Pendulum, device consisting of an object suspended from a fixed point that swings back and forth under the influence of gravity (see Gravitation). Pendulums are used in several kinds of mechanical devices; for example, certain types of clocks use pendulums (see Clocks and Watches).

The most basic type of pendulum is the simple pendulum. In a simple pendulum, which oscillates back and forth in a single plane, all the mass of the device can be considered to reside entirely in the suspended object. The motion of pendulums such as those in clocks closely approximates the motion of a simple pendulum. A spherical pendulum is not confined to a single plane, and as a result its motion can be much more complicated than the motion of a simple pendulum.

The principle of the pendulum was discovered by Italian physicist and astronomer Galileo, who established that the period for the back-and-forth oscillation of a pendulum of a given length remains the same, no matter how large its arc, or amplitude.

(If the amplitude is too large, however, the period of the pendulum is dependent on the amplitude.) This phenomenon is called isochronism, and Galileo noted its possible applications in timekeeping. Because of the role played by gravity, however, the period of a pendulum is related to geographical location, because the strength of gravity varies as a function of latitude and elevation. For example, the period will be greater on a mountain than at sea level. Thus, the pendulum can be used to determine accurately the local acceleration of gravity.

II. Compensation Pendulum Print section

The simple pendulum, used for timekeeping, is accurate as a regulator, if the proper length of the rod is preserved. It was found, however, that in winter clocks went too fast, and at midsummer too slow because cold shortened the metallic rod and heat lengthened it. A refinement was made to ensure uniform length and accurate timekeeping by the use of compensation pendulums. The two common types of compensation pendulum are the mercury pendulum and the gridiron pendulum. The mercury pendulum carries a glass cylinder almost full of mercury. When the pendulum expands downward because of heat, the change is counterbalanced by the upward expansion of the mercury in the cylinder. The gridiron pendulum is composed of a series of upright metal bars, usually of steel and copper, having different compositions and therefore different coefficients of thermal expansion. If the relative lengths of these bars are carefully adjusted, no change of temperature will affect the pendulum’s timekeeping.

III. Other Pendulums Print section

Pendulums used in various types of scientific instruments include the bifilar pendulum, the Foucault pendulum, and the torsion pendulum. Bifilar pendulums employ two strings or wires, and they have been used to record the irregular rotation of the earth as well as to detect earthquakes. The Foucault pendulum, used to demonstrate the rotation of the earth, is named after French physicist Jean Bernard Leon Foucault. The pendulum consists of a heavy bob suspended on a long wire; Foucault used a 28-kg (62-lb) bob attached to a 67-m (220-ft) wire. After the pendulum is set in motion so that it swings back and forth in a single plane, the rotation of the earth causes the orientation of the back-and-forth motions of the pendulum to slowly rotate with respect to the ground underneath the pendulum. The effect is most pronounced at the North Pole, where the pendulum rotates once every 24 hours. The rate of the pendulum’s rotation with respect to the ground decreases with latitude; at the equator the pendulum does not rotate at all.

A torsion pendulum consists of a wire or some other fiber. The pendulum oscillates by repeatedly twisting and untwisting about the axis through the center of the wire. Though it is not strictly a pendulum since it does not oscillate because of the force of gravity, the mathematical formulas that describe the motion of a torsion pendulum are similar to the equations that describe the motion of a simple pendulum.

Galileo (1564-1642), Italian physicist and astronomer, who, with the German astronomer Johannes Kepler, initiated the scientific revolution that flowered in the work of the English physicist Sir Isaac Newton. Born Galileo Galilei, his main contributions were, in astronomy, the use of the telescope in observation and the discovery of sunspots, lunar mountains and valleys, the four largest satellites of Jupiter, and the phases of Venus. In physics, he discovered the laws of falling bodies and the motions of projectiles. In the history of culture, Galileo stands as a symbol of the battle against authority for freedom of inquiry.

Galileo was born near Pisa, on February 15, 1564.

His father, Vincenzo Galilei, played an important role in the musical revolution from medieval polyphony to harmonic modulation. Just as Vincenzo saw that rigid theory stifled new forms in music, so his eldest son came to see Aristotelian physical theology as limiting scientific inquiry. Galileo was taught by monks at Vallombrosa and then entered the University of Pisa in 1581 to study medicine. He soon turned to philosophy and mathematics, leaving the university without a degree in 1585. For a time he tutored privately and wrote on hydrostatics and natural motions, but he did not publish. In 1589 he became professor of mathematics at Pisa, where he is reported to have shown his students the error of Aristotle’s belief that speed of fall is proportional to weight, by dropping two objects of different weight simultaneously from the Leaning Tower. His contract was not renewed in 1592, probably because he contradicted Aristotelian professors. The same year, he was appointed to the chair of mathematics at the University of Padua, where he remained until 1610.

At Padua, Galileo invented a calculating “compass” for the practical solution of mathematical problems. He turned from speculative physics to careful measurements, discovered the law of falling bodies and of the parabolic path of projectiles, studied the motions of pendulums, and investigated mechanics and the strength of materials. He showed little interest in astronomy, although beginning in 1595 he preferred the Copernican theory (see Astronomy: The Copernican Theory)-that the earth revolves around the sun-to the Aristotelian and Ptolemaic assumption that planets circle a fixed earth. Only the Copernican model supported Galileo’s tide theory, which was based on motions of the earth. In 1609 he heard that a spyglass had been invented in Holland. In August of that year he presented a telescope, about as powerful as a modern field glass, to the doge of Venice. Its value for naval and maritime operations resulted in the doubling of his salary and his assurance of lifelong tenure as a professor.

By December 1609, Galileo had built a telescope of 20 times magnification, with which he discovered mountains and craters on the moon. He also saw that the Milky Way was composed of stars, and he discovered the four largest satellites of Jupiter. He published these findings in March 1610 in The Starry Messenger (trans. 1880). His new fame gained him appointment as court mathematician at Florence; he was thereby freed from teaching duties and had time for research and writing. By December 1610 he had observed the phases of Venus, which contradicted Ptolemaic astronomy and confirmed his preference for the Copernican system.

Professors of philosophy scorned Galileo’s discoveries because Aristotle had held that only perfectly spherical bodies could exist in the heavens and that nothing new could ever appear there. Galileo also disputed with professors at Florence and Pisa over hydrostatics, and he published a book on floating bodies in 1612. Four printed attacks on this book followed, rejecting Galileo’s physics. In 1613 he published a work on sunspots and predicted victory for the Copernican theory. A Pisan professor, in Galileo’s absence, told the Medici (the ruling family of Florence as well as Galileo’s employers) that belief in a moving earth was heretical. In 1614 a Florentine priest denounced Galileists from the pulpit. Galileo wrote a long, open letter on the irrelevance of biblical passages in scientific arguments, holding that interpretation of the Bible should be adapted to increasing knowledge and that no scientific position should ever be made an article of Roman Catholic faith.

Early in 1616, Copernican books were subjected to censorship by edict, and the Jesuit cardinal Robert Bellarmine instructed Galileo that he must no longer hold or defend the concept that the earth moves. Cardinal Bellarmine had previously advised him to treat this subject only hypothetically and for scientific purposes, without taking Copernican concepts as literally true or attempting to reconcile them with the Bible. Galileo remained silent on the subject for years, working on a method of determining longitudes at sea by using his predictions of the positions of Jupiter’s satellites, resuming his earlier studies of falling bodies, and setting forth his views on scientific reasoning in a book on comets, The Assayer (1623; trans. 1957).

In 1624 Galileo began a book he wished to call “Dialogue on the Tides,” in which he discussed the Ptolemaic and Copernican hypotheses in relation to the physics of tides. In 1630 the book was licensed for printing by Roman Catholic censors at Rome, but they altered the title to Dialogue on the Two Chief World Systems (trans. 1661). It was published at Florence in 1632. Despite two official licenses, Galileo was summoned to Rome by the Inquisition to stand trial for “grave suspicion of heresy.” This charge was grounded on a report that Galileo had been personally ordered in 1616 not to discuss Copernicanism either orally or in writing. Cardinal Bellarmine had died, but Galileo produced a certificate signed by the cardinal, stating that Galileo had been subjected to no further restriction than applied to any Roman Catholic under the 1616 edict. No signed document contradicting this was ever found, but Galileo was nevertheless compelled in 1633 to abjure and was sentenced to life imprisonment (swiftly commuted to permanent house arrest). The Dialogue was ordered to be burned, and the sentence against him was to be

read publicly in every university.

Galileo’s final book, Discourses Concerning Two New Sciences (trans. 1662-65), which was published at Leiden in 1638, reviews and refines his earlier studies of motion and, in general, the principles of mechanics. The book opened a road that was to lead Newton to the law of universal gravitation that linked Kepler’s planetary laws with Galileo’s mathematical physics. Galileo became blind before it was published, and he died at Arcetri, near Florence, on January 8, 1642.

Galileo’s most valuable scientific contribution was his founding of physics on precise measurements rather than on metaphysical principles and formal logic. More widely influential, however, were The Starry Messenger and the Dialogue, which opened new vistas in astronomy. Galileo’s lifelong struggle to free scientific inquiry from restriction by philosophical and theological interference stands beyond science. Since the full publication of Galileo’s trial documents in the 1870s, entire responsibility for Galileo’s condemnation has customarily been placed on the Roman Catholic church. This conceals the role of the philosophy professors who first persuaded theologians to link Galileo’s science with heresy. An investigation into the astronomer’s condemnation, calling for its reversal, was opened in 1979 by Pope John Paul II. In October 1992 a papal commission acknowledged the Vatican’s error

Italian physicist and astronomer Galileo maintained that the earth revolved around the sun, disputing the belief held by the Roman Catholic church that the earth was the center of the universe. He refused to obey orders from Rome to cease discussions of his theories and was sentenced to life imprisonment. It was not until 1984 that a papal commission acknowledged that the church was wrong.