1 The Birth of Science - MSRI

10.1 Eratosthenes’ Measurement of the Meridian 237
précis meant for readers scared of the complex geometric arguments of the page 294
original work. He attains his goal of explaining Eratosthenes’ method by
taking an ideal case obtained by eliminating all technical difficulties; how
else could he compress into three pages a work that occupied two books?
Cleomedes also rounds off the numbers, evidently so as not to bother the
reader with calculations inessential to an understanding of the method. 7
We should not automatically attribute to Eratosthenes the simplifications
adopted by his popularizer.
Elsewhere Cleomedes records a precious detail: that at noon on the day
of the summer solstice sundials cast no shadow within a zone 300 stadia
wide about the tropic line. 8 Clearly, many measurements with sundials
had been made, over a wide area, and the tropic was fixed as the midline
of the shadowless zone. 9 Thus it is reasonable to think that this line page 295
could be located precisely within a few tens of stadia, or a few minutes
of arc. 10 We must conclude that Eratosthenes, desirous of measuring the
distance from Alexandria to the tropic, first took the trouble to find it precisely
and didn’t just assume on someone’s say-so that it went through
Syene. Cleomedes and other authors probably name Syene because it was
the Egyptian town closest to the tropic and the most convenient base for
an expedition to the tropic. 11 As for the well whose bottom was lit by the
sun at the solstice, Pliny actually says that it was dug out for a demonstration.
12
Here a digression is warranted on an important aspect of experimental
methodology. It is commonly thought that Hellenistic scientists were
ignorant of the technique of averaging multiple measurements, because
7 Cleomedes’ value for the circumference (250,000 stadia, instead of the 252,000 reported by all
other sources) and for the difference in latitude between Syene and Alexandria (1/50 of the whole
circle) are clearly obtained by rounding, an understandable liberty taken by someone whose aim
is avowedly just to illustrate the method.
8 Cleomedes, Caelestia, I, 7, 101–102 (ed. Todd).
9 That this datum must have been determined by personnel sent on site for the purpose is said
already in [Hultsch: PGES], p. 14. But J. Dutka objects that “it is questionable whether in that era
royal surveyors would be used for a purely scientific purpose” ([Dutka], p. 61).
10 We also know that Eratosthenes could detect astronomically differences in latitude between
spots more than 400 stadia apart along the same meridian (Strabo, Geography, II, i, 35). The accuracy
with which one can locate the tropic is much better than this margin of error, since it is easier
to distinguish precisely between no shadow and some shadow than it is to distinguish between
two approximately equal nonzero magnitudes. The main source of subjective error in the shadow
measurement is that the sun is not a point source.
11 Strabo, Pliny and Arrian all say that Syene is on the tropic. The town lies near the first cataract
of the Nile, which marked the boundary between Egypt and Ethiopia: therefore to get to the tropic
one had to cross the border.
12 Pliny, Naturalis historia, II, 183.
Revision: 1.11 Date: 2003/01/06 02:20:46