A
Brief History of Clocks: From Thales to
Ptolemy
By: J. W.
(source)
abstract:
This
article gives a brief overview of the early
times of clockwork: from the greek antkythera
mechanism to the roman/egyptian clepsydra
waterclock.
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on this paper.
The clock
is one of the most influential discoveries in
the history of western science. The division
of time into regular, predictable units is
fundamental to the operation of society. Even
in ancient times, humanity recognized the
necessity of an orderly system of chronology.
H., writing in the 8th century BC., used
celestial bodies to indicate agricultural
cycles: "When the Pleiads, Atlas' daughters,
start to rise begin your harvest; plough when
they go down" ( H. 71). Later Greek
scientists, such as A., developed complicated
models of the heavens--celestial
spheres--that illustrated the "wandering" of
the sun, the moon, and the planets against
the fixed position of the stars. Shortly
after A., C. created the Clepsydra in the 2nd
century BC. A more elaborate version of the
common water clock, the Clepsydra was quite
popular in ancient Greece. However, the
development of stereography by H. in 150 BC.
radically altered physical representations of
the heavens. By integrating stereography with
the Clepsydra and the celestial sphere,
humanity was capable of creating more
practical and accurate devices for measuring
time--the anaphoric clock and the astrolabe.
Although P. was familiar with both the
anaphoric clock and the astrolabe, I believe
that the development of the anaphoric clock
preceded the development of the
astrolabe.
The
earliest example, in western culture, of a
celestial sphere is attributed to the
presocratic philosopher T.. Unfortunately,
little is known about Thales' sphere beyond
C.'s description in the De re
publica:
For G. told
us that the other kind of celestial globe,
which was solid and contained no hollow
space, was a very early invention, the first
one of that kind having been constructed by
T. of M., and later marked by E. with the
constellations and stars which are fixed in
the sky. (P. 56)
This
description is helpful for understanding the
basic form of T.' sphere, and for pinpointing
its creation at a specific point in time.
However, it is clearly a simplification of
events that occurred several hundred years
before C.'s lifetime. Why would T.' create a
spherical representation of the heavens and
neglect to indicate the stars? Of what use is
a bowling ball for locating celestial bodies?
Considering E.' preoccupation with systems of
concentric spheres, a more logical
explanation is that T. marked his sphere with
stars, and E. later traced the ecliptic and
the paths of the planets on the exterior. The
celestial sphere in question probably
resembled this early
Persian
example.
Perhaps the
most famous celestial sphere is the
mechanized globe attributed to A.. C. was
especially impressed by this invention
because of its ability to imitate "the
motions of the sun and moon and of those five
stars which are called wanderers" with a
single rotational focus (P. 56). By turning a
crank, one could observe the "natural" course
of the sun, moon and planets around the
earth. The sphere was also remarkable for a
second reason. Unlike a stationary globe,
like that of T.' and E., a mechanized sphere
requires gears to accurately represent the
motion of the heavens. According to Prof. D.
P., the mean period of Saturn can be
mechanically represented by a gear ratio of
30 to 1. In other words, for every revolution
of the sun around the earth, Saturn will only
accomplish 1/30th of its revolution around
the earth. The mean period of Jupiter can be
represented by a gear ratio of 12 to 1, and
Mars can be represented by a gear ratio of
2.5 to 1.
An
interesting problem arises when one attempts
to mechanically represent the synodic month.
A gear ratio of 235 to 19 is required for an
accurate representation. However, this is
impossible to achieve directly, presenting a
serious challenge to A. and other Greek
scientists. Prof. P. claims that two
different gear arrangements can be used to
create this ratio. First, one may simply use
a more intricate combination of gears, as A.
did in his mechanical sphere. The second
solution is one of the greatest innovations
in Greek engineering; the development and
incorporation of a
differential
gear.
In addition to having been the first
mechanized globe, A.' sphere became a model
for later Greek astronomers. For example, P.
of Rhodes, a contemporary of C., built a
mechanical globe based on A.' sphere. Members
of the school of P. created a device to
compute the positions of the sun and the
moon--what we now call "The
Antikythera
Mechanism."
Challenged by the same, mechanical difficulty
A. faced in representing the synodic month,
these scientists developed the first
differential gear to solve the problem.
Archaeological evidence suggests that after
the Antikythera Mechanism was lost in a
shipwreck, the differential gear essentially
disappeared from western knowledge until
1575, when it reappeared in a globe clock
designed by J. B.. The differential gear
later became a critical component of the
cotton gin, a late 18th century invention
that marked the beginning of the industrial
revolution. However, devices such a the
Antikythera Mechanism were quite rare. The
celestial sphere was the most common form of
celestial representation, prompting a number
of structural modifications.
Because of
the difficulty in imagining the position of
the earth within a solid representation of
the heavens, the celestial globe assumed a
more skeletal appearance over time. This new
model of the heavens, the armillary sphere,
quickly began to replace the more ambiguous
celestial globe. However, the method of
locating celestial bodies remained the same.
Greek astronomers continued to use an
ecliptical system for specifying the position
of the stars and planets. To understand how
this system works it is first necessary to
explain a few terms, and to remember that we
are assuming that the earth is in the center
of the universe--we are using a geocentric
model of the universe. The ecliptic measures
the annual rotation of the sun around the
earth, and is inclined 23deg. from the
celestial equator. It is not a representation
of the daily rising and setting of the sun.
The Greeks divided the ecliptic into twelve
sections, and each section was named after
the constellation it contained--Aries,
Taurus, Gemini, Cancer, Leo, Virgo, Libra,
Scorpio, Sagittarius, Capricorn, Aquarius,
and Pices respectively. The ecliptic, divided
in this fashion, is called the zodiac. The
Greeks further divided each of these twelve
sections into thirty units, effectively
graduating the entire circle for longitudinal
measurement (30 multiplied by 12 is equal to
360). The system began at the vernal equinox,
the intersection of the ecliptic with the
celestial equator in the constellation of
Ares, and completed a 360deg. circle around
the circumference of the celestial sphere.
The Greeks used the ecliptical to measure a
star's horizontal, angular displacement from
the vernal equinox. Vertical, angular
displacement was measured by constructing a
graduated circle perpendicular to the
ecliptical. If you are completely confused by
my written description, take a look
at
the diagram
I have created. Ecliptical coordinates were
used by H. and P.
in their star
catalogues,
and were the standard of celestial
measurement until the Renaissance, when they
were replaced by the equatorial coordinate
system. The equatorial coordinate system is
identical to the ecliptical system, except
that it uses the celestial equator for
horizontal measurement instead of the
ecliptic. Because the celestial equator is
simply a projection of the earth's equator,
the equatorial coordinate system is analogous
to terrestrial longitude and latitude, and
provides a more accurate system of
measurement. This
17th century armillary
sphere
is graduated for both ecliptic and equatorial
coordinate systems--notice how each sign of
the zodiac contains thirty degrees of the
circle.
Measuring
time on an armillary sphere is a simple
matter. First, imagine that you live on the
earth's equator. From this position, the
ecliptic is almost a perfect arch over your
head. As the earth rotates, the sun will rise
and set in a twenty-four hour period. Please
remember that this is not the ecliptic--the
ecliptic will only determine where, on the
horizon, the sun will rise and set each day.
In antiquity, every day is a complete
rotation of the sun around the earth. Time
may be measured simply by dividing this
rotation into twenty-four hours. If the
rotation is a circle of 360deg., dividing it
into 24 sections results in hours that are
15deg. long. In other words, if we know where
the sun will rise on the horizon, according
to the ecliptic, every fifteen degrees that
the sun travels across the sky marks the end
of an hour. Given a constant source of
motion, it is possible to create a clock--an
accurate representation of the heavens, from
an armillary sphere. Although the Greeks had
the means of producing the necessary motion,
the shape and intricacy of an "armillary
sphere clock" may have prevented rigorous
experimentation until the development of
stereography.
Until the
development of stereography by H. in the
middle of the second century BC., the Greeks
measured time with various types
of water
clocks.
The most simple water clock consisted of a
large urn that had a small hole located near
the base, and a graduated stick attached to a
floating base. The hole would be plugged
while the urn was being filled with water,
and then the stick would be inserted into the
urn. The stick would float perpendicular to
the surface of the water, and when the hole
at the base of the urn was unplugged, the
passage of time was measured as the stick
descended farther into the urn. These early
clocks were used when equal measurements of
time needed to be established. For example,
if two orators were to be allotted the same
amount of time to speak before an assembly, a
water clock of this nature would have been
constructed for the occasion. In the second
century BC., a man named C. created a more
elaborate water clock for measuring the time
of day. The Clepsydra, as it is called,
consisted of four major parts: a vessel for
providing a constant supply of water (B), a
reservoir and notched floatation rod (F), a
display (G), and a device for adjusting the
flow of water into the vessel (D).
Water
was continually poured into the vessel (B),
with the overflow escaping from a pipe (I).
Water flowed from this vessel into the
reservoir at a constant rate. As the
reservoir filled with water, the floating,
notched rod ascended at a constant rate. This
rod was attached to the display (G), which
indicated the time of day. The Greeks divided
the day into twelve hours of unequal length
to insure an equal division of day and night.
Because the Greeks divided the day into hours
of unequal length, it was necessary to
include a device (D) to regulate the flow of
water from the vessel (B) into the reservoir
(F). By raising the flat, circular cap in the
conical vessel (B), the flow of water could
be increased, decreasing the length of an
hour. In the summer, the day is longer than
the night, and in the winter the reciprocal
is true. Therefore, in the summer, the clock
would be adjusted to extend the length of
each day hour. A second way the Greeks
standardized the length of a day was by
modifying the clock display. A cylinder with
sloping hour lines was used instead of a
circular face. The mechanism worked as
follows: as water collected in the reservoir,
a pointer would raise as the cylindrical
display rotated. In this manner, the pointer
would gradually trace the course of the
adjusted hours on the cylindrical display.
However, the former example, the circular
face, is more important because of the
modifications made to it after the discovery
of stereography by H..
Stereography
is a technique by which three dimensional
objects are projected on two dimensional
surfaces. H. used stereography to create a
projection of the celestial sphere from its
southern celestial pole to its equatorial
plane. In other words, he created a two
dimensional image of a three dimensional
model--a planispheric projection of the
heavens. By separating the
projection of the
stars
and the ecliptic from
the projection of the horizon and the
equator,
Greek scientists could simultaneously
represent the progression of the sun along
the ecliptic and the daily rotation of the
sun around the earth. In essence, by
separating the two projections scientists
recreated the rotational components of an
armillary sphere on a two dimensional
surface. By incorporating these two
planispheric projections of the sky into the
display of a clepsydra, the Greeks discovered
a way for providing the constant source of
motion necessary for an accurate
representation of time. Recall that an
armillary sphere can be used to tell time
because it allows one to divide the daily
rotation of the sun around the earth into 24
hours, with each hour equal to 15 degrees of
the complete rotation. The problem with
keeping time on an armillary sphere is that a
constant source of motion is required for the
sphere to mimic the actual motion of the sun
around the earth. By using stereography,
scientists were able to project the armillary
sphere on two disks--the first provided the
means for measuring sun's position in the
sky, and the second disk illustrated the
sun's actual path across the sky. There are
two advantages to having the heavens
projected on two disks, as opposed to a
single sphere. First, it is easier to
construct a two dimensional model than a
complicated sphere. Second, it is easy to
provide constant motion for two disks by
using a clepsydra. By incorporating
planispheric projections of the heavens into
the clepsydra, the Greeks created the first
anaphoric clocks.
The
anaphoric clock consists of a rotating star
map behind a fixed, wire representation of
the meridian, the horizon, the equator and
the two tropics. The fixed disk consists of
several concentric circles, divided into
twenty-four sections by a series of small
arcs. Each section represents one hour of the
day. Because the long arc extending from one
end of the disk to the other is the horizon,
the first hour of the day begins on the right
side of the disk at the horizon. The twelve
hours of the day are above the horizon, and
the twelve hours of the night are below the
horizon. A stereographic map of the ecliptic
was attached behind this fixed
representation. Although circular in shape,
the ecliptic did not rotate around its
center. To accurately represent the daily
path of the sun, the ecliptic rotated around
a point approximately halfway between the
center and the bottom edge of the circle. The
ecliptic would complete one rotation around
this point every day. Furthermore, the
ecliptic was fashioned with 365 holes around
its circumference, one for every day of the
year, in which was placed a peg to represent
the sun. The year began at the vernal
equinox, and after each daily rotation of the
ecliptic the peg would advance to the next
hole along the perimeter of the ecliptic.
However, the ecliptic was reset each day so
that the peg always began at the horizon. The
anaphoric clock was both a clock and a
calendar, illustrating the both the time of
day and the progression of the sun along the
ecliptic.
A second
product of stereography is the astrolabe, a
device for locating the position of the stars
at any point in time. The astrolabe consists
of three major parts: First, there is a fixed
disk called a tympanum on which one can
measure the position of the stars. The
tympanum is an engraved plate, making it
easier to use than the wire mesh of the
anaphoric clock, but because the position of
the horizon differs from place to place, each
astrolabe typically contained a number of
tympanum. Only one tympanum was used at a
time, and the inclusion of several tympanum
insured that the astrolabe could be used at a
variety of positions on the earth. Second, a
skeletal projection of the stars--called a
rete--was fastened over the tympanum. The
third primary component of an astrolabe is a
simple device for measuring the distance of a
star above the horizon--usually a rod
attached to the back of the astrolabe. One
could produce a map of the sky on any given
night by locating a known star, measuring its
angular distance above the horizon, and
rotating the rete until the representation of
the star was aligned with its angular
distance on the tympanum. During the
Renaissance, the astrolabe was also included
in clock designs such as this
one by J. R.
The
evolution of the anaphoric clock depended on
several hundred years of Greek science. T.'
crude, spherical representation of the
heavens laid a foundation for other Greek
scientists to build on. After the
construction of the first celestial sphere by
E., A. created the first mechanical
representation of the heavens using a
complicated series of gears. However,
armillary spheres were more commonly used to
study the heavens. Shortly after the
construction of A.' sphere, C. built the
first clepsydra. Although it is possible to
observe the time on an armillary sphere, it
is quite difficult to perpetually mimic the
motion of the sun around the earth. The
invention of stereography by Hipparchos made
the construction of a dynamic representation
of the heavens possible through the
combination of planispheric projections with
the clepsydra. The anaphoric clock and its
cousin, the astrolabe, not only helped P.
create the extensive catalogue in the
Almagest, but also established the foundation
of modern time keeping.
Bibliography