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Huygens's Clocks Revisited

Erica Klarreich

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.

Undergraduate Matthew Bennet . . .Click to Enlarge Image

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.

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, Wiesenfeld 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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