The mystery of Huygens clocks explained

Proceedings of the Royal Society Series A Vol. 458, No. 2019 Cover Date 8 March 2002

Christiaan Huygens` observations in 1665 of anti-phase synchronisation in two pendulum clocks were the subject of some of the earliest deliberations of The Royal Society but have remained a scientific puzzle. Huygens` acute observations are often quoted but have never been adequately explained – until today. The forthcoming issue of Proceedings A, a Royal Society journal, offers a simple and compelling explanation of the phenomena from a research team at Georgia Institute of Technology in the USA led by Drs Kurt Wiesenfeld and Mike Schatz.
Huygens` work has provided the basis for all modern studies on synchronised oscillators in many fields of science and engineering, including physics (e.g. laser arrays), chemistry (e.g. chemical reactions), and biology (e.g. hearts and brains).

“Our experimental and theoretical results suggest Huygens` observations depended rather serendipitously on the circumstances of his 1665 experiments, which he conducted as part of a fruitless attempt to solve the outstanding technological problem of the 17th century: the `longitude problem`”, says Dr Mike Schatz. The Georgia Tech study has reproduced Huygens` experimental set-up from his original observations preserved in his laboratory notes written in Latin and in a letter to his father.

Timely explanation
The reason for two clocks operating simultaneously arose from the practical requirement for redundancy for maritime clocks: if one stopped (or required cleaning) the other could continue timekeeping. However, Huygens` observation of `sympathy` seemed to have depended on both luck and talent.

“The clock boxes where weighted by some 100 lbs (40 kg) of lead in order to keep them upright in stormy seas,” explains Dr Wiesenfeld. “If this had not been the case then the mass ratio (the ratio of the mass of an individual pendulum to the mass of the whole clock apparatus) would have been too large, making the coupling too strong, and eventually stopping the clocks.”

Neither would Huygens` observations have been possible if the coupling was too weak, since the small but inevitable differences in the clock frequencies would have prevented frequency locking. “Only clocks with sufficiently close frequencies could fall into the observed anti-phase lock-step,” continues Dr Wiesenfeld. “As it happened, Huygens` own inventiveness – and the outstanding craftsmanship of his clock maker S Oosterwijck – made such exquisite matching possible.”

Original observation and recreation
While recovering from an illness in 1665, Christiaan Huygens noticed that two of the large pendulum clocks in his room were beating in unison, and would return to this synchronised pattern regardless of how they were started, stopped or otherwise disturbed. As the patented inventor of the pendulum clock, Huygens was understandably intrigued and set out to investigate and analyse this phenomena 20 years before Sir Isaac Newton published the now-familiar laws of mechanics.

The Georgia Tech team have faithfully reconstructed Huygens` apparatus. The system under study consists of two spring-powered pendulum clocks attached to a wooden platform with metal weights added. The platform is set on wheels, free to move along a level metal track. Though the clocks are much smaller than those built by Huygens, the relationship between the masses of the pendulum bobs and that of the overall platform is similar. The clocks` period – time between ticks – is also approximately the same. However, the modern clock system includes a feature not available to Huygens: laser monitoring that records the pendulum swings for computer analysis.

Recreating the system required considerable research that spanned not only 335 years, but also two languages. Dr. Heidi Rockwood, chairperson of Georgia Tech`s Department of Modern Languages, worked with the scientific team to decipher the original Latin — which turned out to be not as scientifically clear as the researchers had hoped.

“Constructing such a system that lends itself to an intuitive and physical understanding is useful,” concludes Dr. Wiesenfeld. “We might be able to learn how this system is like laser systems or superconducting electronic systems. If there are general mechanisms affecting coupled oscillators, then perhaps we can learn about these mechanisms by using the clocks as mechanical analogues for electronic systems. Classical physics still has things to teach us.”