Tag Archives: latitude

Mister Midshipman Hornblower

C.S. Forester’s character, the 19th-century British Royal Navy officer Horatio Hornblower excelled at navigation because he was a math whiz. This got him in trouble as a young midshipman when he showed up a big dumb bully who couldn’t figure out how to work a sextant. https://hornblower.fandom.com/wiki/Sextant
A must-read—https://www.goodreads.com/book/show/84748.Mr_Midshipman_Hornblower

The sextant

The sextant is an instrument used to determine latitude and longitude. It was invented by Edmond Halley or John Hadley or Thomas Godfrey based on Isaac Newton’s ideas. You use a sextant to measure how far above the horizon the Sun is at noon (or how high Polaris is at night).

I’ve talked about finding your latitude or longitude by measuring the angle between a line from you to the moon and a line from you to a star. How do you do that?

Sailors have been using a sextant for centuries. Isaac Newton dreamed up the idea, then Edmond Halley built one in 1692. Several refinements were made around 1730, until we finally got the good old sextant you see people using in the movies with wooden ships and guys wearing wigs. A sextant is like an astrolabe—you sight something familiar in the sky, like a star, by lining it up along a sighter or pointer or alidade. Then you mark the alidade’s position on the frame and use that information to find your location.

Instead of an alidade the sextant has a telescope you look through. Then you find both the object (usually the Sun) and its reflection in the mirror. There are 2 mirrors facing each other and smoked lenses so you don’t fry your eyeballs. One mirror is half mirror/half glass so you can see both images at the same time. You bring the image of the Sun down to the horizon by moving the arm on the sextant and—oh, who am I kidding? Do you think I know what I’m talking about? What I need is a video to show how it’s done. Luckily, there are a bunch of them on the ol’ internet. Listen to these guys.

Here’s an in-depth 4-part tutorial covering everything you ever wanted to know about how to use a sextant.: https://www.youtube.com/watch?v=00ZEIZsl5xk

And a guy who doesn’t own a comb but knows what he’s talking about: https://www.youtube.com/watch?v=DrAkrgZRb9Y

The thing you have to know is: the sextant will give you a precise angle between 2 objects that you can transfer to a chart or map to get your position on Earth.


Look! Look! Here’s a cardboard sextant you can build yourself! https://www.landfallnavigation.com/cardboard-sextant-kit.html?gclid=CjwKCAjwq832BRA5EiwACvCWsWqv38smCfmUdVE5SqxRVkVJI_R0B9aN9jSb-3oaweER7b4KTm4iJhoCUbMQAvD_BwE

Here’s a plastic sextant—https://www.google.com/shopping/product/15301038968540324177?q=navigation+sextant&prds=epd:1143652539522712674,prmr:3,tpim:CKyp-dn168W22QEQ1N-msv7m0OotGMCbhR4iA1VTRCjg3sL8BTCNyIhA,pdprs:6&utm_medium=tu_image&utm_content=eid-lsjeuxoeqt&utm_campaign=134358029&gclid=CjwKCAjwztL2BRATEiwAvnALcqb-eUHLE4Y_XEM7QpPWFcXOcl2YbghLFCIcLIG1ItYYMc__vQ3_jBoCA14QAvD_BwE

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Lunar distancing

Okay, let’s say you’re in a rowboat at night with some friends—and you haven’t seen land for a while. You’re LOST. Nobody’s getting a signal on their cellphones, so you don’t know where you are. The strange old lady at the boat rental place left nothing but a weird navigational device; a map; and a book of star charts in the boat’s locker. Your friends are getting panicky and start blubbering. What do you do?

Because you’re a devoted reader of The Western Civ User’s Guide to Time and Space, you know exactly what to do. You tell your pals to stop their noise so you can concentrate. It’s a clear moonlit night, so you can see the moon, stars, and the horizon. You pick up the lovely brass sextant and set its sights on the moon—and a star, how about Regulus, just there to the left? You measure the altitude (how high above the horizon) of the moon; the altitude of Regulus; and the distance between them. You figure the angle of the 2 lines from you to the moon and you to Regulus. You do this measuring not in feet or miles but in degrees.

From the moon’s altitude you know what time it is (http://www.astrotulsa.com/page.aspx?pageid=27, scroll down)—and your latitude, too (http://www.lewis-clark.org/article/1268). Knowing the distance from the moon to Regulus, you pick up the book of star charts and find that lunar distance for your local time. Run your finger down the chart to find what time it is in Greenwich, England where it’s zero degrees longitude. The difference in time will tell you your longitude (15° for every hour, 1° for every 4 minutes). Find your latitude and longitude on the map and start rowing home. You don’t even need a compass—you keep Polaris, the North Star, above your right knee as you row.

You get safely back to land! Your friends can’t believe you saved the day with that stupid book. The lady at the boat rental gives you a wink and you all go home to bed.

This is how Nevil Maskelyne proposed finding your position while at sea.

I haven’t read these, but here’s a short list of books about ocean-going girls: https://books.google.com/books/about/From_Cabin_Boys_to_Captains.html?id=wBDWSAAACAAJ

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Does this projection make my continent look big?

 I drew this version of Ptolemy’s map showing only the longitude lines. He drew them curved to give you the idea that the world is round.

A challenge navigators faced when reading a flat map of the round Earth is that as the meridians—the longitude lines—got closer to the north and south poles they kind of bent around to simulate the round globe. That’s a problem if you’re trying to chart a course. The meridians and parallels don’t meet at right angles so you need to keep adjusting your calculations about where you are…it’s a hot mess.

Gerard Mercator devised a way to mathematically flatten the globe. He imagined a flat map wrapped like a cylinder around the globe. So far, so good. But as you bend the top and bottom of the map to wrap the globe, they get all bunched up, right? There’s too much paper. So he trimmed some paper off the top and bottom, leaving strips that are wide at the Equator and pointy at the poles. These strips are called ‘gores’ in the cartography business.

Without Mercator, with Mercator.

You can do two things with these gores when you flatten them. One is to leave them as they are, with blank space in between the pointy ends. The other is to fill in the blank space in between the pointy ends with more map. Mercator did that— and he straightened the meridians and drew the continents to fit the new coordinates. The result is that you can use the latitude/longitude lines to chart a course that will be perfectly accurate.

Of course, the land and ocean at the top and bottom get stretched out on Mercator’s projection. That makes sense, because what had been a dot (the pole) has been stretched out across the top or bottom of the map.

Recently, some people have complained that on Mercator’s map, the continents closer to the poles appear to have more land mass than the continents near the Equator. That appearance has caused the residents of the equatorial countries to feel bad about their land mass.

The Western Civ User’s Guide staff is here to help. If you’re feeling bad about your land mass, call 1-800-IFEELBADABOUTMYLANDMASS and talk to one of our concerned and sympathetic counselors.



Here’s a great old video of how globes are made. https://www.youtube.com/watch?v=4RWcWSN4HhI
Notice how when they paste the map onto the globe, the map is cut into sections called ‘gores’—pointy at top and bottom, wide in the middle.


Here’s the amazing 17-year-old Leslie Gore, who is not a section of a map. https://www.youtube.com/watch?v=RjdH_NmmO0I

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Maps for everybody

Printing presses had been around for a while, but printing really took off after Gutenberg invented moveable type. Printing presses can generate many images on paper very quickly compared to drawing each one by hand. Suddenly ordinary people could afford to own books—and navigators could afford to have maps when they sailed.

The first printed maps were woodcuts—what’s called relief printing. This is when you take a flat piece of wood and trace the drawing onto it backwards; you carve away everything that isn’t the drawing; you roll ink onto the wood and press it onto a piece of paper; the ink leaves an impression on the paper. Showing longitude & latitude lines on a woodcut map wouldn’t be easy, because you have to carve wood away leaving the line.

Much better for accurate mapmaking was engraving. With this kind of printing, you take a flat piece of copper and draw lines onto it with a steel stylus. Steel is much harder than copper, so the stylus cuts a precise, v-shaped groove. When the drawing is finished, you rub ink all over the copper plate and into the grooves. Wipe the surface clean and leave the ink in the grooves. Run the copper plate with a damp piece of paper through a tight press and the ink stays on on the paper.

When the paper dries, you can feel the ink lines—they stand up. American paper money is engraved. You can feel the lines on a brand-new dollar bill. Copper is durable so you can make gazillions of copies from one plate.



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The Tropics

Here’s something interesting: the Tropic of Cancer and the Tropic of Capricorn don’t stay put. They move around a little bit. The Tropic of Cancer marks where the Sun will shine the longest in the northern hemisphere for this year—that is, the summer solstice. It’s at around 23-24 degrees north. On the summer solstice, June 21st-ish, the Sun will shine directly over the Tropic of Cancer.

The Tropic of Capricorn marks where the Sun will shine the longest in the southern hemisphere—that is, the winter solstice. It’s at around 23-24 degrees south. On the winter solstice, December 21st-ish, the Sun will shine directly over the Tropic of Capricorn.


Here’s kind of what they look like on a flat map.

The reason the Sun shines directly on the Tropic of Cancer in summer and the Tropic of Capricorn in winter is that our Earth is tilted as she revolves around the Sun. We learned that way back when we read about Eratosthanes.

It takes one year for Earth to orbit the Sun. When the Northern Hemisphere is tilted toward the Sun it’s Summer there. When the Southern Hemisphere is tilted toward the Sun it’s Summer there.

Latitude and Longitude

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The Equator

Human brains are marvelous. Something we humans are able to do is look at a round object, like the Earth, and draw it flattened out as a map. Then, get this: other humans are able to look at the flat map and comprehend a round Earth. Yay, us!

Ptolemy was the first to think of drawing lines of longitude and latitude on a map. Longitude lines travel from north to south poles. Latitude lines travel east to west and are parallel to the Equator. Together they make a grid on a flat map. Longitude and latitude lines are man-made; they don’t exist except on maps. Longitude and latitude lines are the way we organize the Earth’s surface so we can navigate on it. You assign the lines names or numbers.

Latitude lines (also called parallels) are circles that run around the of the Earth and are measured in degrees. The Equator divides the Earth into northern and southern hemispheres (hemi = half, sphere = globe). It’s at 0 degrees. The North & South poles are at 90 degrees.

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