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209
OCEANIC CURRENTS
If we apply this result to the case of the earth we see that
generally the tidal wave in its progress must be followed by a
current in the same direction. In a canal encircling the earth
along a parallel of latitude the current would flow everywhere
from east to west; in a canal situated in any way whatever
it would be from east to west near the equator, in the opposite
direction at a distance from it. In general the current is very
small, but it may become very appreciable when the length and
depth of the canal are such that the period of the oscillation
of the water in it is one day, in which case without friction
the tides would be infinitely great. The formulæ given are
not suitable for getting numerical values, as the differential
equations used are not applicable to the motion of deep seas.
In fact, if we substitute for the coefficient of viscosity the very
small value obtained from experiments with capillary tubes,
we get ridiculously high tides and ridiculously violent currents.
On the other hand we get currents of only about 100 metres
per hour if we use the formula
u = A
and substitute for ₁ values corresponding to actually occurring
tides.
A posteriori, we can from the magnitude of tidal friction
as approximately known draw a conclusion as to the order
of magnitude of the currents caused by gravitation. In one
century the earth lags twenty-two seconds behind a correct
chronometer.¹ To produce such a retardation a force must be
constantly applied at the equator equal to 530 million kilo-
grammes' weight and acting from east to west. If we imagine
this force distributed along a system of coast-lines which run
parallel to the meridian, bound the ocean on the west, and
have a total length of one earth-quadrant, then we get a
pressure of 53 kilogrammes' weight for each metre length of
coast. To produce this pressure the sea must at these western
coasts be elevated 0.3 metre above the level surface with which it
coincides at the eastern coasts. In so far then as the retardation
mentioned of the earth's rotation has its origin in tidal friction,
we can conclude that in consequence of the tide-generating
1 Thomson and Tait, Natural Philosophy, § 830.
M. P.
P