1 The Birth of Science - MSRI

3.5 Pneumatics 67
The function of hydrostatics is clear. Inside the theory we have elegant
and difficult mathematical problems. As for the real-life objects that the
theory models, what can these objects be, about which one wants to calculate
the waterline and the stability of equilibrium theoretically, before placing
them in a homogeneous liquid? Clearly these are problems of naval
architecture. Archimedes not only solves them, but even frames his study
in an elegant and efficient hypothetico-deductive structure that allows the
reduction of other problems analogous to those discussed to “exercises” page 102
internal to the theory (though perhaps solvable only approximately). This
makes possible, in particular, the theoretical design of ships. 74 This interplay
is the essence of scientific method.
Important precursors of Archimedes’ hydrostatics can be found in Democritus
and in Strato of Lampsacus, 75 whereas Aristotle’s ideas in this respect
were much more distant. 76
3.5 Pneumatics
In the case of pneumatics, as in many others, we find an important qualitative
precursor of Hellenistic science in pre-Socratic thought. The earliest
clear reference we have to the concept of atmospheric pressure was made
by Empedocles. 77
However, the first unequivocal testimonia about pneumatics, understood
as the science of compressible fluids, date from the first half of
the third century B.C., when Ctesibius of Alexandria wrote at least two
works on the subject: one, perhaps more theoretical, called Demonstrations
74 The paraboloid considered by Archimedes is not so far from the shape of a ship if we consider
that his proofs apply also to an elliptic paraboloid, so long as one considers roll and pitch
separately.
75 According to Democritus, the upward motion of “light” bodies is explained by the fact that,
though having weight, they are pressed toward the top of the atoms of the surrounding fluid,
if these atoms are heavier (Simplicius, In Aristotelis De Caelo commentaria, [CAG], vol. VII, 569,
5–9 = testim. 61 in [Diels: FV]). Similar ideas are attributed to Strato of Lampsacus, who wrote a
work on the vacuum (Simplicius, In Aristotelis De Caelo commentaria, [CAG], vol. VII, 267, 30 – 268, 4;
Stobaeus, Eclogae, I, xiv, 1h; [Rodier], p. 57; [Diels: Strato], 110–119).
76 According to Aristotle (Physica, IV, 1; De caelo, I, 3; De caelo, IV), levity is a quality opposite to
weight; bodies that have that quality naturally tend to go up.
77 Empedocles, fr. 100 in [Diels: FV] = Aristotle, De respiratione, 473a15–474a6. The clepsydra of this
passage is not a timepiece, but a gadget used to transfer liquids between containers — an inverted
funnel whose wide mouth is closed by a perforated plate. In its normal usage, the clepsydra is
partly immersed in the liquid; after it fills up to the surrounding level, the narrow opening at the
top is capped with one’s finger, and the instrument is lifted with the liquid inside. The girl of this
passage, instead, immerses the clepsydra with the top opening covered, and the water cannot come
in; as she lifts her finger, the air rushes out. The process is discussed, explained and illustrated in
Heron, Pneumatica, I, vii. (For an edition of the fragments of Empedocles with translation, see for
example [Empedocles/Inwood], where our passage appears on pages 138–139 in translation.)
Revision: 1.13 Date: 2002/10/16 19:04:00