The scaphe (Ancient Greek: σκάφη, romanized: scaphe, lit. 'bowl'; also known as a skaphe, scaphion (diminutive) or Latin: scaphium) was a sundial said to have been invented by Aristarchus (3rd century BC). There are no original works still in existence by Aristarchus, but the adjacent image is an image of what it might have looked like; only his would have been made of stone. It consisted of a hemispherical bowl which had a vertical gnomon placed inside it, with the top of the gnomon level with the edge of the bowl. Twelve gradations inscribed perpendicular to the hemisphere indicated the hour of the day. Using this measuring instrument, Eratosthenes of Cyrene (c. 220 BC) measured the length of Earth's meridian arc.
Aristarchus of Samos (//; Ἀρίσταρχος, Aristarkhos; c. 310 – c. 230 BC) was an ancient Greek astronomer and mathematician who presented the first known model that placed the Sun at the center of the known universe with the Earth revolving around it (see Solar system). He was influenced by Philolaus of Croton, but he identified the "central fire" with the Sun, and put the other planets in their correct order of distance around the Sun. His astronomical ideas were often rejected in favor of the geocentric theories of Aristotle and Ptolemy.
Greeks and Romans used large stone sundials based on "a partial sphere or scaphe,” the shadow of the tip of the gnomon was the time-telling index. These dials could in theory tell time accurately if carved to a true sphere and correctly calibrated for a given site.
It took a skilled stone worker and a great deal of time and money to create a sundial. So only wealthy citizens could afford this elaborate contraption, and it was often for their villas or as donations for erection in the town forum. There was a need for cheaper dials that ordinary laborer could construct. But even if it were easier to make, the question of calibrating the scaphe still posed a problem.
The problem of projecting the three-dimensional scaphe dial upon a vertical or horizontal plane was addressed by a number of distinguished nineteenth-century mathematicians, each of whom presumably solved it to his own personal satisfaction. Unfortunately, their publications are so complex, long-winded, and obscure that they were virtually inaccessible to antiquaries and—it would appear from the replication of effort—even to their own (unacknowledged) colleagues. The spherical trigonometry required for the latter endeavor is really quite basic, and the calculations tedious rather than difficult. The availability of computer-generated graphics has, of course, completely altered the situation. A Fortran program was written for the VAX computer at the University of Leicester that enabled vertical or horizontal dials to be plotted for any latitude.
Measurement of the Earth's circumferenceEdit
Eratosthenes of Cyrene calculated the circumference of the Earth without leaving Egypt. He knew that, at local noon on the summer solstice in the Ancient Egyptian city of Swenet (known in ancient Greek as Syene, and now as Aswan) on the Tropic of Cancer, the sun would appear at the zenith, directly overhead. He knew this because he had been told that the shadow of someone looking down a deep well in Syene would block the reflection of the Sun at noon off the water at the bottom of the well. Using a gnomon, he measured the sun's angle of elevation at noon on the solstice in Alexandria, and found it to be 1/50th of a circle (7°12') south of the zenith. He may have used a compass to measure the angle of the shadow cast by the sun. Assuming that the Earth was spherical, and that Alexandria was due north of Syene, he concluded that the meridian arc distance from Alexandria to Syene must therefore be 1/50th of a circle's circumference, or 7°12'/360°.
His knowledge of the size of Egypt after many generations of surveying trips for the Pharaonic bookkeepers gave a distance between Alexandria and Syene of 5,000 stadia. This distance was corroborated by inquiring about the time that it took to travel from Syene to Alexandria by camel. He rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. Some claim Eratosthenes used the Egyptian stade of 157.5 meters, which would imply a circumference of 39,690 km, an error of 1.6%, but the 185 meter Attic stade is the most commonly accepted value for the length of the stade used by Eratosthenes in his measurements of the Earth, which implies a circumference of 46,620 km, an error of 16.3%.
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