Taping the Earth

The U.S. Army has succeeded in shrinking the circumference of the earth by about half a mile. To make the new estimate, according to a paper submitted to the American Geophysical Union by Bernard Chovitz and Irene Fischer of the Army Map Service, the Army's scientists used the latest instruments, but their basic method was the one the Greeks invented more than 2,000 years ago.

Bones & Lions. About 200 B.C. the Greek mathematician Eratosthenes ran a geometrical tape measure about the earth by estimating the distance between Syene in southern Egypt and Alexandria in northern Egypt.*Then he measured shadows cast by the sun in both places. This amounts to measuring an arc of the earth's surface and observing the altitude of the sun at both ends. The Army Map Service did the same thing, but the arc that it measured extended (5,777.5 nautical miles) from Finland to the southern end of Africa, more than one-quarter of the earth's circumference. Part of the arc coincided with the arc that Eratosthenes used.

Data for measuring the Finland-South Africa arc came from many sources. The European section had been measured many times, but the latest information was gathered by a group that ransacked Germany after World War II for the Nazis' geodetic secrets, which were dragged from hiding places, including a room full of human bones under a monastery.

The European segment ended at Crete, and the U.S. Air Force was called in to jump the arc across the Mediterranean to North Africa. The job was done by Hiran (High Precision Shoran), an electronic surveying system.

South of Egypt the arc measurers ran into wild animal country. The lions did not bother them much, but they had some buffalo scares. In tall-grass country they set up prefabricated 100-ft. towers and did their surveying from platforms on their tops. When finished, they would move, towers and all, to an unsurveyed area. The last gap, Khartoum to Uganda, was completed in 1954.

Satellite & Missile. Then began the laborious work of correcting the raw information. Some of the arithmetical work was so burdensome that it would have taken years to complete without the help of the Map Service's UNIVAC computer.

The result of all this effort is a new figure for the equatorial radius of the earth: 6,378,260 meters (3,444 nautical miles)*instead of the 6,378,388 meter figure that had been generally accepted. The Army says that the slight difference will be of use in predicting the orbit of the artificial satellite. This is true, but improved knowledge of the earth's size and shape will also be useful to dispatchers of long-range guided missiles.

*Eratosthenes started with the traditional information that there was a deep well at Syene (Aswan) in southern Egypt to whose bottom the sun's rays penetrate only during the summer solstice (June 20-22). This meant that the sun was directly over Syene at that time. He also had a figure for the distance between Syene and Alexandria: 5,000 stadia. Only one observation was necessary. During a summer solstice, he measured the shadow cast by a vertical pillar in Alexandria. It turned out to be one-fiftieth of a full circle (about 7DEG 12 min.).

Now Eratosthenes had all the information he needed. The shadow cast by the vertical pillar at Alexandria would have the same relation to a full circle that the distance from Alexandria to Syene (where sunlight was vertical) would have to the circumference of the earth. The answer: 250,000 stadia (21,913 nautical miles), which is remarkably accurate. The latest measurement of the earth's circumference around the poles: 21,580 nautical miles.

*The international nautical mile (6,076.10 ft.) is used on long-distance charts. For purposes of navigation it is considered one minute of longitude, although it is derived from the standard meter, not directly from the earth's circumference at the equator.

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