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Go to Brilliant.org/SciShow to check out all of their interactive courses. [♪ INTRO] When you’re walking around your hometown, you can use familiar landmarks to help you find your way. But out at sea, there’s water everywhere you look, so navigation through a lot of human history was kind of... complicated.

In fact, it’s a problem that’s plagued humanity for thousands of years, with clever ancient solutions ranging from stargazing to animal tracking to just plain educated guessing. But as longer ocean voyages became more common in the 1600s, highly accurate navigation became a lot more important; otherwise, ships would be sinking all over the place or getting lost. And at that time, one aspect of the navigation problem was stumping the era's greatest minds: the longitude problem.

The story of why the longitude problem was so hard, compared to latitude, charts an interesting course through the history of seafaring and science. But first, let’s get some terminology straight, because it can be confusing. Latitude measures how far North or South you are of the equator, which we call zero degrees latitude.

The North Pole is then 90 degrees Latitude, and the South Pole is at minus 90 degrees. Longitude is the other one: it measures how far East or West you are from the Prime Meridian Line, which goes through London in the UK. So that means lines of constant latitude run East to West on a globe, and lines of constant longitude run North to South.

This is super easy to get mixed up, so one way to remember them is that lONgitude changes as you move horizONtally. You might have noticed an interesting difference between them there. For latitude, there’s a sensible, natural definition for zero degrees, which we call the equator.

That’s because you can draw the straight line through the Earth that the Earth rotates around Earth rotates around an axis and the equator is at a right angle to that axis. But longitude is pretty much arbitrary: by convention, we put zero degrees at an observatory in Greenwich in London, England, for political reasons from the 1800s. Another difference is that latitude was easy for sailors in the 1600s to calculate aboard their ships.

All they needed was a chart of the Sun’s height above the horizon at midday on each day of the year at each latitude. So, sailors compared the Sun at its peak to where their charts said it should be, then they could work out how far North or South they were of the equator. A similar technique worked for the motion of the Moon and stars, too.

And civilizations across the world had used versions of this technique for millennia. As for longitudes, the way to calculate that in the 1600s was using time differences. Because the Earth completes a full rotation once every twenty-four hours, moving one twenty-fourth of the way around the Equator, or 15 degrees of longitude, means the Sun sets an hour earlier.

If you know the exact time at a reference point like Greenwich, you can use the time of sunset or sunrise to work out how far East or West you are from that reference point. So really, determining longitude boiled down to making an accurate clock, which was a difficult task in the 1600s. At the time, the state-of-the-art was pendulum clocks, and even those lost a few seconds a week to tiny design flaws, so they simply weren't good enough to keep track of Greenwich time, even on fairly short journeys.

Because at sea, that can throw you off by several miles even under the best of circumstances. But then you add in the swaying of the ship, which could make things a lot worse by messing with the clock swing, because older clocks relied on a weighted pendulum that kept time with each swing, making the tick tock sound. And as that pendulum swings back and forth it’s switching between kinetic and potential energy.

When it swings to the highest position it has the maximum potential energy stored. And as it moves to the other side then that stored potential energy becomes kinetic, creating that back and forth oscillation that keeps time. And that pendulum or its swing mechanism could be seriously affected by rough weather and changes in temperature and pressure.

And those errors could easily turn into heading hundreds of miles off course, or worse, directly into rocky waters or a sandbank. Which ended up causing a huge naval disaster in 1707 that claimed upwards of 1400 lives. So the British government mobilized to solve the problem by creating a competition.

In 1714, they offered a series of prizes: the more accurate the solution for measuring longitude, the bigger the prize, under a new group called the Board of Longitude. The Board also offered lots of smaller interim prizes for solving smaller parts of the problem, and many people eventually claimed some of these, including the famous Swiss mathematician Leonhard Euler. In fact, they ended up giving out more than twice the largest single prize’s amount in smaller sums by the end of things.

But the clear winner of the competition was John Harrison, even though he never claimed the biggest prize in full. Harrison, born in 1693, was a working-class carpenter with little formal education, but an interest in clockmaking that led him to teach himself the craft. He worked on several land clock designs with his brother during the 1720s, eventually achieving an accuracy of one lost second per month, far better than other clocks of the time.

In the early to mid-1730s, he showed his clockmaking work to the Astronomer Royal, Edmund Halley, yes, the comet guy, who couldn’t evaluate his work but recommended him to George Graham, another clock maker expert in London, who then became his mentor. After securing funding to work on it, he spent the next five years building a clock in a small village in Northern England. Then, in 1735, he came down to London to show it off.

The clock tackled the ship-swaying problem by using two interconnected swinging balances. That helped them resist being rocked about by the ship’s swaying. The clock he made came to be known in modern times as “H1”, and that, yes, is a sign that there’s going to be a few more!

The Board was very impressed with the device, which worked even when the temperature changed and could run without any lubrication. In fact, in its first test run on a ship, it helped the crew steer away from danger. So, in 1737, Harrison became the first person to claim any prize money from the

Board: £250, or about upwards of forty thousand US dollars today. But H1 wasn’t perfect. First, it was big. An ideal sea clock would be a lot smaller and cheaper, and the board wanted more tests.

Harrison wasn’t entirely happy with H1, so he moved his workshop from Northern England to London to work on improved designs, coming up with more compact frames and lots more features to improve accuracy. The Board funded him and eventually, working with others, Harrison finished his ‘H4’ design in 1759, the fourth in his H series. H4’s design and mechanisms were a radical departure from the first three clocks he submitted: it wasn’t a big contraption; it was a palm-sized pocket watch!

It was also, y’know, a lot more accurate. Design-wise, it used a drive mechanism that had been recently developed, which some mechanical clocks still use today. One ingenious invention Harrison added was a clever system for storing power in the spring, allowing it to be wound less than once a day.

It also gave a warning when it was 30 minutes away from stopping. This was important because it was tricky to restart when out at sea. H4 was put to the test on a transatlantic voyage in 1761.

There, Harrison’s son, William, used the clock to navigate well within the accuracy required for the grand prize. It lost 5 seconds total after 81 days at sea. But the Board wasn't totally happy.

They were worried it might have been a fluke, so they asked for more tests to make sure. In 1765, after another successful test, the Board agreed to pay out, on a few conditions. One was that he should reveal how the clock worked so that it could be replicated.

When he obliged, he was given the second-biggest prize, which was half the grand prize. The full prize would have been given when other workshops could make similarly accurate clocks. Which could be done back then, but the Board stiffed him.

The reason the Board was so hesitant to pay out in full might have had something to do with the fact that by the 1760s, there was a rival method, and the Board wanted to keep their options open for awarding money to that method, too. The rival method, Lunar tables, was a well-known technique that worked by looking at the Moon’s motion relative to background stars. If you knew the position of the Moon at a given time accurately enough, you could work out where you were by looking at how the Moon appeared to be /moving/ in the sky relative to nearby stars.

This method also had an accuracy problem, though: those Moon position tables needed to be very precise. And getting precise tables was harder than the equivalent tables for latitude because you needed to predict the Moon’s motion across the sky instead of measuring its position. Back in 1713, before the prize had even been announced, Isaac Newton suggested that more accurate timekeeping would solve the Longitude problem and expressed skepticism that a good enough clock could be built, favoring the Lunar tables method.

Which might have biased the Board in favor of the ‘high-science’ Lunar tables over the ‘low-science’ improved clocks. And sure enough, by the 1750s, the Lunar tables had gotten a lot better thanks to advances in math. The Lunar method was tested at the same time as H4’s second test, and found to be very good.

Now, there was a lot of drama at this point. Harrison was upset about being denied the full prize, there were arguments in the press. Parliament got involved.

There’s lots of soap opera theatrics between men in old-timey wigs. But the bottom line of the story is that Harrison was never paid in full. And the lunar tables method was used for a long time too!

In fact, the British Nautical Almanac published the tables until 1906. By that point, the timing problem was trivialized by radio: anyone anywhere in the world could learn the time at any location almost instantly by tuning into broadcasts. And today, we use the global positioning satellite system, GPS, to navigate with ships.

But that still works using clocks! A satellite transmits a signal to a ship, and includes in the signal the exact time it was sent. The ship then compares that to the time it received the signal, and works out its distance from the satellite using the constant speed of light.

That allows it to work out its location anywhere on Earth. The clocks on the satellites are atomic clocks that measure the oscillations of quantum states of atoms. It’s a lot more complex, but at its core it’s still just a system that goes back-and-forth.

So, like with clocks themselves, even as time moves on, you always end up back where you started. And if you’re looking to go back to where it all started there’s no better place for that than Brilliant. They’re an interactive STEM-learning platform where you can brush up on different topics or learn something new!

If you liked today’s episode you should check out their newly-updated Logic course! You can stretch your analytic muscles to make predictions on limited information. Like sailors predicting latitude on the sea with just the Sun’s position you can also solve highly-interactive puzzles and riddles.

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