James Croll.

Climate and time in their geological relations: a theory of secular changes ... online

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the slope from the equator to the pole, 3^ foot-poimds 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



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THE GRAVITATION THEORY. 159

whole mass is therefore 3^ feet. And this gives 3^ foot-pounds
as the mean amount of work per pound of water in descending
the slope; this, added to the half foot-pound deriyed 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 colimin 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 repre-
senting 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, how-
ever, the two effects take place simultaneously j but it is need-
less 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 alteraticms 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
colimm. 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



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i6o



CLIMATE AND TIME.



of water in passing from E to P would liave its temperature
reduced from 80° to 32°, and this would produce a slight con-
Fig. 2.




traction. 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 contrac-
tion being to increase by an infinitesimal amoimt the work done
in descending the slope, and to diminish by an equally infinites-
imal amount the work done in the vertical descent. If, for
example, 3 foot-poundsrepresent the amount of work performed
in descending the slope, and one foot-pound the amount per-
formed 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 con-
traction. But the total amoimt 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'.

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 f oot-poimds 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



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THE GRAVITATION THEORY. i6i

foot of water from tlie equatorial columii 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 wiU 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 colimms
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. Con-
sequently 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 equi-
librium, then 4 foot-pounds is the total amoimt of work that i
gravity can perform upon a pound of water in overcoming j
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 PO, 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 ? Wo
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.



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,62 CLIMATE AND TIME.

friction, and other resistances ; it is all spent in counteracting
the eflforts which gravity exerts to stop the current in another
part of the circuit.

I shall now consider the next part of the moyement, viz., the
under or return current from the bottom of the polar to the
bottom of the equatorial colunm. What produces this current P
It is needless to say that it cannot be caused directly by
gravity. Gravitation cannot directly draw any body hori-
zontally along the earth's surface. The water that forms this
current is pressed out laterally by the weight of the polar
colunm, 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 P 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 move-
ment, 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 imder current reaches the equatorial
regions, it ascends to the surface to the point whence it origin-
ally started on its circuit. What, then, lifts the water from
the bottom of the equatorial colunm to its top ? This cannot



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THE GRAVITATION THEORY. 163

be done directly, either by heat or by gravity. When heat,
for example, is applied to the bottom of a yessel, the heated
water at the bottom expands and, becoming lighter than the
water aboye, 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 equa-
torial column. Thus, when the polar column sinks a foot,
the equatorial column rises to the same extent. The equa-
torial water continuing to flow down the slope, the polar
column descends : a foot of water is again pressed from under-
neath the polar column and a foot pressed in under the equa-
torial. As foot after foot is thus removed from the bottom of
the polar column while it sinks, foot after foot is pushed in under



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1 6+ CLIMATE AND TIME.

the equatorial column wliile 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 leyel 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 wiU 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 tiiis 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/'*

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 amoimt 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 coliunn 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 and E Q, but also to the
parts P' P and E E' of the two columns. When a mass of
* Proceedings of the Eoyal Society, voL xix., p. 215.



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THE GRAVITATION THEORY. 165

water E E', say one foot deep, is removed off tlie 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 colunm
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 coliimn, and consequently motion
ceases. It therefore follows that the entire amoimt 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 per-
formed by gravity in sinking it. But whilst inequalities in the
bed of the ocean would not aid the current, they would never-
theless 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
imder current in addition to the raising of the equatorial column.

It follows also that the amoimt of work which can be per-
formed by gravity depends entirely on the difference of tempe-



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1 66 CLIMATE AND TIME.

rature 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 agree-
ment with Dr. Carpenter's idea,* 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
amoimt of work which gravity could perform ; it would simply
make the slope steeper at the two extreme and flatter in the
intervening space. It w^uld 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 inter-
mediate regions. In short, it would merely destroy the unifor-
mity 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 hey comprehends all that can pos-
sibly 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 aU 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 calcidations 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
♦ Ifature for July 6, 1871.



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THE GRA VITA TION THEORY. 1 67

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 desfcroy-
ing 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. Kow 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 P 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 equa-
torial 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.

Ghravitation Theory of the Oihraltar 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 sub-
marine 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 hydro-
static. If we fill a basin with water or any other fluid, the
fluid remains in perfect equilibrium, provided the sides of the



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1 68 CLIMATE AND TIME.

basin be suflSciently strong to resist the pressure. The Medi-
terranean and Athmtic, 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, how-
ever 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 Medi-
terranean 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 Mediter-
ranean 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 betwe^



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THE GRAVITATION THEORY. 169

the two seas, or, wluch is the same thing, the difference of level ,
between a column of the Atlantic and a column of the Mediter- !
ranean, we must take into consideration only the water which I
lies above the level of the ridge. If there be one foot of water j
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 niunber 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
surfece.

Taking Dr. Carpenter's own data as to the density of the
Mediterranean and Atlantic waters, what, then, is the difference
of density P 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
fepm 400 fathoms respectively, that whilst the/r«^ ttvo had the



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170 CLIMATE AND TIME.

cJiaracteristic temperature and density of Atlantic water ^ the last
two liad the characteristics and density of Mediterranean
water" (§ 13). Here, at least to the depth of 100 fathoms or
600 feet, there is little diflference of density between the waters
of the two basins. Consequently down to the depth of 600



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