The history and development of sundials

The History and Development of Sundials

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Colegiul Tehnic Danubiana - Roman, Romania,

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This book is a part of the common effort of our 9 schools from 9 different countries to make a success out of our Comenius multilateral project: “Science around us along history” implemented during the period of two years, 2013 – 2015.

Our project aims to promote cultural and intercultural awareness between European schools as well as the awareness that the existence of diversity between European countries is important and unifies, rather than separates, countries.

Nine schools from Spain, Austria, France, Italy, Poland, Romania, Sweden, Turkey and UK collaborate in carrying out activities that deal with various aspects of The History and Development of Sundials.

Students between 14-18 years old, regardless of origin, gender, ability, religion and socio-economic background and teachers are actively involved in the project developing communication and friendship.

This book is the result of the work of students and teachers from Colegiul Tehnic Danubiana - Roman, Romania, IES EL TABLERO – Cordoba, Spain, Istituto di Istruzione Superiore “PITAGORA” – Montalbano Jonico MT, Italy, Lycee Professionnel Andre Campa – Jurancon, France, Technikum Nr 3 w Zespole Szkół Nr 3 – Zabrze, Poland, Lidköpings kommun Barn och skola, Sweden, ZONGULDAK KOZLU LİSESİ, Turkey, Gloucestershire College – Cheltenham, UK, Bundeshandelsakademie und Bundeshandelsschule, Bundeshandelsakademie für Berufstätige- Graz, Austria.

This project has been funded by the European Commission trough Comenius Lifelong Learning Programme. This publication reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

******************************************* Comenius multilateral partnership “Science around us along history” 2013 - 2015 2

1. History Of Measuring Time Prehistoric man, by simple observation of the stars, changes in the seasons, day and night began to come up with very primitive methods of measuring time. This was necessary for planning nomadic activity, farming, sacred feasts, etc..

The earliest time measurement devices before clocks and watches were the sundial, hourglass and water clock.

The forerunners to the sundial were poles and sticks as well as larger objects such as pyramids and other tall structures. Later the more formal sundial was invented. It is generally a round disk marked with the hours like a clock. It has an upright structure that casts a shadow on the disk - this is how time is measured with the sundial.

The hourglass was also used in ancient times. It was made up of two rounded glass bulbs connected by a narrow neck of glass between them. When the hourglass is turned upside down, a measured amount of sand particles stream through from the top to bottom bulb of glass. Today's egg timers are modern versions of the hourglass.

Another ancient time measurer was the water clock or clepsydra. It was a evenly marked container with a spout in which water dripped out. As the water dripped out of the container one could note by the water level against the markings what time it was.

One of the earliest clocks was invented by Pope Sylvester II in the 990s. Later on chimes or bells were added as well as dials to the clocks.

Early clocks were powered by falling weights and springs. Later clocks with pendulums came into existence in 1657.

Electric clocks came into being after 1850, but were not popular until the twentieth century. An electric motor with alternating current powers these clocks. Later digital clocks with LCD (liquid crystal displays) rivaled the electric clocks. Quartz clocks use the vibrations of a quartz crystal to power the clock.

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Watches are different than clocks in that they are carried about or worn. The first watches appeared by the 1500s and were made by hand. They were very fancy and their faces were covered by fine metal strips to protect the markings. Watches were manufactured by machine in the mid 1800s.

At first watches had knobs on the outside that the wearer wound to keep the mainspring powered inside. Later on, self-winding watches derived power from the movement of the wearer. With the advent of quartz crystal watches with digital displays, the need for motors for watches has decreased.

Today's clocks and watches are increasingly digital devices, often set via satellite guidance.

Telling Time Clocks, whether on the wall, or computers, or on our wrists in the form of watches, are the standard method for measuring time. There are two basic types of clocks used today regardless of the form digital timepieces and standard. It is important to be able to read both types of timepieces.

The first example below is a digital display. It has only the numbers of the current time showing. The first number from left to right is the hour, the second the minute and the third the second. There are sixty seconds in a minute and sixty minutes in an hour. If you run your mouse over this particular display you will see the date as well. From the left is the month, next the day and finally the year.

There are also two methods for writing the time of day as there are twenty-four hours in a day. The more common method is the twelve hour method in which the time is followed by the abbreviations "a.m." and "p.m.". A.M. is an abbreviation for ante meridian and is the twelve hours from midnight until noon. P.M. is an abbreviation for post meridian and measures the hours from noon until midnight.

Thus 10:00 a.m. is ten o'clock in the mornings and 10:00 p.m. is ten o'clock at night.

2. A brief history of time measurement Ever since man first noticed the regular movement of the Sun and the stars, we have wondered about the passage of time. Prehistoric people first recorded the phases of the Moon some 30,000 years ago, and recording time has been a way by which humanity has observed the heavens and represented the progress of civilization.

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Natural Events The earliest natural events to be recognised were in the heavens, but during the course of the year there were many other events that indicated significant changes in the environment. Seasonal winds and rains, the flooding of rivers, the flowering of trees and plants, and the breeding cycles or migration of animals and birds, all led to natural divisions of the year, and further observation and local customs led to the recognition of the seasons.

Measuring time by the Sun, the Moon and the Stars As the sun moves across the sky, shadows change in direction and length, so a simple sundial can measure the length of a day. It was quickly noticed that the length of the day varies at different times of the year. The reasons for this difference were not discovered until after astronomers accepted the fact that the earth travels round the sun in an elliptic orbit, and that the earth's axis is tilted at about 26 degrees. This variation from a circular orbit leads to the Equation of Time (see 'Note 2' below) which allows us to work out the difference between 'clock' time and 'sundial time'.

Another discovery was that sundials had to be specially made for different latitudes because the Sun's altitude in the sky decreases at higher latitudes, producing longer shadows than at lower latitudes.

Today, artists and astronomers find many ways of creating modern sundials.

The progress of the sun can be recorded using the four A sundial with roman numerals. As faces of this cube. Can you Wall Sundial you look at this dial, which discover the orientation of direction are you facing? these faces?

The oldest image of a star pattern, the constellation of Orion, has been recognised on a piece of mammoth tusk some 32,500 years old.

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Prehistoric carving represent the constellation

constellation Orion is symbolized by a man standing with his right arm raised and a sword at his belt and can be seen throughout the world at different times of the year.

Orion was the sun god of the Egyptians and Phonecians and called the 'strong one' by the Arabs. In parts of Africa, his belt and sword are known as 'three dogs chasing three pigs' and the Borana people of East Africa based a sophisticated calendar on observations of star clusters near Orion's belt. Orion contains some of the brightest The three stars of Orion's belt and the stars in the southern part of the red star of his right arm can be easily winter sky in the northern said to recognised hemisphere and can be seen Orion later in the southern hemisphere.

Babylonian records of observations of heavenly events date back to 1,600 BCE. The reason for adopting their arithmetic system is probably because 60 has many divisors, and their decision to adopt 360 days as the length of the year and 3600 in a circle was based on their existing mathematics and the convenience that the sun moves through the sky relative to fixed stars at about 1degree each day.

The constellation Taurus, the bull, a symbol of strength and fertility, figures prominently in the mythology of nearly all early civilizations, from Babylon and India to northern Europe. The Assyrian winged man-headed bull had the strength of a bull, the swiftness of a bird and human intelligence.

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From about 700 BCE the Babylonians began to develop a mathematical theory of astronomy, but the equally divided 12-constellation zodiac appears later about 500 BCE to correspond to their year of 12 months of 30 days each. Their base 60 fraction system which we still use today (degrees / hours, minutes and seconds) was much easier to calculate with than the fractions used in Egypt or Greece, and remained the main calculation tool for astronomers until after the 16th century, when decimal notation began to take over.

The earliest archaeological evidence of Chinese calendars appears about 2,000 BCE. They show a 12 month year with the occasional occurrence of a 13th month. However, traditional Chinese records suggest the origin of a calendar of 366 days depending on the movements of the Sun and the Moon as early as 3,000 BCE. Over such a long period of observation, Chinese astronomers became aware that their calendar was not accurate, and by the second century CE it was recognised that the calendar became unreliable every 300 years. This problem is called Precession and was recorded by Chinese historians in the fourth and fifth centuries CE. In the fifth century CE the scholar Zu Chongzi created the first calendar which took precession into account, and the most comprehensive calendar was the Dayan Calendar compiled in the Tang Dynasty (616-907 CE) well ahead of any such development in Europe.

Precession is due to the gradual movement of the Earth's rotational axis in a circle with respect to the fixed stars.

This movement produces a slow 'wobble' which means that the positions of the stars complete a cycle of about 26,000 years.

The Earth's axis completes a circuit about once every 26,000 years

In the Mediterranean, Hipparchus made the earliest calculations of precession in about 160 BCE. The problem was taken up by astronomers in the Middle East and India who recognized that precession gradually altered the length of the year. Calendars have had to be altered regularly. In 325 CE the spring (vernal) equinox had moved to March 21.

The Emperor Constantine established dates for the Christian holidays, but Easter is based on the date of the vernal equinox which varies every year because the equinox is an astronomical event. By 1582 7

the vernal equinox had moved another ten days and Pope Gregory established a new calendar, and this change is the reason for having an extra day in every leap year. However, there are still small changes accumulating, and one day we shall have to adopt a new calendar!

Inventions for measuring and regulating time The early inventions were made to divide the day or the night into different periods in order to regulate work or ritual, so the lengths of the time periods varied greatly from place to place and from one culture to another.

Oil Lamps There is archaeological evidence of oil lamps about 4,000 BCE, and the Chinese were using oil for heating and lighting by 2,000 BCE. Oil lamps are still significant in religious practices, symbolic of the journey from darkness and ignorance to light and knowledge. The shape of the lamp gradually evolved into the typical pottery style shown. It was possible to devise a way of measuring the level in the oil reservoir to measure the passing of time.

Candle Clocks Marked candles were used for telling the time in China from the sixth century CE. There is a popular story that King Alfred the Great invented the candle clock, but we know they were in use in England from the tenth century CE. However, the rate of burning is subject to draughts, and the variable quality of the wax. Like oil lamps, candles were used to mark the passage of time from one event to another, rather than tell the time of day.

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Water Clocks The water clock, or clepsydra, appears to have been invented about 1,500 BCE and was a device which relied on the steady flow of water from or into a container.

Measurements could be marked on the container or on a receptacle for the water.

In comparison with the candle or the oil lamp, the clepsydra was more reliable, but the water flow still depended on the variation of pressure from the head of water in the container.

Improvements were made to regulate the flow by Astronomical and astrological clock maintaining a constant head of water making was developed in China from 200 to 1300 CE. Early Chinese clepsydras drove various mechanisms illustrating astronomical phenomena. The astronomer Su Sung and his associates built an elaborate clepsydra in 1088 CE. This device incorporated a water-driven bucket system originally invented about 725 CE. Among the displays were a bronze powerdriven rotating celestial globe, and manikins that rang gongs, and indicated special times of the day.

Su Sung's astronomical water clock Hour Glasses or Sandglasses As the technology of glass-blowing developed, from some time in the 14th century it became possible to make sandglasses. Originally, sandglasses were used as a measure for periods of time like the lamps or candles, but as clocks became more accurate they were used to calibrate sandglasses to measure specific periods of time, and to determine the duration of sermons, university lectures, and even periods of torture.

Sandglass 9

The Division of the Day and the Length of the 'Hour' An Egyptian sundial from about 1,500 BCE is the earliest evidence of the division of the day into equal parts, but the sundial was no use at night. The passage of time was extremely important for astronomers and priests who were responsible for determining the exact hour for the daily rituals and for the important religious festivals, so a water clock was invented.

The Merkhet The Egyptians improved upon the sundial with a 'merkhet', one of the oldest known astronomical instruments. It was developed around 600 BCE and uses a string with a weight as a plumb line to obtain a true vertical line, as in the picture. The other object is the rib of a palm leaf, stripped of its fronds and split at one end, making a thin slit for a sight.

A pair of merkhets were used to establish a North-South direction by lining them up one behind the other with the Pole Star. Viewing the plumb lines through the sight made sure the two merkhets and the sight were in the same straight line with the Pole Star. This allowed for the measurement of night-time events with a water clock when certain stars crossed the vertical plumb line (a 'transit line'), and these events could then be recorded by 'night-time lines' drawn on a sundial.

An Egyptian Merkhet. The wooden upright has a notch to use as a sight when using two plumb lines There are various theories about how the 24 hour day developed. The fact that the day was divided into 12 hours might be because 12 is a factor of 60, and both the Babylonian and Egyptian civilisations recognised a zodiac cycle of 12 constellations. On the other hand, (excuse the pun) finger-counting 10

with base 12 was a possibility. The fingers each have 3 joints, and so counting on the joints gives one 'full hand' of 12.

In classical Greek and Roman times they used twelve hours from sunrise to sunset; but since summer days and winter nights are longer than winter days and summer nights, the lengths of the hours varied throughout the year.

In about 50 BCE Andronikos of Kyrrhestes, built the Tower of Winds in Athens. This was a water clock combined with Sundials positioned in the eight principal wind directions. By then it was the most accurate device built for keeping time.

The Tower of the Winds in Athens contained a clepsydra and shows the North-East, North and NorthWest deities in this picture Hours did not have a fixed length until the Greeks decided they needed such a system for theoretical calculations. Hipparchus proposed dividing the day equally into 24 hours which came to be known as equinoctial hours. They are based on 12 hours of daylight and 12 hours of darkness on the days of the Equinoxes. However, ordinary people continued to use seasonally varying hours for a long time. Only 11

with the advent of mechanical clocks in Europe in the 14th Century, did the system we use today become commonly accepted.

Earliest mechanical clock Mechanical clocks replaced the old water clocks, and the first clock escapement mechanism appears to have been invented in 1275. The first drawing of an escapement was given by Jacopo di Dondi in 1364. In the early-to-mid-14th century, large mechanical clocks began to appear in the towers of several cities. There is no evidence or record of the working models of these public clocks that were weight-driven. All had the same basic problem: the period of oscillation of the mechanism depended heavily on the driving force of the weights and the friction in the drive.

In later Mediaeval times elaborate clocks were built in public places. This is the Astronomical clock in Prague, parts of which date from about 1410.

This mechanism illustrates a basic escapement. The Prague Astronomical Clock weight rotates the drum which drives the toothed wheel Showing the Zodiac Circles and early which gives the mechnism its "tick-tock" movement versions of the digits 2, 3, 4 and 7 The earliest surviving spring driven clock can be found in the science museum in London and dates from about 1450. Replacing the heavy drive weights with a spring permitted smaller and portable clocks and watches.

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More Accurate Mechanical Clocks Christiaan Huygens made the first pendulum clock, regulated by a mechanism with a "natural" period of oscillation in 1656. Galileo studied pendulum motion as early as 1582, but his design for a clock was not built before his death. Huygens' pendulum clock had an error of less than 1 minute a day, and his later refinements reduced his clock's errors to less than 10 seconds a day.

There was no device for keeping accurate time at sea until John Harrison, a carpenter and instrument maker, refined techniques for temperature compensation and found new ways of reducing friction. By 1761, he had built a marine chronometer with a spring and balance wheel escapement that kept very accurate time. With the final version of his chronometer, which looked like a large pocket watch, he achieved a means of determining longitude to within one-half a degree.

It was not until 1884 that a conference at Greenwich reached agreement on global time measurement and adopted Greenwich Mean Time as the international standard. Today we rely on atomic clocks for our most accurate time measurements.

The pendulum moves the lever which creates the rocking movement of the escapement

Supporting notes Note 1 When you think about the problem - we can find due South easily from the sun at midday. Looking at the night sky, we eventually deduce that there is a fixed point in the heavens around which all the stars rotate once every day (24 hours). This is where we find the 'Pole Star' (from the Great Bear or Ursa Major, measure the distance of about four lengths of the two stars at the end, 'the pointers' to find Polaris). This is the Celestial Pole - which was different for the Egyptians from today because of the phenomenon of Precession.

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Up to about 1,900 BCE the Celestial Pole was Thuban a star in the 'tail' of the constellation Draco. By 1,000 BCE it was Thuban in the constellation Ursa Minor. Today Polaris is the last star in the 'tail' of Ursa Minor Note 2 'Sun time' and 'clock time' are different. Sun time is based on the fact that the sun reaches its highest point (the meridian), in the middle of the day, and on the next day at its highest point, it will have completed a full cycle. However, the time between the sun reaching successive meridians is often different from clock time. According to clock time, from May to August, the day is close to 24 hours, but in late October the days are about 15 minutes shorter, while in mid February the days are about 14 minutes longer.

For our daily routines, it is important to have a constant 'clock time' of 24 hours. This variation is called the 'Equation of Time' and shows the relationship between sun time and clock time. The variation has two causes; the plane of the Earth's equator is inclined to the Earth's orbit around the Sun, and the orbit of the Earth around the sun is an ellipse and not a circle. The National Maritime Museum website shows two separate graphs for these causes, and a third graph where they are combined to give the full correction.

3. When Time Began: The History and Science of Sundials The earliest sundials known from the archaeological record are the obelisks (3500 BC) and shadow clocks (1500 BC) from ancient Egyptian astronomy and Babylonian astronomy.

Presumably, humans were telling time from shadow-lengths at an even earlier date, but this is hard to verify. In roughly 700 BC, the Old Testament describes a sundial — the "dial of Ahaz" mentioned in Isaiah 38:8 and II Kings. The Roman writer Vitruvius lists dials and shadow clocks known at that time. Italian astronomer Giovanni Padovani published a treatise on the sundial in 1570, in which he included instructions for the manufacture and laying out of mural (vertical) and horizontal sundials. Giuseppe Biancani's Constructio instrumenti ad horologia solaria (ca. 1620) discusses how to make a perfect sundial. They have been commonly used since the 16th century.

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Babylonians and Egyptians built obelisks which moving shadows formed a kind of sundial, enabling citizens to divide the day in two parts by indicating noon.

The oldest known sundial was found in Egypt and dates from the time of Thutmose III, about 1,500 years BC. There were two strips of stone, one that did the needle and another where the hours were marked.

After this first known sundial, we must advance to the 750 BC to have references from another sundial, and is found in several Old Testament passages that describe a sundial, that of Ahaz. A biblical reference tells how Yahweh did the shadow go back ten degrees on the dial. However, we are sure that there were other much earlier among almost all peoples of antiquity, although there is no evidence so clear as in this case.

Moreover, the earliest description and design of a concave sundial is attributed to the Babylonian Berossus in the IV century BC. The earliest sundials known from the archaeological finds are the shadow clocks (1500 BC) in ancient Egyptian astronomy and Babylonian astronomy.

Not, as incorrectly suggested, obelisks at the temples only serving as a memorial in honor of the pharaoh to whom it was devoted.

Presumably, humans were telling time from shadow-lengths at an even earlier date, but this is hard to verify. In roughly 700 BC, the [Old Testament] describes a sundial — the "dial of Ahaz" mentioned in Isaiah 38:8 and II Kings (possibly the earliest account of a sundial that is anywhere to be found in history) — which was likely of Egyptian or Babylonian design. Sundials are believed to have existed in China since ancient times, but very little is known of their history. There is an early reference to sundials from 104 BCE in an assembly of calendar experts.

Hemispherical Greek sundial from Ai Khanoum,Afghanistan, 3rd-2nd century BCE.

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4. How did ancient civilizations use sundials to tell time?

No one alive today can rightly say when early man first began telling time using the sun, moon, stars and other celestial objects. In the modern world, using these heavenly bodies for more than astrology may seem archaic, but keep in mind, much of today's calendar and timekeeping traditions have strong roots in ancient models. Back then, civilizations needed time as a matter of basic survival. For example, activities like crop planting and harvesting made it imperative to have knowledge of seasonal changes.

The first rudimentary methods of telling time involved simple observations of the natural world, perhaps by wedging sticks in the ground and monitoring the movements of the shadows. This particular experiment would have evoked the most fundamental part of a sundial, the gnomon (pronounced nom-on), which is the component that casts the shadow. It's easy to imagine this practice advancing into the use of obelisks, pillars and other megalithic clocks and calendars.

Although some of these monuments can be considered sundials, it's the small, often portable, sundial devices of the ancients that we'll be learning about in this article.

Ancient Egyptians are credited with the invention of sundials. Although obelisks were built as far back as 3500 B.C., perhaps the earliest portable sundial that has survived, often referred to as an Egyptian shadow clock, became popular around 1500 B.C. T-shaped or Lshaped with a raised end bar, these shadow clocks measured the morning hours as the sun swept overhead.

Then, they were turned around to count down the afternoon.

It's important to keep in mind that the Egyptians weren't developing methods for timekeeping in a void. The practice of studying the passage of time -- whether minutes, hours, days, seasons, years or much longer -was a passion of several ancient civilizations. Many of them were astoundingly accurate. The Sumerians, Babylonians, Egyptians, Mayans, Greeks and Chinese all devised clocks and calendars that reflect our current numerical model in a variety of aspects.

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6. The History of Sundials Sundials began as fairly simple devices, but as time passed they became more complex. Let's take a step back and examine some basic astronomy.

The Earth rotates around the sun, but it does so in an elliptical(oval) orbit, not a circular one. This means that when the sun is closer to the Earth, it appears to move faster across a sundial. In addition to this, the Earth's equator is not in line with its orbital path around the sun; it's tilted about 23.5 degrees off-kilter.

Taking the first of these two facts in hand, we find that the time given by a sundial (known sometimes as solar time or sun time) often differs from the time you'll read on your wristwatch (which can be called clock time or mean solar time). The variance can be up to about 15 minutes at different times throughout the year. This might not have been a huge cause for concern before the invention of mechanical clocks, but in the early days, sundials were often called upon to reset these timepieces when they wound down, so innovators had to alter the design of sundials slightly to accommodate.

Another astronomical factor to keep in mind has to do with the rotation of the Earth as it moves along its orbit. The idea may be hard to picture at first, so consider this: You're standing in your backyard, counting off the days from one day to the next. As the Earth is completing each of these revolutions, every 24 hours in that same period, it's also moving slowly along its orbit. Because of this orbital passage, the view from the nighttime side of the planet will see a slightly different display of stars every evening. Nowadays this phenomenon (called a sidereal day as opposed to a solar day) seems most commonly linked to the signs of the zodiac -- as it often was in ancient times -- but it was also another clue to figuring out how the sky could be used to predict events on Earth.

Two complications arise from the tilt of the Earth when it comes to sundials, having to do with longitudeand latitude. In terms of longitude, most sundials need to be set up so they're exactly parallel with the axis of the planet to function properly. For example, people in the Northern Hemisphere need to find the North Pole and aim the gnomon along that line. But don't be too fast whipping out your compass unless you plan to do some quick calculations; the magnetic North Pole is 17

shifty. To find the proper orientation you can also use the alignment of the stars; Polaris, the current North Star, lies at the north celestial pole, and that can show you the way.

7. The Evolution of Sundials Sundials may evoke impressions of primitive, outdated technologies or beautiful backyard ornaments, but that's not the full story. Even with the invention of mechanical clocks, sundials were still used as reliable time devices into the modern era. This continued use stemmed at least in part from the fact that mechanical watches still needed to be accurately reset. Yet, it's the fascination and admiration of people around the world that has really helped ensure this ancient technology's longevity.

This Roman sundial is very similar to the hemicycles created by the Greeks.

But now let's look back. Early sundials showed hours called seasonal hours. The day was divided into 12 hours, but in the wintertime, those hours were shorter than in the summer because summer days are longer. Near the equator, this difference wasn't highly pronounced, but toward the poles timekeeping fluctuated significantly for people in more extreme climes. This shows us an interesting alternative to the regimented timekeeping people in this day and age adhere to.

Sundials served a number of important functions for ancient civilizations as they became used alternatively or conjunctively to track the seasons, solstices and equinoxes. First attributed to the Greeks, sundials such as these (commonly known as hemispherical sundials or a hemispherium) used a hollowed out bowl with a pointed gnomon to tell not only time, but also seasonal information.

This was possible because the point of the gnomon specified the time of day, while the size of the shadow was indicative of the time of year. Sometimes one half of the bowl would be cut away (at which point it might be called a hemicyclium or hemicycle), but in theory, the two models worked basically the same way.

If you remember back to the last page, the tilt of the Earth leads to some pretty tricky complications when it comes to sundial design and placement. It does, however, help determine seasonal information if you know how to harness it. By placing the gnomon across a curved surface, it's possible to trace lines through the dish that correlate with the summer solstice, winter solstice and the equinoxes (which share the same path).

Many different models of sundials were made throughout the centuries in a variety of cultures, and for many, the imagination was the limit. For example, during the stagnation of the European Dark Ages, 18

Muslims used trigonometry principles to make the flat circular sundials that are arguably the most frequently seen today. They're also commonly credited as the first to propose hours of equal length, and Muslim sundials were often marked with the hours at which they prayed. These equal-length hours gradually caught on, but despite the dĂŠbut of mechanical clocks in the 1300s, seasonal hours were still frequently used for many years until they were gradually phased out by mean solar time and eventually time zones.

With innovations like these, ancient civilizations were able to keep records of past events and plan for future ones. They could formalize governmental, religious and societal activities with a unified schedule -- a legacy we have inherited and increasingly restructured to the precision accuracy of cesium atomic clocks.

7.1. Ancient Egyptian Sundial One Of The World's Oldest Ancient Egyptian Sundials Discovered!

Egyptian sundials are considered to be the first portable timepiece. Historians believe the device came into use around 1500 B.C. to measure the passage of "hours."

Sundials divided a sunlit day into 10 parts plus two "twilight hours" in the morning and evening.

When the long stem with 5 variably spaced marks was oriented east and west in the morning, an elevated crossbar on the east end cast a moving shadow over the marks.

At noon, the device was turned in the opposite direction to measure the afternoon "hours." Now a group of scientists have discovered on of the world's oldest Egyptian sundials.

During archaeological excavations in the Kings' Valley in Upper Egypt a team of researchers from the University of Basel made an in intriguing discovery.

The sundial was found while the team was clearing the entrance to one of the tombs. The researchers found a flattened piece of limestone (so-called Ostracon) on which a semicircle in black color had been drawn. The semicircle is divided into twelve sections of about 15 degrees each. A dent in the middle of the approximately 16 centimeter long 19

horizontal baseline served to insert a wooden or metal bolt that would cast a shadow to show the hours of the day.

Small dots in the middle of each section were used for even more detailed time measuring.

Significant find: After thousands of years the Egyptian sun dial was brought back to light. Credit: University of Basel

The sun dial was found in an area of stone huts that were used in the 13th century BC to house the men working at the construction of the graves.

The sundial was possibly used to measure their work hours. However, the division of the sun path into hours also played a crucial role in the so-called netherworld guides that were drawn onto the walls of the royal tombs.

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These guides are illustrated texts that chronologically describe the nightly progression of the sun-god through the underworld. Thus, the su dial could also have served to further visualize this phenomenon.

During this year's excavation in cooperation with the Egyptian authorities and with the help of students of the University of Basel over 500 mostly fragmentary objects that had been recovered in former seasons were documented and prepared for further scientific examination.

This also includes all the material of the lower strata of tomb KV 64 found in 2012.

Inside the roughly 3500 year old tomb Basel researchers had discovered a sarcophagus that was holding the mummy of a woman named Nehemes-Bastet, a temple singer during Egypt's 22nd Dynasty (approximately 945 - 712BC), according to an inscription in the tomb.

A sundial discovered outside a tomb in Egypt's Valley of the Kings may be one of the world's oldest ancient Egyptian sundials, say scientists. Dating to the 19th dynasty, or the 13th century B.C., the sundial was found on the floor of a workman's hut, in the Valley of the Kings, the burial place of rulers from Egypt's New Kingdom period (around 1550 B.C. to 1070 B.C.).

"The significance of this piece is that it is roughly one thousand years older than what was generally accepted as time when this type of time measuring device was used," said researcher Susanne Bickel, of the University of Basel in Switzerland. Past sundial discoveries date to the Greco-Roman period, which lasted from about 332 B.C. to A.D. 395.

The sundial is made of a flattened piece of limestone, called an ostracon, with a black semicircle divided into 12 sections drawn on top. Small dots in the middle of each of the 12 sections, which are about 15 degrees apart, likely served to give more precise times.

A dent in the center of the ostracon likely marks where a metal or wooden bolt was inserted to cast a shadow and reveal the time of day.

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"The piece was found with other ostraca (limestone chips) on which small inscriptions, workmen's sketches, and the illustration of a deity were written or painted in black ink," Bickel told LiveScience in an email.

Bickel and her colleagues aren't sure for what purpose the workmen would've used the sundial, though they suggest it may have represented the sun god's journey through the underworld.

7.2. Greeks The ancient Greeks developed many of the principles and forms of the sundial. Sundials are believed to have been introduced into Greece by Anaximander of Miletus, c. 560 BC. According to Herodotus, the Greeks sundials were initially derived from the Babylonian counterparts. The Greeks were wellpositioned to develop the science of sundials, having founded the science of geometry, and in particular discovering the conic sections that are traced by a sundial nodus. The mathematician and astronomer Theodosius of Bithynia (ca. 160 BC-ca. 100 BC) is said to have invented a universal sundial that could be used anywhere on Earth.

World's oldest sundial, from Egypt's Valley of the Kings (c. 1500 BC), used to measure work hours.

The Greek dials were inherited and developed further by the Islamic Caliphate cultures and the post-Renaissance Europeans. Since the Greek dials were nodus-based with straight hour-lines, they indicated unequal hours — also called temporary hours — that varied with the seasons, since every day was divided into twelve equal segments; thus, hours were shorter in winter and longer in summer.

The idea of using hours of equal time length throughout the year was the innovation of Abu'lHasan Ibn al-Shatir in 1371, based on earlier developments in trigonometry by Muhammad ibn Jābir 22

al-Harrﾄ］ﾄｫ al-Battﾄ］ﾄｫ (Albategni). Ibn al-Shatir was aware that "using a gnomon that is parallel to the Earth's axis will produce sundials whose hour lines indicate equal hours on any day of the year."

His sundial is the oldest polar-axis sundial still in existence. The concept later appeared in Western sundials from at least 1446.

The custom of measuring time by one's shadow has persisted since ancient times.

In Aristophanes' play, Assembly of Women, Praxagora asks her husband to return when his shadow reaches 10 feet (3.0 m). The Venerable Bede is reported to have instructed his followers in the art of telling time by interpreting their shadow lengths.

Greek sundial III-II century BC.

With the Greeks, sundials are studied thoroughly and for the first time, the gnomon stops of being installed vertically and passes the correct position, parallel to the Earth's axis. They developed and constructed complex sundials using their knowledge of geometry.

The watch Greek is called "scaphoid" (bowl) and consisted of a block in which a cavity was emptied hemispheres, at whose end is fixed the needle bar serving.

Put the gnomon parallel to the direction Earth's axis allowed the clock signal throughout the year the hours of a constant duration, making measuring instruments, really. In the previous vertical needle had clocks where summer hours were different from those of winter (as we have already commented above). It should also be mentioned that the scaphoid were also the first sundial that measured time by the direction of the shadow and not, as heretofore, by its length.

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In fact, almost all posterior cultures, at least, those who had direct or indirect contact with the Greeks used for their design sundials Greeks: the Romans, Arabs, Indians, Afghans and so on. The Greeks sundials used refinements like the orientation of the object that casts the shadow or gnomon, which did not have to be perpendicular to the ground, and the geometric shape of the surface on which the shadow cast, which did not have to be flat, and they got excellent precision for the time, precision of a few minutes that would not be surpassed for centuries.

In picture 2 we can see a splendid Greek sundial called Horologion or Tower of the Winds. It consists of an octagonal marble building oriented according to the cardinal points and topped with a conical dome. This building was entrusted to Andronicus Cirrus that he did in 50 BC. With the Roman domination the ancient Agora of Athens was too small for their duties and it was decided to build a new one to move their business activities of the city. This new place was endowed with this advanced sundial: the Horologion.

In the time of the ancient Greeks and Romans, the earth was considered the centre of the universe, which was itself a sphere containing all the stars. This celestial sphere rotated from east to west, carrying not only the stars but also the sun and the planets. Therefore, the sun revolved around the earth. This is what caused day and night. The earth did not rotate. For the purpose of understanding sundials, it is perfectly acceptable and convenient to adopt this geocentric view. The sun did not travel around the earth in a circle at right angles to the earth's axis (which was also the axis of the celestial sphere) as the stars did. Rather, the sun traced a circle along the celestial sphere, centred on the earth, known as the ecliptic.

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The ecliptic plane meets the equatorial plane at approximately 23.5째. This is known as the obliquity of the ecliptic. The circle of the ecliptic more or less intersects the twelve constellations of the zodiac, and the time of year (corresponding to modern months) was reckoned by what sign of the zodiac the sun was traversing. (Regardless of the exact location of the zodiac constellations, the ecliptic was divided into 12 equal arcs of 30째 each, leaving most of the constellations off-centred and often not entirely in their designated 30째 region.) The sun's motion along the ecliptic circle takes a (solar) year. The dual motion of the sun (on the celestial sphere and along the ecliptic) means that the sun follows a different path in the sky each day.

From the perspective of the northern hemisphere, during the summer, the sun is higher in the sky and remains visible for a longer period of time. Since the ancients always divided the daylight into twelve equal hours, these summertime hours were longer. In the winter months, the sun is lower in the sky and visible for a shorter period of time. Consequently, the winter hours were also shorter.

Time in the ancient world was first measured by naturally occurring events, such as sunrise, sunset, and meal times.

In the early ages of Rome and even down to the middle of the fifth century after the foundation of the city no other divisions of the day were known than sunrise, sunset and midday, which were marked by the arrival of the Sun between the Rostra and a place called Graecostasis.

The single greatest literary source that exists for the sundials of Greece and Rome is Vitruvius's Ten Books on Architecture written about 25 B.C. In Book 9, Vitruvius gives a list of a variety of dials and their inventors.

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Berosus the Chaldaean is said to have invented the semicircular one carved out of a squared block and undercut to follow the earth's tilt. The hemisphere, or scaphĂŞ, is attributed to Aristarchus of

Samos, and he also invented the disk on a plane. The Spider was invented by Eudoxus the astronomer; some say by Apollonius. The Plinth or Coffer, of which an example is set in the [region of the City known as the] Circus of Flaminius, was invented by Scopinas of Syracuse; Parmenion invented the "Sundial for Examination"; Theodosius and Andrias the sundial "For Every Climate," Patrocles the Axe, Dionysodorus the Cone, Apollonius the Quiver. The men named here invented other kinds, and many others have left us still other kinds, like the Spider-Cone, the Hollowed Plinth, and the Antiboreus ("Opposite the North"). Many, moreover, have left behind written directions for making portable and hanging versions of these kinds. Anyone who wants to may find additional information in their books, so long as they know how to set up an analemma.

Vitruvius's analemma is the system of lines and curves that denote the changing hours and months on the face of a sundial. His previous chapter is devoted to determining the analemma based upon the observance of the shadow of a gnomon at noon on the equinox. (The gnomon was the upright stick that cast its shadow on the dial face. Depending on the design of the dial, either the side of the shadow's length or the position of the tip of the shadow was used to determine the time.)

Unfortunately, Vitruvius ends his discussion of sundials with the list given above and writes of water clocks for the rest of Book 9.

Before the Greeks developed the sundial into the forms Vitruvius lists, the more ancient civilizations of Egypt and Mesopotamia had shadow measuring devices as early as 1500 B.C. Though this is the date of the earliest surviving sundials [3]:... it is possible that sundials were invented as early as the third millennium when Egyptian priests began to divide the night and day each into twelve equal parts.

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A funerary text from 1290 B.C., referring to astronomical events in the 19th century B.C., gives instructions on how to construct a "shadow stick.".

This shadow clock consisted of a base with an upright stick at one end.

Because of the angular shift in the shadow over the course of the day, it has been speculated that the upright had a crossbar added to it to widen the shadow so that it would always fall on the clock. Neither the funerary text nor surviving examples have the crossbar, though one specimen has holes on either side of its upright which may suggest such an addition.

In practice, the shadow clock needed to be rotated once a day at noon in order to be able to mark the time in both the morning and afternoon.

With the head to the east 4 hours are marked off by decreasing shadow lengths after which the instrument is reversed with head to the west to mark 4 afternoon hours.

The markings on the clock indicating the four hours were very inaccurate, and were possibly not based on observation but rather some fallacy of celestial geometry.

Sundials resembling the kind of which Vitruvius speaks were in use in Egypt from at least 1200 B.C. These were vertical hanging sundials, semicircular in shape with a horizontal gnomon at the top and centre.

"The shadow would sweep around such a dial more rapidly in the early morning and late afternoon than around midday, but the Egyptians simply divided the dial into 12 15째 sectors or 'hours'. This is perhaps the crudest order of gnomon use and provides little of either theoretical or empirical interest for the Greeks.". Further Egyptian development in timekeeping seems to have waned until the Assyrian invasion in the 7th century B.C. A near complete sundial was found at Kantara, Egypt dating back to approximately 320 B.C., well over a thousand years after the shadow clocks were in operation.

The gnomon was a perpendicular block rising at the foot of the sloping face, its height and width being the same as those of the latter. On one side was an arrangement whereby a 27

plummet could be hung so as to swing free of the base. The instrument was put down on a flat surface, and whenever it was to be used, was turned so that it faced the sun directly. The shadow of the gnomon then fell upon the face. The spaces marked off by the parallel lines running from top to bottom of the face showed where the shadow was to be read during the different months of the year, starting with the summer solstice at one edge and turning back again with the winter solstice at the other.

Along the face was a set of obliquely drawn lines sloping from the winter solstice edge to the summer solstice edge.

At six in the morning the shadow would strike the top of the dial; as the sun rose higher the shadow would decrease in length until at noon it touched the lowest line; it reached the top of the dial again at six in the evening.

This sundial and others of similar design that survive today are not terribly accurate.

In the Greek world, the earliest sundials "consisted of a gnomon in the form of a vertical post or peg set in a flat surface, upon which the shadow of the gnomon served to indicate the time.". This is as opposed to modern designs that have their gnomon slanted parallel to the earth's axis. In this modern system, lines on the dial face denoting the hours issue from a central point and remain straight. It is the shadow of the edge of the gnomon lying on these lines that gives the time. Seasonal variations are practically immaterial.

The curves traced out on the dial of such a sundial may have led to the discovery of the conic sections, as attributed to Menaechmus in the fourth century B.C. The sun traces a circular path in the sky in its daily motion. The tip of the gnomon is the vertex of a cone with the sun's rays as elements, and since the dial plane cuts the cone, the shadow path is a conic section. If Menaechmus or someone else marked this path with a series of dots on a given day, he would 'discover' a hyperbola.

The paths of the tip of the gnomon's shadow as traced out on these horizontal sundials formed a pattern resembling an axe called a pelekinon (derived from the Greek word for axe).

The pattern consisted of a hyperbola tracing the shadow's path at the winter solstice, a second for the summer solstice, and a straight east-west line in between marking the equinoctial shadows. A line from the base of the gnomon at the south of the dial running due north denoted noontime. (Since the shadow of the tip of the gnomon was the time telling device, the gnomon may have been inclined. The angle of the gnomon is irrelevant.[9] In such a dial, the noon line would run from the base of a perpendicular line between the gnomon's tip and the dial surface.) The hyperbolae were centred on this noon line.

The winter hyperbola opened north, the summer hyperbola south (assuming the dial is in the northern hemisphere). In addition to the centre noon line, additional oblique lines were added on either side to denote the hours of daylight before and after noon Both Vitruvius and Ptolemy describe analemmas which for given solar positions serve to determine length and direction of the shadow cast by a gnomon on the face of a planar sundial.

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Specifically, in his book, 'On the Analemma', Ptolemy gives methods for deriving, both by trigonometric and also by graphic means, three pairs of spherical coordinates for the sun relative to a given place on earth, given solar declination, terrestrial latitude, and hour of the day. Though he does not say so explicitly, each pair of spherical coordinates is singularly suited for finding the length and direction of a gnomon's shadow for a type of plane sundial.

To complicate matters, the exact specifications of a sundial's network of curves varied with the sundial's latitude. If mathematical means were used to create the pattern on a sundial, it should be expected that the intended latitude would be taken into account. However, sundials have been found in latitudes that vary as much as 7 degrees latitude (a distance of over 700 kilometres). The most significant instance of such a discrepancy was the sundial that was the first official timepiece of Rome.

The Romans captured a sundial during a war on Sicily in 264 B.C. Notwithstanding the difference of about 4 degrees latitude, the sundial served Rome for almost one hundred years before a new dial calibrated for the city was set up. This was despite the time being in observable error.

Although the shadow of a stick in the ground appears to be the simplest form of timekeeper, the horizontal dial is more complex to mark off into the hour spaces for the temporary hour system than are the dials of spherical or conical section ... since a basic understanding of the origins of the hyperbolic shadow paths on the plane surface is necessary in order to adapt the geometrical figure needed to make it.

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The geometrical figure is the analemma which Vitruvius spoke of above. The analemma is the:... projection of the celestial sphere into one plane, from which in turn the positions of the hours on the dial's surface were deduced. Vitruvius describes the basic figure ... though his text at this point is somewhat obscure and he may well have not clearly understood what he was describing in any case.

After describing how the equinoctial line can be found, as well as the point of noon on the solstices, Vitruvius closes his thoughts on the analemma as follows.

Once this construction has been drawn and executed as specified, for the winter lines and for the summer, for the equinoctial lines and the monthly lines, then, in addition, the system of hours should be inscribed along the form of the analemma. To these can be added many varieties and kinds of sundial, and they are all marked off by these inventive methods. However, the result of all these figures and their delineation is identical: namely, that the day at the equinox and at the winter solstice, and again at the summer solstice, is equally divided into twelve parts. Therefore, I have not chosen to omit these matters as if I were deterred by laziness, but so as not to cause annoyance by writing too much ... . Therefore I shall simply tell about the kinds that have been handed down to us, and by whom they were invented.

Vitruvius's dismissiveness supports the claim that he did not fully understand the adaptation of the analemma to the sundial. And though he states that any sundial can be constructed from the analemma, it is only later authors who give the details of such constructions.

Whilst the initial construction required a greater effort, the ease with which day and hour lines could be drawn made spherical sundials in antiquity more popular than their flat counterparts.[9] The basic principle of the spherical sundial was that it mirrored the celestial sphere in which the sun travels.

The basic construction involved hollowing out a hemisphere (or smaller wedge of a sphere) with its top parallel to the horizon.

A gnomon was set up so that its point was at the centre of the hemisphere flush with the plane of the horizon. On any given day, the shadow cast by the tip of the gnomon would trace out the arc of a circle on the surface of the dial.

The arc of the summer solstice was farthest towards the bottom of the hemisphere. As the seasons shifted toward winter, these arcs were closer and closer to the upper edge of the hemisphere. These daily arcs were all parallel, and the arc of the equinox was half of a circle with the same centre as the hemisphere (a great circle).[8] The hour lines were not circular curves, with the exception of those at the horizons (marking sunrise and sunset) and the noon line. These were great circles which ran perpendicular to the equinoctial circle 30

In spite of their noncircular nature, for latitudes below 45° which includes the whole of the Mediterranean Sea] the seasonal hour lines between meridian and horizon are very closely approximated by the great circles which do pass through corresponding seasonal hour points on solstitial and equinoctial curves. The engraved hour lines on preserved spherical sundials appear to be such great circle approximations. The deviation of the hour lines from great circles cannot even be detected on the few dials where more than three day curves have been divided.

Thus the marking of the hour lines needed neither careful observations nor complicated mathematics. All that was needed was to divide the area of the hemisphere that received the gnomon's shadow into twelve equal parts using great circles, in much the same way as a modern globe is divided into lines of longitude. To simplify the spherical dial even more, the day curves did not need to correspond to the equinoxes or solstices if the dial's only purpose was to act as a clock. Two or three parallel circular arcs were all that were needed for ease of reading (being the corresponding lines of "latitude"). Several examples of such dials were found in such sites as Pompeii, Herculaneum, Ostia, and Rome. It was only when the dial was to serve as a calendar that these lines needed to correspond to the equinoxes and solstices.

7.3 Romans The Romans adopted the Greek sundials, and the first record of a sun-dial in Rome is 293 BC according to Pliny. Plautuscomplained in one of his plays about his day being "chopped into pieces" by the ubiquitous sundials. Writing in ca. 25 BC, the Roman author Vitruvius listed all the known types of dials in Book IX of his De Architectura, together with their Greek inventors. All of these are believed to be nodus-type sundials, differing mainly in the surface that receives the shadow of the nodus.  the hemicyclium of Berosus the Chaldean: a truncated, concave, hemispherical surface  the hemispherium or scaphe of Aristarchus of Samos: a full, concave, hemispherical surface  the discus (a disc on a plane surface) of Aristarchus of Samos: a fully circular equatorial dial with nodus  the arachne (spiderweb) of Eudoxus of Cnidus or Apollonius of Perga: half a circular equatorial dial with nodus 31

       

the plinthium or lacunar of Scopinas of Syracuse: an example in the Circus Flaminius) the pros ta historoumena (universal dial) of Parmenio the pros pan klima of Theodosius of Bithynia and Andreas the pelekinon of Patrocles: the classic double-bladed axe design of hyperbolae on a planar surface the cone of Dionysodorus: a concave, conical surface the quiver of Apollonius of Perga the conarachne the conical plinthium  the antiboreum: a hemispherium that faces North, with the sunlight entering through a small hole.

The Romans built a very large sundial in 10 BC, the Solarium Augusti, which is a classic nodus-based obelisk casting a shadow on a planar pelekinon.

The Romans first used the sun's movement to measure the passage of time. Using this method they could precisely measure only sunrise, midday, and sunset, but they used the length of shadows to estimate other times of the day. The introduction of the sundial gave the Romans a new tool to better measure time. Travelers from Sicily brought the sundial to Rome in 263 B.C. and set it up in the Forum, where it became a popular meeting place.

People came to check the time, to socialize, and "to see and to be seen." Other sundials were set up in public buildings or squares. Only the wealthy could afford to have one in their own homes and it quickly became a status symbol. Most people still just used the sun and its movements. The sundial enabled the Romans to divide the day into 12 equal parts, or hours.The hours became a way to mark time and meetings. Courts opened at about the third hour, for example, and lunch was at midday, the sixth hour. People would go home to eat a leisurely lunch and take a siesta, returning to work in a few hours. People in Rome today still leave work at 1:00 and return to work from 4:00 to 7:00.

Picture: sundial

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sunrise solis ortus midday meridies sunset

solis occasus

The day was divided into ante meridiem (before midday) and post meridiem (after midday.) These divisions are still used today and abbreviated a.m. and p.m. first hour (prima hora)

about 7:00 a.m.

Sixth hour (sexta hora)

midday

Twelfth hour (duodecima hora) hour before sunset (about 6:00 p.m.)

The Waterclock The sundial was not the only clock the Romans used. The water clock (clepsydra) was a container with a hole that water flowed out of to mark the passing of time. The inside of the container was marked with "hour" marks which the water passed by. Another variation used a floating rod that ascended to mark the time of day. The water flow began to be used to move hands, bells and even cuckoo birds. The water clock was used to control speakers' times in the Senate. When the water ran out, the speaker's time was up. In case a speech was interrupted, wax was used to stop the water momentarily. Two water clocks equaled about one hour. This water clock was also used to keep time in races. Like the sundial, only the rich could afford to have one.

Picture: waterclock

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The Romans copied the Greek scaphoid, which he called hemispherium. The ancient Romans, from the scientific point of view, did not add anything new with regard to measuring time, continued to use sundials developed by the Greeks.

Pliny the Elder in his Natural History relates the history of the sundial that Emperor Augustus ordered to build in the Campus Martius, using an Egyptian obelisk of Pharaoh Psamtik II, called the Solar Clock Augustus or Augustus Meridian.

Picture: Drawing of the Augustus meridian can be seen in the Champ de Mars, close where the sundial was.

Picture: The Agrippa Pantheon in Rome. The hole in the roof acts as a sundial (I century BC).

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On the astronomical content found in the architecture of the Pantheon in Rome, built by Agrippa in the first century BC, there is no doubt. But now some researchers argue that the Roman building acts as a huge sundial (Picture 4).

According to Roman architect and engineer Vitruvius, were used at least thirteen different types of sundials. Vitruvius wrote a book about gnomonics in which he describes a geometric method for designing sundials called analemma.The Roman Empire's decline and fall because of the barbarian invasions, led in Occident a long period of intellectual darkness.

In the early centuries of the Christian era, the gnomonic, dimly lighted by studies of Hellenistic astronomy is entering a decline that characterizes the entire science of European medieval cultural and economic. There are few items (mostly archaeological) we can find; there are just written to show further progress. Although in this period to the general public cared little time measurement, there are no precise scientific descriptions. However, as oddities at the time, there were two surveyors: the Venerable Bede and Higinio Gromat (II century).

Picture: Sundial on the south facade of stone in the church of Revilla (Huesca, Spain).

You need to wait until feudalism assist the dissemination of sundials on the European continent. It was the religious order Benedictine (529 AD) and his dedication to comply with the schedule dictated by its founder, what encouraged these monks to study the construction of sundials.

Since its origin, the Catholic Church wanted to sanctify certain times of the day with a common prayer. The gnomonic of these centuries led to the construction of Mass clocks or watches of canonical hours and in them the hours of prayer were indicated. These watches are generally located in the southern facades of churches or monasteries.

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First sundials carved on the stone facades of churches and cathedrals are starting to appear early VIII century. In the year 1000 horizontal sundials were constructed for which holes were used in the vaults of cathedrals. In the IX century Arabic astronomy comes in. The caliphate of Al Mamun marks the beginning of an intense cultural activity would continue in later centuries with writers such as Averroes, Ibn Thabit Qurraa (826-901) and Al-Biruni (973-1048) as example. While Christian Europe at the time followed the works of the Venerable Bede, the Arabs had a hectic continued intellectual activity from the destruction of the Alexandria Library. It is only from the X century when Europe begins to look timidly vast compilation of ancient knowledge work done by the Arabs.The majority of Arabs watches were flat at that medieval times, constructed of marble or copper plates.

They all have an indication of the direction of the Kaaba in Mecca because of the religious precept of praying with the face turned to that place regardless of where they are located.

Picture: Sundial at the Sidi Okba Mosque in Kairouan (Tunisia).

Picture: Sundial at the garden of Topkapi Palace in Istanbul (Turkey).

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The XI century, a German mathematician who knows the Arabic language, wrote a treatise on the astrolabe retaining some Arabic terminology. In this treaty are some indications for the shepherd's sundial. The translation of two Arabic manuscripts gnomonic was most important cultural advance of the time in this field.

Picture 8: Cathedral of Teruel. Two sundials, one south facing and one west. Teruel Cathedral began to be built in the Romanesque style in 1171 and concluded with the establishment of the Moorish tower in 1257. It is one of the most characteristic Moorish buildings in Spain.

Picture: Sundials of the Terual Cathedral; in the south facing right and the left of the west face.

In the XIII century in Spain, King of Castile Alfonso X the Wise put together in the city of Toledo a large group of Christians, Greek, Hebrew and Arabic astronomers to translate into Latin many of the works written in Arabic. Thus the Arabic knowledge spread throughout Europe to leave 37

behind all the cultural obscurantism in which it was immersed. Also the gnomonic was developed, like all sciences.

In the XIV century, the first mechanical clock is made. It is a large iron-framed structure, driven by weights. The function of the first European clocks was not to indicate the time on a dial, but to drive dials that give astronomical indications, and to sound the hour. They are located in monasteries and public bell towers. The earliest surviving example, constructed in 1386, is in Salisbury Cathedral, England. Mechanical clocks utilize equal hours.

In Spain during the reign of Enrique III, in 1400, the first mechanical watch with bells was installed in the tower of the church of Santa Maria de Sevilla.

The following centuries were the great age of the European sundial. In the XV century a great effort was made in Europe by the divulgation of the Gnomonic. Sundials with equal hours gradually come into use.

In the American colonies were built many sundials, some of which are still preserved. In the tropics you have to build a double disc with time.

The south-facing disk is used for part of the year, from August to April, and the disk on the other side facing north would use the rest of the year. Two days a year, when the Sun passes directly above the site hours can be seen on both sides.

By the mid-XVI century the first mechanical clocks appear. It is in the XVII when these devices are refined and slowly getting more accurate operation.

7.4. Renaissance In medieval and early modern Europe the sundial was by far the most commonly used instrument for determining the time. From the 16th to the 18th century the steady flow of books and manuals on sundials and their use produced by mathematicians, astronomers and instrument makers attests to the popularity of this instrument and the great variety in its design and construction. Even the development of the mechanical clock from the 14th century onwards by no means made the sundial obsolete, despite improvements in the second half of the 17th century with the introduction of the pendulum and the balance-spring. Until far into the 19th century, an accurate sundial was essential for regularly checking and adjusting the rate of mechanical timekeepers.

Sundials can commonly be divided into two groups: 1) Altitude dials: here the time is determined from the sun's altitude (i.e. angle above the horizon).

In some cases the dial has to be properly oriented to the compass directions, in other cases the dial has to be aligned to the sun.

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2) Direction dials: here the time is determined from the sun's azimuth (compass direction) or hour angle (the angle along its daily arc before or after the meridian passage). In most cases the dial has to be correctly oriented and for that purpose a magnetic compass is often incorporated in the instrument.

Altitude dials can be further subdivided into: i. ii.

iii.

iv.

Plane dials: the sun's shadow or pinhole image is cast on a set of hour lines inscribed on a horizontal, vertical or arbitrarily inclined flat surface.

Cylinder dials: the surfaces bearing the hour lines can be either convex or concave. A common example of this type is the shepherd's dial. Another term for instruments in this category is pillar dial.

Scaphe dials: the hour lines are inscribed on the inner surface of a spherical or a conical cup.

Ring dials: the sun's pinhole image is projected on a set of hour lines inscribed on the inner surface of a thin cylindrical ring.

Direction dials subdivided into:

can be further

i) Horizontal dials: the hour lines are laid out on a horizontal plane surface and all converge to the foot of the gnomon that is directed to the celestial pole. ii) Vertical dials: similar to above, with the hour lines laid out on a vertical plane surface that usually faces south. iii) Polar dials: dials with a gnomon directed to the celestial pole with hour lines laid out on a plane surface with an arbitrary inclination (i.e. neither horizontal nor vertical). iv) Equinoctial dials: here the hour lines are equally spaced and are inscribed either on a plane surface parallel to the celestial equator or on a spherical or cylindrical surface with a symmetry axis perpendicular to the same. Dials under this class include the globe dial, the universal dial, the self-setting dial, the mechanical dial, the astronomical ring-dial, the universal ring-dial, the crescent dial and the crucifix dial. v) Azimuthal dials: in this type the dial is oriented in such a way that the sun's shadow falls along a specified line, the hour is then indicated by the needle of an in-built compass. vi) Multiple dials: these include dials with two or more sets of hour lines laid out on multiple plane surfaces, such as diptych dials, polyhedral dials and dials in compendia.

In additional to conventional sundials, it is also possible to have moon or lunar dials, usually in the form of a sun and moon dial. In principle, a sundial can also be used during the night, provided that the moon is sufficiently bright and that the lunar age is known. The 'solar time' can then be obtained from the 'lunar time' (both expressed in equal hours) by adding four-fifths of an hour for each day of the 39

lunar cycle. In a moondial the correction is effected automatically by adjusting the hour scale for the lunar age.

The onset of the Renaissance saw an explosion of new designs. Giovanni Padovani published a treatise on the sundial in 1570, in which he included instructions for the manufacture and laying out of mural (vertical) and horizontal sundials. Also, Giuseppe Biancani published (1620) other treatise where discusses how to make a perfect sundial with accompanying illustrations. In the XVIII century clocks and watches begin to replace sundials. They have advantage of not requiring sunny skies. There are, however, often unreliable and depend upon sundials to set the true time. In the early 1800’s mechanical clocks become accurate enough and inexpensive to displace sundials as timepiece of choice.

At present, although the accuracy of mechanical clocks outweighed sundials, they continue be built, primarily as a decoration on buildings, monuments and public places. They are constructed of many types with precision and beautiful designs.

Picture: Modern equatorial sundial in Tarragona (Spain).

Picture: Vertical sundial faced to the west a private house in GraĂąen, Huesca (Spain).

40

As a result of this technological support, are living the revival of this ancient instrument for measuring time in recent years, but as mentioned above, its function is currently not precisely what sundial was born but only as a decoration.

7.5 Arabic According to Muslim beliefs, the salat times were taught by Allah to Muhammad. Prayer times are standard for Muslims in the world, especially the fard prayer times. They depend on the condition of the Sun and geography. There are varying opinions regarding the exact salat times, the schools of Islamic thought differing in minor details. All schools agree that any given prayer cannot be performed before its stipulated time. The five prayers are Fajr (pre-dawn), Dhuhr (midday), Asr (afternoon), Maghrib (sunset) and Isha’a (night). Thus a keen interest was instilled in devout Muslims about the time and direction needed for prayers. The beautiful Arabic astrolabe shown above is made of brass inlaid with silver and copper by Abd al-Karim al-Misri from 1235-1236 CE. Abu Abdallah Muhammad ibn Ibrahim al-Fazari (died 796 or 806) is credited with the first astrolabe in the Islamic world in the 8th century. While some sources refer to him as an Arab, other sources state that he was a Persian. Al-Fazārī translated many scientific books into Arabic and Persian.

Reverse Side Brass Arabic Astrolabe Inlaid with Copper and Silver by Abd al-Karim al-Misri from 1235-1236 CE. British Museum Number 1855,0709.1 41

The astrolabe is an object probably invented by the Greeks in the 2nd century BC. Knowledge of it was transmitted to the Muslims through the translation of Hellenistic and Byzantine texts into Arabic.

The translation of scientific texts was done in Baghdad in the early Abbasid era, and the earliest astrolabes and astrolabe treatises date to the 9th century. The astrolabe provides a two-dimensional map of the heavens and it served in particular to find the direction of Mecca which Muslims face when they pray, and was used to determine the times of the times of prayer which were astrologically defined. This extremely important example has figural designs representing the constellations on the front and back. It gives the name of the artist who made it ,”Abd al-Karim”, who is known through other signed astrolabes. This instrument is noted as an early example of a “royal” astrolabe, similar to one signed by the same maker in the Oxford MHS.

Brass Astrolabic Quadrant by by Muhammad Bin Ahmad al-Mizzi 1333-1334 CE. British Museum Number 1888,1201.276, London

Muhammad Bin Ahmad al-Mizzi Signiture, British Museum, London 42

Brass Astrolabic Quadrant by by Muhammad Bin Ahmad al-Mizzi 1333-1334 CE. British Museum Number 1888,1201.276, London This brass astrolabic quadrant, a Quadrans Novus or astrolabe/almucantar quadrant, was made for latitude 33 degrees 30 minutes (i.e. Damascus) from 1333-1334 by Muhammad Bin Ahmad alMizzi. An inscription on the front says that the quadrant was made for the ‘muwaqqit’ (literally: the timekeeper) of the Great Umayyad Mosque of Damascus. The earliest known description of an astrolabe reduced to a quadrant with no moving parts was in 1288 by the Jewish man Jacob ben Mahir ibn Tibbon (1236-1304), more widely known by his Latin name of Prophatius Judaeus or Profeit Tibbon from Montpellier. Tibbon’s treatise was quickly improved by Peter Nightingale whose account received wide distribution. The instrument was quickly named the quadrans novus (new quadrant) to differentiate it from the traditional quadrant or quadrans vetus (old quadrant).

The basic idea behind the idea of the quadrans novus is that the stereographic projection that defines the components of a planispheric astrolabe is just as valid if the astrolabe parts are folded into a single quadrant. The result is an instrument that can perform many of the functions of a standard astrolabe at much lower cost, but without the intuitive representation of the sky provided by the rotating rete. It is not clear how popular the astrolabe quadrant became as few examples survive. The arcs reproduce the ecliptic and horizons of a circular astrolabe folded over the East-West line and then 43

folded again about the meridian. Additional arcs are provided to determine the unequal hours and to find the sines and cosines of angles.

The astrolabe quadrant is equipped with with a thread (usually of silk) with one end attached at the north pole and a weight on the other end. A bead or pearl can be slid up and down the thread to mark positions on the face of the instrument. The thread can be moved to any position on the face of the quadrant to simulate the rotation of the astrolabe rete.

Quadrans Vetus by John of Montpellier 1276. Sotheby’s 2004 This is the book “Quadrans vetus”, a technical manual on the construction and use of the ‘old quadrant’, as distinct from the astrolabe-quadrant, or quadrans novus. The text was written in Montpellier, c.1250-80 (perhaps in 1276), and it is variously ascribed to Johannes Anglicus, John of Montpellier or to Robertus Anglicus. It gives a careful account of how to construct a quadrant, an instrument of Arabic origin which found its way into the West in the twelfth century, used in surveying and for measuring time from observations of the sun. Apparently Montpellier was a center of astrological scholarship.

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Rare Quadrans Vetus with Adjustable Lattitude 14th Century. British Museum 1972,0104.1 This undated and unsigned instrument is a rare example of a quadrans vetus with markings for unequal hours and a movable scale with months and zodiacal signs so that the quadrant can be used at a wide range of latitudes. The quadrant’s design is very similar to the instrument described in a manuscript by John of Montpellier written before 1350 which I discussed above. The Gothic letters and numerals of the original inscriptions make it likely that the quadrant was made in the 14th century.

The letter forms resemble those found on a number of early English instruments. British Museum number 1972,0104.1.

Horary quadrant for a latitude of about 51.5° as depicted in an instructional text of 1744.

45

An anonymous manuscript on various forms of the universal horary quadrant (not fixed to a single latitude) in the Egyptian National Library in Cairo from the 9th century might have been by the celebrated ninth-century astronomer Abū Ja’far al-Khwārizmī, who also authored the earliest known treatises on the horary quadrant or quadrant vetus for a specific latitude and the sine quadrant. It predates the entire Latin quadrant vetus tradition.The figure above shows a horary quadrant for a latitude of about 51.5° as depicted in an instructional text of 1744: To find the Hour of the Day: Lay the thread just upon the Day of the Month, then hold it till you slip the small Bead or Pin-head [along the thread] to rest on one of the 12 o’Clock Lines; then let the Sun shine from the Sight G to the other at D, the Plummet hanging at liberty, the Bead will rest on the Hour of the Day.

Arabic Quadrant Astrolabe by Muhammad al-Sakasi al-Jarkasi 1891-1892. British Museum Number 1997,0210.1, London

Arabic Quadrant Astrolabe by Muhammad al-Sakasi al-Jarkasi 1891-1892. British Museum, London 46

This belongs to a type of quadrant astrolabe which an official or merchant might have used in the Ottoman empire in the 18th and 19th centuries. In the small rectangular panel on the back there is a perpetual calendar calculated for the Islamic lunar year. Its earliest date is 1891 CE (AH 1308) and it has the idiosyncratically Turkish feature of being calculated for cycles of eight years.

Brass Celestial Globe Inlaid with Silver Stars from Mosul 1271. British Museum, London Science was considered the ultimate scholarly pursuit in the Islamic world, and it was strongly supported by the nobility. Most scientists worked in the courts of regional leaders, and were financially rewarded for their achievements. In 830, the Khalifah, al-Ma’muun (813-833), founded Bayt-al47

Hikman, the “House of Wisdom”, as a central gathering place for scholars to translate texts from Greek and Persian into Arabic. These texts formed the basis of Islamic scientific knowledge and in 829 he established the first permanent astronomical observatory in the world. 







One of the greatest Islamic astronomers was al-Khwarizmi (Abu Ja’far Muhammad ibn Musa Al-Khwarizmi), who lived in the 9th century and was the inventor of algebra. The first major Muslim work of astronomy was Zij al-Sindh by al-Khwarizmi in 830. He constructed a table of the latitudes and longitudes of 2,402 cities and landmarks, forming the basis of an early world map.

Around the same time, the Persian Al-Farghani wrote Elements of Astronomy (Kitab fi alHarakat al-Samawiya Jawami Ilm wa al-Nujum), a book based on the Ptolemaic astronomy. It is said that Dante got his astronomical knowledge from al-Farghani’s books.

Around the end of the ninth century, the dominant figure is the Arabic astronomer Al-Battani who observed the sky from Syria and took measurements remarkably accurate for the time. He determined the length of the solar year, the value of the precession of the equinoxes and the obliquity of the ecliptic. He also established a catalog of 489 stars.

In the late 10th century, a huge observatory was built near Tehran, Iran by the astronomer alKhujandi. In Islamic astronomy, Khujandi worked under the patronage of the Buwayhid Amirs at the observatory near Ray, Iran, where he is known to have constructed the first huge mural sextant in 994 AD, intended to determine the Earth’s axial tilt (“obliquity of the ecliptic”) to high precision and was the first astronomer to be capable of measuring to an accuracy of arcseconds.

40 Meter Fakhri Sextant Observatory built by Ulugh Beg in Samarkand 15th Century. Wikipedia In the eleventh century the Persian Omar Khayyam, today best known for his poetry, was also interested in various subjects, particularly algebra and astronomy. I have to name the book, The Rubáiyát of Omar Khayyám, one of my favorites, is the title that Edward FitzGerald gave to his translation of a selection of poems, originally written in Persian and of which there are about a thousand, attributed to Omar Khayyám (1048–1131). He compiled many astronomical tables and performed a reformation of the calendar which was more accurate than the Julian and came close to the Gregorian. An amazing feat was his calculation of the year to be 365.24219858156 days long, which is accurate to the 6th decimal place!

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An observatory was built by Ulugh Beg in Samarkand, in the Timurid Empire (15th century), present day Uzbekistan Ulugh Beg (1394-1449) in which was constructed the “Fakhri Sextant” that had a radius of 40 meters. Seen in the image above, the arc was finely constructed with a staircase on either side to provide access for the assistants who performed the measurements on star positions.

Sundial, Compass and Quibla Indicator by Bayrām Ibn Ilyās 1582-1583. British Museum, London

Sundial, Compass and Quibla Indicator by Bayrām Ibn Ilyās 1582-1583. British Museum, London 49

A Qibla compass or qiblah compass (sometimes also called qibla/qiblah indicator) is a modified compass used by Muslims to indicate the direction to face to perform ritual prayers. In Islam, this direction is called qibla, and points towards the city of Mecca and specifically to the Ka’abah.

While the compass, like any other compass, points north, the direction of prayer is indicated by marks on the perimeter of the dial, corresponding to different cities. To determine the proper direction, one has to know with some precision both the longitude and latitude of one’s own location and those of Mecca, the city toward which one must face. The outermost circle along the rim is divided into 72 sectors that give the names of cities and regions in the Islamic World, all written in black with the exception of Qustantinīa (Istanbul) which is written in red. Each sector contains at least two, often more names, separated from each other by gold dots. Presumably, one finds the city one wants and determines the direction of Mecca from the markings around the compass.

Sundial, Compass and Quibla Indicator by Bayrām Ibn Ilyās 1582-1583. British Museum, London The inside of the main box is laid out in various concentric circles, separated from each other by gold and blue. In the center is a schematic depiction of the Ka’ba in black and gold, surrounded by a red fence. A line drawn in gold from north to south intersecting with the fence and the Ka’ba is labelled in black khatṭ ̣al-zawāl (meridian line). The red sail-shaped feature between the Ka’ba and a small compass in the upper part of the instrument is a sundial that enables the user to find the time of the ‘asr prayer in the afternoon. It is labelled 1 to 4 in Arabic numerals (١, ٢, ٣ and ٤) and is laid out in so-called ‘unequal hours’ (that is the length of daylight between sunrise and sunset divided into twelve parts whose length changes over the course of the year). To the right of the first hour curve is a red inscription arba’a sā’āt (= four hours, i.e. before the ‘asr prayer). You can also use the sundial inscribed on the concentric circles.

50

Silver and Shagreen Triple Cased Verge Watch for the Turkish Market with Stylized Arabic Numbers

by Josiah Bartholomew, London 1815. British Museum, London

Triple Cased Verge Watch for the Turkish Market with Stylized Arabic Numbers by George Prior 1794. British Museum, London 51

The Hindu-Arabic numerals were invented in India between the first and fourth century and were thus called “Hindu numerals” by the Persian mathematician Khowarizmi. They were later called “Arabic” numerals by Europeans, because they were introduced in the West by Arabized Berbers of North Africa.

Hindu-Arabic Numbers Today’s numbers, also called Hindu-Arabic numbers, are a combination of just 10 symbols or digits: 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. These digits were introduced in Europe within the XII century by Leonardo Pisano (aka Fibonacci), an Italian mathematician. L. Pisano was educated in North Africa, where he learned and later carried to Italy the now popular Hindu-Arabic numerals.

Arabic Telephone Keypad.

52

Even today Arabic numbers differ from western numbers. Above is a telephone keypad with Arabic numbers.

During the period when Western civilization was experiencing the dark ages, between 7001400 CE an Islamic empire stretched from Central Asia to southern Europe. Scholarly learning was highly prized by the people, and they contributed greatly to science and mathematics. Many classical Greek and Roman works were translated into Arabic, and scientists expanded on the ideas. A significant number of stars in the sky, such as Aldebaran and Altair, and astronomical terms such as alhidade, azimuth, and almucantar, are still referred to by their Arabic names. A large corpus of literature from Islamic astronomy remains today, numbering approximately 10,000 manuscripts scattered throughout the world. Perhaps the most fascinating aspect of Islamic astronomy is the fact that it built on the sciences of two great cultures, the Greeks and the Indians. Blending and expanding these offen different ideas led to a new science which later profoundly influenced Western scientific exploration beginning in the Renaissance. I hope you have enjoyed this long but I hope interesting introduction to Arabian astronomy.

8. Theory "Sun time" and "clock time" Sundials tell "sun time". Clocks and watches tell "clock time". Neither kind of time is intrinsically "better" than the other - they are both useful and interesting for their separate purposes.

"Sun time" is anchored around the idea that when the sun reaches its highest point (when it crosses the meridian), it is noon and, next day, when the sun again crosses the meridian, it will be noon again. The time which has elapsed between successive noons is sometimes more and sometimes less than 24 hours of clock time. In the middle months of the year, the length of the day is quite close to 24 hours, but around 1 September the days are only some 23 hours, 59 minutes and 41 seconds long while around Christmas, the days are 24 hours and 31 seconds long.

"Clock time" is anchored around the idea that each day is exactly 24 hours long. This is not actually true, but it is obviously much more convenient to have a "mean sun" which takes exactly 24 hours for each day, since it means that mechanical clocks and watches, and, more recently, electronic ones can be made to measure these exactly equal time intervals.

Obviously, these small differences in the lengths of "sun days" and "mean days" build up to produce larger differences between "sun time" and "clock time". These differences reach a peak of just over 14 minutes in mid-February (when "sun time" is slow relative to "clock time") and just over 16 minutes at the beginning of November (when "sun time" is fast relative to "clock time"). There are also two minor peaks in mid-May (when "sun time" is nearly 4 minutes fast) and in late July (when sun time is just over 6 minutes slow) (These minor peaks have the fortunate effect, in the Northern hemisphere, that the differences are relatively minor during most of the months when there is a reasonable amount of sunshine).

The differences do not cumulate across the years, because "clock time" has been arranged so that, over the course of a four year cycle including a leap year, the two kinds of time very nearly come back to the same time they started. (The "very nearly" is because "clock time" still has to be adjusted by not having a leap year at the turn of each century, except when the year is exactly divisible by 400, 53

so 1900 was not a leap year, but 2000 will be). Even with this correction, we had an extra second added to "clock time" recently.

The reasons for these differences are discussed below, followed by some information on what the differences are at given times of year.

8.1 Why the days are of different lengths These differences arise from two quite separate causes. The first is that the plane of the Equator is not the same as the plane of the Earth's orbit around the sun, but is offset from it by the angle of obliquity.

The second is that the orbit of the Earth around the sun is an ellipse and not a circle, and the apparent motion of the sun is thus not exactly equal throughout the year. The sun appears to be moving fastest when the Earth is closest to the sun.

The sum of the two effects is the Equation of Time, which is the red curve with its characteristic twin peaks shown below.

Some people like such information presented in tables rather than in graphs, so two tables are presented for your information below.

These are both handy summary tables, which will give you a different view of the Equation of Time, and may help you to remember some key features, for example, that between the end of March and mid-September the sun is never more than 6 minutes away from "clock time", and for the whole of February it is 13 or 14 minutes slow.

Table showing the dates when "Sun Time" is (nearly) exactly a given number of minutes fast or slow on "Clock Time"

54

Minutes Fast

16

Nov 11

Oct 27

15

Nov 17

Oct 20

14

Nov 22

Oct 15

13

Nov 25

Oct 11

12

Nov 28

Oct

7

11

Dec

1

Oct

4

10

Dec

4

Oct

1

9

Dec

6

Sep 28

8

Dec

9

Sep 25

7

Dec 11

Sep 22

6

Dec 13

Sep 19

5

Dec 15

Sep 16

4

Dec 17

Sep 13

3

Dec 19

May

2

Dec 21

1

Dec 23

4

May 27

Sep 11

Apr 25

Jun

4

Sep

8

Apr 21

Jun

9

Sep

5

The Four Days Watches tell Sun Time - exactly right!

0

Dec 25

Apr 15

Jun 14

Sep

2

Minutes Slow 1

Dec 28

Apr 12

Jun 19

Aug 29

2

Dec 30

Apr

8

Jun 23

Aug 26

3

Jan

1

Apr

5

Jun 29

Aug 22

4

Jan

3

Apr

1

Jul

4

Aug 18

5

Jan

5

Mar 29

Jul

9

Aug 12 55

6

Jan

7

Mar 26

7

Jan

9

Mar 22

8

Jan 12

Mar 19

9

Jan 15

Mar 16

10

Jan 18

Mar 12

11

Jan 21

Mar

8

12

Jan 24

Mar

4

13

Jan 29

Feb 27

14

Feb

Feb 19

5

Jul 18

Aug

4

Table showing the Equation of Time on the 5th, 15th and 25th of each month, together with the average daily change in seconds (given in minutes and second, + = "Sun time" is fast on "clock time" Eq.of time on the: (secs)

15th

25th

-5m03

-9m10

-12m12

20

February

-14m01

-14m16

-13m18

5

March

-11m45

-9m13

-6m16

16

April

-2m57

+0m14

+1m56

18

May

+3m18

+3m44

+3m16

4

June

+1m46

-0m10

-2m20

16

July

-4m19

-5m46

-6m24

20

August

-5m59

-4m33

-2m14

11

September

+1m05

+4m32

+8m04

20

October

+11m20

+14m01

+15m47

13

November

+16m22

+15m28

+13m11

10

December

+9m38

+5m09

+0m13

27

January

5th

Av. change

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8.2 The equation of time The rotation of the Earth makes a good clock because it is, for all practical purposes, constant.

Of course, scientists are not practical and care about the fact that the length of the day increases by one second every 40 000yrs. For the rest of us, it's just a matter of finding a convenient way to determine which way the Earth is pointing. Stars would be good, but they are too dim (and too many) at night and go away during the day. A useful aid is the Sun, which is out and about when we are and hard to overlook. Unfortunately, the apparent position of the sun is determined not just by the rotation of the Earth about its axis, but also by the revolution of the Earth around the Sun. I would like to explain exactly how this complication works, and what you can do about it.

The diameter of the Sun as seen from the Earth is 1/2 degree, so it moves by its own radius every minute.

24hrs

60min

1

------ x ----- x -deg = 1min 360deg

1hr

4

That means it will be hard to read a sundial to better than the nearest minute, but then, we don't bother to set our clocks much more accurately than that either. Unfortunately, if we define the second to be constant (say, the fraction 1/31 556 925.974 7 of the year 1900, the "ephemeris second"), then we find that some days (from high noon to high noon) have more than 86,400 seconds, and some have less.

The solar Christmas day, for example, is 86,430 seconds long. The discrepancy between "apparent time" and "mean time" can add up to +/- 15min. How does it come about?

8.3 The inclination of the ecliptic First note that the Earth rotates on its axis not once in 24hrs but once in 23hrs 56min 4sec. It's just that in the course of a 365dy year, the Earth must turn an extra time to make up for its orbit about the sun.

1day 24hrs 60min --- x ----- x ----- = 3min 56sec 366

1dy

1hr

The trouble comes in because this 3min 56sec is only an average value. Think of an observer sitting at the north pole on a platform which rotates once every 23hrs 56min 4sec. She will see the stars as stationary and the sun as moving in a circle. The plane of this circle is called the "ecliptic" and is tilted by 23.45deg relative to the equatorial plane. The observer will see the sun move from the horizon, up 57

to 23.45deg, then back down to the horizon. The sun will move at a constant speed (I'm lying, but wait till later) along its circle, but the shadow cast by the North Pole (the one with the red and white candy stripes) will not move at a constant rate. When the sun is near the horizon, it must climb at a 23.45deg angle, so that it has to move 1.09deg before the shadow moves 1deg.

1deg ------------- = 1.0900deg cos(23.45deg) On the other hand, in the middle of summer, the sun is high in the sky taking a short cut, so it must move only 1deg along its circle to cause the shadow to move 1.09deg. This effect generalizes to more temperate climates, so that in spring and fall the 3min 56sec is reduced by the factor 1.09 to 3min 37sec, whereas in summer and winter it is correspondingly increased to 4min 17sec. Thus a sundial can gain or lose up to 20sec/dy due to the inclination of the ecliptic, depending on the time of year. If it is accurate on one day, six weeks later it will have accumulated the maximum error of 10min.

20sec

2

1min

----- x 45dys x -- x ----- = 10min 1dy

pi 60sec

The seasonal correction is known as the "equation of time" and must obviously be taken into account if we want our sundial to be exact to the minute.

If the gnomon (the shadow casting object) is not an edge but a point (e.g., a hole in a plate), the shadow (or spot of light) will trace out a curve during the course of a day. If the shadow is cast on a plane surface, this curve will (usually) be a hyperbola, since the circle of the sun's motion together with the gnomon point define a cone, and a plane intersects a cone in a conic section (hyperbola, parabola, ellipse, or circle). At the spring and fall equinox, the cone degenerates to a plane and the hyperbola to a line.

With a different hyperbola for each day, hour marks can be put on each hyperbola which include any necessary corrections. Unfortunately, each hyperbola corresponds to two different days, one in the first half and one in the second half of the year, and these two days will require different corrections. A convenient compromise is to draw the line for the "mean time" and add a curve showing the exact position of the shadow points at noon during the course of the year. This curve will take the form of a figure eight and is known as an "analemma". By comparing the analemma to the mean noon line, the amount of correction to be applied generally on that day can be determined. At the equinox, we found that the solar day is closer to the sidereal day than average, that is, it is shorter, so the sundial is running fast. That means in fall and spring the correct time will be earlier than the shadow indicates, by an amount given by the curve. In summer and winter the correct time will be later than indicated.

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8.4 The eccentricity of the Earth's orbit If you look at such a figure eight calculated correctly, you will see that the fall and winter loop is actually somewhat larger than the spring and summer loop. This is due to the lie I told above. The Earth does not actually orbit at a constant speed around the sun. On January 2, the Earth is 1.7% closer to the Sun than average and thus the angular velocity is 3.4% larger (conservation of angular momentum). This make the solar day longer than the sidereal day by about 8sec more than average, 3min 56sec ---------- x 0.034 = 8.0sec/dy 1dy

and in the course of 3 months a sundial accumulates an error of 8min due to the eccentricity of the Earth's orbit.

8.0sec

2

1min

------ x 91dys x -- x ----- = 8min 1dy

pi

60sec

Thus the correct time will be later than the shadow indicates at the spring equinox and earlier at the fall equinox. This shifts the dates at which the sundial is exactly right from the equinoxes into the summer, making the summer loop of the figure eight smaller.

The 20sec/dy error due to the inclination of the ecliptic and the 8sec/dy error due to the eccentricity work in the same direction around Christmas time and add up exactly (well, almost) to the 30sec/dy mentioned earlier. The accumulated errors of 10min and 8min due to these two effects don't add up quite so neatly, so the maximum accumulated error turns out to be somewhat less than 18min. If you calculate everything correctly, you find that during the course of a year a sundial will be up to 16min 23sec fast (on November 3) and up to 14min 20sec slow (on February 12).

8.4 To find the declination of a wall The declination of a wall is the number of degrees east or west of south made by a perpendicular from the wall' surface. (In the southern hemisphere, it's the number of degrees east or west of north 59

Both figures above show a wall, CD, that declines from due south. In both cases the line OB is perpendicular to the wall and OA represents the meridian, with A to the south. The Angle of Declination is the angle AOB. METHOD 1: Place a horizontal shelf against the wall (straight edge to the the wall, shelf level and perpendicular to the wall). Hold up a plumb line and when the sun souths, mark the position of the noon shadow. Since at the moment of local apparent noon the sun is due south, the shadow of the plumb will lie in the plane of the meridian. If we mark its position on the shelf it will give us the line OA. Draw a line perpendicular to the straight edge of the shelf intersecting OA at O, and measure the angle formed to determine the declination of the wall from true south.

METHOD 2: To find the declination of the wall at any time of the day, you need to determine: (a) the direction of the sun from the wall, and (b) the direction of the sun from the south point.

First determine the angle of the sun relative to the wall. This can be done by using a simple instrument constructed as shown in the figure. Tack a piece of paper to a flat board about a foot square, drive a nail (EF) into the board perpendicular to the face with about 3" left above the surface. Draw a straight line through the base of the nail (EW). Hang a weight by a thin thread at the base of the nail (E). To use, place the board against the wall and rotate till the plump line coincides with the line EW. Note the time for later use.

Mark carefully the end of the shadow cast by the nail (C). Measure the perpendicular distance (CD) to the vertical line (EW). We now have two linear measurements, EF (the length of the nail above the surface of the board), and CD (the displacement of the end of the shadow from the vertical).

Divide CD by EF, and the quotient is the tangent of the angle of the sun from the wall.

This gives us the first of our unknowns- the direction of the sun relative to the wall. We still need to know the direction of the sun from the south point of the horizon. This direction is called the sun's "azimuth from the south". This can be found for any combination of latitude, solar declination, and local apparent time in the proper published tables (Tables of Computed Altitude and Azimuth, U.S. Hydrographic Publication No. 214). Each volume covers 10 degrees of latitude with azimuth from the north. Once you have the right volume, subtract the listed azimuth from 180 degrees to yield results from the south.

Lacking tables, we compute the sun's azimuth, starting with the clock time (Mean Time) of our observation. Depending on the longitude of the observation, add or subtract from the standard meridian (90 degrees west in the central time zone) to obtain Local Mean Time, then add or subtract the proper amount from the Equation of Time for the day of the observation to obtain the Local Apparent Time.

Convert the Local Apparent Time to an hour angle from noon (1hr =15 degrees, thus 9:36 A.M. being 2 hr. 24 min. before noon gives an hour angleof 36 degrees 0 min. 0 sec.). This value will become 't' in our computations.

Finally, we must know the latitude of the place of our observation, 'theta'.

We proceed to find the sun?s azimuth by using these three values in solving two equations: (1) tan M = tan d / cos t (2) tan Z = [( tan t ) ( cos M )] / sin ( theta - M) The intermediate value, M, is used to solve for Z, the sun?s azimuth. This is our second unknown.

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In the figure*, AB is the wall, angle SOP = a = declination of the wall, POL = b = direction of the sun from the wall, SOL = c = direction of the sun from the south point (azimuth). Then: (A) If the observation was 'before' local apparent noon: (1) If the sun was to the right of the wall: (a) The wall declines East by the amount c+b.

(2) If the sun was to the left of the wall: (a) If b>c, the wall declines West by b-c. (b) If c>b, the wall declines East by c-b.

(B) If the observation was 'after' local apparent noon: (1) If the sun was to the left of the wall: (a) The wall declines West by the amount c+b.

(2) If the sun was to the right of the wall: (a) If b>c, the wall declines East by b-c. (b) If c>b, the wall declines West by c-b.

Remember that in the winter the sun's declination is negative, so in solving the formulas, 'd' and M will be negative, and in getting the value of (theta - M) we subtract algebraically.

8.6 How to set up a horizontal sundial A horizontal sundial consists of the dial plate, marked off in hours, and the gnomon which sits on the noon line and projects out from the dial plate.

In order to tell the correct local time the gnomon must be parallel with the earths axis, or, in other words, that it should point towards the celestial pole. In the northern hemisphere, this means, for practical purposes, that the gnomon should point at the Pole Star. One should first check whether or not the sundial is correctly made for the place at which it is to be set up. If it is not, the base plate of the dial must be corrected so that the gnomon is pointing correctly true north, towards the celestial pole.

Finding the direction of true North Various methods are suggested in the literature, and are summarised here, with references to published sources if you need them 1. Use a compass. This is not very accurate, but it will do for a small garden sundial.Remember that the compass points to magnetic north, and a correction must be made for magnetic deviation. (Magnetic deviation at Greenwich in the UK was 3ยบ58 W, and 61

decreasing by 0ยบ08 annually, but in some areas of the world it is much higher, and there are also much more local variations) 2. Mark a shadow at the exact time of local noon The shadow must be cast by a true vertical object. You can use a plumb line, a pole aligned vertically with a spirit level, or a vertical corner of a building. You may need to experiment to get a good shadow, and to find a reliable method of marking the shadow at the instant of local noon.

3. Use the method of equal altitudes This requires a reliably sunny day, and an accurately level board with a true vertical nail or stick. In one variation, concentric circles are drawn around the base of the vertical stick. The position of the tip of the shadow is noted whenever it just touches each of the circles in the morning hours and in the evening hours. If one is lucky there will be two marks on the same circle. Join them with a line. Bisect this line, and draw a line from the bisection point to the base of the stick - this will be a true North- South line.

An alternative is to mark out points on the track of the tip of the shadow first, and then to connect them with a line. Then draw a circle to give the greatest possible distance between the two intersection points, and as before bisect the line, and draw a line from the bisection point to the base of the stick - this will be a true North-South line.

Checking the angle of the gnomon Since horizontal sundials are often mass-produced, they have to be made for just one latitude. Quite often, people bring back a sundial when they have been on holiday, so the angle may be very different.

For example, a sundial made for the south of Spain will have an angle around 37 deg. and will not tell the correct time if it is set up with the dial plate horizontal.

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First, measure the angle of the gnomon with a protractor.

Second, you can if you wish cross-check this measurement and check that the hour lines have been laid out correctly, by "back-calculating the gnomon angle from the angles of the hour lines.

Compensating for an incorrect gnomon angle Third, provide a wedge to bring the gnomon parallel to the earth's axis. For example, the holiday sundial brought back from Spain (lat 37ºN) to be set up in Southern England (lat 51ºN) would have to be wedged up by 14º, so that the gnomon is at 51º to the horizontal. You can either measure this angle with a protractor, or you can calculate the height of the wedge by multiplying the length of the dial plate by the sine of the correction angle. In this case, the wedge required for a square sundial with a side of 10 cm would be 2.4 cm.

Finding your latitude and longitude You need to know your latitude before you order your Spot-On Sundial - the angle of the gnomon (which casts the shadow) has to be the right one for your location, as described on the models page.

You also need to know your longitude later on when you come to set up your Spot-On Sundial, so it is worth writing it down for later.

9. Types of sundials Sundials are classified into a number of different types, mainly by the plane in which the dial lies, as follows:       

horizontal dials vertical dials equatorial dials polar dials analemmatic dials reflected ceiling dials portable dials 63

You Need to Know Much of our initial discussion on sundials will concern the motion of objects in the sky. Therefore, we shall introduce some terminology and a coordinate system that allow us to specify succinctly the location of particular objects in the heavens.

The Celestial Sphere

Figure 1 It is useful in discussing objects in the sky to imagine them to be attached to a sphere surrounding the Earth. This fictitious construction is called the celestial sphere. At any one time we see no more than half of this sphere, but we will refer loosely to the imaginary half-sphere over our heads as just the celestial sphere. (See Figure 1).

The north celestial pole (NCP) and the south celestial pole (SCP) are the imaginary points in the sky directly above the geographic north and south pole, respectively. (See Figures 3 and 5 below.)

The point on the celestial sphere that is directly over our heads at a given time is termed the zenith.

The imaginary circle passing through the north and south points on our horizon and through the zenith is termed the meridian.

The meridian separates the morning and afternoon positions of the Sun. In the morning, the Sun is east of the meridian. At local noon, the Sun is right on the meridian. In the afternoon, the Sun is west of the meridian.

We will introduce additional terminology associated with the celestial sphere later.

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Motion in the Sky It is clear after only minimal observation that objects change their positions in the sky over a period of time. This motion is conveniently separated into two parts: 1. The entire sky appears to turn around the NCP and the SCP once in 24 hours. This is termed the daily or diurnal motion of the celestial sphere, and is in reality a consequence of the daily rotation of the Earth on its axis. The diurnal motion affects all objects in the sky and does not change their relative positions: the diurnal motion causes the sky to rotate as a whole once every 24 hours.

2. Superposed on the overall diurnal motion of the sky is "intrinsic" motion that causes certain objects on the celestial sphere to change their positions with respect to the other objects on the celestial sphere. These are the "wanderers" of the ancient astronomers: the planets, the Sun, and the Moon.

In our discussion, we will imagine the Sun rotating around a stationary Earth, although the Sun's apparent motion around us is actually due to the Earth's rotation about its axis.

9.1 Diurnal Motion at Different Latitudes Actually, all objects are slowly changing their relative positions on the celestial sphere, but for most, the motion is so slow that it cannot be detected over time spans comparable to a human lifetime; only the "wanderers" have sufficiently fast motion for this change to be easily visible.

The "Path of the Sun" on the Celestial Sphere

Figure 2 65

Another important imaginary object on the celestial sphere is the ecliptic or "path of the Sun", which is the imaginary path that the Sun follows on the celestial sphere over the course of a year. As Figure 2 indicates, the apparent position of the Sun with respect to the background stars (as viewed from Earth) changes continuously as the Earth moves around its orbit, and will return to its starting point when the Earth has made one revolution in its orbit.

Figure 3 Because the rotation axis of the Earth is tilted by 23.5ยบ with respect to the plane of its orbital motion (which is also called the ecliptic), the path of the Sun on the celestial sphere is a circle tilted by 23.5ยบ with respect to the celestial equator, which is the imaginary circle around the sky directly above the Earth's equator. It intercepts the horizon at the points directly east and west anywhere on Earth. (See Figure 3).

9.2 East and West on the Celestial Sphere It is useful to define east and west directions on the celestial sphere, as illustrated in Figure 4.

Figure 4 66

Objects to the west of the Sun on the celestial sphere precede the Sun in the diurnal motion of the celestial sphere (they "rise" before the Sun and "set" before the Sun). Likewise, objects to the east of the Sun trail the Sun in the diurnal motion (they "rise" after the Sun and "set" after the Sun). Generally, one object is west of another object if it "rises" before the other object over the eastern horizon as the sky appears to turn, and east of the object if it "rises" after the other object.

Motion of the Sun

Figure 5 The ecliptic and the celestial equator intersect at two points: the vernal (spring) equinox and autumnal (fall) equinox. The Sun crosses the celestial equator moving northward at the vernal equinox around 21st March and crosses the celestial equator moving southward at the autumnal equinox around 22nd September. When the Sun is on the celestial equator at the equinoxes, everybody on the Earth experiences 12 hours of daylight and 12 hours of night for those two days (hence, the name ``equinox'' for ``equal night'').

Figure 6 67

The day of the vernal equinox marks the beginning of the three-month season of spring on our calendar and the day of the autumnal equinox marks the beginning of the season of autumn on our calendar. On those two days of the year, the Sun will rise in the exact east direction, follow an arc right along the celestial equator and set in the exact west direction.

When the Sun is above the celestial equator during the seasons of spring and summer, you will have more than 12 hours of daylight. The Sun will rise in the northeast, follow a long, high arc north of the celestial equator, and set in the northwest. Where exactly it rises or sets and how long the Sun is above the horizon depends on the day of the year and the latitude of the observer. When the Sun is below the celestial equator during the seasons of autumn and winter, you will have less than 12 hours of daylight. The Sun will rise in the southeast, follow a short, low arc south of the celestial equator, and set in the southwest. The exact path it follows depends on the date and the observer's latitude.

No matter where you are on the Earth, you will see 1/2 of the celestial equator's arc. Since the sky appears to rotate around you in 24 hours, anything on the celestial equator takes 12 hours to go from exact east to exact west. Every celestial object's diurnal (daily) motion is parallel to the celestial equator. So for northern observers, anything south of the celestial equator takes less than 12 hours between rise and set, because most of its rotation arc around you is hidden below the horizon.

Anything north of the celestial equator takes more than 12 hours between rising and setting because most of its rotation arc is above the horizon. For observers in the southern hemisphere, the situation is reversed.

Figure 7 However, remember, that everybody anywhere on the Earth sees 1/2 of the celestial equator so at the equinox, when the Sun is on the equator, you see 1/2 of its rotation arc around you, and therefore you have 12 hours of daylight and 12 hours of nightime every place on the Earth.

The geographic poles and equator are special cases. At the geographic poles, the celestial equator is right along the horizon and the full circle of the celestial equator is visible. Since a celestial object's diurnal path is parallel to the celestial equator, stars do not rise or set at the geographic poles.

On the equinoxes the Sun moves along the horizon. At the north pole the Sun ``rises'' on 21st March and ``sets'' on 22nd September. The situation is reversed for the south pole. On the equator observers see one half of every object's full 24-hour path around them, so the Sun is above the horizon for exactly 12 hours for every day of the year.

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9.3 Celestial Coordinate Systems There are a couple of popular ways of specifying the location of a celestial object. The first is what you would probably use to point out a star to your friend: the altitude-azimuth system. The altitude of a star is how many degrees above the horizon it is (anywhere from 0 to 90 degrees). The azimuth of a star is how many degrees along the horizon it is and corresponds to the compass direction.

Figure 8: A star's position in the altitude-azimuth coordinate system. The azimuth = 120º and the altitude = 50º. The azimuth is measured in degrees clockwise along the horizon from due north. The azimuths for the compass directions are shown in the figure. The altitude is measured in degrees above the horizon. The star's altitude and azimuth changes throughout the night and depends on the observer's postion (here at the intersection of the north-south and east-west line.)

The star's position does not depend on the location of the NCP or celestial equator in this system.

Azimuth starts from exactly north = 0º and increases clockwise: exactly east = 90º, exactly south = 180º, exactly west = 27º, and exactly north = 360º = 0º.

The second way of specifying star positions is the equatorial coordinate system. This system is very similar to the longitude-latitude system used to specify positions on the Earth's surface. This system is fixed with respect to the stars so, unlike the altitude-azimuth system, a star's position does not depend on the observer's location or time.

Figure 9 69

The lines on a map of the Earth that run east-west parallel to the equator are lines of latitude and when projected onto the sky, they become lines of declination. Like the latitude lines on Earth, declination (dec) is measured in degrees away from the celestial equator, positive degrees for objects north of the celestial equator and negative degrees for objects south of the celestial equator. Objects on the celestial equator are at 0ยบ dec, objects half-way to the NCP are +45ยบ, objects at the NCP are +90ยบ, and objects at the SCP are -90ยบ.

Parts of a Sundial

Figure 10 The gnomon is usually a rod or a triangular piece of metal or wood on a sundial. The style is the sloping edge of the gnomon. The style is usually used to cast the shadow on the dial plate to show the hour of the day. In a horizontal dial, the angle ร is equal to the latitude of the location.

The hour lines are the numbered time lines that the shadow falls along.

The nodus is a "marker" along the gnomon to get an exact point on the shadow.

Dial furniture are the markers other than the hour lines on the dial plate. It is there to provide other information, such as the date and declination of the Sun.

9.3.1 Different Classification of Hours From the previous section, we know that the gnomon must be set parallel to the Earth's axis in order to get a shadow angle that has a constant magnitude every day, given the same interval of time. However, regardless of the angle between the gnomon and the Earth's axis, the shadow angle does not move at a constant speed in any given day. Hence, to have markings that show equal hours on a sundial, we need to use tables and mathematical calculations. It is with these tables and mathematical calculations that we are able to divide a day into 24 equal hours. However, before these mathematical formulas were derived, people have different classification of time.

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Unequal or Temporary Hours

Figure 11: Canonical sundial from the German Museum in Munich In antiquity, the daily arc of the sun, that is, the time from sunrise until sunset, as well as the night arc, was divided into twelve equally long parts. Since the time from sunrise to sunset was longer in summer than in winter, the "hours" of summer were also longer than the "hours" of winter. These unequal hours or temporary hours were used over much of the earth, for many centuries until the middle ages. The "hours" of any one day were equal, but the "hours" of the winter were short and the "hours" of summer long. It is for this latter reason that we refer to them as unequal hours.

In Europe between the 8th and the 15th century, sundials were built on church walls pointing due south. Their main purpose was to show times of prayer. They are called canonical sundials.

Canonical sundials are not time measurement systems as we would think of them today, but had the task to divide the light of day into certain time periods. The timelines with a cross-line in Figure 11 indicate the hours of prayer.

For the canonical sundial in Figure 11, adjacent hour lines are at equal angles from each other.

In ancient times, people have the misconception that the "hours" measured by this dial in a day are equal. However, in the section on vertical direct south dials, we show a formula which proves this thinking wrong. Hence, the "hours" measured by this dial are "unequal" hours which are not equal within a day.

9.3.2 Equinoctial Hours Around the 14th century, the method for counting the hours changed. The irregular unequal hours were replaced by hours of equal length. The time beginning with the passing of the low meridian, about midnight, until the passing of the next low meridian, was divided into 24 hours of equal length. They were called equinoctial hours.

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Figure 12 shows a south pillar of the Regensburg (German) cathedral which features two sundials. The one below shows temporary hour lines, which measures unequal hours, and a horizontal gnomon. Similar to the canonical sundial in Figure 11, adjacent hour lines are at equal angles from each other. Hence, this sundial again measures "unequal" hours which are not equal within a day.

The sundial above, dated 1509, shows equinoctial hours with a gnomon parallel to the earth's axis.

This sundial is the vertical direct south dial that is commonly found today.

Figure 12: South pillar of the Regensburg (German) Cathedral

9.3.3 Italian Hours In some areas of Europe, particularly in Northern Italy, after the introduction of the equinoctial hours, counting of the 24 hours began at sunset. Consequently, the first hour began at sunset.

The time is read from the shadow of a fixed point or node. The green curves in Figure 13 represent lines of declination. The green straight line in the middle represent the equinoxes, while the upper green curve represent the winter solstice and the lower green curve represent the summer solstice. In Figure 13, only 3 lines of declination are shown. In the actual dial, lines of declination for other days are also shown. The dates corresponding to the lines of declination are stated at the side of the dial (not shown in Figure 13). Usually, only the zodiac signs, and not the actual dates are given.

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When reading the dial, the shadow of the node will fall on one of these green lines. We can thus get the date by reading the corresponding date stated at the side of the dial.

Figure 13: Vertical sundial showing both Italian and Babylonian hours A table of dates and the corresponding sunset times is usually provided at the bottom of the dial.

To explain how to use sundials that use Italian hours, we shall use an example. If the shadow of the node falls on the intersection point of the green straight line in the middle and the blue line indicating the 17th Italian hour (point A), the date of reading is on one of the equinoxes, because this green line represent the equinoxes. Let's assume that the date of reading is on the vernal equinox (21st March). Since the sun sets at 6p.m. on 20th March, the time of reading is thus 17 hours after 6p.m., which is 11a.m. on 21st March.

9.3.4 Babylonian Hours Babylonian hours are measured using the same principles as Italian hours, the only difference being that the counting of the 24 equally long hours started with sunrise.

Again, a table showing dates and the corresponding sunrise time is usually provided at the bottom of the dial.

If the shadow of the node falls on the intersection point of the green straight line in the middle and the red line indicating the 5th Babylonian hour (point A), the date of reading is on one of the equinoxes. Let's again assume that the date of reading is on the vernal equinox (21st March). Since the Sun rises at 6a.m. on the vernal equinox, the time of reading is 5 hours after the Sun rises. Hence, it is 11a.m. on 21st March.

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9.3.5 Equation of Time - Analemma Elliptical Orbit Effect We begin this section by making two assumptions: 1. The Earth is not tilted on its axis.

2. The observer is standing on the equator.

The Earth does not travel around the Sun in a circle, but in an ellipse. If the Earth were to orbit the Sun in a circle, with the Sun as its centre, the Earth's speed around the Sun would be constant. We can think of this as the Earth's average speed. However, because the Earth's orbit is elliptical, the speed of the Earth varies throughout the year. The speed of the Earth is fastest when it is closest to the Sun, in January, and slowest when it is furthest away from the Sun, in July. In other words, in January, it will be moving faster than average, and in July, it will be moving slower than average.

Notice that the green coloured Earth travels around the Sun in a circle. Its speed never varies. The blue coloured Earth travels around the Sun in an ellipse. Its speed is greatest in January, when it is closest to the Sun. Its speed is slowest in July, when it is furthest away from the Sun. Although our clocks say that the day is 24 hours long, it only takes the Earth 23 hours 56 minutes to make a complete revolution about its axis in a day. Hence, at the end of 24 hours, the Earth has actually rotated 361ยบ, instead of 360ยบ. If we superimpose 2 Earths, one having rotated around the Sun for 24 hours in a circular path and the other in an elliptical path, we will get the picture in Figure 15.

Earth A travelled in a circular orbit at a constant speed. Earth B travelled in an elliptical orbit, so in January, it was traveling faster than average.

Figure 15 74

After 24 hours, if you were standing on Earth A looking at the Sun, it would appear to be directly overhead. If you were standing on Earth B looking at the Sun, it would not appear to be directly overhead. Earth B has not quite rotated far enough relative to the Sun. If you were looking at your watch on Earth B and comparing its time to the position of the Sun, it would appear that the Sun's position would be slightly to the east. After another 24 hours, Earth B is still continuing to move faster than average. This error in time will accumulate and the Sun will continue for a time to appear to move further and further east in the sky, again, in comparison to what your watch reads at noon.

Pole - style Sundials A pole-style sundial has a gnomon which casts a line-shaped shadow on a set of hour lines. Pole-style dials use the hour angle, that is the direction of the Sun in the equatorial plane, which is perpendicular to the gnomon. The tip of the pole-style points to the north celestial pole on the northern hemisphere.

Types belonging to this class include the equatorial, vertical and horizontal dials.

Nodal Sundial In a nodal sundial, the time is read from the shadow of a fixed point or node. It may be the tip of a pin or gnomon. The node may also be a knob on a rod or a notch in an edge. Sometimes the node is an aperture in a plate, casting a spot of light on the dial face. A combination of pole-style and nodal dials also exist. In this case, the pole-style usually comes with a marker, such as a knob or a notch Remember that in the section on analemma, we mentioned that if we record the position of the Sun in the sky at the same time everyday, the Sun would take the path of the analemma. In this sundial, the path that the Sun takes every half hourly is computed and drawn on the dial plates. Note that for clarity, the analemmas, which is the path that the Sun takes, have been split and divided over two dial plates. The one on the right is for January to June and the one on the left is for July to December. Date lines are drawn for the first day of each month and for the solstices. The analemmas and times are in red, the date lines and dates in blue. (The colours in Figure 20 are not distinctly shown.)

Figure 20: Right dial plate 75

The dial for the first half of the year has time lines from 8½ to 18 o'clock, of which the last three have not been marked. The date line for the winter solstice has been omitted, as it would almost coincide with the line for January 1.

Figure 21: Left dial plate The dial face for the second half of the year has time lines from 8 to 17½ o'clock, of which the last two have not been marked.

Why should the Gnomon be set Parallel to the Earth's Axis?

The Sun in its apparent daily journeys across the sky gives us a means of telling the time and dividing our daylight hours into convenient intervals, by sundials. Sundials were used in ancient Egypt and were often little more than sticks stuck in the sand, or vertical pillars.These were not at all accurate because the Sun varies its track across the sky according to the season of the year. A rod stuck in the ground can be used to show these variations from month to month by measuring the length and direction of the shadow it makes in sunlight. We cannot mark on the ground the shadow angle, or time by the Sun without tables or mathematical calculations becausethe shadow angle is dependent on the declination of the Sun which changes with the seasons throughout the year.

A great advance in accuracy and convenience was made by the Arabs who had the bright idea of tilting the gnomon such that it points to the north celestial pole (NCP) and lies parallel to the Earth's axis. To explain why the gnomon has to be parallel to the Earth's axis, we look at the case whereby we set the gnomon at an angle to the Earth's axis.

When the gnomon is not parallel to the Earth's axis,

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1. The shadow cast by the gnomon at a given hour points in different directions depending on the seasons.

2. The angle covered by the shadow during a certain time interval depends on the seasons.

These inconsistencies make it impossible to calibrate sundials with a gnomon that is not parallel to the Earth's axis. We shall illustrate these two inconsistencies - the change in direction of the shadow and the different shadow angles resulting from the same interval of time on different days, with the gnomon set at 90ยบ to the ground, at latitude 45ยบN.

Change in direction of the shadow of the gnomon every day at given hour At latitude 45ยบN, if we set the gnomon at 90ยบ to the ground, and fix time at 1p.m., the gnomon casts a shadow, which changes direction every day as depicted in the animation above.

However, when the gnomon is set parallel to the Earth's axis and the time fixed at 1p.m., the gnomon casts shadows toward a fixed direction every day as depicted in the animation above.

By having the same direction every day at given hour, the calibration of the hour lines on our sundials can then be consistent.

Variable shadow angles resulting from the same interval of time on different days Referring to the above animation, on 21st June (summer solstice at the northern hemisphere) at 9a.m., the gnomon casts a shadow at A, and at 12noon, the shadow is at B. On 21st December (winter solstice at the northern hemisphere) at 9a.m., the gnomon casts a shadow at C and at 12 noon, the shadow is again at B. Hence, given the same duration of time (9a.m. to 12 noon) on both days, the shadow has to turn a greater angle on 21st June than on 21st December. Thus, the shadow has a faster angular speed on 21st June than on 21st December. Applying the same reasoning to the other days, the speed of the shadow angle of the gnomon varies every day, when the gnomon is at an angle to the Earth's axis.

However, when the gnomon is placed parallel to the Earth's axis, the gnomon casts a shadow that sweeps out the same angle given the same interval of time on different days.

Length of shadow From the above animations, we note that the length of the shadow varies. The length of the shadow gets longer as the magnitude of the Sun's declination increases.

Also, in the morning and evening, when the angle that the sun rays make with the horizon is the smallest, the shadow is at its longest. On the other hand, at noon, when the Sun crosses the meridian, the shadow is at its shortest.

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9.4 Equation of Time - Analemma Introduction If you record the position of the Sun in the sky at the same time everyday, say sometime around noon, you would notice that the Sun takes a rather strange path. You might notice that at certain times throughout the year, the Sun is not only moving north and south as you would expect with the change of seasons, but also slightly east and west. This figure-of-8 path that the Sun makes in the sky is called the analemma. On some days, you might notice that the Sun is not in the sky where, according to the time on your watch, you would expect it to be.

The difference in time between what your watch reads and the position of the Sun is called the equation of time. If you are on the northern hemisphere and the Sun's position is to the east of where your watch indicates it would be, the equation of time is negative. If the Sun is to the west, the equation of time is positive.

An easier way to see this effect is to find a place where the Sun shines on the ground at noon all year round - winter, spring, summer and autumn. Then place a rod about 3 feet tall into the ground, making sure that it will not move throughout the year.

On the first day of each month, at the same time everyday, place a mark on the ground with another shorter rod (you will need 12 of these) where the Sun makes a shadow with the tip of the longer original rod. At the end of 12 months, you will see that the 12 short rods make a figure-of-8 pattern which is similar to the one shown in Figure 14.

Figure 14 78

There are two independent reasons why the Sun takes this strange path.

1. The Earth is tilted on its axis 23.5° in relation to the plane of its orbit around the sun.

2. The Earth does not orbit the Sun in a circle, but in an ellipse.

It is simply the sum of these two effects that causes the analemma. With the aid of a few diagrams and animations, we hope that the analemma can be easily understood.

Elliptical Orbit Effect We begin this section by making two assumptions: 1. The Earth is not tilted on its axis.

2. The observer is standing on the equator.

The Earth does not travel around the Sun in a circle, but in an ellipse. If the Earth were to orbit the Sun in a circle, with the Sun as its centre, the Earth's speed around the Sun would be constant. We can think of this as the Earth's average speed. However, because the Earth's orbit is elliptical, the speed of the Earth varies throughout the year. The speed of the Earth is fastest when it is closest to the Sun, in January, and slowest when it is furthest away from the Sun, in July. In other words, in January, it will be moving faster than average, and in July, it will be moving slower than average.

Notice that the green coloured Earth travels around the Sun in a circle. Its speed never varies.

The blue coloured Earth travels around the Sun in an ellipse. Its speed is greatest in January, when it is closest to the Sun. Its speed is slowest in July, when it is furthest away from the Sun. Although our clocks say that the day is 24 hours long, it only takes the Earth 23 hours 56 minutes to make a complete revolution about its axis in a day. Hence, at the end of 24 hours, the Earth has actually rotated 361º, instead of 360º. If we superimpose 2 Earths, one having rotated around the Sun for 24 hours in a circular path and the other in an elliptical path, we will get the picture in Figure 15. Earth A travelled in a circular orbit at a constant speed. Earth B travelled in an elliptical orbit, so in January, it was traveling faster than average.

Figure 15 79

After 24 hours, if you were standing on Earth A looking at the Sun, it would appear to be directly overhead. If you were standing on Earth B looking at the Sun, it would not appear to be directly overhead. Earth B has not quite rotated far enough relative to the Sun. If you were looking at your watch on Earth B and comparing its time to the position of the Sun, it would appear that the Sun's position would be slightly to the east. After another 24 hours, Earth B is still continuing to move faster than average. This error in time will accumulate and the Sun will continue for a time to appear to move further and further east in the sky, again, in comparison to what your watch reads at noon.

Earth's Tilt Effect We will begin this section by making two assumptions: 1. The Earth's orbit around the Sun is circular.

2. The observer is standing on the equator.

From the previous section, we know that if we observe the position of the Sun at the same time every day starting from 2nd January, the Sun appears to move slowly to the east, in comparison to what your watch reads and takes one year to return to its starting position. Let's take the stars behind the Sun as markers, and imagine the Sun as being a little less bright so that we can look at it and still see the stars behind it. The Sun would then appear to drift slowly to the east against the background of the stars. At the end of one year, the Sun would return to its original position.

The middle panel shows what we would see if the Earth was not tipped on its axis. If this were so, the motion of the Sun against the stars would be in a horizontal motion only. Every day at noon, the Sun would appear to be at the highest point in the sky or what is known as culmination. After 24 hours, the Sun would again culminate in the sky at noon, however having drifted slightly to the east in relation to the background stars. This Sun represents the mean sun that would travel on the celestial equator.

The bottom panel shows what we will see in reality because the Earth is tipped on its axis. The path of the Sun will follow a slightly different path throughout the year. Not only will the Sun drift slightly to the east (or west) but also to the north (or south) depending on the season. This Sun is the true sun that will travel on the ecliptic. Notice that the true sun is not on the 'noon' line on 22nd March.

Remember that we are assuming the Earth's orbit around the Sun is circular. The velocity of the mean sun and the true sun are constant, each one taking one year to make a complete trip around the celestial sphere. We also notice that at the vernal and autumnal equinoxes, the true sun and the mean sun meet.

We will now explain why the true sun lags behind or moves ahead of the mean sun. Looking at the top view of the celestial sphere, we can see that the path of the ecliptic is nothing more than the path of the celestial equator that has been "tipped" toward us. Therefore, some of the motion of the true sun will be toward or away from us around the time of the vernal equinox or the autumnal equinox respectively. At these times, we will not have the perception of the true sun moving as fast as the mean sun. Imagine someone throwing a ball straight at you to catch.

You may not perceive any motion of the ball because it is coming straight at you. However, if you were an observer standing on the sidelines, you would see the ball moving forward toward you.In other words, on top of the general eastward drift among the background stars, the true sun is moving along the ecliptic northward or southward with respect to the celestial equator. Thus during some periods the true sun appears to move eastward faster than during others. Looking at the graph below, 80

we notice that only at the solstices, all of the true sun's motion is parallel to the celestial equator. At other times of the year, the Sun is also either moving north or south.

Figure 16

10. Different Types of Sundials There are many types of sundials but they can be grouped into three main classes: 1. Those having a gnomon parallel to the Earth's axis, and around which the Sun and all celestial bodies appear to move at a rate of 15º per hour. The earth turns 360º in about 24 hours, therefore the sun's apparent position moves 360/24 = 15º each hour.

2. Those that depend on the altitude of the Sun above the horizon. These dials are known as altitude dials.

3. Those that depend on the Sun's azimuth. They are known as azimuth dials.

These three classes of sundials can again be grouped into 2 different types: 1. Pole – style 2. Nodal

10.1 Pole - style Sundials A pole-style sundial has a gnomon which casts a line-shaped shadow on a set of hour lines. Pole-style dials use the hour angle, that is the direction of the Sun in the equatorial plane, which is perpendicular to the gnomon. The tip of the pole-style points to the north celestial pole on the northern hemisphere.

Types belonging to this class include the equatorial, vertical and horizontal dials.

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10.2 Nodal Sundial In a nodal sundial, the time is read from the shadow of a fixed point or node. It may be the tip of a pin or gnomon. The node may also be a knob on a rod or a notch in an edge. Sometimes the node is an aperture in a plate, casting a spot of light on the dial face.

A combination of pole-style and nodal dials also exist. In this case, the pole-style usually comes with a marker, such as a knob or a notch.

Remember that in the section on analemna, we mentioned that if we record the position of the Sun in the sky at the same time everyday, the Sun would take the path of the analemma. In this sundial, the path that the Sun takes every half hourly is computed and drawn on the dial plates. Note that for clarity, the analemmas, which is the path that the Sun takes, have been split and divided over two dial plates. The one on the right is for January to June and the one on the left is for July to December. Date lines are drawn for the first day of each month and for the solstices. The analemmas and times are in red, the date lines and dates in blue. (The colours in Figure 20 are not distinctly shown.)

Figure 20: Right dial plate The dial for the first half of the year has time lines from 8½ to 18 o'clock, of which the last three have not been marked. The date line for the winter solstice has been omitted, as it would almost coincide with the line for January 1.

Figure 21: Left dial plate 82

The dial face for the second half of the year has time lines from 8 to 17½ o'clock, of which the last two have not been marked.

10.3 Equatorial Dials Equatorial dials are pole - style dials with a gnomon inclined so that it is parallel to the Earth's axis and points to the north celestial pole. This dial is called an equatorial dial because the dial plate, that is the surface used to receive the shadow, is a flat disc in the plane of the celestial equator. Equatorial dials are universal, that is, it can be used at any latitude because the gnomon can be set parallel to the Earth's axis with some adjustments. Equatorial dials can be classified into the equatorial disk dials or the armillary dials.

Figure 22: Equatorial disk dial in Jaipur, India

General Appearance The equatorial disk dial has faces on both upper and lower sides. The gnomon points to the north celestial pole and is set perpendicular to the dial plate in the center of the dial.

Figure 23 83

Also, the angle subtended by the ground and the gnomon is set to the same magnitude as the latitude.

Why 2 dial faces Since the Sun is north of the celestial equator half the year and south of the celestial equator the other half, each dial face, which is parallel to the celestial equator, will only receive sunlight for half the year.

The Sun casts a shadow on the upper dial face from 21st March (the spring or vernal equinox) to 22nd September (the fall or autumnal equinox).

On the other hand, the Sun casts a shadow on the lower dial face from 22nd September (the fall or autumnal equinox) to 21st March (the spring or vernal equinox).

How it works On 21st March (spring equinox), the Sun is at a declination of 0ยบ. The gnomon will cast shadows on both the upper and lower faces because the Sun is moving parallel to the dial plate. This is due to the fact that the Sun is not a point in the sky - it subtends an arc of 30' in the sky. After the spring equinox, the Sun is at a positive declination. The gnomon then casts a shadow only on the upper dial face. This phenomenon will continue till 21st September (autumnal equinox), where the Sun is again moving parallel to the dial plate. The gnomon will then cast shadows on both the upper and lower faces, as in the spring equinox. After the autumnal equinox, the Sun is at a negative declination. The gnomon then casts a shadow only on the lower dial face. This phenomenon will continue until spring equinox.

10.4 Armillary Dial

Figure 24: Armillary sundial 84

The above figure shows an armillary sundial based on a traditional Swedish design. This armillary sundial is made of iron with some brass, and it is about 22 inches tall.

General Appearance The armillary dial consists of an assembly of rings representing the principal circles of the celestial sphere. In Figure 24, only the meridian, celestial equator and equinoctial colure , which is the circle passing through the NCP and the equinoxes, are found on the dial. More complicated armillary dials have several more rings to model the tropics, arctic circles or horizon. This multitude of rings may block the shadow of the gnomon on the time scale, or at least cause confusion when reading the dial.

Its name originated from the Latin word, armilla, which means a ring. The armillary dial is an extension of the equatorial dial, with two rings representing the celestial equator and the meridian. A third ring is usually added to represent the horizon. The hour lines are marked on the inside of the equatorial ring. In Figure 25, the circle ABCDEFG is the meridian, DHGI the celestial equator, CHFI the horizon. The gnomon is the thin long rod which runs through holes pierced in the meridian ring.

Figure 25 More Pictures of Armillary Dials

Figure 26 85

Figure 27

Figure 28

How it works The shadow of the gnomon, cast among the hour lines on the equatorial ring, shows the time. At noon, the shadow of the meridian ring will fall across the gnomon and also across the 12-o'clock line. At the time of the equinoxes, the Sun will be on the celestial equator, and hence in the plane of the equatorial 86

ring of the armillary dial. The shadow of the upper part of the ring (D in Figure 25) will fall on the lower part of the ring, and the hour lines will be shaded.

Measuring the Sun's declination At the times of the equinoxes, the shadow of the equatorial band falls at the center of the gnomon, half way between E and B in Figure 25. In the summer, when the Sun is high, the shadow falls further down the gnomon closer to B, while in winter it falls closer to E. We can calibrate the gnomon rod to show the Sun's declination by the position of the shadow on the gnomon.

10.5 Vertical direct dials Vertical dials are usually placed on walls of buildings and if the building is oriented in such a way that they face exactly toward the cardinal points of the compass (north, south, east and west), the dials are called vertical direct dials - vertical because the dial plate lies in a vertical plane and direct because it faces directly toward one of the cardinal compass points.

Vertical direct dials take their names from the direction that their dial plates face. For instance, a dial placed on a wall facing due south is called a vertical direct south dial. Another type of vertical dial is the vertical declining dial.

Vertical Direct North Dial Characteristics The dial is placed on walls which face directly north. It is not popularly used because the Sun is far too south in the sky to strike a north wall between 22nd September and 21st March. This is illustrated in the animation below.

General appearance Only the early morning and late evening hour lines are drawn on the dial plate, because the Sun will not shine on the dial face at other hours. The earliest hour line and the latest hour line on the dial plate are dependent on the sunrise and sunset times of the latitude at which the sundial is designed to be used. The hour lines run clockwise.

How it works We will show in the below animation how the shadow of the gnomon is cast for a year.

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Vertical Direct South Dial

Figure 35: Vertical direct south dial

Characteristics The dial is placed on walls which face directly south. It is the most commonly used vertical direct dial because it can measure the greatest duration of time each day.

General appearance Unlike the vertical direct north dial, the hour lines run anti-clockwise. The hour lines on any vertical direct south dial are precisely the same as those on a horizontal dial at the colatitude. (This will be explained under the mathematics of vertical direct south dial.) The 6-o'clock hour line is a horizontal line at the top, and the 12-o'clock line is vertical. The Sun can never shine on these dials earlier than 6a.m or later than 6p.m., so we need not include any hour lines other than those shown in the following animation.

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The Mathematics of Vertical Direct South Dial Similar to a horizontal sundial, to find the hour lines of a vertical direct south dial, we use Figure 36.

In Figure 36, Z is the zenith, Z' the nadir. (The point on the celestial sphere that lies directly beneath an observer. It is diametrically opposite the observer's zenith.) P is the north celestial pole and P' the south celestial pole. By using one or more of the relations of spherical trigonometry, we can deduce that

cos Z'P' cos TZ'P' = sin Z'P' cot Z'T - sin P'Z'T cot Z'P'T Since TZ'P' = 90º, Z'T = 0 = sin (90 - Ø) cot tan

, therefore

- cot (HA) --(equation 1)

= tan (HA) cos Ø

Equation 1 is actually the formula for the horizontal dial but with sin (90 - Ø) replacing sin Ø. In this case, equation 1 is actually the formula to find the hour lines for a horizontal dial at the colatitude.

How it works We will show in the below animation how the shadow of the gnomon is cast in a year. .

10.5.1 Vertical Direct East Dial

Figure 37: Vertical direct east dial, kedleston Church 89

Characteristics The vertical direct east dial is placed on walls which face directly east. They can be used on any latitude.

General appearance Only the morning hours are drawn on the dial plate because the Sun only shines on the dial face in the morning. The hour lines are parallel with one another, so there is no dial center. Since the dial plate lies in the meridian, the gnomon must be parallel to the dial plate in order for it to be parallel to the Earth's axis.

The gnomon stands vertically on the hour line of 6a.m. The height of the style above the dial plate is always equal to the distance between the hour lines of 6a.m and 9a.m as shown by x in Figure 37. This is because at 9a.m., the Sun's ray is 45째 away from the Sun's ray at 6a.m. Hence, the height of the gnomon and the Sun's ray at 9a.m. forms an isosceles triangle with the wall. (See Figure 38.)

Figure 38 90

.

10.5.2 Vertical Direct West Dial Characteristics The vertical direct west dial is placed on walls which face directly west. They can be used on any latitude.

General appearance Only the afternoon hours are drawn on the dial plate because the Sun only shines on the dial face in the afternoon. Again, since the hour lines are parallel with one another, there is no dial center. As in the case of the vertical direct east dial, the dial plate lies in the meridian, hence the gnomon must be parallel to the dial plate in order for it to be parallel to the Earth's axis.

Figure 39: This sundial, named "Sheng", is located in front of the Tan Art Center of Central Connecticut State University, New Britain. It is a 19 ft. tall steel sculpture with a circular gnomon, created by Robert Adzema. It is a vertical direct east dial and a vertical direct west dial. The dial facing us is the vertical direct west dial.

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The gnomon stands vertically on the hour line of 6p.m. The height of the style above the dial plate is always equal to the distance between the hour lines of 6p.m. and 3p.m. This is because at 3p.m., the Sun's ray is 45° away from the Sun's ray at 6p.m. Hence, the height of the gnomon and the Sun's ray at 3p.m. forms an isosceles triangle with the wall. (See Figure 40.)

Figure 40

10.5.3 Vertical Declining Dial

Figure 41: Vertical southeast declining dial, Church of St Thomas Ă Becket 92

Figure 42: Vertical southeast dial on the left and vertical northeast declining dial on the right

Figure 43: Vertical west declining dial, St Anne's church.

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Characteristics Vertical declining dials are attached to vertical walls that do not directly face North, South, East and West, but face some intermediate compass points. They can be be categorized into four types    

Southwest decliners, as shown on the wall at the lower left of Figure 44 Southeast decliners, as shown on the wall at the lower right of Figure 44 Northwest decliners, as shown on the wall at the upper left of Figure 44 Northeast decliners, as shown on the wall at the upper right of Figure 44

Figure 44: P is perpendicular to the wall and M lies in the meridian. The declination of the wall is measured by the angle D. We name the declining wall from the direction which we face if we stand with our back to the wall looking straight ahead at right angles to the wall.

General Appearance The gnomon is twisted out of the vertical in order for it to be parallel to the Earth's axis. It lies to the east of the 12-o'clock vertical line and thus among the afternoon lines if the dial declines toward southwest, but to the west among the morning hour lines with southeast decliners. The northerly dial differs from its southerly counterpart in the position of the gnomon and the order of the hour lines. The hour lines on the northerly dial are drawn in an anti-clockwise direction while the hour lines on the southerly dial are drawn in a clockwise direction.

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10. 6 Horizontal sundial

95

Figure 29: Horizontal sundial

Figure 30: Side view of a horizontal sundial 96

Characteristics The horizontal dial is pole - style. It is the one of the most commonly used sundial because it can be used to tell the time whenever the Sun is shining since the dial plate is placed horizontal to the ground.

Some other types of sundials, such as the vertical dials can only be used during restricted hours of the day.

General Appearance A horizontal sundial consists of a flat horizontal dial plate with hour lines which radiate outwards from the tip of the gnomon, which is the upright triangular plate. See Figure 31 for the general configuration. If the line OA is orientated in a true north-south direction, with O toward south and A toward north, the shadow of the style, falling among the hour lines will indicate the time of the day.

Figure 31: Dial plate of a horizontal sundial The Mathematics of Horizontal Sundial We will now show the mathematics of how the hour lines are being drawn for a horizontal sundial.

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Figure 32 In Figure 32, OP is the style pointing to the pole, P. PNS is the meridian, NPT is the hour angle and TON is the shadow angle. By using one or more of the relations of spherical trigonometry, we can deduce that cos NP cos PNT = sin NP cot TON - sin PNT cot NPT in which PNT = 90º, NP = Ø and TON = Since cos PNT = 0, sin PNT = 1, therefore 0 = sin Ø cot tan

- cot (HA)

= sin Ø tan (HA)

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Figure 33: The calculated shadow angles at latitude 51ºN.

Adjustment for various latitudes Most sundials that are available in the market do not work without a little adjusting.

Many of these "popular" horizontal dials have a gnomon which is set at 45º. This means that this dial is, hopefully, designed for use at latitude 45º.

The gnomon needs to point to the north celestial pole, so unless the angle of the gnomon is equal to the latitude, the horizontal dial must be "tipped".

If the gnomon was set at 45 º to the dial plate, but the latitude is 30º, then there is a difference of -15º between the gnomon and the latitude. So we must tip the whole dial so that the gnomon is lowered 15º.

If the latitude was greater than the angle of the gnomon then we would tip the whole dial so that the gnomon is raised the correct magnitude.

These adjustments will correctly adjust for the new latitude.

Figure 34

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10. 7 Altitude dials Altitude dials are dials that use the altitude of the Sun to tell time. The best known altitude sundial is the shepherd's dial.

Shepherd's Dials Characteristics The shepherd's dial is one of the simplest and most widely used portable dials. It is also called the pillar's dial, the traveler's dial, and the cylinder. Although the shepherd's dial is not very accurate, it is easy to make and inexpensive. It indicates the time of day from the Sun's altitude, which depends not only on the time of day, but also on the latitude and time of year. It is designed for a particular latitude and is adjustable for the date.

General Appearance

Figure 45: Shepherd's dial, set for a latitude of 52ยบN

Figure 46: Shepherd's dial made from an empty soup can 100

Figure 47: Hour lines on a shepherd's dial The shepherd's dial consists of a cylinder capped by a movable top to which a gnomon is attached. The cylinder is usually hollow to contain the gnomon when it is not in use.

The hour lines are either drawn on a paper which is glued to the cylinder or inscribed directly on the surface of the cylinder. The hour lines appear as curves on the rounded face of the cylinder and they lie close together in winter, and also near noontime, so that the instrument is least accurate at those dates and times.

The months of the year are traced around the base of the cylinder.

How it works The length of the shadow of an object depends on the altitude of the Sun in the sky. (See Figure 48.)

Since the altitude of the Sun is dependent on the time of the year, the gnomon has to be swung to the correct position of the year. Letters around the base of the cylinder indicate the months. (See Figures 46 and 47.)

101

Figure 48 In use, the dial is hung by a string fixed to the tip of the cap, with the gnomon extended toward the Sun. The shadow of the gnomon then falls straight down and ends somewhere between the hour lines.

10.8 Azimuth dial - analemmatic dial The azimuth dial, as the name implies, depends mainly on the azimuth of the Sun. The only representative of the azimuth dial is the analemmatic dial.

Characteristics The analemmatic dial is a pole - style dial. It is not commonly used because its style requires daily setting. The gnomon is a vertical pin or rod which is moved about from place to place according to the sun's declination.

General Appearance

102

Figure 49:Analemmatic dial in the University of Georgia (USA)

Figure 50: Dial face of an analemmatic dial The analemmatic dial consists of hour points which fall along the circumference of Figure 51 103

a horizontal elliptical dial face. The major axis of the ellipse runs east-west. A date line is set along the minor (north-south) axis. A vertical gnomon, preferably a person with his hands pressed above his head, is placed on the correct date. The time is read from the point where the shadow (or its extension) of the person's finger tips intersects with the ellipse. (See Figure 51.) The size of the dial face should fit a human gnomon.

The shape of the analemmatic dial depends on the latitude. On the equator, the ellipse is pinched into a straight line, with a long date line at right angles. Moving away from the equator, the date line shrinks and the minor axis of the ellipse grows. At the poles, the ellipse would become a circle, and we get the equatorial dial.

How it works

Figure 52

104

The principles behind the analemmatic dial can be derived from the equatorial dial. We shall consider an equatorial dial of the armillary type. Choose a certain time, for instance 11 o'clock. At 11 o'clock on different days, the shadow of the gnomon always hits the 11 o'clock mark on the hour ring.

We can find out which point of the gnomon causes the shadow by drawing a ray of sunlight 'through' the gnomon to the 11 o'clock mark. On the summer solstice (21st June) the Sun is high in the sky, and it is the green ray that causes the shadow. On the equinoxes (21st March or 22nd September), the Sun is lower and gives the yellow ray. In this way a date scale could be constructed along the gnomon, which would run from the green dot (21st June) to the purple dot (21st December) and back again to 21st June. Now project the hour ring vertically onto the ground. The projection is an ellipse, with the major axis running east-west and the minor axis running north-south. The projections of the hour marks are on the ellipse; some are indicated by blue dots. The point for local noon is at the north side, on the minor axis. Also project the date scale that we constructed along the gnomon, vertically on the ground. And imagine that the vertical green, yellow and purple lines are real rods. On 21st June, the shadow of the vertical green rod will just hit the 11 o'clock mark on the ellipse. Likewise, on 21st March and 22nd September, the 11 o'clock mark will be hit by the shadow of the yellow vertical rod, and on 21st December by the shadow of the purple rod.

10. 9 Portable dials Prior to the early seventeenth century, pocket watches were uncommon, expensive, and unreliable. The traveler who wished to keep track of time was forced to rely on a portable sundial. Besides the shepherd's dial, the following are some of the more commonly used portable dials.

Tablet Dial

Figure 53: Tablet dial 105

Figure 54: Tablet dial made in Nuremberg by Johann Gebhart in 1556 A tablet dial is made up of two small distinct sundials hinged together by a common gnomon. One is an ordinary horizontal dial and the other a vertical direct south dial, both sufficiently small in size so that when folded at the hinge, they can fit into the pocket. A tiny compass is embedded in the horizontal dial to align the gnomon to the north. A tiny plumb line is attached to the vertical dial to assure its verticality.

10.10 Cubic dial

Figure 55: Cubic dial 106

The typical cubic dial carries five standard sundials - a horizontal dial on the upper face, and vertical direct north, south, east and west dials on the side faces. A small compass in the base is used for orientation.

The five dials of the cubic dial are all drawn for the same latitude, but the instrument is made usable in all latitudes by placing a joint in the pedestal on which the cube stands. If we want to use the dial in some latitude other than that for which it was designed to be used, we only have to tilt the cube until all the gnomons point toward the NCP.

10.11 Universal ring dial

Figure 56: Universal ring dial This type of portable dial is called universal because it is adjustable for use in any latitude.

Pivoted across the center of the outer ring is a thin metal "bridge". The bridge is slotted and bears a cursor pierced with a tiny hole. The cursor is moved to that point on the bridge which corresponds to the day of the observation. The Sun shining through the tiny hole casts a beam of light on the inner surface of the time ring, which is calibrated to show the hours of the day.

To use the dial, adjust the suspension ring to the correct latitude, using the upper scale if one is at the northern hemisphere and the lower scale if one is at the southern hemisphere. Next, slide the cursor on the bridge to the correct date. Then, put the hour ring 90째 down until it touches the stoppers.

Then hold the sundial on the string and turn it slowly until a sun ray hits the notch on the hour ring.

Now you can tell the local time. If applied correctly, the outer ring will now be aligned in the northsouth direction, the hour ring will be parallel to the equator and the bridge with the cursor will be parallel to the axis of the earth.

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10.11 Perforated ring dial

Figure 57: Perforated ring dials The perforated ring dial is made in the form of a rather broad circular band pierced in the middle of one side with a tiny hole through which a sunbeam was projected among hour numbers inscribed on the opposite interior surface of the ring. The hour numbers are usually too crowded for accurate reading unless the ring is very large, in which case they lose their portability.

Figure 57 shows two perforated ring dials. They can be used at any time of the year by sliding the tiny hole to the correct date. They are designed for use at a certain latitude. The tiny hole is moved such that it points toward the Sun so that the sunray will pass through the tiny hole, and hit the hour numbers on the interior surface of the ring. The hour number that the sunray hits gives the time.

College Sundial Sundials are typically used to tell time. However, by adding other markers on the dials, we can use these dials to provide more information. These markers are known as dial furniture. We shall use the sundial from Queens' College in Cambridge, England to explain dial furniture.

108

Figure 58: College Sundial This photo dates from late 1968. The shadow of the gnomon lies exactly on the 2 o'clock line. The shadow of the ball can be seen at bearing SWBS at roughly 25째 elevation.

Figure 59: Computed dial plate of the College dial 109

This is how the dial would look like if the lines on the dial plate are perfectly computed. The actual dial (see Figure 58 above) only approximates to this form.

Information can be read from the dial as follows.

Time of day Look for the shadow of the gnomon among the lines radiating from top centre to the roman numerals on the border of Figure 58. The roman numerals give the hour of the day, and the minutes between the hours can be estimated. Note that the quarter-hours are marked. The following are points to note when reading sundials, in particular the Queens' College dial shown above: 1. Our watches and clocks are set (during winter) to a mean time based on time at the Greenwich Meridian, called Greenwich Mean Time. Sundials at a longitude different to Greenwich will display the solar time appropriate to their longitude. Cambridge is close enough to the Greenwich Meridian for time in Cambridge to be almost the same as time at Greenwich, so no correction on account of longitude is required when reading this dial.

2. We switch our clocks an hour forward in the summer to make better use of daylight. This is known as daylight saving time. Hence, between the last Sunday of March and the day before the last Sunday of October, clocks and watches are set to British Summer Time, which is one hour ahead of Greenwich Mean Time, and therefore about one hour ahead of mean time in Cambridge. So although our clocks indicate 2p.m., the dial only shows 1p.m.

3. Solar time (as given by the dial) may differ from mean time (as shown by our clocks and watches) by up to 16 minutes in either direction, according to the time of year. This divergence is given by the equation of time.

For all further information, you need to locate the shadow of the ball on the gnomon amongst the pattern of curves and lines on the dial. The ball is indicated in Figure 58.

Time of year (Sign of Zodiac) Look for the shadow of the ball amongst the curves coloured green in Figure 59 above. Then, if you are between midwinter and midsummer, look to the right-hand ends of the green curves; or if you are between midsummer and midwinter, look to the left-hand ends of the green curves.

The two green lines that the ball's shadow lies between will enclose the current sign of the zodiac. On the dial itself (Figure 58), the sign of the zodiac is drawn in full, and accompanied by its symbol (refer to Figure 60). On Figure 59, only the symbol is shown.

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Figure 60: Zodiac signs and symbols

Month of year Written in Latin outside the signs of the zodiac are the names of the months (too small to reproduce in Figure 59), with the breaks between the months shown. By interpolating the position of the ball's shadow between two green lines, and extending that interpolation to the column of month names, you can tell the month of the year, and estimate the date within the month.

Time of Sunrise Note the position of the ball's shadow between the green lines, and extend that relationship to the column on the left labeled ORTUS SOLIS. Times of sunrise are marked for each green line, and you have to interpolate between the given times to find the current time of sunrise.

Length of Daylight Hours Note the position of the ball's shadow between the green lines, and extend that relationship to the column on the right marked LONGITUDO. The length of daylight is given in hours and minutes for each green line, and you have to interpolate between the given figures to find the current length of day.

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Elevation of the Sun above the Horizon Note the position of the ball's shadow amongst the red lines. Each red line is marked with elevation in degrees above the horizon, at intervals of ten degrees. You can interpolate to estimate the elevation to the nearest degree.

We shall go on to explain how we get these red lines.

The relation that connects altitudes with the hour angle (HA) for the Sun for a particular latitude Ă˜ and declination

equation is,

sin (alt) = sin Ă˜ sin

+ cos Ă˜ cos

cos (HA)

Using elementary calculus, we will differentiate the above equation to get,

This equation shows how the altitude varies with respect to the hour angle.

Compass Bearing of the Sun Note the position of the ball's shadow amongst the vertical lines. These are shown blue on the diagram above, but are black on the dial itself. Each vertical line is marked with a compass bearing, as shown in Figure 59.

Temporary Hours There is one further set of lines, shown purple in the diagram above, but black on the dial itself. These lines subdivide daylight hours into twelve equal parts, whatever the time of year, which was a common method of measuring working hours before the advent of clocks. In Figure 59, the temporary hour lines coincide with the solar time lines (the ones projecting to the roman numerals) at the equinox (on Figure 59, the green line which is straight and sloping). On the actual dial (Figure 58), the agreement is not as good.

Time of Night Underneath the dial is a table of numbers: 1

2

3

4

5

6

7

8

9

10 11

12

13

14

15

0.48 1.36 2.24 3.12 4.0 4.48 5.36 6.24 7.12 8.0 8.48 9.36 10.24 11.12 12.0

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16

17

18

19

20 21

22

23

24

25 26

27

28

29

30

You are required to know the day of the lunar month (1-30). For instance, Full Moon is on day 15.

You locate the current day of the lunar month on the top or bottom line, then read off a time from the centre line, in hours and minutes. This gives the time which needs to be added to, or subtracted from, the apparent time as indicated by the shadow of the gnomon as cast by moonlight, in order to yield the time of night.

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Bibliography    

Earle AM (1971). Sundials and Roses of Yesterday. Rutland, VT: Charles E. Tuttle. ISBN 0-80480968-2. LCCN 74142763. Reprint of the 1902 book published by Macmillan (New York).

A.P.Herbert, Sundials Old and New,Methuen & Co. Ltd, 1967.

Mayall RN, Mayall MW (1994). Sundials: Their Construction and Use (3rd ed.). Cambridge, MA: Sky Publishing. ISBN 0-933346-71-9.

Hugo Michnik, Theorie einer Bifilar-Sonnenuhr, Astronomishe Nachrichten, 217(5190), p. 81-90, 1923



Rohr RRJ (1996). Sundials: History, Theory, and Practice (translated by G. Godin ed.). New York: Dover. ISBN 0-486-29139-1. Slightly amended reprint of the 1970 translation published by University of Toronto Press (Toronto). The original was published in 1965 under the title Les Cadrans solaires by Gauthier-Villars (Montrouge, France).



Frederick W. Sawyer, Bifilar gnomonics, JBAA (Journal of the British Astronomical association), 88(4):334–351, 1978



Gerard L'E. Turner, Antique Scientific Instruments, Blandford Press Ltd. 1980 ISBN 0-7137-1068-3



J.L. Heilbron, The sun in the church: cathedrals as solar observatories, Harvard University Press, 2001 ISBN 978-0-674-00536-5.



Make A Sundial, (The Education Group British Sundial Society) Editors Jane Walker and David Brown, British Sundial Society 1991 ISBN 0-9518404-0



Waugh AE (1973). Sundials: Their Theory and Construction. New York: Dover Publications. ISBN 0486-22947-5.



"Illustrating Shadows", Simon Wheaton-Smith, ISBN 0-9765286-8-1, LCN: 2005900674



"Illustrating More Shadows", Simon Wheaton-Smith, both books are over 300 pages long.



Quadrent Vetus: http://adsabs.harvard.edu/full/2002JHA….33..237K



Horary Quadrent: http://www.raco.cat/index.php/Suhayl/article/download/199578/266898



Manuscript: http://www.artfact.com/auction-lot/quadrans-vetus,-and-other-texts-on-the-constructi-584c-3lan5tbzm4



Islamic

Astronomy:

http://www.siasat.pk/forum/showthread.php?102927-Islamic-Astronomy-

Astronomical-instruments 

For further information on (astrolabic) quadrants in the Islamic World see David King, Article ‘Rub” in: The encyclopedia of Islam, vol. 8 (1995), pp. 574-75.



Starteach Astronomy: http://www.starteachastronomy.com/arab.html



See

more

at:

http://traveltoeat.com/arabian-astrolabes-clocks-and-sundials-british-

museum/#sthash.kxHXwz5s.dpuf 

http://www.britannica.com/clockworks/main.html

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

http://freepages.pavilion.net/users/aghelyar



(Andre E. Bouchard is the chairman of Communications ABC inc., a communications research company, and is Secretary General of the Commission des Cadrans Solaires du Quebec)



Make your own sundial at http://www.bbc.co.uk/norfolk/kids/summer_activities/make_sundial.shtml Many interesting sundial designs http://www.sundials.co.uk/newdials.htm Sundials on the internet has many examples from all over the world http://www.sundials.co.uk/ Precession of the Equinoxes explains the way the Earth'??s rotation changes. This site has a good explanation and a useful animation: http://en.wikipedia.org/wiki/Precession A comprehensive explanation of many different calendars and how they work can be found at:http://astro.nmsu.edu/~lhuber/leaphist.html For Galileo, Huygens and Harrison go to the MacTutor website: http://www-history.mcs.st-and.ac.uk/history/ National Maritime Museum: http://www.nmm.ac.uk/index.php Jackie Carson wrote in to us to recommend this article too: http://www.timecenter.com/articles/when-time-began-the-history-and-science-of-sundials/

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