Eratosthenes: The Shadow That Measured Earth

Welcome back to Learn English with Podcasts. Sarah, here is a question. Could you measure the whole Earth without leaving your city, without a ship, and without any machine? Just a stick, a well, and one shadow.欢迎回到 Learn English with Podcasts。Sarah，考你一个问题：不离开自己的城市、不坐船、不用任何机器，你能量出整个地球有多大吗？只用一根棍子、一口井和一个影子。

A man did it more than 2,200 years ago, around 240 BC. His name was Eratosthenes, and he worked at the great library in Alexandria, in Egypt.大约2200多年前的公元前240年，有个人做到了。他叫埃拉托色尼，在埃及亚历山大城的大图书馆工作。

They had enough. And here is the nice part. He was not trying to prove the Earth is round. People already knew that. Sailors watched ships sink below the horizon, bottom first, and in an eclipse the Earth's shadow on the Moon is always round.他们知道得够多了。有意思的是，他并不是想证明地球是圆的，这事当时已经知道了。水手看着船底部先沉到地平线下，月食时地球投在月亮上的影子也一直是圆的。

Exactly. How big is the ball? And he could not walk around it. He had to find a shortcut.没错。这个球到底有多大？他又不能绕着走一圈，得找条捷径。

South of Alexandria there was a town called Syene. We call it Aswan today. Eratosthenes had read that on the longest day of the year, at noon, the sun shone straight down a deep well there. All the way to the water. No shadow at all.亚历山大城往南有座城叫 Syene，今天叫阿斯旺。埃拉托色尼读到过：一年里白天最长的那天，正午的阳光会直直照进当地一口深井，一直照到水面，一点影子都没有。

Right above. A pole standing in the ground at Syene cast no shadow at that moment. If you looked into the well, your own head would block the sun's reflection in the water.正上方。那一刻 Syene 插在地上的杆子完全没有影子。你往井里看，自己的头会挡住水面上太阳的倒影。

But in Alexandria, at the same moment on the same day, a pole did cast a shadow. He measured it. The sun was about 7.2 degrees away from straight up.但同一天同一时刻，亚历山大城的杆子却投下了影子。他量了那个影子，太阳偏离正上方大约7.2度。

That is the whole story, really. If the ground were flat, the sun would be at the same angle in both places. It was not. So the ground must curve between them.整个故事其实就在这一点上。如果地面是平的，两地的太阳角度应该一样，可它不一样。所以两地之间的地面一定是弯的。

Yes. And the sun is so far away that its rays arrive almost parallel. So the tilt you measure on the ground is the same as the tilt between the two towns at the centre of the Earth.对。而太阳远到光线几乎是平行照过来的。所以你在地面量到的那个倾斜角，就等于两座城在地心张开的角。

A full circle is 360 degrees. Divide 360 by 7.2 and you get fifty. So that little shadow was one fiftieth of a whole turn around the Earth.一整圈是360度。360除以7.2等于五十。所以那道小小的影子，是绕地球一整圈的五十分之一。

Now he needed only one number. How far is it between the two towns? The figure he used was 5,000 stadia, roughly 800 kilometres.现在他只差一个数：两城之间有多远？他用的数字是5,000斯塔德，大约800公里。

We are not completely sure. One old account says professional step-counters measured the roads for tax records. Another says he used the travel time of camel caravans. Both stories are still told.我们并不完全确定。一种古老说法是专业测距员为了税收丈量道路；另一种说法是他用了骆驼商队的行程时间。两种说法至今都还在讲。

Then came the easy line. 5,000 times fifty is 250,000 stadia. That was his answer for the whole Earth.接下来就简单了。5,000乘以五十等于250,000斯塔德。这就是他给出的整个地球的答案。

And here is where I have to be honest with you. A stade was not one fixed length. An Egyptian stade was about 157.5 metres; an Athenian one was about 185 metres.这里我得跟你说实话。「斯塔德」并不是一个固定长度。埃及的1斯塔德约157.5米，雅典的约185米。

We can, but we get two very different answers. With the Egyptian stade, 250,000 stadia is about 39,375 kilometres. With the Athenian one, about 46,250 kilometres.能验，只是会得到两个差很远的答案。按埃及斯塔德，250,000斯塔德约39,375公里；按雅典的，约46,250公里。

Around 40,000 kilometres. About 40,008 from pole to pole, and 40,075 around the equator. So the Egyptian version is astonishingly close. The other one is about 16% too big.大约4万公里。南北极一圈约40,008公里，赤道一圈约40,075公里。所以按埃及单位算的结果准得惊人，另一个则偏大约16%。

They do. His own book, On the Measure of the Earth, is lost. What we have is a simpler version written later by a Greek called Cleomedes. An old Roman writer, Pliny, gives 252,000 stadia instead of 250,000.是的。他自己的书 On the Measure of the Earth 已经失传。我们今天看到的是后来一位叫 Cleomedes 的希腊人写下的简化版。古罗马作家 Pliny 给的数字是252,000斯塔德，而不是250,000。

Nobody knows for sure. 252,000 divides neatly by every number from one to ten. Some historians think a friendly round number was chosen on purpose.没人能确定。252,000能被从一到十的每个数整除。有些历史学家认为，是有人特意选了个好算的整数。

There were real errors too. Syene is not exactly on the tropic, and it sits about three degrees east of Alexandria, not due south. Land distance along the Nile was hard to measure.误差本身也确实存在。Syene 并不正好在北回归线上，而且在亚历山大以东大约三度，不是正南。沿着尼罗河量陆地距离本来就很难准。

That is fair. But the method was not luck. Take a shadow, find what fraction of a circle it is, and multiply. Anyone could repeat it.这话说得公道。但方法本身不是运气。量一道影子，看它是圆周的几分之几，再乘回去。谁都能照着做一遍。

A scholar at the great library in Alexandria, born in Cyrene, in today's Libya. His friends called him Beta, the second letter, because he seemed to come second in everything. He also invented a simple way to find prime numbers that students still learn.亚历山大城大图书馆的学者，出生在昔兰尼，也就是今天的利比亚。朋友叫他 Beta，第二个字母，因为他好像干什么都排第二。他还发明了一种找质数的简单办法，今天学生还在学。

And he did it from a library. The story we have never says he travelled to Syene. He needed a report about a well, a pole in his own city, and a number from people who walked.而且他是在图书馆里做到的。留下来的记载从没说他去过 Syene。他要的只是一份关于那口井的记载、自己城里的一根杆子，还有别人走出来的一个数字。

Here is one last twist. About 1,700 years later, Christopher Columbus read Eratosthenes before he sailed west. He decided the Earth was much smaller instead.还有最后一个转折。大约1700年后，哥伦布西航之前读过埃拉托色尼，却选择相信地球要小得多。

It did. He could never have carried enough food for the real distance. If he had accepted the bigger number, he might have stayed home.没错。真正的那段距离，他根本不可能带上足够的食物。要是他信了那个更大的数字，也许就待在家里了。

And the right one came from noticing that a stick had a shadow at noon.而那个正确的数字，只是来自有人注意到正午的杆子有影子。

Tell me what you get. Thanks for listening to Learn English with Podcasts. See you in the next episode.记得告诉我你量出多少。感谢收听 Learn English with Podcasts。我们下期见。