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Scaphe
The scaphe was a sundial said to have been invented by Aristarchus (3rd century BC). 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. The scaphe is also known as a skaphe, scaphium, or scaphion.



Inventor
Aristarchus 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.

Chunk of text
"The best Greek and Roman seasonal-hour sundials were quite large three- dimensional stone forms based on a partial sphere or 'scaphe': only the shadow of the tip of the gnomon 6 was the time-telling index. These dials have been analysed elsewhere, so will not be elaborated on here. They could in theory tell time accurately if  carved to a true sphere and correctly calibrated for a given site, but many extant examples s appear to be sadly deficient in these respects.

Nevertheless, the amount of stone and skilled work required no doubt meant that a scaphe dial was an expensive object, affordable only by prosperous citizens for their villas or as donations for erection in the town forum. There would have been a need for cheaper dials, particularly if they could be made by oneself or by an ordinary labourer. A projection on the vertical plane, as could be visualized by looking from a distance directly along the horizontal pointed gnomon of a scaphe dial, would be ideal. This fiat dial would certainly have been easier to make, but unfortunately it was by no means easy to calibrate. Comparison with a well-made scaphe could suggest that the hour lines should bunch upwards in pairs, but it is obviously only too easy for oral instruction or personal memory to deteriorate down the easy path towards equian- gular straight hour lines converging on the base of the gnomon, although we have seen that this is correct only for a site on the equator. An example of such a 'debased diar is provided by a fragment 1~ recovered from the Borcovicus station on Hadrian's Wall in northern England.

Ancient peoples never completely solved the problem of projecting the three- dimensional scaphe dial upon a vertical or horizontal plane, although skilled geometers could achieve close approximations that would have been perfectly adequate south of the Alps. It is therefore relevant to enquire what the correct patterns should be. This problem 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 efforteven to their own (unacknowledged) colleagues. Part of the problem would appear to stem from a desire to obtain general equations for all the hour lines at any latitude and orientation, rather than presenting a few calculated dial patterns. The spherical trigonometry required for the latter endeavour 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. The results are summarized in Figures 5 and 6. The patterns for latitudes 50 ~ to 60 ~ at 2 ~ intervals have been published on a larger scale. "

Heyday
Made famous by Eratosthenes of Cyrene

Measurement of the Earth's circumference
Eratosthenes calculated the circumference of the Earth without leaving Egypt. Eratosthenes 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 Erathostenes 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%.

Also see
Measuring Instrument

Sundial

History
"The best Greek and Roman seasonal-hour sundials were quite large three- dimensional stone forms based on a partial sphere or 'scaphe': only the shadow of the tip of the gnomon was the time-telling index. These dials have been analyzed elsewhere, so will not be elaborated on here. They could in theory tell time accurately if carved to a true sphere and correctly calibrated for a given site, but many extant examples s appear to be sadly deficient in these respects. Nevertheless, the amount of stone and skilled work required no doubt meant that a scaphe dial was an expensive object, affordable only by prosperous citizens for their villas or as donations for erection in the town forum. There would have been a need for cheaper dials, particularly if they could be made by oneself or by an ordinary laborer. A projection on the vertical plane, as could be visualized by looking from a distance directly along the horizontal pointed gnomon of a scaphe dial, would be ideal. This fiat dial would certainly have been easier to make, but unfortunately it was by no means easy to calibrate. Comparison with a well-made scaphe could suggest that the hour lines should bunch upwards in pairs, but it is obviously only too easy for oral instruction or personal memory to deteriorate down the easy path towards equiangular straight hour lines converging on the base of the gnomon, although we have seen that this is correct only for a site on the equator.

Ancient peoples never completely solved the problem of projecting the three- dimensional scaphe dial upon a vertical or horizontal plane, although skilled geometers could achieve close approximations that would have been perfectly adequate south of the Alps. It is therefore relevant to enquire what the correct patterns should be. This problem 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 efforteven to their own (unacknowledged) colleagues. Part of the problem would appear to stem from a desire to obtain general equations for all the hour lines at any latitude and orientation, rather than presenting a few calculated dial patterns. 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."