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.