Authors Note

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

In the 4th 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 24th, 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.


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 (

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 (

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

Authors Note #1 Do cats see color?

When we look around us we see trees which are green. We see sky that is blue. When cats look around, what do they see? Do cat’s see color the way we do? Is the yellow we see, the yellow your cat sees? When you see a rainbow, does your cat see a rainbow?

We use our eyes to see. We use our ears to hear.

The parts of the eyes have certain names. Do you know what they are all called?

The colored part of the eye is called the iris. The black dot in the middle is called the pupil. When it is dark the pupil is large. When it is light, like bright sunlight during the day that pupil shrinks.

If you look in a mirror you can see your eyes. You can see the iris and the pupil. What color are your eyes?

Some people have blue eyes, some brown, some green. Some people have eyes that are called hazel. Hazel colored eyes are a mix of green and brown.

There are parts of the eye that we cannot see when we look at ourselves in the mirror. But these parts are important even if we cannot see them. The other parts of the eye are the cornea, the lens, the retina and the optic nerve.

The cornea is a special layer forming the front of the eye. It is transparent. That means you can see through it. It controls and focuses light as it enters the eye.

The lens is inside your eye. It sits behind the pupil. It changes the focal distance. This means it helps to make objects at various distances in focus.

The retina sits at the back of the eye. It is the inner surface which lines the back of the eyeball. The retina collects the light that passes through the pupil, and the lens. It converts the light into signals. It then sends those signals along the optic nerve to the brain.

When we look at a tree in the park. The backs of our eyeballs are collecting all those signals and sending them to our brains. And that’s how we see.

You might be wondering why this is important. How does this answer the question whether cats see color.

We know the colors that you and I see. We know that we see blues, greens, yellows and reds. One way to figure out whether cats see color like we do is to compare our eyes.

If you look into a mirror, or look at your friend’s eye what do we see?

We have two eyes.

Cats have two eyes.

Our eyes are not the same shape. Our eyes are rounder, and a cat’s eyes are pointy and slanted.

But there are differences. The shape of the pupil. Remember that is the black dot. Our pupil’s are round. Cats have slit pupils. At night, or in the dark, their pupils do open and they look round. But during the day a cat’s pupils are slits.

What other differences can you think of?

The colors of cat’s eyes are different. There are yellow, and green and blue.

I do not think I have ever seen a person with yellow eyes.

Scientists have studied cat’s eyes and compared them to humans.

Remember the parts of our eyes? Iris, pupil, cornea, lens, retina and the optic nerve. Well cats have those parts too. Both the retina in us and in cats have special cells. These cells are called photoreceptors. That is a big word. “Photo” means light. “Receptor” is a receiver. That means that these special cells receive light.

Remember that the retina sits at the back of the eyeball. It is the inner lining of the back of the eyeball. It collects the light and converts the light to signals. It then sends those signals along the optic nerve to the brain.

The special photoreceptor cells are made up of rods and cones. Both humans and cats have special cells – rods and cones.

Rods detect brightness and shades of gray. They are particularly good for night vision. The more rods an animal has in its eyes, the better its night vision. Rods are also responsible for peripheral vision. That means they are used for seeing things out of the corner of your eye.

Cones are responsible for day vision and color perception.

Scientists compared rods and cones photoreceptor cells found in human eyes with cat’s eyes.

Cats also have these special cells. But there are some differences.

Cats have more rods and they have less cones. That means they are better at seeing things at night. They do have cones, so we know that they must see some color, just not the same color that we see.

That is how we know that cats do see color. They just do not see color the same way people do.