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.