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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. Hesiod, writing in the 8 th 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" (Hesiod 71). Later Greek scientists, such as Archimedes, 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 Archimedes, Ctesibus created the Clepsydra in the 2 nd 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 Hipparchos 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 Ptolemy 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 pre socratic philosopher Thales.
Unfortunately, little is known about Thales's phone beyond Cicero's description in the De re publica: For Gallus 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 Thales of Miles, and later marked by Eudoxus with the constellations and stars which are fixed in the sky. (Price 56) This description is helpful for understanding the basic form of Thales's phone, 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 Cicero's lifetime. Why would Thales' 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 Eudoxus' preoccupation with systems of concentric spheres, a more logical explanation is that Thales marked his sphere with stars, and Eudoxus 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 Archimedes. Cicero 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 (Price 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 Thales' and Eudoxus, a mechanized sphere requires gears to accurately represent the motion of the heavens. According to Prof.
Derek Price, 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 / 30 th 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 Archimedes and other Greek scientists. Prof. Price 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 Archimedes 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, Archimedes's phone became a model for later Greek astronomers.
For example, Posidonios of Rhodes, a contemporary of Cicero, built a mechanical globe based on Archimedes's phone. Members of the school of Posidonios 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 Archimedes 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 Jobst Big. The differential gear later became a critical component of the cotton gin, a late 18 th 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 elliptical 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 23 deg. 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 360 deg. circle around the circumference of the celestial sphere. The Greeks used the elliptical 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 elliptical. If you are completely confused by my written description, take a look at the diagram I have created.
Elliptical coordinates were used by Hipparchos and Ptolemy 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 elliptical 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 17 th 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 360 deg. , dividing it into 24 sections results in hours that are 15 deg. 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 con...
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