## Coordinates, Longitude and Latitude - The Story of Imagination & Geometry

##### 02/19/2021

In the 4^{th} book, The Forgetful Ferret, Caitlin, and her friends solve a secret code – a set of coordinates. That got me thinking. How do we know where we are and where we are going? Thanks to modern technology, our smart phones, available apps and a legion of satellites orbiting our planet it takes a couple of taps, and before you know it, your smartphone is giving you directions.

Imagination is a wonderful thing. I am not so sure about geometry. But the story of longitude and latitude is really a story about imagination and geometry.

Ancient Greeks and Phoenicians had great imaginations. The Phoenicians were great explorers. They observed the night sky with its patterns and constellations. They noticed that one star remained constant throughout the four seasons – and that was the North Star (or Polaris.)

Ancient Greeks, Eratosthenes and Hipparchus imagined that the Earth had imaginary lines - with two sets of parallel lines – one running north – south, the other running east – west. This was first used by Eratosthenes. Eratosthenes was a mathematician, geographer, poet, astronomer, and music theorist (quite a guy.) He was born in 276 BC. Hipparchus, a Greek astronomer, geographer, and mathematician was the first to use these lines as coordinates for specific locations.

Geometry is important to our story of longitude and latitude. Without geometry we would not be able calculate either latitude or longitude. For instance, the Phoenicians were the first to determine latitude (imaginary east – west lines)– the distance from Earth’s poles. The Phoenicians determined latitude in this way - at night they would use the stars such as the North Star or Polaris in the Northern Hemisphere. Once Polaris is located then work out the angle in degrees between Polaris’ position and the northern horizon. Navigators would use a quadrant or a sextant to do this. This angle measure is the same latitude north of the equator.

Longitude (imaginary north-south lines) cannot be determined this way. To accurately calculate longitude, one needs a fixed known point (a meridian) and accurate time. On land with easily identified landmarks the calculation of longitude was easier. (Although it took several centuries before accurate time pieces were invented.) But at sea, the accurate calculation of longitude was difficult – there were no identifiable landmarks on the open seas.

There were many disastrous shipping disasters due to the inaccuracy of the longitude calculations at sea. Navigators would follow the latitudes (easier to calculate) and then hope for the best. The Eighteenth century was a century of exploration. Britain, and France competed for supremacy of the seas. It made a huge difference to be able to accurately navigate where they needed to sail. There were a couple of Government initiatives designed to reward innovation.

In 1714 the British government offered a £10,000 prize for accuracy within one degree of latitude (60 nautical miles at the equator) to £20,000 for accuracy within one-half of a degree for any person or persons who could accurately calculate longitude while at sea. That was a lot of money back then. According to the BBC the prize was won by John Harrison. But this is not entirely true. The official prize was never awarded. (reference John Harrison - Scientist of the Day - Linda Hall Library )

John Harrison, was born March 24^{th}, 1693 and was a British clockmaker. He built a series of clocks that could accurately measure time. (These clocks were accurate for their time, one such clock (the H4) sailed for Jamaica in 1761, and 2 months later was only 5 seconds slow.) The Board of Longitude (no doubt not very eager to pay out the prize money) demanded a re-trial. The second voyage in 1764, the timepiece gave a longitude error of 10 miles. Still the Board resisted paying out the prize money. It took an appeal to King George III himself before final payments were made. Harrison was required to give the Board all his clocks, notes and drawings.

A prime meridian is the line of longitude where the longitude is defined to be 0 degrees. In October 1884 the Greenwich Meridian was selected by delegates representing 25 nations to be common zero of longitude and standard time of reckoning around the world.

This is a good thing. Because before that was decided there were a number of prime meridians around the world. This would have made it extremely confusing. Now with the Greenwich Meridian being a common zero then all lines of longitude can be calculated using the relative position to the Greenwich Meridian, the position of the sun and the reference time.

Oddly enough time and the ability to accurately tell the time was very important to calculating longitude. The reason why is that to pinpoint a location, it needed to be compared to the corresponding time at two different locations.

This seems very confusing. But it is not when you picture the earth turning on its axis as it moves around the Sun. Now picture a fixed point on the earth. Now look at your watch and what is the time?

Say the time is noon. Let us call that local time. But the time at the prime meridian is 5pm. Which means if someone were standing on the prime meridian at noon our time it would be 5pm their time. Each hour represents 15 degrees in the earth’s rotation. (360 degrees divided by 24 hours.) That means the longitude at the place were we are standing is 5 times 15 which is 75 degrees.

Sources:

See Wikipedia Eratosthenes - Wikipedia for more information about Eratosthenes

Wikipedia mentions Hipparchus in a nice entry about the History of Longitude. History of longitude - Wikipedia For more information about Hipparchus see Hipparchus - Biography, Facts and Pictures (famousscientists.org)

For an interesting in depth description of Harrison’s first Sea Watch (H4) see In-Depth: The Microscopic Magic of H4, Harrison’s First Sea Watch | SJX Watches (watchesbysjx.com)

The Linda Hall Library has an interesting write up of John Harrison the British clockmaker who “won” the Board of Longitude’s competition. John Harrison - Scientist of the Day - Linda Hall Library

Britannica has the clearest description and explanation. latitude and longitude | Definition, Examples, Diagrams, & Facts | Britannica