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History of sundials
A sundial is a device that indicates time by using a light spot or shadow cast by the position of the Sun on a reference scale.  As the Earth turns on its polar axis, the sun appears to cross the sky from east to west, rising at sun-rise from beneath the horizon to a zenith at mid-day and falling again behind the horizon at sunset. Both the azimuth (direction) and the altitude (height) can be used to create time measuring devices. Sundials have been invented independently in every major culture and became more accurate and sophisticated as the culture developed. 
Tower of the Winds
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Tower of the Winds, also called Horologium, Greek Horologion (“Timepiece”), building in Athens erected about 100–50 bc by Andronicus of Cyrrhus for measuring time. Still standing, it is an octagonal marble structure 42 feet (12.8 m) high and 26 feet (7.9 m) in diameter. Each of the building’s eight sides faces a point of the compass and is decorated with a frieze of figures in relief representing the winds that blow from that direction below, on the sides facing the sun, are the lines of a sundial. The Horologium was surmounted by a weather vane in the form of a bronze Triton and contained a water clock (clepsydra) to record the time when the sun was not shining. The Greeks invented the weather vane the Romans used them in the belief that the wind’s direction could foretell the future.
Initially described by the Roman architect Vitruvius (1st century bc ), the Tower of the Winds was fancifully reconstructed in the 16th-century editions of his work by Cesare Cesariano and Giovanni Rusconi. Although these fanciful images influenced designs by 17th-century English architects Christopher Wren and Nicholas Hawksmoor, accurate illustrations were not published until 1762, when they appeared in volume one of James Stuart and Nicholas Revett’s The Antiquities of Athens. The Tower of the Winds was subsequently influential in the Greek Revival, notably in the versions of it built by Stuart in the landscaped pairs at Shugborough, Staffordshire, Eng. (c. 1764), and at Mount Stuart, County Down, Ire. (1782), and in James Wyatt’s more imaginative Radcliffe Observatory Tower, Oxford, Eng. (1776).
This article was most recently revised and updated by Kathleen Kuiper, Senior Editor.
The Function of Sundials in Ancient Civilizations
The sundial is the oldest known device used for the measurement of time. The history of sundials dates back to approximately 3,500 years ago. The function of a sundial depends on the position of the Sun in the sky at a given time. It´s based on the fact that the shadow of an object will move sideways as the Sun travels from east to west. Before the invention of clocks and watches, sundials had been used by diverse civilizations, to tell time. The purpose of historical sundials for early civilizations might have been to maintain a record of time throughout the day.
The earliest and simplest type of sundial is the shadow stick (gnomon). The time of day is determined by the position of the shadow cast on the ground. There are many types of sundials. Some sundials use the edge of a shadow to tell the time. Others use a line of light. On a shadow casting sundial, the sundial´s gnomon may be a thin rod or any other object with a sharp end. Sundials utilize distinct types of gnomon a gnomon may be rigid or movable according to the season. The surfaces of sundials may also be plane, spherical, cylindrical, or conical. The use of many sundials requires knowing the local latitude and a precise vertical orientation.
The Egyptians were the first civilization known to have used sundials. Their sundials consisted in a t-shaped cross rod with a vertical stick, which was marked with five lines, representing five hours. In the morning, the stick would be placed facing east to measure the hours, and later, the stick would be placed facing west to measure the following 5 hours. Later, the Egyptians built obelisks at the entrance of their temples. Obelisks are tall four sided structures that end with a pyramid-like top. The Egyptians built obelisks, utilizing the shadow cast of a sundial to calculate time. Obelisks also helped them calculate the longest and shortest day of the year (solstices). For the Egyptians, Obelisks represented the flesh of Gods. Overtime, the Egyptians built smaller versions of the obelisks to use them as portable sundials.
The Greeks created a sundial known as the &ldquopelekinon&rdquo which consisted on placing a vertical rod on a horizontal half spherical face. The sundial was marked to help them more accurately predict time in the course of a year. Based on this idea, they later invented the hemicycle which consisted of a cubical block of wood or stone that is cut in half and a rod attached on one end. The hemicycle varied in length depending on the season of the year. The hemicycle was later divided into 12 equal quadrants, indicating the length of each day. The Tower of Winds in Athens used eight sundials, each, facing a cardinal point.
In china, sundials date back to (1368-1644) in the era of the Ming Dynasty. The Rigou sundial, as it was known in China, comprise a base made of stone, which is aligned with the equatorial plane, and a gnomon that is placed perpendicular to the base. As in any culture, time keeping was an important function in ancient China. In China, the emperor was considered the basis of the norms of time. Two examples of Rigou sundials can be seen: one at the Beijing Ancient Observatory, and another at the Hall of Supreme Harmony.
There are three different types of sundials: the horizontal, equatorial, and vertical sundials. The base of the horizontal type is set horizontally, and the gnomon is slanted according to the Earth´s axis. The base of the equatorial sundial is aligned with the equatorial plane, while the gnomon is positioned perpendicular to the base. The base of a vertical sundial, which is the most common, is placed vertically, while the gnomon is placed in line with the Earth´s axis. To tell the time accurately, vertical sundials must be designed for specific Earth latitudes and longitudes. The Sun´s rotation is also taken into account when designing and finding a location for a sundial.
What Time is It? The History of the Sundial
Sun clocks or sundials are the oldest device known to man that was and still are used to tell time. The principle behind a sundial is very simple. As the sun rotates around the earth and moves from east to west, it casts a shadow. This shadow is then used to predict time.
Egyptians were the first ones to use sundials. These beginning time telling devices consisted of a t-shaped cross ban with a vertical stick. This stick was marked with five lines that represented five hours. In the morning, the stick was placed facing east and measured the next five hours. Afternoon times were measured by moving the stick so that if faced the west.
Later on, obelisks were built by the Egyptians and Babylonians that were used to calculate time. These structures were very important in the calculation of the longest and shortest days of the year.
Eventually, smaller, more portable sundials were designed that resembled smaller versions of the obelisk.
The Greeks created sundials called “pelekinon.” This type of sundial consisted of a gnomon or vertical rod that was placed on a horizontal or half-spherical face. This sundial was then marked so that they more accurately predicted time throughout the year using a new math called geometry. This knowledge allowed the Greeks to invent the hemicycle. This invention consisted of a cubical block of wood or stone that was divided into hemisphere with a stick or rod that was attached to one end. The circular arc that was created varied in length depending on the season of the year. To get a more accurate reading, these arcs were then divided into twelve equal quadrants, which indicated the length of each day. An example of this is the Tower of Winds in Athens. This timepiece consists of eight sundials that face the cardinal points of the compass.
China had their version of the sundial called “Rigou.” This type of sundial was very popular during the Zhou Dynasty. Later on, more portable types of sundials were invented during the Song Dynasty.
There is more to sundials then measuring shadows throughout the season. A sundial is made of a base or faceplate that can be any shape. Attached to this faceplate is a gnomon or needle. As the sun hits the gnomon, it will cast a shadow upon the plate. The plate is then marked with time related measurements. These can consist of hourly time, seasonal time, shortest and longest days, and dates.
But since the sun rotates around the sun, the axis of the sun needs to be added to the sundial equation. Without taking into consideration the axis, the time calculated by the shadow will be different every week. To address the earth’s axis, one simply needs to line up the gnomon with the earth’s axis.
Types of Sundials
There are three types of sundials, which include horizontal, equatorial, and vertical. The horizontal type of sundial is set up so that the base is placed horizontal while the gnomon is tilted in line with the earth’s axis. The equatorial sundial, on the other hand, has its base placed at an angle that is parallel to the equator while the gnomon is placed perpendicular to the base. The vertical sundial is the most common and consists of a base that is placed vertical while the gnomon is aligned with the earth’s axis.
Another component of sundial placement is the hemisphere. The latitude that the sundial is placed in one hemisphere should be the opposite for the other hemisphere. To aid in this placement, set up the sundial according to the area’s true north or south, then adjust the axis by the longitude.
To enjoy a sundial in your own yard, browse Outdora’s wide selection of sundials. To please both bird watchers and add even more beauty to your backyard, there are also birdbath/sundial combos like the Hummingbird Sundial Birdbath Combination. Whatever type of sundial you choose, now know a little bit of history about the backyard accessory to wow friends and family.
ABOUT THE AUTHOR
Mindy McIntosh-Shetter has been an Agricultural Science educator, and is a horticulture and/or environmental blogger who earned a degree from Purdue University in Agriculture Education with a minor in biology, and natural resources. Presently she is finishing up her Masters in Environmental Education and Urban Planning for the University of Louisville while working on her own agriculture/environmental blog.
The Ancient Invention of the Water Clock
Today, the ability to keep track of time seems to be taken for granted. One just simply needs to glance at a watch, clock, or mobile phone to know the exact time, even down to the nearest second. Prior to the invention of such battery-operated gadgets, time-keeping was done quite differently. In the ancient world, for instance, sundials were commonly used. This method of measuring time, however, had its flaws. Sundials would, of course, only function when there was sunlight, and they could not maintain a constant division of time. To compensate for these shortcomings, the water clock was invented. Although no one is certain when or where the first water clock was made, the oldest known example is dated to 1500 BC, and is from the tomb of the Egyptian pharaoh Amenhotep I.
In the ancient world, there were two forms of water clocks: outflow and inflow. In an outflow water clock, the inside of a container was marked with lines of measurement. The container was filled with water, which was allowed to leak out at a steady pace. Observers were able to tell time by measuring the change in water level. An inflow water clock followed the same principle as an outflow one, i.e. the steady dripping of water. Unlike the latter, the former’s measurements were in a second container instead. Based on the amount of water that dripped from the first container, one was able to tell how much time had passed.
Around 325 BC, water clocks began to be used by the Greeks, who called this device the clepsydra (‘water thief’). One of the uses of the water clock in Greece, especially in Athens, was for the timing of speeches in law courts. Some Athenian sources indicate that the water clock was used during the speeches of various well-known Greeks, including Aristotle, Aristophanes the playwright, and Demosthenes the statesman. Apart from timing their speeches, the water clock also prevented their speeches from running too long. Depending on the type of speech or trial that was going on, different amounts of water would be filled into the vessels.
The water clock, however, was not without its flaws. First of all, a constant pressure of water was needed to keep the flow of water at a constant rate. To solve this problem, the water clock was supplied with water from a large reservoir in which the water was kept at a constant level. An example of this can be seen in the ‘Tower of the Winds’ which was built by the Greek astronomer Andronikos in Athens during the 1 st century BC. Still standing, it is an octagonal marble structure 42 feet (12.8 m) high and 26 feet (7.9 m) in diameter. Each of the building’s eight sides faces a point of the compass and is decorated with a frieze of figures in relief representing the winds that blow from that direction below, on the sides facing the sun, are the lines of a sundial. The Horologium was surmounted by a weather vane in the form of a bronze Triton and contained a water clock (clepsydra) to record the time when the sun was not shining.
The Tower of the Winds, Greece. Photo source: BigStockPhoto
Another problem with the water clock was that as the length of day and night varied with the seasons, it was necessary for the clocks to be calibrated each month. Several solutions were employed to counter this problem. For instance, a disc with 365 holes of varying sizes was used to regulate the flow of water. The largest hole corresponded to the winter solstice, as the day would be shortest, while the smallest hole corresponded to the longest day of the year, the summer solstice. These two holes were at opposite ends of the disk, with the other holes arranged between them in increasing or decreasing sizes. The holes corresponded to the days of the year, and would be rotated by one hole at the end of each day.
Although the fundamental principle of the water is a relatively simple one, there were some challenges related to the physics of water pressure and the changing seasons that the ancients had to deal with, resulting in the water clocks becoming more and more complex over time. When compared to the ease at which we keep track of time today, it seems that we have come quite a long way.
Featured image: Three different depictions of ancient water clocks .
Fact Monster/Information Please® Database, 2007. Water Clocks. [Online]
Available at: http://www.factmonster.com/ipka/A0855491.html
Lamb, R., 2014. How Water-powered Clocks Work. [Online]
The British Museum, 2014. Fragment of a basalt water clock. [Online]
Wu Mingren (‘Dhwty’) has a Bachelor of Arts in Ancient History and Archaeology. Although his primary interest is in the ancient civilizations of the Near East, he is also interested in other geographical regions, as well as other time periods. Read More
Scientific Secrets of Athens
Athens is known all over the world for its history and culture. It was also one of the most famous cities in ancient Greece, where it is said that science was born in the western world. Remnants of this golden age are everywhere in the city. All you have to do is to discover them!
I grew up in Athens, I love traveling but also writing about popular science. When I visit new places, I look for hidden gem cafes that help me relax and digest my new discoveries. This why I created a guide that presents some of the lesser known scientific monuments of Athens, such as the place where astronomical measurements were taken 2,500 years ago! At the same time, the guide informs you of science museums, planetariums and observatories. For each location I suggest a nearby cafe as one of my favourites to digest your newly acquired knowledge in.
1) Meton’s ObservatoryI will begin with the ancient Greek astronomer, Meton, who lived in Athens in the 5th century BC. He is most famous for the Metonic Cycle, an astronomical cycle on which calendars, such as the Jewish one (currently used mainly for Jewish religious festivals) and the calendar of the Christian orthodox church used to calculate the Easter date, are based on.Historical sources report that Meton (along with his assistant Euktemon) placed an observation instrument (called the “heliotropion” or “helioscopion”) just above the podium on the Pnyx hill, where the ancient Athenians held their public assemblies. The site of Meton’s Observatory is located on the hill of Pnyx, near the National Observatory of Athens. The visit is free of charge and a sign informs you of the presence of the observatory.
Site of Meton’s Observatory ?:
☕️ Suggested Cafe: The Museum of Islamic Art may not be directly related to science, but the beautifully decorated rooftop cafe is one of the hidden gems of Athens. Here you will also find a terrace overlooking this astronomical observatory! Address: 12, Dipylou Street, Athens 105 53
Mini tip: For access to the cafe is not necessary to enter the museum.
2) National Observatory of AthensThe exploration of Meton’s Observatory has shown us that ancient Greek astronomers played a central role in the advancement of astronomy. Following this tradition, the National Observatory of Athens, founded in 1842, was one of the first educational and research institutes of the modern Greek state. The main building is located on the hill of the Nymphs, next to the hill of Pnyx, where Meton had set up his own observatory centuries before.
The National Observatory of Athens ?:
The National Observatory has its own fascinating stories, such as that of the astronomer who designed one of the most accurate lunar maps of his time. For many years, it was also the point of reference by which, through observation of the sky, all the clocks of Athens were synchronized. For all this, but also for the unforgettable view, it is sure worth visiting!
☕️ Suggested Cafe: The place to digest a visit to an observatory should include a stunning view. One of the best spots for this is the Byron Hotel’s rooftop cafe. The views of Pnyx, Acropolis and Lycabettus are great and the prices are very reasonable. Address: 19 Vyronos Street, Athens 105 58
3) Sundial of the National GardenAs we have already mentioned time measurement, let us talk about sundials, constructions that are based on the shadow of the sun to measure time. It is characteristic of the rich history of Athens that a sundial referred to as “modern” is actually almost 200 years old! It is located at the main entrance of the National Garden (formerly known as the Royal Garden), an oasis right in the city center over 15 hectares full of vegetation, rare plants and bird species.
The sundial initially decorated the palace of Otto von Wittelsbach, the first king of the modern Greek state, who reigned Greece from 1832 to 1862. Otto built his palace (the building in Syntagma Square which today is the Greek Parliament) in the 1840s. The sundial was placed as a decoration next to the marble staircase leading to the Royal Garden. After the monarchy was abolished and the Garden became accessible to the public (renamed National Garden), the famous solar clock was moved to its current location.
The sundial of the National Garden ?:
☕️ Suggested Cafe: Once you finish your walk in the National Garden, a good place to relax is Athens Cook. More a beer restaurant than a cafe is recommended to enjoy a cold frappe coffee on a hot summer day. Alternatively, try one of the local beers that even the god Dionysus would have enjoyed. Address: Nikis 20, Athens 105 57
4) Tower of the WindsMany of you will have heard of one the most famous monuments of Athens, the Tower of the Winds. But how many realise that it was also the first meteorological station? The Horologion of Andronikos Kyrrhestes (the official name of the monument) was also used for astronomical observations as well as for the measurement of time. The name comes from its designer, Andronikos of Cyrrhus, who was an ancient Greek astronomer, engineer and architect, and possibly the sponsor for the construction of the monument. According to recent surveys, the Tower was built around 100 BC.
The Tower of the Winds ?:
☕️ Suggested Cafe: As a refuge from the Athenian winds (or possibly the hot sun), the nearby traditional cafe, Glykys, is recommended. With a beautiful outdoor area for the summer and a traditional stove burning indoors in the winter, it is an ideal place to rest after wandering in Plaka. Address: Aggelos Gerontas 2, Athens 105 58.
5) Aritstotle’s Lyceum
It is well known that apart from the sciences, ancient philosophy also flourished in Athens. Did you know that you can now visit the area where in 335 BC, Aristotle founded his Lyceum? The exact location of the Lyceum had remained unknown for centuries until it was discovered by excavations in 1996. Visiting the archaeological site of 11.5 acres, you can see and learn about the ruins of various constructions with the help of many information points. Moreover, it is an ideal place to relax or read in a beautiful setting, sitting on one of the many benches that have been installed all around.
Aristotle’s Lyceum excavation area ?:
☕️ Suggested Cafe: Petite Fleur is a cozy little cafe in a quiet square, a 10-minute walk from Aristotle’s Lyceum. It also serves great hot chocolate! Address: Amynta 1, Athens 116 35
Ohio University Sundial
Topics. This historical marker is listed in these topic lists: Education &bull Man-Made Features. A significant historical year for this entry is 1807.
Location. 39° 19.58′ N, 82° 5.952′ W. Marker is in Athens, Ohio, in Athens County. Marker is on University Terrace 0.1 miles south of East Union Street, on the left when traveling north. The marker stands in the lawn in front of Galbreath Chapel on the Ohio University campus. Touch for map. Marker is at or near this postal address: 35 University Terrace, Athens OH 45701, United States of America. Touch for directions.
Other nearby markers. At least 8 other markers are within walking distance of this marker. Ohio University's Distinguished Visitors (within shouting distance of this marker) Memorial Auditorium (within shouting distance of this marker) Manasseh Cutler Hall (about 300 feet away, measured in a direct line) The Elms (about 300 feet away) Bicentennial of the Northwest Ordinance (about 400 feet away) The Kissing Circle (about 500 feet away) Athens County Civil War Soldiers and Sailors Memorial (about 600 feet away) Student Voices (about 600 feet away). Touch for a list and map of all markers in Athens.
History of Sundials Quest
2. The sun shining on the gnomon, which is pronounced no-men, causes a shadow to appear. When the shadow falls on the appropriate line on the base, it displays the time. The placement of the lines on the ground are dependent upon the particular location of the sundial, and vary according to a number of factors such as the latitude of the sundial. Go to Stonehenge in Medieval Age and say, "A shadow can tell time!"
3. Around 2500-2000 BC, the Egyptians and Babylonians made sundials by building obelisks. These tapering four-sided monuments enabled the people to divide the day into two parts. Which two parts?
a. Morning and Afternoon b. Night and Day c. Dawn and Dusk d. Noon and Midnight
4. The Egyptians could determine not only noon, but also the shortest and longest days of the year. They would place markers around the obelisk base to indicate these time periods. Additional markers would subdivide the day into even smaller increments. The biggest drawback to these sun clocks was that they were not movable. Go to the Wild Woods in Western Age and say, "Pardon me, do you have the time?"
5. As time went by, the Egyptians built more precise sundials. One of the oldest surviving sundials dates from approximately 800 BC. This Egyptian shadow clock was composed of a straight base where a scale of six time divisions was inscribed and had a raised crosspiece at one end. Of what material was this ancient sundial made?
a. Oolatic Hematite b. Green Schist c. Pink Granite d. Black Marble
6. The base was oriented in an east-west direction. The crosspiece was at the east end in the morning and the west end in the afternoon. The shadow cast by the crosspiece onto the base told the time. Go to the Galactic Trading Post in Space and say: "There is no time to lose!"
7. Ancient writings from around 300 BC first describe a sundial. The writer, Berossus, a Babylonian priest, described a sundial as a cubical block. A half-sphere had been cut into the block and at the center, a small bead was placed. The shadow of the bead moved in an arc which had been subdivided into twelve equal sections. Depending upon the season of the year, the length of the day varies. In addition, the length of the hours also changes. What were these early variable hours called?
a. Variational Hours b. Fluctuating Hours c. Temporary Hours d. Dependant Hours
8. It was not until around 1300 AD, when mechanical type clocks were developed that an hour not dependent upon daylight was decided upon. These hours were called "Equal hours." Go to the waterfall in Australia and say: "Don't count every hour in the day, make every hour in the day count."
9. Between 250 BC and 100 AD, the Greeks make a number of advancements in the construction of sundials. Using geometry, they develop complex sundials. An interesting advancement to the sundial was a device used by Ptolemy. The device projected shadows geometrically onto planes which were slanted at various angles relative to the horizontal plane. What was this device called?
a. Horologion b. Hemicyclium c. Armillary Sphere d. Analemma
9. Around 100 BC, The Tower of the Winds was built in Athens. The amazing octagonal shaped tower included a combination of sundials, a water clock and a wind direction vane. The sundials faced different cardinal compass points. Later, it was discovered that a slanting object's shadow was a more accurate timekeeper than a shadow cast by a vertical object because of the angle of the earth's axis. Go to the Victorian House in the Victorian Age and say: "Life is all about timing!"
Time and Time Intervals 4111 Sundials
We have already mentioned the gnomon, essentially a rod, the permanent placement of which permits calibration of its shadow direction to time of day. A gnomon placed perpendicular in level ground must have constituted the first sundial, and there is indeed a very early "shadow-clock" from Egypt, which seems to be precisely this. It measures in projection the hour angle of the Sun. Many examples exist of horizontal sundials, although, according to Gibbs (1976, pp. 4, 78), Greek and Roman sundial makers preferred rounded surfaces. Of 256 sundials from the Greco-Roman world, of the 3rd century b.c. to the 4th century a.d., described by Gibbs, only 15 are flat and horizontal and only 25 vertical. There are conical, cylindrical, and spherical shapes in abundance. Among the most ingenious (op. cit., p. 23) are the "roofed" sundials, which had a notch or a small carefully drilled hole on the midline of the roof that would act as a tip of a gnomon. Other sundials used the tip of a small pyramid-shaped metal gnomon, and not the side of the gnomon shadow, as in most modern sundials, to mark the hours (see Figure 4.1).
3 187° = 18 + 7/60 = 18.11667°. Multiplied by 51/2, this yields 99.64167°, and divided by 15 degrees/hour, the result is 6.64278 hrs. = 6h + (60 x
0.64278 = 38.57) mins. = 638,34 or about 638. Apparently, Ptolemy is rounding off. The rate, 15°/hour, is from the equivalence between 360°
Figure 4.1. A modern cyclindrical sundial with a pyramidal stylus, from a private home in Calgary. Photo by Dr. T.A. Clark.
Much of the description of these sundials comes from Vitruvius's De architectura, which dates from about 80 b.c. The largest in this collection are the vertical sundials on the eight facings of the "Tower of the Winds" in the Plaka district, of Athens, below the Acropolis. This structure, still visible today (see Figure 4.2), was known in the first century b.c. as the Horologium of Andronikos (from Kyrrhos in Macedonia) or Andronicus Cyrrestes in Latin sources we discuss this structure and its place in the culture of its time in §7 and report the informed speculation concerning a water clock in the structure in §18.104.22.168.
Figure 4.3 shows a 15th-century horizontal sundial now located in the courtyard of the "Old Beijing Observatory" in Beijing, China. A modern vertical sundial in Lucerne, Switzerland can be seen in Figure 4.4. A small vertical sundial dating from the Greco-Roman period was found in Luxor (Figure 4.5).
A stone sundial in a courtyard in the Forbidden City in Beijing, China is shown in Figure 4.6. In the latter case, the distortion due to the projection of the hour angle is avoided, because the dial is set in the plane of the equator, and the cursor is a narrow rod projecting through the center onto both faces. This type of sundial has an added advantage: Between the equinoxes, the Sun will illuminate only one of the two faces. At an equinox, the cursor shadow will appear on both faces equally, and thereafter, only one of the surfaces will be fully illuminated.
Sundials were among the elaborate reconstructions of astronomical instruments at Delhi and Jaipur (Figures 3.24 and 9.10) by the Maharajah of Jaipur in the 18th century (see Figure 4.7). Sundials came in an array of geometric styles, including the cylindrical (see Figure 4.1).
The sundial was widely used in the ancient Mediterranean world. Properly used,4 it could be read to a few minutes or better, perhaps to one minute. Precision is ultimately limited by the lack of sharpness of the shadow because of the finite size of the solar disk, a shortcoming of which Ptolemy was well aware (Almagest, Book II, §5 Toomer 1984, p. 80).
The use of the shadow of a gnomon as an indicator of time requires in principle at least empirical knowledge of the altitudes of the Sun at particular times of day and seasons of the year. Where projections are involved, as in flat sundials, the effect at the latitude of the intended site must be known. Finally, the markings should be long enough to extend over the annual range of shadow length at each hour. As we noted in the previous section, the Greco-Roman world did not use mean solar time, and their hours were usually not of uniform length but literally varied over time scales of days. Seasonal hours divided the daylight interval into 12 hours, regardless of the season. This meant that a winter day had shorter seasonal hours than did a summer day. Moreover, at the same time of year, the seasonal hour had a different length as one traveled to a location with a different latitude. Table 4.1 lists the lengths of daylight (2H0rise/set) and length of the seasonal hour for seasonal extremes at selected sites. Note that the ratio of the lengths of the longest to shortest days is a strong indication of the latitude of the site. The accuracy of a sundial reading depended on the time of year, and the suitability of the sundial for the latitude and maybe longitude of a particular place (the noon meridian of the sundial should have agreed with the celestial meridian of the site). In the ancient Mediterranean world, the establishment of the length of daylight was an important function of astronomy. Neugebauer (1957/1969, pp. 158ff.) shows that this was carried out by studying the "ascensions" of the zodiacal signs during the course of the night. For Alexandria, the night lasted about 10 hours in the summer (thus the day lasted 14 hours), and in the winter, the night lasted 14 hours (and thus the day, 10 hours). This ratio, 7:5, was determined in antiquity.
Table 4.1 contains no correction for atmospheric refraction, which lifts the Sun by slightly more than its diameter, on average (see §3 for a discussion of both the mean refraction and its variation from the mean value). Because the Sun
4 Gibbs (1976) relates that a case is known of a sundial that was designed for use in Catania in Sicily but used quite happily in Rome for a considerable interval of time, although the markings were no longer quite right for the site.