Stokes' law, viscometry, and the Stokes falling sphere clock

Clocks run through the history of physics. Galileo conceived of using the pendulum as a timing device on watching a hanging lamp swing in Pisa cathedral; Huygens invented the pendulum clock; and Einstein thought about clock synchronization in his Gedankenexperiment that led to relativity. Stokes derived his law in the course of investigations to determine the effect of a fluid medium on the swing of a pendulum. I sketch the work that has come out of this, Stokes drag, one of his most famous results. And to celebrate the 200th anniversary of George Gabriel Stokes’ birth I propose using the time of fall of a sphere through a fluid for a sculptural clock—a public kinetic artwork that will tell the time. This article is part of the theme issue ‘Stokes at 200 (part 2)’.

Harrison Decoded

This volume centres on a clock, known as Clock B, built in the mid-1970s that achieved considerable acclaim after an extraordinary performance in a 2015 peer-reviewed public trial at the Royal Observatory, Greenwich. The clock was built according to an understanding of John Harrison’s unique theoretical approach to making precision pendulum clocks, which defies the standard approaches to making accurate clocks. The clock represents the culmination of over forty years of collaborative research into Harrison’s writing on the subject, which is scattered across a number of manuscripts and a book, printed shortly before his death. Ostensibly, Harrison set out to describe how to make his precision pendulum clock, but it is a mixture of his peripheral interests. Horological information is almost completely lost among vitriolic sentiments relating to his experiences with the Board of Longitude. However, as one reviewer surmised: ‘we are sorry to say that the public will be disappointed’ and another concluded that ‘it can only be excused by superannuated dotage’. The chapters provides contextual history and documentation of the analysis and decoding of the cryptic written descriptions. It presents this in parallel to the modern horological story of making, finishing, and adjusting Clock B; the process of testing, using electronic equipment to monitor the its performance and reaction to changes in environmental conditions, and, indeed, the mechanics behind the various compensating features of the design.

Analysis of the Mechanisms for Compensation in Clock B

This chapter assesses the design requirements of the grasshopper escapement, the pendulum and suspension spring to provide compensation for changing density and viscosity of the air surrounding the pendulum and changing escapement torque. It assesses the key components of the Harrison system: a pendulum bob of modest mass; a pendulum operating at a large running arc; and the grasshopper escapement’s increased torque delivery, ability to run without lubrication, its composers that allow fine adjustment to the torques delivered before and after the escaping arcs are reached and the importance of the thickness of the suspension spring that runs within circular cheeks. It also compares the system to the traditional pendulum clock design that traditionally employs a pendulum with a large mass and high-quality factor—high Q. Furthermore, it discusses Harrison’s stipulation that the pendulum needed to slightly reduce its length when warm.

The Origins of John Harrison’s ‘Pendulum-Clock’ Technology

Working in Lincolnshire in the 1720s, John Harrison (1693–1776) established a unique approach to making accurate pendulum clocks that was born from his experiences in the family business that served country estates in Yorkshire and Lincolnshire. The chapter charts Harrison’s early clock-making practice, inspired by local traditional clocks, and his unique interpretation. He used wood for the frames and most of the wheelwork before key elements of his precision timekeeping crystallised in the making of an estate clock for Brocklesby Park in Lincolnshire. Notably, the elimination of requirement for lubrication formed a solid bedrock for his life’s work in precision in this field. It examines Harrison’s early influences and progression of thinking through documentary evidence and artefacts to introduce the beginnings of his unique approach to precision pendulum clock making.

Introducing Martin Burgess, Clockmaker

In 1775, two years after receiving the second half of the Longitude Prize, John Harrison (1693–1776) published a book, which, among other things, described a pendulum clock that could keep time to one second in 100 days. His claim of such unprecedented accuracy for a clock with a pendulum swinging in free air (i.e. not in a vacuum) was met with ridicule both at the time of its publication and for the next two centuries. This chapter describes the early life of Martin Burgess, the clockmaker who proved that Harrison’s claim was indeed true. Like Harrison, Martin was a self-taught clockmaker. From his training in the arts and crafts, he saw the mechanics of clockwork as sculpture in its own right, each element contributing to the overall design. Martin’s upbringing, his education, and his unusual lifestyle and approach were all crucial to his quest to prove that John Harrison was right.

Introducing the Precision Pendulum Clock

This chapter provides historical context to the development of the precision pendulum clock. It primarily looks at the historical astronomical clocks at the Royal Observatory, Greenwich; their use, acquisition, and modification to demonstrate that there was continual desire for better timekeeping in the Observatory. It argues that the core theoretical principals in clock making began with Robert Hooke’s demonstration to the Royal Society in 1669 and remained largely unchanged through to the obsolescence of pendulum time standards in the mid-1900s. By studying historical experiments into the effects of weather variation on pendulum clocks, it will familiarise the reader with the physical effects on pendulum clocks that are critical to the study of Martin Burgess’s Clock B.

Computer-Aided Design and Kinematic Simulation of Huygens’s Pendulum Clock

This article presents both the three-dimensional modelling of the isochronous pendulum clock and the simulation of its movement, as designed by the Dutch physicist, mathematician, and astronomer Christiaan Huygens, and published in 1673. This invention was chosen for this research not only due to the major technological advance that it represented as the first reliable meter of time, but also for its historical interest, since this timepiece embodied the theory of pendular movement enunciated by Huygens, which remains in force today. This 3D modelling is based on the information provided in the only plan of assembly found as an illustration in the book Horologium Oscillatorium, whereby each of its pieces has been sized and modelled, its final assembly has been carried out, and its operation has been correctly verified by means of CATIA V5 software. Likewise, the kinematic simulation of the pendulum has been carried out, following the approximation of the string by a simple chain of seven links as a composite pendulum. The results have demonstrated the exactitude of the clock.