What’s in a Gnomon?
The unexpected power of the world’s first scientific instrument
The shadow by my finger cast
Divides the future from the past:
Before it, sleeps the unborn hour
In darkness, and beyond thy power:
Behind its unreturning line,
The vanished hour, no longer thine:
One hour alone is in thy hands, —
The NOW on which the shadow stands.—Henry Van Dyke, The Sun-Dial at Wells College
I f you’re at all familiar with the word gnomon, you probably think of it as that vertical thing in the middle that casts its shadow on the face of a sundial. But the gnomon is far more than just that. It is, in fact, one of the earliest (perhaps the very first) scientific measuring instruments.
The sundial, of course, uses the direction of the gnomon’s shadow to mark the time of day. But now suppose you also measure the length of the shadow periodically throughout the day. At local high noon, the moment the shadow reaches its shortest length, it points due north (or due south, if you’re in that other hemisphere). Plot a perpendicular to this line, using traditional geometric compass-and-straightedge construction methods, and you have determined due east and west. So in addition to being a clock, the gnomon also serves as a directional compass.
Now measure and record the length of the noon shadow from day to day over the course of the year. The day on which it is shortest is the summer solstice; longest, the winter solstice. The direction of the shadow at sunrise or sunset tells the day of the year; the days on which it points directly along your previously constructed east-west line are the equinoxes. So besides a clock and a compass, the gnomon is also a solar calendar.
Finally, at noon on the day of the equinox, the angle from the top of the gnomon itself to the tip of the shadow is equal to your local latitude. So the gnomon serves the same function as a sextant, as well. Quite a lot of useful information for a simple stick in the ground!
Probably the best-known scientific application of the gnomon in the ancient world was by Eratosthenes, head librarian of the fabled Library of Alexandria in the third century BCE. He had heard travelers’ tales of a certain well in the town of Syene (now Aswan) on the upper Nile, where the sun at noon on Midsummer’s Day shone directly down the well’s shaft and reflected off the water at the bottom. (If you look at a map, you’ll see that Aswan lies almost smack on the Tropic of Cancer, where the sun passes directly overhead on the summer solstice.)
So Eratosthenes set up a gnomon at Alexandria, down at the mouth of the Nile, and measured the angle of the noon sun on the day of the solstice. Knowing the distance from Syene to Alexandria, he was able to extrapolate the Earth’s circumference to within an accuracy of 40 miles, or about 99.8%. By comparing the angles at the summer and winter solstices, he also measured the obliquity of the ecliptic (the tilt of the Earth’s axis) at 23°. No wonder it’s called a gnomon (from Greek gnoskein, “to know”; gnosis, “knowledge”)!
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“What’s in a Gnomon?” by Stephen Chernicoff is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
