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10 Statistics and Other Concerns
10.1 Tides
Kapteyn had a broad interest and did engage in other fields of science,
sometimes—as in the case of tides below—with little success, sometimes—
in the case of statistics, in the next section—to help others and then spend a
disproportionate amount of time on it. We saw earlier that in his first years in
Groningen he had, among other things, done research into periodicity in the
weather and climate with the help of growth rings in trees.
Kapteyn gave a lecture on the for him unusual subject of The theory of ebb
and flow on February 27, 1909 for the Mining Society in Delft. It is not clear
why he was asked to speak on this subject. As far as I know he had not done
any research in this field and although it was somewhat related to astronomy,
it was still first and foremost a subject for someone in earth sciences. His son
had studied mining engineering, but not in Delft. The lecture was published
in the Society’s Yearbook, in the form of notes by one F.T. Mesdag, probably the
mining expert Ferdinand Taco Mesdag (1886–1961). These notes also contain
a number of footnotes, which are obviously comments by Mesdag.
Kapteyn was completely wrong. The tides on Earth are a consequence of
the attraction of the Moon and to a lesser extent the Sun. Suppose (which
Kapteyn also did in his lecture) that the Earth is covered with a large ocean
without continents and that it is equally deep everywhere. Then consider the
point on this ocean exactly below the Moon, so where the Moon is directly
above. The Moon exerts a certain attraction on the surface of the ocean. And
also on the Earth’s surface at the bottom. But the latter force is smaller because
the Earth’s surface is further away from the Moon and the ocean is more easily
distorted by the Moon’s gravitation. The result is that the surface of the ocean
is pulled up a bit more than the bottom, and so there will be a bulge towards
the Moon. The same goes for the opposite side of the Earth, but the effect is
smaller there because that side is further away from the Moon. However, one
must also take into account that there are centrifugal forces due to the rotation
of the Earth and especially due to the motion of the Earth around the center
of gravity on the Earth-Moon system. That point is outside, but not far from
the Earth’s surface, and the effect is greatest on the side turned away from the
Moon. This causes a bulge on that side as well, which is comparable to the one
directly under the Moon. So the ocean surface becomes a kind of ellipsoid, like
the ball for rugby or American football, with the largest diameter away from
and towards the Moon. In such simple considerations it is assumed initially,
that the Moon is always above the equator. In reality, the plane of the Moon’s
orbit makes an angle of about 6 ◦ with the Earth’s orbit around the Sun, and
that angle makes another 23 ◦ with the equator. So the position on Earth at
10 Statistics and Other Concerns
10.1 Tides
Kapteyn had a broad interest and did engage in other fields of science,
sometimes—as in the case of tides below—with little success, sometimes—
in the case of statistics, in the next section—to help others and then spend a
disproportionate amount of time on it. We saw earlier that in his first years in
Groningen he had, among other things, done research into periodicity in the
weather and climate with the help of growth rings in trees.
Kapteyn gave a lecture on the for him unusual subject of The theory of ebb
and flow on February 27, 1909 for the Mining Society in Delft. It is not clear
why he was asked to speak on this subject. As far as I know he had not done
any research in this field and although it was somewhat related to astronomy,
it was still first and foremost a subject for someone in earth sciences. His son
had studied mining engineering, but not in Delft. The lecture was published
in the Society’s Yearbook, in the form of notes by one F.T. Mesdag, probably the
mining expert Ferdinand Taco Mesdag (1886–1961). These notes also contain
a number of footnotes, which are obviously comments by Mesdag.
Kapteyn was completely wrong. The tides on Earth are a consequence of
the attraction of the Moon and to a lesser extent the Sun. Suppose (which
Kapteyn also did in his lecture) that the Earth is covered with a large ocean
without continents and that it is equally deep everywhere. Then consider the
point on this ocean exactly below the Moon, so where the Moon is directly
above. The Moon exerts a certain attraction on the surface of the ocean. And
also on the Earth’s surface at the bottom. But the latter force is smaller because
the Earth’s surface is further away from the Moon and the ocean is more easily
distorted by the Moon’s gravitation. The result is that the surface of the ocean
is pulled up a bit more than the bottom, and so there will be a bulge towards
the Moon. The same goes for the opposite side of the Earth, but the effect is
smaller there because that side is further away from the Moon. However, one
must also take into account that there are centrifugal forces due to the rotation
of the Earth and especially due to the motion of the Earth around the center
of gravity on the Earth-Moon system. That point is outside, but not far from
the Earth’s surface, and the effect is greatest on the side turned away from the
Moon. This causes a bulge on that side as well, which is comparable to the one
directly under the Moon. So the ocean surface becomes a kind of ellipsoid, like
the ball for rugby or American football, with the largest diameter away from
and towards the Moon. In such simple considerations it is assumed initially,
that the Moon is always above the equator. In reality, the plane of the Moon’s
orbit makes an angle of about 6 ◦ with the Earth’s orbit around the Sun, and
that angle makes another 23 ◦ with the equator. So the position on Earth at