Science Observer July-August, 2002
Huygens’s Clocks Revisited
In 1665, the great Dutch scientist Christiaan Huygens, inventor of the
pendulum clock, wrote to the Royal Society of London to tell them of his
discovery of an “odd kind of sympathy” between the pendulums of two
clocks hung together. This effect remained a mystery for three and a
half centuries, but the Royal Society has now published an explanation
of the curious interaction Huygens observed, the result of a study done
at the Georgia Institute of Technology.
Huygens devised the pendulum clock to attack the foremost technological
challenge of his time: finding longitude at sea. The development of an
accurate clock would solve this problem, because mariners could then
keep track of the time at their home port, and the difference between
that time and the local time would tell them their longitude. Huygens’s
clocks, which tended to lose only 15 seconds a day, were a vast
improvement over earlier timekeepers. Nevertheless, even the pendulum
clocks of 1665 were not accurate enough for determining longitude, so
Huygens was keen to improve them.
Undergraduate Matthew Bennet holds the pendulum of one clock used to
recreate a 1665 experiment of Christiaan Huygens. Image courtesy of Gary
Meek/Georgia Tech.
Laid up in bed during a brief illness and idly watching two clocks
mounted in one case, Huygens noticed something strange: No matter how
the pendulums started out, eventually they always ended up swinging in
exactly opposite directions. Huygens wondered whether this odd sympathy
might solve the longitude problem. Perhaps, he thought, two such clocks
could regulate each other. If one got dirty, for instance, and started
running slow, the influence of the other clock would lessen this effect.
Ironically, Huygens’s discovery that the pendulums influenced each other
in this way led the Royal Society to lose faith in pendulum clocks as a
solution to the longitude problem. At one of their meetings at the time,
it was recorded that “occasion was taken here by some of the members to
doubt the exactness of the motion of these watches at sea, since so
slight and almost insensible motion was able to cause an alteration in
their going.”
Just what was this insensible motion? Huygens thought at first that tiny
air currents were causing the interaction between the two pendulums. But
when he blocked the flow of air, the pendulums still swung into
synchronization—or rather, antisynchronization. He eventually concluded
that the effect was due to “imperceptible movements” in the beam from
which the clocks were suspended—an explanation that is quite correct,
according to Kurt Wiesenfeld and Michael Schatz, the Georgia Tech
physicists who led the newly published study.
To reproduce Huygens’s observations, Wiesen-feld and his colleagues
attached two clocks to a supporting beam and mounted the structure in a
case that could move along a track. They then used lasers to measure
precisely the swinging pendulums. To Wiesenfeld’s surprise, the
antisynchronization only arose when the ratio of the weight of the
pendulums to the weight of the entire structure fell into a rather
narrow range. If the case was much heavier than the pendulums, their
interaction was too weak to produce the effect. If, however, the case
was not very heavy compared with the pendulums, one of the pendulums
eventually stopped swinging. It halted because the interaction between
the two pendulums produced violent changes in the size of their swings,
and eventually one of the pendulums made such a small movement that the
clock’s escapement—the mechanism that gives the pendulum regular kicks
of energy—failed to engage. This is the same reason, Wiesenfeld
explains, that shaking a clock often stops it.
Because Huygens intended his clocks to go on board a ship, where the
rolling motion might easily topple them, he had placed two 100-pound
weights inside their case to keep them stable. This put the weight ratio
in the range for antisynchronization to arise. “If the situation hadn’t
been exactly right, Huygens wouldn’t have seen what he saw,” Wiesenfeld
says.
To explain why the pendulums move in opposite directions, the team set
up a system of equations that took into account the pertinent properties
of the system, including the weights of the various components and
friction. The structure of the equations made it clear that friction is
the cause of the antisynchronized motion. As Huygens originally
postulated, the swinging of the pendulums exerts small forces on the
supporting beam. If the pendulums are moving in the same direction,
together they nudge the beam the other way, giving rise to frictional
forces that naturally put a damper on this kind of motion. If the
pendulums are moving in opposite directions, however, the forces they
exert on the beam cancel each other, and the beam doesn’t move. So over
time, antisynchronized motion wins out over synchronized motion.
According to Steven Strogatz, an applied mathematician at Cornell
University, Huygens’s discovery was the first-ever observation of what
physicists call coupled oscillation—at least in inanimate objects. In
the 20th century, coupled oscillators took on great practical importance
because of two discoveries: lasers, in which different atoms give off
light waves that all oscillate in unison, and superconductors, in which
pairs of electrons oscillate in synchrony, allowing electricity to flow
with almost no resistance. Coupled oscillators are even more ubiquitous
in nature, showing up, for example, in the synchronized flashing of
fireflies and chirping of crickets, and in the pacemaker cells that
regulate heartbeats. “The theme of synchronization between coupled
oscillators is one of the most pervasive in nature,” Strogatz says.
The Georgia Tech team is now trying to extend its mathematical analysis
to formulate a single law that would apply to all coupled oscillators
and predict under what conditions they will become synchronized or
antisynchronized. “It looks as if there is a mathematical principle that
would be equally valid in all these cases,” Wiesenfeld says. “I’m pretty
sure we wouldn’t have stumbled across it if we hadn’t had the experience
of looking at the problem of Huygens’s clocks.”—Erica Klarreich
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