The Day the Earth Was Measured
by Nirupama Raghavan

Once upon a time, long long ago (~ 250 B.C.)  there was a Greek named Eratosthenes ( Whew!  What a name. Lets call him Erat from now on!) He was a bright kind of fellow in many things but not bright enough to be the first in any of them. Being second in every thing earned for him the nickname ‘Beta’, the second Greek alphabet. He became the head librarian in Alexandria, one of the most famous of ancient libraries, instead of being a hotshot professor some where. Alexandria is in modern Egypt but you know that the Greeks often attached other lands to their own, after winning friendly contests.

Well, some librarians may actually read the books that they guard over and lend out. One day, our Erat was reading a book, no doubt to capture an ‘Alpha’ status in something. As he took a sip of his wine, his eyes popped out. “ By Jove” he might well have said, “ they don’t see a shadow of a vertical stick at noon in Syene!”  This happened on one particular day, the longest day of the year. Now Syene was a city that lay directly south of Alexandria. As he read on, he found that they could see the reflection of the sun inside a deep well on the noon of that day in Syene. He had seen no such thing in Alexandria. In fact on the longest day of the year the noon shadow in Alexandria was about 1/8^th of the length of the vertical stick.

“Well!” he thought to himself, ‘everyone knows the earth is flat! How then, could there be no shadow in Syene when there is a definite shadow in Alexandria? What could be wrong? ” He sipped more wine. He walked to a rack with scrolls containing translations of works from that far off land Inde. Alexander the great (yes, the same one after whom the city was named) had crossed the river Indus to engage in one of his friendly contests some seventy five years before. He had shopped a great deal there for ideas and goods. All that was now in the Library.

“There it is!” our Erat exclaimed as he tapped on one scroll. “The earth is a sphere!   If it is, I can measure how big it is.” He clanged his bell to summon a friend. “ Thou shall walk to Syene this instant and measure the distance between Alexandria and Syenne” he said or its Greek equivalent to him. The friend wore a sturdy pair of Greek sandals and put together a supply of cheese, olives and wine. Off he went, thinking he would do it in a leisurely way. When he was done, the distance was over 700 kilometres - 718 to be exact. He re-checked the number on his walk back and reported it to our Erat. Erat got instantly busy with his geometry scroll, papyrus and quill.

Noon shadow length at Syene = 0

Therefore sun is overhead Syenne

Noon shadow length at Alexandria = 1/8^th of vertical stick

Therefore sun is at 7.2 ⁰  to the vertical

SO THE EARTH MUST CURVE BY 7.2⁰ from Alexandria to Syene

My friend has measured this curve to be 718 km

If he had walked around the whole earth this curve would be 360 ⁰ and the length he walked would be the circumference of the earth.

Therefore 360/circumference of the earth = 7.2/718

circumference of the earth   = 360/7.2 (718) = 35,900 km

Our Erat had measured the circumference of the earth! He had achieved Alpha status. Next time you pass a library full of dusty old books don’t pass up a chance to become an Alpha!

The above account is mostly real and the science is exact!