+----------+-------------+

| 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:—

[Illustration: Fig. 1.]

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′.

[Illustration: Fig. 2.]

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]

[Illustration: Fig. 3.]

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.