The librarian who first measured the Earth

Part I

One morning the heralds spread the news through the town: King Ptolemy III Evergetes had appointed Eratosthenes of Cyrene librarian of the great library of Alexandria.

Some people might have found it dull to be a librarian, but Eratosthenes was not despondent. He decided to read everything he could find on travels and on discoveries of the Earth’s secrets. Then he would write a big scientific book containing all the geographical knowledge of those times.

This work, which Eratosthenes called Geographica, took up a great deal of time. Still sometimes the librarian would leave his quiet office and go out into the sunny streets of the city. He would make his way to the Alexandrian bazaar where simple folk argued and bargained.

The royal librarian was wont to sit down somewhere in the shade of a shop wall and start a conversation with the visiting merchants. One of them said: “ Our town of Syene is the hottest place ever. They say there is no other such place on the sacred Earth. Here when we sit in the shade it seems a bit cooler. But in Syene there is a day once a year when there is no shade to be found. ”

Eratosthenes was surprised.

“ Wait, I don’t quite understand what you mean. A shadow may grow longer or shorter, but I’ve never seen there to be none at all. ”

“ Nevertheless, in our Syene, on June 22 at mid-day you will find no shade at all, ” retorted the merchant stubbornly. “ Oh yes, on that day you can see the bottom of the deepest and narrowest well. Believe me”.

Part II

The stranger’s story made Eratosthenes fall to thinking. He sought out and reread manuscript after manuscript, trying to understand: “ How can such a thing be? ” It was the works of the great Aristotle that suggested the answer. That wise philosopher asserted that the sun illuminates different parts of the Earth’s surface differently and that its rays have different angles of incidence because the Earth is a sphere; hence, the length of the sun's shade cannot be the same everywhere at the same time.

Now what if we turn to the Sun for help in measuring the size of the globe?

That is just what the Alexandrian librarian decided to do. He had no intention of making a long journey to measure the distance from one town to another step by step. His idea was to measure the Earth without leaving the little courtyard of the Alexandrian library. He constructed a special scatha or bowl, resembling a greatly enlarged half nutshell. At the centre of the bowl he fixed a column. Then he set up his invention in the library courtyard

and waited for the longest day in the year.

On June 22 the sun arose in the sky above Alexandria. At that moment the scientist measured the length of the shadow the column threw on to the bottom of the bowl. He found it to be one-fiftieth of the scatha circumference. At that same moment there was no shade at all at Syene (vicinity of the modern Aswan): there the sunbeams fell vertically. The distance between the two cities was 5,000 stadia (the stadium was a Greek unit of length) or 800 kilometres. Such would be the length of one of 50 equal arcs constituting the complete circumference of the Earth. From this Eratosthenes calculated the entire circumference to be 800_*50=40,000 kilometres. Then by a simple calculation he found the radius of the globe to be equal to 6,370 kilometres.

Since then investigators have measured the Earth’s surface many times, but their results always coincide in the main with the figures derived in ancient times by Eratosthenes. The space laboratories of artificial Earth satellites have also confirmed these figures.

Thus, the Alexandrian librarian measured the earth correctly almost 2,200 years ago.