Continuing from part I of the history of the equation of time. In the late 17th century, London’s clockmaking landscape experienced a remarkable surge of innovation and collaboration, fuelled by interactions among prominent horologists and the broader scientific community. Among this period’s leading figures were Christian Huygens and Robert Hooke, who made substantial strides in crafting clocks that could precisely display solar time without the need for cumbersome equation tables.

This era marked the advent of the equation cam, a revolutionary mechanism designed to reconcile the disparities between solar time and mean time. Inspired by the analemma—a figure-eight pattern illustrating the Sun’s varying positions in the sky throughout the seasons—these mechanisms featured a distinctive mathematically calculated kidney-shaped cam, symbolising a pivotal step forward in horological precision and accuracy.

At the heart of this innovation lies the cam and lever mechanism, an integral component of the invention. It comprises a shaft propelled by the clock’s mechanism, completing a full rotation annually. Affixed to this shaft is a meticulously crafted kidney-shaped cam, tailored precisely to match the annual fluctuations outlined by the equation. This cam engages with a follower and a connected lever, facilitating the seamless translation of its rotational motion into practical adjustments within the timepiece.

Drawing of an equation pendulum by Ferdinand Berthoud (1727-1807). Image – Encyclopédie de Diderot et d´Alembert

As the cam rotates throughout the year, the follower meticulously follows its evolving contour, adjusting to its dynamic profile. This precise interaction effectively translates the cam’s slow motion into direct, understandable adjustments. Such a mechanism guarantees that the clock faithfully reflects the shifts between solar and mean time across the year, adeptly capturing both the advancements and the delays in solar time in comparison to meantime.

The date indication feature plays a crucial role in this mechanism, ensuring the cam rotates at the appropriate pace all year round. It also facilitates daily precision adjustments according to the current date, reinforcing the timepiece’s function as a reliable indicator of solar time.

Christiaan Huygens contributed to the development of solar time indication, hinting that the concept of the equation clock was already known among clockmakers. By 1695, he would be credited with devising a nephroid-shaped equation kidney mechanism. Unfortunately, the specific equation clock that featured this innovation, intended for the University of Leiden, has since been lost to history.

Portrait of Robert Hooke as depicted by Rita Greer.

Robert Hooke, known for his deep interest in horology and his significant partnership with Thomas Tompion, may also have contributed to the development of equation clocks. Tompion’s creations, frequently inscribed with “Tho. Tompion Invenit,” indicate a collaborative effort with Hooke that can significantly have contributed to refining the equation clock mechanism.

Joseph Williamson (1673-1725), an Irish clockmaker who moved to London, further contributed to this field. Trained in Dublin, Williamson gained recognition by the 1690s and collaborated with Daniel Quare to produce sophisticated longcase clocks with EoT indication. Despite claims in a letter to the Royal Society about crafting all equation movements sold in England before 1720, verifying his contributions still needs to be determined due to the loss of historical pieces, such as the clock made for King Charles II of Spain.

The invention and refinement of the equation clock underscore a period rich in innovation. Despite the speculative nature surrounding their claims, the contributions of Huygens, Hooke, Tompion, Quare, and Williamson highlight a shared pursuit of precision in timekeeping. While unresolved, the debate over the origins of the kidney cam clocks reflects the complexity of scientific communication and, to a certain level, the collaborative spirit that drove horological advancements in the 17th and 18th centuries.

Tompion fecit: Equation clocks with movable minute markings

Equation clocks with movable minute markings represented the next step, enabled by the innovative use of the equation cam. These precision instruments featured a minute plate that could rotate independently around the clock’s axis, a design that accurately mirrored the EoT, eliminating the need for manual adjustments and aligning perfectly with solar time.

Thomas Tompion, a distinguished English clockmaker and the son of a Bedfordshire blacksmith, established his reputation in the field upon setting up his workshop near Fleet Street in 1671. His collaboration with the mathematician and scientist Robert Hooke significantly contributed to his fame.

An engraving of Thomas Tompion by John Smith. Image – Yale Museum of Art

Tompion’s 1695 equation timepiece for King William III, now a prized item in Buckingham Palace, exemplifies his horological mastery. This clock introduced a way to display the EoT directly on its face, with the hour hand completing a full rotation every 24 hours, eliminating the need for an additional hour-equating ring.

A floor standing clock made by Thomas Tompion from 1695. Image – The Royal Collection Trust

The Equation Kidney mechanism, pivotal to the mechanism’s design, is cleverly mounted alongside the annual calendar disc. It employs a pin attached to a lever, which, depending on its position, moves a minute ring forward or backward to adjust for the EoT, showcasing Tompion’s inventive engineering.

Among Tompion’s notable creations is the Drayton House Year Equation longcase clock, made between 1696 and 1700. Intended initially for Drayton House, it became part of the Duchess of Norfolk’s estate, reflecting its artistic value and the turbulent history of its ownership. This clock features a unique design with a silvered chapter ring and a rotating minute ring for dynamic time measurement, underscoring Tompion’s signature innovation.

The Drayton House Clock made by Thomas Tompion for the Duchess of Norfolk. Image – The Fitzwilliam Museum, Cambridge

Tompion’s collaboration with his nephew Edward Banger (1668-1720) from 1699 to 1704 resulted in another remarkable timepiece with movable minute markings. Their joint effort produced a clock with advanced features like a dual representation of apparent and mean time and a sophisticated calendar mechanism that accounted for leap years.

Commissioned for Prince George of Denmark and later chosen by George III for Buckingham House, this clock is recognised for its exceptional craftsmanship and intricate design. It survived historical challenges like the 1809 fire at St. James’s Palace.

17th to 18th century: Blending Timekeeping with Celestial Wonder

The transition from the rudimentary practice of aligning timekeeping with solar time through sundials and the EoT tables to integrating complex astronomical features in clocks mirrors a significant evolution in horology and societal engagement with the cosmos. As the 17th century drew to a close, despite the advancements in clockmaking exemplified by figures like Thomas Tompion, setting clocks to mean time remained cumbersome, tethered to the direct observation of sundials and subsequent adjustments using EoT tables. While practical, this method underscored contemporary timekeeping’s limitations in accurately capturing the nuances of celestial mechanics.

Recognising the inconvenience and inaccuracy of perpetual reliance on EoT tables, clockmakers in the early 18th century began exploring more sophisticated solutions. This period witnessed a renewed interest in clocks that served as timekeeping instruments and conduits for astronomical education and display. With their elaborate dial indications, these timepieces offered their owners a platform to showcase their understanding and appreciation of the universe. This trend was not merely a reflection of technological progress but also an expression of the era’s intellectual curiosity and the social prestige associated with astronomical knowledge.

An engraving of the astronomical clock at the Strasbourg Cathedral by Tobias Stimmer, 1574. Image – The Metropolitan Museum of Art

The phenomenon of creating clocks with intricate celestial displays harks back to the medieval era, when monumental public clocks, such as those in Strasbourg Cathedral and the Old Town Square in Prague, were designed to illustrate the marvels of the divine cosmos to the masses. This tradition of blending clockmaking with astronomical display continued into the Renaissance, finding expression in the princely courts of Europe, such as the Viennese’ Kunstkammer. Here, grand astronomical clocks crafted by luminaries like Eberhard Baldewein (1525-1593) and Jost Bürgi were not just mechanisms for marking time but statements of power, knowledge, and the cosmic order.

The 18th century’s resurgence in astronomical clockmaking thus can be seen as part of a long historical continuum, where the mechanics of timekeeping converge with the aesthetics of cosmic representation. These clocks, far from mere technical achievements, were symbols of their owners’ erudition and the broader human quest to understand and articulate our place within the universe. Through the intricate dance of gears and hands, they narrated the story of humanity’s timeless fascination with the stars and the ceaseless pursuit of precision in our temporal and celestial comprehension.

Tracing the Arc of Time: The Innovation of Variable Pendulum Clocks

The dawn of the 18th century saw the introduction of variable pendulum clocks, designed to accurately mimic the annual variations of solar time. These clocks featured an ingenious mechanism to adjust the pendulum’s length, altering its oscillation speed to match the Earth’s irregular rotation. This technological marvel directly reflected solar time, eliminating the need for cumbersome conversions typically associated with equation tables.

As noted by Joseph Williamson, these clocks incorporated a directly actuated equation kidney that influenced the pendulum’s suspension. This permitted an alteration in pendulum length, facilitating a direct readout of apparent solar time with a singular set of hands. Remarkably, some of these timepieces were designed to toggle between mean and apparent time displays, demonstrating their versatility to accommodate varying timekeeping needs. An exemplary model of this innovation is the year clock by Quare, housed at Hampton Court and later refined by Benjamin Vulliamy (1747-1811), reflecting the dynamic evolution of these sophisticated mechanisms. Williamson’s inventive approach considered the strategic up-and-down movement of the suspension spring through a slit.

A floor standing clock made by Daniel Quare for King William III. Image – The Royal Collection Trust

The Encyclopédie by Diderot and d’Alembert further illuminated this subject, introducing Father Alexandre’s (1705-1772) design that also utilised an elliptical lever to adjust the pendulum length according to the solar year’s requirements. This approach elegantly bridged theoretical physics and practical mechanics, although adapting the design to accommodate heavier pendulums posed considerable challenges.

Visualising the Equation: Introduction of Subsidiary Dials

Beginning in 1767, the Nautical Almanac and Astronomical Ephemeris published by the Royal Greenwich Observatory introduced tables for the equation of time (EoT), broadly guiding users to adjust apparent time by a simplified method that required adding or subtracting indicated minutes and seconds to obtain meantime.

Representing the third phase in the evolution of timekeeping mechanisms accommodating the EoT, these systems employed a “Wand” or rocking hand moving across a fixed semicircular dial or arc. This approach, from -16 to +14 minutes, visually represented the Equation of Time, enabling users to discern the difference between mean and true solar time easily. However, this method still necessitated mental calculations for accurately converting mean solar time to true solar time.

Early astronomical and equation clock dial by Jack Willmore (1674-1720) and A. Malines from circa 1711. Image – Sothebys

This wave of innovation underscored a dedication to creating a more intuitive and accessible means for the public to grasp the EoT. By incorporating visual indicators that illustrated the mathematical variance between solar time and mean time, clockmakers made it significantly more user-friendly.

Prominent figures in this movement include Daniel Quare, who was credited with producing five notable examples, the earliest of which dates between 1690 and 1700, as documented by the British Museum. Edward Cockey, Thomas Tompion, Jack Willmore and John Ellicott (1706-1772) also stand out for their contributions to this sophisticated blend of artistry and science. Their work collectively marks a significant period of advancement and creativity, bridging complex astronomical phenomena with the everyday act of timekeeping.

Detail of the dial of the astronomical longcase clock made by Edward Cockey (died 1768). Image – British Museum

Mechanical Mastery: Advent of Built-in Equation Calculations

The next step introduced further developments in a sophisticated system capable of adjusting rotational speeds. This solution underscored early clockmakers’ profound understanding of mechanics by enabling clocks to synchronise and automatically exhibit solar and mean time.

Featuring a sophisticated arrangement of interlocking gears, this system transmitted rotational motion from various sources to a single output, ensuring the seamless integration of different time measurements within a single timepiece. Through synchronising hour and minute hands with the variable speed driven by the EoT cam, a differential gear facilitated its direct indication on the clock face.

This elaborate system achieved remarkable accuracy by harmonising the constant rotation of the meantime gear with the fluctuating rotation controlled by the EoT cam, accurately representing true solar time. Typically highlighted on the clock face by a distinct hand or sub-dial, this significantly elevated the complexity and functionality of the timepiece.

Obverse of the Antikythera mechanism found in 1901 and on display at the National Archaeological Museum, Athens. Image – Wikimedia Commons

The historical journey of epicyclic and differential gears is deeply intertwined with advancements in watchmaking and mechanical engineering. These gears have proven indispensable, from their crucial role in depicting the EoT in timekeeping devices to their extensive application in modern machinery, computing, and control systems. Notably, the innovation at the heart of this dual-time display has predated its modern application for centuries.

The discovery of the Antikythera mechanism in 1901, recovered from the depths of the Greek Mediterranean, revealed an ancient artefact dating back to 100 BC to 70 BC. This device, a testament to ancient mechanical prowess, evidences one of the earliest forays into complex mechanical engineering.

Reverse of the Antikythera mechanism found in 1901 and on display at the National Archaeological Museum, Athens. Image – Wikimedia Commons

Modern analysis suggests that the Antikythera mechanism utilised a system similar to differential gearing to calculate lunar phases by determining the angular difference between the Sun and Moon’s positions on the ecliptic. This early use of differential gearing highlights a sophisticated understanding of mechanical operations and showcases the advanced technological capabilities of ancient civilisations.

The resurgence of this mechanism in 1575 with Baldewein’s globe clock marked a revival in its application. It proliferated during the Renaissance through the advent of astronomical clocks in South Germany and Austria, marking a significant advancement in horological science.

A celestial globe clock made by Eberhard Baldewein from 1574. Image – Kugel Collection, Paris

By the 18th century, horologists such as Tompion, Graham, and Joseph Williamson had refined the differential gear, laying the groundwork for its later use in industrial machinery.

Williamson Double-Dialled EoT clock

A singular category in this type of time indication comprises clocks and watches featuring dual displays or double dials. These timepieces simultaneously display mean and solar time through separate hands and dials, allowing observers to view the current time according to the conventional mean and natural solar time.

An example of such a timepiece emerged around 1720, made by Joseph Williamson, just a few years before his passing in 1725. Unlike earlier examples, this timepiece featured separate dials for mean and apparent time, both driven by a single movement housed between them.

The clock’s subsidiary dials were arranged in a unique configuration. One dial displayed the days of the week, each symbolised by intricately engraved representations of their corresponding deities. Another dial indicated the age of the moon and high tide times, allowing for practical maritime use.

A double dialed clock with an equation of time made by John Williamson from 1720. Image – British Museum

At the heart of the clock lay the equation dial, where the equation kidney, responsible for adjusting the clock to display apparent solar time, was driven by an endless worm gearing mechanism allowing for precise synchronisation between mean and apparent time.

A clever feature of the clock was the ability to switch between mean and apparent time displays. By manipulating a knob located near the winding drum, the roller on the equation dial could be disengaged, allowing mean time to be shown on both dials simultaneously.

Additional features, such as a disc indicating the approximate rising and setting of the Sun and a revolving blued steel band tracking the Sun’s daily position in the heavens, added to the clock’s functionality.

The clock’s engineering brilliance is evident in its construction. Both sets of hands are driven by a single driving train, simplifying the mechanism while ensuring smooth and accurate timekeeping. Additionally, a second disc attached to the arbour carrying the calendar hand and equation kidney facilitates the rotation of the Sun’s motion plate, providing essential astronomical information.

1750 to 1850: the Golden Era

The period from 1750 to 1850 was indeed a golden era for advancing horology, particularly in the refinement and application of the EoT in timekeeping devices. This period saw a remarkable transition in measuring and displaying time, reflecting the era’s broader scientific understanding and technological capability shifts.

In post-1755 England, the production of equation clocks saw a decline. This shift may reflect changing tastes, technological advancements, or the practical considerations of manufacturing and maintaining such complex devices. Despite this, the fascination with and the craft of creating equation clocks persisted more robustly among French horologists, indicating a divergence in horological traditions between the two countries.

French makers like Ferdinand Berthoud and the Lepaute brothers (Jean-André 1720-1789 and Jean-Baptiste 1727-1802), alongside others such as Robert Robin (1741-1799) and Charles Oudin (1768-1840), continued to innovate, developing clocks and watches that not only were masterpieces of mechanical complexity but also served as luxury items and symbols of scientific progress.

A longcase astronomical regulator clock made by Ferdinand Berthoud dating from circa 1768 to 1770. Image – Metropolitan Museum of Art

This divergence underscores the unique cultural and scientific contexts in which these horologists worked. In France, the continued popularity and production of equation clocks may have been driven by patronage, the prestige of scientific instruments, and a national interest in astronomy and navigation. Meanwhile, British horological interests shifted towards the practical and commercial aspects of timekeeping, as seen in the emphasis on marine chronometry and the quest for determining longitude at sea.

The period’s legacy in horology is not just in the advancements made but in the enduring fascination with the equation of time and the relentless pursuit of precision. It was a time when the artistic and the scientific were intricately linked in the craft of timekeeping, leading to innovations that would lay the groundwork for future developments in the field.Overall, this era’s significance in horological history cannot be overstated. It was a period of refinement and revolution, where the challenges of accurately measuring and displaying time spurred remarkable innovations.

Rise of the “Equation Marchante”

“In principle, the indication of true solar time with a mean time clock is simple enough. It is necessary only to arrange a suitably shaped cam to revolve once a year and a pivoted hand to indicate the equation for the day by its rise and height on the cam. The indication of the equation as a relative interval of time between two continuously revolving hands is more complicated.”

– George Daniels, The Art of Breguet (1975)

The “running equation” mechanism, also known as équation marchante, represents the last step in the historical and technical evolution of displaying the EoT. It offers users a more intuitive experience, allowing for direct readings of solar time without manual adjustments due to its automatical compensating capability.

As seen in Williamson’s double-dialled clock, the mechanism uses a feeler lever to interact with a differential system, controlling the position of the Equation hand relative to the minute hand. As both hands progress around the dial simultaneously, users can quickly identify true solar noon when the Equation hand aligns with noon.

An astronomical stop-watch with equation of time by John Ellicott (1706-1772) in collaboration with Thomas Mudge (1715-1794), London, circa 1742. Image – Antiquorum

At the core of this system lies the already discussed differential gear capable of combining two inputs into one output. One input represents the constant rotation reflecting mean solar time, while the other adjusts for the variable EoT.

This sophisticated setup features two coaxially positioned minute hands: one dedicated to precisely tracking mean solar time, and the other—the EoT hand—dynamically adjusts to reflect true solar time variations. This way, users gain a deeper understanding of temporal variations by observing the real-time fluctuation between solar and conventional clock time.

Despite its complexity, reading the indication on the dial is surprisingly straightforward. A hand, often crafted in gold as a nod to tradition and adorned with a small sun, moves alongside the conventional minute hand but at a variable speed dictated by the Earth’s movements. The continuous gap between these two hands vividly illustrates the irregularity inherent in true solar time, offering a captivating and intuitive display of this celestial phenomenon.

A Louis XVI table regulator with running equation and remontoire by Robert Robin (1741-1799), 1781. Image – Christies

EoT watches and regulators crafted during this era were engineering marvels created only by the most skilled artisans in the field. For instance, Mudge’s equation of time regulator boasted a complex month-going movement comprising 18 wheels with 1,581 teeth. The largest wheel, the annual calendar wheel, featured a staggering 365 teeth. To provide context, a month-going regulator without the equation of time function typically had only eight wheels and 266 teeth in total.

Given their highly complex craftsmanship, such timepieces commanded exorbitant prices and were produced in very limited quantities. They were sought after by royalty and the wealthiest individuals, serving as precise timekeepers, prestigious status symbols, and conversation pieces. They were nothing short of mechanical marvels.

Only a select group of renowned makers crafted watches with this complexity throughout the 18th and early 19th centuries. In England, besides Mudge, other masters like George Graham and John Ellicott spearheaded this horological innovation.

Centre seconds pocket watch with running equation by Ferdinand Berthoud from circa 1756-1762. Image – The British Museum

Similarly, on the continent, notable figures such as Pierre Le Roy (1717-1785), Jean-Antoine Lépine (1720-1814), and Ferdinand Berthoud also pushed the boundaries of horological innovation.

The legacy of these master clockmakers extended beyond their contributions. Collaborations, such as those between Jean-Baptiste Lepaute and his brother Jean-André Lepaute, yielded several remarkable examples of running equation timepieces. Similarly, the intricate works of Antide Janvier (1751-1835) and Abraham Louis Breguet (1747-1823) epitomised a harmonious blend of mechanical precision and artistic finesse, setting new standards for horological excellence.

An astronomical clock by Eardley Norton (1676-1766) from 1765. Image – The Royal Collection Trust

Across the centuries, notable examples of clocks featuring running equations of time testified to the relentless pursuit of accuracy and innovation. Each timepiece, from Eardley Norton’s pioneering astronomical clock to Victor Chatriot’s (1828-1889) ornate masterpieces, represented a milestone in horological engineering.But as the 19th century dawned, the advent of mean solar time marked a pivotal shift in timekeeping practices, reflecting a broader transition towards standardised measurement systems.

19th Century Timekeeping: The Path to Global Coordination

As the 19th century unfolded, the symbiosis between timekeeping innovation and navigational necessities led to the widespread acceptance of Local Mean Time as the definitive standard for measuring time. This era distinguished itself by prioritising meantime over solar time, leveraging the concept of an imaginary sun that traverses the equator at a consistent speed. This notion was pivotal for the intricate calculations required in determining longitude, offering a degree of uniformity essential for navigation that solar time could not provide.

While not observable directly, the position of this hypothetical Sun was inferred through the consistent and predictable motion of stars around the equator, known as Sidereal Time. This celestial regularity laid a robust foundation for the computation of Mean Time, facilitating a transition that would have profound implications for timekeeping and navigation. The notable time differences between different locales highlighted the necessity for a standardised approach to time measurement, marking a significant leap toward harmonising timekeeping practices.

A sidereal and running equation of time deck watch by Stromgren og Olsen, circa 1920. Image – Antiquorum

This shift from Solar to Local meantime was not merely a technical adjustment; it represented a fundamental transformation in how time was conceptualised and utilised globally. Establishing a more consistent and universally applicable system laid the groundwork for future advancements in global time coordination. This period underscored the indispensable role of precise time measurement in the broader narrative of navigation and global exploration, setting the stage for today’s interconnected world.

Through these developments, the 19th century emerged as an essential chapter in the history of timekeeping, bridging the gap between regional timekeeping practices and the global coordination efforts that would eventually culminate in establishing standardised time zones and universal time. The legacy of this era’s timekeeping innovation continues to influence our understanding and management of time in the context of navigation and beyond, highlighting the enduring significance of these advancements in shaping our global society.

However, although this standardised measurement greatly and unequivocally simplified the structuring of daily activities, it also distanced humanity from the natural cycles that had previously dictated our existence.