Galileo & Pheidippides

I’m thinking about using this image to promote The Western Civ User’s Guide to Time & Space.

It’s Galileo, who invented the pendulum clock, and the Greek hero Pheidippides, who ran 26 miles from Marathon to Athens with news of victory over the Persians.

Back to the beginning of The Western Civ User’s Guide to Time & Space.

Pittsburgh Society of Illustrators Spring newsletter

Holy cow—the jam-packed lavishly-illustrated 16-page Spring 2019 edition of PSInside just hit the newsstands! You can find it here. Swing on over and download your own copy.

It is chock-full of goodies for illustration fans, including a mention of The Western Civ User’s Guide to Time & Space.

Thanks, Anni & Yelena!

How he did it

Just to recap from the last couple of posts: First, Eratosthenes guessed the Earth was round like a ball. Second, he knew that at noon on the Summer solstice, the Sun shone directly overhead in the town of Syene, which was 5,000 stadia south of Eratosthenes.

Third, Eratosthenes guessed the Sun was really big—huge, even. He noticed that shadows cast by the Sun are all parallel, so all the Sun’s rays must be parallel, too. Parallel means 2 or more lines that never touch—they stay the same distance from each other. Think train tracks.

SO, Eratosthenes—in Alexandria, 5,000 stadia north of Syene—put a stick (like the gnomon of a sundial) in the ground and made sure it was plumb. That stick was pointing down to the center of the Earth. If Earth is round, the well in Syene and Eratosthenes’ stick won’t be parallel, right? They’ll be at an angle to each other. Eratosthenes didn’t know exactly how many degrees that angle was, but in Alexandria at noon on June 21st, his stick cast a shadow.

There weren’t any shadows in Syene, because the Sun was directly overhead. He measured the stick, he measured the shadow, and used those measurements to draw an angle. The angle turned out to be a little over 7 degrees, or 1/50 of a circle.

Eratosthenes knew the distance from Alexandria to Syene was 5,000 stadia. He multiplied 5,000 by 50 to get the circumference of the Earth—250,000 stadia. In modern measurements that works out to be 28,738.418 miles or 46,250 kilometers.

The actual polar circumference of Earth is about 24,860 miles or just a bit over 40 thousand kilometers. The stadion Eratosthenes used may have been a little different from the standard unit. But even today, right now, if you search the internet for the circumference of the Earth, you won’t get just one answer.

Eratosthenes was a genius who used what he knew and observed, along with what he guessed at, to calculate something that no one knew—and he did it pretty accurately.

Back to the beginning of The Western Civ User’s Guide to Time & Space

Plumb

A plumb line or plumb bob.

Last post I rattled on about how the well at Syene was plumb.

‘Plumb’ means straight up-and-down. Builders used to use a plumb line—a string with a weight tied onto it—to check that their walls were straight up-and-down. A plumb line will always point to the center of the Earth. Nowadays they use a spirit level. Builders who dug wells made sure that the hole they dug was plumb—pointing directly toward the Earth’s center.

Why was it so important to Eratosthenes that the well at Syene (a town located on the Tropic of Cancer) was pointing directly at the Earth’s center at noon on June 21st—the Summer solstice?

Back to the beginning of The Western Civ User’s Guide to Time & Space

The well at Syene

So how did Eratosthenes figure out how big around the Earth is? Here’s how:

First, he assumed the Earth is round like a ball.

Well at Syene.

Second, he knew several things about a little town called Syene. It is 5,000 stadia (575 miles or 925 kilometers) directly south of Alexandria. There was a well in the center of town, dug deep and plumb—straight toward the Earth’s center. At noon on June 21st, the Summer solstice, you could see the Sun reflected on the water way down in that well, which means the Sun is directly overhead.

Bird’s-eye view of the Sun’s reflection in the well at Syene.

That’s because Syene is located on the Tropic of Cancer. If you happen to be standing on the Tropic of Cancer and it’s noon where you are on June 21 you can draw a straight line from the center of the Earth, through the Tropic of Cancer, to the Sun.

A stadion is an ancient Greek unit of measurement—it’s 600 feet (an eighth of a mile). Stadion is singular (nominative, singular, second declension); stadia is plural (nominative, plural, second declension). 5,000 stadia = 575 miles or 925 kilometers. I hope I declenched in all the right spots. Many thanks to my Greek-scholar pals Jackie J., Michele J. & Joann W!

Eratosthenes


Head-Librarian Eratosthenes explains to a student how to laminate a dust jacket.

In an earlier post, I hinted about how over 2,000 years ago somebody calculated the circumference (how big around) of the Earth. This guy did it using only a well, a protractor and a stick (okay, maybe instead of a stick he used a column, but you could use a stick and get the same result).

I’m talking about Eratosthenes, the head librarian at the Great Library of Alexandria. Alexandria is an ancient city in Egypt, located where the Nile River flows into the Mediterranean Sea. Many scholars lived in Alexandria—like Ctesibius, who perfected the water-clock.

Back to the beginning of The Western Civ User’s Guide to Time & Space

Summer solstice

Okay, here comes some sciency stuff.

Summer solstice happens twice a year—once in the Northern Hemisphere (June 21) and once in the Southern Hemisphere (December 22). Those are the two days when the Sun spends the most time in the sky.

If you have a globe handy, you’ll see that there’s a line that goes all the way around the middle of the Earth. That’s the equator. It separates the Earth into a northern half and a southern half. Each half is called a hemisphere—’hemi’ means ‘half’ and ‘sphere’ is another word for ‘globe’.

The Sun appears to travel across the sky, but ackshually the Earth is traveling around the Sun and spinning on her axis at the same time. An axis is the line that goes through the center of the Earth from the North Pole to the South Pole. Did you notice that your globe’s axis is tilted? It’s tilted at a little over 27 degrees, because Earth is tilted at a little over 27° in relation to its orbit around the Sun. Because of this tilt, half the year (the time it takes to orbit the Sun) the Northern Hemisphere receives more of the Sun’s rays. The other half of the year, the Southern Hemisphere receives more of the Sun’s rays. The equator gets the Sun’s rays all year round, so it’s always hot there.

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.

Getting back to that equator—let’s look at the globe again. There are 2 other lines that also run around the Earth. In the Northern Hemisphere, there’s the Tropic of Cancer. In the Southern Hemisphere, there’s the Tropic of Capricorn. On June 21, the Northern Hemisphere tilts toward the Sun and the Tropic of Cancer gets the Sun’s rays directly. You could draw a line from the Earth’s center through the Tropic of Cancer to the Sun. On December 22, the Southern Hemisphere tilts toward the Sun and the Tropic of Capricorn gets the Sun’s rays directly. You could draw a line from the Earth’s center through the Tropic of Capricorn to the Sun.

On June 21, the Northern Hemisphere has the most daylight of any day of the year. Six months later, on December 22, the Southern Hemisphere has the most daylight of any day of the year.

Remember, when the Northern Hemisphere has the most hours of daylight (Summer solstice) the Southern Hemisphere has the fewest hours of daylight (Winter solstice). The opposite is true at solstice six months later.

Three months after solstice is the day when the day is split equally in two, with 12 hours of daylight and 12 hours of nighttime. This is the equinox. The autumnal (Fall) equinox is September 22 in the Northern Hemisphere. March 21 is the vernal (Spring) equinox.

Why am I telling you this? Well, over two thousand years ago a Greek librarian figured out exactly how big around the Earth is using only a well and a stick—and he did it at noon during the Summer solstice.

Back to the beginning of The Western Civ User’s Guide to Time & Space

What’s a Grecian earn?

About 14 drachmas an hour! Har har har!

Okay, can I get a do-over? I’m not entirely happy with the drawing I did for that last post about Greek measurements. Didn’t look Greek enough, or just didn’t have pizazz or something. So I drew a new version of it, this time taking the drawings on those wonderful old Grecian urns as my inspiration. Tell me what you think.

Here’s an old Greek urn—these drawings are gorgeous. I love the light terra-cotta-colored figures on a rich black background.

Here’s the new sketch.

Greek measurements

The Greeks measured length roughly the way the Egyptians did: a daktylos is a finger-joint, or inch; a pous is a foot, or 12 inches; a pēchys is a cubit, half a yard, or 18 inches. Longer distances were a bēma, a pace, 5 feet; an orgyia, a fathom, 6 feet; a stadion, 600 feet (an eighth of a mile); a milion, a mile.

Marathon

One of the important battles in the wars between the Greeks and Persians took place on the Plains of Marathon. Herodotus tells about how in 490 bc, when the Greeks were seriously outnumbered, a messenger named Pheidippides (Fay DIP e deez) ran from Athens to Sparta to get their help. Then he ran to Marathon to join the fight, THEN ran back to Athens to tell everybody that the Greeks won.

Around the world we still celebrate Pheidippides’ heroic run in races called marathons. If you run a marathon, it’s 26 miles and 385 yards—the distance from the Plains of Marathon to Athens. The very fastest runners have done it in a little over 2 hours!