Eric Vittoz - IEEE

TECHNICAL LITERATURE
motion of the foliot may have given the bar its name
(folle is French for crazy).
An electrical analog of this type of clock is an RC
relaxation oscillator. A constant force on the main
weights (a battery) accelerates (charges up) a mass
(capacitor) up to some limit, which mass then gives
up its all of its kinetic energy prior to the cycle beginning
anew. As with electrical relaxation oscillators,
the verge-and-foliot escapement permits oscillation
over a wide range of frequencies, and thus enables
the subdivision of time into almost arbitrarily fine
intervals. And as with RC oscillators, the stability of a
verge-type clock is somewhat less than ideal. Nevertheless,
the escapement permitted the construction of
clocks with “good enough” performance for a great
many tasks. Measurements on the oldest working
clock in Europe, at the Salisbury Cathedral in England,
give us a rough idea about the typical accuracy
one could expect. The Salisbury clock, built in 1386,
drifts a large fraction of an hour per day. With care,
one could perhaps expect to lose or gain half an hour
per day [7]. By today’s standards, of course, that level
of error is considered unacceptable, but in the 14 th
century, it was unheard-of precision. Indeed, as late
as the 15 th century, soldiers were still using roosters
as portable alarm clocks [4], conveying some idea of
what performance level was tolerable. As a bonus,
severely off-spec roosters could always be eaten.
As with many other clocks of this period, the Salisbury
has no face. Instead, a bell chimes every hour, a
function that is reflected in etymology: The very word
clock comes from the Latin clocca (bell); other cognates
include glocke (German), klocke (Dutch), and
cloche (French), highlighting the universality of this
early use of clocks. Prior to the mid-14th century,
derivatives of the Latin term horologium had applied
to all timekeeping devices. The development of the
vastly superior escapement-controlled clocks required
a new word to distinguish this invention from the sundials,
water and sand clocks, and graduated slowburning
candles that had previously represented the
state of the art.
Replacement of the suspended weights by a spring
drive enabled much more compact shapes, bringing
the wristwatch a step closer to reality. Peter Henlein
of Nuremberg gets credit for building the first springdriven
clocks in the period 1500-1510, and is thus the
father of the portable clock, and the grandfather of
the wristwatch. Although the torque applied to the
foliot diminished as the spring unwound, the revolutionary
portability itself made the spring drive attractive
despite the systematic drift. Later developments,
such as the invention of the fusée – a cone-shaped
coupler that provides a continually varying gear ratio
as the spring unwinds – helped to reduce the variation
in foliot torque until still better compensation
methods came along [4].
Huygens’ Resounding Success
The verge-and-foliot arrangement, though revolutionary,
suffers from several important deficiencies that
one may readily identify from a circuit analogy. The
verge’s palettes are in contact with the crown wheel’s
teeth a large fraction of the time, ensuring substantial
frictional losses. Perhaps worse, the verge-and-foliot’s
oscillation frequency is a function of several variables
that are hard to maintain constant, and so it is
inevitable that accuracy suffers.
From circuit theory, we know that many of these
problems can be mitigated through the introduction
of a resonator – every circuit designer knows that an
LC oscillator is generally much better than an RC
relaxation oscillator. The introduction of a resonator
into clocks began with observations by Galileo. By
1602, he had deduced important facts about a free
pendulum’s motion. In a letter that year to his patron,
Guidobaldo del Monte, Galileo described experiments
that revealed an independence of oscillation period
on the mass of the pendulum. Within his limits of
measurement precision, he concluded that the period
is similarly independent of amplitude, and only a
function of length [8].
The Dutch astronomer Christiaan Huygens later
performed a careful theoretical analysis, and realized
that Galileo was somewhat in error: In truth, amplitude
does matter. However, this same analysis
revealed the result now taught in every elementary
physics class: For “small enough” angular displacements,
the period of oscillation is indeed a function
only of length. From there, it is a short intellectual
step to exploit the near-isochrony of the pendulum to
enable better clocks. Huygens himself took that next
step, allegedly inventing the pendulum clock on
Christmas Day, 1656 by proposing the replacement of
the aperiodic weighted foliot with the resonant pendulum.
Not being an instrument-maker himself, he
had the clock built in 1657 by someone who was:
Salomon Coster, whose clock now resides at the
Boerhaave National Museum of the History of Science,
in Leiden. Clocks of that type are capable of
errors measured in minutes per day, representing an
order-of-magnitude improvement over the older
verge-and-foliot clocks. Huygens described these
developments the following year, in his much-celebrated
Horologium Oscillatorium [9]. In short order,
clocks all over Europe were being upgraded by
replacing foliots with pendulums.
The superiority of the pendulum highlighted deficiencies
in the rest of the clock mechanism by contrast.
The largest remaining error source was the very
large swings forced on the pendulum by the legacy
verge escapement. The amplitudes were somewhat in
excess of the 90-degree spacing of the palettes, and
thus well outside the “small-swing” regime that corresponds
to near isochrony. Conscious realization that
44 IEEE SSCS NEWS Summer 2008