The History of Horology and Chronometry
History of the Pendulum Clock
132 CE, a pendulum used in a seismoscope or earthquake recording instrument invented by a Chinese philosopher named Chang Heng.
Galileo Galilei was credited with the invention of the pendulum clock. He started research around 1602 and discovered the property of pendulums called isochronism: the period of the pendulum is approximately independent of the amplitude or width of the swing.
Circular Error
Christiaan Huygens built the first pendulum clock in 1656 and wrote the Horologium Oscillatorium in 1673. He also discovered circular error.
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Circular error occurs since in order to be isochronous, a pendulum must swing with a path of a cycloidal curve.
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Pendulums, however, swing in an arc.
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To compensae for this, a pendulum with a smaller amplitude will have less error than a pendulum with a higher amplitude.
Coupled Pendulums
1665, Huygens discovered that two clocks placed on his mantelpiece had acquired an opposing motion; their pendulums were beating in unison but in opposite direction, 180˚ out of phase. The cause of this phenomena is this:
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The two pendulums were affecting each other through slight motions of the supporting mantelpiece.
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This process is called entrainment or mode locking and is observed in coupled oscillators
1680, William Clement invented the Longcase/Grandfather clock.
1793, Torsion pendulum invented by Robert Leslie and patented by American Aaron Crane in 1841. More information on Robert Leslie here.
The Airy Condition
1826, British astronomer George Airy proved a known occurrence now called the Airy Condition.
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The disturbing effect of a drive force on the period of a pendulum is smallest if given as a short impulse as the pendulum passes through its bottom equilibrium position
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If a pendulum is driven by an impulse that is symmetrical about its bottom equilibrium position, the pendulum's period will be unaffected by changes in the drive force
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Accurate escapements, such as the deadbeat, approximately satisfy this condition
1921, British railway engineer William Hamilton Shortt in collaboration with horologist Frank Hope-Jones created the Shortt-Synchronome clock/free pendulum clock. This clock became the most accurate pendulum clock in the world. It involved a complex electromechanical pendulum clock involving a slave and master pendulum.
Temperature Compensated Pendulums
The mercury pendulum
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George Graham, 1721
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Liquid metal mercury in container replaced bob (weight) of pendulum
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Temp rises, rod gets longer, but mercury surface level increases moving center of mass closer to pendulum pivot; ideally change in rod length and center of mass cancel out
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Still can be fluctuations since mercury takes time to change temperature
The gridiron pendulum
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John Harrison, 1726
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Alternating rods of two different metals, one with lower thermal expansion, steel, and the other with higher thermal expansion, zinc or brass
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Temp increase, steel rods expand, zinc rods shrink; with correct lengths, cancels out
Invar and fused quartz
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1900, low thermal expansion materials developed so that elaborate temp compensation unneeded, but a few high precision clocks needed it
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Charles Édouard Guillaume, 1896 invented iron-nickel alloy invar
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Used in Riefler regulator clock
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Fused quartz used later had lower CTE (thermal expansion)
Pendulum Gravimeters
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Henry Kater, 1818
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reversible free-swinging pendulum
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Early gravity measurements
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a pendulum that can be supported from either of two movable knife edges that is used to accurately measure the acceleration of gravity
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Kater introduced idea of relative gravity movements to supplement absolute measurements made by Kater’s pendulum
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Compare gravity at two different spots
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Time the period of an ordinary (single pivot) pendulum at the first point, then transport the pendulum to the other point and time its period there
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time-consuming and error-prone to repeatedly swing the Kater's pendulum and adjust the weights until the periods were equal
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Friedrich Bessel showed in 1835 that this was unnecessary
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As long as the periods were close together, the gravity could be calculated from the two periods and the center of gravity of the pendulum
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Reversible pendulum didn't need to be adjustable, it could just be a bar with two pivots
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Bessel didn't construct such a pendulum, but in 1864 Adolf Repsold, under contract by the Swiss Geodetic Commission made a pendulum along these lines
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Repsold pendulum was about 56 cm long and had a period of about 3⁄4 second
Von Sterneck and Mendenhall gravimeters
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1887 Austro-Hungarian scientist Robert von Sterneck developed a small gravimeter pendulum mounted in a temperature-controlled vacuum tank to eliminate the effects of temperature and air pressure and it was non-reversible
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Swing of the pendulum caused a slight swaying of the tripod stand used to support portable pendulums, introducing error
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Two pendulums swining in opposite directions would cancel out error
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suggested in 1877 by Hervé Faye and advocated by Peirce, Cellérier and Furtwangler
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developed in 1929 by the Gulf Research and Development Co
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Used two pendulums made of fused quartz, each 10.7 inches (270 mm) in length with a period of 0.89 second, swinging on pyrex knife edge pivots, 180° out of phase