IT’S ABOUT TIME

Rabbi Shlomo Cohen
www.HIQJEW.com

PART I – A HISTORY OF TRYING TO MEASURE TIME
PART II – DEVELOPMENT OF THE CALENDAR
PART III – UNITS OF TIME
PART IV – CALENDRICAL SYSTEMS OF THE ANCIENT & MODERN WORLD
PART V – A COMPARISON OF CALENDRICAL ACCURACIES
PART VI THE ACCURACY OF THE JEWISH CALENDAR
PART VII – CYCLES OF TIME IN YIDDISHKEIT
PART VIII – UNITS OF TIME IN HALACHA

The concept of time is very easy to understand on the one hand, quite difficult on the other. Simply put, we all live within the parameters and constraints of time. Our lives are bound by the concepts of past, present and future. On the other hand, time is viewed as a dimension. We cannot really put a finger on exactly what time is. We know it passes, or do we? Perhaps time does not pass us by, but rather, we live within the current and move along with the current of time. Clearly we are unable to recognize exactly how time operates. Cosmologists are in a continual struggle to explain this phenomenon of time. Time could be linear, or it could act as a stream. We could move in time, we could be moving within a framework that moves with us. As yet we simply do not know. Nonetheless, man has, from time immemorial, attempted to measure the passage of time.

PART I -A HISTORY OF TRYING TO MEASURE TIME
In fact, today, we take our wristwatches for granted, yet they are a relatively new invention. Without clocks you would be hard pressed to tell time with any degree of accuracy. On a clear day those familiar with the movement of the sun may get within 1/2 hour or forty minutes of the correct time. Those unfamiliar with the sun’s movement, or on a cloudy day, and certainly at night, the degree of accuracy slips to over an hour or more easily. In fact, the Tiferes Yisroel, in Mishnayos Sanhedrin [Perek 5, sif katan 21] tells us that Bes Din would forgive inaccuracies in testimony of up to three hours even in the testimony regarding capital cases.

All of this means that today’s precise standards of Mitzva observance were literally impossible to previous generations.

A Jewish life is defined by time. Our lives are broken up by many different time frames. Many Mitzvos are time dependent. Yet, until only 100 years ago telling time was nowhere near as easy as it is today.

Until the advent of relatively quick transportation, local time was not even an issue. With the development of the train or a fast sailing ship problems began to crop up. Although those who knew the Earth was round recognized the problem, Magellan’s crew was perplexed when they circumnavigated the globe in 1522 and returned to their starting point. According to the ship’s log it was Wednesday while those on shore were calling it Thursday. By 1883 the governments of the world needed to do something so that commerce could proceed smoothly. By international treaty they established 24 time zones, each one hour behind the last, each measuring 15o. They also agreed upon one line of longitude in the world where the date would change. Known as the international date-line, it was purposely placed in the middle of the Pacific Ocean where it would, at that time, inconvenience very few people. For a variety of Halachic reasons the Jewish date line, at least according to some Poskim, is farther west.

This simple fact raises an amazing question, which I’ve never seen dealt with in any Sefer. During the six days of creation exactly how did the process of creation proceed? When Hashem said, “Let there be vegetation”, did grass simply spring up all around the world at the same time? If so, this would mean that at the “Grand Cosmic Dateline” grass sprung up at the very beginning and the very end of the day simultaneously. Had the grass sprung up as the world turned (say at 3:33pm as every latitude hit that point), it solves one problem, that of grass growing around the clock simultaneously, but creates a new problem; that of Hashem’s words not having an immediate effect. One of the few solutions to this problem is found in Pirkei D’Rebbe Eliezer in Parshas Noach, where the idea that all creation occurred locally in Gan Eden alone and then spread out from there. This idea clearly deserves further thought and elucidation.

Accurate timepieces are a relatively new phenomenon. How did they tell time ‘once upon a time’? For all of antiquity attempts were made to measure the passage of time by utilizing water clocks, sand clocks or candle clocks. Even so, these needed some objective benchmark to establish what exactly was being measured.

Sundials were used in antiquity and have been found dating as far back as 2000BCE. There is even a reference in Tanach to one. In Yishaya 38:8 the Pasuk reads:
הנני משיב את צל המעלות אשר ירדה במעלות אחז בשמש אחורנית עשר מעלות ותשב השמש עשר מעלות במעלות אשר ירדה
They are also mentioned in the Mishna ”
“מסמר של אבן שעות” משניות עדיות פרק ג’ משנה ח’ as well as in משניות כלים פרק י”ב משנה ה’.

These worked relatively well in gross terms but were anything other than accurate. Sundials, perforce, measured shorter hours in the winter than the summer. Sand clocks lost their accuracy since sand is an abrasive and quickly wore the little hole larger and larger. Good sand clocks use crushed eggshells or other non-abrasive substance to avoid this problem. Water will double its rate of flow as it drops from 900F to near freezing rendering water clocks temperature sensitive and therefor, inaccurate. One also needed a benchmark to use as a starting point. Having made a sand clock, could you say what, exactly, it is actually measuring?

For the most part, people told time by watching the sun’s march across the daytime sky. Generally, they arose at sun up and went to sleep after sundown. By the Middle Ages, in some cities, people were able to measure time by the church or monastery bells rung five times a day to call the priests or monks to prayer. In Arab countries the Muezzin filled the same function.

By legend, church bells were invented in the 5th century in Nola, Campania. Some say that Pope Sabinianus (pope from 604-606) ordered churches to mark the hours of the day by ringing church bells. Weight driven clocks were invented in Europe around the end of the 13th century.

The invention of the mechanical clock occurred in the early 1300’s although nobody knows by whom or where the first mechanical clocks were made. Clearly, this invention needed to wait for the prior development of a technology capable of producing strong enough metals and fine enough tools to produce the gear trains, axles, pulleys, weights and hands. The first mechanical clocks were powered by water.

Clock towers in large cities, generally in churches, appeared as early as 1335 in Milan, Italy. The first large clock appeared in England at Windsor palace in 1351. These clocks simply sounded the hours by ringing bells. As late as 1500, although clocks were sounding the quarter hours, sand glasses were still necessary to measure minutes. Galileo Galilei, in 1538, discovered that the time of a pendulum’s swing varies, not with the width of the swing, but with the length of the pendulum. This simple discovery paved the way for accurate timepieces. The first pendulum clock was built in 1658. The balance spring was first invented in 1674. Spring driven clocks were invented in 1675.

The Clock makers Company in England, reported to the board of trade in 1786 that they were exporting about 80,000 clocks a year. Thus it was not until the late eighteenth century that the ability to accurately tell time was sufficiently widespread that the average person had the ability to tell time to the nearest few minutes (given inaccuracies in timepieces.).

There is a very interesting historical note here. Gebrucht, the stringency of not allowing Matzo to become wet, is first mentioned in the Halachic literature by the Shulchan Aruch HaRav [Vol. 5 Sheilos & Tshuvos #5?]. There, he mentions that until his day the people were careful to knead the dough very well prior to baking. In his time and place people became less careful with the kneading in order to bake the Matzos within the eighteen minute time frame. Hence, the possibility that some unmixed flour remained in the baked Matzo. What changed? I would guess the advent of the clock. Before then, there was no accurate way to measure the passage of eighteen minutes. Now that they had an exact means to do so, the bakers became stricter.

Electric clocks, based on the frequency of alternating current, didn’t develop until the 20th century. More recently, watches are regulated by the vibrations of a quartz crystal

Try leaving your watch at home and turning off all the various clocks around you and then see how much more difficult life becomes. Today, people sit in Shul and watch the clock to see if they’ve made the first Z’man Krias Shema to within seconds. Without that clock I would suggest that the average person is really unable to tell time to within a 40 minute error plus or minus. Even the date is something we often need to check against the calendar on the wall. Thus, the Tannaim, Amoraim, Gaonim, Rishonim and early Achronim had a problem. By the later Achronim improvements in measuring time made many Chumros more tenable.

PART II – DEVELOPMENT OF THE CALENDAR
There are over 40 different calendars in use in the world today.

It would be true to say that calendars were not only developed by cultures but by religions. Calendars are crucial for business as well as religious times. Jews, Christians, Moslems, Buddhists, Jains, Hindus, Zoroastrians and Bahai’s each have their own calendar. Amongst the Christians the Julian, Gregorian, Coptic and Ethiopian calendars are all in use today. Most religions utilize their religious calendars to date holidays but use the Gregorian for secular purposes.

Try to picture a society functioning without a calendar. Meetings become improbable. Contracts, impossible. Courts couldn’t function. Try sending out invitations to a wedding.

We will visit, in this paper, the various factors that delineate time. It is fascinating to follow the development of the calendar in various societies and to see some of the problems associated with the simple act of telling time.

A COSMIC CONUNDRUM
Accurate calendars are difficult to achieve. One question that really bothered me involves the methodology utilized by the ancients. How was it possible to achieve any degree of accuracy having only primitive, non-calibrated, non-standard measuring instruments? I tried, as a mental exercise, to figure out how they may have accomplished just that.

Scenario one: Joe Babylonian, a student at BIT [Babylonian Institute of Technologies] is required to attend the flag raising ceremony every morning in the Institute’s courtyard. Over time he happens to notice that the shadow of the flagpole changes slightly every morning moving further across the courtyard every day. He watches this for a while and notes that toward the end of March, which he called Nisanu, the shadow stopped moving and then began a slow march back around the courtyard in the other direction. This went on for 6 “months” and then the whole process repeated itself. “Eureka”, shouts Joe in a rare burst of Greek, “I’ve just invented the YEAR the EQUINOX [and Greek].” He patiently waits for 182 days and then gets up a betting pool among the other scholars as to when the shadow will change direction. For three consecutive years he wins handily. In the fourth year, to his chagrin, he loses the bet since it takes an extra day for the equinox to occur. A decade or two later, after accounting for the extra 1/4 day, he finally completes his research and publishes his findings in a 52 page cuneiform text weighing 125 pounds and calmly announces that he has just invented the LEAP YEAR [as well as cuneiform, books, fractions, pages and pounds]. His son, Joe Jr. continues his research. The betting is getting heavy. Joe Jr. always wins. A few decades pass and Joe Jr. begins losing. He carefully checks his records and notes that the extra 1/4 day his dad had been adding was just a bit too much. There appear to be slightly less than 365 1/4 days in the year. Joe Jr’s problem: How can he manage to account for the loss of time? He carefully counts off 365 1/4 days. But we now know the length of tropical year is about 365d, 5h, 48m, 45seconds.

How can he accurately determine when 365 1/4 days have elapsed since the last equinox? The 365, of course is easy. So he draws 12 equidistant rays from the base of the flagpole, [thus inventing the sundial and the hour and the first Babylonian parking meter]. With this instrument “hours” are easy to measure. So, he can determine when the six hours are up. The flagpole, being relatively tall, casts a long shadow. Since the rays get further apart farther from the base of the flagpole Joe III is able to subdivide the hour into smaller parts, [thus inventing minutes and billable units for the local lawyers]. He is now able to recognize that the extra time is about 12 minutes [1/5 of an hour] shy of a full 1/4 of a day. This is an amazing degree of accuracy being off only 45 seconds a year. Joe IV and Joe V are still winning the office pool decades later. Joe V has already noted that after only 20 years the sundial is registering the equinox almost 15 minutes earlier. Is he able to devise a more accurate timepiece? Can he figure out a mathematical process for figuring out the length of a true solar tear? Joe VII, a real math whiz, figures out that if he simply divides the total number of solar days by the number of years that records were kept his figure would get more accurate.

Somewhat earlier, Sam Sumerian, the official court astronomer to King Anorexis the Skinny, was charged with the holy office of Court Lunatic. Counting the days of the moons waxing and waning, he informs the king that he has invented the lunar month. He baldly states that it is 29 days long. The King expresses some doubts to the accuracy of this. Sam says, ” I’m right and I’d bet my life on it” Several months later when Sam Jr. inherits his late father’s post he much more carefully measures the elapsed time from one new moon to the next. He notes, after several months that the progression is about an extra 1/2 day per month. He reports to the king that lunar months alternate between 29 days, then 30 days. Anorexis is thrilled. He erects a stela in the market place with the new, improved lunar calendar. All is well for several years. Anorexis II notes that his father’s calendar is experiencing precession, which is a really big word for him since he’s almost illiterate. The moon year is out of phase with the Sun year. Actually, he couldn’t care less but his wife, Queen Corpulanis, complained that she could only do her royal Muumuu shopping when the moon is in the seventh house, whatever that means. She’s unhappy, making Anorexis miserable. He calls in Sam Jr., reminds him what happened to his father and demands a more accurate degree of lunacy, ‘or else’. Sam II begins the task, which is continued by Sam III, Sam IV and Sam V. Sam VI, having records of the lunar month over the course of 50 years or so is able to determine that every few years all he needs to do is add an additional month of 29 days and all is well. This method clearly did well enough to last well beyond the Anorexis dynasty.

Sooner or later, someone noticed that even that method left something to be desired. Finally, they learned to rely on the mean synodic period. This was accomplished by taking the number of days over the course of many months and dividing to get the average number of days. The larger the number of months used the more accurate the figure becomes. This is not the same as knowing the true solar or lunar positions.

Devising a sola-lunar calendar carries with a whole new set of problems.

PART III – UNITS OF TIME

WAIT A SECOND
Seconds are a relatively new invention. There are 60 of them to the minute due to the same Sumerian and Babylonian influence that gave us 60 minutes in an hour. Most probably, the 60 second minute was a carryover from mathematicians and mapmakers who broke up the 3600 degree circle into 60 minutes and those into 60 seconds which could be measured on a map. The Earth measures approximately 25,000 miles in circumference at the Equator. Divided by 3600 gives us about 69.44 miles per degree. Dividing this by 60 minutes means that each minute measures about 1.157 miles. Dividing again by 60 seconds gives us a figure of .019 miles or about 104 feet in a second. Spatially, this is a very easily measured amount. For time, this was clearly a mathematical construct as they had no accurate way of actually measuring a standard second having no timepiece that accurate…

The ancients had a major problem in writing fractional parts of numbers. Symbols or Roman numerals don’t cut it. Try figuring a value for pi using Roman numerals. The first use of zero as a fully formed number appears in India around the 7th cent. Mayans also had a true zero by about the 3rd cent. CE. Romans used fractions figured around 1 in 12 parts using special symbols. Really precise numbers were impossible to write down until Arab mathematicians, borrowing from al-Khwarizmi (born near the Aral Sea in what is now Turkestan in 780CE, he was summoned to Baghdad in 820 by al-Mamun and was appointed head astronomer. He wrote what was to become the standard textbook on mathematics. It was translated into Latin and remained standard in Europe well into the 16th cent.). The Arabs began using positional notation to create decimal fractions, the first of which appears in a book written by a Syrian mathematician, Abul Hassan al- Uqlidisi around 952. This opened the door to far more accurate figuring and recording. However, this neat trick took almost a century and a half to reach Spain and other outposts of the Moslem world and even longer to reach Europe, still mired in the Dark Ages and uninterested in new ideas, particularly those associated with those they considered pagans. Thus, while Gemora, Rashi and Rambam utilize fractions, decimal numbers are not found at all.

GIVE ME A MINUTE
Essentially, the minute was developed by the Babylonians although the same problem occurred as with seconds.

AN HOUR HERE, AN HOUR THERE
How did the concept of the twenty-four hour day develop? Before clocks, time was imprecise and were given as morning, noon, mid-afternoon, early evening etc. The Egyptians, using sun-dials, first divided the day into 24 hours. These were “temporal” hours, that is, the 12 hours of daylight were longer in summer than in winter. These temporal hours were used for over a millennia by most people although Hipparchus had divided the day into 24 hours, for astronomical purposes, based on the length of the hour measured on the day of the equinox [equinoctial hours]. Thus all 24 were of equal length year round. This is the method used by most people since about the 1300’s because it would be far too complicated to manufacture a mechanical clock able to account for temporal hours. The 24 hour day was also used by the Babylonians. 24 is divisible by 6 and divides evenly into 360. It was probably based on the Zodiac although the centuries have obscured the real reasons.

WHAT A DAY!
A day is simply the time from one sunrise, or sunset, to the next, or is it?

Note that the Earth rotates on its axis while, simultaneously revolving around the sun. The sidereal day measures one rotation, 360o, on its axis relative to the stars. However, as the Earth has moved further it must rotate a little further on its axis to face the star again, [about 1o] since it had moved in its trajectory around the sun. The solar day is ever so slightly longer [1/360] and the sidereal day is about 4 minutes shorter than 24 hours. In the course of a year this difference adds up to about 4 minute’s difference between the sidereal year and the solar year.

Although the day is an easily observed phenomenon, measuring it is something else. The first problem is deciding exactly when the day begins and ends. The ancient Egyptians began it at dawn while the Babylonians began it at dusk. The Romans and the Chinese started their day at midnight. Until 1925, astronomers used noon as their starting point but today use midnight.

The length of a day was found to vary with the seasons as well as there being a difference in the length measured from noon to noon and the length of the sidereal day [measured against a fixed star]. The mean solar day is the average period of the rotation of the Earth on its axis which may vary by up to 50 seconds.

Recently, it has been determined that the length of the day is increasing, albeit extremely slowly. The effects of tidal friction add to the slowing of Earth’s rotation by about half a millisecond per century.

TGIF
Where did weeks come from? The seven day week was not universal. Apparently, in ancient times, weeks varied from culture to culture from as few as five days to as many as fifteen. Different societies have used a week of 5, 6, 8 or ten days. The Romans had an 8 day week while the Mayans had both a concurrent 13 day and 20 cycle. The most widely used is the 7 day week attributable to the Jews. The seven day week had its debut with the giving of the Torah at Sinai. The Babylonians adopted it in 700BCE. They called each day of the week after one of their gods. Rome adopted the seven day week when Constantine introduced his calendar reforms in 321BCE. At that time 10% of the Roman Empire was Jewish. Also at that time Constantine made Christianity the official state religion. They, of course, had ‘borrowed’ the seven day week from Judaism.

In ancient times only five planets were known. Adding the sun and moon which were often treated as planets gives us the number seven and thus the names of the days of the week.

PLANET PLANET GODS MODERN DAY NAMES
BABYLONIAN ROMAN ANGLO-SAXON ENGLISH FRENCH SPANISH HEBREW
Sun shamash sol sun Sunday dimanche Domingo Shemesh
moon sin Luna moon Monday lundi lunes Yorai’ach
Mars nergal mars tiw Tuesday mardi martes Ma’adim
Mercury nabu mercurious woden Wednesday mercredi miercoles Kochav
Jupiter marduk jupiter thor Thursday jeudi jueves Tzedek
Venus ishtar venus freya Friday vendredi viernes Nuga
Saturn ninurta saturnus saturn Saturday samedi sabato Shabsai

Possibly one of the few widespread holdovers from idol worship is the reference of the days of the week to ancient gods.

MONTH
How was this broken into months? One of the more obvious celestial phenomena is the regular waxing and waning of the moon. However, in ancient times twelve months was not necessarily a year. In fact, the earliest Roman calendar had only 10 months in the year.

THE MOON AND THE MONTH
The moon reflects sunlight. At conjunction, when the moon is between the Earth and the sun, all the sunlight is reflected off the far side if the moon which we cannot see. Therefore the moon reflects no light back to Earth. As the moon revolves around the Earth the angle of the three bodies change and a small sliver of light will be visible, the ‘new’ moon. This crescent of light grows as the moon proceeds in its orbit. This is called waxing, or growing. The crescent moon is sighted, about 2 days after the new moon. This continues until the moon reaches opposition, the Earth is now between the sun and the moon. The entire face of the moon is illuminated and we have a ‘full’ moon. As the moon continues in its path the angle changes and the lit up part becomes smaller, or wanes. It will then disappear again at conjunction.
put in graphic of the phases

The average cycle between two successive new moons is known as the synodic period. This period can actually vary from month to month by up to seven hours due to complex interactions between the Earth and moon as well as other planets to a lesser degree.

A different measurement of the lunar month is known as the sidereal period based on the moon’s position relative to a fixed star. The sidereal period is shorter than the synodic period.

Just look at the problems associated with trying to measure a month.
• The sidereal month measures the revolution of the moon relative to the stars as seen from Earth. It is 27.32166 days long.
• The tropical month is the time between two successive passages of the moon through the first point of Aries. It is 27.32158 days long.
• The Draconic month is measured as the period of the revolution of the moon through the nodes of its orbit. The nodes are the intersecting points of the plane of rotation with the ecliptic.
• It is 27.21222 days long.
• The anomalistic month is the interval between two successive perigees of the moon.
• It is 27.55455 days long.
• The synodic month is the time between two conjunctions of the moon. Generally, the mean synodic month is utilized by most calendar makers.
• ADD CHART OF DIFFERENCES
•
• Interestingly, and disconcertingly, the interval from the time the old moon disappears until conjunction, or from conjunction until the new moon appears, is different at different latitudes. Moreover, even at the same latitude it differs by between 16 1/2 to 42 hours in the course of a year partially due to differences in the speed of the moon and partially due to differences in the moon’s distance from the ecliptic.
•
• The moons orbit is not parallel to the ecliptic but at an angle of about 5o. Were the moon to be parallel, there would be an eclipse of the sun at every conjunction and an eclipse of the moon at every opposition.
•
• Nobody attempts a long range lunar calendar based on the exact length of the month. In fact the mean length of the month is slowly increasing. Instead they rely on the mean synodic period by taking the number of days over the course of many months and dividing to get the average number of days. The Sumerians did just this long, long ago. The larger the number of days used the more accurate the figure becomes. Something similar can be done with eclipses since they recur at intervals of about 18 years and 11 days. [That explanation is beyond the scope of this paper.]
•
• As with the day, people needed to agree on when the new month actually started. As Jews, we believe that the month starts with the advent of the new moon. Others civilizations started with the disappearance of the old moon, others used the gibbous [?] moon, still others used a formula in conjunction with the sun.
•
• Because the ancients found that months varied between 29 and 30 days long, they set up calendars in which the months alternated. This was found to be unsatisfactory as the calendar was soon out of step.
•
• The Babylonians achieved a pretty accurate lunar calendar. There were several different Babylonian dynasties including the Sumerian, Kassite and Seleucid. Each had differing names for the months. The Semitic Babylonian names are, in order, transliterated as: Nisanu – Ayaru – Simanu – Du’uzu – Abu – Ululu- Tashritu – Arakhsamnu – Kislimu – Tebetu – Shabatu – Adaru. Sound a little familiar? These names were ultimately borrowed by the Jews during the Babylonian exile.
•
• From at least the reign of Hammurabi around 1800BCE and extra month was added when needed. By 500BCE this was formalized in adding an Adaru II in years 3,6,8,11,14 &19 and an Ululu II in year 17. Meton later used these figures in developing the Metonic cycle.
•
• In 432BCE Meton and Euctemon of Athens introduced a calendar with a 19 year cycle. They intercalated a 13th month in the 3rd, 5th, 8th, 11th, 13th, 16th, and 19th years. Therefore, there were 125 full months of 30 days, 110 months of 29 days. In total there were 6940 days. The Metonic cycle was off by only 24 minutes a year. This error was corrected by Calippus about a hundred years later. The Calippic cycle ran for 76 years reducing the error to only about 22 seconds a year. By 143BCE Hipparchus of Nicea dropped one additional day every 4 Calippic cycles further reducing the error to 1/2 second less than the actual synodic period.
•
• The lunar-solar gap equals 1 hour 27.5 minutes. That is, the moons cycles run slower than the 19 year solar cycle. The moon drifts against the solar calendar by a whole day every 312.7 years.
•
• There is a complex range of gravitational influences on the Earth from the Sun, the moon and other planets.
• There is a steady degradation of the orbits of the Earth and moon.
• The orbits aren’t spherical but ellipsoid.
• The Earth actually wobbles on its axis.
• There are complex tidal effects.
•
• FITTING THE MONTHS INTO A YEAR AIN’T EASY
• All that is fine as long as the society was interested in a calendar which was totally based on the moon. Attempting to keep it in step with the seasons required adjustments to fit it to the solar cycle. The problem is that the moon goes through its phases in 29.5306 days. Compare this to the length of a true solar year at 365.242199 days. The lunar year is the length of 12 mean lunations. It is 354.3671 days long, 10.8751 days shorter than a tropical year.
•
• Trying to link the two has frustrated astronomers for centuries. There are simply no easy common factors to work with.
•
How come the year creates such problems? If we note the factors, it is easily seen that the lengths of the year have very few factors to work with and those are all difficult.

Factors of the days of a solar year:
364 – 2 4 7 13 14 365- 5, 73 366- 2 3 6
182 91 52 28 26 183 122 61

Now try reconciling this with the lunar year of 354 days.
The factors of 354 are:
2 3 6
177 118 59

Note that the two types of years have no common factors.

Additionally, it wasn’t until science had advanced sufficiently that other circumstances were discovered which effect the accurate determination of a day, month or year:

THAT WAS THE YEAR THAT WAS
The Calendar Year, or Solar year, can refer to:
• The Tropical year: the length of time between two successive vernal equinoxes, which occur at the exact moment when the center of the sun appears to cross the Equator as is moves from South to North. This fluctuates from year to year, so the tropical year is usually calculated as an average of several years.
• The Sidereal year measures the length of time it takes the Earth to orbit the sun, returning to a starting point as measured by a fixed star.
• Years may also be measured from one June solstice to the next, a September equinox to the next etc.
• The Anomalistic year is measured between successive perihelions (the point in an orbit nearest the sun) of the Earth in its orbit around the sun.
•
The values for each vary due to Earth’s wobble, gravitational influences, rotational slowing and planetary fluctuations.
Here are the mean interval length values for the year 2000:
Sidereal 365.25636
• Tropical 365.2421896698 or 365d, 5h, 48m, 45seconds
• Between 2 March equinoxes 365.24237
• Between 2 June solstices 365.24162
• Between 2 September equinoxes 365.24201
• Between 2 December solstices 365.24274
• Anomalistic year 365.25964

You can begin to see the problem already.
Using the Sidereal year as the standard, the differences, in which the Sidereal year is longer, are:
• Tropical 0.01417
• Between 2 March equinoxes 0.01399
• Between 2 June solstices 0.01474
• Between 2 September equinoxes 0.01435
• Between 2 December solstices 0.01362
• Anomalistic year 0.00328

The ancient Egyptians used a 365 day year which wandered backward through the seasons. The Romans, under Julius Caesar, accounted for an extra 1/4 of a day per year by adding a leap year every 4 years. Their calendar was a little too long, gaining 1 day every 128 years. Nonetheless, this calendar was used for over 1,600 years by all Christian countries until Pope Gregory modified it.

Even with all our modern technology, it would be extremely difficult to determine a more accurate calendar without resorting to such complications as to make it usable only by rocket scientists which is actually what is being done. So, for those of you who really like accuracy, atomic time replaced Earth time in 1972 and the year has been measured in oscillations of atomic Cesium 133 – 290,091,200,500,000,000 oscillations per year or 9,192,631,770 oscillations per second. This atomic clock is accurate to within a billionth of a second per year or .0000000000114079 of a year. Now you can really be on time for meetings!

However, since the Earth’s orbit is slowly degrading by about 1/2 second per century, any long term solution would be out of synch over the course of millennia anyway. The year has slowed down since 1CE: by 10 seconds. The Atomic clocks are actually computer corrected on an ongoing basis.

SEASONS ADD SPICE TO LIFE
The Earth does not move at a constant speed in its elliptical orbit so the seasons are not of equal length. Spring is 92.8 days long, summer 93.6, fall 89.8 and winter 89.0. This applies to temperate climates. Nearer the poles, or the equator, seasons tend to drop to two.

How did a universal measurement of time come into being? It is obvious that years are measured by the seasons. In an agricultural society, seasons determined the pace of life and the jobs to be done. All life revolved around plowing, sowing and harvesting. Cattle and sheep bear their young in spring. In ancient times, people were easily able to determine methods of measuring this progression in order to be able to foretell when to prepare for the next cycle. [Often this had religious overtones as well.] This can be accomplished by noting the return of certain constellations to the same place in the sky. It may also be measured by noting where a shadow falls from one part of the year to another. The ancient Egyptians noticed that the annual flooding of the Nile coincided with the appearance of the Dog Star, Sirius. A complete cycle of seasons became a year, the amount of time required for the Earth to complete one revolution around the sun. These measurements, however, were anything but precise though, back then, they really didn’t have to be.

THE PLANETS [move back to planets or move planets here]
The ancients were aware of only five planets; Mercury, Mars, Venus, Saturn and Jupiter. Although they knew the orbital periods of these planets they do not figure in any calendrical considerations.

THE ZODIAC
The Zodiac was most likely developed by the very early Babylonians, probably well before the time of Avraham Avinu, the zodiac notes the constellations lying in the path of the sun, called the ecliptic. By dividing the constellations into 12 equal parts, the sun will be located in a different sector of the sky in a cyclical manner so that each constellation, or zodiacal sign, ends up corresponding to a particular time of the year. They do not match the months though each is one month long.

Season Latin English Hebrew
Spring Aries Ram Ram מזל ניסן טלה
Taurus Bull Bull מזל אייר שור
Gemini Twins Twins מזל סיון תאוים
Summer Cancer Crab Scorpion מזל תמוז סרטן
Leo Lion Lion מזל אב אריה
Virgo Virgin Virginמזל אלול בתולה
Autumn Libra Scales Scales מזל תשרי מאזנים
Scorpio Scorpion Crabמזל חשון עקרב
Sagittarius Archer Archerמזל כסלו קשת
Winter Capricorn Goat Goat מזל טבת גדי Aquarius Water Bearer Water Bearerמזל שבט דלי
Pisces Fish Fish מזל אדר דגים
add graphic of constellations/ zodiac here

Due to some complicated celestial mechanics relating the angle of the ecliptic against the equator, there are small changes over time. This is known as the precession of the ecliptic. Basically the equinoxes and solstices today are no longer where they were at the time of the Avos.

Position of the sun 2250BCE-100BCE 100BCE- 2050CE
vernal equinox aries pisces
summer solstice cancer gemini
autumn equinox libra virgo
winter solstice capricorn sagittarius

ERAS
Every civilization had to count their years from some beginning. Most ancient societies counted anew from the ascension of their current king to the throne. At some point Romans began counting from the founding of Rome, supposedly in 753BCE. The Church began using the birth of Jesus [wrongly dated to 1CE by Exiguus]. Jews began using the creation of the world [Anno Mundi] sometime in the Gaonic period. Seder Olam Raba, written by a Tana, uses year of creation, however, this was for commentary only.

The Greek & Russian churches dated the creation to 5508BCE. Others have even different figures. Moslems date from the Hegira [Mohammed’s flight from Mecca] in 622CE. Ostensibly, the newest era is that of the Ba’hai counting from 1844CE when Ali Muhammed was declared Bab.

PART IV – CALENDRICAL SYSTEMS OF THE ANCIENT & MODERN WORLD

All calendars are based on either the Sun, the Moon or some combination of the two.
Lunar: – Moslem
Solar:
Arithmetic solar- Julian, Gregorian, Coptic, Ethiopian
Astronomical solar- French Revolutionary, Ba’hai
Wandering- Egyptian, Mayan
Luna-solar:
Arithmetic lune-solar- Jewish, Christian ecclesiastical (for dating Easter)
Astronomical Luna-solar- Chinese, Indian

There are about 40 different calendars in use today. Several ancient calendars are still known. Here are some short descriptions of some of them:

Egyptian- Solar, 365 days in 12 months of 30 days, with an added 5 days at the end of each year. In not allowing for the extra quarter day each year their calendar quickly drifted into error. This is called a wandering year. Originally, it was 365 days long losing a day every four years causing a drift across the seasons that would repeat itself every 1,460 years. Early on, Egyptian astronomers recognized the problem but the priests considered the calendar too sacred to alter. Ptolemy III corrected it in 238BCE. The priests still resisted until 30BCE when Rome conquered Egypt and forced the change.

Sumerians had a 360 day year of 12 lunar months of 30 days each. Apparently they did not correct for this. It was 6 days longer than a true lunar calendar and 5 days shorter than a solar one. However, this was based on the Sumerian system of counting using 6 and 60. This equals 360 when multiplied. All of this may have had religious meaning making it more important than astronomical accuracy. Thousands of years later we are still using this system for minutes/hour, seconds/minute, degrees in a circle, location at sea, position of stars in the sky, latitude & longitude etc.

Babylonian- Lunar, 354 day year composed of alternate 29 and 30 day months. It was necessary for the lunar year of about 354 days to be brought into line with the solar year. This was accomplished by the use of an intercalated month. To coordinate this with the Solar (agricultural) year of approximately 365 days, they would add an additional month 3 times in a cycle of eight years. This was done on an as needed basis so the calendar was rather confused.

Thus, in the 21st century B.C.E., a special name for the intercalated month iti dirig appears in the sources. The intercalation was operated haphazardly, according to real or imagined needs, and each city inserted months at will; e.g., 11 months in 18 years or two months in the same year.

Around 430BCE the Babylonian, Meton, figured out that 7 years of 13 months interspersed among 12 years of 12 months would equal almost exactly 19 solar years. This is known as the Metonic cycle. Even this system runs several hours fast over time.

Later, the empires centralized the intercalation, and as late as 541 B.C.E. it was proclaimed by royal fiat. Improvements in astronomical knowledge eventually made possible the regularization of intercalation; and, under the Persian kings (c. 380 B.C.E.), Babylonian calendar calculators succeeded in computing an almost perfect equivalence in a luni-solar cycle of 19 years (235 months) with intercalations in the years 3, 6, 8, 11, 14, 17, and 19 of the cycle.This is the same as we use today in the Jewish calendar. The new year’s day (Nisanu 1) now oscillated around the spring equinox within a period of 27 days.
The Babylonian month names were Nisanu, Ayaru, Simanu, Du’uzu, Abu, Ululu, Tashritu, Arakhsamna, Kislimu, Tebetu, Shabatu, and Adaru. The month Adaru II was intercalated six times within the 19-year cycle but never in the year that was 17th of the cycle, when Ululu II was inserted. The day began at sunset. Sundials and water clocks served to count hours.
The influence of the Babylonian calendar was seen in many continued customs and usages of its neighbor and vassal states long after the Babylonian Empire had been succeeded by others. In particular, the Jewish calendar employed similar systems of intercalation of months, month names, and other details (see below The Jewish calendar). The Jewish adoption of Babylonian calendar names dates from the period of the Babylonian Exile in the 6th century B.C.E.as seen by the use of these month names by Zecharya, Nechemya and Esther.

Chinese- Lunar, 12 months of 29 or 30 days. A month is repeated 7 times in every 19 year period. The months remain roughly in line with the seasons. Their calendar follows a 60 year cycle. The year in each cycle is a word combination from two series of terms one of which is a list of twelve animals. Chinese New Year can fall on any day between January 20 and February 20.

Greek- lunar

Roman-The Roman calendar went through several changes. Its earliest manifestation was simply borrowed from the Greeks.

Early Romans had a 304 day calendar of ten months, attributed to Romulus, the legendary founder of Rome.

Around 700BCE King Numa added 2 additional months to the end of the year, Januarius and Februarius making the year a standard lunar year of 354 days to which Numa added another day, 355, because of a Roman superstition about even numbers. Another month, Mercedinus, had 22 or 23 days and was inserted between February 23 and 24 when needed. Politics, religion and slipshod record keeping left the Romans with a calendar that was continually slipping back and forth against the Solar year.

This calendar lasted from about 500BCE until Julius Caesar reformed it in 46BCE by which time the calendar was misaligned 80 days ahead of the seasons.

Julian- Caesar asked the astronomer Sosigenes to suggest reforms. Eventually, Sosigenes chose to disregard the moon in favor of a totally solar calendar. He divided the year into 12 months of 30 and 31 days except for February which had 28 days. Every fourth year it would have 29 days. (In order to realign the calendar Caesar declared, on Jan 1,45BCE, that 46BCE would have 445 days. Romans knew this as the “year of confusion”.) The Julian calendar was widely used for almost 1,500 years. It provided for a year of 365 1/4 days. This however, was actually about 11 minutes and 14 seconds longer than the solar year.

Already, by the mid-1100’s it was known that the Church calendar was drifting by about a day every 300 some odd years (the calculations become more exact as time passed), and they were aware that by then the calendar was already off since Caesar’s time. It was to be over 400 years before the Church actually got around to fixing this anomaly. Of course, there was some interest along the way however, events, like the Black Plague conspired to get in the way of reform. They were also somewhat busy with the Crusades, having somewhat interesting priorities…

The Romans had no idea of a minute and, when necessary, divided the day into simple named fractions. Writing them in Roman numerals required special symbols.

By 1514 Pope Leo was sending letters to various christian monarchs with proposals to reform the calendar. His letter to Henry VIII, still in the British archives, laments the fact that “Jews and heretics” were laughing at the flawed Christian calendar. Few Monarchs even bothered responding to the Pope’s letter. By 1580 the error had accrued to 10 days.

Gregorian- In 1582, upon the advice of astronomers, figuring that the Julian calendar overestimated by 11minutes 45 seconds per year, Pope Gregory XIII corrected the error by simply dropping 10 days. October 5, 1582 simply became October 15. To correct the Julian calendar he decreed that February would have an extra day in century years which were divisible by 400. Actually, the church was less concerned with the calendar as such. This was a religious issue centering on the date of Easter.

THE PROBLEM OF EASTER
“By the unanimous judgment of all, it has been decided that the most holy festival of Easter should be everywhere celebrated on one and the same day”
Constantine the Great 325CE.

The very name “easter” derives from Eostre, the ancient northern god of spring. Many European languages use a different term, paschal, a derivative from the Hebrew Pesach. The christian bible makes no mention of any celebration of what is now called easter. Obviously, the early Jewish christians continued to observe Pesach. Other pagan christians may have retained a vernal festival celebrated at that time of year. It wasn’t until well into the second century that some form of official holiday was established.

A further complication arose as some folks chose to observe the day of the month, 14 Nisan as the anniversary of the crucifixion. They were called Quartodecimans. Others observed the day of the week and held their holiday on the Sunday following the 14th of Nisan. They were called Quintadecimans. There followed a whole series of popes who attempted to resolve the issue to no avail. Finally, as the christians were becoming a laughingstock of their pagan neighbors, the Council of Arles, in 314, decided that everyone should celebrate Easter on the same day. Alas, the council gave no instruction on how this was to be done so the various factions continued on their merry way. Constantine finally decided the issue in the Nicene Creed. Nonetheless, despite excommunication, the Quartodeciman “heresy” lingered on for several centuries.

The proper date for the holiest day in the christian calendar is complicated by the fact that Jesus’ ‘resurrection’ occurred during Pesach. The date of Pesach is the result of a lune-solar calendar, which means the date of Pesach varies in the solar calendar from year to year. The christians were using a solar calendar in which all their other holidays had fixed dates whereas Easter needed to wander.

The problem was further exacerbated by the fact that there were no eyewitnesses who wrote down a date for the crucifixion or resurrection [or anything else]. There is one point of agreement- that he ‘rose’ on the first day of the Jewish week, Sunday. Three of the gospels, Matthew, Mark and Luke write that it was the Sunday after the Seder. John, however, reports a different date entirely. By the time the problem became critical, even the exact year of the crucifixion was already in question.

By the time of the Council of Nicaea in 325CE the only agreement was that the day should be preceded by a fast and it should have some relationship to the full moon of the Jewish month of Nisan. Beyond that, individual churches argued about whether it always needed to be on a Sunday or was it better to hold Easter on the correct day of the month, amongst other issues.

By the third century, a growing anti-Semitism added to the problem as christians became increasingly loathe to use dates dependent on the Jewish calendar. In a letter addressed to the Bishops at the council, Constantine wrote, “We ought not to have anything in common with the Jews, as the savior has shown another way.” In fact the bishops of Nicaea dictated to the calendar makers that Easter may never fall on the day Pesach begins. Their equation stated that Easter should fall on the first Sunday after the first full moon after the spring equinox. If their calculations indicated that Easter fell on 14 Nisan they were ordered to move Easter to the following Sunday.

The council’s solution ended up being way off base. They arbitrarily fixed the date of the vernal equinox on March 21. Since the original flaw in the Julian calendar had not yet been fixed, the calendar continued to lose 11 minutes a year losing a full day every 128 years. By 325 the Julian calendar was already 3 days behind where Caesar placed it in 45BCE. Thus the equinox continued drifting backward in the calendar. In 387CE Augustine noted that the Alexandrians were celebrating Easter on April 25, the Romans on April 18 and the Arian churches on March 21. Before it was fixed by Gregory the true equinox had dropped back to March 14 while the church rigidly adhered to fixing Easter according to a March 21 equinox.

Constantine’s solution failed in another respect. The rift between East and West was already forming. These different churches celebrate Easter on a different date right up to the present. The churches in Jerusalem, Russia, Serbia and the monasteries on Mt. Athos in Greece continue to use Julius Caesar’s calendar although it is now running 13 days behind the Gregorian.

It is possible for easter to occur anywhere from March 22 to April 25. A spread of 35 days. The full explanation of the church’s calculations runs to several pages and are too complicated by far to interest the average reader. Suffice it to say that all those complex calculations are done simply to avoid having to rely on the Jews for the proper date.

Adoption of the Gregorian Calendar- Better late than never
Roman Catholic nations adopted this calendar almost immediately. Other Christian nations, generally being anti-papist, were content to remain on the Julian calendar, mistakes and all. Ridiculous situations developed where Easter was celebrated 10 days apart by two groups in the same village, or even a husband and wife in the same house.

Many German states did not change until 1700.
England waited until 1752. England, by order of Parliament under King George II, finally passed a bill in 1752 expunging 11 days with Wednesday, September 2 followed by Thursday September 14.
Sweden changed in 1753
Japan switched in 1873 during the westernization under the Meiji emperors
China in 1912 although it did not take hold until the communist victory in 1949
Bulgaria changed in either 1912 or 1915
Latvia, Lithuania and Estonia in 1915 during the German occupation
Romania and Yugoslavia in 1919
Russia changed after the revolution in 1918, but had to drop 13 days. In 1908 the Imperial Russian Olympic team arrived in London 12 days too late for the games because of the calendar difference. [See Revolutionary Calendars further on}
Turkey changed in 1926

The Russian Orthodox Church still celebrates Xmas on the old calendar.

The situation in the United States was interesting.

The legal code of the United States does not specify an official national calendar. Use of the Gregorian calendar in the United States stems from an Act of Parliament, under King George II, of the United Kingdom in 1752, which specified use of the Gregorian calendar in England and its colonies. However, its adoption in the United Kingdom and other countries was fraught with confusion, controversy, and even violence. So, for instance, George Washington’s birthday was actually February 11 1732 OS. OS stands for Old Style since he was born prior to the changeover. We celebrate it on February 22.

The accuracy of the Gregorian calendar is such that there is only a 26 second per year difference between it and the length of the actual solar year. This will increase by about .53 seconds per century as the solar year is gradually growing shorter.

The actual repeatable cycle of the Gregorian calendar is 400 gregorian years, of which 97 years are gregorian leap years, that is, 366-day years. Hence, the average Gregorian year is
(400 x 365) + 97 / 400 = 365.2425 days long.
The Gregorian calendar is therefore slower than the mean tropical solar year by about 3 days in every 10,000 years.

Mayan- In ancient times, the Mayans had a tradition of a 360-day year. But by the 4th century B.C.E. they took a different approach than either Europeans or Asians. (Not that they had any idea of what the Europeans or Asians were doing.) They maintained three different calendars at the same time.

The Long Count,
The Tzolkin (divine calendar),
And the Haab (civil calendar).

Of these, only the Haab has a direct relationship to the length of the year. The Haab has 365 days with 18 months of 20 days to which they added 5 extra days at the end, considered unlucky. They apparently were aware that the year had 365 1/4 days but simply ignored this fact in their calendar. Of course, this caused their year to drift just like the Egyptian calendar, about 6 hours a year.

They also used a 260 day calendar, called tzolkin. This developed around 1000BCE. The two calendars were joined in a complicated cycle of 52 years known as a “calendar round”, the time it takes for both calendars to begin anew on the same day.

The third calendar was called the “long count” based on a 360 day unit called a tun. This long count ran in a cycle of 5,130 years. Current scholarship is attempting to understand the Mayan calendar. They have little to work with as the Spanish conquistadors, representing missionary Catholicism, destroyed much of their culture and destroyed any manuscripts they found.

Any discussion of the accuracy of the Mayan Calendar is moot. They simply weren’t concerned with their calendar being tied to astronomical events or the seasons. The “accuracy” noted by many is the ‘calendar round’ which is accurate being the factor of 260 x 365.

A typical Mayan date looks like this: 12.18.16.2.6, 3 Cimi 4 Zotz.
12.18.16.2.6 is the Long Count date,.3 Cimi is the Tzolkin date, 4 Zotz is the Haab date.
Although there were only 365 days in the Haab year, the Maya were aware that a year is slightly longer than 365 days.
We can therefore derive a value for the Mayan estimate of the year by dividing 1,101,600 by 365,subtracting 2, and taking that number and dividing 1,101,600 by the result, which gives us an answer of 365.242036 days, which is slightly more accurate than the 365.2425 days of the Gregorian calendar.
This apparent accuracy could, however, be a simple coincidence. The Maya estimated that a 365-day year precessed through all the seasons twice in 7.13.0.0.0 days. These numbers are only accurate to 2-3 digits. Suppose the 7.13.0.0.0 days had corresponded to 2.001 cycles rather than 2 cycles of the 365-day year, would the Maya have noticed?
Was this a priori on the part of the Maya? Did they first notice it expost facto? Was this only noted by later scholars? Did the Maya simply multiply it out until the 1/4 day was accounted for? How did they achieve a figure of 1,101,600 in the first place?
The Maya calendar was adopted by the other Mesoamerican nations, such as the Aztecs and the Toltec, which adopted the mechanics of the calendar unaltered but changed the names of the days of the week and the months
Aztec-There is not just one Aztec calendar, there are two more or less independent systems essentially borrowed from the Maya. One calendar, called the xiuhpohualli, has 365 days. It describes the days and rituals related to the seasons, and therefor might be called the agricultural year or the solar year. The other calendar has 260 days. In Nahuatl, the language of the Aztecs, it is called the tonalpohualli or, in English, the day-count. Most information on Aztec calendars refers to the tonalpohualli, which is the sacred calendar.

The 365-day year, or xihuit l consists of 18 months (meztli) of 20 days plus five extra (unlucky) days. Every 52 years (4 times 13) the name of the year will be the same. A combination of 52 years is called a calendar round or xiuhmolpilli.

Moslem – Totally lunar. There is no connection to the solar year. Mohammed specifically chose this format to differentiate Islam from the Christian Solar and the Jewish Luna-solar calendars. The Islamic calendar was established by Umar, the second caliph and Mohammed’s son-in-law, around 634CE. His solution was a 30 year cycle of 360 lunar months alternately 29 and 30 days long. In every 30 year cycle 19 have 354 days and 11 years have an extra day each. This is accurate against the true orbit of the moon to within a day of drift every 2,500 years. It requires frequent intercalations with 1 day being added to the final month, Dhi’l-Hijjih, in years 2, 5, 7, 10, 13, 16, 18, 21, 24, 26, 29 of each 30 year cycle. Each month in the Islamic calendar begins when the first sliver of the crescent moon is sighted, about 2 days after the new moon.

{It so happens that by the mid 1400’s an Arab astronomer, Ulugh Beg [1394-1449], gave a measurement for the solar year of 365d, 5h, 49m, 15s – just 25 seconds too long.}

With an 11 day annual difference between the solar and lunar year the Islamic calendar moves backward through the seasons completing a full cycle once every 32 1/2 years. The Islamic calendar will be one day off every 2,570 years with respect to the moon. The Gregorian calendar is only slightly more accurate with regard to the sun.

INDIA
There were as many as 30 different calendars in use in India, according to Nehru, writing in 1953. Several of them were solar and ignored the precession of the equinoxes. Each of these is presently off by about 60 days. Under English rule the Gregorian calendar was foisted on the Indians. After gaining independence in 1947 the Indian government instituted the reformed Saka calendar. It basically follows the Gregorian with several differences in leap years.

There have been two attempts at revolutionary calendars. The first, the French revolution in 1792, and the second the Russian revolution of 1917. Both attempted to abolish the 7 day week which both perceived as reactionary and as a particularly Christian institution by which the priests wielded too much power over the peasantry.

The French revolutionaries abolished the week in a national convention on November 24, 1793. They replaced it with a 10 day week, the days of which were numbered, not named. Gilbert Romme, who devised the system, was asked what his prime objective was. He answered, “To abolish Sunday.” The 10th day of the new week, and the new “day of rest”, was called “Decadi” using the metric system which was introduced at the same time. Heavy fines were imposed on shopkeepers who did not open their stores on Sunday as well as on those who went to church on Sunday. Napoleon’s coup d’état in November 1799 ended the decree. It wasn’t until 1805 that the Gregorian calendar and the Sunday “day of rest” were officially returned to the people of France.

The Russian revolution, in 1917, replaced the Julian calendar with the Gregorian. By 1929, the Fifth Soviet Congress proposed a system to make more efficient use of factories. The proposed plan was to institute a continuous production week. It operated by dividing the entire Russian population into 5 parts. 1/5 of the workers would work 4 days and have the 5th off. The next 5th would start a day later and have the following day off and so on. This meant that 4/5’s of the work force would always be working. They chose a 5 day cycle rather than one of 7 days both to have a larger percent of the work force on hand as well as to abolish the ability of anyone to observe Saturday or Sunday as days of rest. The tremendous inconveniences entailed in this system eventually forced the government to rescind. By November 1931 the staggered work week was ended, however, the seven day week was not restored. Finally, in the interests of wartime production, the seven day week and Sundays were replaced, after an 11 year hiatus, in June 1940.

PART V – A COMPARISON OF CALENDRICAL ACCURACIES

NOTE: – Inaccuracies in today’s calendars are an artifact of attempting to exactly quantify an inexact physical process. Both the sun and the moon revolve. These revolutions, however, are affected by outside gravitational forces as well as other things. Thus, no two revolutions are ever exactly the same. The differences are minute but over time do accrue. No calendar can take these differences into account on an ongoing basis. Therefore, there is really no such thing as real-time accuracy in any given month or year. How the calendar makes up for these differences over time will determine its accuracy, but only over time.

To make a comparison as to the accuracy of the various calendars we need to reduce the numbers to a common denominator. I have chosen 1,000 years.
The Egyptian calendar would be off by 250 days, or almost 8.3 months in 1,000 years.
• The Mayan calendar would be off by 14.324 days
The Julian calendar will be off by 11,230 minutes, or 187.16 hours, or 7.8 days.
• The Gregorian calendar will be off by 26,005.3 seconds or 433.42 minutes, or 7.22 hours.
Length of time Gregorian is off true solar year 25.96768 seconds/year. In 414 years as of 2000 Gregorian is off 2h, 59m, 12s
• The Moslem calendar will be off just under 540 minutes or 9 hours with respect to the moon.
• The Jewish calendar will be off 98.4 minutes or 1.64 hours for the lunar month every 1,000 years although the solar year will be off by 4.6 days [110 hours] in that same 1,000 years.
•
•
• PART VI – THE ACCURACY OF THE JEWISH CALENDAR
• The exact modern astronomical times given are:
• Lunar month – 29 days, 12 hours, 44 minutes, 2.841 seconds
• Solar Year- 365 days, 5 hours, 48 minutes, 46.069 seconds
• The lengths used by Chazal are:
• Lunar month – 29 days, 12 hours, 44 minutes, 3.333 seconds
• Solar [tropical] Year- 365 days, 5 hours, 55 minutes, 25.438 seconds
•
• The difference between the figures used by Chazal and current astronomical values in the length of the month is .492 seconds per month. This works out to 5.904 seconds per year. About 10 minutes a century or, only about 98.4 minutes in 1,000 years.
•
• The difference in the length of the solar year is 6 minutes 39.369 seconds per year. This works out to 110 hours, about 4.6 days per 1,000 years.
•
• The accuracy of the Jewish calendar is such that the Jewish lunar month has barely deviated from the astronomical lunar month over time.
•
• We use a theoretical moon, that is, is the number 29d 12h & 793 Chalakim represents the mean synodic period. As the mean deviation is accurate to within 1/2 second per month, the calendar will remain accurately in synch with the moon to within 1 day for over 16,000 years.
•
There is, however a cumulative error in the difference between the Jewish solar year and the astronomical solar year. The accuracy of the Hebrew calendar is fixed by the value of its mean lunation period coupled to the 19 year cycle of 235 lunar months.
That leads to an average Hebrew year length of approximately 365.2468 days.
Since the mean tropical solar year is about 365.2422 days, the average Hebrew year is slower than the average solar year by about one day in every 216 years. The Jewish months advance against the solar year by approximately 4 1/2 days per thousand years. Therefore we are sitting down to our Pesach Seder 4 1/2 days later than Rashi did and about nine days later than Rebbe Akiva and almost two weeks later than Dovid HaMelech. Eventually, this anomaly will require correction lest Pesach start before the onset of spring. Should no Hebrew calendar reform take place to account for the known astronomical differences, then over the next few millennia, all of our holidays will have drifted out of their anticipated seasons and Pesach could theoretically be observed in winter. The Mishna Brura addresses a slightly different problem in Simen 428 in the first Biur Halacha and resolves it by saying ” and we need not worry overmuch since, certainly, by that time, or even much before, the redemption will occur and we will be Mikadesh Levana by means of witnesses] sighting [the new moon].”

The first Hebrew book devoted solely to the calendar of which we are aware was written by Avraham Bar Chiyya HaNasi [1070-1136] writing in Barcelona under the Arabs.

PART VII – CYCLES OF TIME IN HALACHA
The largest time cycles mentioned in Seforim actually stretches into billions of years. {See Part II of my article “Counter-Evolution” at www.HIQJEW.com}

יובל Yovel
On a life scale the largest cycle is that of éåáì Yovel – the Jubilee year – occurring every fifty years. It is, in turn, made up of seven Shmitta years – Sabbatical years. Every seventh year is a Sabbatical year. Seven sevens equals forty-nine. After the seventh cycle the following year is a Yovel. Even this fact is a matter of disagreement. The Gemora [Eruchin 12b] records that Rav Yehuda maintained that the Yovel year was not counted separately, but was part of the Shmitta count. The Rabbanim disagreed, writing that Yovel was a separate year.

According to the Rambam, Yovel years were only counted in the time of the Bais HaMikdash. In Hilchos Shmitta V’Yovel, Perek 10, the Rambam gives us his accounting of the Shmitta and Yovel years. In short, The Jews left Mitzraim in 2448. Moshe Rabbeinu died in 2488 at which time the Jews entered the Land. There followed 7 years of conquering the land and then 7 years of dividing the land. After that the count for the first Shmitta began. Thus, the first Shmitta year was 21 years after entering the land, 2509. The first Yovel occurred 64 years after entering, 2552. There followed a total of 17 Yovel years before the destruction of the first Bais HaMikdash in 3339 in the 36th year of that Yovel cycle, the year after a Shmitta year. This encompassed a period of 836 years.
2488 -enter the Land
+ 21 – years of conquering, settling and planting
2503 -begin the Yovel count
17 Yovel cycles = 850 years
-14 years left of the last cycle
836 years

2503 begin Yovel count
+836 total Yovel Years
3339 year of the destruction of the first Bais HaMikdash

There followed the 70 years between the two Batei Mikdash. The Second was built and Ezra came to Eretz Yisroel seven years later. According to the Rambam the first Shmitta year was 13 years after the Second Bais HaMikdash was built. It too was destroyed on the year after a Shmitta in 3830 having stood 420 years, in the fifteenth year of the ninth Yovel Cycle.
400 years in 8 Yovel cycles
+15 years of the ninth cycle
415 Yovel years
+ 6 years before the count started
421
The count of the Second Bais HaMikdash was not connected to that of the First Bais HaMikdash. The count was based on the years of actual farming. Shmitta and Yovel are thus not ordained as particular years. Today, in Israel, the people follow the Mesora of the Gaonim in figuring the proper year to observe Shmitta. Apparently this is based on a continuation of the count begun by Ezra.

Yom HaChama. – מחזור גדול
Every 28 years is Yom HaChama. This is called îçæåø âãåì. This is the 206th solar cycle since Creation. We make a special Bracha at the time the sun returns to its original position in the sky as it was when it was created. Although this occurs annually at the time of the vernal equinox, we only say the Bracha when the sun is in this position on the same day of the week and the same hour of the day as when it was created. Therefore, we wait until the vernal equinox happens at the beginning of the fourth day, the day the sun was created. The beginning of the fourth day at the time of the vernal equinox is Tuesday evening at 6PM since the Jewish day is reckoned from nightfall. This concurrence happens only once every twenty-eight years. The Bracha is actually recited the following morning. The last occurrence of Yom HaChama was April 8, 1981. The next occurrence will be, BE”H, on April 8, 2009. There will then be another on April 8, 2037, 2065 and 2093.

מחזור קטן
There is a nineteen year cycle called a îçæåø ÷èï. This is the 304th lunar cycle since creation. Seven times every nineteen years there are leap years in which we add an additional month to maintain the calendar in a way that the lunar and solar years remain in synch. The 3rd, 6th, 8th, 11th, 14th, 17th and 19th year of each Machzor is a leap year. This is the 304 repetition of the 19 year cycle.

עיגול
Thirteen of these 19 year cycles together [247 years] is called an עיגול. The various year types, קביאות, repeat themselves for the most part. To achieve true repetition requires 36,288 cycles of 19 years [689,472 years]. This has no practical consequence.

Every seventh year is a Shmitta year. See above – Yovel.

THE YEAR
On a yearly basis, we have the cycle of holidays. Originally, Bes Din would declare the new moon and would intercalate an additional month in order to keep Pesach in the spring or else, as in the Moslem calendar, the Holidays would retrograde backward through the months at the rate of over 11 days per year. The length of a solar year, according to Rav Adda, is 365 days, 5 hours, 997 Chalakim and 48 Regaim. This is equivalent to 365 days, 5hours, 55 minutes and 25.438 seconds which is known as the tropical year. Astronomy has provided us with a more exact figure of 365 days, 5 hours, 48 minutes and 46.069 seconds for an average year. This slight difference has caused the Jewish calendar to advance about 4 1/2 days over the past thousand years.

There are a total of 14 types of years based on three variables:
a- The day of the week the first day of Rosh HaShana falls. (Never on Sunday, Wednesday or Friday) There are several complicated rules, called דחיות determining this day.
b- Regular or leap year
c- The length of the year (see below)
This has led to a three letter acronym for each type of year. The first letter refers to the day of the week of the first day of Rosh HaShana, ב-ג-ה-ז Monday, Tuesday, Thursday or Shabbos.
The second letter tells us the type of year-
חסרה – ח-defective
-כ – כסדרregular
-שלמה ש – full
The third letter tells us which day of the week will be the first day of Pesachא—ג-ה-זSunday, Tuesday, Thursday or Shabbos.

The 14 possibilities are thus:
בשנה פשוטה בשנה מעוברת
בחג בחה
בשה בשז
גכה גכו
השא השג
הכו החא
זשג זשה
זחא זחג

An ordinary year consists of 50 weeks plus 3, 4, or 5 days. The number of excess days identifies the year as being deficient, regular, or complete, respectively. A leap year consists of 54 weeks plus 5, 6, or 7 days, which again are designated deficient, regular, or complete, respectively. The length of a year can therefore be determined by comparing the weekday of Tishri 1 with that of the next Tishri 1.

The computations to determine these configurations are beyond the scope of this paper although they are not terribly complicated. The Rambam tells us that a school child could master these calculations in 3 or 4 days. The Mishna Brura at the end of Chailek four and the Tiferes Yisroel in the beginning of Moed each have an explanation of these calculations.

תקופות
Several times a year we pass the Tekufos. There are four Tekufos a year:
• Tekufas Tishrei, analogous though no longer on the same date as the Fall Equinox
• Tekufas Teves, analogous though no longer on the same date as the Winter Solstice.
• Tekufas Nissan, analogous though no longer on the same date as the Spring Equinox.
• Tekufas Tammuz, analogous though no longer on the same date as the Summer Solstice.

The Tekufos are generally based on the figure of Shmuel [Shmuel Yarchini, 3rd century Amora and noted astronomer whom the Gemora quotes as having said that he was as familiar with the heavens as he was with the streets of Neharda] who gives a round number of 365 1/4 days as the length of the solar year [as opposed to the more accurate figure of Rav Adda given above.} Thus, there is a difference of about one day every hundred years. Currently, our Tekufos are 17 days later that the dates given for the solstices and equinoxes in the secular calendars. So, for instance, we are supposed to begin saying ‘Tal U’Matar’ 60 days after Tekufas Tishrei which should be November 18. Siddurim of the last century gave the date as December 3. Current Siddurim give the date as December 4. By the next century it will begin on Dec.5.

THE MONTH-החדש הזה לכם
Monthly we have the Molad, Rosh Chodesh and Kiddush HaLivana (Kiddush Livana has no direct connection to calendrical calculations.). The Lunar month, on which the Jewish calendar is based, is the length of time from one Molad (new moon) to the next. This is equal to a mean length of 29 days, 12 hours and 793 Chalakim, or 29 days 12 hours 44 minutes and 3 1/3 seconds. A more exact astronomical figure is given as 29 days, 12 hours, 44 minutes and 2.841 seconds for the average month.

Because a month has twenty nine days, Rosh Chodesh will always fall on consecutive days of the week month after month. For example, if last month’s Rosh Chodesh fell on Sunday and Monday, this month’s will occur on Tuesday and the month after on Wednesday and Thursday, then on a Friday etc.

The months of the year alternate between 29 and 30 days each. The two exceptions to this rule are Cheshvan and Kislev which may each have either 29 or 30 days. Additionally, 7 times every nineteen years an additional month is placed between Adar and Nissan known as Adar Sheni. Thus the length of the year varies according to these two factors. The possible variations are;
354 days in 12 months alternately having 29 & 30 days
1. 353 days in 12 months alternately having 29 & 30 days except Kislev with only 29 instead of 30 days.
2. 355 days in 12 months alternately having 29 & 30 days except Cheshvan with 30 instead of 29 days
3. 384 days in 13 months alternately having 29 & 30 days with 1 added month, Adar Sheni of 30 days
4. 383 days in 13 months alternately having 29 & 30 days except Kislev with only 29 instead of 30 days. With 1 added month, Adar Sheni of 30 days
5. 385 days in 13 months alternately having 29 & 30 days except Cheshvan with 30 instead of 29 days with 1 added month, Adar Sheni of 30 days

1 &4 are called regular years
2 & 5 are called defective years
3 & 6 are called excessive years
1, 2 & 3 are common years
4, 5 & 6 are leap years

Above we noted the Babylonian names for the months adopted by the Jews. The Torah refers to the months only by number as the first month, second month etc. Throughout the Torah the first month is the spring month in which Pesach occurs. The Torah makes no mention of the need to intercalate the years by adding leap months. Thus, we must conclude that all these calculations were given to Moshe Rabbeinu on Har Sinai as part of Torah She’B’Al Peh, the Oral Law. Had they not been, the Yomim Tovim would have been out of synch almost immediately in the desert. (Is there any mention of leap years in Navi?)

Apparently, by the time of the early monarchy, during the reigns of Dovid and Shlomo HaMelech, the months had other names. Three are mentioned in Navi.
– – Melachim 1 Perek 6:1- The month of Ziv is the second month.
The Bais HaMikdash was founded in the month of Ziv. Melachim 1 Perek 6:3 In the month of Kul which is the eighth month. Melachim 1 Perek 6:38
In the month of Eisanim on the holiday which is the seventh month. – Melachim 1 Perek 8:2
Somewhat later, Megilas Esther, Sefer Nechemia and Sefer Zecharia utilize the Babylonian names we are familiar with today. Thus, we see that the changeover occurred during the 70 year exile between the two Batei Mikdash.

ONCE A WEEK
Weekly comes Shabbos. The week is the longest invariable unit of time. It is independent of the sun or the moon as the year or month. It is not an artifact of human convention as is the 24 hour day, 60 minute hour or 60 second minute, rather it was ordained by Hashem. Its length is unaffected by the sun, the moon, latitude, longitude, orbits or rotation. It has achieved virtually global recognition.

EVERY DAY
On a daily basis we find that the twenty four hour day is broken into Sha’ose Z’manios. Each hour of the day and night is figured to be one-twelfth the available time from sunrise to sunset, or sunset to sunrise. Thus, the length of the hour changes across the seasons. For Monsey, New York, the shortest daytime hour occurs at the end of December, beginning of January and is about 46.3 minutes long. The longest daytime hour is at the end of June, beginning of July and is about 75.4 minutes long. By comparison, London, England, considerably farther north>>>>>>>>

For most purposes, the Jewish day begins at sunset. Actually, the new day begins with the appearance of three stars. While the actual day has a duration of twenty-four hours, due to the exigencies of accurate time telling, to prevent Shabbos and Yom Tov desecration, some time has been added to either end making these days closer to twenty-six hours.

THE MIL
At a time when short units of time were essentially non-measurable, Chazal needed to utilize a unit of measure which would be usable. In many instances they chose the îéì. They measured the day as a 40 Mil walk. The Gemora in Pesachim {94} tells us the opinion of Rav Yehuda who stated that “a man can travel 40 mil in an average day [12 clock hours]. Therefor from Alos Ha’Shachar to Netz HaChama is the distance of 4 Mil in the spring and fall. The same applies to the time from Shkiya to Tzais HaKochavim; it is the distance of 4 mil.”

However, in Gemora Shabbos [34b] Rav Yehuda states that there is a period of only 3/4 of a mil from Shkiya to Tzais. Rabbeinu Tam offers an explanation of the contradiction by telling us that there are two different Shkiyos.

The mil is a distance of 2,000 Amos. An Amah is generally given at 1 1/2 to 2 feet. Therefor a Mil computes to between 3,000 – 4,000 feet. Chazal determined that an average person is able to walk this distance in about 18 minutes [Mishna Brura 459; 15]. Other Poskim put the time of walking a Mil at 23 1/2 minutes {see Biur Hal. ibid.] Anyone can approximate this distance and would know how long it would take them to walk it. Voila, a means of measuring time usable by anyone anywhere. It suffers the dual drawbacks of not being precise because of the reliance on the individual’s approximation of distance and their estimation of their walking speed.

Using an Amah of 18 inches, a Mil equals 3,000 feet which, in turn equals 914.4 meters, or, 85.6 meters [280.8 feet, a little less than a football field] short of a kilometer. An Amah of 24 inches, would give us a Mil equaling 4,000 feet which, in turn equals 1219.2 meters, or, 219.2 meters [719 feet, about two and 1/3 football fields] longer than a kilometer. Walking the 3,000 foot Mil in 18 minutes gives us a walking speed of under 2mph. The 4,000 foot Mil gives us a walking speed of about 2.5 miles per hour. Either choice results in a very slow rate. The average person walking at a reasonable rate is able to easily walk at 4 mph. Chazal apparently used a very conservative rate, virtually doubling the length of time involved, in order to be very lenient, Halachically. We must also remember that Chazal needed to take into account that most people did not live on Main Street, nicely paved with well-tended sidewalks. Although we are easily able to maintain a 4 mph walking speed, I doubt we could maintain it on a muddy, rutted, dirt track. Our pace of life tends to be much faster than the pace in a rural setting. People simply didn’t rush around then. Thus, Chazal’s slow speed was most likely representative of the reality of the vast majority of people over time.

Chalakim are essentially the smallest regular time unit used by Chazal. Rather than minutes and seconds, an hour is broken into 1,080 Chalakim. Why such an odd number? It happens to be divisible by many numbers. The factors of 1080 are:
1, 2. 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 27, 30,
1080, 540, 360, 270 ,216, 180, 135, 120, 108, 90, 72, 60, 54, 40, 36,
This makes the number eminently usable.

There is apparently no source given for this number and it shows up rather late.. The Babylonian figure of 360 works equally well.

There are 18 Chalakim in a minute, thus, each Chailek is 3 1/3 seconds long.
There are 1,080 Chalakim in an hour. 25,920 in a day. 765,433 in the interval between two Molados

The Chailek is never used in ordinary time statements by Chazal. No Mitzva, other than astronomical calculations use Chalakim. The average person couldn’t hope to measure time with such exactitude. Even for Chazal this was only a mathematical construct.

רק רגע
The smallest unit of time used by Chazal, albeit rarely, is the רגע, moment. There are 76 רגעים in one חלק. Thus, one Regah equals 5/114 or .044, seconds. There are, 1,201.33 Regoim in a minute, 82,080 Regaim in an hour.

What about time in space?
Some time ago, an Israeli astronaut went up in the space shuttle. He chose to light Chanuka candles aboard the shuttle. If he was careful in Zemanim, he needed the light near nightfall. The shuttle circles the Earth in about 90 minutes. The astronaut would, therefor, experience a “day”, that is a sunrise and sunset, every 90 minutes. Theoretically then, he would have lit all 8 day’s-worth of Chanuka lights in the course of 630 minutes. Shabbos would occur every 560 minutes. And of course the biggest problem would be Shacharis – Mincha – Ma’Ariv; Shacharis – Mincha – Ma’Ariv; Shacharis – Mincha – Ma’ariv…….

This, of course, does not make sense. In fact, the Halachic parameters of this question had long since been decided. As Jews were sent to Siberia, several centuries ago, the nearer they came to the Arctic Circle the greater the differential in night and day. At a certain latitude, the difference disappears. There is no real night for weeks on end in the summer and no real day for weeks on end in the winter. All of the Z’manim are called into question. The answer they were given was to follow the actual times used by the nearest established Jewish community.

Our Astronaut would then use the times of the point he blasted off from. This leads to the next question. One Frum American astronaut blasts off from Cape Canaveral. At the same time a Frum Russian Astronaut blasts off from the Russian base on the other side of the world. They both come to the same space shuttle. Will each follow their own times? This cannot be. Perhaps the first one into the Shuttle establishes Minhag HaMakom?

All of this would apply equally to the Moon. What will happen when a Mars base is established? It is a planet in its own right. However, the length of its day, month and year are significantly different than Earth’s. What Halacha will apply there?

PART VIII – UNITS OF TIME IN HALACHA

TIME AND MITZVOS
For purposes of this paper we will assume an even day with a 6AM sunrise and a 6PM sunset although such a perfect day never actually occurs but to within a few minutes either way.

We must also take into account the definition of “day”. According to the Mishna Brura [Simen 443 sif katan 8] there is a difference of opinion. Many Achronim maintain that the day starts at Alos Ha’Shachar and lasts until Tzais HaKochavim {Shitas HaMechaber and Magen Avraham}. Others say that the day is from Neitz HaChama until Shkiya {Shitas HaL’vush and the Gra}.

Elsewhere, the Mishna Brura [588: 2] points out that Halachically, it is day from Amud Ha’Shachar for all purposes. In some instances Chazal required us to wait until Netz HaChama since we are not expert in determining the exact time of Alos.

The same requirement for a working definition of night exists. D’Orysa, night is defined as the appearance of three medium size stars even if they are scattered across the sky {Mishna Brura 235:1-4 & 261:24 & Biur Hal. ibid.](Except for Motzei Shabbos when we have to add on from Chol to Kodesh, which requires three small stars that are close together. {Mechaber 293:2 & Sha’ar HaTzion 235:3). As we are not adept in knowing the difference between large, medium or small stars, we are strict to wait until we can see three small stars. The Mishna Brura defines this as 72 minutes after Shkiya. Living as we do in cities with large haloes of light above them, we are unable to see many stars at all until quite late.

Several further problems exist. Quite obviously, the length of Bain Ha’Sh’mashos varies with latitude. This is not taken into account at all. Also, simple observation tells us that is dark, with many stars in the sky far before 72 minutes during the shorter days of winter. In the summer the sky is often still quite light even after 72 minutes. Using Sha’ose Z’manios would certainly solve this problem but no mention of this solution is made anywhere. Rabbeinu Tam (who lived in France) makes clear that his calculations were specific to Bavel only in Nissan and Tishrei, when the days are about of equal lengths with the nights.

Furthermore, our perception of sunrise and sunset are additionally affected by latitude, longitude, barometric pressure, humidity, haze and whether the horizon is flat or hilly.

Although the buildings no longer stand, an interesting situation was noted in respect to the Twin Towers. Had there been a Vosikin Bris on the bottom floor and a Vosikin Bris on the top floor on the same day, the baby on the top floor would have had his Milah considerably before the baby on the bottom floor.

A typical day would look like this:
Using a Monsey, N.Y. calendar, the closest to an equal day I found was for March 16 with only a one minute difference between Netz and Shkiya on Eastern Standard Time.

According to the GRA the differences are italicized According to the Magen Avraham
Alos 4:54AM [72 minute z’man] Alos 4:54AM
Misheyakir 5:21AM [45 minute z’man] Misheyakir 5:21AM
Netz 6:06AM Netz 6:06AM
Sof Z’man Krias Shema 9:05AM Sof Z’man Krias Shema 8:29AM
Sof Z’man Tefila 10:05AM Sof Z’man Tefila AM
{Z’man Musaf} {Z’man Musaf}
Chatzos HaYom 12:05PM Chatzos HaYom PM
Mincha Gedola 12:35PM Mincha Gedola PM
Bain HaArbayim Bain HaArbayim
Mincha K’tana 3:35PM Mincha K’tana PM
Plag HaMincha 4:50 Plag HaMincha
[Hadlakas HaNeiros 5:46PM Hadlakas HaNeiros PM
Shkiya 6:05PM Shkiya PM
Bain Ha’Sh’mashos Bain Ha’Sh’mashos
Tzais HaKochavim 7:17PM [72 minute z’man] Tzais HaKochavim 7:17PM
Tichle Regel Min HaShuk Tichle Regel Min HaShuk
Chatzos HaLeila 12:05 AM Chatzos HaLeila AM

The pertinent terms in the course of a day are:
עלות השחר or עמוד השחר Alos HaShachar, or Amud Ha’Shachar, according to some opinions, occurs when the center of the sun is 19.75 degrees below the horizon (90 minutes prior to Netz during Nisan & Tishrei). This opinion is usually used L’Chumra as the latest time to recite Shema or Shemona Esray from Ma’Ariv, count Sefira with a Bracha or to begin the day fasts.
According to the Shita of the Shulchan Aruch the Rama and the Chazon Ish, Alos occurs when the sun is 16.1 degrees below the horizon. This occurs 72 minutes before sunrise. These Poskim would say that one may recite Ma’Ariv Shema and Shemona Esray, count Sefira with a Bracha, recite the Hagada and read the Megila from the evening. As it demarcates the beginning of day according to some Poskim it also signals the earliest time, B’dieved, to take the Lulav, read Megila, blow Shofar, recite Hallel and begin the day fasts.
The Mechaber quotes the Gra and other Achronim that Amud Ha’Shachar occurs when the eastern sky is light. The Pri Migadim maintains that Amud is prior to the lighting up of the Eastern sky. Rashi, however, in Maseches Succa, Daf 95, implies that Amud Ha’Shachar is really two times. The Mishna Brura [89:2] tells us it occurs as the sky slowly begins to lighten. In the Biur Halacha [ibid] he further defines this as being prior to Netz by 1 1/5 hours, [72 minutes]. He goes on to say that it is not like those who mistakenly say that this refers to the morning star, as that is even earlier. He quotes [89:3] Rebbe Akiva Eiger to the effect that it is day at that point even if stars are still visible in the sky.
One may take the Lulav on Succos as early as Amud Ha’Shachar although it is preferable to wait until Netz. It is the last time to recite Sefira with a Bracha. The 4 minor fasts begin at the earlier [16.1 degree] time and one may still recite Krias Shema Shel Arvis, B’dieved, until this Z’man. Even B’dieved one cannot start any day Mitzva prior to the later 72 minute Z’man.
משיכיר
Misheyakir, according to some opinions, occurs when the center of the sun is 11 degrees below the horizon. This is earlier than the more commonly accepted view that Misheyakir occurs 45 minutes before sunrise, although some maintain that we have no source for measuring this in degrees or minutes.
By definition, Misheyakir is the point at which it is light enough to differentiate between green and blue. The back of your eye contains two types of cells that detect light; rods and cones. Rods see only black and white and are more sensitive than cones. Cones are able to detect very subtle shades of colors. Being less sensitive they require a higher level of light to operate efficiently. This explains why things all appear gray in a dimly lit room. A certain level of light is necessary to see color. When this amount of light is available, it is Misheyakir.
This is the earliest time for Talis with a Bracha, Tefillin and Krias Shema of Shacharis L’Chatchila

וותיקין
The term Vosikin is translated as students and referred to those Talmidim who loved Mitzvos and who woke up early to recite Shma in order to finish it precisely at Netz in order to achieve S’michas Geula L’Tefila and then start Shemona Esray at its earliest possible time. So the reference to Davening Vosikin means Davening in such a way as to reach Shemona Esray at Netz.

קריאת הגבר
The crowing of the rooster occurs early in the day The Mishna in Tamid (Perek 1 Mishna 2) tells us that the Memuna (the Cohain who cast lots to choose who did which Avoda in the Bais HaMikdash.) would begin the day’s activities in the Bais HaMikdash around this time.
תמיד של שחר
The morning Tamid offering was brought when the Memuna instructed a Cohain to climb to a high point in the Bais HaMikdash and report on the sunrise. The Memuna would ask “Barkai?”, “Has the Eastern sky gotten light?” The watchman would answer, “Hain”, “Yes, and the Memuna would instruct the Cohanim to go get the calf for the sacrifice. The Mishna in Tamid (Perek 1 Mishna 2) further tells us that Masya Ben Shmuel reported that the Cohain asked, “Has the entire Eastern sky lit up? This time is after that of Barkai.

נץ החמה
Netz HaChama occurs when the upper edge of the sun becomes visible on the horizon. This is sunrise. This occurs 1 hour prior to the sun being fully above the horizon according to the Rama [58:1]. The Mishna Brura [ibid. sk 9] tells us that others say that it occurs 6 minutes before the entire sun is above the horizon. The Gra maintains it is 18 minutes before. According to the Levush and the Gra, this is the start of Sha’ose Z’manios.

This is the earliest time, L’Chatchila, for Shemona Esray, L’Chatchila as well as the earliest time for Megila, Hallel, Lulav and Shofar.
סוף זמן קריאת שמע
There is a major difference of opinion between the Magen Avraham and the Gra. According to the Gra the last time for Krias Shema is 1/4 of the day שעות זמניות]] between Netz HaChama and Shkiya. The Magen Avraham’s time, always 36 minutes before that of the Gra, is between Alos and Tzais.
סוף זמן תפלה
The last time for reciting the Shemona Esray is 1/3 of the day [שעות זמניות] between Netz HaChama and Shkiya according to the Gra. Though the Magen Avraham’s Z’man is rarely given, it would be 1/3 of the day between Alos and Tzais.
חצות היום – חצות הלילה
Mid-day equals 1/2 of the day שעות זמניות]] between Netz HaChama and Shkiya according to the .לבושRav Moshe Feinstein maintained [source???] the mid-day and midnight are always 12PM and 12AM regardless of the length of day or night. The B’air Haitaiv [Simen 1 sif katan 6 & Simen 89 sif katan 3] and Sha’aray Tshuva [Simen 1 sif katan 6] both bring various opinions stating that midnight is measured as 12 hours from the high point of the sun in the daytime sky, which is, itself, mid-day. Both agree that for purposes of Krias Shema and Tefila we use Sha’ose Z’manios.
By day: Latest preferred time to make Kiddush Shabbos morning. Latest time for Tefilas Shacharis, B’dieved. Latest time to do Melacha on Erev Pesach.
At night: Afikomen on Pesach, Sof Z’man Krias Shema D’Rabbanan, the beginning time for Tikkun Chatzos, 13 Midos and Selichos

מנחה גדולה
The earliest time to Daven Mincha is the later of 1/2 hour (equal hours) and 1/2 hour (Z’manios) after Chatzos (See Shlchan Aruch Sif 233:1), 6 1/2 hours into the day. While some Rishonim maintain the preferred time is from 9 1/2 hours in the day the Mishna Brura says that one may, L’Chatchila, Daven Mincha from 6 1/2 hours.
According to the Rabbanan, Mincha Gedola ran until night fall. According to Rav Yehuda it lasts until Plag HaMincha; 10 3/4 hours into the day [Shulchan Aruch 333:1]
This was the beginning time, D’Orysa, that the Korbon Tamid of Bain Ha’erbin was brought. As other Korbonos could not be brought after it, this Korbon was usually postponed until 9 1/2 hours in the day other than Erev Pesach which occurred Erev Shabbos.( See Mishna Brura Simen 233 Sif Katan!)
בין הערבים
Bain HaArbayim occurs when the sun begins to go down in the western sky. The Sha’ar HaTzion [333:1] gives a time from 6 1/2 hours in the day (Sha’os Z’manios). The Mishna Brura [333:1] speaks about the connection to the Korbon Tamid of Bain HaArbayim. He writes, “Tefilas Mincha was instituted because the Korbon Tamid of Bain HaArbayim. The time for slaughtering the Korbon, D’Orysa, was after 6 1/2 hours in the day which is 1/2 hour after Chatzos [mid-day]. In order to be able to allow for other, individual Korbonos, which could not be offered after the Korbon Tamid, the Tamid was postponed daily until 9 1/2 hours in the day [except on Erev Pesach that occurred on Erev Shabbos]. Thus, the time for Mincha begins at 9 1/2 hours in the day, L’Chatchila. Should there be compelling reason to do so, Mincha may be recited as early as 6 1/2 hours in the day as that was the D’Orysa time for the Korbon Tamid.”
מנחה קטנה
9.5/12 of the day between Netz HaChama and Shkiya. This is the Mechaber’s preferred time to begin Davening Mincha.

פלג המנחה
Plag HaMincha is at 10.75/12 of the day between Netz HaChama and Shkiya. That is, it is 1 1/4 hours, Sha’ose Z’manios, before nightfall. As there is a Machlokes concerning the time of nightfall; whether it is at Shkiya or at Tzais HaKochavim, we are generally strict on Erev Shabbos to treat it as Shkiya. Thus, one may not take in Shabbos before 1 1/4 hours prior to Shkiya [Mishna Brura 261:25] The L’vush and the Gra are of the opinion that it is measured as 1 1/4 hours, Sha’ose Z’manios, prior to Shkiya {Mishna Brura 263:19].
Plag is the earliest time one can accept Shabbos on Friday afternoon.
הדלקת הנרות
Candle lighting time for Shabbos is 18 minutes before Shkiya. (In Yerushalayim, Hadlakas HaNeiros is 40 minutes before Shkiya). This is a Siyug to prevent Chilul Shabbos as well as a Mitzva of Tosfos Shabbos.
שקיעת החמה
Shkiya occurs when the upper edge of the sun disappears below the horizon
It is the last time for Melacha on Erev Shabbos or Erev Yom Tov, the end of time to recite Mincha, the last time to wash for Seuda Shlishis and the last time to eat on Shabbos without washing before Havdalah.
בין השמשות
As noted earlier in the article, agreement is necessary to make a determination when to actually begin or end any given time frame. As we have seen, this has created some problems in other areas of telling time. Nowhere will we find a greater problem than that of determining the true end of one day and the real beginning of the next. The day naturally segues slowly from light to dark. L’Halacha, everybody agrees that it is still day as long as any portion of the sun is above the horizon. Night is clearly defined as being when stars are visible in the night sky. The time in between is questionable. Chazal have determined that at least some of this time is to be considered neither day nor night, rather an intermediate period called Bain Ha’Sh’mashos. Note that there is no equivalent “Bain HaSmashos” for the morning.
We begin our look at Bain HaSmashos in the Gemora [Shabbos 34b]. The Gemora begins its discussion by telling us that Bain Ha’Sh’mashos is the time of day when we are in doubt that day has actually ended and night has started. The Gemora reports a three way disagreement.
1. Rav Yehuda maintains that this occurs after the sun has gone below the horizon as long as the redness of the sun is yet reflected on the clouds in the Eastern sky.
2. Rav Nechemia says that Bain Ha’Sh’mashos is the time it takes a person to walk half a Mil after sunset after which, it is night.
3. Rav Yosi tells us that Bain Ha’Sh’mashos is literally over in the blink of an eye. [According to Rashi, this is a fraction of a second prior to Tzais HaKochavim.]

The Gemora continues its discussion trying to reach a conclusion. In regard to Shabbos, the Gemora says, we are strict like Rav Yehuda. When it comes to the Cohanim eating Truma we Posken according to Rav Yosi. In this regard the Gemora concludes that as long as only one medium size star is visible in the sky it is still day. Two medium size stars is Bain Ha’Sh’mashos. Three medium size stars is definitively night.
There are many other applications of this Halacha. The Rishonim continue the discussion in terms of how to apply Bain Ha’Sh’mashos.

The Mishna Brura discusses Rabbeinu Tam’s view [261; sif katan 20]. Rabbeinu Tam solves an apparent contradiction between two Gemoras by saying that there are two different times for Shkiya. The first occurs when the sun sets. When the sun is no longer visible is the beginning of the first Shkiya. Then we wait 3 1/4 Mil, which is still day. At that point the second Shkiya starts. When there is no more light from the sun is the end of Shkiya. The period of 3 1/4 Mil [1,500 Amos] in between is Bain Ha’Sh’mashos. From that point three starts are visible and it is certainly night. Therefore, according to Rabbeinu Tam, from the beginning of Shkiya until Tzais HaKochavim equals 4 Mil.

The Mishna Brura does say that at, approximately, 15 minutes prior to Tzais it is Bain Ha’Sh’mashos according to everybody [Simen 333 sk 2]
Other Rishonim disagree. The Gra goes along with them. They maintain that as soon as the sun sets it and is no longer visible, that is the beginning of Bain Ha’Sh’mashos.
This time is latitude dependent as well as changing throughout the seasons. The times given by Rabbeinu Tam are given only for Bavel and only for Tishrei and Nissan when the days and nights are relatively equal. The further north or south of the equator the longer Bain Ha’Sh’mashos becomes. It is also longer in summer than winter. For some reason this factor is simply disregarded and our times are figured on this basis year round.
For all practical purposes, we tend to be Machmir according to both sides. On Erev Shabbos we will stop all Melacha at Shkiya. On Motzei Shabbos we will not begin doing Melacha until after the later Z’man. Of course, this Machlokes is also dependent on the decisions regarding the actual time for Tzais HaKochavim.
צאת הכוכבים
Tzais HaKochavim, according to some opinions occurs when the center of the sun is 8.5 degrees below the horizon. According to others it is 72 minutes after Shkiya.

It is the earliest time for: Ma’Ariv, Sefiras HaOmer, Krias Shema, Havdalah, Lighting Yom Tov candles after Shabbos

שתכלה רגל מן השוק
The time that people are normally off the streets at night is given as about 1/2 hour after Tzais HaKochavim [Biur Hal. 672:4]. This has applications to Chanuka candles as well as Yichud. It is interesting to note that, historically, prior to the advent of streetlamps, the streets were empty because people could not see where they were going. This is no longer true today. In some places, parts of Manhattan come to mind, there are people out and about until the wee hours of the morning. In fact, New York City’s night work force is, itself, larger than most other large towns or small cities in the country. Does Tichle Regel apply?

APPENDIX
EQUINOX- One of the two days in the year when the sun is directly above the Earth’s equator. On these days, day and night are of equal length. The time interval from the March to the September equinox is longer than from the September to the March equinox, due to the Earth’s elliptical orbit around the sun. The positions of the two equinoctial points shift westward about 1 degree every 70 years caused by a slight change in the direction of the Earth’s axis of rotation.

SOLSTICE
The two days a year on which the sun appears at its northernmost or southernmost position in the sky.

AUTUMNAL EQUINOX- In the northern hemisphere, on September 22 or 23, the equinox marks the beginning of autumn and is called the autumnal equinox.

SUMMER SOLSTICE- occurs when the sun reaches its most northerly point, directly overhead at the Tropic of Cancer (23o 27′ north latitude). Approximately June 21. In the northern hemisphere it is the longest day of the year and marks the beginning of summer.

VERNAL EQUINOX- In the northern Hemisphere, on March 20 or 21, the equinox marks the beginning of spring and is called the vernal equinox.

WINTER SOLSTICE- occurs when the sun reaches its most southerly point, directly overhead at the Tropic of Capricorn (23o 27′ south latitude). Approximately December 21.In the northern hemisphere it is the shortest day of the year and marks the beginning of winter.