10.1 Tides
207
where the Moon is directly above, varies in latitude from about 30 ◦ south to
30 ◦ north. That is a considerable deviation, so one will have to include it in
every theory of tides.
In this idealized case with a large ocean, the long diameter of the ocean’s
surface remains oriented towards the Moon and travels around the Earth. Now
at a certain position in reality we do not see a wave passing by every twelve
hours, because the Moon also moves around the Earth; that causes a cycle of
twelve hours and 25 min. In practice it is even more complicated, because the
influence of the Sun also makes itself felt, although that effect is smaller. Do
Sun and Moon work together (when they are in the same direction as seen
from the Earth), then we speak of spring tide; if the effect is minimal of neap
tide. 1
Kapteyn had a completely different theory. He took the simple case that
the Moon orbits exactly above the equator. The attraction of the Moon can
be understood as consisting of one component perpendicular to the Earth’s
surface and another one parallel to it. The latter is zero directly below the
Moon and at maximum at those places where the Moon is on the horizon. At
the equator, that component is along or directly opposite the rotation of the
Earth. Water (not the Earth’s surface itself, because it is solid) is accelerated
or slowed down as a result, so that water flows away from the place where the
velocity is greatest. And then you get a ‘valley’ in the surface of the ocean right
under the Moon. Kapteyn summarized the result as: ‘There is low tide under
the Moon and high tide 90 ◦ from the Moon’. Exactly the opposite of what is
actually the case! Mesdag seems to think the same and wrote in a footnote: ‘So
this conclusion differs from the widely accepted view’. How Kapteyn came up
with his theory and why he did not present the usual explanation, which by
the way goes back to Newton, Laplace and others, is a mystery.
If high tide is directly below the Moon, then one can—one would think—
check that by comparing the times of high and low tide at a certain position
on Earth with the times when the Moon is highest above the horizon. So
it would be easy to verify Kapteyn’s theory. Unfortunately, it is much more
complicated in practice because of the presence of the continents. The largest
water surface on Earth is the Pacific Ocean, and that is where the tides are
strongest. This results in a tidal wave, which propagates around Cape of Good
Hope underneath Africa and Cape Horn underneath South America into the
Atlantic Ocean. The Dutch coast is reached via the Strait of Dover or around
the British Isles. The wave takes a day or two and so the tide is very much behind
1 For readers with a physics background: what counts is the difference of the attraction over a relatively
small distance. Gravitation is inversely proportional to the square of the distance, but the tidal effect is
then inversely proportional to the third power. This means a relatively large effect over a small distance.
This third power is also why the influence of the Sun is less than that of the Moon.
207
where the Moon is directly above, varies in latitude from about 30 ◦ south to
30 ◦ north. That is a considerable deviation, so one will have to include it in
every theory of tides.
In this idealized case with a large ocean, the long diameter of the ocean’s
surface remains oriented towards the Moon and travels around the Earth. Now
at a certain position in reality we do not see a wave passing by every twelve
hours, because the Moon also moves around the Earth; that causes a cycle of
twelve hours and 25 min. In practice it is even more complicated, because the
influence of the Sun also makes itself felt, although that effect is smaller. Do
Sun and Moon work together (when they are in the same direction as seen
from the Earth), then we speak of spring tide; if the effect is minimal of neap
tide. 1
Kapteyn had a completely different theory. He took the simple case that
the Moon orbits exactly above the equator. The attraction of the Moon can
be understood as consisting of one component perpendicular to the Earth’s
surface and another one parallel to it. The latter is zero directly below the
Moon and at maximum at those places where the Moon is on the horizon. At
the equator, that component is along or directly opposite the rotation of the
Earth. Water (not the Earth’s surface itself, because it is solid) is accelerated
or slowed down as a result, so that water flows away from the place where the
velocity is greatest. And then you get a ‘valley’ in the surface of the ocean right
under the Moon. Kapteyn summarized the result as: ‘There is low tide under
the Moon and high tide 90 ◦ from the Moon’. Exactly the opposite of what is
actually the case! Mesdag seems to think the same and wrote in a footnote: ‘So
this conclusion differs from the widely accepted view’. How Kapteyn came up
with his theory and why he did not present the usual explanation, which by
the way goes back to Newton, Laplace and others, is a mystery.
If high tide is directly below the Moon, then one can—one would think—
check that by comparing the times of high and low tide at a certain position
on Earth with the times when the Moon is highest above the horizon. So
it would be easy to verify Kapteyn’s theory. Unfortunately, it is much more
complicated in practice because of the presence of the continents. The largest
water surface on Earth is the Pacific Ocean, and that is where the tides are
strongest. This results in a tidal wave, which propagates around Cape of Good
Hope underneath Africa and Cape Horn underneath South America into the
Atlantic Ocean. The Dutch coast is reached via the Strait of Dover or around
the British Isles. The wave takes a day or two and so the tide is very much behind
1 For readers with a physics background: what counts is the difference of the attraction over a relatively
small distance. Gravitation is inversely proportional to the square of the distance, but the tidal effect is
then inversely proportional to the third power. This means a relatively large effect over a small distance.
This third power is also why the influence of the Sun is less than that of the Moon.