Central to our comprehension of time is the intricate interplay between the celestial dance of heavenly bodies and the pursuit of accuracy. Throughout history, mankind’s perception and quantification of time has evolved with its interaction with the natural environment.
From ancient times when the rhythm of the Sun governed daily existence to the modern day of standardised timekeeping ushered in by mechanical innovations, human ingenuity has been instrumental in shaping this odyssey. Unfolding within this tale is the rare horological complication, the equation of time, a captivating chapter in the ongoing saga of humanity’s temporal exploration.
The Breguet Marine Tourbillon Equation Marchante 5887 with its kidney-shaped cam that governs the equation of time display. Image – Breguet
Dawn of Timekeeping: Celestial Observations and Ancient Innovations
The genesis of civilisation ushered in humanity’s bond with the cosmos, as early communities devotedly charted the celestial events that dictated the rhythm of their lives. This connection was not merely academic; the alternation of day and night, the moon’s phases, and the Sun’s shifting journey through the heavens were the foundation upon which the ancients built their methods of marking time.
In civilisations like those of Mesopotamia, Egypt, and ancient China, a deep-seated knowledge of the heavens was crucial for survival. The predictable cycles of day and night governed the timing of essential activities such as hunting and gathering. At the same time, the moon’s waxing and waning phases were indispensable guides for agricultural practices.
These societies were pioneers in the science of timekeeping, centring their systems around the concept of “true” solar time, with the Sun’s path as the ultimate timekeeper. The sundial, a quintessential example of early-time measurement devices, showcased this solar dependence, facilitating the division of the day into quantifiable parts. In 1500 BC, the Egyptians advanced this concept by splitting the day into 24 segments, a revolutionary step despite the fluctuating length of the day with the seasons and geography.
An Egyptian “shadow” clock from the Ptolemaic period (306–30 B.C.E.). Image – Metropolitan Museum of Art
Going even further back to 2000 BC, the Babylonians devised a sophisticated base-60 numerical system. Their contributions to time division were monumental, paving the way for the modern understanding of hours, minutes, and seconds. This comprehensive segmentation of the day marked a critical leap forward in the human capacity to grasp and manage time, fostering the development of more complex timekeeping instruments across subsequent generations.
The quest for more precise timekeeping can be traced back to Claudius Ptolemy in the second century AD. In his Almagest, the Alexandrian mathematician, astronomer, astrologer and geographer addressed the Sun’s elliptical orbit and its varying speeds, setting the stage for future time measurement corrections. His insights laid foundational knowledge that would ultimately guide advancements in timekeeping accuracy.
Aligning Shadows: The Evolution of Sundials and the Quest for Equinoctial Hours
In the 13th century, Islamic mathematicians and astronomers achieved a landmark advancement in time measurement by enhancing the accuracy of sundials. They innovated by adjusting the sundial’s gnomon to align parallel with the Earth’s axis, enabling it to consistently measure hours of equal length throughout the year, regardless of the season.
This innovation led to the creation of the apparent solar day, the time between consecutive solar transits at a given location, which varies throughout the year but is approximately 24 hours. The mean solar day, on the other hand, is made up of equinoctial hours – 24 hours of equal length.
A horizontal sundial with a qibla indicator and compass made by Bayram Ibn Ilyas dating from 1582-83. Image – British Museum
The profound understanding of the connection between celestial dynamics and timekeeping manifests itself in the ancient design of Analemma sundials. The pioneering works of astronomers like Tycho Brahe (1546-1601) and Johannes Kepler (1571-1630) further highlight it.
Kepler’s significant contributions, in particular, were applied by the Flemish astronomer Johannes Stadius, or Estadius, (1527-1579) in an ephemeris published around 1570. This work contained a detailed table known as the Canon aequationis dierum naturalium ex Copernici doctrina, or “Canon of the equation of natural days from Copernicus’s doctrine,” showcasing the ongoing endeavour to bridge the gap between solar time and mean time.
Jost Bürgi: Bridging Seconds and Celestial Cycles in the Dawn of Precision Timekeeping
In 1584, Jost Bürgi (1552-1632), a Swiss clockmaker, astronomer, and mathematician employed at the observatory of William IV, Margrave of Hesse-Kassel, unveiled a groundbreaking creation: the world’s first observation clock capable of measuring time to the second.
This innovation marked a revolution in timekeeping accuracy, facilitating the inaugural star survey using the horizontal method and slashing the daily error margin of clocks from a substantial quarter-hour to just one minute—an unprecedented improvement for the time, but for many years, unfortunately, unique to Bürgi’s work.
Jost Bürgi. Image – Wikimedia Commons
The cornerstone of Bürgi’s success was his introduction of the cross-beat escapement and a weight-driven remontoire, coupled with his precision in gear crafting. These innovations enabled the tracking of seconds visually and audibly, significantly enhancing the accuracy of astronomical observations.
Among his remarkable achievements is the Vienna Crystal Globe Clock, an exquisite timepiece Bürgi produced in his Prague workshop. Commissioned by the Prince of Liechtenstein for Emperor Ferdinand II, this clock is a testament to Bürgi’s legacy in marrying fine craftsmanship with precision timekeeping. His work, including an astronomical clock commissioned by William IV in 1591, exemplifies the fusion of science and art, featuring technological novelty and aesthetic elegance.
The Viennese Crystal Clock made by Jost Bürgi. Image – Kunsthistorisches Museum.
The historical discourse on Bürgi’s clocks often delves into their classification as the first “equation” clocks, acknowledging Bürgi’s role in introducing this concept. While debate exists over whether his clocks were more aligned with lunar than solar equations, Bürgi’s collaborations with Tycho Brahe and Johannes Kepler and his inclusion of mechanisms to measure true solar time underscore his significant contributions to solar equations.
But before the advent of the pendulum clock, Bürgi encountered significant challenges in synchronising meantime with solar time, partly due to the absence of precise tables and the mechanical limitations of his era. Despite these hurdles, Bürgi’s innovations laid crucial groundwork for future timekeeping advancements.
Solar Time and Mean Time: An Evolution in Timekeeping
The fluctuations in the length of solar days throughout the year stem from two key astronomical factors: the Earth’s axial tilt and its elliptical orbit around the Sun. Johannes Kepler’s seminal work on the Laws of Planetary Motion, particularly his first two laws published in 1609 in Astronomia Nova, revolutionised our understanding of the solar system. Kepler showed that planets travel in elliptical orbits with the Sun at one focus, not in perfect circles as previously thought. This fundamental shift in understanding was a crucial advancement in astronomy and significantly impacted timekeeping and navigation.
Despite their inherent inaccuracies, even the earliest mechanical clocks were designed to follow the Sun’s cycle. Consequently, communities faced the perpetual task of tweaking their public and personal timepieces to synchronise with the irregular length of solar days. Yet, with advancements in clockmaking technology, the constraints of strictly adhering to solar time became evident. This impracticality prompted the quest for a more dependable method of timekeeping, with “mean time” emerging as a solution.
An engraving of Johannes Kepler by N. Dietz. Image – Wikimedia Commons
The comprehension of time measurement using the Sun’s position and establishing a standardised timekeeping system to counter the Sun’s irregular movement illustrates the transition from Solar Time to Mean Time. Solar Time, reliant on the Sun’s peak position between consecutive solar noons, experiences variability, prompting the widespread acceptance of Mean Time, which normalises a day’s duration to precisely twenty-four hours.
Central to Mean Time are the conceptual models of the Mean Sun and the Dynamical Mean Sun. These idealise the Sun’s motion as if it traversed the sky uniformly, a solution ingeniously designed to counterbalance the actual Sun’s apparent erratic path. This system ensures that our timekeeping methods remain synchronised with the cosmic cycle. Establishing the benchmark, the Mean Sun figuratively traverses the Greenwich meridian precisely at 12:00 pm GMT on the Vernal Equinox, acting as a distinct temporal landmark.
Diagrams of the three models of planetary motion as mentioned in Kepler’s Astronomia Nova published in 1609. Image – Wikimedia Commons
Huygens Pendulum: Bridging Timekeeping and the Cosmos
As communities expanded and the intricacies of trade, governance, and navigation grew more complex, the mid-17th-century introduction of precise mechanical clocks engineered for consistency precipitated the shift towards mean solar time.
In 1656 Christiaan Huygens postulated that an oscillator makes for a good timekeeping base, thus presenting the world with the pendulum clock. A mathematician, Huygens recognised that a free gravity pendulum is not intrinsically isochronous and invented the so called “cycloidal pendulum”. His pendulum would feature a flexible string weighted at one end, with the string coming in contact with cycloidal flanks which would shorten the pendulum’s length for large amplitudes.
In 1657, with the help of clockmaker Salmon Coster, Huygens turned his concept into a prototype timekeeper which was said to run at a daily deviation of only 15 seconds per day . In practice the specialised cycloidal pendulum proved not all that reliable and was mostly abandoned in favour of large pendulums oscillating at small amplitudes.
The validity of Huygens’ cycloidal pendulum can be verified today by differential calculus, which makes his discovery all the more impressing, since differentials were invented by Sir Isaac Newton only some 30 years later. Huygens only used graphical reasoning and geometry in building his curve theories, which still stand today.
Portrait by Christiaan Huygens made by Caspar Netscher in 1671. Image – Kunstmuseum Den Haag
What Huygens did for horology cannot be understated. He introduced true oscillating systems as timebases — compared to the previous inertial-only foliots, and summed up his findings in the seminal work Horologium Oscillatorium (1673). In the same volume he also wrote about the resonance principle and various escapements.
Huygens was probably the first to take a rigorous mathematical approach to watchmaking. If before him watchmaking was mostly an artisan craft, his findings turned horology into a proper science. He later went on to invent the modern hairspring-balance assembly (invention disputed by the English Rober Hooke, who claimed priority).
Huygens’ inventions laid the foundation for future advancements in horology, paving the way for more sophisticated timekeeping mechanisms and techniques. His pioneering work, both theoretical and practical, underscored the profound impact of mechanical precision on our comprehension and organisation of time, shaping the trajectory of timekeeping science for centuries to come.
A pendulum clock built by Dutch clockmaker Salomon Coster from 1657 (left) next to a copy of Huygens’s Horologium Oscillatorium published in 1653 (right) as displayed in the Museum Boerhaave, Leiden. Image – Wikimedia Commons
Equation Tables: Revolutionising Timekeeping
The advent of Huygens’ pendulum clock in precision timekeeping heralded a significant breakthrough. It laid the groundwork for developing more accurate equation tables, a crucial tool for reconciling solar and mean time.
As already understood, the length of a solar day is not constant. It fluctuates throughout the year, leading to time differences ranging from +14 minutes and 16 seconds to -16 minutes and 24 seconds. These differences are particularly noticeable on specific days, such as February 11th and November 3rd.
In 1665, Huygens introduced groundbreaking tables leveraging the precision of the pendulum to elaborate on the equation of time. By integrating this innovative technology, Huygens effectively bridged the divide between human-made timekeeping systems and the natural cadences of celestial bodies.
Thanks to the unparalleled precision of the pendulum clock, these tables quickly became indispensable for a more dependable and precise approach to timekeeping, effectively aligning mechanical timekeeping with the natural progression of days.
Equation Tables published by Robert Sayer, London. Image – Tobias Birch Clocks
Expanding on Huygens’ pioneering work, the astronomer royal John Flamsteed (1649-1719) released enhanced tables in 1672 and 1673, providing vital corrections and refinements. These tables underwent continuous improvement and standardisation efforts, reflecting a concerted push to elevate the accuracy and reliability of timekeeping instruments.
This innovation set the stage for creating clocks capable of directly displaying the equation of time. Its impact extended beyond history and astronomy, proving invaluable in practical areas such as navigation.
Deriving from the medieval Latin phrase aequātiō diērum, meaning “equation of days,” the concept of the equation of time (EoT) emerged as a crucial mathematical tool in timekeeping.
Aligning Sun and Clock: Innovations in Manual Time Correction Methods
In the latter part of the 17th century, the refinement of equation tables led to the creation of timekeepers that allowed for manual adjustments for the Equation of Time. Integrating the Sun’s equations into clock mechanisms was realised through four primary methods, each offering a unique approach to aligning mechanical time with solar time.
The first and most straightforward method involved using a sundial alongside a regulator clock. This approach allowed for a basic comparison between solar time, as indicated by the sundial, and meantime, as kept by the clock, necessitating manual adjustments to reconcile the two.
The second method employed an analemma, a figure-eight curve that graphically represents the Sun’s apparent movement over a year. By marking a specific point on the analemma, clocks could visually display solar time and approximate the necessary corrections for the EoT, offering a visual guide for adjustment.
Analemma depicted on a globe. Image – Wikimedia Commons
A more interactive third method required frequent manual adjustments of a clock’s dial based on equation tables. This method could involve various modifications, such as using minute hands divided into segments or an adjustable minute ring to reflect the day-to-day changes in the EoT accurately. This hands-on approach allowed clock users to directly apply the corrections, making the timepiece as accurate as possible.
The fourth and most complex method involved creating clocks with a full-year calendar mechanism. This mechanism forgoed traditional zodiac signs in favour of a calendar that presented the equations in a tabular format. This more sophisticated system aimed to provide a comprehensive overview of the corrections needed throughout the year, albeit at a higher cost and complexity.
Notably, none of these methods offered an “automatic correction” for the EoT; instead, they necessitated either direct manual adjustment or extrapolation based on equation tables. This reliance on manual intervention highlighted the ongoing challenge of achieving a seamless integration of solar and meantime, underscoring the technical limitations of the era’s timekeeping solutions.
Nicholas Mercator and the Advent of EoT Clocks
As seen previously, the introduction of the pendulum clock represented a leap in accuracy. It set the stage for a more profound reconciliation of the fundamental differences between solar and mean time, underscoring the continual quest for precision in measuring time.
In 1666, Nicholas Mercator (1620-1687), a mathematician distinct from the renowned cartographer Gerardus Mercator, contributed to developing EoT timekeepers. John Evelyn, a diarist and founding Fellow of the Royal Society, documented his efforts. Mercator’s innovative clock, unveiled at Gresham College, caught the attention of the Royal Society, capturing the interest of figures like Sir Robert Moray and Dudley Palmer, both Fellows of the scientific institution.
An entry from Evelyn’s diary on August 29th, 1666, highlights the moment Mercator showcased his invention. At the time, an antiquary and natural philosopher, John Aubrey, noted the clock’s substantial size at “a foot across,” hinting at its complexity and the formidable challenges it posed to even skilled clockmakers like Joseph Knibb (1640-1711).
Designed “to perform the equation,” Mercator’s clock was engineered to correct the equation of time, thereby synchronising solar and mean time. The lack of comprehensive records or evidence of widespread usage leads to speculation regarding the functionality and popularity of the device. Although detailed mechanics of Mercator’s equation clock are not fully documented, theories suggest it might have featured a pendulum capable of automatically correcting for the equation of time. Mercator’s induction into the Royal Society on November 14th, 1666, is a testament to his significant contributions to the horology field.
An excerpt from John Evelyn’s diary entry for August 28, 1666. Image – Internet Archives
Furthermore, Nicholas Mercator’s collaboration with Ahasuerus Fromanteel (1607-1693), a distinguished clockmaker from London and a protégé of Salomon Coster—who had crafted the initial pendulum clock prototype for Christiaan Huygens—symbolised a significant effort to blend mathematical breakthroughs with the art of clockmaking.
Mercator’s pioneering initiatives seem to have paved the way for future advancements by a cadre of English scientists and clockmakers, including Robert Hooke (1635-1703), Thomas Tompion (1639-1713), Daniel Quare (1649-1724), and George Graham (1673-1751), who pursued further innovations in equation clocks.
Continue reading with part II.
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