XXIX. On Ocean-currents.-Part III. On the Physical Cause of Ocean-currents. By JAMES CROLL, of the Geological Survey of Scotland.

[Continued from vol. xl. p. 259.]

Dr. Carpenter's Theory of a General Oceanic Circulation. THE

HE two great causes which have been assigned for oceancurrents are the influence of the winds and the difference of specific gravity between the ocean in equatorial and polar regions. 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. It is only when we adopt the more rigid method of determining in absolute measure the amount of the forces resulting from difference of specific gravity that we become aware that this is a cause utterly insufficient to produce the motions attributed to it. In my last paper* I examined at considerable length Lieut. Maury's theory, and endeavoured to show that difference of specific gravity between the sea in equatorial and polar regions could not, as he supposed, bee cause of the Gulf-stream and other currents. Since the publication of that paper, an interesting and elaborate memoir on ocean-currents has been read before the Royal Geographical Society by Dr. Carpenter. In this memoir he states that my objections do not apply to the slow movement, imperceptible to

* Phil. Mag. for October 1870.

Phil. Mag. S. 4. Vol. 42. No. 280. Oct. 1871.

ordinary observation, which he advocates. The conclusion at which I arrived was that the motive force resulting from the difference of specific gravity is equal to one fourth of a grain on the cubic foot (63 lbs.); and I also adduced evidence to show that a force so infinitesimal is not only insufficient to move the water at the rate of several miles an hour, as in the case of the Gulf-stream and other currents, but is actually insufficient to produce any sensible motion whatever,-in short, that Dr. Carpenter's theory of a general interchange of Equatorial and Polar water resulting from difference of specific gravity is quite as physically impossible as Lieut. Maury's theory. But as Dr. Carpenter, in the memoir referred to*, has stated his theory with much fulness, and supported his positions with much ingenuity of argument, it will be necessary for me to enter a little more minutely into some of the points under discussion before considering the influence of the winds as a cause of currents. This will, undoubtedly, be best effected by an examination of Dr. Carpenter's arguments. Until these are shown to be insufficient to support the theory maintained by him, it is needless to begin the consideration of the effects of the winds. And as he has in his memoir done me the honour to discuss at considerable length some of my objections to his theory, I trust that it will not be deemed either discourteous or presumptuous in me that I should enter somewhat more fully into the subject.

There are three ways whereby it may be determined whether or not the circulation of the ocean is due to difference in specific gravity: viz. (1) the matter may be determined by direct experiment; (2) it may be determined by ascertaining the absolute amount of force acting on the water to produce motion, in virtue of difference of specific gravity, and then 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. It is strange that Dr. Carpenter nor any of the advocates of the gravitation theory have ever adopted any of these methods. Dr. Carpenter seems to take for granted that a circulation of the ocean similar to what he advocates is a "physical necessity." But this is the very point at issue. If the work of gravity so far exceeds the work of the resistances in such a motion of the waters as that supposed by Dr. Carpenter, then, indeed, such a motion is a physical necessity;

*"On the Gibraltar Current, the Gulf-stream, and the General Oceanic Circulation," Proceedings of the Royal Geographical Society, vol. xv. p. 54.

but, on the other hand, if the work of gravity falls short of the work of the resistances (and Dr. Carpenter has nowhere proved that it does not), the motion which he supposes is not only not a physical necessity, but is actually a physical impossibility.

Dr. Carpenter states that his doctrine of a General Oceanic Circulation has been accepted as valid by some of the most distinguished mathematicians and physicists of this country. This is, no doubt, true; but I cannot help thinking that those eminent physicists who have given a general assent to the correctness of his theory have done so without giving it special consideration-and that when they come to examine the question more minutely they will be satisfied that the forces resulting from difference of density, whether that difference be caused by difference of temperature or by difference in saltness, is so infinitesimal as to be wholly insufficient to produce the great currents of the ocean. With the exception of Dr. Colding, of Copenhagen*, I am not aware that any physicist holding the gravitation theory has attempted to determine the absolute amount of the forces acting on the water so as to produce motion. Dr. Carpenter's experiment.-True, Dr. Carpenter has exhibited an experiment to show the motion of the water. 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

Dr. Colding, of Copenhagen, in a memoir lately published (Om Stromningsforholdene i almindelige Ledninger og i Havet, 1870), has determined with much labour and skill the influence of difference of specific gravity and of the earth's rotation as causes of the Gulf-stream. The following are some of the conclusions at which he has arrived. Between Bemini and St. Augustine, the only motive power he considers is difference of level, which he estimates to be 6 feet. From St. Augustine to New York Bay the stream is propelled by the rotation of the earth, the force of which is equal to that of a slope of 9 or 10 feet. From New York Bay to Europe it is propelled east by rotation up a slope of about 1 foot. Near Europe the current divides into two branches. One, under the influence of the diminished force of rotation, goes south-east to the coast of Africa; the other goes along the British coast, and is turned north by the direction of the coast, rotation causing it to rise from left to right about 1 foot. The estimated force of rotation exercised on the Gulf-stream from St. Augustine to lat. 60° N. he considers to be equal to that of a difference of level of 25 feet. He has in like manner shown the influence of difference of level and rotation on the return current from the Arctic regions to the Gulf of Mexico.

Dr. Colding appears, however, to leave out of account molecular resistance to motion. He says, "we do not know at present if the molecules of water or air move without resistance." But, for reasons which will come under our consideration, Dr. Colding appears to have greatly overestimated the influence of gravity in the production of motion.

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 the conditions of his experiment agree with what actually exists in the ocean. These conditions I have already stated at considerable length in my last paper*. If his trough be as much as 1 inch in depth, it will require to be upwards of 120 feet in length. Let the surface-temperature of the water at one end of such a trough be 80°, decreasing from the surface downwards till at the depth of half an inch it is as low as 30° or 32°, and let the water at the other end be kept at 32°, or as low as it can be kept without freezing. If the experiment succeeds under these conditions, his point will be established.

But I most 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 pretty 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 spiritlamp. 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, but will 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.

The case referred to by him of the heating-apparatus in the London University is also unsatisfactory. The water leaves the boiler at 120° and returns to it at 80°. The difference of spe

* Phil. Mag. Oct. 1870, p. 254.

cific 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 exist in the theory of oceanic circulation at present under our consideration.

But, be all this as it may, though I do not believe that in Dr. Carpenter's experiments circulation is effected by difference of specific gravity, still I freely admit that difference of specific gravity will produce a circulation such as that supposed by him. Neither do I deny that the thing can be shown experimentally. What I affirm is, that no experiment can show that water will circulate under difference of specific gravity if the conditions of the experiment be made to agree with what exists in the ocean; and unless these conditions are complied with, any experiment, no matter what it may be, is useless so far as concerns the question at issue.

The Force exerted by Gravity.-Sir John Herschel, in proving that difference of specific gravity could not be the cause of oceancurrents, adopted the second of the three methods to which I have referred; viz. he showed that the force of gravitation, acting on the waters of the ocean in virtue of specific gravity, is not sufficient to produce the required motion. Sir John in his calculations had taken 39° as the temperature of maximum density. The temperature of maximum density, however, is much lower than this; and as Dr. Carpenter maintained that all determinations based upon the supposition that 39° is the temperature of maximum density gave too low an estimate of the effect of difference of specific gravity in causing motion, I calculated in my paper what would be the force of gravity, taking 32° to be the temperature of the greatest density instead of 39°, and found that the force of gravitation was about the same as when the temperature was taken at 39°,-the reason being, that when we take 32° as the temperature of maximum density, we have 18 feet as the height of the ocean at the equator above the place of maximum density, but then this place is the pole, whereas when we take 39° as the temperature of maximum