Lucille Malone, Age 12, Of Rockford, I11., for her question:

How did Eratosthenes measure the earth's circumference?

The space age seemed to dawn upon us suddenly  but its roots go back thousands of years. Many facts that our spacemen must know were gathered by scholars through the ages. The wise men of ancient Egypt and Babylon charted the heavens. The thoughtful Greeks figured the shape and almost the true size of the earth.
This amazing feat was performed around 230 b.c. Eratosthenes estimated the circumference and diameter of our globe  and he never traveled more than a few hundred miles from his native Greece. The language of science is math, and a knowledge of math was needed to solve such a problem. The star charting wise men of Babylon coped with the circle by dividing it into 360 equal degrees. The Greeks borrowed and used this idea.
In the 5th century B.C. the brilliant Greek scholar Pythogoras invented a system of math. He or one of his students figured out that the earth is a sphere, though this truth later was lost for centuries. Eratosthenes of the 3rd century b.c. inherited all this knowledge and used it like a master. He solved his problem by using data from two points in Egypt. One was at Alexandria, near the mouth of the Nile, the other at some several hundred miles south, near the modern Aswan Dam.
 Eratosthenes studied the shadows made by sticks at noon on the day of the summer Solstice. At some there was no shadow, proving that the sun was directly overhead. At Alexandria a stick cast a shadow at an ang1e of 7 degrees and 12 minutes. This ang1e forms 150th part of the Babylonian circle. This led Eratosthenes to figure that the distance between Alexandria and Syene was 1/50 of the earth's circumference.   
The next job was to measure the mileage between Alexandria and Syene. This distance, reasoned Eratosthenes, multiplied by 50 is the earth's circumferenee, the size of a circle around the globe. He divided this figure by pi, which is about 3.14, to get the diameter  a line straight through the middle of his sphere. His answer was 7850 miles  which is about 70 miles less than the most up to date estimate of the earth's diameter. His estimate of the earth's circumference was some 200 miles short of our modern figuring of the distance around the earth.

The mile, of course, was not invented when eratosthenes did his brilliant work. He used an ancient unit of long measure to find the distance between alexandria and syme. Some experts of our times were doubtful about this unit and therefore doubtful about the findings of the brilliant Greek mathematician. More recently scholars took a new look and gave a different value to his ancient unit of long measure. This was used to recheck his findings and award old Eratosthenes his rightful. Role among the math geniuses of human history.