AN EERIE link between two 17th-century clocks has finally been explained, say
scientists who have retraced the work of Dutch genius Christiaan Huygens.
Huygens invented the pendulum clock in 1657, in an effort to solve the
problem of determining longitude at sea. In his design there was a pair of
clocks, so that if one stopped or needed cleaning, the other would still keep
time. The pendulums were suspended from a single frame, but were housed in two
separate cases, each weighted down to stop it from toppling over at sea.
But when he set them swinging, Huygens noticed something strange鈥攚hat
he called 鈥渁n odd kind of sympathy鈥�. Regardless of how he started the two
pendulums moving, they always ended up swinging in opposite directions. Till
now, no one has managed to explain the phenomenon.
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So Kurt Wiesenfeld of Georgia Institute of Technology in Atlanta set up a
similar pendulum system and analysed its behaviour. He saw the same synchrony,
but only if the pendulums were much lighter than the whole clock, as in
Huygens鈥檚 weighted design.
Wiesenfeld says this is because the heavy frame resists any sideways force
exerted by the pendulums as they swing. So eventually they settle into a stable
state where their opposite swings cancel each other out. If the ratio of the
mass of each pendulum to the total mass of the clock was less than 1:120, the
pendulums tended to swing in opposite directions. But if the ratio was greater
than 1:80, one or both pendulums gradually ground to a halt, as forces from the
pendulums moved the lighter casing around. 鈥淚t鈥檚 something akin to shaking the
clock box,鈥� says Wiesenfeld.
He thinks the solution has taken so long because people have only recently
become interested in non-linear problems. By the time this explosion of interest
occurred, nobody cared any more about pendulum clocks, he says. 鈥淚t鈥檚 just a
problem that time forgot.鈥�
More at: Proceedings of the Royal Society A (DOI 10.1098/rspa.2001.0888)