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 surfaceslope, 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 CW, 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 rertical 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 surfacewater 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.*

• Proc. of Roy. Geog. Soc., January 9, 1871, § 29.

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 underestimate the Volume of the Gulf-stream.-Volume of the Stream as determined by the Challenger.-Iminense 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, 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 Gulfstream 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

• Trans. of Geol. Soc. of Glasgow for April, 1867; Phil. Mag. for June, 1867.

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 652, 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."*

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 dredgingexpeditions came directly from the equatorial regions, and not from the Gulf-stream, then the principal part of the heatingeffect 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 intertropical regions, it will, of course, be equal to twice that conveyed by the Gulf-stream alone.

* Nature, vol. i., p. 541. Proc. Roy. Soc., vol. xviii., p. 473.