by Clifford J. Cunningham In a 1679 letter to Robert Hooke, Isaac Newton explained his idea that
Earth's rotation could be proved from the fact that an object dropped
from the top of a tower should have a greater tangential velocity than
one dropped near the foot of the tower. By saying that the velocity
of falling bodies in the eastward direction was greater than the velocity
of Earth's surface, Newton thus predicted an eastward deviation for
a falling body. Hooke said that the deviation "would not be directly
east, as Mr. Newton supposed, but to the southeast." Newton's suggestion presented a novel way to confirm the Copernican
system, which most astronomers had accepted by this time. Those who
didn't "were a bit slow-witted or under the superstitions imposed
by merely human activity," wrote Dutch astronomer Christian Huygens. Even so, acceptance is not proof. Hooke had already discovered that
Jupiter rotates on its axis. Proving that Earth itself rotates was a
tempting prize. Hooke dropped balls from a height of 8.2 meters and
claimed to have noted a deviation to the southeast, but because the
magnitude of the deviations differed, Hooke did not know "which
was true:' A century passed before Giovanni Guglielmini repeated the experiment.
Between June and September 1791, Guglielmini scaled the 78-meter city
tower of Bologna, from which he dropped 16 balls. This was reminiscent
of Galileo 200 years earlier, who reputedly dropped weights from the
Leaning Tower of Pisa. But Galileo was studying motion in the direction
of the gravitational center, and was thus not looking for a deviation.
While Guglielmini successfully noted a southeast deviation, both his
measurement and the calculated deviation were incorrect. Physics in
the late 18th century was not grounded in mathematics as it is today. Lack of a firm mathematical basis did not deter a 25-year-old teacher
newly arrived in Hamburg in 1802. Johann Benzenberg was determined to
make his mark by proving Earth's rotation. He chose the highest point
available, the spire of St. Michael's church, from which he dropped
31 balls onto a prepared wooden surface. He also noted a deviation to
the southeast, but the results begged the question: What results should
be expected according to theory? Benzenberg turned his results over to Wilhelm Olbers, who was unable
to solve the problem. Fresh from his triumph in calculating the orbit
of the first asteroid, Ceres, the mathematician Carl Gauss developed
a workable theory. This spurred Benzenberg to repeat the tests in a
mine shaft. In 1804 he dropped 29 balls a distance of 80.4 meters. The
eastward deviation differed only one-twelfth from Gauss's predicted
value. It fell to French physicist Leon Foucault to offer indisputable proof
of Earth's rotation. He did so in a novel manner. Realizing that the
free fall of a weight was difficult to measure accurately, he began
experimenting in his cellar using a 2-meter pendulum with a 5-kilogram
bob. On February 3, 1851 he presented his experiment to his colleagues,
and Prince Louis Bonaparte asked him to give a public demonstration.
The scene could hardly have been more dramatic. Foucault set up a pendulum
more than 60 meters long hanging from the domed ceiling of the Pantheon
in Paris. The pendulum never retraced its path as each swing deviated
to the right, which meant that the floor of the Pantheon was moving!
Foucault had at last provided the first dynamical proof of Earth's rotation.
Foucault pendulums now hold a place of honor in science museums worldwide. The interest in falling bodies did not end with Foucault. In 1902 E.
H. Hall at Harvard University conducted a careful experiment in which
948 balls were dropped 23 meters. Using Gauss's theory, he predicted
an eastward deviation of 1.8 millimeters. His experimental result was
1.5 millimeters, but he also observed a southward deviation of 0.05
millimeters, which is not expected from Gauss's theory. As late as the 1940s some authors regarded the southward deviation as a mystery, but it is explicable as part of the Coriolis force. The basic equation predicts only an eastward deviation, but inclusion of further mathematical terms reveals that a small southward deviation should occur. What is amazing is that Robert Hooke expected it more than 300 years ago. High school students seeking a challenging science fair project need look no further!
The article above appeared in the July-Aug, 2002 issue of Mercury Magazine,
p. 13, and is used with permission of the author. Mercury Magazine is
a publication of the Astronomical
Society of the Pacific. |