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.
Public-domain text, read in full here on John Shaqi.
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