Celestial bodies — the Sun, Moon, planets, and stars — have provided us a reference for measuring the passage of time throughout our existence. Ancient civilizations relied upon the apparent motion of these bodies through the sky to determine seasons, months, and years.

We know little about the details of timekeeping in prehistoric eras, but wherever we turn up records and artifacts, we usually discover that in every culture, some people were preoccupied with measuring and recording the passage of time. Ice-age hunters in Europe over 20,000 years ago scratched lines and gouged holes in sticks and bones, possibly counting the days between phases of the moon. Five thousand years ago, Sumerians in the Tigris-Euphrates valley in today's Iraq had a calendar that divided the year into 30 day months, divided the day into 12 periods (each corresponding to 2 of our hours), and divided these periods into 30 parts (each like 4 of our minutes). We have no written records of Stonehenge, built over 4000 years ago in England, but its alignments show its purposes apparently included the determination of seasonal or celestial events, such as lunar eclipses, solstices and so on.

The earliest Egyptian calendar was based on the moon's cycles, but later the Egyptians realized that the "Dog Star" in Canis Major, which we call Sirius, rose next to the sun every 365 days, about when the annual inundation of the Nile began. Based on this knowledge, they devised a 365 day calendar that seems to have begun in 4236 BCE (Before the Common Era), which thus seems to be one of the earliest years recorded in history.

Before 2000 BCE, the Babylonians (in today's Iraq) used a year of 12 alternating 29 day and 30 day lunar months, giving a 354 day year. In contrast, the Mayans of Central America relied not only on the Sun and Moon, but also the planet Venus, to establish 260 day and 365 day calendars. This culture and its related predecessors spread across Central America between 2600 BCE and 1500 CE, reaching their apex between 250 and 900 CE. They left celestial-cycle records indicating their belief that the creation of the world occurred in 3114 BCE. Their calendars later became portions of the great Aztec calendar stones. Our present civilization has adopted a 365 day solar calendar with a leap year occurring every fourth year (except century years not evenly divisible by 400).

*****

Early Clocks

Not until somewhat recently (that is, in terms of human history) did people find a need for knowing the time of day. As best we know, 5000 to 6000 years ago great civilizations in the Middle East and North Africa began to make clocks to augment their calendars. With their attendant bureaucracies, formal religions, and other burgeoning societal activities, these cultures apparently found a need to organize their time more efficiently

Sun Clocks

The Sumerian culture was lost without passing on its knowledge, but the Egyptians were apparently the next to formally divide their day into parts something like our hours. Obelisks (slender, tapering, four-sided monuments) were built as early as 3500 BCE. Their moving shadows formed a kind of sundial, enabling people to partition the day into morning and afternoon. Obelisks also showed the year's longest and shortest days when the shadow at noon was the shortest or longest of the year. Later, additional markers around the base of the monument would indicate further subdivisions of time.

Another Egyptian shadow clock or sundial, possibly the first portable timepiece, came into use around 1500 BCE. This device divided a sunlit day into 10 parts plus two "twilight hours" in the morning and evening. When the long stem with 5 variably spaced marks was oriented east and west in the morning, an elevated crossbar on the east end cast a moving shadow over the marks. At noon, the device was turned in the opposite direction to measure the afternoon "hours."

The merkhet, the oldest known astronomical tool, was an Egyptian development of around 600 BCE. A pair of merkhets was used to establish a north-south line (or meridian) by aligning them with the Pole Star. They could then be used to mark off nighttime hours by determining when certain other stars crossed the meridian.

In the quest for better year-round accuracy, sundials evolved from flat horizontal or vertical plates to more elaborate forms. One version was the hemispherical dial, a bowl-shaped depression cut into a block of stone, carrying a central vertical gnomon (pointer) and scribed with sets of hour lines for different seasons. The hemicycle, said to have been invented about 300 BCE, removed the useless half of the hemisphere to give an appearance of a half-bowl cut into the edge of a squared block. By 30 BCE, Vitruvius could describe 13 different sundial styles in use in Greece, Asia Minor, and Italy.

Elements of a Clock

Before we continue describing the evolution of ways to mark the passage of time, perhaps we should broadly define what constitutes a clock. All clocks must have two basic components:

The history of timekeeping is the story of the search for ever more consistent actions or processes to regulate the rate of a clock.

Water Clocks

Water clocks were among the earliest timekeepers that didn't depend on the observation of celestial bodies. One of the oldest was found in the tomb of the Egyptian pharaoh Amenhotep I, buried around 1500 BCE. Later named clepsydras ("water thieves") by the Greeks, who began using them about 325 BCE, these were stone vessels with sloping sides that allowed water to drip at a nearly constant rate from a small hole near the bottom. Other clepsydras were cylindrical or bowl-shaped containers designed to slowly fill with water coming in at a constant rate. Markings on the inside surfaces measured the passage of "hours" as the water level reached them. These clocks were used to determine hours at night, but may have been used in daylight as well. Another version consisted of a metal bowl with a hole in the bottom; when placed in a container of water the bowl would fill and sink in a certain time. These were still in use in North Africa in the 20th century.
 

More elaborate and impressive mechanized water clocks were developed between 100 BCE and 500 CE by Greek and Roman horologists and astronomers. The added complexity was aimed at making the flow more constant by regulating the pressure, and at providing fancier displays of the passage of time. Some water clocks rang bells and gongs; others opened doors and windows to show little figures of people, or moved pointers, dials, and astrological models of the universe.

A Macedonian astronomer, Andronikos, supervised the construction of his Horologion, known today as the Tower of the Winds, in the Athens marketplace in the first half of the first century BCE. This octagonal structure showed scholars and shoppers both sundials and mechanical hour indicators. It featured a 24 hour mechanized clepsydra and indicators for the eight winds from which the tower got its name, and it displayed the seasons of the year and astrological dates and periods. The Romans also developed mechanized clepsydras, though their complexity accomplished little improvement over simpler methods for determining the passage of time.

In the Far East, mechanized astronomical/astrological clock making developed from 200 to 1300 CE. Third-century Chinese clepsydras drove various mechanisms that illustrated astronomical phenomena. One of the most elaborate clock towers was built by Su Sung and his associates in 1088 CE. Su Sung's mechanism incorporated a water-driven escapement invented about 725 CE. The Su Sung clock tower, over 30 feet tall, possessed a bronze power-driven armillary sphere for observations, an automatically rotating celestial globe, and five front panels with doors that permitted the viewing of changing manikins which rang bells or gongs, and held tablets indicating the hour or other special times of the day.

Since the rate of flow of water is very difficult to control accurately, a clock based on that flow could never achieve excellent accuracy. People were naturally led to other approaches.
 

**

In Europe during most of the Middle Ages (roughly 500 CE to 1500 CE), technological advancement virtually ceased. Sundial styles evolved, but didn't move far from ancient Egyptian principles.

During these times, simple sundials placed above doorways were used to identify midday and four "tides" (important times or periods) of the sunlit day. By the 10th century, several types of pocket sundials were used. One English model even compensated for seasonal changes of the Sun's altitude.

Then, in the first half of the 14th century, large mechanical clocks began to appear in the towers of several large Italian cities. We have no evidence or record of the working models preceding these public clocks, which were weight-driven and regulated by a verge-and-foliot escapement. Variations of the verge-and-foliot mechanism reigned for more than 300 years, but all had the same basic problem: the period of oscillation of the escapement depended heavily on the amount of driving force and the amount of friction in the drive. Like water flow, the rate was difficult to regulate.

Another advance was the invention of spring-powered clocks between 1500 and 1510 by Peter Henlein of Nuremberg. Replacing the heavy drive weights permitted smaller (and portable) clocks and watches. Although they ran slower as the mainspring unwound, they were popular among wealthy individuals due to their small size and the fact that they could be put on a shelf or table instead of hanging on the wall or being housed in tall cases. These advances in design were precursors to truly accurate timekeeping.

Accurate Mechanical Clocks

In 1656, Christiaan Huygens, a Dutch scientist, made the first pendulum clock, regulated by a mechanism with a "natural" period of oscillation. (Galileo Galilei is credited with inventing the pendulum-clock concept, and he studied the motion of the pendulum as early as 1582. He even sketched out a design for a pendulum clock, but he never actually constructed one before his death in 1642.) Huygens' early pendulum clock had an error of less than 1 minute a day, the first time such accuracy had been achieved. His later refinements reduced his clock's error to less than 10 seconds a day.

Around 1675, Huygens developed the balance wheel and spring assembly, still found in some of today's wristwatches. This improvement allowed portable 17th century watches to keep time to 10 minutes a day. And in London in 1671, William Clement began building clocks with the new "anchor" or "recoil" escapement, a substantial improvement over the verge because it interferes less with the motion of the pendulum.

In 1721, George Graham improved the pendulum clock's accuracy to 1 second per day by compensating for changes in the pendulum's length due to temperature variations. John Harrison, a carpenter and self-taught clock-maker, refined Graham's temperature compensation techniques and developed new methods for reducing friction. By 1761, he had built a marine chronometer with a spring and balance wheel escapement that won the British government's 1714 prize (worth more than $10,000,000 in today's currency) for a means of determining longitude to within one-half degree after a voyage to the West Indies. It kept time on board a rolling ship to about one-fifth of a second a day, nearly as well as a pendulum clock could do on land, and 10 times better than required to win the prize.

Over the next century, refinements led in 1889 to Siegmund Riefler's clock with a nearly free pendulum, which attained an accuracy of a hundredth of a second a day and became the standard in many astronomical observatories. A true free-pendulum principle was introduced by R.J. Rudd about 1898, stimulating development of several free-pendulum clocks. One of the most famous, the W.H. Shortt clock, was demonstrated in 1921. The Shortt clock almost immediately replaced Riefler's clock as a supreme timekeeper in many observatories. This clock contained two pendulums, one a slave and the other a master. The slave pendulum gave the master pendulum the gentle pushes needed to maintain its motion, and also drove the clock's hands. This allowed the master pendulum to remain free from mechanical tasks that would disturb its regularity.

Quartz Clocks

The performance of the Shortt clock was overtaken as quartz crystal oscillators and clocks, developed in the 1920s and onward, eventually improved timekeeping performance far beyond that achieved using pendulum and balance-wheel escapements.

Quartz clock operation is based on the piezoelectric property of quartz crystals. If you apply an electric field to the crystal, it changes its shape, and if you squeeze it or bend it, it generates an electric field. When put in a suitable electronic circuit, this interaction between mechanical stress and electric field causes the crystal to vibrate and generate an electric signal of relatively constant frequency that can be used to operate an electronic clock display.

Quartz crystal clocks were better because they had no gears or escapements to disturb their regular frequency. Even so, they still relied on a mechanical vibration whose frequency depended critically on the crystal's size, shape and temperature. Thus, no two crystals can be exactly alike, with just the same frequency. Such quartz clocks and watches continue to dominate the market in numbers because their performance is excellent for their price. But the timekeeping performance of quartz clocks has been substantially surpassed by atomic clocks.

Internet Source Reference:

http://www.nmm.ac.uk/server.php?navId=005

 Sundial Theory

Sundials are naturally limited in their usefulness and a cynic might complain that they are of little more than academic interest in a climate such as that 'enjoyed' in the British Isles. Nevertheless the study of sundials, or gnomonics as it is sometimes called, will also provide a good understanding of some fundamental astronomical principles.

As the Earth rotates on its axis, so the Sun appears to move uniformly across the sky and if a rod is placed parallel to the Earth's axis its shadow will naturally move uniformly around itself. In other words, as the Sun moves through an arc of 15° in the sky in one hour so will the shadow move at the same rate. This is the principle on which most (but not all) sundials are based, and in fact the same idea is used with telescopes which are then said to be 'equatorially mounted'.

Because the Earth's distance from the Sun varies throughout the year and also because its equator is inclined to its orbit (by 23.5°), there is a difference between apparent solar time (time told by the Sun) and mean solar time which is the time kept by mechanical and electrical clocks. In fact it is possible for the Sun to be as much as a quarter of an hour fast or slow when compared with a clock which keeps mean solar time (i.e. Greenwich Mean Time). This difference is called the equation of time and is described in the leaflet 'The Equation of Time'.

If we know this correction as a function of the date it is possible to adjust certain types of sundial (those where equal intervals of time are indicated by equal angles) to allow for the change in the equation of time; or alternatively, for any type of dial, to apply a correction to the time read from the dial.

Another correction that has to be made is to allow for the longitude of the place. We are all familiar with the fact that 'New York is five hours behind Greenwich' meaning, for example, that when it is midday at Greenwich it is only 7am in New York. This is because New York is 5 hours of longitude west of Greenwich. Even if we move only as far west as Bristol we find that this town is 10 minutes of time west of Greenwich so that the Sun crosses the meridian 10 minutes later than it does at Greenwich. Therefore if you had a sundial in Bristol and wanted to find the Greenwich Mean Time, you would have to add 10 minutes to the time from the dial, unless this longitude correction had already been allowed for in the construction of the dial.

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Internet Source Reference:

http://www.newadvent.org/cathen/03738a.htm 

Chronological Notes

Chronology (Greek chronos time, logos, discourse), the science of time-measurement, has two branches:

It is thus for history what latitude and longitude are for geography. The first requisite in any system of historical chronology is an era, that is to say a fixed point of time, the distance from which shall indicate the position of all others. The term era, the derivation of which is not certainly known, appears first to have been employed in France and Spain to signify a number or rule. Since the need of a definite system of chronology was first recognized by mankind, many and various eras have been employed at different periods and by different nations. For practical purposes it is most important to understand those which affect Christian history.

CHRISTIAN ERA

Foremost among these is that which is now adopted by all civilized peoples and known as the Christian, Vulgar, or Common Era, in the twentieth century of which we are now living. This was introduced about the year 527 by Dionysius Exiguus, a Scythian monk resident at Rome, who fixed its starting point in the year 753 from the foundation of Rome, in which year, according to his calculation, the birth of Christ occurred. Making this the year 1 of his era, he counted the years which followed in regular course from it, calling them years "of the Lord", and we now designate such a date A.D. (i.e. Anno Domini). The year preceding A.D. 1 is called Ante Christum (A.C.) or Before Christ (B.C.). It is to be noted that there is no year O intervening, as some have imagined, between B.C. and A.D. It is supposed by many that the calculation of Dionysius was incorrect, and that the birth of Christ really occurred three years earlier than he placed it, or in the year of Rome 760 which he styles 3 B.C. This, however, is immaterial for the purposes of chronology, the first year of the Christian Era being that fixed, rightly or wrongly, by Dionysius. His system was adopted but gradually, first in Italy, then in other parts of Christendom. England would appear to have been among the earliest regions to have made use of it, under the influence of the Roman missioners, as it is found in Saxon charters of the seventh century. In Gaul it made its appearance only in the eighth, and its use did not become general in Europe until after A.D. 1000; accordingly in French the term millésime was frequently used to signify a date A.D. In Spain, although not unknown as early as the seventh century, the use of the Christian Era, as will presently be shown, did not become general until after the middle of the fourteenth century.

PRE-CHRISTIAN CHRONOLOGY

Of the chronological systems previously in use it will be sufficient to briefly describe a few.

The Greeks dated events by Olympiads, or periods of four years intervening between successive celebrations of the Olympic games, and this mode of computation, having been largely adopted at Rome, continued to be frequently used in the first centuries of Christianity. The Olympiads started from 776 B.C., and consequently A.D. 1 was the fourth year of the 194th Olympiad.

The Romans frequently reckoned from the traditional foundation of their city (ab urbe conditâ--A.U.C.), which date, as has been said, coincided with 753 B.C. They likewise often designated years by the names of the consuls then in office (e.g. console Planco). Sometimes the Romans dated by post-consular years (i.e. so long after the consulate of a well-known man). Naturally the regnal years of Roman emperors presently supplanted those of consuls, whose power in later times was merely nominal, and from the emperors this method of describing dates was imitated by popes, kings, and other rulers, with or without the addition of the year A.D. It became in fact universal in the Middle Ages, and it subsists in documents, both ecclesiastical and civil, down to our own day.

REGNAL YEARS

The pontifical years of the popes are historically important (see chronological list in article POPE). Care must be taken, of course, in the case of such dates, to observe from what point of time each reign is reckoned. In an elective monarchy like the papacy there is necessarily an interval between successive reigns, which is occasionally considerable. Moreover, the reckoning is sometimes from the election of a pontiff, sometimes from his coronation.

In determining dates by the regnal years of other sovereigns there are of course various points to which attention must be paid. Confining ourselves to English history, the earlier kings after the Norman Conquest dated their reigns only from their coronation, or some other public exhibition of sovereignty, so that there was sometimes an interval of days or even weeks between the close of one reign and the commencement of the next. Only from the accession of Richard II (22 June, 1377) was the reign of a monarch held to begin with the death or deposition of his predecessor. Even subsequently to this it was reckoned sometimes from the day itself upon which the preceding monarch ceased to reign, sometimes from the day following. Not till the first year of Queen Elizabeth was it enacted that the former should be the rule. In certain particular instances the matter was still further complicated. King John dated his reign from his coronation, 27 May, 1199, but this being the Feast of the Ascension, his years were counted from one occurrence of this festival to the next, and were accordingly of varying length. Edward I dated from noon, 20 November, 1272, and in consequence this day in each year of his reign was partly in one regnal year and partly in another. In the civil wars of York and Lancaster, Henry VI and Edward IV equally ignored the period during which his rival assumed or recovered power, and counted their years continuously onwards from the time when they mounted the throne. Charles II, though he began to reign de facto only at the Restoration (29 May, 1660), reckoned his years, de jure, from his father's execution, 30 January, 1648-9, ignoring the Commonwealth and Protectorate. Queen Mary Tudor reckoned her reign from the death of Edward VI, 6 July, 1553, but the interval until 19 July of the same year being occupied by the abortive reign of Lady Jane Grey, public documents in her name commence only with the latter date. William III and Mary II began to reign 13 Feb., 1688-9, as "William and Mary". Mary died 28 December, 1694, when the style was altered to "William" alone; but no change was made in the computation of regnal years. Within the year, it was long usual to specify dates by reference to some well-known feast in the ecclesiastical calendar, as, for instance, "the Friday before Pentecost" or "the day of St. John the Baptist".

INDICTIONS

In papal and other documents, another epoch is often added, namely, the Indiction. This had originally been a period of fifteen years, at the close of which the financial accounts of the Roman Empire were balanced; but for purposes of chronology the indictions are conventional periods of fifteen years, the first of which began in the reign of Constantine the Great. Unlike the Olympiads, the indictions themselves were not numbered, but only the place of a year in the indiction in which it fell. Thus indictione quartâ; signifies not "in the fourth indiction", but "in the fourth year of its indiction", whatever this was. It was obvious that such an element of computation could serve only to verify more precisely the date of a year already approximately known. Moreover, the indictions were calculated on different systems, which have to be understood and distinguished:

BEGINNING OF THE YEAR

The date at which the year commenced varied at different periods and in different countries. When Julius Caesar reformed the calendar (45 B.C.) he fixed 1 January as New Year's Day, a character which it seems never quite to have lost, even among those who for civil and legal purposes chose another starting point. The most common of such starting points were 25 March (Feast of the Annunciation, "Style of the Incarnation") and 25 December (Christmas Day, "Style of the Nativity"). In England before the Norman Conquest (1066) the year began either on 25 March or 25 December; from 1087 to 1155 on 1 January; and from 1155 till the reform of the calendar in 1752 on 25 March, so that 24 March was the last day of one year, and 25 March the first day of the next. But though the legal year was thus reckoned, it is clear that 1 January was commonly spoken of as New Year's Day. In Scotland, from 1 January, 1600, the beginning of the year was reckoned from that day. In France the year was variously reckoned: from Christmas Day, from Easter eve, or from 25 March. Of all starting points a movable feast like Easter is obviously the worst. From 1564 the year was reckoned in France from 1 January to 31 December. In Germany the reckoning was anciently from Christmas, but in 1544 and onwards, from 1 January to 31 December. In Rome and a great part of Italy, it was from 25 December, until Pope Gregory XIII reformed the calendar (1582) and fixed 1 January as the first day of the year. The years, however, according to which papal Bulls are dated still commence with Christmas Day. Spain, with Portugal and Southern France, observed an era of its own long after the rest of Christendom had adopted that of Dionysius. This era of Spain or of the Cæsars, commenced with 1 January, 38 B.C., and remained in force in the Kingdom of Castile and Leon till A.D. 1383, when a royal edict commanded the substitution of the Christian Era. In Portugal the change was not made till 1422. No satisfactory explanation has been found of the date from which this era started.

THE GREGORIAN REFORM

The introduction of the Gregorian Calendar entailed various discrepancies between the dates which different people assigned to the same events. The Julian system of time-measurements, introduced by Cæsar, was not sufficiently accurate, as it made the year slightly too long, with the result that by the sixteenth century it had fallen ten days in arrear, so that, for instance, the day of the vernal equinox, which should have been called 21 March, was called 11 March. To remedy this, besides substituting an improved system which should prevent the error from operating in future, it was necessary to omit ten full days in order to bring things back to the proper point. Pope Gregory XIII, who introduced the reformed system, or "New Style", ordained that ten days in October, 1582, should not be counted, the fourth of that month being immediately followed by the fifteenth. He moreover determined that the year should begin with 1 January, and in order to prevent the Julian error from causing retardation in the future as in the past, he ruled that three leap years should be omitted in every four centuries, viz. those of the centennial years the first two figures of which are not exact multiples of four, as 1700, 1800, 1900, 2100, etc. The New Style (N.S.) was speedily adopted by Catholic States, but for a long time the Protestant States retained the Old (O.S.), from which there followed important differences in marking dates according as one or other style was followed. In the first place there was the original difference of ten days between them, increased to eleven by the O.S. 29 February in A.D. 1700, to twelve days in 1800, and to thirteen in 1900. Moreover, the period from 1 January to 24 March inclusive, which was the commencement of the year according to N.S., according to O.S. was the conclusion of the year previous. From want of attention to this, important events have sometimes been misquoted by a year. In illustration may be considered the death of Queen Elizabeth. This occurred in what was then styled in England 24 March 1602, being the last day of that year. In France and wherever the N.S. prevailed, this day was described as 3 April, 1603. To avoid all possible ambiguity such dates are frequently expressed in fractional form as 24 March/3 April, 1602/3. In our modern histories years are always given according to N.S., but dates are otherwise left as they were originally recorded. Thus Queen Elizabeth is said to have died 24 March, 1603. Not till 1700 was the Gregorian reform accepted by the Protestant States of Germany and the Low Countries, and not till 1752 by Great Britain, there being by that time a difference of eleven days between O.S. and N.S. Sweden, after some strange vacillation, followed suit in 1753. O.S. was still followed by Russia and other Eastern Orthodox countries well into the twentieth century, and their dates consequently were thirteen days behind those of the rest of Christendom.

JULIAN PERIOD

The Christian Era has this disadvantage for chronological purposes, that dates have to be reckoned backwards or forwards according as they are B.C. or A.D., whereas in an ideally perfect system all events would be reckoned in one sequence. The difficulty was to find a starting point whence to reckon, for the beginnings of history in which this should naturally be placed are those of which chronologically we know least. At one period it was attempted to date from the Creation (A.M. or Anno Mundi), that event being placed by Christian chronologists, such as Archbishop Usher, in 4004 B.C., and by the Jews in 3761 B.C. But any attempt thus to determine the age of the world has been long since abandoned. In the year 1583, however--that following the Gregorian reform--Joseph Justus Scaliger introduced a basis of calculation which to a large extent served the purpose required, and, according to Sir John Herschel, first introduced light and order into chronology. This was the Julian Period--one of 7980 Julian years, i.e. years of which every fourth one contains 366 days. The same number of Gregorian years would contain 60 days less. For historians these commence with the midnight preceding 1 January, 4713 B.C., for astronomers with the following noon. The period 7980 was obtained by multiplying together 28, 19, and 15, being respectively the number of years in the Solar Cycles the Lunar Cycle, and the Roman Indiction, and the year 4713 B.C. was that for which the number of each of these subordinate cycles equals 1. The astronomical day is reckoned from noon to noon instead of from midnight to midnight. Scaliger calculated his period for the meridian of Alexandria to which Ptolemy had referred his calculation.

OTHER ERAS

Various eras employed by historians and chroniclers may be briefly mentioned, with the dates from which they were computed.

At the French Revolution it was determined to introduce an entirely new system of chronology, dating from that event and having no affinity with any previously adopted. In the first form this was the Era of Liberty, commencing 1 January, 1789. This was soon replaced by the Republican Era, at first appointed to commence 1 January, 1792, and afterwards 22 September, 1792. This was the date of the proclamation of the Republic, which coincided with the autumnal equinox, calculated on the meridian of Paris. The year was divided into twelve months of thirty days each, and the days into decades, weeks being abolished. The months had names given to them according to their seasonal character.

As these months contained only 360 days, five jours complémentaires were added at the end of Fructidor, officially called Primidi, Duodi, Tridi, Quartidi, Quintidi, but commonly known as Sans-culottides. Olympic or leap years occurred every fourth year of the Republic, and had a sixth intermediary day called Sextidi. The period thus terminated was called Franciade. This calendar was enforced in France till 1 January, 1806, when it was abolished by Napoleon, and the use of the Gregorian calendar resumed.

DAYS OF THE MONTH AND WEEK

Various methods have been devised for ascertaining upon what day of the week any given date falls. The best known is that of Dominical Letters, which has this disadvantage, that a table is usually required to find out what is the Dominical Letter for the year in question. Complication is likewise caused by the necessity of passing from one letter to another in leap years, on reaching the intercalary day in February. The following method is free from these inconveniences, and can be worked without any reference to tables:

The days of the week are numbered according to their natural order, viz. Sunday=1, Monday=2, Tuesday=3, Wednesday=4, Thursday=5, Friday=6, Saturday=7. (At the time from which the Christian Era starts there were of course no weeks, such a measure of time not being known among the Greeks and Romans. Counting backwards, however, according to our present system, we can divide all time into weeks, and it is to be noted that in the Christian period the order of days of the week has never been interrupted. Thus, when Gregory XIII reformed the Calendar, in 1582, Thursday, 4 October, was followed by Friday, 15 October. So in England, in 1752, Wednesday, 2 September, was followed by Thursday, 14 September. What we style 14 August, 1907, the Russians style 1 August, but both call it Wednesday.) For our present purpose the year commences with March; January and February being reckoned as the 11th and 12th months of the preceding year; thus 29 February, when it occurs, is the last day of the year and causes no further disturbance.

As a matter of fact, it is found by computation that 1 March of the year known as A.D. 1 was a Tuesday. Assigning to this year the figure 1 as its year number, to March the figure 1 as its month number, and adding these to 1, the day number of 1 March, we get 3, indicating Tuesday the third day of the weeks. From this first datum all the rest follows. The succeeding days of March increase their figures each by 1, on account of the increased day number. When 7 is passed it is only the figures which remain, after division by that number, which are to be considered; thus 11 may be treated as 4 (7+4) and 30 as 2 (28+2). In general, any exact multiple of 7 (14, 21, 28) may be added or subtracted when convenient without affecting the result. Instead of adding any number (e.g. 1 or 4) we may subtract its difference from 7 or a multiple of 7 (e.g. 6 or 3). The remainder 0 in a division is equivalent to 7, and thus in calculating for the day of the week it signifies Saturday.

As the days of the leading month, so those of the months preceding it follow naturally. As March contains 31 days (i.e. 28+3), April necessarily begins with a day 3 places later in the weekly sequence, and its month number instead of 1 is 4. So of other months, according to the number of days in that which preceded. The following are the month numbers throughout the year which never change:--March 1; April 4; May 6; June 2; July 4; August 0; September 3; October 5; November 1; December 3; January 6; February 2. A.D. 1, being a common year of 365 days (or 52 weeks+1 day), ends with the same day of the week--Tuesday--with which it commenced. Consequently the next year, A.D. 2, commences a day later, with Wednesday for 1 March, and as its year number is increased to 2, we get 2+1+1=4. So in A.D. 3, the year number becomes 3, and 1 March is Thursday. But on account of 29 February preceding 1 March, A.D. 4, this day falls 366 days (or 52 weeks+2 days) after 1 March, A.D. 3, or on Saturday, and its year number must be increased to 5; 5+1+1=7. Thus, to find the number belonging to any year within its own century, we must find how many days beyond an exact number of weeks there have been since that century commenced. As every common year contains one day more than fifty-two weeks, and every leap year two days more, by adding at any period the number of leap years which there have been in the century to the total number of years in the same, we obtain the number of days required. To obtain the number of leap years, we divide the last two figures of the date (i.e. those in the tens and units place) by four. The quotient (neglecting any remainder) shows the number of leap years; which, added to the same two figures, gives the number of days over and above the sets of fifty-two weeks which the years contain. Thus, for example, the year '39 of any century (939, 1539, 1839, 1939) will have 6 for its year number; for in such year 48 extra days will have accumulated since the corresponding day of the centurial year (00), viz. 1 day for each of the 30 common years, and 18 days for the 9 leap years.

THE CENTURY

One more element of calculation remains to be considered -- the Century. We begin with the Julian system, or Old Style (O.S.)--according to which all centuries contain 75 common years of 365 days, and 25 leap years of 366, and accordingly 125 days in all, over and above 5200 weeks. But 125 days=17 weeks+6 days. Therefore a Julian century ends with the day of the week two days previous to that with which if began, and the succeeding century will begin with the day of the week, one day earlier than its predecessor. Thus, A.D. 1 March, 1300, being Tuesday, in 1400 it would be Monday, in 1500 Sunday, in 1600 Saturday. Having obtained the centurial number for any century, we add to it the year numbers of the years which follow to the close of that century. Centurial numbers O.S. are obtained by subtracting the centurial figure or figures (viz. those preceding 00) from the multiple of 7 next above, the remainder being the number required. Thus for A.D. 1100 the centurial number is 3 (14-11), for 1500, 6 (21-15), for 1900, 2 (21-19).

Under the N.S. three centuries in every four contain 76 common years and 24 leap years, and thus have only 124 days over 5200 weeks, or 17 weeks and 5 days, and end with the day of the week three earlier than they began. The following century, beginning two days earlier than that which it follows, has its centurial number less by 2. Thus 1 March, A.D. 1700, was Monday, and the centurial number 0 (or 7). 1 March, 1800, was Saturday, and the centurial number 5. Every fourth centurial year N.S., being a leap year (1600, 2000, 2400, etc.), has 366 days; and the century to which it belongs, like those of the O.S., diminishes its centurial number only by 1 from the preceding. N.S. having been introduced in the sixteenth century, it is only for dates 15-- and upwards that N.S. centurial numbers are required. They are as follows: for 1500=3; 1600=2; 1700=7; 1800=5; 1900=3; 2000=2. It will be seen that the same figures constantly recur. Leap year centuries (with the first two figures exactly divisible by 4) having the centurial number 2, and the three centuries following having 7 (or 0), 5, and 3 respectively, after which 2 comes round again. The centurial number N.S. can be obtained from that of O.S. if the difference of days between O.S. and N.S. be allowed for. This is done by subtracting the said difference from the O.S. centurial number, increased by as many times 7 as the subtraction requires. As we have seen, for the sixteenth and seventeenth centuries, the difference was 10 days; for the eighteenth, 11; for the nineteenth, 12; for the twentieth and twenty-first, 13. Thus:

Rule to find day of week for any date: Take the sum of the centurial number+year number+month number+day number; divide this by 7; the remainder gives day of week, O.S. or N.S., according to century number used.

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