Clocks

Summary: Clocks are devices for timekeeping and are used for a variety of mathematical calculations, including finding one’s longitude.

The term “clock” in a generic sense is applicable to a broad range of devices for timekeeping usually concerning fractions of the natural unit of time—the day. Modern clocks operate through various physical processes. It does not matter what kind of periodic signals a clock produces—ringing a bell, firing a cannon, flashing a light, moving a hand, displaying a number, or generating electric impulses. Mathematics has been fundamental both in the design of clocks and in the measurement of their accuracy. Modular arithmetic, an algebraic concept involving cycles, is sometimes informally known as “clock arithmetic.” In the realm of biology, mathematicians have also worked on theories related to the operation of humans’ internal biological clocks and bacterial genetic clocks.

History of Clocks

In everyday English language, watches and other timepieces that can be carried individually sometimes continue to be distinguished from clocks. Via Dutch, Northern French, and Medieval Latin, the word “clock” is derived from the Celtic clagan and clocca meaning “bell.” Those old clocks had a striking mechanism for announcing intervals of time acoustically. The history of clocks is much deeper, however. It started in early prehistoric times with sundials (often a vertical post or pillar on horizontal ground exposed to the sun or a post parallel to the Earth’s axis) that were the first and oldest scientific instruments of archaic humankind. They worked only in the daytime. In the terminology of ancient Greece, such a device was called a gnomon, and the entire branch of science on sundials is gnomonics. Famous Egyptian obelisks—now reerected in some European capitals—were also sundials.

Timekeeping devices of different types were called horologium by the Romans. In its corrupted forms, this term later on entered many languages of the world. A noticeable step in the history of timekeeping was the invention of a “water clock” (the specific Greek name is the clepsydra). Water clocks could be used at night. Some of the water clocks in China and the Near East were quite large. Another type of simple clock was the “sandglass.”

The modern era of clock-art started with the invention of weight-driven mechanical clocks (sometimes known as “chimes”). The inventor of such a novelty is unknown. Because daily prayer and work schedules in medieval times were strictly regulated, religious institutions required clocks, and it is certain that the earliest medieval European clockmakers were Christian clerics. Mechanical clocks were designed en masse in the thirteenth century in Western Europe. They were bulky and appeared on cathedral towers in many countries. Some of them have survived up to now and are among the great artifacts of the medieval epoch.

After the invention of tower clocks, efforts were made to design smaller pieces for tabletops and personal “pocket” clocks (watches) for individuals. Peter Henlein (c. 1480–1542), a locksmith from Nuremberg, Germany, is often credited as the forerunner of the first portable timekeeper, but this claim is disputed. His drum-shaped Taschenuhr was too big for a pocket. The first individual clocks were usually worn on the neck or beneath the knee. Timepieces of this type were often known as “Nuremberg eggs.” The earliest clocks are very expensive now and are subjects for collectors.

Clocks for Navigation

A great chapter in clock-making began in conjunction with the rapid development of seafaring after the European discovery of the Americas. In order to determine one’s position at sea, it is necessary to calculate two geographical coordinates: latitude and longitude. Latitude is easily computed directly from trivial astronomical considerations (the latitude of a locale is equal to the altitude of the celestial pole). As for longitude, it is equal to the difference between local time and the time of a prime meridian chosen specifically for cartographic purposes; navigators used different prime meridians in different countries in different epochs. To discover one’s longitude, an observer must know the time at the prime meridian, which requires the art of “transporting” accurate time.

The search for accurate and convenient timekeeping became one of the most impressive scientific and technological challenges of the seventeenth century. Numerous mathematical and astronomical methods were proposed, such as observations of the moon. However, the computations would have been difficult for the typical sailor and the mathematical methods were not yet well-developed enough to provide an accurate prediction. This problem was among the foci of scientific activities of Galileo Galilei of Italy (1564–1642), who discovered the key property of pendulums that makes them useful for timekeeping: isochronism, which means that the period of swing of a pendulum is approximately the same for different sized swings. Galileo developed the idea for a pendulum clock in 1637, but did not have enough time to complete the design.

Dutch scholar Christian Huygens (1629–1695) successfully built a pendulum clock in 1656 and patented it the following year. Its design incorporated concepts derived from mathematical work on cycloids. The introduction of the pendulum—the first harmonic oscillator for timekeeping—increased the accuracy of clocks enormously, from about 15 minutes per day to 15 seconds per day. In addition to building a clock, Huygens investigated the properties of synchronization of identical pendulum clocks. Researchers have been interested in the subject of synchronization of clocks and oscillators since that time.

The design of the first marine chronometer was performed by the self-educated English carpenter and clockmaker John Harrison (1693–1776). This device dramatically revolutionized and extended the possibility of safe long-distance sea travel. At the time, the problem was considered so intractable that the British Parliament offered a prize of 20,000 British pounds sterling (comparable to about $4.72 million in modern currency) for the solution. Sailors and astronomers continued to be the principal consumers of accurate timekeeping. Precise clocks became essential equipment for each and every astronomical observatory.

Modern Clocks

The problem of “transportation” of accurate time to determine longitudes lost its actuality with the invention of the telegraph and, later on, with utilization of radio signals. But with the advancement of the twentieth century, new scientific and applied challenges demanded increasingly accurate time reckoning. As a result, new clocks were created based on newly discovered physical principles that were operationalized using mathematics. The crucial step in this direction was the invention of so-called quartz clocks. A quartz crystal has the unusual property of piezoelectricity—when stimulated with voltage and pressure, it oscillates at a constant frequency.

The vibration of a quartz crystal regulates the clock very precisely. Quartz crystal clocks were designed in 1927 by two engineers at Bell Telephone Laboratories: the Canadian-born telecommunications engineer Warren Marrison (1896–1980) and an electrical engineer from the Massachusetts Institute of Technology (MIT), Joseph Warren Horton (1889–1967). Since the 1970s, quartz clocks have become the most widely used timekeeping technology. Atomic clocks followed quartz clocks toward the end of the century. The U.S. National Bureau of Standards (now the National Institute of Standards and Technology) based the time standard of the land on quartz clocks between the 1930s and the 1960s. Eventually, it changed to atomic clocks, the best of which are accurate to 5×10^-15 seconds per day. Researchers are now developing optical clocks that can be up to 100 times more accurate than the best atomic clocks. Further, satellite-based global positioning systems are now a primary source of time for some scientists and people in everyday life. This system provides almost unlimited transportation of time using variety of mobile devices in space and on Earth.

Today, the reckoning and keeping of precise and super-precise time continues to be requisite for numerous scientific and applied problems. Astronomers are still important users of this data. It is important, for instance, in cosmic navigation, in the measurement of variations of the rotation of Earth, and in the implementation of a particular technology into everyday life, such as radio interferometry with a hyperlong base. Every developed country now has a specialized national service for addressing questions regarding precise timekeeping and time reckoning. For a long time in the Paris Observatory, there was the Bureau International de l’Heure (The International Time Bureau), which played an important role in the research of timekeeping. In 1987, the responsibilities of the Bureau were taken over by the International Bureau of Weights and Measures (BIPM) and the International Earth Rotation and Reference Systems Service (IERS).

Bibliography

Bruton, Eric. The History of Clocks and Watches. New York: Time Warner Books, 2003.

Collier, J. L. Clocks. New York: Benchmark Books, 2004.

Landes, David S. Revolution in Time: Clocks and the Making of the Modern World. Cambridge, MA: Belknap Press of Harvard University Press, 2000.

Sobel, Dava. Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time. New York: Walker, 1995.

Uresova, Libuse. European Clocks. An Illustrated History of Clocks and Watches. London: Peerage Books, 1986.