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© Copyright 1999, Jim Loy
Columbus underestimated the size of the earth, by a big margin. The world is about twice as big as he thought it was. Was he stupid, or what? Didn't Eratosthenes measure the earth, fairly accurately, many centuries earlier?
Yes, Eratosthenes accurately measured the size of the earth. But his estimate was not accepted, at the time and later. Instead, the size of the earth was deduced by the use of maps and a kind of sloppy logic, by map makers and scientists. They did not know about the American continents. And they did not imagine that most of the world would be water. They did not imagine a Pacific Ocean. It just made sense that Europe was close to Asia, if you sailed West. So Columbus was not being stupid. He followed the ideas of his times. The estimates (of the size of the earth) varied. And Columbus used the smallest available estimate.
But there were many ways to
estimate the size of the earth. I am amazed that nobody tried to do that. A
ship does not have to sail very far before it disappears over the horizon. A
little triangulation (surveying) and they would know the size of the earth to
within a few hundred miles.
Eratosthenes' method makes
plenty of sense. It should have been duplicated and refined. The story is that
Eratosthenes had heard that the sun was directly overhead at the town of Syene
(Aswan) at the Summer Solstice. They say that you could see the sun's
reflection, down a well. And he measured the angle (about 7.2 degrees) that the
sun was from overhead, at Alexandria, where he lived. And he knew that Syene
was about 5000 stadia south of Alexandria. That is all you need to find the
circumference of the earth:
360/7.2=circumference/5000 stadia
5000(360/7.2)=250,000 stadia
That is approximate, as there are numerous possible sources of error. Historians are not sure how big a stadium was. He probably did not measure the angle very accurately. Syene is not directly south of Alexandria; so distance measurements were probably inaccurate. They probably measured the distance by how long it took a boat to float down river from Syene to Alexandria, as they knew the speed of flow of the Nile, to some extent. But, it would seem that Eratosthenes was very accurate, in his estimate of the size of the Earth.
Columbus discovered America, except that Vikings discovered it hundreds of years earlier, and the Native Americans had been living here for many hundreds of years before that. Columbus' voyages started a flow of people into the Americas, which does not make everyone happy. This destruction of a stone age America was probably inevitable. But Columbus Day is not a day to celebrate for most Native Americans.
Addendum:
Columbus obviously knew that the world was round. Later, Magellan's ships sailed all the way around the earth. That proved that the world was round. But that had already been proved, back in Greek times. Most educated people knew that the world was round. The most convincing proof was that you could see the earth's shadow on the moon, during a lunar eclipse. During partial eclipses (and at the beginning and end of a total eclipse) the edge of the earth's shadow is always round, a portion of a circle. For this to happen every time, from all angles, the earth would have to be a sphere.
The way that a ship disappears over the horizon, long before it would appear to be a dimensionless point, was another strong piece of evidence showing that the earth was round.
Eratosthenes' measurement, whether it was accurate or not, was a further proof that the world was round.
Similar to Eratosthenes' observation is the fact that people at different latitudes see different constellations at night. You can measure your latitude by measuring how far the North Star (or the Sun) is above the horizon. People south of the equator cannot even see the North Star, as it is below the horizon. The stars could have been used to measure the size of the earth, in the same way that Eratosthenes used the sun. This would be a somewhat sounder measurement, as the stars are much farther away than the sun is.