History of timekeeping devices
The history of
In medieval Europe, purely mechanical clocks were developed after the invention of the bell-striking alarm, used to signal the correct time to ring
The next major improvement in clock building, from the 17th century, was the discovery that clocks could be controlled by harmonic oscillators. Leonardo da Vinci had produced the earliest known drawings of a pendulum in 1493–1494, and in 1582 Galileo Galilei had investigated the regular swing of the pendulum, discovering that frequency was only dependent on length, not weight. The pendulum clock, designed and built by Dutch polymath Christiaan Huygens in 1656, was so much more accurate than other kinds of mechanical timekeepers that few verge and foliot mechanisms have survived. Other innovations in timekeeping during this period include inventions for striking clocks, the repeating clock and the deadbeat escapement.
Error factors in early pendulum clocks included temperature variation, a problem tackled during the 18th century by the English clockmakers
The
The most accurate timekeeping devices in practical use today are atomic clocks, which can be accurate to a few billionths of a second per year and are used to calibrate other clocks and timekeeping instruments.
Continuous timekeeping devices
Ancient civilizations observed
All timekeepers before the 13th century relied upon methods that used something that moved continuously. No early method of keeping time changed at a steady rate.[6] Devices and methods for keeping time have improved continuously through a long series of new inventions and ideas.[7]
Shadow clocks and sundials
The first devices used for measuring the position of the Sun were
A sundial is referred to in the Bible, in 2 Kings 20:9–11, when Hezekiah, king of Judea during the 8th century BC, is recorded as being healed by the prophet Isaiah and asks for a sign that he would recover:[13]
And Isaiah said, This sign shalt thou have of the Lord, that the Lord will do the thing that he hath spoken: shall the shadow go forward ten degrees, or go back ten degrees? And Hezekiah answered, It is a light thing for the shadow to go down ten degrees: nay, but let the shadow return backward ten degrees. And Isaiah the prophet cried unto the Lord: and he brought the shadow ten degrees backward, by which it had gone down in the dial of Ahaz.
A
The Romans inherited the sundial from the Greeks.[19] The first sundial in Rome arrived in 264 BC, looted from Catania in Sicily. This sundial offered the innovation of the hours of the “horologium” throughout the day where before the Romans simply split the day into early morning and forenoon (mane and ante merididiem). [20] Still, there were unexpected astronomical challenges; this clock gave the incorrect time for a century. This mistake was noticed only in 164 BC, when the Roman censor came to check and adjusted for the appropriate latitude.[21][20]
According to the German historian of astronomy Ernst Zinner, sundials were developed during the 13th century with scales that showed equal hours. The first based on polar time appeared in Germany c. 1400; an alternative theory proposes that a Damascus sundial measuring in polar time can be dated to 1372.[22] European treatises on sundial design appeared c. 1500.[23]
An Egyptian method of determining the time during the night, used from at least 600 BC, was a type of
The Jantar Mantar in Jaipur built in 1727 by Jai Singh II includes the Vrihat Samrat Yantra, 88 feet (27 m) tall sundial. [25] It can tell local time to an accuracy of about two seconds.[26]
Water clocks
The oldest description of a clepsydra, or water clock, is from the tomb inscription of an early 18th Dynasty (c. 1500 BC) Egyptian court official named Amenemhet, who is identified as its inventor.[27] It is assumed that the object described on the inscription is a bowl with markings to indicate the time.[28] The oldest surviving water clock was found in the tomb of pharaoh Amenhotep III (c. 1417–1379 BC).[29] There are no recognised examples in existence of outflowing water clocks from ancient Mesopotamia, but written references have survived.[14]
The introduction of the water clock to China, perhaps from Mesopotamia, occurred as far back as the 2nd millennium BC, during the Shang dynasty, and at the latest by the 1st millennium BC. Around 550 AD, Yin Kui (殷蘷) was the first in China to write of the overflow or constant-level tank in his book "Lou ke fa (漏刻法)". Around 610, two Sui dynasty inventors, Geng Xun (耿詢) and Yuwen Kai (宇文愷), created the first balance clepsydra, with standard positions for the steelyard balance.[30] In 721 the mathematician Yi Xing and government official Liang Lingzan regulated the power of the water driving an astronomical clock, dividing the power into unit impulses so that motion of the planets and stars could be duplicated.[31] In 976, the Song dynasty astronomer Zhang Sixun addressed the problem of the water in clepsydrae freezing in cold weather when he replaced the water with liquid mercury.[32] A water-powered astronomical clock tower was built by the polymath Su Song in 1088,[33] which featured the first known endless power-transmitting chain drive.[34]
The Greek philosophers Anaxagoras and Empedocles both referred to water clocks that were used to enforce time limits or measure the passing of time.[35][36] The Athenian philosopher Plato is supposed to have invented an alarm clock that used lead balls cascading noisily onto a copper platter to wake his students.[37]
A problem with most clepsydrae was the variation in the flow of water due to the change in fluid pressure, which was addressed from 100 BC when the clock's water container was given a conical shape. They became more sophisticated when innovations such as gongs and moving mechanisms were included.
Ibn Khalaf al-Muradi in medieval Al-Andalus described a water clock that employed both segmental and epicyclic gearing. Islamic water clocks, which used complex gear trains and included arrays of automata, were unrivalled in their sophistication until the mid-14th century.[40][41] Liquid-driven mechanisms (using heavy floats and a constant-head system) were developed that enabled water clocks to work at a slower rate.[41] Some have argued that the first known geared clock was rather invented by the great mathematician, physicist, and engineer Archimedes during the 3rd century BC. Archimedes created his astronomical clock,[42][citation needed] which was also a cuckoo clock with birds singing and moving every hour. It is the first carillon clock as it plays music simultaneously with a person blinking his eyes, surprised by the singing birds. The Archimedes clock works with a system of four weights, counterweights, and strings regulated by a system of floats in a water container with siphons that regulate the automatic continuation of the clock. The principles of this type of clock are described by the mathematician and physicist Hero,[43] who says that some of them work with a chain that turns a gear in the mechanism.[44]
The 12th-century
Chinese incense clocks
The
Incense seal clocks had a disk etched with one or more grooves, into which incense was placed.[56] The length of the trail of incense, directly related to the size of the seal, was the primary factor in determining how long the clock would last; to burn 12 hours an incense path of around 20 metres (66 ft) has been estimated.[57] The gradual introduction of metal disks, most likely beginning during the Song dynasty, allowed craftsmen to more easily create seals of different sizes, design and decorate them more aesthetically, and vary the paths of the grooves, to allow for the changing length of the days in the year. As smaller seals became available, incense seal clocks grew in popularity and were often given as gifts.[58]
Astrolabes
Sophisticated timekeeping
Muslim astronomers constructed a variety of highly accurate astronomical clocks for use in their mosques and observatories,[62] such as the astrolabic clock by Ibn al-Shatir in the early 14th century.[63]
Candle clocks and hourglasses
One of the earliest references to a
The invention of the candle clock was attributed by the
The 12th century Muslim inventor
His so-called "scribe" candle clock was invented to mark the passing of 14 hours of equal length: a precisely engineered mechanism caused a candle of specific dimensions to be slowly pushed upwards, which caused an indicator to move along a scale.The hourglass was one of the few reliable methods of measuring time at sea, and it has been speculated that it was used on board ships as far back as the 11th century, when it would have complemented the compass as an aid to navigation. The earliest unambiguous evidence of the use an hourglass appears in the painting Allegory of Good Government, by the Italian artist Ambrogio Lorenzetti, from 1338.[68]
The Portuguese navigator Ferdinand Magellan used 18 hourglasses on each ship during his circumnavigation of the globe in 1522.[69] Though used in China, the hourglass's history there is unknown,[70] but does not seem to have been used before the mid-16th century,[71] as the hourglass implies the use of glassblowing, then an entirely European and Western art.[72]
From the 15th century onwards, hourglasses were used in a wide range of applications at sea, in churches, in industry, and in cooking; they were the first dependable, reusable, reasonably accurate, and easily constructed time-measurement devices. The hourglass took on symbolic meanings, such as that of death, temperance, opportunity, and Father Time, usually represented as a bearded, old man.[73]
History of early oscillating devices in timekeepers
The English word clock first appeared in Middle English as clok, cloke, or clokke. The origin of the word is not known for certain; it may be a borrowing from French or Dutch, and can perhaps be traced to the post-classical Latin clocca ('bell'). 7th century Irish and 9th century Germanic sources recorded clock as meaning 'bell'.[74]
Judaism, Christianity and Islam all had times set aside for prayer, although Christians alone were expected to attend prayers at specific hours of the day and night—what the historian Jo Ellen Barnett describes as "a rigid adherence to repetitive prayers said many times a day".[75] The bell-striking alarms warned the monk on duty to toll the monastic bell. His alarm was a timer that used a form of escapement to ring a small bell. This mechanism was the forerunner of the escapement device found in the mechanical clock.[76][77]
13th century
The first innovations to improve on the accuracy of the hourglass and the water clock occurred in the 10th century, when attempts were made to slow their rate of flow using friction or the force of gravity.[78] The earliest depiction of a clock powered by a hanging weight is from the Bible of St Louis, an illuminated manuscript made between 1226 and 1234 that shows a clock being slowed by water acting on a wheel. The illustration seems to show that weight-driven clocks were invented in western Europe.[79] A treatise written by Robertus Anglicus in 1271 shows that medieval craftsmen were attempting to design a purely mechanical clock (i.e. only driven by gravity) during this period.[80] Such clocks were a synthesis of earlier ideas derived from European and Islamic science, such as gearing systems, weight drives, and striking mechanisms.[81]
In 1250, the artist Villard de Honnecourt illustrated a device that was the step towards the development of the escapement.[82] Another forerunner of the escapement was the horologia nocturna, which used an early kind of verge mechanism to operate a knocker that continuously struck a bell.[83] The weight-driven clock was probably a Western European invention, as a picture of a clock shows a weight pulling an axle around, its motion slowed by a system of holes that slowly released water.[84] In 1271, the English astronomer Robertus Anglicus wrote of his contemporaries that they were in the process of developing a form of mechanical clock.[85][note 3]
14th century
The invention of the verge and foliot escapement in c.1275
At around the same time as the invention of the escapement, the Florentine poet Dante Alighieri used clock imagery to depict the souls of the blessed in Paradiso, the third part of the Divine Comedy, written in the early part of the 14th century. It may be the first known literary description of a mechanical clock.[93] There are references to house clocks from 1314 onwards; by 1325 the development of the mechanical clock can be assumed to have occurred.[94]
Large mechanical clocks were built that were mounted in towers so as to ring the bell directly. The tower clock of Norwich Cathedral constructed c. 1273 (reference to a payment for a mechanical clock dated to this year) is the earliest such large clock known. The clock has not survived.[95] The first clock known to strike regularly on the hour, a clock with a verge and foliot mechanism, is recorded in Milan in 1336.[96] By 1341, clocks driven by weights were familiar enough to be able to be adapted for grain mills,[97] and by 1344 the clock in London's Old St Paul's Cathedral had been replaced by one with an escapement.[98] The foliot was first illustrated by Dondi in 1364,[99] and mentioned by the court historian Jean Froissart in 1369.[100]
The most famous example of a timekeeping device during the medieval period was a clock designed and built by the clockmaker
During the 14th century, striking clocks appeared with increasing frequency in public spaces, first in Italy, slightly later in France and England—between 1371 and 1380, public clocks were introduced in over 70 European cites.[105] Salisbury Cathedral clock, dating from about 1386, is one of the oldest working clocks in the world, and may be the oldest; it still has most of its original parts.[106][note 5] The Wells Cathedral clock, built in 1392, is unique in that it still has its original medieval face. Above the clock are figures which hit the bells, and a set of jousting knights who revolve around a track every 15 minutes.[107][note 6]
Later developments
The invention of the
Clock towers in Western Europe in the Middle Ages struck the time. Early clock dials showed hours; a clock with a minutes dial is mentioned in a 1475 manuscript.[112] During the 16th century, timekeepers became more refined and sophisticated, so that by 1577 the Danish astronomer Tycho Brahe was able to obtain the first of four clocks that measured in seconds,[113] and in Nuremberg, the German clockmaker Peter Henlein was paid for making what is thought to have been the earliest example of a watch, made in 1524.[114] By 1500, the use of the foliot in clocks had begun to decline.[115] The oldest surviving spring-driven clock is a device made by Bohemian Jacob Zech in 1525.[111][116] The first person to suggest travelling with a clock to determine longitude, in 1530, was the Dutch instrument maker Gemma Frisius. The clock would be set to the local time of a starting point whose longitude was known, and the longitude of any other place could be determined by comparing its local time with the clock time.[117][118]
The Ottoman engineer Taqi ad-Din described a weight-driven clock with a verge-and-foliot escapement, a striking train of gears, an alarm, and a representation of the Moon's phases in his book The Brightest Stars for the Construction of Mechanical Clocks (Al-Kawākib al-durriyya fī wadh' al-bankāmat al-dawriyya), written around 1565.[119] Jesuit missionaries brought the first European clocks to China as gifts.[120]
The Italian polymath Galileo Galilei is thought to have first realized that the pendulum could be used as an accurate timekeeper after watching the motion of suspended lamps at Pisa Cathedral.[121] In 1582, he investigated the regular swing of the pendulum, and discovered that this was only dependent on its length. Galileo never constructed a clock based on his discovery, but prior to his death he dictated instructions for building a pendulum clock to his son, Vincenzo.[122]
Era of precision timekeeping
Pendulum clocks
The first accurate timekeepers depended on the phenomenon known as
The period when clocks were controlled by harmonic oscillators was the most productive era in timekeeping.[102][note 7] The first invention of this type was the pendulum clock, which was designed and built by Dutch polymath Christiaan Huygens in 1656. Early versions erred by less than one minute per day, and later ones only by 10 seconds, very accurate for their time. Dials that showed minutes and seconds became common after the increase in accuracy made possible by the pendulum clock. Brahe used clocks with minutes and seconds to observe stellar positions.[112] The pendulum clock outperformed all other kinds of mechanical timekeepers to such an extent that these were usually refitted with a pendulum—a task that could be done without difficulty[127]—so that few verge escapement devices have survived in their original form.[128]
The first pendulum clocks used a verge escapement, which required wide swings of about 100° and so had short, light pendulums.[129] The swing was reduced to around 6° after the invention of the anchor mechanism enabled the use of longer, heavier pendulums with slower beats that had less variation, as they more closely resembled simple harmonic motion, required less power, and caused less friction and wear.[130] The first known anchor escapement clock was built by the English clockmaker William Clement in 1671 for King's College, Cambridge,[131] now in the Science Museum, London.[132] The anchor escapement originated with Hooke, although it has been argued that it was invented by Clement,[133] or the English clockmaker Joseph Knibb.[132]
The
Huygens first used a clock to calculate the equation of time (the difference between the apparent solar time and the time given by a clock), publishing his results in 1665. The relationship enabled astronomers to use the stars to measure sidereal time, which provided an accurate method for setting clocks. The equation of time was engraved on sundials so that clocks could be set using the Sun. In 1720, Joseph Williamson claimed to have invented a clock that showed solar time, fitted with a cam and differential gearing, so that the clock indicated true solar time.[137][138][139]
Other innovations in timekeeping during this period include the invention of the rack and snail striking mechanism for striking clocks by the English mechanician Edward Barlow, the invention by either Barlow or Daniel Quare, a London clock-maker, in 1676 of the repeating clock that chimes the number of hours or minutes,[140] and the deadbeat escapement, invented around 1675 by the astronomer Richard Towneley.[141]
Any inherent errors in early pendulum clocks were smaller than other errors caused by factors such as temperature variation.[144] In 1729 the Yorkshire carpenter and self-taught clockmaker John Harrison invented the gridiron pendulum, which used at least three metals of different lengths and expansion properties, connected so as to maintain the overall length of the pendulum when it is heated or cooled by its surroundings.[145] In 1781 the clockmaker George Graham compensated for temperature variation in an iron pendulum by using a bob made from a glass jar of mercury—a liquid metal at room temperature that expands faster than glass. More accurate versions of this innovation contained the mercury in thinner iron jars to make them more responsive. This type of temperature compensating pendulum was improved still further when the mercury was contained within the rod itself, which allowed the two metals to be thermally coupled more tightly.[146] In 1895, the invention of invar, an alloy made from iron and nickel that expands very little, largely eliminated the need for earlier inventions designed to compensate for the variation in temperature.[147]
Between 1794 and 1795, in the aftermath of the
Marine chronometer
After the
In 1715, at the age of 22, John Harrison had used his carpentry skills to construct a wooden eight-day clock.[153] His clocks had innovations that included the use of wooden parts to remove the need for additional lubrication (and cleaning), rollers to reduce friction, a new kind of escapement, and the use of two different metals to reduce the problem of expansion caused by temperature variation.[154] He travelled to London to seek assistance from the Board of Longitude in making a sea clock. He was sent to visit Graham, who assisted Harrison by arranging to finance his work to build a clock. After 30 years, his device, now named "H1" was built and in 1736 it was tested at sea. Harrison then went on to design and make two other sea clocks, "H2" (completed in around 1739) and "H3", both of which were ready by 1755.[155][156]
Harrison made two watches, "H4" and "H5". Eric Bruton, in his book The History of Clocks and Watches, has described H4 as "probably the most remarkable timekeeper ever made".[157] After the completion of its sea trials during the winter of 1761–1762 it was found that it was three times more accurate than was needed for Harrison to be awarded the Longitude prize.[158][159]
Electric clocks
In 1815, the prolific English inventor
In 1840 the Scottish clock and instrument maker
In 1857, the French
The most accurate pendulum clocks were controlled electrically.[166] The Shortt–Synchronome clock, an electrical driven pendulum clock designed in 1921, was the first clock to be a more accurate timekeeper than the Earth itself.[167]
A succession of innovations and discoveries led to the invention of the modern quartz timer. The
Development of the watch
The first wristwatches were made in the 16th century.
Dials that showed minutes and seconds became common after the increase in accuracy made possible by the balance spring (or hairspring).[112] Invented separately in 1675 by Huygens and Hooke, it enabled the oscillations of the balance wheel to have a fixed frequency.[177] The invention resulted in a great advance in the accuracy of the mechanical watch, from around half an hour to within a few minutes per day.[178] Some dispute remains as to whether the balance spring was first invented by Huygens or by Hooke; both scientists claimed to have come up with the idea of the balance spring first. Huygens' design for the balance spring is the type used in virtually all watches up to the present day.[178]
Other notable 18th-century English horologists include John Arnold and Thomas Earnshaw, who devoted their careers to constructing high-quality chronometers and so-called 'deck watches', smaller versions of the chronometer that could be kept in a pocket.[183]
Military use of the watch
Watches were worn during the
During
Modern watches
Fob watches were starting to be replaced at the turn of the 20th century.
The first battery-driven watches were developed in the 1950s.[195] High quality watches were produced by firms such as Patek Philippe, an example made in 1933, an example being a Patek Philippe ref. 1518, possibly the most complicated wristwatch ever made in stainless steel, which fetched a world record price in 2016 when it was sold at auction for $11,136,642.[196][197][198]
The manual winding Speedmaster Professional or "Moonwatch" was worn during the first United States spacewalk as part of NASA's Gemini 4 mission and was the first watch worn by an astronaut walking on the Moon during the Apollo 11 mission.[199] In 1969, Seiko produced the world's first quartz wristwatch, the Astron.[200]
During the 1970s, the introduction of
Smartwatches, essentially wearable computers in the form of watches, were introduced to the market in the early 21st century.
Atomic clocks
The idea of using atomic transitions to measure time was first suggested by the British scientist Lord Kelvin in 1879,[204] although it was only in the 1930s with the development of magnetic resonance that there was a practical method for measuring time in this way.[205] A prototype ammonia maser device was built in 1948 at NIST. Although less accurate than existing quartz clocks, it served to prove the concept of an atomic clock.[206]
The first accurate atomic clock, a
In 1967 the International System of Units (SI) standardized its unit of time, the second, on the properties of caesium.[206] The SI defined the second as 9,192,631,770 cycles of the radiation which corresponds to the transition between two electron spin energy levels of the ground state of the 133Cs atom.[209] The caesium atomic clock maintained by NIST is accurate to 30 billionths of a second per year.[206] Atomic clocks have employed other elements, such as hydrogen and rubidium vapor, offering greater stability (in the case of hydrogen clocks) and smaller size, lower power consumption, and thus lower cost (in the case of rubidium clocks).[206]
See also
- Dimensional metrology
- Forensic metrology
- Smart Metrology
- Time metrology
- Quantum metrology
Explanatory notes
- ^ The inventor of the quartz clock, Warren Marrison, noted that the sundial is not a timekeeping device, as it could only "at best keep local solar time".[7]
- ^ A verse by Plautus (c. 254 – 184 BC) shows that sundials were familiar to the Romans:[17][18]
The gods confound the man who first found out
How to distinguish hours! Confound him too,
Who in this place set up a sundial,
To cut and hack my days so wretchedly
Into small portions—When I was a boy,
My belly was my sun-dial: one more sure,
Truer, and more exact than any of them.
This dial told me when 'twas proper time
To go to dinner, when I had aught to eat—
But now-a-days, why, even when I have,
I can't fall to, unless the sun gives leave.
The town's so full of these confounded dials,
The greatest part of its inhabitants
Shrunk up with hunger, creep along the streets. - Latin: Nec est hoc possibile, quod aliquod horologium sequatur omnino iudicium astronomie secundum veritatem. Conantur tamen artifices horologiorum facere circulum unum qui omnino moveatur secundum motum circuli equinoctialis, sed non possunt omnino complere opus eorum, quod, si possent facere, esset horologium verax valde et valeret plus quam astrolabium quantum ad horas capiendas vel aliud instrumentum astronomie, si quis hoc sciret facere secundum modum antedictum.)[86]
- ^ Giovanni de Dondi's work has been replicated based on the designs. His clock was a seven-faced construction with 107 moving parts, showing the positions of the Sun, Moon, and five planets, as well as religious feast days. His clock has inspired several modern replicas, including some in London's Science Museum and the Smithsonian Institution.[104][95]
- verge and foliot timekeeping mechanism for the Salisbury Cathedral clock is lost, having been converted to a pendulum, which was replaced by a replica verge in 1956. It has no dial, as its purpose was to strike a bell.[106] The wheels and gears are mounted in a 1.2 metres (3 ft 11 in) iron frame, held together with metal dowels and pegs. Two large stones supply the power, and cause ropes to unwind from wooden barrels. The barrels drive the main wheel (regulated by the escapement), and the striking mechanism and air brake.[106]
- ^ The clock was converted to pendulum-and-anchor escapement in the 17th century, and was installed in London's Science Museum in 1884, where it continues to operate.[108]
- ^ Harmonically-driven clocks depend on some form of deformation from an equilibrium position; the resulting oscillations have a maximum amplitude when they receive energy at a frequency close to their natural undamped frequency. The main examples of such harmonic oscillators used to keep time are: the electrical resonance circuit; the gravity pendulum; the quartz crystal oscillator and the tuning fork; the balance spring; the torsion spring; and the vertical pendulum.[126]
- frequency stability.[171]
Citations
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- ^ Bruton 2000, pp. 235–237.
- ^ Richards 1999, p. 130.
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- ^ a b Barnett 1999, p. 64.
- ^ a b Marrison 1948, p. 510.
- ^ Major 1998, p. 9.
- ^ "One of world's oldest sun dial dug up in Kings' Valley, Upper Egypt". ScienceDaily. March 14, 2013. Retrieved May 10, 2021.
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- ^ Dolan 1975, p. 34.
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- ^ von Lieven 2016, p. 218.
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- ^ Ajram 1992, Appendix B.
- ^ King 1983, pp. 545–546.
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- ^ Asser 1983, p. 108.
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- ^ Bergreen 2003, p. 53.
- ^ Blaut 2000, p. 186.
- ^ Needham 1965, figure 995.
- ^ Needham 1965, p. 570.
- ^ Macey 1994, p. 209.
- ^ "Clock". OED. 2021. Retrieved May 29, 2021.
- ^ Barnett 1999, pp. 33–34, 37.
- ^ Landes 1985, p. 67.
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- ^ Marrison 1948, pp. 813–814.
- ^ White 1964, pp. 120–121.
- ^ White 1964, p. 122.
- ^ Hill 1997, pp. 223, 242–243.
- ^ Baillie, Clutton & Ilbert 1969, p. 4.
- ^ Landes 1985, pp. 67–68.
- ^ White 1964, p. 120.
- ^ Barnett 1999, p. 67.
- ^ Thorndike, de Sacro Bosco & Robertus Anglicus 1949, pp. 180, 230.
- ^ Bruton 2000, p. 49.
- ^ a b Marrison 1948, p. 514.
- ^ a b Hill 1997, p. 243.
- ^ Barnett 1999, pp. 64, 79.
- ^ Bruton 2000, p. 248.
- ^ Barnett 1999, pp. 87–88.
- ^ Moevs 1999, pp. 59–60.
- ^ Baillie, Clutton & Ilbert 1969, pp. 5–6.
- ^ a b Landes 1985, p. 53.
- ^ Barnett 1999, p. 75.
- ^ White 1964, p. 134.
- ^ Baillie, Clutton & Ilbert 1969, p. 5.
- ^ Bruton 2000, p. 244.
- ^ Bruton 2000, p. 35.
- ^ Barnett 1999, pp. 64–65.
- ^ a b Marrison 1948, p. 515.
- ^ Baillie, Clutton & Ilbert 1969, p. 7.
- ^ Davies 1996, p. 434.
- ^ Bradbury & Collette 2009, pp. 353, 356.
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External links
- Relativity Science Calculator – Philosophic Question: are clocks and time separable?
- Ancient Discoveries Islamic Science Part 4 clip from History Repeating of Islamic time-keeping inventions (YouTube).