PHYSICS PROJECT REPORT ON SAND/CANDLE/WATER DROP CLOCK
An hourglass (or sandglass, sand timer, or sand clock) is a device used to measure the passage of time. It comprises two glass bulbs connected vertically by a narrow neck that allows a regulated trickle of material (historically sand) from the upper bulb to the lower one. Factors affecting the time interval measured include sand quantity, sand coarseness, bulb size, and neck width. Hourglasses may be reused indefinitely by inverting the bulbs once the upper bulb is empty.
The origin of the hourglass is unclear. Its predecessor the clepsydra, or water clock, is known to have existed in Babylon and Egypt as early as the 16th century BCE. According to the Journal of the British Archaeological Association the so-called clepsammia were in use before the time of St. Jerome (335 CE), and the first potential representation of an hourglass is in a sarcophagus dated c. 350 CE,representing the wedding of Peleus and Thetis, discovered in Rome in the 18th century, and studied by Winckelmann in the 19th century, who remarked the hourglass held by Morpheus in his hands.However, it is disputed whether object in question is a clepsammia or a similarly-shaped clepsyndra; no other hourglass clearly appears in the historical record for another thousand years.
Reappearance in the Early Middle Ages
There are no records of the hourglass existing in Europe prior to the Early Middle Ages, such as invention by the Ancient Greeks; the first supported evidences appears from the 8th century CE, crafted by a Frankish monk named Liutprand who served at the cathedral in Chartres, France.But it was not until the 14th century that the hourglass was seen commonly, the earliest firm evidence being a depiction in the 1338 fresco Allegory of Good Government by Ambrogio Lorenzetti.
Use of the marine sandglass has been recorded since the 14th century. The written records about it were mostly from logbooks of European ships.In the same period it appears in other records and lists of ships stores. The earliest recorded reference that can be said with certainty to refer to a marine sandglass dates from c. 1345, in a receipt of Thomas de Stetesham, clerk of the King’s ship La George, in the reign of Edward III of England; translated from the Latin, the receipt says: in 1345
“The same Thomas accounts to have paid at Lescluse, in Flanders, for twelve glass horologes (” pro xii. orlogiis vitreis “), price of each 4½ gross’, in sterling 9s. Item, For four horologes of the same sort (” de eadem secta “), bought there, price of each five gross’, making in sterling 3s. 4d.“
Marine sandglasses were very popular on board ships, as they were the most dependable measurement of time while at sea. Unlike the clepsydra, the motion of the ship while sailing did not affect the hourglass. The fact that the hourglass also used granular materials instead of liquids gave it more accurate measurements, as the clepsydra was prone to get condensation inside it during temperature changes.Seamen found that the hourglass was able to help them determine longitude, distance east or west from a certain point, with reasonable accuracy.
The hourglass also found popularity on land. As the use of mechanical clocks to indicate the times of events like church services became more common, creating a “need to keep track of time”, the demand for time-measuring devices increased. Hourglasses were essentially inexpensive, as they required no rare technology to make and their contents were not hard to come by, and as the manufacturing of these instruments became more common, their uses became more practical.
Hourglasses were commonly seen in use in churches, homes, and work places to measure sermons, cooking time, and time spent on breaks from labor. Because they were being used for more everyday tasks, the model of the hourglass began to shrink. The smaller models were more practical and very popular as they made timing more discreet.
After 1500, the hourglass was not as widespread as it had been. This was due to the development of the mechanical clock, which became more accurate, smaller and cheaper, and made keeping time easier. The hourglass, however, did not disappear entirely. Although they became relatively less useful as clock technology advanced, hourglasses remained desirable in their design. The oldest known surviving hourglass resides in the British Museum in London.
Not until the 18th century did John Harrison and his son James, come up with a marine chronometer that significantly improved on the stability of the hourglass at sea. Taking elements from the design logic behind the hourglass, they made a marine chronometer in 1761 that was able to accurately measure the journey from England to Jamaica accurate within five seconds.
Little written evidence exists to explain why its external form is the shape that it is. The glass bulbs used, however, have changed in style and design over time. While the main designs have always been ampoule in shape, the bulbs were not always connected. The first hourglasses were two separate bulbs with a cord wrapped at their union that was then coated in wax to hold the piece together and let sand flow in between.It was not until 1760 that both bulbs were blown together to keep moisture out of the bulbs and regulate the pressure within the bulb that varied the flow
While some early hourglasses actually did use sand as the granular mixture to measure time, many did not use sand at all. The material used in most bulbs was a combination of “powdered marble, tin/lead oxides, and pulverized, burnt eggshell”. Over time, different textures of granule matter were tested to see which gave the most constant flow within the bulbs. It was later discovered that for the perfect flow to be achieved the ratio of granule bead to the width of the bulb neck needed to be 1/12 or more but not greater than 1/2 the neck of the bulb.
Hourglasses were an early dependable and accurate measure of time. The rate of flow of the sand is independent of the depth in the upper reservoir, and the instrument will not freeze in cold weather.From the 15th century onwards, hourglasses were being used in a range of applications at sea, in the church, in industry, and in cookery.
During the voyage of Ferdinand Magellan around the globe, 18 hourglasses from Barcelona were in the ship’s inventory, after the trip being authorized by emperor Charles V.It was the job of a ship’s page to turn the hourglasses and thus provide the times for the ship’s log. Noon was the reference time for navigation, which did not depend on the glass, as the sun would be at its zenith. A number of sandglasses could be fixed in a common frame, each with a different operating time, e.g. as in a four-way Italian sandglass likely from the 17th century, in the collections of the Science Museum, in South Kensington, London, which could measure intervals of quarter, half, three-quarters, and one hour (and which were also used in churches, for priests and ministers to measure lengths of sermons).
Modern practical uses
While they are no longer widely used for keeping time, some institutions do maintain them. Both houses of the Australian Parliament use three hourglasses to time certain procedures, such as divisions.
The sandglass is still widely used as the kitchen egg timer; for cooking eggs, a three-minute timer is typical,hence the name “egg timer” for three-minute hourglasses. Egg timers are sold widely as souvenirs. Sand timers are also sometimes used in games such as Pictionary and Boggle to implement a time constraint on rounds of play.
Unlike most other methods of measuring time, the hourglass concretely represents the present as being between the past and the future, and this has made it an enduring symbol of time itself.
The hourglass, sometimes with the addition of metaphorical wings, is often depicted as a symbol that human existence is fleeting, and that the “sands of time” will run out for every human life. It was used thus on pirate flags, to strike fear into the hearts of the pirates’ victims. In England, hourglasses were sometimes placed in coffins, and they have graced gravestones for centuries. The hourglass was also used in alchemy as a symbol for hour.
The former Metropolitan Borough of Greenwich in London used an hourglass on its coat of arms, symbolising Greenwich’s role as the origin of GMT. The district’s successor, the Royal Borough of Greenwich, uses two hourglasses on its coat of arms.
Modern symbolic uses
Recognition of the hourglass as a symbol of time has survived its obsolescence as a timekeeper. For example, the American television soap opera Days of Our Lives, since its first broadcast in 1965, has displayed an hourglass in its opening credits, with the narration, “Like sands through the hourglass, so are the days of our lives,” spoken by Macdonald Carey.
Various computer graphical user interfaces may change the pointer to an hourglass during a period when the program is in the middle of a task, and may not accept user input. During that period other programs, for example in different windows, may work normally. When such an hourglass does not disappear, it suggests a program is in an infinite loop and needs to be terminated, or is waiting for some external event (such as the user inserting a CD). Unicode has an HOURGLASS symbol at
Because of its symmetry, graphic signs resembling an hourglass are seen in the art of cultures which never encountered such objects. Vertical pairs of triangles joined at the apex are common in Native American art; both in North America,] where it can represent, for example, the body of the Thunderbird or (in more elongated form) an enemy scalp, and in South America, where it is believed to represent a Chuncho jungle dweller.In Zulu textiles they symbolise a married man, as opposed to a pair of triangles joined at the base, which symbolise a married woman.Neolithic examples can be seen among Spanish cave paintings. Observers have even given the name “hourglass motif” to shapes which have more complex symmetry, such as a repeating circle and cross pattern from the Solomon Islands Both the members of Project Tic Toc,from television series the Time Tunnel and the Challengers of the Unknown use symbols of the hourglasse representing either time travel or time running out.
This article is missing information about contrasting descriptions of different types of water clocks.(January 2018)
A water clock or clepsydra (Greek κλεψύδρα from κλέπτειν kleptein, ‘to steal’; ὕδωρ hydor, ‘water’) is any timepiece in which time is measured by the regulated flow of liquid into (inflow type) or out from (outflow type) a vessel where the amount is then measured.
Water clocks are one of the oldest time-measuring instruments. Where and when they were first invented is not known, and given their great antiquity it may never be. The bowl-shaped outflow is the simplest form of a water clock and is known to have existed in Babylon and in Egypt around the 16th century BCE. Other regions of the world, including India and China, also have early evidence of water clocks, but the earliest dates are less certain. Some authors, however, claim that water clocks appeared in China as early as 4000 BCE.
Some modern timepieces are called “water clocks” but work differently from the ancient ones. Their timekeeping is governed by a pendulum, but they use water for other purposes, such as providing the power needed to drive the clock by using a water wheel or something similar, or by having water in their displays.
The Greeks and Romans advanced water clock design to include the inflow clepsydra with an early feedback system, gearing, and escapement mechanism, which were connected to fanciful automata and resulted in improved accuracy. Further advances were made in Byzantium, Syria and Mesopotamia, where increasingly accurate water clocks incorporated complex segmental and epicyclic gearing, water wheels, and programmability, advances which eventually made their way to Europe. Independently, the Chinese developed their own advanced water clocks, incorporating gears, escapement mechanisms, and water wheels, passing their ideas on to Korea and Japan.
Some water clock designs were developed independently and some knowledge was transferred through the spread of trade. These early water clocks were calibrated with a sundial. While never reaching a level of accuracy comparable to today’s standards of timekeeping, the water clock was the most accurate and commonly used timekeeping device for millennia, until it was replaced by more accurate pendulum clocks in 17th-century Europe.
A water clock uses a flow of water to measure time. If viscosity is neglected, the physical principle required to study such clocks is Torricelli’s law. There are two types of water clocks: inflow and outflow. In an outflow water clock, a container is filled with water, and the water is drained slowly and evenly out of the container. This container has markings that are used to show the passage of time. As the water leaves the container, an observer can see where the water is level with the lines and tell how much time has passed. An inflow water clock works in basically the same way, except instead of flowing out of the container, the water is filling up the marked container. As the container fills, the observer can see where the water meets the lines and tell how much time has passed.
In ancient China, as well as throughout East Asia, water clocks were very important in the study of astronomy and astrology. The oldest written reference dates the use of the water-clock in China to the 6th century BCE.From about 200 BCE onwards, the outflow clepsydra was replaced almost everywhere in China by the inflow type with an indicator-rod borne on a float. The Han dynasty philosopher and politician Huan Tan (40 BCE – 30 CE), a Secretary at the Court in charge of clepsydrae, wrote that he had to compare clepsydrae with sundials because of how temperature and humidity affected their accuracy, demonstrating that the effects of evaporation, as well as of temperature on the speed at which water flows, were known at this time. In 976, the Song dynasty military engineer and astronomer Zhang Sixun addressed the problem of the water in clepsydrae freezing in cold weather by using liquid mercury instead. Again, instead of using water, the early Ming Dynasty engineer Zhan Xiyuan (c. 1360-1380) created a sand-driven wheel clock, improved upon by Zhou Shuxue (c. 1530-1558).
The use of clepsydrae to drive mechanisms illustrating astronomical phenomena began with the Han Dynasty polymath Zhang Heng (78-139) in 117, who also employed a waterwheel Zhang Heng was the first in China to add an extra compensating tank between the reservoir and the inflow vessel, which solved the problem of the falling pressure head in the reservoir tank. Zhang’s ingenuity led to the creation by the Tang dynasty mathematician and engineer Yi Xing (683–727) and Liang Lingzan in 725 of a clock driven by a waterwheel linkwork escapement mechanism. The same mechanism would be used by the Song dynasty polymath Su Song (1020–1101) in 1088 to power his astronomical clock tower, as well as a chain drive. Su Song‘s clock tower, over 30 feet (9.1 m) tall, possessed a bronze power-driven armillary sphere for observations, an automatically rotating celestial globe, and five front panels with doors that permitted the viewing of changing mannequins which rang bells or gongs, and held tablets indicating the hour or other special times of the day. In the 2000s, in Beijing‘s Drum Tower an outflow clepsydra is operational and displayed for tourists. It is connected to automata so that every quarter-hour a small brass statue of a man claps his cymbals.
N. Kameswara Rao suggested that pots excavated from Mohenjo daro may have been used as water clocks. They are tapered at the bottom, have a hole on the side, and are similar to the utensil used to perform abhishekam (pour holy water) on shivalingam. N. Narahari Achar and Subhash Kak suggest that the use of the water clock in ancient India is mentioned in the Atharvaveda from the 2nd millennium BCE. Ghati or Kapala (clepsydra or water clock) is referred to in Jyotisha Vedanga, where the amount of water that measures a nadika (24 minutes) is mentioned. A more developed form of the clepsydra is described in chapter xiii, 23 of the Suryasiddhanta. At Nalanda, a Buddhist university, four hours a day and four hours at night were measured by a water clock, which consisted of a copper bowl holding two large floats in a larger bowl filled with water. The bowl was filled with water from a small hole at its bottom; it sank when completely filled and was marked by the beating of a drum at daytime. The amount of water added varied with the seasons and this clock was operated by the students of the university The description of a water clock in astrologer Varahimira’s Pancasiddhantika (505) adds further detail to the account given in the Suryasiddhanta. The description given by mathematician Brahmagupta in his work Brahmasphutasiddhanta matches with that given in the Suryasiddhanta. Astronomer Lallacharya describes this instrument in detailn practice, the dimensions were determined by experiment.
Water clock calculations by Nabû-apla-iddina.
|Size||H:8.2 cm (3.2 in)
W:11.8 cm (4.6 in)
D:2.5 cm (0.98 in)
|Present location||Room 55, British Museum|
In Babylon, water clocks were of the outflow type and were cylindrical in shape. Use of the water clock as an aid to astronomical calculations dates back to the Old Babylonian period (c. 2000 BCE–c. 1600 BCE) While there are no surviving water clocks from the Mesopotamian region, most evidence of their existence comes from writings on clay tablets. Two collections of tablets, for example, are the Enuma-Anu-Enlil (1600–1200 BCE) and the MUL.APIN (7th century BCE).In these tablets, water clocks are used in reference to payment of the night and day watches (guards).
These clocks were unique, as they did not have an indicator such as hands (as are typically used today) or grooved notches (as were used in Egypt). Instead, these clocks measured time “by the weight of water flowing from” it The volume was measured in capacity units called qa. The weight, mana (the Greek unit for about one pound), is the weight of water in a water clock.
In Babylonian times, time was measured with temporal hours. So, as seasons changed, so did the length of a day. “To define the length of a ‘night watch’ at the summer solstice, one had to pour two mana of water into a cylindrical clepsydra; its emptying indicated the end of the watch. One-sixth of a mana had to be added each succeeding half-month. At equinox, three mana had to be emptied in order to correspond to one watch, and four mana were emptied for each watch of the winter solstitial night.”
The oldest water clock of which there is physical evidence dates to c. 1417-1379 BCE, during the reign of Amenhotep III where it was used in the Temple of Amen-Re at Karnak The oldest documentation of the water clock is the tomb inscription of the 16th century BCE Egyptian court official Amenemhet, which identifies him as its inventor. These simple water clocks, which were of the outflow type, were stone vessels with sloping sides that allowed water to drip at a nearly constant rate from a small hole near the bottom. There were twelve separate columns with consistently spaced markings on the inside to measure the passage of “hours” as the water level reached them. The columns were for each of the twelve months to allow for the variations of the seasonal hours. These clocks were used by priests to determine the time at night so that the temple rites and sacrifices could be performed at the correct hour.These clocks may have been used in daylight as well.
According to Callisthenes, the Persians were using water clocks in 328 BC to ensure a just and exact distribution of water from qanats to their shareholders for agricultural irrigation. The use of water clocks in Iran, especially in Zibad, dates back to 500BC. Later they were also used to determine the exact holy days of pre-Islamic religions, such as the Nowruz, Chelah, or Yaldā – the shortest, longest, and equal-length days and nights of the years. The water clocks used in Iran were one of the most practical ancient tools for timing the yearly calendar.The water clock, or Fenjaan, was the most accurate and commonly used timekeeping device for calculating the amount or the time that a farmer must take water from a qanat or well for irrigation, until it was replaced by more accurate current clocks Persian water clocks were a practical and useful tool for the qanat’s shareholders to calculate the length of time they could divert water to their farm. The qanat(Kariz) was the only water source for agriculture and irrigation so a just and fair water distribution was very important. Therefore, a very fair and clever old person was elected to be the manager of the water clock(MirAab), and at least two full-time managers were needed to control and observe the number of fenjaans and announce the exact time during the days and nights.
The Fenjaan consisted of a large pot full of water and a bowl with a small hole in the center. When the bowl became full of water, it would sink into the pot, and the manager would empty the bowl and again put it on the top of the water in the pot. He would record the number of times the bowl sank by putting small stones into a jar The place where the clock was situated, and its managers, were collectively known as khaneh Fenjaan. Usually this would be the top floor of a public-house, with west- and east-facing windows to show the time of Sunset and Sunrise. There was also another time-keeping tool named a staryab or astrolabe, but it was mostly used for superstitious beliefs and was not practical for use as a farmers’ calendar. The Zeebad Gonabad water clock was in use until 1965 when it was substituted by modern clocks.
The word “clepsydra” comes from the Greek meaning “water thief”. The Greeks considerably advanced the water clock by tackling the problem of the diminishing flow. They introduced several types of the inflow clepsydra, one of which included the earliest feedback control system. Ctesibius invented an indicator system typical for later clocks such as the dial and pointer. The Roman engineer Vitruvius described early alarm clocks, working with gongs or trumpets A commonly used water clock was the simple outflow clepsydra. This small earthenware vessel had a hole in its side near the base. In both Greek and Roman times, this type of clepsydra was used in courts for allocating periods of time to speakers. In important cases, such as when a person’s life was at stake, it was filled completely, but for more minor cases, only partially. If proceedings were interrupted for any reason, such as to examine documents, the hole in the clepsydra was stopped with wax until the speaker was able to resume his pleading.
In the 4th century BCE, the clepsydra is known to have been used as a stop-watch for imposing a time limit on clients’ visits in Athenianbrothels. Slightly later, in the early 3rd century BCE, the Hellenistic physician Herophilos employed a portable clepsydra on his house visits in Alexandria for measuring his patients’ pulse-beats. By comparing the rate by age group with empirically obtained data sets, he was able to determine the intensity of the disorder
Between 270 BCE and 500 CE, Hellenistic (Ctesibius, Hero of Alexandria, Archimedes) and Roman horologists and astronomers were developing more elaborate mechanized water clocks. The added complexity was aimed at regulating the flow and at providing fancier displays of the passage of time. For example, some water clocks rang bells and gongs, while others opened doors and windows to show figurines of people, or moved pointers, and dials. Some even displayed astrological models of the universe. The 3rd century BCE engineer Philo of Byzantium referred in his works to water clocks already fitted with an escapement mechanism, the earliest known of its kind
The biggest achievement of the invention of clepsydrae during this time, however, was by Ctesibius with his incorporation of gears and a dial indicator to automatically show the time as the lengths of the days changed throughout the year, because of the temporal timekeeping used during his day. Also, a Greek astronomer, Andronicus of Cyrrhus, supervised the construction of his Horologion, known today as the Tower of the Winds, in the Athens marketplace (or agora) in the first half of the 1st century BCE. This octagonal clocktower showed scholars and shoppers both sundials and mechanical hour indicators. It featured a 24-hour mechanized clepsydra and indicators for the eight winds from which the tower got its name, and it displayed the seasons of the year and astrological dates and periods.
Medieval Islamic world
In the medieval Islamic world (632-1280), the use of water clocks has its roots from Archimedes during the rise of Alexandria in Egypt and continues on through Byzantium. The water clocks by Persian engineer Al-Jazari, however, are credited for going “well beyond anything” that had preceded them. In al-Jazari’s 1206 treatise, he describes one of his water clocks, the elephant clock. The clock recorded the passage of temporal hours, which meant that the rate of flow had to be changed daily to match the uneven length of days throughout the year. To accomplish this, the clock had two tanks, the top tank was connected to the time indicating mechanisms and the bottom was connected to the flow control regulator. Basically, at daybreak the tap was opened and water flowed from the top tank to the bottom tank via a float regulator that maintained a constant pressure in the receiving tank.
The most sophisticated water-powered astronomical clock was Al-Jazari‘s castle clock, considered by some to be an early example of a programmable analog computer, in 1206 It was a complex device that was about 11 feet (3.4 m) high, and had multiple functions alongside timekeeping. It included a display of the zodiac and the solar and lunar orbits, and a pointer in the shape of the crescent moon which traveled across the top of a gateway, moved by a hidden cart and causing automatic doors to open, each revealing a mannequin, every hour.] It was possible to re-program the length of day and night in order to account for the changing lengths of day and night throughout the year, and it also featured five musician automata who automatically play music when moved by levers operated by a hidden camshaft attached to a water wheel. Other components of the castle clock included a main reservoir with a float, a float chamber and flow regulator, plate and valve trough, two pulleys, crescent disc displaying the zodiac, and two falcon automata dropping balls into vases[unreliable source]
The first water clocks to employ complex segmental and epicyclic gearing was invented earlier by the Arab engineer Ibn Khalaf al-Muradi in Islamic Iberia c. 1000. His water clocks were driven by water wheels, as was also the case for several Chinese water clocks in the 11th century. Comparable water clocks were built in Damascus and Fez. The latter (Dar al-Magana) remains until today and its mechanism has been reconstructed. The first European clock to employ these complex gears was the astronomical clock created by Giovanni de Dondi in c. 1365. Like the Chinese, Arab engineers at the time also developed an escapement mechanism which they employed in some of their water clocks. The escapement mechanism was in the form of a constant-head system, while heavy floats were used as weights
In 1434 during the Choson (or Joseon) Dynasty, Chang Yongsil (or Jang Young Sil) (장영실 in Korean), Palace Guard and later Chief Court Engineer, constructed the Jagyeongnu (self-striking water clock or striking clepsydra) for King Sejong. What made the Jagyeongnu self-striking (or automatic) was the use of jack-work mechanisms, by which three wooden figures (jacks) struck objects to signal the time. This innovation no longer required the reliance of human workers, known as “rooster men”, to constantly replenish it. By 1554, the water clock spread from Korea to Japan. Water clocks were used and improved upon throughout Asia well into the 15th century.
Only a few modern water clocks exist today. In 1979, French scientist Bernard Gitton began creating his Time-Flow Clocks, which are a modern-day approach to the historical version. His unique glass tube designs can be found in over 30 locations throughout the world, including one at NEMO Science Museum in Amsterdam, Europa-Center‘s The Clock of Flowing Time in Berlin, Centre Commercial Milenis in Guadeloupe, the Giant Water Clock at The Children’s Museum of Indianapolis in Indianapolis, Indiana, the Abbotsford International Airport (formerly at Sevenoaks Shopping Centre) in Abbotsford, British Columbia, and the Shopping Iguatemi in São Paulo and Porto Alegre, Brazil.
Gitton’s design relies on gravity powering multiple siphons in the same principle as the Pythagorean cup; for example, after the water level in the minute or hour display tubes is reached, an overflow tube starts to act as a siphon and thus empties the display tube. Actual time keeping is done by a calibrated pendulum powered by a water stream piped from the clock’s reservoir. The pendulum has a carefully constructed container attached to it; this measures the water that is then poured into the display system. This means that strictly speaking these are not water clocks. The water is used to power the pendulum and to show the time in the display system. There are other modern designs of water clocks, including the Royal Gorge water clock in Colorado, the Woodgrove Mall in Nanaimo, British Columbia, and the Hornsby Water Clockin Sydney, Australia.
Temperature, water viscosity, and clock accuracy
When viscosity can be neglected, the outflow rate of the water is governed by Torricelli’s law, or more generally, by Bernoulli’s principle. Viscosity will dominate the outflow rate if the water flows out through a nozzle that is sufficiently long and thin, as given by the Hagen–Poiseuille equation. Approximately, the flow rate is for such design inversely proportionalto the viscosity, which depends on the temperature. Liquids generally become less viscous as the temperature increases. In the case of water, the viscosity varies by a factor of about seven between zero and 100 degrees Celsius. Thus, a water clock with such a nozzle would run about seven times faster at 100 °C than at 0 °C. Water is about 25 percent more viscous at 20 °C than at 30 °C, and a variation in temperature of one degree Celsius, in this “room temperature” range, produces a change of viscosity of about two percent.Therefore, a water clock with such a nozzle that keeps good time at some given temperature would gain or lose about half an hour per day if it were one degree Celsius warmer or cooler. To make it keep time within one minute per day would require its temperature to be controlled within 1⁄30°C (about 1⁄17° Fahrenheit). There is no evidence that this was done in antiquity, so ancient water clocks with sufficiently thin and long nozzles (unlike the modern pendulum-controlled one described above) cannot have been reliably accurate by modern standards. Note, however, that while modern timepieces may not be reset for long periods, water clocks were likely reset every day, when refilled, based on a sundial, so the cumulative error would not have been great.