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134-558: The regular motion of pendulums was used for timekeeping and was the world's most accurate timekeeping technology until the 1930s. The pendulum clock invented by Christiaan Huygens in 1656 became the world's standard timekeeper, used in homes and offices for 270 years, and achieved accuracy of about one second per year before it was superseded as a time standard by the quartz clock in the 1930s. Pendulums are also used in scientific instruments such as accelerometers and seismometers . Historically they were used as gravimeters to measure

268-476: A compound pendulum ), discovering the center of oscillation , and its interchangeability with the pivot point. The existing clock movement, the verge escapement , made pendulums swing in very wide arcs of about 100°. Huygens showed this was a source of inaccuracy, causing the period to vary with amplitude changes caused by small unavoidable variations in the clock's drive force. To make its period isochronous, Huygens mounted cycloidal-shaped metal guides next to

402-435: A harmonic oscillator , and its motion as a function of time, t , is approximately simple harmonic motion : θ ( t ) = θ 0 cos ⁡ ( 2 π T t + φ ) {\displaystyle \theta (t)=\theta _{0}\cos \left({\frac {2\pi }{T}}\,t+\varphi \right)} where φ {\displaystyle \varphi }

536-409: A longcase clock , tall-case clock , grandfather's clock , hall clock or floor clock ) is a tall, freestanding, weight-driven pendulum clock , with the pendulum held inside the tower or waist of the case. Clocks of this style are commonly 1.8–2.4 metres (6–8 feet) tall with an enclosed pendulum and weights, suspended by either cables or chains, which have to be occasionally calibrated to keep

670-420: A quartz crystal in the module, and the swinging pendulum is merely a decorative simulation. The pendulum in most clocks (see diagram) consists of a wood or metal rod (a) with a metal weight called the bob (b) on the end. The bob is traditionally lens-shaped to reduce air drag. Wooden rods were often used in quality clocks because wood had a lower coefficient of thermal expansion than metal. The rod

804-438: A strong sensitivity to initial conditions . The motion of a double pendulum is governed by a set of coupled ordinary differential equations and is chaotic . One of the earliest known uses of a pendulum was a 1st-century seismometer device of Han dynasty Chinese scientist Zhang Heng . Its function was to sway and activate one of a series of levers after being disturbed by the tremor of an earthquake far away. Released by

938-492: A "Royal" pendulum ) meaning that each swing (or half-period) takes one second. They are about 1 metre (3 ft 3 in) long (to the centre of the bob), requiring a long, narrow case. That case pre-dated the anchor clock by a few decades, appearing in clocks in 1660, to allow a long drop for the powering weights. However, once the seconds pendulum began to be used, the long case proved perfect for housing it as well. British clockmaker William Clement, who disputed credit for

1072-423: A "seconds pendulum", in which each swing of the pendulum takes one second (a complete cycle takes two seconds), which is approximately one metre (39 inches) long from pivot to center of bob. Mantel clocks often have a half-second pendulum, which is approximately 25 centimetres (9.8 in) long. Only a few tower clocks use longer pendulums, the 1.5 second pendulum, 2.25 m (7.4 ft) long, or occasionally

1206-491: A 33 °C (59 °F) change. Wood rods expand less, losing only about 6 seconds per day for a 33 °C (59 °F) change, which is why quality clocks often had wooden pendulum rods. The wood had to be varnished to prevent water vapor from getting in, because changes in humidity also affected the length. The first device to compensate for this error was the mercury pendulum, invented by George Graham in 1721. The liquid metal mercury expands in volume with temperature. In

1340-419: A bellows arrangement. The Atmos clock , one example, uses a torsion pendulum with a long oscillation period of 60 seconds. The escapement is a mechanical linkage that converts the force from the clock's wheel train into impulses that keep the pendulum swinging back and forth. It is the part that makes the "ticking" sound in a working pendulum clock. Most escapements consist of a wheel with pointed teeth called

1474-421: A case, so most free-standing clocks had short pendulums. The anchor mechanism reduced the pendulum's swing to around 4 to 6 degrees, allowing clockmakers to use longer pendulums, which had slower "beats". They consumed less power, allowing clocks to run longer between windings, caused less friction and wear in the movement, and were more accurate. Almost all longcase clocks use a seconds pendulum (also called

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1608-563: A compound pendulum is given by T = 2 π I O m g r C M {\displaystyle T=2\pi {\sqrt {\frac {I_{O}}{mgr_{\mathrm {CM} }}}}} for sufficiently small oscillations. For example, a rigid uniform rod of length ℓ {\displaystyle \ell } pivoted about one end has moment of inertia I O = 1 3 m ℓ 2 {\textstyle I_{O}={\frac {1}{3}}m\ell ^{2}} . The center of mass

1742-405: A constant amplitude . Real pendulums are subject to friction and air drag , so the amplitude of their swings declines. The period of swing of a simple gravity pendulum depends on its length , the local strength of gravity , and to a small extent on the maximum angle that the pendulum swings away from vertical, θ 0 , called the amplitude . It is independent of the mass of the bob. If

1876-413: A different latitude. Also called torsion-spring pendulum, this is a wheel-like mass (most often four spheres on cross spokes) suspended from a vertical strip (ribbon) of spring steel, used as the regulating mechanism in torsion pendulum clocks . Rotation of the mass winds and unwinds the suspension spring, with the energy impulse applied to the top of the spring. The main advantage of this type of pendulum

2010-550: A few centimeters of aluminium under the pendulum bob (this can be seen in the Riefler clock image above). Invar pendulums were first used in 1898 in the Riefler regulator clock which achieved accuracy of 15 milliseconds per day. Suspension springs of Elinvar were used to eliminate temperature variation of the spring's restoring force on the pendulum. Later fused quartz was used which had even lower CTE. These materials are

2144-525: A few large tower clocks use longer pendulums, the 1.5 second pendulum, 2.25 m (7.4 ft) long, or occasionally the two-second pendulum, 4 m (13 ft) which is used in Big Ben . The largest source of error in early pendulums was slight changes in length due to thermal expansion and contraction of the pendulum rod with changes in ambient temperature. This was discovered when people noticed that pendulum clocks ran slower in summer, by as much as

2278-406: A few of the highest precision clocks before the pendulum became obsolete as a time standard. In 1896 Charles Édouard Guillaume invented the nickel steel alloy Invar . This has a CTE of around 0.9  ppm /°C ( 0.5 ppm/°F ), resulting in pendulum temperature errors over 22 °C (71 °F) of only 1.3 seconds per day, and this residual error could be compensated to zero with

2412-516: A greater amount of time than lighter objects. The earliest extant report of his experimental research is contained in a letter to Guido Ubaldo dal Monte, from Padua, dated November 29, 1602. His biographer and student, Vincenzo Viviani , claimed his interest had been sparked around 1582 by the swinging motion of a chandelier in Pisa Cathedral . Galileo discovered the crucial property that makes pendulums useful as timekeepers, called isochronism;

2546-399: A higher accuracy than relying on the sound of the beat; precision regulators often have a built-in spirit level for the task. Older freestanding clocks often have feet with adjustable screws to level them, more recent ones have a leveling adjustment in the movement. Some modern pendulum clocks have 'auto-beat' or 'self-regulating beat adjustment' devices, and do not need this adjustment. Since

2680-497: A length change of only 0.02%, 0.2 mm in a grandfather clock pendulum, will cause an error of a minute per week. Pendulums in clocks (see example at right) are usually made of a weight or bob (b) suspended by a rod of wood or metal (a) . To reduce air resistance (which accounts for most of the energy loss in precision clocks) the bob is traditionally a smooth disk with a lens-shaped cross section, although in antique clocks it often had carvings or decorations specific to

2814-463: A lever, a small ball would fall out of the urn-shaped device into one of eight metal toads' mouths below, at the eight points of the compass, signifying the direction the earthquake was located. Many sources claim that the 10th-century Egyptian astronomer Ibn Yunus used a pendulum for time measurement, but this was an error that originated in 1684 with the British historian Edward Bernard . During

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2948-482: A lot of maintenance, which is one reason for their popularity. As in any mechanism with moving parts, regular cleaning and lubrication is required. Specific low viscosity lubricants have been developed for clocks, one of the most widely used being a polyalcanoate synthetic oil . Springs and pins may wear out and break and need replacing. Pendulum clocks were more than simply utilitarian timekeepers; due to their high cost they were status symbols that expressed

3082-449: A means of adjusting the rate. This is usually an adjustment nut (c) under the pendulum bob which moves the bob up or down on its rod. Moving the bob up reduces the length of the pendulum, reducing the pendulum's period so the clock gains time. In some pendulum clocks, fine adjustment is done with an auxiliary adjustment, which may be a small weight that is moved up or down the pendulum rod. In some master clocks and tower clocks, adjustment

3216-463: A mercury pendulum, the pendulum's weight (bob) is a container of mercury. With a temperature rise, the pendulum rod gets longer, but the mercury also expands and its surface level rises slightly in the container, moving its centre of mass closer to the pendulum pivot. By using the correct height of mercury in the container these two effects will cancel, leaving the pendulum's centre of mass, and its period, unchanged with temperature. Its main disadvantage

3350-409: A minute per week (one of the first was Godefroy Wendelin , as reported by Huygens in 1658). Thermal expansion of pendulum rods was first studied by Jean Picard in 1669. A pendulum with a steel rod will expand by about 11.3 parts per million (ppm) with each degree Celsius increase, causing it to lose about 0.27 seconds per day for every degree Celsius increase in temperature, or 9 seconds per day for

3484-402: A more accurate variation of the anchor escapement called the deadbeat escapement . Traditionally, longcase clocks were made with two types of movement : eight-day and one-day (30-hour) movements. A clock with an eight-day movement required winding only once a week, while generally less-expensive 30-hour clocks had to be wound daily. Eight-day clocks are often driven by two weights – one driving

3618-481: A pendulum; the pulsilogium . In 1641 Galileo dictated to his son Vincenzo a design for a mechanism to keep a pendulum swinging, which has been described as the first pendulum clock; Vincenzo began construction, but had not completed it when he died in 1649. In 1656 the Dutch scientist Christiaan Huygens built the first pendulum clock . This was a great improvement over existing mechanical clocks; their best accuracy

3752-526: A precise time interval dependent on its length, and resists swinging at other rates. From its invention in 1656 by Christiaan Huygens , inspired by Galileo Galilei , until the 1930s, the pendulum clock was the world's most precise timekeeper, accounting for its widespread use. Throughout the 18th and 19th centuries, pendulum clocks in homes, factories, offices, and railroad stations served as primary time standards for scheduling daily life, work shifts, and public transportation. Their greater accuracy allowed for

3886-401: A rigid rod pendulum has the same period as a simple pendulum of two-thirds its length. Christiaan Huygens proved in 1673 that the pivot point and the center of oscillation are interchangeable. This means if any pendulum is turned upside down and swung from a pivot located at its previous center of oscillation, it will have the same period as before and the new center of oscillation will be at

4020-487: A rigid support. During operation, any elasticity will allow tiny imperceptible swaying motions of the support, which disturbs the clock's period, resulting in error. Pendulum clocks should be attached firmly to a sturdy wall. The most common pendulum length in quality clocks, which is always used in grandfather clocks , is the seconds pendulum , about 1 metre (39 inches) long. In mantel clocks , half-second pendulums, 25 cm (9.8 in) long, or shorter, are used. Only

4154-539: A second per year. The timekeeping accuracy of the pendulum was exceeded by the quartz crystal oscillator , invented in 1921, and quartz clocks , invented in 1927, replaced pendulum clocks as the world's best timekeepers. Pendulum clocks were used as time standards until World War 2, although the French Time Service continued using them in their official time standard ensemble until 1954. Pendulum gravimeters were superseded by "free fall" gravimeters in

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4288-402: A short push. The clock's wheels, geared to the escape wheel, move forward a fixed amount with each pendulum swing, advancing the clock's hands at a steady rate. The pendulum always has a means of adjusting the period, usually by an adjustment nut (c) under the bob which moves it up or down on the rod. Moving the bob up decreases the pendulum's length, causing the pendulum to swing faster and

4422-502: A small aneroid barometer mechanism attached to the pendulum compensated for this effect. Pendulums are affected by changes in gravitational acceleration, which varies by as much as 0.5% at different locations on Earth, so precision pendulum clocks have to be recalibrated after a move. Even moving a pendulum clock to the top of a tall building can cause it to lose measurable time from the reduction in gravity. The timekeeping elements in all clocks, which include pendulums, balance wheels ,

4556-407: A spring of elinvar which has low temperature coefficient of elasticity. A torsion pendulum clock requiring only annual winding is sometimes called a " 400-Day clock" or " anniversary clock ", sometimes given as a wedding gift. Torsion pendulums are also used in "perpetual" clocks which do not need winding, as their mainspring is kept wound by changes in atmospheric temperature and pressure with

4690-527: A style of longcase clock made in the French region Franche-Comté (hence their name). Features distinguishing this style are a curving "potbellied" case and a greater use of curved lines. A heavy, elongated, highly ornamented pendulum bob often extends up the case (see photo). Production of these clocks began in 1680 and continued for about 230 years. During the peak production years (1850–1890) over 60,000 clocks were made each year. These clocks were trendy across

4824-404: A temperature increase, the low expansion steel rods make the pendulum longer, while the high expansion zinc rods make it shorter. By making the rods of the correct lengths, the greater expansion of the zinc cancels out the expansion of the steel rods which have a greater combined length, and the pendulum stays the same length with temperature. Zinc-steel gridiron pendulums are made with 5 rods, but

4958-451: A tooth catches on the other pallet. These releases allow the clock's wheel train to advance a fixed amount with each swing, moving the hands forward at a constant rate, controlled by the pendulum. Although the escapement is necessary, its force disturbs the natural motion of the pendulum, and in precision pendulum clocks this was often the limiting factor on the accuracy of the clock. Different escapements have been used in pendulum clocks over

5092-1339: Is 1% larger than given by (1). The period increases asymptotically (to infinity) as θ 0 approaches π radians (180°), because the value θ 0 = π is an unstable equilibrium point for the pendulum. The true period of an ideal simple gravity pendulum can be written in several different forms (see pendulum (mechanics) ), one example being the infinite series : T = 2 π L g [ ∑ n = 0 ∞ ( ( 2 n ) ! 2 2 n ( n ! ) 2 ) 2 sin 2 n ⁡ ( θ 0 2 ) ] = 2 π L g ( 1 + 1 16 θ 0 2 + 11 3072 θ 0 4 + ⋯ ) {\displaystyle T=2\pi {\sqrt {\frac {L}{g}}}\left[\sum _{n=0}^{\infty }\left({\frac {\left(2n\right)!}{2^{2n}\left(n!\right)^{2}}}\right)^{2}\sin ^{2n}\left({\frac {\theta _{0}}{2}}\right)\right]=2\pi {\sqrt {\frac {L}{g}}}\left(1+{\frac {1}{16}}\theta _{0}^{2}+{\frac {11}{3072}}\theta _{0}^{4}+\cdots \right)} where θ 0 {\displaystyle \theta _{0}}

5226-418: Is a constant value, dependent on initial conditions . For real pendulums, the period varies slightly with factors such as the buoyancy and viscous resistance of the air, the mass of the string or rod, the size and shape of the bob and how it is attached to the string, and flexibility and stretching of the string. In precision applications, corrections for these factors may need to be applied to eq. (1) to give

5360-439: Is a narrow natural band of frequencies (or periods), called the resonance width or bandwidth , where the harmonic oscillator will oscillate. In a clock, the actual frequency of the pendulum may vary randomly within this resonance width in response to disturbances, but at frequencies outside this band, the clock will not function at all. The resonance width is determined by the damping , the frictional energy loss per swing of

5494-411: Is accomplished by a small tray mounted on the rod where small weights are placed or removed to change the effective length, so the rate can be adjusted without stopping the clock. The period of a pendulum increases slightly with the width (amplitude) of its swing. The rate of error increases with amplitude, so when limited to small swings of a few degrees the pendulum is nearly isochronous ; its period

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5628-411: Is called the movement. The movements of all mechanical pendulum clocks have these five parts: Additional functions in clocks besides basic timekeeping are called complications . More elaborate pendulum clocks may include these complications: In electromechanical pendulum clocks such as used in mechanical Master clocks the power source is replaced by an electrically powered solenoid that provides

5762-591: Is fully operational, with chimes on each quarter hour. It was made by Svoboda Industries in 1976 as a Bicentennial project and is located in Kewaunee, Wisconsin . The advent of the longcase clock was due to the invention of the anchor escapement mechanism by Robert Hooke in about 1658. Before adopting the anchor mechanism, pendulum clock movements used an older verge escapement mechanism, which required very wide pendulum swings of about 80–100 degrees. Long pendulums with such wide swings could not be fitted within

5896-416: Is in radians. The difference between this true period and the period for small swings (1) above is called the circular error . In the case of a typical grandfather clock whose pendulum has a swing of 6° and thus an amplitude of 3° (0.05 radians), the difference between the true period and the small angle approximation (1) amounts to about 15 seconds per day. For small swings the pendulum approximates

6030-399: Is independent of amplitude . This property, called isochronism , is the reason pendulums are so useful for timekeeping. Successive swings of the pendulum, even if changing in amplitude, take the same amount of time. For larger amplitudes , the period increases gradually with amplitude so it is longer than given by equation (1). For example, at an amplitude of θ 0 = 0.4 radians (23°) it

6164-413: Is independent of changes in amplitude. Therefore, the swing of the pendulum in clocks is limited to 2° to 4°. Small swing angles tend toward isochronous behavior due to the mathematical fact that the approximation sin ⁡ ( x ) = x {\displaystyle \sin(x)=x} becomes valid as the angle approaches zero. With that substitution made, the pendulum equation becomes

6298-436: Is its low energy use; with a period of 12–15 seconds, compared to the gravity swing pendulum's period of 0.5—2s, it is possible to make clocks that need to be wound only every 30 days, or even only once a year or more. Since the restoring force is provided by the elasticity of the spring, which varies with temperature, it is more affected by temperature changes than a gravity-swing pendulum. The most accurate torsion clocks use

6432-413: Is located at the center of the rod, so r C M = 1 2 ℓ {\textstyle r_{\mathrm {CM} }={\frac {1}{2}}\ell } Substituting these values into the above equation gives T = 2 π 2 3 ℓ g {\textstyle T=2\pi {\sqrt {\frac {{\frac {2}{3}}\ell }{g}}}} . This shows that

6566-407: Is pushed back and forth by the clock's escapement , (g,h) . Each time the pendulum swings through its centre position, it releases one tooth of the escape wheel (g) . The force of the clock's mainspring or a driving weight hanging from a pulley, transmitted through the clock's gear train , causes the wheel to turn, and a tooth presses against one of the pallets (h) , giving the pendulum

6700-449: Is the moment of inertia of the pendulum about the pivot point O {\displaystyle O} , m {\displaystyle m} is the total mass of the pendulum, and r C M {\displaystyle r_{\mathrm {CM} }} is the distance between the pivot point and the center of mass . Substituting this expression in (1) above, the period T {\displaystyle T} of

6834-423: Is the mass of the bob, ω = 2 π / T is the pendulum's radian frequency of oscillation, and Γ is the frictional damping force on the pendulum per unit velocity. Pendulum clock A pendulum clock is a clock that uses a pendulum , a swinging weight, as its timekeeping element. The advantage of a pendulum for timekeeping is that it is an approximate harmonic oscillator : It swings back and forth in

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6968-402: Is usually suspended from the clock frame with a short straight spring of metal ribbon (d) ; this avoids instabilities that were introduced by a conventional pivot. In the most accurate regulator clocks the pendulum is suspended by metal knife edges resting on flat agate (a hard mineral that will retain a highly polished surface). The pendulum is driven by an arm hanging behind it attached to

7102-518: The Renaissance , large hand-pumped pendulums were used as sources of power for manual reciprocating machines such as saws, bellows, and pumps. Italian scientist Galileo Galilei was the first to study the properties of pendulums, beginning around 1602. The first recorded interest in pendulums made by Galileo was around 1588 in his posthumously published notes titled On Motion , in which he noted that heavier objects would continue to oscillate for

7236-532: The acceleration of gravity had to correct the period for the air pressure at the altitude of measurement, computing the equivalent period of a pendulum swinging in vacuum. A pendulum clock was first operated in a constant-pressure tank by Friedrich Tiede in 1865 at the Berlin Observatory , and by 1900 the highest precision clocks were mounted in tanks that were kept at a constant pressure to eliminate changes in atmospheric pressure. Alternatively, in some

7370-477: The acceleration of gravity in geo-physical surveys, and even as a standard of length. The word pendulum is Neo-Latin , from the Latin pendulus , meaning ' hanging ' . The simple gravity pendulum is an idealized mathematical model of a pendulum. This is a weight (or bob ) on the end of a massless cord suspended from a pivot , without friction . When given an initial push, it will swing back and forth at

7504-586: The electric power grid . The most accurate experimental pendulum clock ever made may be the Littlemore Clock built by Edward T. Hall in the 1990s (donated in 2003 to the National Watch and Clock Museum , Columbia, Pennsylvania, USA). The largest pendulum clocks, exceeding 30 m (98 ft), were built in Geneva (1972) and Gdańsk (2016). The mechanism which runs a mechanical clock

7638-400: The escape wheel which is turned by the clock's wheel train, and surfaces the teeth push against, called pallets . During most of the pendulum's swing the wheel is prevented from turning because a tooth is resting against one of the pallets; this is called the "locked" state. Each swing of the pendulum a pallet releases a tooth of the escape wheel. The wheel rotates forward a fixed amount until

7772-469: The orbital motions of the planets . Hooke suggested to Isaac Newton in 1679 that the components of orbital motion consisted of inertial motion along a tangent direction plus an attractive motion in the radial direction. This played a part in Newton's formulation of the law of universal gravitation . Robert Hooke was also responsible for suggesting as early as 1666 that the pendulum could be used to measure

7906-407: The quartz crystals used in quartz watches , and even the vibrating atoms in atomic clocks , are in physics called harmonic oscillators . The reason harmonic oscillators are used in clocks is that they vibrate or oscillate at a specific resonant frequency or period and resist oscillating at other rates. However, the resonant frequency is not infinitely 'sharp'. Around the resonant frequency there

8040-481: The 1920s the Shortt-Synchronome briefly became the highest standard for timekeeping in observatories before quartz clocks superseded pendulum clocks as precision time standards. The indicating system is almost always the traditional dial with moving hour and minute hands. Many clocks have a small third hand indicating seconds on a subsidiary dial. Pendulum clocks are usually designed to be set by opening

8174-445: The 1950s, but pendulum instruments continued to be used into the 1970s. For 300 years, from its discovery around 1582 until development of the quartz clock in the 1930s, the pendulum was the world's standard for accurate timekeeping. In addition to clock pendulums, freeswinging seconds pendulums were widely used as precision timers in scientific experiments in the 17th and 18th centuries. Pendulums require great mechanical stability:

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8308-743: The 19th century, factory production of clock parts gradually made pendulum clocks affordable by middle-class families. During the Industrial Revolution , the faster pace of life and scheduling of shifts and public transportation like trains depended on the more accurate timekeeping made possible by the pendulum. Daily life was organized around the home pendulum clock. More accurate pendulum clocks, called regulators , were installed in places of business and railroad stations and used to schedule work and set other clocks. The need for extremely accurate timekeeping in celestial navigation to determine longitude on ships during long sea voyages drove

8442-598: The US time standard on Riefler pendulum clocks, accurate to about 10 milliseconds per day. In 1929 it switched to the Shortt-Synchronome free pendulum clock before phasing in quartz standards in the 1930s. With an error of less than one second per year, the Shortt was the most accurate commercially produced pendulum clock. Pendulum clocks remained the world standard for accurate timekeeping for 270 years, until

8576-409: The amplitude is limited to small swings, the period T of a simple pendulum, the time taken for a complete cycle, is: where L {\displaystyle L} is the length of the pendulum and g {\displaystyle g} is the local acceleration of gravity . For small swings the period of swing is approximately the same for different size swings: that is, the period

8710-460: The anchor escapement and is now used in most modern pendulum clocks. Observation that pendulum clocks slowed down in summer brought the realization that thermal expansion and contraction of the pendulum rod with changes in temperature was a source of error. This was solved by the invention of temperature-compensated pendulums; the mercury pendulum by Graham in 1721 and the gridiron pendulum by John Harrison in 1726. With these improvements, by

8844-420: The anchor escapement with Robert Hooke, had made the first longcase clocks by 1680. Later the same year, Thomas Tompion , the most prominent British clockmaker, was making them too. Longcase clocks spread rapidly from England to other European countries and Asia. The first longcase clocks, like all clocks prior to the anchor escapement, had only one hand; an hour hand . The increased accuracy made possible by

8978-531: The anchor escapement, became known as grandfather clocks . The increased accuracy resulting from these developments caused the minute hand, previously rare, to be added to clock faces beginning around 1690. The 18th and 19th century wave of horological innovation that followed the invention of the pendulum brought many improvements to pendulum clocks. The deadbeat escapement invented in 1675 by Richard Towneley and popularized by George Graham around 1715 in his precision "regulator" clocks gradually replaced

9112-531: The anchor motivated the addition of the minute hand to clock faces in the next few decades. Between 1680 and 1800, the average price of a grandfather clock in England remained steady at £1 10s. In 1680, that was the amount paid by an average working family for a year's rent, so the purchase of clocks was confined to the wealthy. But by 1800, wages had increased enough to allow many lower middle-class households to own grandfather clocks. Modern longcase clocks use

9246-404: The anchor piece (h) of the escapement , called the "crutch" (e) , ending in a "fork" (f) which embraces the pendulum rod. Each swing of the pendulum releases the escape wheel, and a tooth of the wheel presses against one of the pallets , exerting a brief push through the crutch and fork on the pendulum rod to keep it swinging. Most quality clocks, including all grandfather clocks, have

9380-405: The chain hanging down next to the weight. To wind a chain-driven longcase clock, one pulls on the end of each chain , lifting the weights until they are just under the clock's face. In the early 20th century, quarter-hour chime sequences were added to longcase clocks. A full chime sequence sounds at the top of each hour, immediately followed by the hour strike. At 15 minutes after each hour, 1/4 of

9514-423: The chime sequence plays. Proceeding that, at the bottom of each hour, 1/2 of the chime sequence plays. Then finally, at 15 minutes before each hour, 3/4 of the chime sequence plays. The chime tune used in almost all longcase clocks is Westminster Quarters . Many also offer the option of Whittington chimes or St. Michael's chimes , selectable by a switch mounted on the right side of the dial, allowing one to silence

9648-437: The chimes if desired. As a result of adding chime sequences, all modern mechanical longcase clocks have three weights instead of only two. The left weight provides power for the hour strike, the middle-weight provides power for the clock's pendulum and general timekeeping functions, and the right weight provides power for the quarter-hour chime sequences. Comtoise clocks , also known as Morbier clocks or Morez clocks , are

9782-531: The choice for modern high accuracy pendulums. The effect of the surrounding air on a moving pendulum is complex and requires fluid mechanics to calculate precisely, but for most purposes its influence on the period can be accounted for by three effects: Increases in barometric pressure increase a pendulum's period slightly due to the first two effects, by about 0.11 seconds per day per kilopascal (0.37 seconds per day per inch of mercury ; 0.015 seconds per day per torr ). Researchers using pendulums to measure

9916-434: The clock became inaccurate, and when the second owner died, the clock stopped working altogether. The story inspired Henry to create the song. Grandfather clocks are of a certain height, usually at least 1.9 metres (6 ft 3 in). There are also so-called "grandmother" and "granddaughter" clocks, which are slightly shorter. The world's tallest grandfather clock is 35 feet 10 inches (10.92 m) tall and

10050-447: The clock to gain time. Some precision clocks have a small auxiliary adjustment weight on a threaded shaft on the bob, to allow finer adjustment. Some tower clocks and precision clocks use a tray attached near to the midpoint of the pendulum rod, to which small weights can be added or removed. This effectively shifts the centre of oscillation and allows the rate to be adjusted without stopping the clock. The pendulum must be suspended from

10184-461: The clock to the top of a tall building would cause it to lose measurable time due to lower gravity. The local gravity also varies by about 0.5% with latitude between the equator and the poles, with gravity increasing at higher latitudes due to the oblate shape of the Earth. Thus precision regulator clocks used for celestial navigation in the early 20th century had to be recalibrated when moved to

10318-446: The clock's movement to keep it swinging, to replace the energy the pendulum loses to friction. These pushes, applied by a mechanism called the escapement , are the main source of disturbance to the pendulum's motion. The Q is equal to 2 π times the energy stored in the pendulum, divided by the energy lost to friction during each oscillation period, which is the same as the energy added by the escapement each period. It can be seen that

10452-596: The development of the most accurate pendulum clocks, called astronomical regulators . These precision instruments, installed in clock vaults in naval observatories and kept accurate within a fraction of a second by observation of star transits overhead, were used to set marine chronometers on naval and commercial vessels. Beginning in the 19th century, astronomical regulators in naval observatories served as primary standards for national time distribution services that distributed time signals over telegraph wires. From 1909, US National Bureau of Standards (now NIST ) based

10586-502: The distance between the two points was equal to the length of a simple gravity pendulum of the same period. In 1818 British Captain Henry Kater invented the reversible Kater's pendulum which used this principle, making possible very accurate measurements of gravity. For the next century the reversible pendulum was the standard method of measuring absolute gravitational acceleration. In 1851, Jean Bernard Léon Foucault showed that

10720-816: The distance from the pivot to a point called the center of oscillation . This point is located under the center of mass of the pendulum, at a distance which depends on the mass distribution of the pendulum. If most of the mass is concentrated in a relatively small bob compared to the pendulum length, the center of oscillation is close to the center of mass. The radius of oscillation or equivalent length ℓ e q {\displaystyle \ell ^{\mathrm {eq} }} of any physical pendulum can be shown to be ℓ e q = I O m r C M {\displaystyle \ell ^{\mathrm {eq} }={\frac {I_{O}}{mr_{\mathrm {CM} }}}} where I O {\displaystyle I_{O}}

10854-423: The equation of a harmonic oscillator, which has a fixed period in all cases. As the swing angle becomes larger, the approximation gradually fails and the period is no longer fixed. A major source of error in pendulum clocks is thermal expansion; the pendulum rod changes in length slightly with changes in temperature, causing changes in the rate of the clock. An increase in temperature causes the rod to expand, making

10988-427: The escapement from the varying force of the wheel train, was used in a few precision clocks. In tower clocks the wheel train must turn the large hands on the clock face on the outside of the building, and the weight of these hands, varying with snow and ice buildup, put a varying load on the wheel train. Gravity escapements were used in tower clocks. By the end of the 19th century specialized escapements were used in

11122-487: The faster pace of life which was necessary for the Industrial Revolution . The home pendulum clock was replaced by less-expensive synchronous electric clocks in the 1930s and 1940s. Pendulum clocks are now kept mostly for their decorative and antique value. Pendulum clocks must be stationary to operate. Any motion or accelerations will affect the motion of the pendulum, causing inaccuracies, so other mechanisms must be used in portable timepieces. The pendulum clock

11256-493: The force of gravity. During his expedition to Cayenne , French Guiana in 1671, Jean Richer found that a pendulum clock was 2 + 1 ⁄ 2 minutes per day slower at Cayenne than at Paris. From this he deduced that the force of gravity was lower at Cayenne. In 1687, Isaac Newton in Principia Mathematica showed that this was because the Earth was not a true sphere but slightly oblate (flattened at

11390-424: The friction and 'play' caused by a pivot, and the slight bending force of the spring merely adds to the pendulum's restoring force . The highest precision clocks have pivots of 'knife' blades resting on agate plates. The impulses to keep the pendulum swinging are provided by an arm hanging behind the pendulum called the crutch , (e) , which ends in a fork , (f) whose prongs embrace the pendulum rod. The crutch

11524-814: The generations; they kept the time on farms throughout France. Many Comtoise clocks can be found in France but they are also frequently found in Spain, Germany, and other parts of Europe , less in the United States. Many Comtoise clocks were also exported to other countries in Europe and even farther, to the Ottoman Empire and as far as Thailand. A wooden sheath usually protected the metal mechanisms during transport. Bornholm clocks are Danish longcase clocks and were made on Bornholm from 1745 to 1900. In Sweden

11658-421: The glass face cover and manually pushing the minute hand around the dial to the correct time. The minute hand is mounted on a slipping friction sleeve which allows it to be turned on its arbor. The hour hand is driven not from the wheel train but from the minute hand's shaft through a small set of gears, so rotating the minute hand manually also sets the hour hand. Pendulum clocks are long lived and don't require

11792-424: The highest precision clocks and other instruments, first invar , a nickel steel alloy, and later fused quartz , which made temperature compensation trivial. Precision pendulums were housed in low pressure tanks, which kept the air pressure constant to prevent changes in the period due to changes in buoyancy of the pendulum due to changing atmospheric pressure . The best pendulum clocks achieved accuracy of around

11926-421: The highest precision scientific clocks had pendulums made of ultra-low-expansion materials such as the nickel steel alloy Invar or fused silica , which required very little compensation for the effects of temperature. The viscosity of the air through which the pendulum swings will vary with atmospheric pressure, humidity, and temperature. This drag also requires power that could otherwise be applied to extending

12060-399: The impulses to the pendulum by magnetic force , and the escapement is replaced by a switch or photodetector that senses when the pendulum is in the right position to receive the impulse. These should not be confused with more recent quartz pendulum clocks in which an electronic quartz clock module swings a pendulum. These are not true pendulum clocks because the timekeeping is controlled by

12194-411: The invention of the quartz clock in 1927, and were used as time standards through World War II . The French Time Service included pendulum clocks in their ensemble of standard clocks until 1954. The home pendulum clock began to be replaced as domestic timekeeper during the 1930s and 1940s by the synchronous electric clock , which kept more accurate time because it was synchronized to the oscillation of

12328-450: The key property that makes pendulums useful timekeepers: they are isochronic, which means that the period of swing of a pendulum is approximately the same for different sized swings. Galileo in 1637 described to his son a mechanism which could keep a pendulum swinging, which has been called the first pendulum clock design (picture at top) . It was partly constructed by his son in 1649, but neither lived to finish it. The introduction of

12462-425: The limiting accuracy achievable by a harmonic oscillator as a time standard. The Q is related to how long it takes for the oscillations of an oscillator to die out. The Q of a pendulum can be measured by counting the number of oscillations it takes for the amplitude of the pendulum's swing to decay to 1/ e = 36.8% of its initial swing, and multiplying by 'π . In a clock, the pendulum must receive pushes from

12596-425: The mercury pendulum in 1721 and the gridiron pendulum in 1726, reducing errors in precision pendulum clocks to a few seconds per week. The accuracy of gravity measurements made with pendulums was limited by the difficulty of finding the location of their center of oscillation . Huygens had discovered in 1673 that a pendulum has the same period when hung from its center of oscillation as when hung from its pivot, and

12730-402: The mid-18th century precision pendulum clocks achieved accuracies of a few seconds per week. Until the 19th century, clocks were handmade by individual craftsmen and were very expensive. The rich ornamentation of pendulum clocks of this period indicates their value as status symbols of the wealthy. The clockmakers of each country and region in Europe developed their own distinctive styles. By

12864-525: The most accurate clocks, called astronomical regulators , which were employed in naval observatories and for scientific research. The Riefler escapement, used in Clemens-Riefler regulator clocks was accurate to 10 milliseconds per day. Electromagnetic escapements, which used a switch or phototube to turn on a solenoid electromagnet to give the pendulum an impulse without requiring a mechanical linkage, were developed. The most accurate pendulum clock

12998-458: The old pivot point. In 1817 Henry Kater used this idea to produce a type of reversible pendulum, now known as a Kater pendulum , for improved measurements of the acceleration due to gravity. In physics and mathematics , in the area of dynamical systems , a double pendulum also known as a chaotic pendulum is a pendulum with another pendulum attached to its end, forming a simple physical system that exhibits rich dynamic behavior with

13132-406: The pendulum and the other the striking mechanism , which usually consisted of a bell or chimes. Such movements usually have two keyholes, one on each side of the dial, to wind each weight. By contrast, 30-hour clocks often had a single weight to drive the timekeeping and striking mechanisms. Some 30-hour clocks were made with false keyholes for customers who wanted guests to think that the household

13266-406: The pendulum inaccurate, causing its period, and thus the rate of the clock, to vary with unavoidable variations in the driving force provided by the movement . Clockmakers' realization that only pendulums with small swings of a few degrees are isochronous motivated the invention of the anchor escapement by Robert Hooke around 1658, which reduced the pendulum's swing to 4–6°. The anchor became

13400-459: The pendulum longer, so its period increases and the clock loses time. Many older quality clocks used wooden pendulum rods to reduce this error, as wood expands less than metal. The first pendulum to correct for this error was the mercury pendulum invented by Graham in 1721, which was used in precision regulator clocks into the 20th century. These had a bob consisting of a container of the liquid metal mercury . An increase in temperature would cause

13534-439: The pendulum rate will increase with an increase in gravity, and local gravitational acceleration g {\displaystyle g} varies with latitude and elevation on Earth, the highest precision pendulum clocks must be readjusted to keep time after a move. For example, a pendulum clock moved from sea level to 4,000 feet (1,200 m) will lose 16 seconds per day. With the most accurate pendulum clocks, even moving

13668-432: The pendulum rod to expand, but the mercury in the container would also expand and its level would rise slightly in the container, moving the center of gravity of the pendulum up toward the pivot. By using the correct amount of mercury, the centre of gravity of the pendulum remained at a constant height, and thus its period remained constant, despite changes in temperature. The most widely used temperature-compensated pendulum

13802-437: The pendulum's operation even more accurate by avoiding changes in atmospheric pressure. Fine adjustment of the rate of the clock could be made by slight changes to the internal pressure in the sealed housing. To keep time accurately, pendulum clocks must be level. If they are not, the pendulum swings more to one side than the other, upsetting the symmetrical operation of the escapement. This condition can often be heard audibly in

13936-460: The pendulum, Horologium Oscillatorium sive de motu pendulorum . Marin Mersenne and René Descartes had discovered around 1636 that the pendulum was not quite isochronous; its period increased somewhat with its amplitude. Huygens analyzed this problem by determining what curve an object must follow to descend by gravity to the same point in the same time interval, regardless of starting point;

14070-596: The pendulum, the first harmonic oscillator used in timekeeping, increased the accuracy of clocks enormously, from about 15 minutes per day to 15 seconds per day leading to their rapid spread as existing ' verge and foliot ' clocks were retrofitted with pendulums. By 1659 pendulum clocks were being manufactured in France by clockmaker Nicolaus Hanet , and in England by Ahasuerus Fromanteel . These early clocks, due to their verge escapements , had wide pendulum swings of 80–100°. In his 1673 analysis of pendulums, Horologium Oscillatorium , Huygens showed that wide swings made

14204-421: The pendulum. The measure of a harmonic oscillator's resistance to disturbances to its oscillation period is a dimensionless parameter called the Q factor equal to the resonant frequency divided by the resonance width . The higher the Q , the smaller the resonance width, and the more constant the frequency or period of the oscillator for a given disturbance. The reciprocal of the Q is roughly proportional to

14338-446: The period accurately. A damped, driven pendulum is a chaotic system. Any swinging rigid body free to rotate about a fixed horizontal axis is called a compound pendulum or physical pendulum . A compound pendulum has the same period as a simple gravity pendulum of length ℓ e q {\displaystyle \ell ^{\mathrm {eq} }} , called the equivalent length or radius of oscillation , equal to

14472-406: The period of the pendulum is approximately independent of the amplitude or width of the swing. He also found that the period is independent of the mass of the bob, and proportional to the square root of the length of the pendulum. He first employed freeswinging pendulums in simple timing applications. Santorio Santori in 1602 invented a device which measured a patient's pulse by the length of

14606-443: The pivots in his clocks, that constrained the suspension cord and forced the pendulum to follow a cycloid arc (see cycloidal pendulum ). This solution didn't prove as practical as simply limiting the pendulum's swing to small angles of a few degrees. The realization that only small swings were isochronous motivated the development of the anchor escapement around 1670, which reduced the pendulum swing in clocks to 4°–6°. This became

14740-562: The plane of oscillation of a pendulum, like a gyroscope , tends to stay constant regardless of the motion of the pivot, and that this could be used to demonstrate the rotation of the Earth . He suspended a pendulum free to swing in two dimensions (later named the Foucault pendulum ) from the dome of the Panthéon in Paris. The length of the cord was 67 m (220 ft). Once the pendulum

14874-452: The poles) from the effect of centrifugal force due to its rotation, causing gravity to increase with latitude . Portable pendulums began to be taken on voyages to distant lands, as precision gravimeters to measure the acceleration of gravity at different points on Earth, eventually resulting in accurate models of the shape of the Earth . In 1673, 17 years after he invented the pendulum clock, Christiaan Huygens published his theory of

15008-594: The popular 1876 song My Grandfather's Clock is responsible for the common name "grandfather clock" being applied to the longcase clock. The song was composed by the American songwriter Henry Clay Work , who discovered a longcase clock in The George Hotel in Piercebridge , County Durham , England. When he asked about the clock, he was informed that it had had two owners. After the first owner died,

15142-629: The proper time. The case often features elaborately carved ornamentation on the hood (or bonnet), which surrounds and frames the dial, or clock face . The English clockmaker William Clement is credited with developing the form in 1670. Pendulum clocks were the world's most accurate timekeeping technology until the early 20th century, and longcase clocks, due to their superior accuracy, served as time standards for households and businesses. Today, they are kept mainly for their decorative and antique value, having been superseded by analog and digital timekeepers. The Oxford English Dictionary states that

15276-423: The smaller the fraction of the pendulum's energy that is lost to friction, the less energy needs to be added, the less the disturbance from the escapement, the more 'independent' the pendulum is of the clock's mechanism, and the more constant its period is. The Q of a pendulum is given by: Q = M ω Γ {\displaystyle Q={\frac {M\omega }{\Gamma }}} where M

15410-411: The so-called tautochrone curve . By a complicated method that was an early use of calculus , he showed this curve was a cycloid , rather than the circular arc of a pendulum, confirming that the pendulum was not isochronous and Galileo's observation of isochronism was accurate only for small swings. Huygens also solved the problem of how to calculate the period of an arbitrarily shaped pendulum (called

15544-437: The standard escapement used in pendulum clocks. During the 18th and 19th century, the pendulum clock 's role as the most accurate timekeeper motivated much practical research into improving pendulums. It was found that a major source of error was that the pendulum rod expanded and contracted with changes in ambient temperature, changing the period of swing. This was solved with the invention of temperature compensated pendulums,

15678-594: The standard escapement used in pendulum clocks. In addition to increased accuracy, the anchor's narrow pendulum swing allowed the clock's case to accommodate longer, slower pendulums, which needed less power and caused less wear on the movement. The seconds pendulum (also called the Royal pendulum), 0.994 m (39.1 in) long, in which the time period is two seconds, became widely used in quality clocks. The long narrow clocks built around these pendulums, first made by William Clement around 1680, who also claimed invention of

15812-423: The thermal expansion of brass is closer to steel, so brass-steel gridirons usually require 9 rods. Gridiron pendulums adjust to temperature changes faster than mercury pendulums, but scientists found that friction of the rods sliding in their holes in the frame caused gridiron pendulums to adjust in a series of tiny jumps. In high precision clocks this caused the clock's rate to change suddenly with each jump. Later it

15946-434: The ticking sound of the clock. The ticks or "beats" should be at precisely equally spaced intervals to give a sound of, "tick...tock...tick...tock"; if they are not, and have the sound "tick-tock...tick-tock..." the clock is out of beat and needs to be leveled. This problem can easily cause the clock to stop working, and is one of the most common reasons for service calls. A spirit level or watch timing machine can achieve

16080-406: The time between windings. Traditionally the pendulum bob is made with a narrow streamlined lens shape to reduce air drag, which is where most of the driving power goes in a quality clock. In the late 19th century and early 20th century, pendulums for precision regulator clocks in astronomical observatories were often operated in a chamber that had been pumped to a low pressure to reduce drag and make

16214-405: The top of each weight. The mechanical advantage of that arrangement also doubles the running time allowed by a given weight drop. Cable clocks are wound by inserting a special crank (called a "key") into holes in the clock's face and turning it. Others, however, are chain-driven, meaning that the weights are suspended by chains that wrap around gears in the clock's mechanism, with the other end of

16348-469: The two-second pendulum, 4 m (13 ft) which is used in the Great Clock of Westminster which houses Big Ben . The pendulum swings with a period that varies with the square root of its effective length. For small swings the period T , the time for one complete cycle (two swings), is where L is the length of the pendulum and g is the local acceleration of gravity . All pendulum clocks have

16482-412: The type of clock. In quality clocks the bob is made as heavy as the suspension can support and the movement can drive, since this improves the regulation of the clock (see Accuracy below). A common weight for seconds pendulum bobs is 15 pounds (6.8 kg). Instead of hanging from a pivot , clock pendulums are usually supported by a short straight spring (d) of flexible metal ribbon. This avoids

16616-482: The wealth and culture of their owners. They evolved in a number of traditional styles, specific to different countries and times as well as their intended use. Case styles somewhat reflect the furniture styles popular during the period. Experts can often pinpoint when an antique clock was made within a few decades by subtle differences in their cases and faces. These are some of the different styles of pendulum clocks: Grandfather clock A grandfather clock (also

16750-442: The years to try to solve this problem. In the 18th and 19th centuries, escapement design was at the forefront of timekeeping advances. The anchor escapement (see animation) was the standard escapement used until the 1800s when an improved version, the deadbeat escapement , took over in precision clocks. It is used in almost all pendulum clocks today. The remontoire , a small spring mechanism rewound at intervals which serves to isolate

16884-405: Was able to afford the more expensive eight-day clock. All modern striking longcase clocks have eight-day mechanical quarter chiming and full hour striking movements. Most longcase clocks are cable-driven, meaning that cables suspend the weights. If the cable was attached directly to the weight, the load would cause rotation and untwist the cable strands, so the cable wraps around a pulley mounted to

17018-568: Was found that zinc is subject to creep . For these reasons mercury pendulums were used in the highest precision clocks, but gridirons were used in quality regulator clocks. Gridiron pendulums became so associated with good quality that, to this day, many ordinary clock pendulums have decorative 'fake' gridirons that don't actually have any temperature compensation function. Around 1900, low thermal expansion materials were developed which could be used as pendulum rods in order to make elaborate temperature compensation unnecessary. These were only used in

17152-411: Was improved from around 15 minutes deviation a day to around 15 seconds a day. Pendulums spread over Europe as existing clocks were retrofitted with them. The English scientist Robert Hooke studied the conical pendulum around 1666, consisting of a pendulum that is free to swing in two dimensions, with the bob rotating in a circle or ellipse. He used the motions of this device as a model to analyze

17286-423: Was invented on 25 December 1656 by Dutch scientist and inventor Christiaan Huygens , and patented the following year. He described it in his manuscript Horologium published in 1658. Huygens contracted the construction of his clock designs to clockmaker Salomon Coster , who actually built the clock. Huygens was inspired by investigations of pendulums by Galileo Galilei beginning around 1602. Galileo discovered

17420-411: Was set in motion, the plane of swing was observed to precess or rotate 360° clockwise in about 32 hours. This was the first demonstration of the Earth's rotation that did not depend on celestial observations, and a "pendulum mania" broke out, as Foucault pendulums were displayed in many cities and attracted large crowds. Around 1900 low- thermal-expansion materials began to be used for pendulum rods in

17554-440: Was that when the temperature changed, the rod would come to the new temperature quickly but the mass of mercury might take a day or two to reach the new temperature, causing the rate to deviate during that time. To improve thermal accommodation several thin containers were often used, made of metal. Mercury pendulums were the standard used in precision regulator clocks into the 20th century. The most widely used compensated pendulum

17688-636: Was the gridiron pendulum invented by John Harrison around 1726. This consisted of a "grid" of parallel rods of high-thermal-expansion metal such as zinc or brass and low-thermal-expansion metal such as steel . If properly combined, the length change of the high-expansion rods compensated for the length change of the low-expansion rods, again achieving a constant period of the pendulum with temperature changes. This type of pendulum became so associated with quality that decorative "fake" gridirons are often seen on pendulum clocks, that have no actual temperature compensation function. Beginning around 1900, some of

17822-404: Was the gridiron pendulum , invented in 1726 by John Harrison . This consists of alternating rods of two different metals, one with lower thermal expansion ( CTE ), steel , and one with higher thermal expansion, zinc or brass . The rods are connected by a frame, as shown in the drawing at the right, so that an increase in length of the zinc rods pushes the bob up, shortening the pendulum. With

17956-472: Was the Shortt-Synchronome clock, a complicated electromechanical clock with two pendulums developed in 1923 by W.H. Shortt and Frank Hope-Jones , which was accurate to better than one second per year. A slave pendulum in a separate clock was linked by an electric circuit and electromagnets to a master pendulum in a vacuum tank. The slave pendulum performed the timekeeping functions, leaving the master pendulum to swing virtually undisturbed by outside influences. In

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