Comment: Robert P Crease
physicsworld.com
Critical Point Measuring the Earth
In his travel book The Innocents Abroad
(1869), Mark Twain describes his visit to the
Baptistery of the Duomo of Pisa, where,
according to legend, in 1581 the young
Galileo noticed the regularity of the building’s swinging chandelier. Using his pulse as
a stopwatch, the then 17-year-old medical
student observed that the chandelier took
the same time to swing back and forth
whether traversing a short or a long arc.
Twain marvelled at how “insignificant” the
chandelier looked, even though we had
learned from it that such swinging objects
were not mere lamps but pendulums. The
awestruck Twain concluded that this was no
common pendulum, “but the old original
patriarchal Pendulum – the Abraham pendulum of the world”.
The principle Galileo noticed – that a pendulum’s period, T, depends only on its
length, L – is strictly true only in a vacuum,
applies just for small swings, and ignores friction and other factors. Still, the very simplicity of the principle makes the pendulum
useful as an instrument. Indeed, the pendulum is one of the oldest scientific instruments
still in service – older, though just barely,
than the telescope, the use of which in astronomy dates to 1609. (As a historical aside, it
is worth noting that the Duomo’s pendulum
was actually replaced in 1587, but if Twain
saw an offspring of the Abraham pendulum,
it stood in the same spot and obeyed the
same laws.)
Seeking to study the laws of falling bodies,
in 1603–1604 Galileo built his own pendulums from heavy balls and cord. He also used
pendulums to measure short time periods,
which was their first use as time standards.
Others, meanwhile, realized that pendulums
could also be used to create length standards.
In 1644 the French scientist and philosopher
Marin Mersenne (1588–1648) appears to
have been the first to accurately measure the
length of a “seconds pendulum” – an ordinary pendulum but with the special property
that its swing (half-oscillation or T/2) is
exactly 1 s. Luckily, the length of a seconds
pendulum at standard gravity is almost a
metre (99.4 cm), making it a convenient
length for a standard. This result sparked
investigations into factors that disturbed the
pendulum’s simple motion, including string
Physics World March 2012
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The precise shape of the Earth is
now remarkably well known, but it
was first measured by perhaps
the oldest and most humble of
instruments – the pendulum.
Robert P Crease explains
Simply useful Pendulums proved that the Earth is
shaped like a pumpkin.
The very simplicity of
the principle makes
the pendulum useful
as an instrument
stiffness, air resistance and suspension.
Later, in about 1656, the Dutch scientist
Christiaan Huygens (1629–1695) began creating clocks out of pendulums, vastly increasing the accuracy of time measurements and
triggering a revolution in navigation. Because
the Earth rotates at a known and fixed rate,
the longitude of a ship’s position can be determined by comparing the time of some astronomical observation as measured on board
ship with that at some reference point.
However, this only became possible once
clocks that could keep accurate time on ships
had been developed. Huygens also devised
the theory of the compound pendulum,
which does not use a string but a solid rod,
and the reversible pendulum – a compound
pendulum that can be turned upside down
and swings on two adjustable knife edges
(one for each direction) embedded in the rod.
In 1673, in Horologium Oscillatorium,
Huygens produced the equation of motion
of a simple pendulum: T = 2π √(L/g). He
also proved that if a reversible pendulum
swings with an equal period when turned
upside down, the distance between its two
knife edges is equal to the length of an ideal
or simple pendulum of the same period.
Most disturbing factors can then be ignored,
allowing pendulums to become valuable scientific instruments, sensitive to factors that
disturbed their simple motion.
Much of the pendulum’s subsequent history consists of discoveries and corrections
for these factors, or of its use to measure
these factors. In 1672, for instance, the
French astronomer Jean Richer (1630–
1696) discovered that the length of a seconds
pendulum changes with latitude: if g is
smaller, as it is at the equator, a pendulum
has to be shortened to keep T/2 to 1 s.
Richer’s work revealed that the Earth is not
spherical but flattened slightly at the poles,
like a pumpkin. Pendulums therefore proved
to be multipurpose instruments that could
help determine not only laws of motion, but
also the Earth’s shape. “[W]ithout the pendulum,” wrote Newton’s biographer Richard Westfall, “there would be no Principia.”
In the 18th century pendulums were increasingly used to measure time and speed.
In 1784 the English mathematician George
Atwood invented a device, the Atwood
Machine, incorporating a pendulum to
measure the laws of motion with constant
acceleration. Numerous scientists – Thomas
Jefferson among them – also assumed that a
seconds pendulum could be used to define a
natural standard of length. In 1851 JeanBernard-Léon Foucault (1819–1868) noticed
that the plane of oscillation of a long enough
pendulum slowly drifted over time because
of the Earth’s spin about its axis. This demonstrated directly and accessibly the Earth’s
rotation, and “Foucault pendulums” quickly
became popular science demonstrations
installed in museums the world over.
By 1867, the year that Twain witnessed the
Abraham pendulum, the pendulum had
become the principal instrument used to
measure the geoid, the shape of the Earth. In
1872 the International Geodetic Association
organized a network of gravimetric surveys
with reversible pendulums in one of the first
large-scale international science collaborations. Later, in the 19th century and into the
20th, a type of pendulum was used in a series
of experiments to try to detect a difference
between inertial and gravitational masses.
Today, the geoid is measured from space
with precise electronic instrumentation able
to detect gravity fluctuations (see p33). But
this is a recent development. Until the
advent of satellites and electronic equipment, the geoid was determined by lowly offspring of the Abraham pendulum, which
continue to serve productively in areas
including education, engineering, physics
and mathematics.
Robert P Crease is chairman of the Department
of Philosophy, Stony Brook University, and historian
at the Brookhaven National Laboratory, US,
e-mail [email protected]
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