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Critical Pointmeasuring the Earth physicsworld.com Comment: Robert P Crease Critical Point Measuring the Earth The precise shape of the Earth is disturbed their simple motion. Much of the pendulum’s subsequent his- now remarkably well known, but it tory consists of discoveries and corrections was first measured by perhaps for these factors, or of its use to measure these factors. In 1672, for instance, the the oldest and most humble of French astronomer Jean Richer (1630– instruments – the pendulum. iStockphoto.com/raw206 1696) discovered that the length of a seconds pendulum changes with latitude: if g is Robert P Crease explains smaller, as it is at the equator, a pendulum has to be shortened to keep T/2 to 1 s. In his travel book The Innocents Abroad Richer’s work revealed that the Earth is not (1869), Mark Twain describes his visit to the spherical but flattened slightly at the poles, Baptistery of the Duomo of Pisa, where, like a pumpkin. Pendulums therefore proved according to legend, in 1581 the young to be multipurpose instruments that could Galileo noticed the regularity of the build- help determine not only laws of motion, but ing’s swinging chandelier. Using his pulse as also the Earth’s shape. “[W]ithout the pen- a stopwatch, the then 17-year-old medical dulum,” wrote Newton’s biographer Rich- student observed that the chandelier took ard Westfall, “there would be no Principia.” the same time to swing back and forth In the 18th century pendulums were in- whether traversing a short or a long arc. Simply useful Pendulums proved that the Earth is creasingly used to measure time and speed. Twain marvelled at how “insignificant” the shaped like a pumpkin. In 1784 the English mathematician George chandelier looked, even though we had Atwood invented a device, the Atwood learned from it that such swinging objects Machine, incorporating a pendulum to were not mere lamps but pendulums. The The very simplicity of measure the laws of motion with constant awestruck Twain concluded that this was no acceleration. Numerous scientists – Thomas common pendulum, “but the old original the principle makes Jefferson among them – also assumed that a patriarchal Pendulum – the Abraham pen- seconds pendulum could be used to define a dulum of the world”. natural standard of length. In 1851 Jean- The principle Galileo noticed – that a pen- the pendulum useful Bernard-Léon Foucault (1819–1868) noticed dulum’s period, T, depends only on its that the plane of oscillation of a long enough length, L – is strictly true only in a vacuum, as an instrument pendulum slowly drifted over time because applies just for small swings, and ignores fric- of the Earth’s spin about its axis. This demon- tion and other factors. Still, the very simpli- stiffness, air resistance and suspension. strated directly and accessibly the Earth’s city of the principle makes the pendulum Later, in about 1656, the Dutch scientist rotation, and “Foucault pendulums” quickly useful as an instrument. Indeed, the pendu- Christiaan Huygens (1629–1695) began cre- became popular science demonstrations lum is one of the oldest scientific instruments ating clocks out of pendulums, vastly increas- installed in museums the world over. still in service – older, though just barely, ing the accuracy of time measurements and By 1867, the year that Twain witnessed the than the telescope, the use of which in astro- triggering a revolution in navigation. Because Abraham pendulum, the pendulum had nomy dates to 1609. (As a historical aside, it the Earth rotates at a known and fixed rate, become the principal instrument used to is worth noting that the Duomo’s pendulum the longitude of a ship’s position can be deter- measure the geoid, the shape of the Earth. In was actually replaced in 1587, but if Twain mined by comparing the time of some astro- 1872 the International Geodetic Association saw an offspring of the Abraham pendulum, nomical observation as measured on board organized a network of gravimetric surveys it stood in the same spot and obeyed the ship with that at some reference point. with reversible pendulums in one of the first same laws.) However, this only became possible once large-scale international science collabora- Seeking to study the laws of falling bodies, clocks that could keep accurate time on ships tions. Later, in the 19th century and into the in 1603–1604 Galileo built his own pendu- had been developed. Huygens also devised 20th, a type of pendulum was used in a series lums from heavy balls and cord. He also used the theory of the compound pendulum, of experiments to try to detect a difference pendulums to measure short time periods, which does not use a string but a solid rod, between inertial and gravitational masses. which was their first use as time standards. and the reversible pendulum – a compound Today, the geoid is measured from space Others, meanwhile, realized that pendulums pendulum that can be turned upside down with precise electronic instrumentation able could also be used to create length standards. and swings on two adjustable knife edges to detect gravity fluctuations (see p33). But In 1644 the French scientist and philosopher (one for each direction) embedded in the rod. this is a recent development. Until the Marin Mersenne (1588–1648) appears to In 1673, in Horologium Oscillatorium, advent of satellites and electronic equip- have been the first to accurately measure the Huygens produced the equation of motion ment, the geoid was determined by lowly off- length of a “seconds pendulum” – an ordi- of a simple pendulum: T =2π√(L/g). He spring of the Abraham pendulum, which nary pendulum but with the special property also proved that if a reversible pendulum continue to serve productively in areas that its swing (half-oscillation or T/2) is swings with an equal period when turned including education, engineering, physics exactly 1 s. Luckily, the length of a seconds upside down, the distance between its two and mathematics. pendulum at standard gravity is almost a knife edges is equal to the length of an ideal metre (99.4 cm), making it a convenient or simple pendulum of the same period. Robert P Crease is chairman of the Department length for a standard. This result sparked Most disturbing factors can then be ignored, of Philosophy, Stony Brook University, and historian investigations into factors that disturbed the allowing pendulums to become valuable sci- at the Brookhaven National Laboratory, US, pendulum’s simple motion, including string entific instruments, sensitive to factors that e-mail [email protected] Physics World March 2012 23.
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