While clocks and calendars are indispensable in our everyday lives, they are also taken for granted, and rarely warrant a second thought. But for young students just beginning to explore their world and universe, questions like "Why are there twenty-four hours in a day?" are important, for it indicates that they are trying to discover the underlying order and sense of everyday life. It is important to address such questions, lest a youngster draw the incorrect conclusion that no one really knows why things are the way they are, or, even worse, that there is no underlying reason or order, and that things just are the way they are.

Already the students have many examples of the importance of time keeping devices. They use alarm clocks to wake up in the morning (or have parents who use alarm clocks), they check the clock to wait until lunch or recess. The calendar even helps the student check if it's a vacation day! Ask the class to help you list all the ways in which they use clocks and calendars on the blackboard, and everyone might be surprised by the length of the list! Most of the uses volunteered by the class will be eminently practical; more than for any other reason, clocks and calendars were developed to satisfy very practical needs. Ancient Egyptian farmers needed to know when the Nile would flood. Farmers today still need to know when to plant certain crops. Carpenters and other workers need to know how much more sunlight they have to work under. Mariners have always needed reliable times for high and low tides.

In this chapter, we explore many different ways to measure and record time. The most important points are these:

• Almost any regular, predictable phenomenon can be used to record the passage of time
• Orderly patterns of these phenomena help to construct useful frames of reference
• Calendars grew out of such phenomena
• The development of calendars is still evolving
• Any proposed calendar must be compatible with observations (100-day years are contrary to observations!)
• Many cultures have divined mystical significance from the timing of natural phenomena, often integrated into their calendars

Discussion

How could we lengthen the amount of time it takes to empty one of the bottles? How could we shorten the time? How does the size of the hole between the bottles affect this time? What advantages does this type of clock have over the sundial? Are there any disadvantages? Would this be a good clock to try to keep the time of day? What about timing specific events, like hard-boiling an egg?

Activity 3-2: The Water Clock

Uniformly dripping or flowing water also can be used to mark time. This activity builds a clock based on dripping water.

Materials: Coffee can; glass or clear plastic container to collect water; small nail; hammer; masking tape; marker; water; wristwatch or classroom clock for calibration.

• 1. Poke a small hole in the center of the bottom of the coffee can with the nail and hammer.

• 2. Over a sink, put some water in the coffee can. Ideally, water should drip from the hole at a uniform rate. Adjust the size of the hole as necessary, perhaps using a larger nail, for example.

• 3. Place the coffee can on top of the clear container. The clear container must be narrow enough so that the coffee can does not fall through its opening and strong enough to support the coffee can filled with water.

• 4. Place a strip of masking tape along the height of the clear container, on which will be recorded the time required for the water to reach a given level.

• 5. Fill the coffee can with water and see how much of the clear container is filled in one minute. Mark the height of the water at convenient intervals (e.g. minutes) on the masking tape.

Discussion

What advantages does the water clock have over the sand clock? Does it have any disadvantages? Does it serve the same purpose? How does it compare with the sundial?

Activity 3-3: The Candle Clock

Any process which is observed to occur at a constant rate can be used to mark the passage of time. The burning of a candle is just such an example. As a candle flame burns, it consumes the fuel contained in the paraffin on the candle. As it is used up, the candle appears to shrink in length. The rate of shrinkage should be roughly constant throughout the life of the candle, and, therefore, can be used as a marker of the passage of time.

Because fire is involved, it may be best to perform this activity as a demonstration for the class instead of as a strictly "hands-on" activity.

Materials: Two identical, thin candles; candle holders; sharp pencil; match or lighter; wristwatch or classroom clock.

• 1. Set the two candles next to one another in their candle holders. Light one of the candles and note the time.

• 2. At convenient intervals (e.g. one, five, or ten minutes depending on the size of the candle), mark the new height of the burning candle on the unlit one.

• 3. When complete, the unlit candle will be "calibrated" with timing marks and can therefore be used as a clock. The timing marks could also be transferred to other identical candles.

• 4. This activity could be repeated with a variety of candles, from thin birthday cake candles to very thick candles in order to make clocks of different durations.

What advantages does this clock have over either the sand or water clocks? What about its disadvantages? How does it compare to clocks like the sundial? Could the candle clock be used to measure the time of day? Could it measure time intervals? Why might someone choose a sand or water clock over a candle clock?

Activity 3-4: The Atomic Clock

Keeping precise time is very important not only for astronomers, but for navigators, both civilian and military, as well. As a result, governments often keep precise time and provide signals to navigators, astronomers, and anyone else who wants to "listen in". Today's atomic clocks are indeed very precise; the best will only be off by one second in 300,000 years, and more improvements are on the way!

While atomic clocks are very complicated pieces of machinery which rely on complicated nuclear theory, their overall concept is simple. Cesium is the element which is used in most atomic clocks. Exposing a certain amount of cesium to microwave radiation, electrons in orbit around the nuclei inside cesium atoms will become excited and will change their orbit. Scientists are able to observe how many cycles of electrons jumping between orbits in the cesium atom will happen in a certain time period (say, a second). The clock only needs to detect and count all the cycles until the expected number (in the case of cesium, it is 9,192,631,770 cycles!) is reached. The clock then declares one second to have passed, and starts all over. Instead of grains of sand or drops of water, we are now counting leaping electrons, but the basic idea is the same!

International agreements between many governments have led to the establishment of a standard time, called Coordinated Universal Time, which is coordinated by the Bureau International de l'Heure in Paris. With Coordinated Universal Time (UTC or UT), most time stations are able to remain within one-tenth of a millisecond (0.0001 seconds)!

In North America, radio time signals based on UTC are available from two sources: WWV at Fort Collins, Colorado, and CHU in Ottawa, Ontario. Similar signals are available by telephone from the U.S. Naval Observatory in Washington, D.C., and from Canada's National Research Council in Ottawa. While the service is free via short-wave, there are toll charges for the telephone calls. Either way, it's fun to listen in!

• 1. If a short-wave radio is available, tune in to either CHU or WWV at one of the listed frequencies. Otherwise call one of the telephone numbers listed on the next page, preferably from a speakerphone so all can listen in.

• 2. Synchronize a wristwatch or the classroom clock with the signals from the atomic clock. (You may need to account for your time zone.)

• 3. Check the atomic clock again in a week or so, and see if your clock still agrees. If not, by how much do the clocks differ?. Repeat this measurement and make a chart of this time difference for each week. After a while, you should be able to predict the time difference.

Discussion

Why would anyone need the accuracy afforded by atomic clocks? Why does our clock differ from the atomic clock? We can only assume that our clock is less accurate than the atomic clock, and that our clock is responsible for the discrepancy. How could we prove this assumption?

In the activities of Chapter 1, we found that midday, when the Sun is highest and directly South in the sky, rarely corresponds to noon, as told by the clock. It used to be common for each city to keep its own time according to the position of the Sun in the sky. Long train rides, particularly easterly and westerly trips, often required travelers to change their watches several times.

About a century ago, this problem was addressed at an international meeting and twenty-four standard time zones were adopted. All of the clocks in a given time zone are set to the same time, and adjacent time zones differ by one hour. Each time zone is centered about a line of longitude, or meridian. Since it takes twenty-four hours for the Earth to rotate (or for the Sun to pass over all of the Earth), and a circle is 360° around, the width of each time zone is one hour or 15° in longitude.

The establishment of standard time zones is intimately linked with the establishment of the standard grid of latitude and longitude. The prime meridian, corresponding to longitude 0° and passing through Greenwich, England, is the center of time zone zero. Coordinated Universal Time (UTC) is the time at time zone zero and is often given as a standard time for astronomical and navigational purposes. Since the Earth rotates to the east, time zones to the east of time zone zero are ahead; time zones to the west are behind. Accordingly, the time zone to the west of Greenwich, is centered about the 15°W meridian and is one hour behind (-1) Greenwich. Similarly, the time zone centered about 15°E is one hour ahead (+1) Greenwich.

The boundaries between time zones are often altered to correspond to geographical and political borders. The International Date Line corresponds to the meridian at longitude 180°, for the most part passing through the sparsely populated Pacific Ocean. The calendar date jumps discontinuously across this line, moving ahead one day from east to west and moving back from west to east.

Because of this line, a traveler may leave Japan late Monday night and arrive in Hawaii first thing Monday morning! As confusing as this may seem, a simple example should demonstrate the necessity of the Date Line. Pretend it's six o'clock Monday evening in London (1800 UT). Moving 90° to the east, in Tashkent (UT +6), it would be midnight, ending Monday and beginning Tuesday. At the International Date Line (180°), it should be six o'clock Tuesday morning. As we cross the International Date Line, continuing eastward, we should decrement the calendar day back to Monday. If we don't, however, Chicago's time (UT -6) would be Tuesday's Noon and London's would be six o'clock Tuesday evening. But we started this example assuming it was six o'clock Monday evening in London. If we do decrement the calendar day while crossing the International Date Line, however, both Chicago and London are still in Monday, as expected.

There are four time zones in North America: Eastern (-5), Central (-6), Mountain (-7) and Pacific (-8). Alaska and Hawaii are in their own time zone (-8). Between the first Sunday in April and the Last Sunday in October, the United States observes Daylight Savings Time, during which clocks are set ahead one hour of the standard time for their time zone.

Activity 3-5: What Time Is It?

Through the activities of Chapter 1, especially "Day and Night on the Spinning Globe", the students should already understand that different locations on the globe experience day and night at different times. Even still, the whole notion of time zones may seem a bit mysterious at first glance. Concrete examples should help, though, especially if they can be personalized, perhaps by associating different time zones with relatives or friends of the students living in them.

Materials: Globe or world map; Post-It pads; scissors; wristwatch or classroom clock.

• 1. Cut a Post-It pad into inch-wide strips.

• 2. Write the approximate local time on one section (making sure to indicate AM or PM, and the day). Place this at your location on the map or globe.

• 3. Label several other cities and time zones similarly. Try to pick cities with some personal meaning to the students; students may have recently visited other cities on vacations, seen them on TV, or have close relatives living there.

• 4. Also try to pick some very distant cities so some of them will be in night time. If this is done on a globe, a light source could be shone above that time zone for which it is currently noon to approximate the current appearance of the Earth.

• 5. Ask the students "What time is it?" at various locations, both marked and unmarked. Remember that even if a time zone is not marked, every 15° of longitude is about one hour of time.

Discussion

If it's noon in New York, what time is it in Chicago? Why do Miami, New York, and Boston all share the same time, but Chicago is an hour behind? Is there anywhere on the globe where it's "tomorrow"? Is there any time when every time zone is in the same day?

Does noon as given by the "standard time" of your time zone correspond to midday as observed with a sundial or shadow stick? If they don't correspond, where might they? Why doesn't each city just use its own local solar time? What complications would there be?

Activity 3-6: Daylight Savings Time

Through our studies of the seasons in Chapter 1, we have already seen that the number of daylight hours increases as the summer solstice (around June 21) approaches and decreases as the winter solstice (around December 21) nears (see Chapter 1, Topic 5, "Seasons"). How, then, can we "save" daylight?

Daylight savings time doesn't "save" daylight in the traditional sense, since we can't save daylight during the summer and spend it during the winter when we need it; unfortunately, daylight's not like the money we can save for a rainy day! We have already investigated the change of sunrise and sunset times during the year in Chapter 1 (see Chapter 1, Topic 5, Activity "Sunrise and Sunset Changes"). We can use the graph of sunrise and sunset times from that activity or make a new one from an almanac like the Farmer's Almanac. Such a graph shows us that as the number of daylight hours increase, not only does the sun set later, but it also rises earlier. On June 21 in Boston, for example, the Sun rises at 4:07 AM (EST). Few of us are even awake at that hour!

What Daylight Savings Time really does is "save" that early morning light until more of us are awake. By setting the clocks ahead by one hour, the Sun rises at 5:07 instead - still early enough for most of us - and doesn't set until 8:24 in the evening. That extra hour doesn't affect many of us in the morning, but the extra hour of light in the evening when most of us are awake lessens our demand for artificial lighting, thereby saving energy. And it is energy, not daylight, which Daylight Savings Time is really intended to save.

Materials: Chart of sunrise and sunset times from Activity "Sunrise and Sunset Changes" in Chapter 1 or the materials to make one

• 1. If necessary, make a new chart of sunrise and sunset times along the vertical axis and dates during the year along the horizontal. One or two times per month should be sufficient to draw a smooth curve connecting them. Label the daylight and night hours.

• 2. Have the students compare the times of sunrise and sunset during the winter months with those during the summer months. How much earlier does the Sun rise during the summer than during the winter?

• 3. With the assumption that more people need light in the evening than during the early morning, can the students devise a system to "transfer" the early morning light to the evening? The current model of one hour ahead from April to October is only one possibility! Have each student or group study the problem, devise a solution, and propose a solution to the class.

Is there any cause for disagreement about the duration or extent of Daylight Savings Time between people living in the same time zone? Does Daylight Savings Time affect people living in the western parts of time zones the same as those living in the eastern parts? What would happen if we always used Daylight Savings Time? Would the effects be felt equally across each time zone?

What makes one solution better than another? Might we not choose to set the clocks ahead by only half an hour for a while and then set them ahead a full hour for June, for example? What advantages or disadvantages might this scheme have?

An old New England anecdote describes how farmers received reliable weather reports before radio, TV, and even the Farmer's Almanac. Each morning, the farmer would look at a stone hung outside his window. Just a glance could tell him just as much about the weather as any high-tech modern gadgets: if it's wet, it's raining; if it's white, it's snowing; if it's swaying, it's windy; and if it can't be seen, it's foggy. Similarly, many of the simplest ways of determining time are obvious: if it's dark, it's night; if light, day; if warm, summer; if cold, winter. Unfortunately, such simple indicators are usually not sufficient. It is not enough for people planning winter rations of food to know that it's winterя they need to know for how much longer it will be winter. Farmers planning their crops need to know when to plant their fields.

Nature does provide several other ways to keep track of time, however. As we have seen in Chapter 1, the motion of the stars can be used as a calendar of sorts. Even more conspicuous in the evening sky than the stars, however, is the Moon. The Moon shines very brightly with reflected sunlight. As the Moon orbits the Earth, we view it from different angles, and see its different phases. The phases of the Moon provided the foundation for many early calendars. In this Topic, we will explore how we might keep track of time with the Moon.

Activity 3-7: Make a Lunar Calendar

The moon is the most conspicuous object in the night sky. Its differing appearance as it follows its cycle of phases is a natural and obvious way to track time. This activity encourages students to think about our calendar and alternate calendars and also will raise their awareness of the moon.

Materials: Calendar for current year with moon phases; paper; pencil.

• 1. Students should count and write down the number of days between full moons. Is this number the same? What about the number of days between quarter moons? waning crescents? waxing crescents?

• 2. Students should try to devise calendars based on their observations and calculations. They must decide where in the moon's cycle to begin the month. They may name their months.

• 3. Some students may be able to make a whole year of moon months and join them together into a calendar or paste them to charts. They can calculate the number of days in twelve lunar months and devise a strategy to deal with any extra days.

Discussion

How useful are the moon's monthly cycles in constructing a calendar? Are there any difficulties involved with basing a calendar on the lunar cycle? Is seven a good number of days per week? Could we have 5 days in a week or 10? What strategies can be used to insert the extra days into the lunar calendar? How could these days be used? In what ways could this calendar be used? What other data could we use to help improve these calendars? How would we compensate for the 1/4 day extra each solar year? Could there by another system than leap year to even up the calendar?

As the Earth orbits the Sun during the year, our perspective changes, causing the Sun to appear to move with respect to the much more distant "fixed" stars. During the day, of course, it is impossible to see any stars near the Sun because it appears so much brighter than the other stars. By observing just before sunrise and just after sunset, however, it is possible to determine which stars are presently near the Sun. There are twelve constellations through which the Sun appears to move during the course of one yearя the constellations of the Zodiac.

Zodiac comes from Greek words meaning "wheel of life". This name gives an indication of the importance these constellations must have had for ancient people. Indeed, these "sun signs" are the most familiar remnants of the pagan religion of Astrology. About 3,000 years ago, when the Babylonians adopted the twelve familiar constellations of the Zodiac, the Sun appeared to be in the constellation of Aries (The Ram) at the time of the Spring Equinox (around March 21). After Aries, the Sun appears to move through Taurus (The Bull), Gemini (The Twins), Cancer (The Crab), Leo (The Lion), Virgo (The Virgin), Libra (The Scales), Scorpio (The Scorpion), Sagittarius (The Hunter), Capricorn (The Mountain Goat), Aquarius (The Water Bearer), Pisces (The Fish), and back to Aries, thereby completing the yearly cycle (see table).

Astrologers classify people according to which constellation the Sun appeared to be in at the time of their birth. People born near the Spring Equinox, for instance, are "Aries". Horoscopes in newspapers are given according to this assignment of Sun signs. The first activity in this Topic gives the students an opportunity to find out their Sun signs and learn about their zodiacal constellation. We mentioned that when the Babylonians adopted the twelve Zodiacal constellations, the Spring Equinox's Sun was in the constellation of Aries. This is important because in the 3,000 years which have passed, the Earth's axis has moved such that the Sun now appears to be in Pisces on the Spring Equinox, and relatively soon (in about 400 years), the Sun will be in Aquarius on the Spring Equinox. People who are Aries (by the calendar) are actually Pisces (by the stars)! This motion of the Earth's axis is called precession, and we will investigate this phenomenon in the final activity of this Topic.

Activity 3-8: The Sun's Yearly Trip Though the Zodiac

As the Earth travels around the Sun during its yearly path, the Sun appears to move through the sky with respect to the distant, "fixed" stars. In this activity, the students will play the role of the Earth and walk around the Sun to watch this motion.

Materials: 12 index cards; 13 chairs; masking tape; a yellow ball or similar object to represent the sun

• 1. Place one chair in the middle of an open area. Put the Sun on that chair. Place twelve chairs in a large circle around the Sun chair. The fronts of the chairs should point away from the Sun.

• 2. Label each index card with the name of one zodiacal constellation. Tape these cards to the backs of the twelve chairs in order (counterclockwise): Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces.

• 3. Have the students walk along the outside of the chairs (counterclockwise). Notice that even though it is the Earth (student) which is moving, it is the Sun which appears to move through the entire Zodiac!

There are twelve constellations in the Zodiac, just as there are twelve months in the year. While the alignment is not perfect, each month basically has its own Zodiac sign. This fact allows us to use the Zodiac as a crude calendar, accurate to the nearest month. People often refer to their Zodiac sign. This just refers to the constellation which the Sun appeared to be in when they were born, if they were born in Babylonian times! Since then, we know the earth's axis has precessed and has caused an apparent shift of the sun against the background stars. The next activity will allow each student to learn about his own zodiacal constellation.

Activity 3-9: Hi! What's Your Sign?

People's "Zodiac Signs" are just the constellations in which the Sun appeared to be on their birthday 3000 years ago. Perhaps the students will notice that the sun was actually several constellations across the sky from the one claimed. This activity is an attempt to personalize the zodiacal constellations for the student by learning his own zodiac constellation. The students can choose to calculate the actual constellation in which the sun was at the time of their birth. The students then compare their constellations with others in the class, and hopefully learn from one another's work.

Materials: One 3"x 5" index card for each student; markers; chart of zodiac constellations.

• 1. Each student should determine his Sun sign from the chart provided.

• 2. On an index card, each student should write the name of the constellation (e.g., Aries), what it stands for (e.g., The Ram), and draw the stars which comprise the constellation.

• 3. On the other side of the card, each student should determine the constellation the sun was in on their birthday in the year of their birth. They can do this by looking at the monthly star charts provided.

• 4. Have the students compare their constellations and share information about them.

Discussion

Can we make other constellations with the same stars along the Zodiac? Where do the names for the Zodiac constellations come from? Does the sun travel through any other constellations?

Activity 3-10: Precession of the Earth's Axis

Because of the gravitational pull of the Sun, the rotational axis of the Earth moves slowly through a circle with a radius of 23.5° on the sky. This effect is called precession and it can be demonstrated with a spinning toy top. It takes about 26,000 years for the Earth's axis to precess a full circle and return to its starting place. As a result of this precession, in another 14,000 years, the Earth's axis will no longer point toward Polaris, but to Vega, another bright star in our Galaxy. Perhaps Earth's inhabitants then will call Vega "Polaris"!

We need not wait 14,000 years to notice an effect of this precessional motion, however. At a rate of 50 seconds of arc per year, astronomers must correct for it when they consult star catalogs. It also causes the position of the equinox to drift westwards along the zodiac. When the Babylonians adopted the twelve constellations of the Zodiac with which we are familiar, the Spring Equinox did, indeed, occur when the Sun was in Aries. Today, however, the Spring Equinox occurs in Taurus and in about 400 years, it will occur in Aquarius. This is the "Dawning of the Age of Aquarius" popularized by a song of that name.

Materials: A toy top; hard, flat surface.

• 1. Spin a top on a hard, flat surface and observe the small circle the axis makes. As the top loses more energy and slows down, this circle should get larger and larger, until the top actually falls over.

• 2. The Earth is not in any danger of "falling over" since there is no "down" in space. The gravitational pull of the Earth is making the top precess; the gravitational pull of the Sun is making the Earth precess.

Discussion

If we could watch the Earth's axis precess, would each star be shifted by the same amount or would the star nearer the North Celestial Pole be moved more than those near the Celestial Equator? How would the precession of the Earth's axis affect the seasons? In 13,000 years (half the precessional cycle), will there still be a summer and a winter? If so, will the stars and constellations which we associate with each season still be visible in their season, or will they be visible in opposite seasons? If the Babylonians lived in the "Age of Aries" and the "Age of Aquarius" is coming, what "Age" do we live in now?

Even the earliest people noticed that certain celestial phenomena occurred in cycles: the rising and setting of the Sun, the motion of the stars, and the phases of the Moon are but a few examples. Their observations eventually allowed them to predict many celestial phenomena. While the power to predict may have brought a sense of order to their lives, more importantly, it allowed systematic planning for agricultural activity and religious observances.

There is an important distinction to be made between the ability to predict an event and the ability to understand the underlying causes of an event. For thousands of years, people have been able to predict the rising and setting of the Sun and Moon, but until about five centuries ago, it was widely believed that the Sun and Moon moved around the earth. It was not until about 440 years ago that the heliocentric theory of the Solar System of Nicolaus Copernicus (1473-1543) finally removed the Earth from the center of the Universe.

One fact that ancient people were able to infer, however, was the length of the year. The Sun took 365 1/4 days to rise at the same position in the sky. They also recognized the connection between the position of the Sun and the changing seasons. Naturally the Moon, as the most conspicuous night time object, was also studied. Its phases from the dark of the new moon to the bright full moon, with all manners of crescents in between, were carefully observed and recorded. It was discovered that the cycle from new to full Moon and back again took about 29 days. This is very close to a calendar month. The English word "month", in fact, shares the same root as the word "moon". Twelve lunar months almost equal a solar year. The problem is with the "almost"; there are eleven fewer days in twelve lunar months than in a solar year. These days needed to be made up or the seasons would gradually shift on the calendar.

Mesopotamia is widely believed to have been the Earth's first civilization. About 3000 years before the birth of Christ, the Mesopotamians established the city of Sumer in a fertile region between the Tigris and Euphrates Rivers in modern-day Iraq. The Sumerians developed a lunar calendar of 30 day cycles to help them plan their farming. They also devised a form of writing which involved marking clay with triangularly-cut reeds. Their written language allowed them to keep the first written historical, economic, and astronomical records. The Babylonians eventually replaced the Mesopotamian civilization, and in 1750 B.C., replaced the old calendar with one of their own. The Babylonian calendar was a lunar one consisting of 12 months made of 29 and 30 days in a cycle. As mentioned earlier, this lunar measuring was not consistent with the solar year; thus it was 11 1/4 days shorter than the 365 1/4 days which comprise a solar year. To make up for this shortfall, seven times in every span of 19 years, the Babylonians added one month. Interestingly, the Babylonians were one of the first to separate the year into weeks of 7 days. They arrived at this because they worshipped the Sun and Moon and five stars they observed not to twinkle. These "stars" were actually the five closest planets: Mercury, Venus, Mars, Jupiter, and Saturn. The Babylonians noticed that the planets moved across the sky through the constellations. Even today, the days of the week are named for the Sun, Moon, and five bright planets, albeit partially from the Germanic nomenclature: Sunday for the Sun, Monday for the Moon, Tuesday for Mars (Tiv in German), Wednesday for Mercury (Woden in German), Thursday for Jupiter (Thor in German), Friday for Venus (Frigg in German), and Saturday for Saturn.

The Egyptians also developed a lunar calendar to regulate their crop planting. In addition, it was important to predict the annual flooding of the Nile River which irrigated their land. The Egyptians were able to predict the flooding by noticing that before the flooding, Sirius would rise on the eastern horizon just before the Sun. Their calendar year began with the first new moon after this rising. Later, they devised a more accurate solar calendar and added a seven-day week. They needed to add a leap year day too, but their priests refused to let them do this and so the calendar moved away from the original flood time.

The Romans in 753 B.C. developed a calendar based on the solar year. The year began at the vernal (spring) equinox in March (Martius in Latin). Interestingly, the choice of March as the first month of the year is still reflected in our calendar; our names for the months of September, October, November, and December come from the Latin words for seventh, eighth, ninth, and tenth, respectively, reflecting their positions in the Roman year. The year had 305 days made up of 30 and 31 days. Sixty days which were left over had to be interspersed throughout the year. This left 1/4 of a day each year which was not compensated for and so each 120 years, the calendar would be a month late. Later two months were added, Januarius and Februarius and the 12 months were divided into four 31 day and seven 29 day months as well as one 28-day month. This added up to 355 days or 10-1/4 days less than a solar year. Days were added but usually too many so this calendar also proved inaccurate.

By 49 B.C., however, the Roman calendar was a full four months off. Julius Caesar ordered the Roman calendar improved. The politicians wanted Januarius to be the first month of the year to coincide with their terms which began in that month. The new calendar was based on a solar year of 365-1/4 days and began with Januarius, to appease the politicians. A Leap Day was to be added in Februarius every fourth year. When the Julian calendar was implemented, ninety days had to be added to resynchronize the calendar. The Julian names for the months are still with us, with the notable exception of August, named for Caesar's successor. The Julian calendar was not perfect, however, nor was it always strictly followed, so errors continued to propagate.

By the sixteenth century after Christ, these errors became a problem. There were ten extra days before the vernal equinox. But the Catholic Church was supposed to celebrate Easter on the first Sunday after the first full moon after March 21, the vernal equinox. The Pope, Gregory XIII, ordered modifications to correct the calendar. As a result, October 5, 1582 became October 15, 1582 to eliminate the accumulated 10 extra days. But the calendar required fine tuning as well. The Julian calendar's method of adding a Leap Year every fourth year was not accurate enough. As a result, the Gregorian calendar called for a Leap Year every fourth year (when the year number could be divided by four). Also, the last year in a century (1800, 1900, 2000) had to be able to be divisible by 400 in order to be a leap year. With these changes, it will take about 30,000 years to add only 10 days to the calendar.

The Gregorian Calendar has been the dominant calendar in the West ever since. It is universally used in the business world. It was not adopted by Russia until 1918, a year after the Czar fell. Many churches such as the Moslem, Jewish, and Greek Orthodox, still use their own calendars to determine religious observances, however. The state of Israel uses the Hebrew calendar. While China uses the Gregorian Calendar for daily business, it still uses its ancient lunar-solar calendar to calculate holidays such as the Chinese New Year.

Discussion

What kinds of help do calendars provide? What would it be like if there were no calendars? How might this effect people's lives? How would it effect your life? If you examine the calendar carefully, what do you notice about its construction? Does it ever change? What do you think of the way it is organized? Have you ever heard of a different form of calendar? Could the new year start on another day? Could there be more than seven days in the week?

Activity 3-11: Exploring the Calendar

Materials: Calendar for each small group of students (can be last year's calendar); glue; markers

• 1. Students meet in small groups to investigate the calendar. They may discuss and list all the uses and assistance a calendar gives us.

• 2. The group finds and records the number of days in each month. Can they devise a system for remembering these numbers?

• 3. Students can find holidays and special days and discuss if holidays and birthdays occur on the same day each year. If not, why not? If they do, why does this happen?

• 4. Some students may wish to research the names of the months or the days of the week.

• 5. Some of the students could divide their calendars by months, seasons, paste them on four large charts by seasons and illustrate them.

• 6. Students should meet to share their discoveries about the calendar.

Discussion

What did students learn about the calendar? What did they predict about the changes in holidays and birthdays? Could they design a strategy to remember the numbers of days in each month? How do they think the calendar was developed? Does anyone know of another calendar that is used? How can the calendars people use help us to learn more about them?

Activity 3-12: Make Personalized Calendars

The students can now make a calendar for themselves or as a gift, personalized with their own pictures for the months, and their own special days (birthdays, favorite holidays, etc.) included!

Materials: Colored or manila file folders (twelve each); photographs or drawings; date grids for each month to be included in the calendar from a current calendar; scissors; paste; paper punch; yarn; 8-1/2"x 11" plain white paper or 1" graph paper 8-1/2"x 11".

• 1. For each students, photocopy a set of date grids for each month to be included in the calendar from a current calendar.

• 2. Each student takes twelve file folders and cuts off the tabs. Place these together as if making a book, one inside the other.

• 3. Turn these folders sideways so that the fold is upwards. Label and glue a photo or illustration on the top side of each folder for each month. Paste the corresponding date grid for each month on the bottom side.

• 4. Personalize the date grid by annotating special days like birthdays and holidays.

• 5. When complete, punch two equidistant holes on the folds and thread yarn through these holes. Tie a secure knot to hold the calendar together.

• 6. Students can further personalize their calendars by decorating the covers.

The Gregorian calendar is fairly accurate but it is still not completely without flaws. While attempts have been made to improve upon it, none have yet been adopted. One such attempt to devise a more convenient calendar is the one by Elizabeth Achelis in 1930 called the World Calendar. One really important improvement in this calendar over the Gregorian one is that it would repeat itself without change yearly. Therefore, every year would start on a Sunday, the first of January. Also, all holidays would be on the same days each year. The year would be divided into four quarters each of which consist of 3 months or 91 days. Each of these quarters would start on Sunday and end on Saturday.

These quarters of 91 days each total 364 days or 1 1/4 days short of the solar year. To make up for this shortfall, a day called Worldsday would be added after December 30 each year and would be celebrated as a universal holiday called W Day. In addition, a day would be added at the end of June every fourth year. This would be called L day for Leap Year Day. Although this calendar would make it easier for people to remember dates and share holidays, it has not been adopted. Many religious groups still use lunar calendars and ancient rules to determine special observances and they are not willing to adapt a universal calendar. Therefore, World Calendar would have to be used in place of the Gregorian Calendar but it would not be accepted universally.

Questions to Ask: Would it be possible to devise a calendar to improve on the present one? What kinds of changes could be made? Using the experiences of organizing data into lunar, solar, and stellar calendars, what could be done to improve upon these phenomena as determining factors? Could we use the computer to help us in this task? Would it be possible to devise a calendar in which all dates would fall on the same day each year?

Activity 3-13: Invent a New Calendar

The Gregorian calendar is probably accurate enough, but might it not be possible to make a calendar which is more convenient? Perhaps each year and each month could start on the same day. Maybe a different number of days per week would allow holidays to fall on the same day each year.

Materials: Computer and database program; data diskette; paper; pencils.

• 1. Students work in small groups to plan a new calendar which solves some of the problems in the present one.

• 2. Some students can enter facts such as the number of days in a lunar month, the days in a solar year, the length of the zodiac months and rearrange the months into the most useful order they can devise. They may then develop a yearly calendar which eliminates some of the current difficulties in our calendar.

Discussion

Discuss innovations developed to improve the existing calendar and discuss examples. What would be the reaction of peoples in the world to this new system? What would be the objections? Who would support these changes?

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