, then there must be a cause which maintains this difference. The current is simply the effort to restore the equilibrium lost by the difference; and the current would very soon do this, and then all motion would cease, were there not a constantly operating cause maintaining the disturbance. What, then, according to Maury, is the cause of this disturbance, or, in other words, what is it that keeps the equatorial waters salter than the polar?
The agencies in operation are stated by him to be heat, radiation, evaporation, precipitation, and secretion of solid matter in the form of shells, &c. The two most important, however, are evaporation and precipitation.
The trade-winds enter the equatorial regions as relatively dry winds thirsting for vapour; consequently they absorb far more moisture than they give out; and the result is that in inter-tropical regions, evaporation is much in excess of precipitation; and as fresh water only is taken up, the salt being left behind, the process, of course, tends to increase the saltness of the inter-tropical seas. Again, in polar and extra-tropical regions the reverse is the case; precipitation is in excess of evaporation. This tends in turn to diminish the saltness of the waters of those regions. (See on these points §§ 31, 33, 34, 37, 179, 517, 526, and 552.)
In the system of circulation produced by difference of temperature, as we have already seen, the surface-currents flow from the equator to the poles, and the under or return currents from the poles to the equator; but in the system produced by difference of saltness, the surface currents flow from the poles to the equator, and the return under currents from the equator to the poles. That the surface currents produced by difference of saltness flow from the poles to the equator, Maury thinks is evident for the two following reasons:—
(1) As evaporation is in excess of precipitation in inter-tropical regions, more water is taken off the surface of the ocean in those regions than falls upon it in the form of rain. This excess of water falls in the form of rain on temperate and polar regions, where, consequently, precipitation is in excess of evaporation. The lifting of the water off the equatorial regions and its deposit on the polar tend to lower the level of the ocean in equatorial regions and to raise the level in polar; consequently, in order to restore the level of the ocean, the surface water at the polar regions flows towards the equatorial regions.
(2) As the water taken up at the equator is fresh, and the salt is left behind, the ocean, in inter-tropical regions, is thus made saltier and consequently denser. This dense water, therefore, sinks and passes away as an under current. This water, evaporated from inter-tropical regions, falls as fresh and lighter water in temperate and polar regions; and therefore not only is the level of the ocean raised, but the waters are made lighter. Hence, in order to restore equilibrium, the waters in temperate and polar regions will flow as a surface current towards the equator. Under currents will flow from the equator to the poles, and surface or upper currents from the poles to the equator. Difference in temperature and difference in saltness, therefore, in every respect tend to produce opposite effects.
That the above is a fair representation of the way in which Maury supposes difference in saltness to act as a cause in the production of ocean-currents will appear from the following quotations:—
“In those regions, as in the trade-wind region, where evaporation is in excess of precipitation, the general level of this supposed sea would be altered, and immediately as much water as is carried off by evaporation would commence to flow in from north and south toward the trade-wind or evaporation region, to restore the level” (§ 509). “On the other hand, the winds have taken this vapour, borne it off to the extra-tropical regions, and precipitated it, we will suppose, where precipitation is in excess of evaporation. Here is another alteration of sea-level, by elevation instead of by depression; and hence we have the motive power for a surface current from each pole towards the equator, the object of which is only to supply the demand for evaporation in the trade-wind regions” (§ 510).
The above result would follow, supposing the ocean to be fresh. He then proceeds to consider an additional result that follows in consequence of the saltness of the ocean.
“Let evaporation now commence in the trade-wind region, as it was supposed to do in the case of the freshwater seas, and as it actually goes on in nature—and what takes place? Why a lowering of the sea-level as before. But as the vapour of salt water is fresh, or nearly so, fresh water only is taken up from the ocean; that which remains behind is therefore more salt. Thus, while the level is lowered in the salt sea, the equilibrium is destroyed because of the saltness of the water; for the water that remains after evaporation takes place is, on account of the solid matter held in solution, specifically heavier than it was before any portion of it was converted into vapour” (§ 517).
“The vapour is taken from the surface-water; the surface-water thereby becomes more salt, and, under certain conditions, heavier. When it becomes heavier, it sinks; and hence we have, due to the salts of the sea, a vertical circulation, namely, a descent of heavier—because salter and cooler—water from the surface, and an ascent of water that is lighter—because it is not so salt—from the depths below” (§ 518).
In section 519 he goes on to show that this vapour removed from the inter-tropical region is precipitated in the polar regions, where precipitation is in excess of evaporation. “In the precipitating regions, therefore, the level is destroyed, as before explained, by elevation, and in the evaporating regions by depression; which, as already stated, gives rise to a system of surface currents, moved by gravity alone, from the poles towards the equator” (§ 520).
“This fresh water being emptied into the Polar Sea and agitated by the winds, becomes mixed with the salt; but as the agitation of the sea by the winds is supposed to extend to no great depth, it is only the upper layer of salt water, and that to a moderate depth, which becomes mixed with the fresh. The specific gravity of this upper layer, therefore, is diminished just as much as the specific gravity of the sea-water in the evaporating regions was increased. And thus we have a surface current of saltish water from the poles towards the equator, and an under current of water salter and heavier from the equator to the poles” (§ 522).
“This property of saltness imparts to the waters of the ocean another peculiarity, by which the sea is still better adapted for the regulation of climates, and it is this: by evaporating fresh water from the salt in the tropics, the surface water becomes heavier than the average of sea-water. This heavy water is also warm water; it sinks, and being a good retainer, but a bad conductor, of heat, this water is employed in transporting through under currents heat for the mitigation of climates in far distant regions” (§ 526).
“For instance, let us suppose the waters in a certain part of the torrid zone to be 90°, but by reason of the fresh water which has been taken from them in a state of vapour, and consequently, by reason of the proportionate increase of salts, these waters are heavier than waters that may be cooler, but not so salt. This being the case, the tendency would be for this warm but salt and heavy water to flow off as an under current towards the polar or some other regions of lighter water” (§ 554).
That Maury supposes the warm water at the equator to flow to the polar regions as an under current is further evident from the fact that he maintains that the climate of the arctic regions is mitigated by a warm under current, which comes from the equatorial regions, and passes up through Davis Straits (see §§ 534−544).
The question now suggests itself: to which of these two antagonistic causes does Maury really suppose ocean-currents must be referred? Whether does he suppose, difference in temperature or difference in saltness, to be the real cause? I have been unable to find anything from which we can reasonably conclude that he prefers the one cause to the other. It would seem that he regards both as real causes, and that he has failed to perceive that the one is destructive of the other. But it is difficult to conceive how he could believe that the sea in equatorial regions, by virtue of its higher temperature, is lighter than the sea in polar regions, while at the same time it is not lighter but heavier, in consequence of its greater saltness—how he could believe that the warm water at the equator flows to the poles as an upper current, and the cold water at the poles to the equator as an under current, while at the same time the warm water at the equator does not flow to the poles as a surface current, nor the cold water at the poles to the equator as an under current, but the reverse. And yet, unless these absolute impossibilities be possible, how can an ocean-current be the result of both causes?
The only explanation of the matter appears to be that Maury has failed to perceive the contradictory nature of his two theories. This fact is particularly seen when he comes to apply his two theories to the case of the Gulf-stream. He maintains, as has already been stated, that the waters of the Gulf-stream are salter than the waters of the sea through which they flow (see §§ 3, 28, 29, 30, 34, and several other places). And he states, as we have already seen (see p. 104), that the existence of the Gulf-stream is due principally to the difference of density of the water of the Caribbean Sea and the Gulf of Mexico as compared with that of the great Polar Basin and the North Sea. There can be no doubt whatever that it is the density of the waters of the Gulf-stream at its fountain-head, the Gulf of Mexico, resulting from its superior saltness, and the deficiency of density of the waters in polar regions and the North Sea, &c., that is here considered to be unmasked as one of the agents. If this be a cause of the motion of the Gulf-stream, how then can the difference of temperature between the waters of inter-tropical and polar regions assist as a cause? This difference of temperature will simply tend to undo all that has been done by difference of saltness: for it will tend to make the waters of the Gulf of Mexico lighter, and the waters of the polar regions heavier. But Maury maintains, as we have seen, that this difference of temperature is also a cause, which shows that he does not perceive the contradiction.
This is still further apparent. He holds, as stated, that “the waters of the Gulf-stream are salter than the waters of the sea through which they flow,” and that this excess in saltness, by making the water heavier, is a cause of the motion of the stream. But he maintains that, notwithstanding the effect which greater saltness has in increasing the density of the waters of the Gulf-stream, yet, owing to their higher temperature, they are actually lighter than the water through which they flow; and as a proof that this is the case, he adduces the fact that the surface of the Gulf-stream is roof-shaped (§§ 39−41), which it could not be were its waters not actually lighter than the waters through which the stream flows. So it turns out that, in contradiction to what he had already stated, it is the lesser density of the waters of the Gulf-stream that is the real cause of their motion. The greater saltness of the waters, to which he attributes so much, can in no way be regarded as a cause of motion. Its effect, so far as it goes, is to stop the motion of the stream rather than to assist it.
But, again, although he asserts that difference of saltness and difference of temperature are both causes of ocean-currents, yet he appears actually to admit that temperature and saltness neutralize each other so as to prevent change in the specific gravity of the ocean, as will be seen from the following quotation:—
“It is the trade-winds, then, which prevent the thermal and specific gravity curves from conforming with each other in inter-tropical seas. The water they suck up is fresh water; and the salt it contained, being left behind, is just sufficient to counterbalance, by its weight, the effect of thermal dilatation upon the specific gravity of sea-water between the parallels of 34° north and south. As we go from 34° to the equator, the water grows warmer and expands. It would become lighter; but the trade-winds, by taking up vapour without salt, make the water salter, and therefore heavier. The conclusion is, the proportion of salt in sea-water, its expansibility between 62° and 82°, and the thirst of the trade-winds for vapour are, where they blow, so balanced as to produce perfect compensation; and a more beautiful compensation cannot, it appears to me, be found in the mechanism of the universe than that which we have here stumbled upon. It is a triple adjustment; the power of the sun to expand, the power of the winds to evaporate, and the quantity of salts in the sea—these are so proportioned and adjusted that when both the wind and the sun have each played with its forces upon the inter-tropical waters of the ocean, the residuum of heat and of salt should be just such as to balance each other in their effects; and so the aqueous equilibrium of the torrid zone is preserved” (§ 436, eleventh edition).
“Between 35° or 40° and the equator evaporation is in excess of precipitation; and though, as we approach the equator on either side from these parallels, the solar ray warms and expands the surface-water of the sea, the winds, by the vapour they carry off, and the salt they leave behind, prevent it from making that water lighter” (§ 437, eleventh edition).
“Philosophers have admired the relations between the size of the earth, the force of gravity, and the strength of fibre in the flower-stalks of plants; but how much more exquisite is the system of counterpoises and adjustments here presented between the sea and its salts, the winds and the heat of the sun!” (§ 438, eleventh edition).
How can this be reconciled with all that precedes regarding ocean-currents being the result of difference of specific gravity caused by a difference of temperature and difference of saltness? Here is a distinct recognition of the fact that difference in saltness, instead of producing currents, tends rather to prevent the existence of currents, by counteracting the effects of difference in temperature. And so effectually does it do this, that for 40°, or nearly 3,000 miles, on each side of the equator there is absolutely no difference in the specific gravity of the ocean, and consequently nothing, either as regards difference of temperature or difference of saltness, that can possibly give rise to a current.
But it is evident that, if between the equator and latitude 40° the two effects completely neutralize each other, it is not at all likely that between latitude 40° and the poles they will not to a large extent do the same thing. And if so, how can ocean-currents be due either to difference in temperature or to difference in saltness, far less to both. If there be any difference of specific gravity of the ocean between latitude 40° and the poles, it must be only to the extent by which the one cause has failed to neutralize the other. If, for example, the waters in latitude 40°, by virtue of higher temperature, are less dense than the waters in the polar regions, they can be so only to the extent that difference in saltness has failed to neutralize the effect of difference in temperature. And if currents result, they can do so only to the extent that difference in saltness has thus fallen short of being able to produce complete compensation. Maury, after stating his views on compensation, seems to become aware of this; but, strangely, he does not appear to perceive, or, at least, he does not make any allusion to the fact, that all this is fatal to his theories about ocean-currents being the combined result of differences of temperature and of saltness. For, in opposition to all that he had previously advanced regarding the difficulty of finding a cause sufficiently powerful to account for such currents as the Gulf-stream, and the great importance that difference in saltness had in their production, he now begins to maintain that so great is the influence of difference in temperature that difference in saltness, and a number of other compensating causes are actually necessary to prevent the ocean-currents from becoming too powerful.
“If all the inter-tropical heat of the sun,” he says, “were to pass into the seas upon which it falls, simply raising the temperature of their waters, it would create a thermo-dynamical force in the ocean capable of transporting water scalding hot from the torrid zone, and spreading it while still in the tepid state around the poles.... Now, suppose there were no trade-winds to evaporate and to counteract the dynamical force of the sun, this hot and light water, by becoming hotter and lighter, would flow off in currents with almost mill-tail velocity towards the poles, covering the intervening sea with a mantle of warmth as a garment. The cool and heavy water of the polar basin, coming out as under currents, would flow equatorially with equal velocity.”
“Thus two antagonistic forces are unmasked, and, being unmasked, we discover in them a most exquisite adjustment—a compensation—by which the dynamical forces that reside in the sunbeam and the trade-wind are made to counterbalance each other, by which the climates of inter-tropical seas are regulated, and by which the set, force, and volume of oceanic currents are measured” (§§ 437 and 438, eleventh edition).
Chapter VII
EXAMINATION OF THE GRAVITATION THEORY OF OCEANIC CIRCULATION.—LIEUT. MAURY’S THEORY (continued).
Methods of determining the Question.—The Force resulting from Difference of Specific Gravity.—Sir John Herschel’s Estimate of the Force.—Maximum Density of Sea-Water.—Rate of Decrease of Temperature of Ocean at Equator.—-The actual Amount of Force resulting from Difference of Specific Gravity.—M. Dubuat’s Experiments.
How the Question may be Determined.—Whether the circulation of the ocean is due to difference in specific gravity or not may be determined in three ways: viz. (1) by direct experiment; (2) by ascertaining the absolute amount of force acting on the water to produce motion, in virtue of difference of specific gravity, and thereafter comparing it with the force which has been shown by experiment to be necessary to the production of sensible motion; or (3) by determining the greatest possible amount of work which gravity can perform on the waters in virtue of difference of specific gravity, and then ascertaining if the work of gravity does or does not equal the work of the resistances in the required motion. But Maury has not adopted either of these methods.
The Force resulting from Difference of Specific Gravity.—I shall consider first whether the force resulting from difference of specific gravity be sufficient to account for the motion of ocean-currents.
The inadequacy of this cause has been so clearly shown by Sir John Herschel, that one might expect that little else would be required than simply to quote his words on the subject, which are as follows:—
“First, then, if there were no atmosphere, there would be no Gulf-stream, or any other considerable ocean-current (as distinguished from a mere surface-drift) whatever. By the action of the sun’s rays, the surface of the ocean becomes most heated, and the heated water will, therefore, neither directly tend to ascend (which it could not do without leaving the sea) nor to descend, which it cannot do, being rendered buoyant, nor to move laterally, no lateral impulse being given, and which it could only do by reason of a general declivity of surface, the dilated portion occupying a higher level. Let us see what this declivity would amount to. The equatorial surface-water has a temperature of 84°. At 7,200 feet deep the temperature is 39°, the level of which temperature rises to the surface in latitude 56°. Taking the dilatability of sea-water to be the same as that of fresh, a uniformly progressive increase of temperature, from 39° to 84° Fahr., would dilate a column of 7,200 feet by 10 feet, to which height, therefore, above the spheroid of equilibrium (or above the sea-level in lat. 56°), the equatorial surface is actually raised by dilatation. An arc of 56° on the earth’s surface measures 3,360 geographical miles; so that we have a slope of 1/28th of an inch per geographical mile, or 1/32nd of an inch per statute mile for the water so raised to run down. As the accelerating force corresponding to such a slope (of 1/10th of a second, 0″·1) is less than one two-millionth part of gravity, we may dismiss this as a cause capable of creating only a very trifling surface-drift, and not worth considering, even were it in the proper direction to form, by concentration, a current from east to west, which it could not be, but the very reverse.”[55]
It is singular how any one, even though he regarded this conclusion as but a rough approximation to the truth, could entertain the idea that ocean-currents can be the result of difference in specific gravity. There are one or two reasons, however, which may be given for the above not having been generally received as conclusive. Herschel’s calculations refer to the difference of gravity resulting from difference of temperature; but this is only one of the causes to which Maury appeals, and even not the one to which he most frequently refers. He insists so strongly on the effects of difference of saltness, that many might think that, although Herschel may have shown that difference in specific gravity arising from difference of temperature could not account for the motion of ocean-currents, yet nevertheless that this, combined with the effects resulting from difference in saltness, might be a sufficient explanation of the phenomena. Such, of course, would not be the case with those who perceived the contradictory nature of Maury’s two causes; but probably many read the “Physical Geography of the Sea” without being aware that the one cause is destructive of the other. Again, a few plausible objections, which have never received due consideration, have been strongly urged by Maury and others against the theory that ocean-currents can be caused by the impulses of the winds; and probably these objections appear to militate as strongly against this theory as Herschel’s arguments against Maury’s.
There is one trifling objection to Herschel’s result: he takes 39° as the temperature of maximum density. This, however, as we shall see, does not materially affect his conclusions.
Observations on the temperature of the maximum density of sea-water have been made by Erman, Despretz, Rossetti, Neumann, Marcet, Hubbard, Horner, and others. No two of them have arrived at exactly the same conclusion. This probably arises from the fact that the temperature of maximum density depends upon the amount of salt held in solution. No two seas, unless they are equal as to saltness, have the same temperature of maximum density. The following Table of Despretz will show how rapidly the temperature of both the freezing-point and of maximum density is lowered by additional amounts of salt:—
+-----------+-----------------+------------------+ | Amount | Temperature of | Temperature of | | of salt. | freezing-point. | Maximum density. | +-----------+-----------------+------------------+ | | ° | ° | | 0·000123 | −1·21 C. | + 1·19 C. | | 0·0246 | −2·24 | − 1·69 | | 0·0371 | −2·77 | − 4·75 | | 0·0741 | −5·28 | −16·00 | +-----------+-----------------+------------------+
He found the temperature of maximum density of sea-water, whose density at 20°C. was 1·0273, to be −3°·67C. (25°·4F.), and the temperature of freezing-point −2°·55C. (27°·4F.).[56] Somewhere between 25° and 26° F. may therefore be regarded as the temperature of maximum density of sea-water of average saltness. We have no reason to believe that the ocean, from the surface to the bottom, even at the poles, is at 27°·4F., the freezing-point.
The actual slope resulting from difference of specific gravity, as we shall presently see, does not amount to 10 feet. Herschel’s estimate was, however, made on insufficient data, both as to the rate of expansion of sea-water and that at which the temperature of the ocean at the equator decreases from the surface downwards. We are happily now in the possession of data for determining with tolerable accuracy the amount of slope due to difference of temperature between the equatorial and polar seas. The rate of expansion of sea-water from 0°C. to 100°C. has been experimentally determined by Professor Muncke, of Heidelberg.[57] The valuable reports of Captain Nares, of H.M.S. Challenger, lately published by the Admiralty, give the rate at which the temperature of the Atlantic at the equator decreases from the surface downwards. These observations show clearly that the super-heating effect of the sun’s rays does not extend to any great depth. They also prove that at the equator the temperature decreases as the depth increases so rapidly that at 60 fathoms from the surface the temperature is 62°·4, the same as at Madeira at the same depth; while at the depth of 150 fathoms it is only 51°, about the same as that in the Bay of Biscay (Reports, p. 11). Here at the very outset we have broad and important facts hostile to the theory of a flow of water resulting from difference of temperature between the ocean in equatorial and temperate and polar regions.
Through the kindness of Staff-Captain Evans, Hydrographer of the Admiralty, I have been favoured with a most valuable set of serial temperature soundings made by Captain Nares of the Challenger, close to the equator, between long. 14° 49′ W. and 32° 16′ W. The following Table represents the mean of the whole of these observations:—
+----------+-------------+ | Fathoms. | Temperature.| +----------+-------------+ | | ° | | Surface. | 77·9 | | 10 | 77·2 | | 20 | 77·1 | | 30 | 76·9 | | 40 | 71·7 | | 50 | 64·0 | | 60 | 60·4 | | 70 | 59·4 | | 80 | 58·0 | | 90 | 58·0 | | 100 | 55·6 | | 150 | 51·0 | | 200 | 46·6 | | 300 | 42·2 | | 400 | 40·3 | | 500 | 38·9 | | 600 | 39·2 | | 700 | 39·0 | | 800 | 39·1 | | 900 | 38·2 | | 1000 | 36·9 | | 1100 | 37·6 | | 1200 | 36·7 | | 1300 | 35·8 | | 1400 | 36·4 | | 1500 | 36·1 | | Bottom. | 34·7 | +----------+-------------+
We have in this Table data for determining the height at which the surface of the ocean at the equator ought to stand above that of the poles. Assuming 32°F. to be the temperature of the ocean at the poles from the surface to the bottom and the foregoing to be the rate at which the temperature of the ocean at the equator decreases from the surface downwards, and then calculating according to Muncke’s Table of the expansion of sea-water, we have only 4 feet 6 inches as the height to which the level of the ocean at the equator ought to stand above that at the poles in order that the ocean may be in static equilibrium. In other words, the equatorial column requires to be only 4 feet 6 inches higher than the polar in order that the two may balance each other.
Taking the distance from the equator to the poles at 6,200 miles, the force resulting from the slope of 4½ feet in 6,200 will amount to only 1/7,340,000th that of gravity, or about 1/1000th of a grain on a pound of water. But, as we shall shortly see, there can be no permanent current resulting from difference of temperature while the two columns remain in equilibrium, for the current is simply an effort to the retardation of equilibrium. In order to have permanent circulation there must be a permanent disturbance of equilibrium. Or, in other words, the weight of the polar column must be kept in excess of that of the equatorial. Suppose, then, that the weight of the polar column exceeds that of the equatorial by 2 feet of water, the difference of level between the two columns will, in that case, amount to only 2 feet 6 inches. This would give a force of only 1/13,200,000th that of gravity, or not much over 1/1,900th of a grain on a pound of water, tending to draw the water down the slope from the equator to the poles, a force which does not much exceed the weight of a grain on a ton of water. But it must be observed that this force of a grain per ton would affect only the water at the surface; a very short distance below the surface the force, small as it is, would be enormously reduced. If water were a perfect fluid, and offered no resistance to motion, it would not only flow down an incline, however small it might be, but would flow down with an accelerated motion. But water is not a perfect fluid, and its molecules do offer considerable resistance to motion. Water flowing down an incline, however steep it may be, soon acquires a uniform motion. There must therefore be a certain inclination below which no motion can take place. Experiments were made by M. Dubuat with the view of determining this limit.[58] He found that when the inclination was 1 in 500,000, the motion of the water was barely perceptible; and he came to the conclusion that when the inclination is reduced to 1 in 1,000,000, all motion ceases. But the inclination afforded by the difference of temperature between the sea in equatorial and polar regions does not amount to one-seventh of this, and consequently it can hardly produce even that “trifling surface-drift” which Sir John Herschel is willing to attribute to it.
There is an error into which some writers appear to fall to which I may here refer. Suppose that at the equator we have to descend 10,000 feet before water equal in density to that at the poles is reached. We have in this case a plain with a slope of 10,000 feet in 6,200 miles, forming the upper surface of the water of maximum density. Now this slope exercises no influence in the way of producing a current, as some seem to think; for it is not a case of disturbed equilibrium, but the reverse. It is the condition of static equilibrium resulting from a difference between the temperature of the water at the equator and the poles. The only slope that has any tendency to produce motion is that which is formed by the surface of the ocean in the equatorial regions being higher than the surface at the poles; but this is an inclination of only 4 feet 6 inches, and is therefore wholly inadequate to produce such currents as the Gulf-stream.
Chapter VIII
EXAMINATION OF THE GRAVITATION THEORY OF OCEANIC CIRCULATION.—DR. CARPENTER’S THEORY.
Gulf-stream according to Dr. Carpenter not due to Difference of Specific Gravity.—Facts to be Explained.—The Explanation of the Facts.—The Explanation hypothetical.—The Cause assigned for the hypothetical Mode of Circulation.—Under currents account for all the Facts better than the Gravitation Hypothesis.—Known Condition of the Ocean inconsistent with that Hypothesis.
Dr. Carpenter does not suppose, with Lieut. Maury, that the difference of temperature between the ocean in equatorial and polar regions can account for the Gulf-stream and other great currents of the ocean. He maintains, however, that this difference is quite sufficient to bring about a slow general interchange of water between the polar and inter-tropical areas—to induce a general movement of the upper portion of the ocean from the equator to the poles and a counter-movement of the under portion in a contrary direction. It is this general movement which, according to that author, is the great agent by which heat is distributed over the globe.[59]
In attempting to estimate the adequacy of this hypothesis as an explanation of the phenomena involved, there are obviously two questions to be considered: namely, (1) is the difference of temperature between the sea in inter-tropical and polar regions sufficiently great to produce the required movement? and (2) assuming that there is such a movement, does it convey the amount of heat which Dr. Carpenter supposes? I shall begin with the consideration of the first of these two points.
But before doing so let us see what the facts are which this gravitation theory is intended to explain.
The Facts to be Explained.—Dr. Carpenter considers that the great mass of warm water proved during recent dredging expeditions to occupy the depths of the North Atlantic, must be referred, not to the Gulf-stream, but to a general movement of water from the equator. “The inference seems inevitable,” he says, “that the bulk of the water in the warm area must have come thither from the south-west. The influence of the Gulf-stream proper (meaning by this the body of super-heated water which issues through the ‘Narrows’ from the Gulf of Mexico), if it reaches this locality at all (which is very doubtful), could only affect the most superficial stratum; and the same may be said of the surface-drift caused by the prevalence of south-westerly winds, to which some have attributed the phenomena usually accounted for by the extension of the Gulf-stream to these regions. And the presence of the body of water which lies between 100 and 600 fathoms deep, and the range of whose temperature is from 48° to 42°, can scarcely be accounted for on any other hypothesis than that of a great general movement of equatorial water towards the polar area, of which movement the Gulf-stream constitutes a peculiar case modified by local conditions. In like manner the Arctic stream which underlies the warm superficial stratum in our cold area constitutes a peculiar case, modified by the local conditions to be presently explained, of a great general movement of polar water towards the equatorial area, which depresses the temperature of the deepest parts of the great oceanic basins nearly to the freezing-point.”
It is well-known that, wherever temperature-observations have been made in the Atlantic, the bottom of that ocean has been found to be occupied by water of an ice-cold temperature. And this holds true not merely of the Atlantic, but also of the ocean in inter-tropical regions—a fact which has been proved by repeated observations, and more particularly of late by those of Commander Chimmo in the China Sea and Indian Ocean, where a temperature as low as 32° Fahr. was found at a depth of 2,656 fathoms. In short, the North Atlantic, and probably the inter-tropical seas also, may be regarded, Dr. Carpenter considers, as divided horizontally into two great layers or strata—an upper warm, and a lower cold stratum. All these facts I, of course, freely admit; nor am I aware that their truth has been called in question by any one, no matter what his views may have been as to the mode in which they are to be explained.
The Explanation of the Facts.—We have next the explanation of the facts, which is simply this:—The cold water occupying the bottom of the Atlantic and of inter-tropical seas is to be accounted for by the supposition that it came from the polar regions. This is obvious, because the cold possessed by the water could not have been derived from the crust of the earth beneath: neither could it have come from the surface; for the temperature of the bottom water is far below the normal temperature of the latitude in which it is found. Consequently “the inference seems irresistible that this depression must be produced and maintained by the convection of cold from the polar towards the equatorial area.” Of course, if we suppose a flow of water from the poles towards the equator, we must necessarily infer a counter flow from the equator towards the poles; and while the water flowing from equatorial to polar regions will be warm, that flowing from polar to equatorial regions will be cold. The doctrine of a mutual interchange of equatorial and polar water is therefore a necessary consequence from the admission of the foregoing facts. With this explanation of the facts I need hardly say that I fully agree; nor am I aware that its correctness has ever been disputed. Dr. Carpenter surely cannot charge me with overlooking the fact of a mutual interchange of equatorial and polar water, seeing that my estimate of the thermal power of the Gulf-stream, from which it is proved that the amount of heat conveyed from equatorial to temperate and polar regions is enormously greater than had ever been anticipated, was made a considerable time before he began to write on the subject of oceanic circulation.[60] And in my paper “On Ocean-currents in relation to the Distribution of Heat over the Globe”[61] (the substance of which is reproduced in Chapters II. and III. of this volume), I have endeavoured to show that, were it not for the raising of the temperature of polar and high temperate regions and the lowering of the temperature of inter-tropical regions by means of this interchange of water, these portions of the globe would not be habitable by the present existing orders of beings.
The explanation goes further:—“It is along the surface and upper portion of the ocean that the equatorial waters flow towards the poles, and it is along the bottom and under portion of the ocean that polar waters flow towards the equator; or, in other words, the warm water keeps the upper portion of the ocean and the cold water the under portion.” With this explanation I to a great extent agree. It is evident that, in reference to the northern hemisphere at least, the most of the water which flows from inter-tropical to polar regions (as, for example, the Gulf-stream) keeps to the surface and upper portion of the ocean; but for reasons which I have already stated, a very large proportion of this water must return in the form of under currents; or, which is the same thing, the return compensating current, whether it consist of the identical water which originally came from the equator or not, must flow towards the equator as an under current. That the cold water which is found at the bottom of the Atlantic and of inter-tropical seas must have come as under currents is perfectly obvious, because water which should come along the surface of the ocean from the polar regions would not be cold when it reached inter-tropical regions.
The Explanation hypothetical.—Here the general agreement between us in a great measure terminates, for Dr. Carpenter is not satisfied with the explanation generally adopted by the advocates of the wind theory, viz., that the cold water found in temperate and inter-tropical areas comes from polar regions as compensating under currents, but advances a hypothetical form of circulation to account for the phenomenon. He assumes that there is a general set or flow of the surface and upper portion of the ocean from the equator to polar regions, and a general set or flow of the bottom and under portion of the ocean from polar regions to the equator. Mr. Ferrel (Nature, June 13, 1872) speaks of that “interchanging motion of the water between the equator and the pole discovered by Dr. Carpenter.” In this, however, Mr. Ferrel is mistaken; for Dr. Carpenter not only makes no claim to any discovery of the kind, but distinctly admits that none such has yet been made. Although in some of his papers he speaks of a “set of warm surface-water in the southern oceans toward the Antarctic pole” as being well known to navigators, yet he nowhere affirms, as far as I know, that the existence of such a general oceanic circulation as he advocates has ever been directly determined from observations. This mode of circulation is simply inferred or assumed in order to account for the facts referred to above. “At present,” Dr. Carpenter says, “I claim for it no higher character than that of a good working hypothesis to be used as a guide in further inquiry” (§ 16); and lest there should be any misapprehension on this point, he closes his memoir thus:—“At present, as I have already said, I claim for the doctrine of a general oceanic circulation no higher a character than that of a good working hypothesis consistent with our present knowledge of facts, and therefore entitled to be provisionally adopted for the purpose of stimulating and directing further inquiry.”
I am unable to agree with him, however, on this latter point. It seems to me that there is no necessity for adopting any hypothetical mode of circulation to account for the facts, as they can be quite well accounted for by means of that mode of circulation which does actually exist. It has been determined from direct observation that surface-currents flow from equatorial to polar regions, and their paths have been actually mapped out. But if it is established that currents flow from equatorial to polar regions, it is equally so that return currents flow from polar to equatorial regions; for if the one actually exists, the other of necessity must exist. We know also on physical grounds, to which I have already referred, and which fall to be considered more fully in a subsequent chapter, that a very large portion of the water flowing from polar to equatorial regions must be in the form of under currents. If there are cold under currents, therefore, flowing from polar to temperate and equatorial regions, this is all that we really require to account for the cold water which is found to occupy the bed of the ocean in those regions. It does not necessarily follow, because cold water may be found at the bottom of the ocean all along the equator, that there must be a direct flow from the polar regions to every point of the equator. Water brought constantly from the polar regions to various points along the equator by means of under currents will necessarily accumulate, and in course of time spread over the bottom of the inter-tropical seas. It must either do this, or the currents on reaching the equator must bend upwards and flow to the surface in an unbroken mass. Considerable portions of some of those currents may no doubt do so and join surface-currents; but probably the greater portion of the water coming from polar regions extends itself over the floor of the equatorial seas. In a letter in Nature, January 11, 1872, I endeavoured to show that the surface-currents of the ocean are not separate and independent of one another, but form one grand system of circulation, and that the impelling cause keeping up this system of circulation is not the trade-winds alone, as is generally supposed, but the prevailing winds of the entire globe considered also as one grand system. The evidence for this opinion, however, will be considered more fully in the sequel.
Although the under currents are parts of one general system of oceanic circulation produced by the impulse of the system of prevailing winds, yet their direction and position are nevertheless, to a large extent, determined by different laws. The water at the surface, being moved by the force of the wind, will follow the path of greatest pressure and traction,—the effects resulting from the general contour of the land, which to a great extent are common to both sets of currents, not being taken into account; while, on the other hand, the under currents from polar regions (which to a great extent are simply “indraughts” compensating for the water drained from equatorial regions by the Gulf-stream and other surface currents) will follow, as a general rule, the path of least resistance.
The Cause assigned for the Hypothetical Mode of Circulation.—Dr. Carpenter assigns a cause for his mode of circulation; and that cause he finds in the difference of specific gravity between equatorial and polar waters, resulting from the difference of temperature between these two regions. “Two separate questions,” he says, “have to be considered, which have not, perhaps, been kept sufficiently distinct, either by Mr. Croll or by myself;—first, whether there is adequate evidence of the existence of a general vertical oceanic circulation; and second, whether, supposing its existence to be provisionally admitted, a vera causa can be found for it in the difference of temperature between the oceanic waters of the polar and equatorial areas” (§ 17). It seems to me that the facts adduced by Dr. Carpenter do not necessarily require the assumption of any such mode of circulation as that advanced by him. The phenomena can be satisfactorily accounted for otherwise; and therefore there does not appear to be any necessity for considering whether his hypothesis be sufficient to produce the required effect or not.
An important Consideration overlooked.—But there is one important consideration which seems to have been overlooked—namely, the fact that the sea is salter in inter-tropical than in polar regions, and that this circumstance, so far as it goes, must tend to neutralize the effect of difference of temperature. It is probable, indeed, that the effect produced by difference of temperature is thus entirely neutralized, and that no difference of density whatever exists between the sea in inter-tropical and polar regions, and consequently that there is no difference of level nor anything to produce such a general motion as Dr. Carpenter supposes. This, I am glad to find, is the opinion of Professor Wyville Thomson.
“I am greatly mistaken,” says that author, “if the low specific gravity of the polar sea, the result of the condensation and precipitation of vapour evaporated from the inter-tropical area, do not fully counterbalance the contraction of the superficial film by arctic cold.... Speaking in the total absence of all reliable data, it is my general impression that if we were to set aside all other agencies, and to trust for an oceanic circulation to those conditions only which are relied upon by Dr. Carpenter, if there were any general circulation at all, which seems very problematical, the odds are rather in favour of a warm under current travelling northwards by virtue of its excess of salt, balanced by a surface return current of fresher though colder arctic water.”[62]
This is what actually takes place on the west and north-west of Spitzbergen. There the warm water of the Gulf-stream flows underneath the cold polar current. And it is the opinion of Dr. Scoresby, Mr. Clements Markham, and Lieut. Maury that this warm water, in virtue of its greater saltness, is denser than the polar water. Mr. Leigh Smith found on the north-west of Spitzbergen the temperature at 500 fathoms to be 52°, and once even 64°, while the water on the surface was only a degree or two above freezing.[63] Mr. Aitken, of Darroch, in a paper lately read before the Royal Scottish Society of Arts, showed experimentally that the polar water in regions where the ice is melting is actually less dense than the warm and more salt tropical waters. Nor will it help the matter in the least to maintain that difference of specific gravity is not the reason why the warm water of the Gulf-stream passes under the polar stream—because if difference of specific gravity be not the cause of the warm water underlying the cold water in polar regions, then difference of specific gravity may likewise not be the cause of the cold water underlying the warm at the equator; and if so, then there is no necessity for the gravitation hypothesis of oceanic circulation.
There is little doubt that the super-heated stratum at the surface of the inter-tropical seas, which stratum, according to Dr. Carpenter, is of no great thickness, is less dense than the polar water: but if we take a column extending from the surface down to the bottom of the ocean, this column at the equator will be found to be as heavy as one of equal length in the polar area. And if this be the case, then there can be no difference of level between the equator and the poles, and no disturbance of static equilibrium nor anything else to produce circulation.
Under Currents account for all the Facts better than Dr. Carpenter’s Hypothesis.—Assuming, for the present, the system of prevailing winds to be the true cause of oceanic currents, it necessarily follows (as will be shown hereafter) that a large quantity of Atlantic water must be propelled into the Arctic Ocean; and such, as we know, is actually the case. The Arctic Ocean, however, as Professor Wyville Thomson remarks, is a well-nigh closed basin, not permitting of a free outflow into the Pacific Ocean of the water impelled into it.
But it is evident that the water which is thus being constantly carried from the inter-tropical to the arctic regions must somehow or other find its way back to the equator; in other words, there must be a return current equal in magnitude to the direct current. Now the question to be determined is, what path must this return current take? It appears to me that it will take the path of least resistance, whether that path may happen to be at the surface or under the surface. But that the path of least resistance will, as a general rule, lie at a very considerable distance below the surface is, I think, evident from the following considerations. At the surface the general direction of the currents is opposite to that of the return current. The surface motion of the water in the Atlantic is from the equator to the pole; but the return current must be from the pole to the equator. Consequently the surface currents will oppose the motion of any return current unless that current lie at a considerable depth below the surface currents. Again, the winds, as a general rule, blow in an opposite direction to the course of the return current, because, according to supposition, the winds blow in the direction of the surface currents. From all these causes the path of least resistance to the return current will, as a general rule, not be at the surface, but at a very considerable depth below it.
A large portion of the water from the polar regions no doubt leaves those regions as surface currents; but a surface current of this kind, on meeting with some resistance to its onward progress along the surface, will dip down and continue its course as an under current. We have an example of this in the case of the polar current, which upon meeting the Gulf-stream on the banks of Newfoundland divides—a portion of it dipping down and pursuing its course underneath that stream into the Gulf of Mexico and the Caribbean Sea. And that this under current is a real and tangible current, in the proper sense of the term, and not an imperceptible movement of the water, is proved by the fact that large icebergs deeply immersed in it are often carried southward with considerable velocity against the united force of the wind and the Gulf-stream.
Dr. Carpenter refers at considerable length (§ 134) to Mr. Mitchell’s opinion as to the origin of the polar current, which is the same as that advanced by Maury, viz., that the impelling cause is difference of specific gravity. But although Dr. Carpenter quotes Mr. Mitchell’s opinion, he nevertheless does not appear to adopt it: for in §§ 90−93 and various other places he distinctly states that he does not agree with Lieut. Maury’s view that the Gulf-stream and polar current are caused by difference of density. In fact, Dr. Carpenter seems particularly anxious that it should be clearly understood that he dissents from the theory maintained by Maury. But he does not merely deny that the Gulf-stream and polar current can be caused by difference of density; he even goes so far as to affirm that no sensible current whatever can be due to that cause, and adduces the authority of Sir John Herschel in support of that opinion:—“The doctrine of Lieut. Maury,” he says, “was powerfully and convincingly opposed by Sir John Herschel; who showed, beyond all reasonable doubt, first, that the Gulf-stream really has its origin in the propulsive force of the trade-winds, and secondly, that the greatest disturbance of equilibrium which can be supposed to result from the agencies invoked by Lieut. Maury would be utterly inadequate to generate and maintain either the Gulf-stream or any other sensible current” (§ 92). This being Dr. Carpenter’s belief, it is somewhat singular that he should advance the case of the polar current passing under the Gulf-stream as evidence in favour of his theory; for in reality he could hardly have selected a case more hostile to that theory. In short, it is evident that, if a polar current impelled by a force other than that of gravity can pass from the banks of Newfoundland to the Gulf of Mexico (a distance of some thousands of miles) under a current flowing in the opposite direction and, at the same time, so powerful as the Gulf-stream, it could pass much more easily under comparatively still water, or water flowing in the same direction as itself. And if this be so, then all our difficulties disappear, and we satisfactorily explain the presence of cold polar water at the bottom of inter-tropical seas without having recourse to the hypothesis advanced by Dr. Carpenter.
But we have an example of an under current more inexplicable on the gravitation hypothesis than even that of the polar current, viz., the warm under current of Davis Strait.
There is a strong current flowing north from the Atlantic through Davis Strait into the Arctic Ocean underneath a surface current passing southwards in an opposite direction. Large icebergs have been seen to be carried northwards by this under current at the rate of four knots an hour against both the wind and the surface current, ripping and tearing their way with terrific force through surface ice of great thickness.[64] A current so powerful and rapid as this cannot, as Dr. Carpenter admits, be referred to difference of specific gravity. But even supposing that it could, still difference of temperature between the equatorial and polar seas would not account for it; for the current in question flows in the wrong direction. Nor will it help the matter the least to adopt Maury’s explanation, viz., that the warm under current from the south, in consequence of its greater saltness, is denser than the cold one from the polar regions. For if the water of the Atlantic, notwithstanding its higher temperature, is in consequence of its greater saltness so much denser than the polar water on the west of Greenland as to produce an under current of four knots an hour in the direction of the pole, then surely the same thing to a certain extent will hold true in reference to the ocean on the east side of Greenland. Thus instead of there being, as Dr. Carpenter supposes, an underflow of polar water south into the Atlantic in virtue of its greater density, there ought, on the contrary, to be a surface flow in consequence of its lesser density.
The true explanation no doubt is, that the warm under current from the south and the cold upper current from the north are both parts of one grand system of circulation produced by the winds, difference of specific gravity having no share whatever either in impelling the currents, or in determining which shall be the upper and which the lower.
The wind in Baffin’s Bay and Davis Strait blows nearly always in one direction, viz. from the north. The tendency of this is to produce a surface or upper current from the north down into the Atlantic, and to prevent or retard any surface current from the south. The warm current from the Atlantic, taking the path of least resistance, dips under the polar current and pursues its course as an under current.
Mr. Clements Markham, in his “Threshold of the Unknown Region,” is inclined to attribute the motion of the icebergs to tidal action or to counter under currents. That the motion of the icebergs cannot reasonably be attributed to the tides is, I think, evident from the descriptions given both by Midshipman Griffin and by Captain Duncan, who distinctly saw the icebergs moving at the rate of about four knots an hour against a surface current flowing southwards. And Captain Duncan states that the bergs continued their course northwards for several days, till they ultimately disappeared. The probability is that this northward current is composed partly of Gulf-stream water and partly of that portion of polar water which is supposed to flow round Cape Farewell from the east coast of Greenland. This stream, composed of both warm and cold water, on reaching to about latitude 65°N., where it encounters the strong northerly winds, dips down under the polar current and continues its northward course as an under current.
We have on the west of Spitzbergen, as has already been noticed, a similar example of a warm current from the south passing under a polar current. A portion of the Gulf-stream which passes round the west coast of Spitzbergen flows under an arctic current coming down from the north; and it does so no doubt because it is here in the region of prevailing northerly winds, which favour the polar current but oppose the Gulf-stream. Again, we have a cold and rapid current sweeping round the east and south of Spitzbergen, a current of which Mr. Lamont asserts that he is positive he has seen it running at the rate of seven or eight miles an hour. This current, on meeting the Gulf-stream about the northern entrance to the German Ocean, dips down under that stream and pursues its course southwards as an under current.
Several other cases of under currents might be adduced which cannot be explained on the gravitation theory, and which must be referred to a system of oceanic circulation produced by the impulse of the wind; but these will suffice to show that the assumption that the winds can produce only a mere surface-drift is directly opposed to facts. And it will not do to affirm that a current which forms part of a general system of circulation produced by the impulse of the winds cannot possibly be an under current; for in the case referred to we have proof that the thing is not only possible but actually exists. This point, however, will be better understood after we have considered the evidence in favour of a general system of oceanic currents.
Much of the difficulty experienced in comprehending how under currents can be produced by the wind, or how an impulse imparted to the surface of the ocean can ever be transmitted to the bottom, appears to me to result, to a considerable extent at least, from a slight deception of the imagination. The thing which impresses us most forcibly in regard to the ocean is its profound depth. A mean depth of, say, three miles produces a striking impression; but if we could represent to the mind the vast area of the ocean as correctly as we can its depth, shallowness rather than depth would be the impression produced. If in crossing a meadow we found a sheet of water one hundred yards in diameter and only an inch in depth, we should not call that a deep, but a very shallow pool. The probability is that we should speak of it as simply a piece of ground covered with a thin layer of water. Yet such a thin layer of water would be a correct representation in miniature of the ocean; for the ocean in relation to its superficial area is as shallow as the pool of our illustration. In reference to such a pool or thin film of water, we have no difficulty in conceiving how a disturbance on its surface would be transmitted to its bottom. In fact our difficulty is in conceiving how any disturbance extending over its entire surface should not extend to the bottom. Now if we could form as accurate a sensuous impression of the vast area of the ocean as we do of such a pool, all our difficulty in understanding how the impulses of the wind acting on the vast area of the ocean should communicate motion down to its bottom would disappear. It is certainly true that sudden commotions caused by storms do not generally extend to great depths. Neither will winds of short continuance produce a current extending far below the surface. But prevailing winds which can produce such immense surface-flow as that of the great equatorial currents of the globe and the Gulf-stream, which follow definite directions, must communicate their motion to great depths, unless water be frictionless, a thing which it is not. Suppose the upper layer of the ocean to be forced on by the direct action of the winds with a constant velocity of, say, four miles an hour, the layer immediately below will be dragged along with a constant velocity somewhat less than four miles an hour. The layer immediately below this second layer will in turn be also dragged along with a constant velocity somewhat less than the one above it. The same will take place in regard to each succeeding layer, the constant velocity of each layer being somewhat less than the one immediately above it, and greater than the one below it. The question to be determined is, at what depth will all motion cease? I presume that at present we have not sufficient data for properly determining this point. The depth will depend, other things being equal, upon the amount of molecular resistance offered by the water to motion—in other words, on the amount of the shearing-force of the one layer over the other. The fact, however, that motion imparted to the surface will extend to great depths can be easily shown by direct experiment. If a constant motion be imparted to the surface of water, say, in a vessel, motion will ultimately be communicated to the bottom, no matter how wide or how deep the vessel may be. The same effect will take place whether the vessel be 5 feet deep or 500 feet deep.
The known Condition of the Ocean inconsistent with Dr. Carpenter’s Hypothesis.—Dr. Carpenter says that he looks forward with great satisfaction to the results of the inquiries which are being prosecuted by the Circumnavigation Expedition, in the hope that the facts brought to light may establish his theory of a general oceanic circulation; and he specifies certain of these facts which, if found to be correct, will establish his theory. It seems to me, however, that the facts to which he refers are just as explicable on the theory of under currents as on the theory of a general oceanic circulation. He begins by saying, “If the views I have propounded be correct, it may be expected that near the border of the great antarctic ice-barrier a temperature below 30° will be met with (as it has been by Parry, Martens, and Weyprecht near Spitzbergen) at no great depth beneath the surface, and that instead of rising at still greater depths, the thermometer will fall to near the freezing-point of salt water” (§ 39).
Dr. Carpenter can hardly claim this as evidence in favour of his theory; for near the borders of the ice-barrier the water, as a matter of course, could not be expected to have a much higher temperature than the ice itself. And if the observations be made during summer months, the temperature of the water at the surface will no doubt be found to be higher than that of the bottom; but if they be carried on during winter, the surface-temperature will doubtless be found to be as low as the bottom-temperature. These are results which do not depend upon any particular theory of oceanic circulation.
“The bottom temperature of the North Pacific,” he continues, “will afford a crucial test of the truth of the doctrine. For since the sole communication of this vast oceanic area with the arctic basin is a strait so shallow as only to permit an inflow of warm surface water, its deep cold stratum must be entirely derived from the antarctic area; and if its bottom temperature is not actually higher than that of the South Pacific, the glacial stratum ought to be found at a greater depth north of the equator than south of it” (§ 39).
This may probably show that the water came from the antarctic regions, but cannot possibly prove that it came in the manner which he supposes.
“In the North Atlantic, again, the comparative limitation of communication with the arctic area may be expected to prevent its bottom temperature from being reduced as low as that of the Southern Atlantic” (§ 39). Supposing the bottom temperature of the South Atlantic should be found to be lower than the bottom temperature of the North Atlantic, this fact will be just as consistent with the theory of under currents as with his theory of a general movement of the ocean.
I am also wholly unable to comprehend how he should imagine, because the bottom temperature of the South Atlantic happens to be lower, and the polar water to lie nearer to the surface in this ocean than in the North Atlantic, that therefore this proves the truth of his theory. This condition of matters is just as consistent, and even more so, as will be shown in Chapter XIII., with my theory as with his. When we consider the immense quantity of warm surface water which, as has been shown (Chapter V.), is being constantly transferred from the South into the North Atlantic, we readily understand how the polar water comes nearer to the surface in the former ocean than in the latter. Every pound of water, of course, passing from the southern to the northern hemisphere must be compensated by an equal amount passing from the northern to the southern hemisphere. But nevertheless the warm water drained off the South Atlantic is not replaced directly by water from the north, but by that cold antarctic current, the existence of which is, unfortunately, too well known to navigators from the immense masses of icebergs which it brings along with it. In fact, the whole of the phenomena are just as easily explained upon the principle of under currents as upon Dr. Carpenter’s theory. But we shall have to return to this point in Chapter XIII., when we come to discuss a class of facts which appear to be wholly irreconcilable with the gravitation theory.
Indeed I fear that even although Dr. Carpenter’s expectations should eventually be realised in the results of the Circumnavigation Expedition, yet the advocates of the wind theory will still remain unconverted. In fact the Director of this Expedition has already, on the wind theory, offered an explanation of nearly all the phenomena on which Dr. Carpenter relies;[65] and the same has also been done by Dr. Petermann,[66] who, as is well known, is equally opposed to Dr. Carpenter’s theory. Dr. Carpenter directs attention to the necessity of examining the broad and deep channel separating Iceland from Greenland. The observations which have already been made, however, show that nearly the entire channel is occupied, on the surface at least, by water flowing southward from the polar area—a direction the opposite of what it ought to be according to the gravitation theory. In fact the surface of one half of the entire area of the ocean, extending from Greenland to the North Cape, is moving in a direction the opposite of that which it ought to take according to the theory under review. The western half of this area is occupied by water which at the surface is flowing southwards; while the eastern half, which has hitherto been regarded by almost everybody but Dr. Carpenter himself and Mr. Findlay as an extension of the Gulf-stream, is moving polewards. The motion of the western half must be attributed to the winds and not to gravity; for it is moving in the wrong direction to be accounted for by the latter cause; but had it been moving in the opposite direction, no doubt its motion would have been referred to gravitation. To this cause the motion of the eastern half, which is in the proper direction, is attributed;[67] but why not assign this motion also to the impulse of the winds, more especially since the direction of the prevailing winds blowing over that area coincides with that of the water? If the wind can produce the motion of the water in the western half, why may not it do the same in the eastern half?
If there be such a difference of density between equatorial and polar waters as to produce a general flow of the upper portion of the ocean poleward, how does it happen that one half of the water in the above area is moving in opposition to gravity? How is it that in a wide open sea gravitation should act so powerfully in the one half of it and with so little effect in the other half? There is probably little doubt that the ice-cold water of the western half extends from the surface down to the bottom. And it is also probable that the bottom water is moving southwards in the same direction as the surface water. The bottom water in such a case would be moving in harmony with the gravitation theory; but would Dr. Carpenter on this account attribute its motion to gravity? Would he attribute the motion of the lower half to gravity and the upper half to the wind? He could not in consistency with his theory attribute the motion of the upper half to gravity: for although the ice-cold water extended to the surface, this could not explain how gravity should move it southward instead of polewards, as according to theory it ought to move. He might affirm, if he chose, that the surface water moves southwards because it is dragged forward by the bottom water; but if this view be held, he is not entitled to affirm, as he does, that the winds can only produce a mere surface drift. If the viscosity and molecular resistance of water be such that, when the lower strata of the ocean are impelled forward by gravity or by any other cause, the superincumbent strata extending to the surface are perforce dragged after them, then, for the same reason, when the upper strata are impelled forward by the wind or any other cause, the underlying strata must also be dragged along after them.
If the condition of the ocean between Greenland and the north-western shore of Europe is irreconcilable with the gravitation theory, we find the case even worse for that theory when we direct our attention to the condition of the ocean on the southern hemisphere; for according to the researches of Captain Duperrey and others on the currents of the Southern Ocean, a very large portion of the area of that ocean is occupied by water moving on the surface more in a northward than a poleward direction. Referring to the deep trough between the Shetland and the Faroe Islands, called by him the “Lightning Channel,” Dr. Carpenter says, “If my view be correct, a current-drag suspended in the upper stratum ought to have a perceptible movement in the N.E. direction; whilst another, suspended in the lower stratum, should move S.W.” (§ 40).
Any one believing in the north-eastern extension of the Gulf-stream and in the Spitsbergen polar under current, to which I have already referred, would not feel surprised to learn that the surface strata have a perceptible north-eastward motion, and the bottom strata a perceptible south-westward motion. North-east and east of Iceland there is a general flow of cold polar water in a south-east direction towards the left edge of the Gulf-stream. This water, as Professor Mohn concludes, “descends beneath the Gulf-stream and partially finds an outlet in the lower half of the Faroe-Shetland channel.”[68]
An Objection Considered.—In Nature, vol. ix. p. 423, Dr. Carpenter has advanced the following objection to the foregoing theory of under-currents:—“According to Mr. Croll’s doctrine, the whole of that vast mass of water in the North Atlantic, averaging, say, 1,500 fathoms in thickness and 3,600 miles in breadth, the temperature of which (from 40° downwards), as ascertained by the Challenger soundings, clearly shows it to be mainly derived from a polar source, is nothing else than the reflux of the Gulf-stream. Now, even if we suppose that the whole of this stream, as it passes Sandy Hook, were to go on into the closed arctic basin, it would only force out an equivalent body of water. And as, on comparing the sectional areas of the two, I find that of the Gulf-stream to be about 1/900th that of the North Atlantic underflow; and as it is admitted that a large part of the Gulf-stream returns into the Mid-Atlantic circulation, only a branch of it going on to the north-east, the extreme improbability (may I not say impossibility?) that so vast a mass of water can be put in motion by what is by comparison a mere rivulet (the north-east motion of which, as a distinct current, has not been traced eastward of 30° W. long.) seems still more obvious.”
In this objection three things are assumed: (1) that the mass of cold water 1,500 fathoms deep and 3,600 miles in breadth is in a state of motion towards the equator; (2) that it cannot be the reflux of the Gulf-stream, because its sectional area is 900 times as great as that of the Gulf-stream; (3) that the immense mass of water is, according to my views, set in motion by the Gulf-stream.
As this objection has an important bearing on the question under consideration, I shall consider these three assumptions separately and in their order: (1) That this immense mass of cold water came originally from the polar regions I, of course, admit, but that the whole is in a state of motion I certainly do not admit. There is no warrant whatever for any such assumption. According to Dr. Carpenter himself, the heating-power of the sun does not extend to any great depth below the surface; consequently there is nothing whatever to heat this mass but the heat coming through the earth’s crust. But the amount of heat derived from this source is so trifling, that an under current from the arctic regions far less in volume than that of the Gulf-stream would be quite sufficient to keep the mass at an ice-cold temperature. Taking the area of the North Atlantic between the equator and the Tropic of Cancer, including also the Caribbean Sea and the Gulf of Mexico, to be 7,700,000 square miles, and the rate at which internal heat passes through the earth’s surface to be that assigned by Sir William Thomson, we find that the total quantity of heat derived from the earth’s crust by the above area is equal to about 88 × 10^{15} foot-pounds per day. But this amount is equal to only 1/894th that conveyed by the Gulf-stream, on the supposition that each pound of water carries 19,300 foot-pounds of heat. Consequently an under current from the polar regions of not more than 1/35th the volume of the Gulf-stream would suffice to keep the entire mass of water of that area within 1° of what it would be were there no heat derived from the crust of the earth; that is to say, were the water conveyed by the under current at 32°, internal heat would not maintain the mass of the ocean in the above area at more than 33°. The entire area of the North Atlantic from the equator to the arctic circle is somewhere about 16,000,000 square miles. An under current of less than 1/17th that of the Gulf-stream coming from the arctic regions would therefore suffice to keep the entire North Atlantic basin filled with ice-cold water. In short, whatever theory we adopt regarding oceanic circulation, it follows equally as a necessary consequence that the entire mass of the ocean below the stratum heated by the sun’s rays must consist of cold water. For if cold water be continually coming from the polar regions either in the form of under currents, or in the form of a general underflow as Dr. Carpenter supposes, the entire under portion of the ocean must ultimately become occupied by cold water; for there is no source from which this influx of water can derive heat, save from the earth’s crust. But the amount thus derived is so trifling as to produce no sensible effect. For example, a polar under current one half the size of the Gulf-stream would be sufficient to keep the entire water of the globe (below the stratum heated by the sun’s rays) at an ice-cold temperature. Internal heat would not be sufficient under such circumstances to maintain the mass 1° Fahr. above the temperature it possessed when it left the polar regions.
It follows therefore that the presence of the immense mass of ice-cold water in the great depths of the ocean is completely accounted for by under currents, and there is no necessity for supposing it to be all in a state of motion towards the equator. In fact, this very state of things, which the general oceanic circulation hypothesis was devised to explain, results as a necessary consequence of polar under currents. Unless these were entirely stopped it is physically impossible that the ocean could be in any other condition.
But suppose that this immense mass of cold water occupying the great depths of the ocean were, as Dr. Carpenter assumes it to be, in a state of constant motion towards the equator, and that its sectional area were 900 times that of the Gulf-stream, it would not therefore follow that the quantity of water passing through this large sectional area must be greater than that flowing through a sectional area of the Gulf-stream; for the quantity of water flowing through this large sectional area depends entirely on the rate of motion.
I am wholly unable to understand how it could be supposed that this underflow, according to my view, is set in motion by the Gulf-stream, seeing that I have shown that the return under current is as much due to the impulse of the wind as the Gulf-stream itself.
Dr. Carpenter lays considerable stress on the important fact established by the Challenger expedition, that the great depths of the sea in equatorial regions are occupied by ice-cold water, while the portion heated by the sun’s rays is simply a thin stratum at the surface. It seems to me that it would be difficult to find a fact more hostile to his theory than this. Were it not for this upper stratum of heated water there would be no difference between the equatorial and polar columns, and consequently nothing to produce motion. But the thinner this stratum is the less is the difference, and the less there is to produce motion.
Chapter IX
EXAMINATION OF THE GRAVITATION THEORY OF OCEANIC CIRCULATION.—THE MECHANICS OF DR. CARPENTER’S THEORY.
Experimental Illustration of the Theory.—The Force exerted by Gravity.—Work performed by Gravity.—Circulation not by Convection.—Circulation depends on Difference in Density of the Equatorial and Polar Columns.—Absolute Amount of Work which can be performed by Gravity.—How Underflow is produced.—How Vertical Descent at the Poles and Ascent at the Equator is produced.—The Gibraltar Current.—Mistake in Mechanics concerning it.—The Baltic Current.
Experiment to illustrate Theory.—In support of the theory of a general movement of water between equatorial and polar regions, Dr. Carpenter adduces the authority of Humboldt and of Prof. Buff.[69] I have been unable to find anything in the writings of either from which it can be inferred that they have given this matter special consideration. Humboldt merely alludes to the theory, and that in the most casual manner; and that Prof. Buff has not carefully investigated the subject is apparent from the very illustration quoted by Dr. Carpenter from the “Physics of the Earth.” “The water of the ocean at great depths,” says Prof. Buff, “has a temperature, even under the equator, nearly approaching to the freezing-point. This low temperature cannot depend on any influence of the sea-bottom.... The fact, however, is explained by a continual current of cold water flowing from the polar regions towards the equator. The following well-known experiment clearly illustrates the manner of this movement. A glass vessel is to be filled with water with which some powder has been mixed, and is then to be heated at bottom. It will soon be seen, from the motion of the particles of powder, that currents are set up in opposite directions through the water. Warm water rises from the bottom up through the middle of the vessel, and spreads over the surface, while the colder and therefore heavier liquid falls down at the sides of the glass.”
This illustration is evidently intended to show not merely the form and direction of the great system of oceanic circulation, but also the mode in which the circulation is induced by heat. It is no doubt true that if we apply heat (say that of a spirit-lamp) to the bottom of a vessel filled with water, the water at the bottom of the vessel will become heated and rise to the surface; and if the heat be continued an ascending current of warm water will be generated; and this, of course, will give rise to a compensating under current of colder water from all sides. In like manner it is also true that, if heat were applied to the bottom of the ocean in equatorial regions, an ascending current of hot water would be also generated, giving rise to an under current of cold water from the polar regions. But all this is the diametrically opposite of what actually takes place in nature. The heat is not applied to the bottom of the ocean, so as to make the water there lighter than the water at the surface, and thus to generate an ascending current; but the heat is applied to the surface of the ocean, and the effect of this is to prevent an ascending current rather than to produce one, for it tends to keep the water at the surface lighter than the water at the bottom. In order to show how the heat of the sun produces currents in the ocean, Prof. Buff should have applied the heat, not to the bottom of his vessel, but to the upper surface of the water. But this is not all, the form of the vessel has something to do with the matter. The wider we make the vessel in proportion to its depth, the more difficult it is to produce currents by means of heat. But in order to represent what takes place in nature, we ought to have the same proportion between the depth and the superficial area of the water in our vessel as there is between the depth and the superficial area of the sea. The mean depth of the sea may be taken roughly to be about three miles.[70] The distance between pole and pole we shall take in round numbers to be 12,000 miles. The sun may therefore be regarded as shining upon a circular sea 12,000 miles in diameter and three miles deep. The depth of the sea to its diameter is therefore as 1 to 4,000. Suppose, now, that in our experiment we make the depth of our vessel one inch, we shall require to make its diameter 4,000 inches, or 333 feet, say, in round numbers, 100 yards in diameter. Let us, then, take a pool of water 100 yards in diameter, and one inch deep. Suppose the water to be at 32°. Apply heat to the upper surface of the pool, so as to raise the temperature of the surface of the water to 80° at the centre of the pool, the temperature diminishing towards the edge, where it is at 32°. It is found that at a depth of two miles the temperature of the water at the equator is about as low as that of the poles. We must therefore suppose the water at the centre of our pool to diminish in temperature from the surface downwards, so that at a depth of half an inch the water is at 32°. We have in this case a thin layer of warm water half an inch thick at the centre, and gradually thinning off to nothing at the edge of the pool. The lightest water, be it observed, is at the surface, so that an ascending or a descending current is impossible. The only way whereby the heat applied can have any tendency to produce motion is this:—The heating of the water expands it, consequently the surface of the pool must stand at a little higher level at its centre than at its edge, where no expansion takes place; and therefore, in order to restore the level of the pool, the water at the centre will tend to flow towards the sides. But what is the amount of this tendency? Its amount will depend upon the amount of slope, but the slope in the case under consideration amounts to only 1 in 7,340,000.
Dr. Carpenter’s Experiment.—In order to obviate the objection to Professor Buff’s experiment Dr. Carpenter has devised another mode. But I presume his experiment was intended rather to illustrate the way in which the circulation of the ocean, according to his theory, takes place, than to prove that it actually does take place. At any rate, all that can be claimed for the experiment is the proof that water will circulate in consequence of difference of specific gravity resulting from difference of temperature. But this does not require proof, for no physicist denies it. The point which requires to be proved is this. Is the difference of specific gravity which exists in the ocean sufficient to produce the supposed circulation? Now his mode of experimenting will not prove this, unless he makes his experiment agree with the conditions already stated.
But I decidedly object to the water being heated in the way in which it has been done by him in his experiment before the Royal Geographical Society; for I feel somewhat confident that in this experiment the circulation resulted not from difference of specific gravity, as was supposed, but rather from the way in which the heat was applied. In that experiment the one half of a thick metallic plate was placed in contact with the upper surface of the water at one end of the trough; the other half, projecting over the end of the trough, was heated by means of a spirit-lamp. It is perfectly obvious that though the temperature of the great mass of the water under the plate might not be raised over 80° or so, yet the molecules in contact with the metal would have a very high temperature. These molecules, in consequence of their expansion, would be unable to sink into the cooler and denser water underneath, and thus escape the heat which was being constantly communicated to them from the heated plate. But escape they must, or their temperature would continue to rise until they would ultimately burst into vapour. They cannot ascend, neither can they descend: they therefore must be expelled by the heat from the plate in a horizontal direction. The next layer of molecules from beneath would take their place and would be expelled in a similar manner, and this process would continue so long as the heat was applied to the plate. A circulation would thus be established by the direct expansive force of vapour, and not in any way due to difference of specific gravity, as Dr. Carpenter supposes.
But supposing the heated bar to be replaced by a piece of ice, circulation would no doubt take place; but this proves nothing more than that difference of density will produce circulation, which is what no one calls in question.
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.
“(c) In imparting a downward movement to each new surface-stratum as its temperature undergoes reduction; so that the entire column may be said to be in a state of constant descent, like that which exists in the water of a tall jar when an opening is made at its bottom, and the water which flows away through it is replaced by an equivalent supply poured into the top of the jar” (§ 23).
But if this be his theory, as it evidently is, then the 4 foot-pounds (the amount of work performed by the descent of the water down the slope) comprehends all the work that gravitation can perform on a pound of water in making a complete circuit from the equator to the pole and from the pole back to the equator.
This, I trust, will be evident from the following considerations. When a pound of water has flowed down from the equator to the pole, it has descended 4 feet, and is then at the foot of the slope. Gravity has therefore no more power to pull it down to a lower level. It will not sink through the polar water, for it is not denser than the water beneath on which it rests. But it may be replied that although it will not sink through the polar water, it has nevertheless made the polar column heavier than the equatorial, and this excess of pressure forces a pound of water out from beneath and allows the column to descend. Suppose it may be argued that a quantity of water flows down from the equator, so as to raise the level of the polar water by, say, one foot. The polar column will now be rendered heavier than the equatorial by the weight of one foot of water. The pressure of the one foot will thus force a quantity of water laterally from the bottom and cause the entire column to descend till the level of equilibrium is restored. In other words, the polar column will sink one foot. Now in the sinking of this column work is performed by gravity. A certain amount of work is performed by gravity in causing the water to flow down the slope from the equator to the pole, and, in addition to this, a certain amount is performed by gravity in the vertical descent of the column.
I freely admit this to be sound reasoning, and admit that so much is due to the slope and so much to the vertical descent of the water. But here we come to the most important point, viz., is there the full slope of 4 feet and an additional vertical movement? Dr. Carpenter seems to conclude that there is, and that this vertical force is something in addition to the force which I derive from the slope. And here, I venture to think, is a radical error into which he has fallen in regard to the whole matter. Let it be observed that, when water circulates from difference of specific gravity, this vertical movement is just as real a part of the process as the flow down the slope; but the point which I maintain is that there is no additional power derived from this vertical movement over and above what is derived from the full slope—or, in other words, that this primum mobile, which he says I have overlooked, has in reality no existence.
Perhaps the following diagram will help to make the point still clearer:—
Let P (fig. 1) be the surface of the ocean at the pole, and E the surface at the equator; P O a column of water at the pole, and E Q a column at the equator. The two columns are of equal weight, and balance each other; but as the polar water is colder, and consequently denser than the equatorial, the polar column is shorter than the equatorial, the difference in the length of the two columns being 4 feet. The surface of the ocean at the equator E is 4 feet higher than the surface of the ocean at the pole P; there is therefore a slope of 4 feet from E to P. The molecules of water at E tend to flow down this slope towards P. The amount of work performed by gravity in the descent of a pound of water down this slope from E to P is therefore 4 foot-pounds.
But of course there can be no permanent circulation while the full slope remains. In order to have circulation the polar column must be heavier than the equatorial. But any addition to the weight of the polar column is at the expense of the slope. In proportion as the weight of the polar column increases the less becomes the slope. This, however, makes no difference in the amount of work performed by gravity.
Suppose now that water has flowed down till an addition of one foot of water is made to the polar column, and the difference of level, of course, diminished by one foot. The surface of the ocean in this case will now be represented by the dotted line P′ E, and the slope reduced from 4 feet to 3 feet. Let us then suppose a pound of water to leave E and flow down to P′; 3 foot-pounds will be the amount of work performed. The polar column being now too heavy by the extent of the mass of water P′ P one foot thick, its extra pressure causes a mass of water equal to P′ P to flow off laterally from the bottom of the column. The column therefore sinks down one foot till P′ reaches P. Now the pound of water in this vertical descent from P′ to P has one foot-pound of work performed on it by gravity; this added to the 3 foot-pounds derived from the slope, gives a total of 4 foot-pounds in passing from E to P′ and then from P′ to P. This is the same amount of work that would have been performed had it descended directly from E to P. In like manner it can be proved that 4 foot-pounds is the amount of work performed in the descent of every pound of water of the mass P′ P. The first pound which left E flowed down the slope directly to P, and performed 4 foot-pounds of work. The last pound flowed down the slope E P′, and performed only 3 foot-pounds; but in descending from P′ to P it performed the other one foot-pound. A pound leaving at a period exactly intermediate between the two flowed down 3½ feet of slope and descended vertically half a foot. Whatever path a pound of water might take, by the time that it reached P, 4 foot-pounds of work would be performed. But no further work can be performed after it reaches P.
But some will ask, in regard to the vertical movement, is it only in the descent of the water from P′ to P that work is performed? Water cannot descend from P′ to P, it will be urged, unless the entire column P O underneath descend also. But the column P O descends by means of gravity. Why, then, it will be asked, is not the descent of the column a motive power as real as the descent of the mass of water P′ P?
That neither force nor energy can be derived from the mere descent of the polar column P O is demonstrable thus:—The reason why the column P O descends is because, in consequence of the mass of water P′ P resting on it, its weight is in excess of the equatorial column E Q. But the force with which the column descends is equal, not to the weight of the column, but to the weight of the mass P′ P; consequently as much work would be performed by gravity in the descent of the mass P′ P (the one foot of water) alone as in the descent of the entire column P′ O, 10,000 feet in height. Suppose a ton weight is placed in each scale of a balance: the two scales balance each other. Place a pound weight in one of the scales along with the ton weight and the scale will descend. But it descends, not with the pressure of a ton and a pound, but with the pressure of the pound weight only. In the descent of the scale, say, one foot, gravity can perform only one foot-pound of work. In like manner, in the descent of the polar column, the only work available is the work of the mass P′ P laid on the top of the column. But it must be observed that in the descent of the column from P′ to P, a distance of one foot, each pound of water of the mass P′ P does not perform one foot-pound of work; for the moment that a molecule of water reaches P, it then ceases to perform further work. The molecules at the surface P′ descend one foot before reaching P; the molecules midway between P′ and P descend only half a foot before reaching P, and the molecules at the bottom of the mass are already at P, and therefore cannot perform any work. The mean distance through which the entire mass performs work is therefore half a foot. One foot-pound per pound of water represents in this case the amount of work derived from the vertical movement.
That such is the case is further evident from the following considerations. Before the polar column begins to descend, it is heavier than the equatorial by the weight of one foot of water; but when the column has descended half a foot, the polar column is heavier than the equatorial by the weight of only half a foot of water; and, as the column continues to descend, the force with which it descends continues to diminish, and when it has sunk to P the force is zero. Consequently the mean pressure or weight with which the one foot of water P′ P descended was equal to that of a layer of half a foot of water; in other words, each pound of water, taking the mass as a whole, descended with the pressure or weight of half a pound. But a half pound descending one foot performs half a foot-pound; so that whether we consider the full pressure acting through the mean distance, or the mean pressure acting through the full distance, we get the same result, viz. a half foot-pound as the work of vertical descent.
Now it will be found, as we shall presently see, that if we calculate the mean amount of work performed in descending the slope from the equator to the pole, 3½ foot-pounds per pound of water is the amount. The water at the bottom of the mass P P′ moved, of course, down the full slope E P 4 feet. The water at the top of the mass which descended from E to P′ descended a slope of only 3 feet. The mean descent of the whole mass is therefore 3½ feet. And this gives 3½ foot-pounds as the mean amount of work per pound of water in descending the slope; this, added to the half foot-pound derived from vertical descent, gives 4 foot-pounds as the total amount of work per pound of the mass.
I have in the above reasoning supposed one foot of water accumulated on the polar column before any vertical descent takes place. It is needless to remark that the same conclusion would have been arrived at, viz., that the total amount of work performed is 4 foot-pounds per pound of water, supposing we had considered 2 feet, or 3 feet, or even 4 feet of water to have accumulated on the polar column before vertical motion took place.
I have also, in agreement with Dr. Carpenter’s mode of representing the operation, been considering the two effects, viz., the flowing of the water down the slope and the vertical descent of the polar column as taking place alternately. In nature, however, the two effects take place simultaneously; but it is needless to add that the amount of work performed would be the same whether the effects took place alternately or simultaneously.
I have also represented the level of the ocean at the equator as remaining permanent while the alterations of level were taking place at the pole. But in representing the operation as it would actually take place in nature, we should consider the equatorial column to be lowered as the polar one is being raised. We should, for example, consider the one foot of water P′ P put upon the polar column as so much taken off the equatorial column. But in viewing the problem thus we arrive at exactly the same results as before.
Let P (Fig. 2), as in Fig. 1, be the surface of the ocean at the pole, and E the surface at the equator, there being a slope of 4 feet from E to P. Suppose now a quantity of water, E E′, say, one foot thick, to flow from off the equatorial regions down upon the polar. It will thus lower the level of the equatorial column by one foot, and raise the level of the polar column by the same amount. I may, however, observe that the one foot of water in passing from E to P would have its temperature reduced from 80° to 32°, and this would produce a slight contraction. But as the weight of the mass would not be affected, in order to simplify our reasoning we may leave this contraction out of consideration. Any one can easily satisfy himself that the assumption that E E′ is equal to P′ P does not in any way affect the question at issue—the only effect of the contraction being to increase by an infinitesimal amount the work done in descending the slope, and to diminish by an equally infinitesimal amount the work done in the vertical descent. If, for example, 3 foot-pounds represent the amount of work performed in descending the slope, and one foot-pound the amount performed in the vertical descent, on the supposition that E′ E does not contract in passing to the pole, then 3·0024 foot-pounds will represent the work of the slope, and 0·9976 foot-pounds the work of vertical descent when allowance is made for the contraction. But the total amount of work performed is the same in both cases. Consequently, to simplify our reasoning, we may be allowed to assume P′ P to be equal to E E′.
The slope E P being 4 feet, the slope E′ P′ is consequently 2 feet; the mean slope for the entire mass is therefore 3 feet. The mean amount of work performed by the descent of the mass will of course be 3 foot-pounds per pound of water. The amount of work performed by the vertical descent of P′ P ought therefore to be one foot-pound per pound. That this is the amount will be evident thus:—The transference of the one foot of water from the equatorial column to the polar disturbs the equilibrium by making the equatorial column too light by one foot of water and the polar column too heavy by the same amount of water. The polar column will therefore tend to sink, and the equatorial to rise till equilibrium is restored. The difference of weight of the two columns being equal to 2 feet of water, the polar column will begin to descend with a pressure of 2 feet of water; and the equatorial column will begin to rise with an equal amount of pressure. When the polar column has descended half a foot the equatorial column will have risen half a foot. The pressure of the descending polar column will now be reduced to one foot of water. And when the polar column has descended another foot, P′ will have reached P, and E′ will have reached E; the two columns will then be in equilibrium. It therefore follows that the mean pressure with which the polar column descended the one foot was equal to the pressure of one foot of water. Consequently the mean amount of work performed by the descent of the mass was equal to one foot-pound per pound of water; this, added to the 3 foot-pounds derived from the slope, gives a total of 4 foot-pounds.
In whatever way we view the question, we are led to the conclusion that if 4 feet represent the amount of slope between the equatorial and polar columns when the two are in equilibrium, then 4 foot-pounds is the total amount of work that gravity can perform upon a pound of water in overcoming the resistance to motion in its passage from the equator to the pole down the slope, and then in its vertical descent to the bottom of the ocean.
But it will be replied, not only does the one foot of water P′ P descend, but the entire column P O, 10,000 feet in length, descends also. What, then, it will be asked, becomes of the force which gravity exerts in the descent of this column? We shall shortly see that this force is entirely applied in work against gravity in other parts of the circuit; so that not a single foot-pound of this force goes to overcome cohesion, friction, and other resistances; it is all spent in counteracting the efforts which gravity exerts to stop the current in another part of the circuit.
I shall now consider the next part of the movement, viz., the under or return current from the bottom of the polar to the bottom of the equatorial column. What produces this current? It is needless to say that it cannot be caused directly by gravity. Gravitation cannot directly draw any body horizontally along the earth’s surface. The water that forms this current is pressed out laterally by the weight of the polar column, and flows, or rather is pushed, towards the equator to supply the vacancy caused by the ascent of the equatorial column. There is a constant flow of water from the equator to the poles along the surface, and this draining of the water from the equator is supplied by the under or return current from the poles. But the only power which can impel the water from the bottom of the polar column to the bottom of the equatorial column is the pressure of the polar column. But whence does the polar column derive its pressure? It can only press to the extent that its weight exceeds that of the equatorial column. That which exerts the pressure is therefore the mass of water which has flowed down the slope from the equator upon the polar column. It is in this case the vertical movement that causes this under current. The energy which produces this current must consequently be derived from the 4 foot-pounds resulting from the slope; for the energy of the vertical movement, as has already been proved, is derived from this source; or, in other words, whatever power this vertical movement may exert is so much deducted from the 4 foot-pounds derived from the full slope.
Let us now consider the fourth and last movement, viz., the ascent of the under current to the surface of the ocean at the equator. When this cold under current reaches the equatorial regions, it ascends to the surface to the point whence it originally started on its circuit. What, then, lifts the water from the bottom of the equatorial column to its top? This cannot be done directly, either by heat or by gravity. When heat, for example, is applied to the bottom of a vessel, the heated water at the bottom expands and, becoming lighter than the water above, rises through it to the surface; but if the heat be applied to the surface of the water instead of to the bottom, the heat will not produce an ascending current. It will tend rather to prevent such a current than to produce one—the reason being that each successive layer of water will, on account of the heat applied, become hotter and consequently lighter than the layer below it, and colder and consequently heavier than the layer above it. It therefore cannot ascend, because it is too heavy; nor can it descend, because it is too light. But the sea in equatorial regions is heated from above, and not from below; consequently the water at the bottom does not rise to the surface at the equator in virtue of any heat which it receives. A layer of water can never raise the temperature of a layer below it to a higher temperature than itself; and since it cannot do this, it cannot make the layer under it lighter than itself. That which raises the water at the equator, according to Dr. Carpenter’s theory, must be the downward pressure of the polar column. When water flows down the slope from the equator to the pole, the polar column, as we have seen, becomes too heavy and the equatorial column too light; the former then sinks and the latter rises. It is the sinking of the polar column which raises the equatorial one. When the polar column descends, as much water is pressed in underneath the equatorial column as is pressed from underneath the polar column. If one foot of water is pressed from under the polar column, a foot of water is pressed in under the equatorial column. Thus, when the polar column sinks a foot, the equatorial column rises to the same extent. The equatorial water continuing to flow down the slope, the polar column descends: a foot of water is again pressed from underneath the polar column and a foot pressed in under the equatorial. As foot after foot is thus removed from the bottom of the polar column while it sinks, foot after foot is pushed in under the equatorial column while it rises; so by this means the water at the surface of the ocean in polar regions descends to the bottom, and the water at the bottom in equatorial regions ascends to the surface—the effect of solar heat and polar cold continuing, of course, to maintain the surface of the ocean in equatorial regions at a higher level than at the poles, and thus keeping up a constant state of disturbed equilibrium. Or, to state the matter in Dr. Carpenter’s own words, “The cold and dense polar water, as it flows in at the bottom of the equatorial column, will not directly take the place of that which has been drafted off from the surface; but this place will be filled by the rising of the whole superincumbent column, which, being warmer, is also lighter than the cold stratum beneath. Every new arrival from the poles will take its place below that which precedes it, since its temperature will have been less affected by contact with the warmer water above it. In this way an ascending movement will be imparted to the whole equatorial column, and in due course every portion of it will come under the influence of the surface-heat of the sun.”[73]
But the agency which raises up the water of the under current to the surface is the pressure of the polar column. The equatorial column cannot rise directly by means of gravity. Gravity, instead of raising the column, exerts all its powers to prevent its rising. Gravity here is a force acting against the current. It is the descent of the polar column, as has been stated, that raises the equatorial column. Consequently the entire amount of work performed by gravity in pulling down the polar column is spent in raising the equatorial column. Gravity performs exactly as much work in preventing motion in the equatorial column as it performs in producing motion in the polar column; so that, so far as the vertical parts of Dr. Carpenter’s circulation are concerned, gravity may be said neither to produce motion nor to prevent it. And this remark, be it observed, applies not only to P O and E Q, but also to the parts P′ P and E E′ of the two columns. When a mass of water E E′, say one foot deep, is removed off the equatorial column and placed upon the polar column, the latter column is then heavier than the former by the weight of two feet of water. Gravity then exerts more force in pulling the polar column down than it does in preventing the equatorial column from rising; and the consequence is that the polar column begins to descend and the equatorial column to rise. But as the polar column continues to descend and the equatorial to rise, the power of gravity to produce motion in the polar column diminishes, and the power of gravity to prevent motion in the equatorial column increases; and when P′ descends to P and E′ rises to E, the power of gravity to prevent motion in the equatorial column is exactly equal to the power of gravity to produce motion in the polar column, and consequently motion ceases. It therefore follows that the entire amount of work performed by the descent of P′ P is spent in raising E′ E against gravity.
It follows also that inequalities in the sea-bottom cannot in any way aid the circulation; for although the cold under current should in its progress come to a deep trough filled with water less dense than itself, it would no doubt sink to the bottom of the hollow; yet before it could get out again as much work would have to be performed against gravity as was performed by gravity in sinking it. But whilst inequalities in the bed of the ocean would not aid the current, they would nevertheless very considerably retard it by the obstructions which they would offer to the motion of the water.
We have been assuming that the weight of P′ P is equal to that of E E′; but the mass P′ P must be greater than E E′ because P′ P has not only to raise E E′, but to impel the under current—to push the water along the sea-bottom from the pole to the equator. So we must have a mass of water, in addition to P′ P, placed on the polar column to enable it to produce the under current in addition to the raising of the equatorial column.
It follows also that the amount of work which can be performed by gravity depends entirely on the difference of temperature between the equatorial and the polar waters, and is wholly independent of the way in which the temperature may decrease from the equator to the poles. Suppose, in agreement with Dr. Carpenter’s idea,[74] that the equatorial heat and polar cold should be confined to limited areas, and that through the intermediate space no great difference of temperature should prevail. Such an arrangement as this would not increase the amount of work which gravity could perform; it would simply make the slope steeper at the two extremes and flatter in the intervening space. It would no doubt aid the surface-flow of the water near the equator and the poles, but it would retard in a corresponding degree the flow of the water in the intermediate regions. In short, it would merely destroy the uniformity of the slope without aiding in the least degree the general motion of the water.
It is therefore demonstrable that the energy derived from the full slope, whatever that slope may be, comprehends all that can possibly be obtained from gravity.
It cannot be urged as an objection to what has been advanced that I have determined simply the amount of the force acting on the water at the surface of the ocean and not that on the water at all depths—that I have estimated the amount of work which gravity can perform on a given quantity of water at the surface, but not the total amount of work which gravity can perform on the entire ocean. This objection will not stand, because it is at the surface of the ocean where the greatest difference of temperature, and consequently of density, exists between the equatorial and polar waters, and therefore there that gravity exerts its greatest force. And if gravity be unable to move the water at the surface, it is much less able to do so under the surface. So far as the question at issue is concerned, any calculations as to the amount of force exerted by gravity at various depths are needless.
It is maintained also that the winds cannot produce a vertical current except under some very peculiar conditions. We have already seen that, according to Dr. Carpenter’s theory, the vertical motion is caused by the water flowing off the equatorial column, down the slope, upon the polar column, thus destroying the equilibrium between the two by diminishing the weight of the equatorial column and increasing that of the polar column. In order that equilibrium may be restored, the polar column sinks and the equatorial one rises. Now must not the same effect occur, supposing the water to be transferred from the one column to the other, by the influence of the winds instead of by the influence of gravity? The vertical descent and ascent of these columns depend entirely upon the difference in their weights, and not upon the nature of the agency which makes this difference. So far as difference of weight is concerned, 2 feet of water, propelled down the slope from the equatorial column to the polar by the winds, will produce just the same effect as though it had been propelled by gravity. If vertical motion follows as a necessary consequence from a transference of water from the equator to the poles by gravity, it follows equally as a necessary consequence from the same transference by the winds; so that one is not at liberty to advocate a vertical circulation in the one case and to deny it in the other.
Gravitation Theory of the Gibraltar Current.—If difference of specific gravity fails to account for the currents of the ocean in general, it certainly fails in a still more decided manner to account for the Gibraltar current. The existence of the submarine ridge between Capes Trafalgar and Spartel, as was shown in the Phil. Mag. for October, 1871, p. 269, affects currents resulting from difference of specific gravity in a manner which does not seem to have suggested itself to Dr. Carpenter. The pressure of water and other fluids is not like that of a solid—not like that of the weight in the scale of a balance, simply a downward pressure. Fluids press downwards like the solids, but they also press laterally. The pressure of water is hydrostatic. If we fill a basin with water or any other fluid, the fluid remains in perfect equilibrium, provided the sides of the basin be sufficiently strong to resist the pressure. The Mediterranean and Atlantic, up to the level of the submarine ridge referred to, may be regarded as huge basins, the sides of which are sufficiently strong to resist all pressure. It follows that, however much denser the water of the Mediterranean may be than that of the Atlantic, it is only the water above the level of the ridge that can possibly exercise any influence in the way of disturbing equilibrium, so as to cause the level of the Mediterranean to stand lower than that of the Atlantic. The water of the Atlantic below the level of this ridge might be as light as air, and that of the Mediterranean as heavy as molten lead, but this could produce no disturbance of equilibrium; and if there be no difference of density between the Atlantic and the Mediterranean waters from the surface down to the level of the top of the ridge, then there can be nothing to produce the circulation which Dr. Carpenter infers. Suppose both basins empty, and dense water to be poured into the Mediterranean, and water less dense into the Atlantic, until they are both filled up to the level of the ridge, it is evident that the heavier water in the one basin can exercise no influence in raising the level of the lighter water in the other basin, the entire pressure being borne by the sides of the basins. But if we continue to pour in water till the surface is raised, say one foot, above the level of the ridge, then there is nothing to resist the lateral pressure of this one foot of water in the Mediterranean but the counter pressure of the one foot in the Atlantic. But as the Mediterranean water is denser than the Atlantic, this one foot of water will consequently exert more pressure than the one foot of water of the Atlantic. We must therefore continue to pour more water into the Atlantic until its lateral pressure equals that of the Mediterranean. The two seas will then be in equilibrium, but the surface of the Atlantic will of course be at a higher level than the surface of the Mediterranean. The difference of level will be proportionate to the difference in density of the waters of the two seas. But here we come to the point of importance. In determining the difference of level between the two seas, or, which is the same thing, the difference of level between a column of the Atlantic and a column of the Mediterranean, we must take into consideration only the water which lies above the level of the ridge. If there be one foot of water above the ridge, then there is a difference of level proportionate to the difference of pressure between the one foot of water of the two seas. If there be 2 feet, 3 feet, or any number of feet of water above the level of the ridge, the difference of level is proportionate to the 2 feet, 3 feet, or whatever number of feet there may be of water above the ridge. If, for example, 13 should represent the density of the Mediterranean water and 12 the density of the Atlantic water, then if there were one foot of water in the Mediterranean above the level of the ridge, there would require to be one foot one inch of water in the Atlantic above the ridge in order that the two might be in equilibrium. The difference of level would therefore be one inch. If there were 2 feet of water, the difference of level would be 2 inches; if 3 feet, the difference would be 3 inches, and so on. And this would follow, no matter what the actual depth of the two basins might be; the water below the level of the ridge exercising no influence whatever on the level of the surface.
Taking Dr. Carpenter’s own data as to the density of the Mediterranean and Atlantic waters, what, then, is the difference of density? The submarine ridge comes to within 167 fathoms of the surface; say, in round numbers, to within 1,000 feet. What are the densities of the two basins down to the depth of 1,000 feet? According to Dr. Carpenter there is little, if any, difference. His own words on this point are these:—“A comparison of these results leaves no doubt that there is an excess of salinity in the water of the Mediterranean above that of the Atlantic; but that this excess is slight in the surface-water, whilst somewhat greater in the deeper water” (§ 7). “Again, it was found by examining samples of water taken from the surface, from 100 fathoms, from 250 fathoms, and from 400 fathoms respectively, that whilst the first two had the characteristic temperature and density of Atlantic water, the last two had the characteristics and density of Mediterranean water” (§ 13). Here, at least to the depth of 100 fathoms or 600 feet, there is little difference of density between the waters of the two basins. Consequently down to the depth of 600 feet, there is nothing to produce any sensible disturbance of equilibrium. If there be any sensible disturbance of equilibrium, it must be in consequence of difference of density which may exist between the depths of 600 feet and the surface of the ridge. We have nothing to do with any difference which may exist between the water of the Mediterranean and the Atlantic below the ridge; the water in the Mediterranean basin may be as heavy as mercury below 1,000 feet: but this can have no effect in disturbing equilibrium. The water to the depth of 600 feet being of the same density in both seas, the length of the two columns acting on each other is therefore reduced to 400 feet—that is, to that stratum of water lying at a depth of from 600 to the surface of the ridge 1,000 feet below the surface. But, to give the theory full justice, we shall take the Mediterranean stratum at the density of the deep water of the Mediterranean, which he found to be about 1·029, and the density of the Atlantic stratum at 1·026. The difference of density between the two columns is therefore ·003. Consequently, if the height of the Mediterranean column be 400 feet, it will be balanced by the Atlantic column of 401·2 feet; the difference of level between the Mediterranean and the Atlantic cannot therefore be more than 1·2 foot. The amount of work that can be performed by gravity in the case of the Gibraltar current is little more than one foot-pound per pound of water, an amount of energy evidently inadequate to produce the current.
It is true that in his last expedition Dr. Carpenter found the bottom-water on the ridge somewhat denser than Atlantic water at the same depth, the former being 1·0292 and the latter 1·0265; but it also proved to be denser than Mediterranean water at the same depth. He found, for example, that “the dense Mediterranean water lies about 100 fathoms nearer the surface over a 300-fathoms bottom, than it does where the bottom sinks to more than 500 fathoms” (§ 51). But any excess of density which might exist at the ridge could have no tendency whatever to make the Mediterranean column preponderate over the Atlantic column, any more than could a weight placed over the fulcrum of a balance have a tendency to make the one scale weigh down the other.
If the objection referred to be sound, it shows the mechanical impossibility of the theory. It proves that whether there be an under current or not, or whether the dense water lying in the deep trough of the Mediterranean be carried over the submarine ridge into the Atlantic or not, the explanation offered by Dr. Carpenter is one which cannot be admitted. It is incumbent on him to explain either (1) how the almost infinitesimal difference of density which exists between the Atlantic and Mediterranean columns down to the level of the ridge can produce the upper and under currents carrying the deep and dense water of the Mediterranean over the ridge, or (2) how all this can be done by means of the difference of density which exists below the level of the ridge.[75] What the true cause of the Gibraltar current really is will be considered in Chap. XIII.
The Baltic Current.—The entrance to the Baltic Sea is in some places not over 50 or 60 feet deep. It follows, therefore, from what has already been proved in regard to the Gibraltar current, that the influence of gravity must be even still less in causing a current in the Baltic strait than in the Gibraltar strait.
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]
Chapter XI
THE INADEQUACY OF THE GRAVITATION THEORY PROVED BY ANOTHER METHOD.
Quantity of Heat which can be conveyed by the General Oceanic Circulation trifling.—Tendency in the Advocates of the Gravitation Theory to under-estimate the Volume of the Gulf-stream.—Volume of the Stream as determined by the Challenger.—Immense Volume of Warm Water discovered by Captain Nares.—Condition of North Atlantic inconsistent with the Gravitation Theory.—Dr. Carpenter’s Estimate of the Thermal Work of the Gulf-stream.
I shall now proceed by another method to prove the inadequacy of such a general oceanic circulation as that which Dr. Carpenter advocates. By contrasting the quantity of heat carried by the Gulf-stream from inter-tropical to temperate and polar regions with such amount as can possibly be conveyed in the same direction by means of a general oceanic circulation, it will become evident that the latter sinks into utter insignificance before the former.
In my earlier papers on the amount of heat conveyed by the Gulf-stream,[84] I estimated the volume of that stream as equal to that of a current 50 miles broad and 1,000 feet deep, flowing (from the surface to the bottom) at 4 miles an hour. Of course I did not mean, as Dr. Carpenter seems to suppose, that the stream at any particular place is 50 miles broad and 1,000 feet deep, or that it actually flows at the uniform rate of 4 miles an hour at surface and bottom. All I meant was, that the Gulf-stream is equal to that of a current of the above size and velocity. But in my recent papers on Ocean-currents, the substance of which appears in the present volume, to obviate any objections on the grounds of having over-estimated the volume, I have taken that at one half this estimate, viz., equal to a current 50 miles broad and 1,000 feet deep flowing at the rate of 2 miles an hour. I have estimated the mean temperature of the stream as it passes the Straits of Florida to be 65°, and have supposed that the water in its course becomes ultimately cooled down on an average to 40°. In this case each pound of water conveys 19,300 foot-pounds of heat from the Gulf of Mexico, to be employed in warming temperate and polar regions. Assuming these data to be correct, it follows that the amount of heat transferred from the Gulf of Mexico by this stream per day amounts to 77,479,650,000,000,000,000 foot-pounds. This enormous quantity of heat is equal to one-fourth of all that is received from the sun by the whole of the Atlantic Ocean from the Tropic of Cancer up to the Arctic Circle.
This is the amount of heat conveyed from inter-tropical to temperate and polar regions by the Gulf-stream. What now is the amount conveyed by means of the General Oceanic Circulation?
According to this theory there ought to be as much warm water flowing from inter-tropical regions towards the Antarctic as towards the Arctic Circle. We may, therefore, in our calculations, consider that the heat which is received in tropical regions to the south of the equator goes to warm the southern hemisphere, and that received on the north side of the equator to warm the northern hemisphere. The warm currents found in the North Atlantic in temperate regions we may conclude came from the regions lying to the north of the equator,—or, in other words, from that part of the Atlantic lying between the equator and the Tropic of Cancer. At least, according to the gravitation theory, we have no reason to believe that the quantity of warm water flowing from tropical to temperate and polar regions in the Atlantic is greater than the area between the equator and the Tropic of Cancer can supply—because it is affirmed that a very large proportion of the cold water found in the North Atlantic comes, not from the arctic, but from the antarctic regions. But if the North Atlantic is cooled by a cold stream from the southern hemisphere, the southern hemisphere in turn must be heated by a warm current from the North Atlantic—unless we assume that the compensating current flowing from the Atlantic into the southern hemisphere is as cold as the antarctic current, which is very improbable. But Dr. Carpenter admits that the quantity of warm water flowing from the Atlantic in equatorial regions towards the south is even greater than that flowing northwards. “The unrestricted communication,” he says, “which exists between the antarctic area and the great Southern Ocean-basins would involve, if the doctrine of a general oceanic circulation be admitted, a much more considerable interchange of waters between the antarctic and the equatorial areas than is possible in the northern hemisphere.”[85]
We have already seen that, were it not for the great mass of warm water which finds its way to the polar regions, the temperature of these regions would be enormously lower than they really are. It has been shown likewise that the comparatively high temperature of north-western Europe is due to the same cause. But if it be doubtful whether the Gulf-stream reaches our shores, and if it be true that, even supposing it did, it “could only affect the most superficial stratum,” and that the great mass of warm water found by Dr. Carpenter in his dredging expeditions came directly from the equatorial regions, and not from the Gulf-stream, then the principal part of the heating-effect must be attributed, not to the Gulf-stream, but to the general flow of water from the equatorial regions. It surely would not, then, be too much to assume that the quantity of heat conveyed from equatorial regions by this general flow of water into the North Atlantic is at least equal to that conveyed by the Gulf-stream. If we assume this to be the amount of heat conveyed by the two agencies into the Atlantic from inter-tropical regions, it will, of course, be equal to twice that conveyed by the Gulf-stream alone.
We shall now consider whether the area of the Atlantic to the north of the equator is sufficient to supply the amount of heat demanded by Dr. Carpenter’s theory.
The entire area of the Atlantic, extending from the equator to the Tropic of Cancer, including the Caribbean Sea and the Gulf of Mexico, is about 7,700,000 square miles.
The quantity of heat conveyed by the Gulf-stream through the Straits of Florida is, as we have already endeavoured to show, equal to all the heat received from the sun by 1,560,935 square miles at the equator. The annual quantity of heat received from the sun by the torrid zone per unit surface, taking the mean of the whole zone, is to that received by the equator as 39 to 40, consequently the quantity of heat conveyed by the Gulf-stream is equal to all the heat received by 1,600,960 square miles of the Atlantic in the torrid zone.
But if, according to Dr. Carpenter’s views, the quantity of heat conveyed from the tropical regions is double that conveyed by the Gulf-stream, the amount of heat in this case conveyed into the Atlantic in temperate regions will be equal to all the heat received from the sun by 3,201,920 square miles of the Atlantic between the equator and the Tropic of Cancer. This is 32/77ths of all the heat received from the sun by that area.
Taking the annual quantity received per unit surface at the equator at 1,000, the quantities received by the three zones would be respectively as follows:—
Equator 1000 Torrid zone 975 Temperate zone 757 Frigid zone 454
Now, if we remove from the Atlantic in tropical regions 32/77ths of the heat received from the sun, we remove 405 parts from every 975 received from the sun, and consequently only 570 parts per unit surface remain.
It has been shown[86] that the quantity of heat conveyed by the Gulf-stream from the equatorial regions into the temperate regions is equal to 100/412ths of all the heat received by the Atlantic in temperate regions. But according to the theory under consideration the quantity removed is double this, or equal to 100/206ths of all the heat received from the sun. But the amount received from the sun is equal to 757 parts per unit surface; add then to this 100/206ths of 757, or 367, and we have 1,124 parts of heat per unit surface as the amount possessed by the Atlantic in temperate regions. The Atlantic should in this case be much warmer in temperate than in tropical regions; for in temperate regions it would possess 1,124 parts of heat per unit surface, whereas in tropical regions it would possess only 570 parts per unit surface. Of course the heat conveyed from tropical regions does not all remain in temperate regions; a very considerable portion of it must pass into the arctic regions. Let us, then, assume that one half goes to warm the Arctic Ocean, and the other half remains in the temperate regions. In this case 183·5 parts would remain, and consequently 757 + 183·5 = 940·5 parts would be the quantity possessed by the Atlantic in temperate regions, a quantity which still exceeds by no less than 370·5 parts the heat possessed by the Atlantic in tropical regions.
As one half of the amount of heat conveyed from the tropical regions is assumed to go into the Arctic Ocean, the quantity passing into that ocean would therefore be equal to that which passes through the Straits of Florida, an amount which, as we have found, is equal to all the heat received from the sun by 3,436,900 square miles of the Arctic Ocean.[87] The entire area covered by sea beyond the Arctic Circle is under 5,000,000 square miles; but taking the Arctic Ocean in round numbers at 5,000,000 square miles, the quantity of heat conveyed into it by currents to that received from the sun would therefore be as 3,436,900 to 5,000,000.
The amount received on the unit surface of the arctic regions we have seen to be 454 parts. The amount received from the currents would therefore be 312 parts. This gives 766 parts of heat per unit surface as the quantity possessed by the Arctic Ocean. Thus the Arctic Ocean also would contain more heat than the Atlantic in tropical regions; for the Atlantic in these regions would, in the case under consideration, possess only 570 parts, while the Arctic Ocean would possess 766 parts. It is true that more rays are cut off in arctic regions than in tropical; but still, after making due allowance for this, the Arctic Ocean, if the theory we are considering were true, ought to be as warm as, if not warmer than, the Atlantic in tropical regions. The relative quantities of heat possessed by the three zones would therefore be as follows:—
Atlantic, in torrid zone 570 〃 in temperate zone 940 〃 in frigid zone 766
It is here assumed, however, that none of the heat possessed by the Gulf-stream is derived from the southern hemisphere, which, we know, is not the case. But supposing that as much as one half of the heat possessed by the stream came from the southern hemisphere, and that the other half was obtained from the seas lying between the equator and the Tropic of Cancer, the relative proportions of heat possessed by the three zones per given area would be as follows:—
Atlantic, in torrid zone 671 〃 in temperate zone 940 〃 in frigid zone 766
This proves incontestably that, supposing there is such a general oceanic circulation as is maintained, the quantity of heat conveyed by means of it into the North Atlantic and Arctic Oceans must be trifling in comparison with that conveyed by the Gulf-stream; for if it nearly equalled that conveyed by the Gulf-stream, then not only the North Atlantic in temperate regions, but even the Arctic Ocean itself would be much warmer than the inter-tropical seas. In fact, so far as the distribution of heat over the globe is concerned, it is a matter of indifference whether there really is or is not such a thing as this general oceanic circulation. The enormous amount of heat conveyed by the Gulf-stream alone puts it beyond all doubt that ocean-currents are the great agents employed in distributing over the globe the excess of heat received by the sea in inter-tropical regions.
It is therefore, so far as concerns the theory of a General Oceanic Circulation, of the utmost importance that the advocates of that theory should prove that I have over-estimated the thermal power of the Gulf-stream. This, however, can only be done by detecting some error either in my computation or in the data on which it is based; yet neither Dr. Carpenter nor any one else, as far as I know, has challenged the accuracy of my figures. The question at issue is the correctness of the data; but the only part of the data which can possibly admit of being questioned is my estimate of the volume and temperature of the stream. Dr. Carpenter, however, does not maintain that I have over-estimated the temperature of the stream; on the contrary, he affirms that I have really under-estimated it. “If we assume,” he remarks, “the limit of the stratum above 60° as that of the real Gulf-stream current, we shall find its average temperature to be somewhat higher than it has been stated by Mr. Croll, who seems to have taken 65° as the average of the water flowing through the entire channel. The average surface temperature of the Florida channel for the whole year is 80°; and we may fairly set the average of the entire outgoing stream, down to the plane of 60°, at 70°, instead of 65° as estimated by Mr. Croll” (§ 141). It follows, then, that every pound of water of the Gulf-stream actually conveys 5 units of heat more than I have estimated it to do—the amount conveyed being 30 units instead of 25 units as estimated by me. Consequently, if the Gulf-stream be equal to that of a current of merely 41½ miles broad and 1,000 feet deep, flowing at the rate of 2 miles an hour, it will still convey the estimated quantity of heat. But this estimate of the volume of the stream, let it be observed, barely exceeds one-third of that given by Herschel, Maury, and Colding,[88] and is little more than one-half that assigned to it by Mr. Laughton, while it very little exceeds that given by Mr. Findlay,[89] an author whom few will consider likely to overrate either the volume or heating-power of the stream.
The important results obtained during the Challenger expedition have clearly proved that I have neither over-estimated the temperature nor the volume of the Gulf-stream. Between Bermuda and Sandy Hook the stream is 60 miles broad and 600 feet deep, with a maximum velocity of from 3½ to 4 miles an hour. If the mean velocity of the entire section amounts to 2¼ miles an hour, which it probably does, the volume of the stream must equal that given in my estimate. But we have no evidence that all the water flowing through the Straits of Florida passes through the section examined by the officers of the Challenger. Be this, however, as it may, the observations made between St. Thomas and Sandy Hook reveal the existence of an immense flow of warm water, 2,300 feet deep, entirely distinct from the water included in the above section of the Gulf-stream proper. As the thickest portion of this immense body of water joins the warm water of the Gulf-stream, Captain Nares considers that “it is evidently connected with it, and probably as an offshoot.” At Sandy Hook, according to him, it extends 1,200 feet deeper than the Gulf-stream itself, but off Charleston, 600 miles nearer the source, the same temperature is found at the same depth. But whether it be an offshoot of the Gulf-stream or not, one thing is certain, it can only come from the Gulf of Mexico or from the Caribbean Sea. This mass of water, after flowing northwards for about 1,000 miles, turns to the right and crosses the Atlantic in the direction of the Azores, where it appears to thin out.
If, therefore, we take into account the combined heat conveyed by both streams, my estimate of the heat transferred from inter-tropical regions into the North Atlantic will be found rather under than above the truth.
Dr. Carpenter’s Estimate of the Thermal Work of the Gulf-stream.—In the appendix to an elaborate memoir on Oceanic Circulation lately read before the Geographical Society, Dr. Carpenter endeavours to show that I have over-estimated the thermal work of the Gulf-stream. In that memoir[90] he has also favoured us with his own estimate of the sectional area, rate of flow, and temperature of the stream. Even adopting his data, however, I find myself unable to arrive at his conclusions.
Let us consider first his estimate of the sectional area of the stream. He admits that “it is impossible, in the present state of our knowledge, to arrive at any exact estimate of the sectional area of the stream; since it is for the most part only from the temperatures of its different strata that we can judge whether they are, or are not, in movement, and what is the direction of their movement.” Now it is perfectly evident that our estimate of the sectional area of the stream will depend upon what we assume to be its bottom temperature. If, for example, we assume 70° to be the bottom temperature, we shall have a small sectional area. Taking the temperature at 60°, the sectional area will be larger, and if 50° be assumed to be the temperature, the sectional area will be larger still, and so on. Now the small sectional area obtained by Dr. Carpenter arises from the fact of his having assumed the high temperature of 60° to be that of the bottom of the stream. He concludes that all the water below 60° has an inward flow, and that it is only that portion from 60° and upwards which constitutes the Gulf-stream. I have been unable to find any satisfactory evidence for assuming so high a temperature for the bottom of the stream. It must be observed that the water underlying the Gulf-stream is not the ordinary water of the Atlantic, but the cold current from the arctic regions. In fact, it is the same water which reaches the equator at almost every point with a temperature not much above the freezing-point. It is therefore highly improbable that the under surface of the Gulf-stream has a temperature so high as 60°.
Dr. Carpenter’s method of measuring the mean velocity of the Gulf-stream is equally objectionable. He takes the mean annual rate at the surface in the “Narrows” to be two miles an hour and the rate at the bottom to be zero, and he concludes from this that the average rate of the whole is one mile an hour—the arithmetical mean between these two extremes. Now it will be observed that this conclusion only holds true on the supposition that the breadth of the stream is as great at the bottom as at the surface, which of course it is not. All admit that the sides of the Gulf-stream are not perpendicular, but slope somewhat in the manner of the banks of a river. The stream is broad at the surface and narrows towards the bottom. It is therefore evident that the upper half of the section has a much larger area than the lower; the quantity of water flowing through the upper half with a greater velocity than one mile an hour must be much larger than the quantity flowing through the lower half with a less velocity than one mile an hour.
His method of estimating the mean temperature of the stream is even more objectionable. He says, “The average surface temperature of the Florida Channel for the whole year is 80°, and we may set the average of the entire outgoing stream down to the plane of 60° at 70°, instead of 65°, as estimated by Mr. Croll.” If 80° be the surface and 60° be the bottom temperature, temperature and rate of velocity being assumed of course to decrease uniformly from the surface downwards, how is it possible that 70° can be the average temperature? The amount of water flowing through the upper half of the section, with a temperature above 70°, is far more than the amount flowing through the under half of the section, with a temperature below 70°. Supposing the lower half of the section to be as large as the upper half, which it is not, still the quantity of water flowing through it would only equal one-third of that flowing through the upper half, because the mean velocity of the water in the lower half would be only half a mile per hour, whereas the mean velocity of that in the upper half would be a mile and a half an hour. But the area of the lower half is much less than that of the upper half, consequently the amount of water whose temperature is under 70° must be even much under one-third of that, the temperature of which is above 70°.
Had Dr. Carpenter taken the proper method of estimating the mean temperature, he would have found that 75°, even according to his own data, was much nearer the truth than 70°. I pointed out, several years ago,[91] the fallacy of estimating the mean temperature of a stream in this way.
So high a mean temperature as 75° for the Gulf-stream, even in the Florida Channel, is manifestly absurd, but if 60° be the bottom temperature of the stream, the mean temperature cannot possibly be much under that amount. It is, of course, by under-estimating the sectional area of the stream that its mean temperature is over-estimated. We cannot reduce the mean temperature without increasing the sectional area. If my estimate of 65° be taken as the mean temperature, which I have little doubt will yet be found to be not far from the truth, Dr. Carpenter’s estimate of the sectional area must be abandoned. For if 65° be the mean temperature of the stream, its bottom temperature must be far under 60°, and if the bottom temperature be much under 60°, then the sectional area must be greater than he estimates it to be.
Be this, however, as it may; even if we suppose that 60° will eventually be found to be the actual bottom temperature of the Gulf-stream, nevertheless, if the total quantity of heat conveyed by the stream from inter-tropical regions be estimated in the proper way, we shall still find that amount to be so enormous, that there is not sufficient heat remaining in those regions to supply Dr. Carpenter’s oceanic circulation with a quantity as great for distribution in the North Atlantic.
It therefore follows (and so far as regards the theory of Secular changes of climate, this is all that is worth contending for) that Ocean-currents and not a General Oceanic Circulation resulting from gravity, are the great agents employed in the distribution of heat over the globe.
XII. MR. A. G. FINDLAY’S OBJECTIONS CONSIDERED
Mr. Findlay’s Estimate of the Volume of the Gulf-stream.—Mean Temperature of a Cross Section less than Mean Temperature of Stream.—Reason of such Diversity of Opinion regarding Ocean-currents.—More rigid Method of Investigation necessary.
At the conclusion of the reading of Dr. Carpenter’s paper before the Royal Geographical Society, on January 9th, 1871, Mr. Findlay made the following remarks:—
“When, by the direction of the United States Government, ten or eleven years ago, the narrowest part of the Gulf-stream was examined, figures were obtained which shut out all idea of its ever reaching our shores as a heat-bearing current. In the narrowest part, certainly not more than from 250 to 300 cubic miles of water pass per diem. Six months afterwards that water reaches the banks of Newfoundland, and nine or twelve months afterwards the coast of England, by which time it is popularly supposed to cover an area of 1,500,000 square miles. The proportion of the water that passes through the Gulf of Florida will not make a layer of water more than 6 inches thick per diem over such a space. Every one knows how soon a cup of tea cools; and yet it is commonly imagined that a film of only a few inches in depth, after the lapse of so long a time, has an effect upon our climate. There is no need for calculations; the thing is self-evident.”[92]
About five years ago, Mr. Findlay objected to the conclusions which I had arrived at regarding the enormous heating-power of the Gulf-stream on the ground that I had over-estimated the volume of the stream. He stated that its volume was only about the half of what I had estimated it to be. To obviate this objection, I subsequently reduced the volume to one-half of my former estimate.[93] But taking the volume at this low estimate, it was nevertheless found that the quantity of heat conveyed into the Atlantic through the Straits of Florida by means of the stream was equal to about one-fourth of all the heat received from the sun by the Atlantic from the latitude of the Strait of Florida up to the Arctic Circle.
Mr. Findlay, in his paper read before the British Association, affirmed that the volume of the stream is somewhere from 294 to 333 cubic miles per day; but in his remarks at the close of Dr. Carpenter’s address, he stated it to be not greater than from 250 to 300 cubic miles per day. I am unable to reconcile any of those figures with the data from which he appears to have derived them. In his paper to the British Association, he remarks that “the Gulf-stream at its outset is not more than 39½ miles wide, and 1,200 feet deep.” From all attainable data, he computes the mean annual rate of motion to be 65·4 miles per day; but as the rate decreases with the depth, the mean velocity of the whole mass does not exceed 49·4 miles per day. When he speaks of the mean velocity of the Gulf-stream being so and so, he must refer to the mean velocity at some particular place. This is evident; for the mean velocity entirely depends upon the sectional area of the stream. The place where the mean velocity is 49·4 miles per day must be the place where it is 39½ miles broad and 1,200 feet deep; for he is here endeavouring to show us how small the volume of the stream actually is. Now, unless the mean velocity refers to the place where he gives us the breadth and depth of the stream, his figures have no bearing on the point in question. But a stream 39½ miles broad and 1,200 feet deep has a sectional area of 8·97 square miles, and this, with a mean velocity of 49·4 miles per day, will give 443 cubic miles of water. The amount, according to my estimate, is 459 cubic miles per day; it therefore exceeds Mr. Findlay’s estimate by only 16 cubic miles.
Mr. Findlay does not, as far as I know, consider that I have over-estimated the mean temperature of the stream. He states[94] that between Sand Key and Havana the Gulf-stream is about 1,200 feet deep, and that it does not reach the summit of a submarine ridge, which he states has a temperature of 60°. It is evident, then, that the bottom of the stream has a temperature of at least 60°, which is within 5° of what I regard as the mean temperature of the mass. But the surface of the stream is at least 17° above this mean. Now, when we consider that it is at the upper parts of the stream, the place where the temperature is so much above 65°, that the motion is greatest, it is evident that the mean temperature of the entire moving mass must, according to Mr. Findlay, be considerably over 65°. It therefore follows, according to his own data, that the Gulf-stream conveys into the Atlantic an amount of heat equal to one-fourth of all the heat which the Atlantic, from the latitude of the Straits of Florida up to the arctic regions, derives from the sun.
But it must be borne in mind that although the mean temperature of the cross section should be below 65°, it does not therefore follow that the mean temperature of the water flowing through this cross section must be below that temperature, for it is perfectly obvious that the mean temperature of the mass of water flowing through the cross section in a given time must be much higher than that of the cross section itself. The reason is very simple. It is in the upper half of the section where the high temperature exists; but as the velocity of the stream is much greater in its upper than in its lower half, the greater portion of the water passing through this cross section is water of high temperature.
But even supposing we were to halve Mr. Findlay’s own estimate, and assume that the volume of the stream is equal to only 222 cubic miles of water per day instead of 443, still the amount of heat conveyed would be equal to one-eighth part of the heat received from the sun by the Atlantic. But would not the withdrawal of an amount of heat equal to one-eighth of that received from the sun greatly affect the climate of the Atlantic? Supposing we take the mean temperature of the Atlantic at, say, 56°; this will make its temperature 295° above that of space. Extinguish the sun and stop the Gulf-stream, and the temperature ought to sink 295°. How far, then, ought the temperature to sink, supposing the sun to remain and the Gulf-stream to stop? Would not the withdrawal of the stream cause the temperature to sink some 30°? Of course, if the Gulf-stream were withdrawn and everything else were to remain the same, the temperature of the Atlantic would not actually remain 30° lower than at present; for heat would flow in from all sides and partly make up for the loss of the stream. But nevertheless 30° represents the amount of temperature maintained by means of the heat from the stream. And this, be it observed, is taking the volume of the stream at a lower estimate than even Mr. Findlay himself would be willing to admit. Mr. Findlay says that, by the time the Gulf-stream reaches the shores of England, it is supposed to cover a space of 1,500,000 square miles. “The proportion of water that passes through the Straits of Florida will not make,” according to him, “a layer of water more than 6 inches thick per diem over such a space.” But a layer of water 6 inches thick cooling 25° will give out 579,000 foot-pounds of heat per square foot. If, therefore, the Gulf-stream, as he asserts, supplies 6 inches per day to that area, then every square foot of the area gives off per day 579,000 foot-pounds of heat. The amount of heat received from the sun per square foot in latitude 55°, which is not much above the mean latitude of Great Britain, is 1,047,730 foot-pounds per day, taking, of course, the mean of the whole year; consequently this layer of water gives out an amount of heat equal to more than one-half of all that is received from the sun. But assuming that the stream should leave the half of its heat on the American shores and carry to the shores of Britain only 12½° of heat, still we should have 289,500 foot-pounds per square foot, which notwithstanding is more than equal to one-fourth of that received from the sun. If an amount of heat so enormous cannot affect climate, what can?
I shall just allude to one other erroneous notion which prevails in regard to the Gulf-stream; but it is an error which I by no means attribute either to Mr. Findlay or to Dr. Carpenter. The error to which I refer is that of supposing that when the Gulf-stream widens out to hundreds of miles, as it does before it reaches our shores, its depth must on this account be much less than when it issues from the Gulf of Mexico. Although the stream may be hundreds of miles in breadth, there is no necessity why it should be only 6 inches, or 6 feet, or 60 feet, or even 600 feet in depth. It may just as likely be 6,000 feet deep as 6 inches.
The Reason why such Diversity of Opinion prevails in Regard to Ocean-currents.—In conclusion I venture to remark that more than nine-tenths of all the error and uncertainty which prevail, both in regard to the cause of ocean-currents and to their influence on climate, is due, not, as is generally supposed, to the intrinsic difficulties of the subject, but rather to the defective methods which have hitherto been employed in its investigation—that is, in not treating the subject according to the rigid methods adopted in other departments of physics. What I most particularly allude to is the disregard paid to the modern method of determining the amount of effects in absolute measure.
But let me not be misunderstood on this point. I by no means suppose that the absolute quantity is the thing always required for its own sake. It is in most cases required simply as a means to an end; and very often that end is the knowledge of the relative quantity. Take, for example, the Gulf-stream. Suppose the question is asked, to what extent does the heat conveyed by that stream influence the climate of the North Atlantic? In order to the proper answering of this question, the principal thing required is to know what proportion the amount of heat conveyed by the stream into the Atlantic bears to that received from the sun by that area. We want the relative proportions of these two quantities. But how are we to obtain them? We can only do so by determining first the absolute quantity of each. We must first measure each before we can know how much the one is greater than the other, or, in other words, before we can know their relative proportions. We have the means of determining the absolute amount of heat received from the sun by a given area at any latitude with tolerable accuracy; but the same cannot be done with equal accuracy in regard to the amount of heat conveyed by the Gulf-stream, because the volume and mean temperature of the stream are not known with certainty. Nevertheless we have sufficient data to enable us to fix upon such a maximum and minimum value to these quantities as will induce us to admit that the truth must lie somewhere between them. In order to give full justice to those who maintain that the Gulf-stream exercises but little influence on climate, and to put an end to all further objections as to the uncertainty of my data, I shall take a minimum to which none of them surely can reasonably object, viz. that the volume of the stream is not over 230 cubic miles per day, and the heat conveyed per pound of water not over 12½ units. Calculating from these data, we find that the amount of heat carried into the North Atlantic is equal to one-sixteenth of all the heat received from the sun by that area. There are, I presume, few who will not admit that the actual proportion is much higher than this, probably as high as 1 to 3, or 1 to 4. But, who, without adopting the method I have pursued, could ever have come to the conclusion that the proportion was even 1 to 16? He might have guessed it to be 1 to 100 or 1 to 1000, but he never would have guessed it to be 1 to 16. Hence the reason why the great influence of the Gulf-stream as a heating agent has been so much under-estimated.
The same remarks apply to the gravitation theory of the cause of currents. Viewed simply as a theory it looks very reasonable. There is no one acquainted with physics but will admit that the tendency of the difference of temperature between the equator and the poles is to cause a surface current from the equator towards the poles, and an under current from the poles to the equator. But before we can prove that this tendency does actually produce such currents, another question must be settled, viz. is this force sufficiently great to produce the required motion? Now when we apply the method to which I refer, and determine the absolute amount of the force resulting from the difference of specific gravity, we discover that not to be the powerful agent which the advocates of the gravitation theory suppose, but a force so infinitesimal as not to be worthy of being taken into account when considering the causes by which currents are produced.