rity, from classical times
and through the middle ages, with the use of gears to turn power through
a right angle.

[Illustration: Figure 2.--ASTRONOMICAL CLOCK of de Dondi, showing
gearing on the dial for Mercury and escapement crown wheel. Each of the
seven side walls of the structure shown in figure 1 was fitted with a
dial.]

Granted, then, this use of gears, one must guard against any conclusion
that the fine-mechanical use of gears to provide special ratios of
angular movement was similarly general and widespread. It is customary
to adduce here the evidence of the hodometer (taximeter) described by
Vitruvius (1st century B.C.) and by Hero of Alexandria (1st century
A.D.) and the ingenious automata also described by this latter author
and his Islamic followers.[6] One may also cite the use of the reduction
gear chain in power machinery as used in the geared windlass of
Archimedes and Hero.

Unfortunately, even the most complex automata described by Hero and by
such authors as Ri[d.]w[=a]n contain gearing in no more extensive context
than as a means of transmitting action around a right angle. As for the
windlass and hodometer, they do, it is true, contain whole series of
gears used in steps as a reduction mechanism, usually for an
extraordinarily high ratio, but here the technical details are so
etherial that one must doubt whether such devices were actually realized
in practice. Thus Vitruvius writes of a wheel 4 feet in diameter and
having 400 teeth being turned by a 1-toothed pinion on a cart axle, but
it is very doubtful whether such small teeth, necessarily separated by
about 3/8 inch, would have the requisite ruggedness. Again, Hero
mentions a wheel of 30 teeth which, because of imperfections, might need
only 20 turns of a single helix worm to turn it! Such statements behove
caution and one must consider whether we have been misled by the
16th- and 17th-century editions of these authors, containing
reconstructions now often cited as authoritative but then serving as
working diagrams for practical use in that age when the clock was
already a familiar and complex mechanism. At all events, even if one
admits without substantial evidence that such gear reduction devices
were familiar from Hellenistic times onwards, they can hardly serve as
more than very distant ancestors of the earliest mechanical clocks.

Mechanical Clocks

Before proceeding to a discussion of the controversial evidence which
may b