The Scaphe ( Ancient Greek : σκάφη , transliterated scaphe , lit. ‘bowl’) 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 accurate image of what it might have looked like, only its made of stone. It has a vertical hemispherical bowl with 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(220 BC) measured the length of Earth’s meridian arc . The scaphe is also known as a skaphe, scaphion (diminutive) or Latin : scaphium .
Aristarchus of Samos ( / ˌ æ r ə s t ɑːr k ə s / ; Ἀρίσταρχος , Aristarkhos ;.. C 310 – c 230 BC) Was an ancient Greek astronomer and mathematician Who presented the first model Known Placed That 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 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 wide stone sundials based on “a partial sphere scaphe gold,” 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 properly 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 contraption, and it was often for their villas or donations for erection in the town forum. There was a need for cheaper dials that ordinary laborer could construct. But even if it was easier to make the question of calibrating the Scaphe still posed a problem.
The problem of projecting the three- dimensional scoring of a vertical or horizontal plane, was addressed by a number of nineteenth-century distinguished 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 antiquarians and would-seem to be replicated from the effort of their own (unacknowledged) colleagues.  The spherical trigonometry required for the latter endeavor is quite 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 theUniversity of Leicester that enabled vertical or horizontal dials to be plotted for any latitude. 
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 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 deep in Syene would be the reflection of the Sun at noon off the water 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 thezenith . 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 be 1 / 50th of a circle circumference, or 7 ° 12 ‘/ 360 °.
His knowledge of the size of Egypt After Many generations of surveying trips for the Pharaonic bookkeepers Gave distance entre Alexandria and Syene of 5,000 stadia . This distance was corroborated by Syene to Alexandria by camel. He rounded up the final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. Some claim Eratosthenes used the Egyptian stage of 157.5 meters, which would imply a circumference of 39.690 km, an error of 1.6%, but the 185 meter Attic stage is the most commonly accepted value for the length of the stage used by Eratosthenes in his measurements of the Earth,  which implies a circumference of 46.620 km, an error of 16.3%.
- Jump up^ Draper, John William ” History of the Conflict Between Religion and Science ” in Joshi, ST, 1874 (2007). The Agnostic Reader . Prometheus. pp. 172-173. ISBN 978-1-59102-533-7 .
- ^ Jump up to:a b c Mills, Allan A. ” Seasonal-Hour Vertical and Horizontal Sundials are Planes, with an Explanation of the Scratch Dial ” in Annals of Science, 50, 1993. “History of Science, Technology & Medicine” . pp. 83-93.
- Jump up^ How did Eratosthenes measure the circumference of the earth?
- Jump up^ Eratosthenes and the Mystery of the Stadia – How Long Is a Stadium?