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Starts With A Bang

The Physics Of Why Timekeeping First Failed In The Americas

The world’s greatest clockmaker sent a clock to the new world, and everything went haywire. The reason why will shock you.

For millennia, humanity’s one-and-only reliable way to keep time was based on the Sun. Over the course of a year, the Sun, at any location on Earth, would follow a predictable pattern and path through the sky. Sundials, no more sophisticated than a vertical stick hammered into the ground, were the best timekeeping devices available to our ancestors.

For countless millennia, sundials were the most accurate way of keeping time. Despite the repetitious nature of orbits, there is an inherent uncertainty, at any given moment, of approximately 15 minutes in what a sundial records. (Public domain)

All of that began to change in the 17th century. Galileo, among others, noted that a pendulum would swing with the same exact period regardless of the amplitude of the swing or the magnitude of the weight at the bottom. Only the length of the pendulum mattered. Within mere decades, pendulums with a period of exactly one second were introduced. For the first time, time could be accurately kept here on Earth, with no reliance on the Sun, the stars, or any other sign from the Universe.

One of the very first clocks ever produced by Christiaan Huygens, which operated on the principles of a fixed-period pendulum. The clock still survives today, and can be found in the Rijksmuseum in Amsterdam. (HANSMULLER / WIKIMEDIA COMMONS)

The most renowned clockmakers of the 17th century were Dutch, led by the great physicist Christiaan Huygens. Huygens made tremendous advances in the science of wave mechanics, optics, physics (discovering centripetal force), and astronomy (including investigating Saturn’s rings and discovering its giant moon, Titan). In 1656, however, he made his greatest contribution as a scientist and inventor: the pendulum clock.

The schematic design of the second pendulum clock built by Christiaan Huygens, published in 1673. (C. HUYGENS)

Huygens wasn’t the first to recognize that the gravitational acceleration at Earth’s surface, known today as g, was constant, but he was the first to put it to such tremendously good use. By applying that phenomenon to the problem of an oscillating pendulum, he was able to derive an extremely useful mathematical formula for the period of a pendulum:

T = 2π √(L/g),where T is the pendulum’s period, L is the length of the pendulum, and g is the gravitational acceleration at Earth’s surface. For this derivation, there are many historians who classify Huygens as the first modern theoretical physicist.

A pendulum will swing with a specific period dependent not on its mass, the amplitude of its swing, or a host of other factors. Only the length of the pendulum and the value of the location gravitational field determine the pendulum’s rate of oscillation. (Public domain / Getty Images)

But this was the beginning of Huygens’ work on pendulum clocks. He realized that, so long as you kept your pendulum powered so that it would continuously tick away with the same, small amplitude to its swings, you could keep time indefinitely. He then went a step further, and not only built his own clocks, but published a design by which anyone could do it.

Within just a few years, clockmakers in the Netherlands and England were able to keep the time, accurately, to within a few seconds over the span of a full day. For nearly 300 years, until the early 20th century, the pendulum clock remained the most accurate timekeeping standard accessible to humanity.

A new standard in the world’s most accurate timing device was set by this ‘atomic clock’ invented in 1955 at Columbia University by Professor Charles H. Townes (left) with the assistance of Dr. J.P. Gordon (right). Atomic clocks were temporarily surpassed by pulsars, but have regained the crown as the most accurate way humans keep time in the Universe. (Columbia University / Getty Images)

The American continents, however, then known as the New World, had no such clockmakers available. It wouldn’t be until 100 years after Huygens that the first American-made pendulum clock was constructed. The way, then, to keep time more accurately than a sundial would be to take one of the world’s best, Dutch-made clocks, and bring them, via ship, to the New World.

Any motion would disturb the period of a pendulum, so accurate timekeeping — at that time — was only possible in a stationary location. The clock would be constructed and calibrated in the Netherlands, shipped overseas, and then restarted at its destination. Compared to a sundial, whose accuracy was limited to about ±15 minutes a day, the pendulum clock should have reduced those errors to merely a few seconds.

The location of the Netherlands and the location of the clock in the New World are highlighted by large relative differences in both longitude and latitude. When you’re closer to the equatorial bulge, in general, the local value of g, the acceleration due to gravity, is less. (GOOGLE EARTH / E. SIEGEL)

As soon as the clock arrived and was set up, it began keeping time more accurately than any timepiece before ever located on the North American continent. At least, that was what everyone assumed was happening for about a week or so. But after that amount of time, it became clear that something was amiss. The Sun and Moon weren’t rising at their predicted times, but rather were off by a bit.

Even worse, the amount that the clock was off by appeared to be getting worse over time: whatever error was at play was accumulating. Instead of these reliable, celestial events occurring at the predicted times on the clock, they were occurring earlier, according to the clock. Something was wrong. The clock was not only running slow, but appeared to be losing close to a minute per day.

The balance spring system, developed by Christiaan Huygens, is one of the many components that went into a well-engineered pendulum clock. When the clock was returned to the location of its manufacture, it kept time perfectly once again, allowing people to determine that it wasn’t a flaw with the clock, but rather gravitational variations, that caused the clock to keep inaccurate time in the New World. (Public domain / Getty Images)

This was completely unacceptable! Timekeeping, by the end of the 17th century, was accurate to within 2-to-4 seconds per day. Why would that be happening? The only assumption that the colonists of the New World could figure out — since there were no clockmakers (or clock-repair experts) present — was that the timepiece must have somehow been damaged during the journey.

So what can you do in that situation? The same thing you do today: send it back to the manufacturer for repairs. So this enormous, heavy, complicated clock was shipped all the way back to Europe, where the Dutch clockmakers examined it for defects.

The long length of a pendulum to swing with a half-swing period of one second, approximately 0.994 meters, led to the popular creation of grandfather clocks as accurate timepieces. These were the world’s best timekeeping measures up through the early 20th century. (Public domain / Getty Images)

When they restarted the clock back in the Netherlands, they received the biggest shock of all: the clock worked exactly as designed, keeping time as precisely as any other similar timepiece: to within just a few seconds per day. Although this experience will sound familiar to anyone who’s noticed funny behavior in their car, took it to the mechanic, only to have the problem disappear when it arrived, there was a reasonable explanation for what happened here.

In fact, no one’s observations or measurements were wrong, nor were there any mechanical problems. The only thing that was different, that nobody realized at the time, was that the acceleration due to gravity at Earth’s surface, g, isn’t the same everywhere on Earth.

The layers of Earth’s interior are well-defined and understood thanks to seismology and other geophysical observations. The gravitational acceleration is determined by the masses beneath your feet and your distance to the Earth’s center, meaning there are gravitational variations due to latitude, altitude, and the composition of Earth’s interior from place to place. (WIKIMEDIA COMMONS USER SURACHIT)

Our Earth isn’t a perfect, uniform sphere, but a rotating layer-cake. The atmosphere sits atop the surface, which has a complex and unique topography that rises miles and miles above sea level in many locations, and dips down miles beneath sea level in the deepest trenches. There’s an enormous, massive ocean atop the crust, which floats atop the mantle, which itself envelops the outer and inner core. As the Earth rotates, it bulges at the equator and compresses at the poles.

Travel the Universe with astrophysicist Ethan Siegel. Subscribers will get the newsletter every Saturday. All aboard!

When you take all of these factors into account, you’ll learn that the value of g you learned in physics class — 9.81 m/s2 — is only the average value of g at planet Earth’s surface. If you went all over the world, you’d find that g actually varies by about ±0.2% in either direction: from 9.79 to 9.83 m/s2.

The Earth as viewed from a composite of NASA satellite images from space in the early 2000s. The Earth’s diameter is slightly larger at the equator than at the poles, causing a difference in the local gravitational acceleration. Over the entire surface of Earth, 9.81 m/s² is average, but some locations have a value as low as 9.79 m/s² and others are as high as 9.83 m/s². (NASA / BLUE MARBLE PROJECT)

The difference in g is most pronounced with latitude: equatorial (smaller) latitudes have lower values of g and polar (higher) latitudes have larger values. Because of the latitude differences between the Netherlands and the location where the clock resided in the New World, g was different (smaller) by about 0.01 m/s2 in the Americas. This is what caused the clock, operating with a period given by T = 2π √(L/g), to lose about 45 seconds per day.

The solution? You have to make sure that the ratio, (L/g), stays constant. If g is 0.1% smaller in a new location, shorten the length of your pendulum (L) by 0.1%, and you’ll keep time properly again. If g is larger, lengthen your pendulum accordingly. Only with the proper period can a pendulum clock keep the time as it was designed.

A clock that has a pendulum of a specific length will keep time accurately so long as the precise gravitational field of Earth is at the correct value for the pendulum’s calibration. If moved to a location with a different local value for gravity, a different length for the pendulum will be required. (Public domain/Getty Images)

The reason your pendulum clock keeps track of time so well is because each swing of a pendulum takes the same amount of time to complete. The only two factors that determine the swing time, under ideal conditions, are the length of the pendulum and the gravitational acceleration at Earth’s surface. Even though the Earth is very close to a perfect sphere, and even though the acceleration due to gravity is almost constant everywhere, these tiny differences can add up. We had no idea that the Earth’s gravitational acceleration varied in the 17th century, and it’s arguable that we found out in the most unceremonious way. Yet even an unintentional experiment can be groundbreaking and educational, as bringing a Dutch-made pendulum clock to the New World proved to be. At the end of the day, whenever you learn something new about the Universe, it has to be considered a victory.

Ethan Siegel is the author of Beyond the Galaxy and Treknology. You can pre-order his third book, currently in development: the Encyclopaedia Cosmologica.


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