SOURCE: “Part I,” in The Calendar: Its History, Structure and Improvement, Cambridge University Press, 1921, pp. 1-27.

[In the following excerpt, Philip surveys the historical measurement of time, reviews the development and reform of the Western calendar, and looks at several world calendars.]

I

THE MEASUREMENT OF TIME

Our knowledge of time is wholly dependent on measurement. Without the specification of magnitude or quantity the idea of time is meaningless. Now, we can measure time—physically—in one way only—by counting repeated motions. Apart, therefore, from physical pulsations we should have no natural measure of time. In particular the operation of the astronomical Law of Periodicity supplies us with the principal time units.

The primary periodic movements to which we owe our knowledge of time are the two movements of our own earth in which we necessarily participate. These are (1) the rotation of the earth on its axis—which gives us day and night—and (2) the revolution of the earth round the sun—which gives us the year and the seasons. A third uniquely important periodic motion is the revolution of the moon round the earth—which gives us the month.

THE DAY

The earth's rate of rotation on its axis is constant, and a day is the interval between two successive passages of a given celestial object across the meridian. The sidereal day is the interval between two successive passages of a given star. The stars being at an infinite distance, the length of the sidereal day is exactly the same as the time taken by one complete rotation of the earth, and by reference to the record of ancient eclipses it is known that the length of the sidereal day has been invariable for at least two thousand years. The solar day is the interval between two successive passages of the sun across the meridian. As the earth's rate of rotation is constant, it follows that the length of the mean solar day is also a constant quantity. But as the sun has an apparent motion in opposition to the revolution of the starry sphere amounting to nearly one degree per day, it follows that there is a corresponding difference between the length of the sidereal and the mean solar day.

It follows also that in 365 solar days the earth has really rotated about 366 times. If we go round the earth from east to west we neutralise the effect of the motion above referred to and lose one day. Whereas, if we go from west to east, whilst each day is shorter, we gain a day in the course of the journey.

Again, the sun's apparent eastward motion is not a constant quantity in each successive day. This is owing to the facts, (1) that the rate of the earth's motion in its elliptic orbit is not uniform, and (2) that the ecliptic is inclined at an angle to the equator. There is, therefore, a variation in the actual length of the solar day amounting at its maximum to about 30 seconds. This accumulating from day to day makes a variation in the time of apparent noon amounting to upwards of half an hour—being at a maximum of 16[frac14] minutes before mean noon about 4th November, and of 14[frac12] minutes after mean noon about 12th February. Four times annually, viz. on 4th Nov., 12th Feb., 15th May and 29th July, the actual length coincides with the average length of the solar day, which is exactly 24 hours. Four times annually, viz. at or about 15th April, 15th June, 1st September and 24th December, the time shown by an accurate clock and a true sundial would coincide. In almanacs the difference between the clock and the sun is usually noted at its maximum point under the entry “clock before” or “clock after” sun.

It is usual to describe the whole period of 24 hours as the civil day—distinguishing it thus from the natural day, which is the interval between sunrise and sunset. The beginning and end of the civil day have been variously computed. In the earliest times it appears to have been usually held to commence with the evening. In the Book of Genesis the account of the creation refers to the evening and the morning as composing the day. This method of computation was also observed by the Greeks, and, according to Caesar,¹ and Tacitus² the ancient Gauls and Germans computed their times and seasons by the night—a relic of which is found in our own expression “a fortnight.” Amongst the Jews it was also the custom to commence the day with the evening. With the Romans the day began at various hours. According to Macrobius³ the civil day of the Romans began from the sixth hour of the night, that is midnight. At other times the Romans computed the day from 6 a.m. The hour of Christ's death was said to be the ninth hour, equal to 3 p.m. The night amongst the Jews and other early nations was divided into three watches. The Greeks and the Romans divided it into four watches. In modern times it is usual to compute the day commencing from midnight, but by astronomers the day is held to commence at noon. In 1925 the civil reckoning is to be adopted by them.

THE YEAR

The true length of the year is also susceptible of various interpretations. Astronomers distinguish: (1) The sidereal year or length of the year measured by reference to the fixed stars; (2) the anomalistic year—being the interval between two successive returns of the earth to perihelion; and (3) the tropical year—being the interval between two successive returns of the sun to the equinox. It is on this latter that the seasons depend, and this year is the only one of the three with which we have any concern in the ordering of human affairs, or in the construction of a Calendar.

Arising out of a primitive seasonal or vegetational year the idea of a year astronomically determined was developed amongst the most ancient civilisations of the East at a very early date. At first its length seems to have been taken at 360 days. In the earliest Chinese, Chaldean, Egyptian, Greek,⁴ and, according to Plutarch,⁵ also in the earliest Latin records, this was the assumed length of the year.

Indeed, all over the Mediterranean area 360 days was the length of the original astronomical year. But long before the Christian era its length was known more accurately. Plutarch tells us that the five odd days were discovered by the second Hermes in Egypt. Herodotus also ascribes the discovery to the Egyptians, and tells us (II, 4) that they added the five days at the end of the twelve months.

According to Sir Isaac Newton the 360-day year was essentially a lunar twelve-month, the month being taken to be 30 days in length as the lunation was completed on the 30th day, and the idea of the year being furnished by the seasons and by the succession of the equinoxes and solstices. He suggests that the Egyptians by observing the heliacal risings of prominent stars first directed attention to the solar year.⁶ which they computed to comprise 365 days. Plutarch mentions that the five odd days added at the end of the year were named after five divinities of the Osiris family. This gives a clue to the date when these days were first added to the calendar. The Chinese also, from a very early date, had reached the computation of 365 days. The addition of the odd five days at the end of the year was common to Egyptian, Chaldean,⁷ Chinese and several other early calendars.

The Egyptians seem to be entitled to the further discovery of the other six hours required to complete the tropical year. Though the odd quarter of a day was not placed in the calendar till the time of Greek influence its recognition is involved in the Sothiacal period,⁸ and must therefore draw back to a remote antiquity. A still closer approximation to the truth was reached by Hipparchus, the greatest of ancient and perhaps of all astronomers; most famous as the discoverer of the precession of the equinoxes. He detected an excess of at least five minutes in the year length of 365[frac14] days. According to Mommsen⁹ the exact length determined by Hipparchus was 365 days, 5 hours, 52 minutes, 12 seconds. Essays by Hipparchus on the length of the year, on the length of the month and on the intercalary or embolismic month are referred to but are now lost. His estimates of the tropical year and of the lunation were adopted by Hillel II when he reorganised the Jewish Calendar in 358 a.d.

The exact length of the tropical year is now known to be 365 days, 5 hours, 48 minutes, 46.15 seconds.

The time of reckoning the commencement of the year has also varied frequently. In the earliest times it would seem that the vernal equinox was the most usual date of commencement. With the Egyptians the commencement was made at the autumnal equinox—the reason probably being that that date coincided with the greatest height of the Nile Flood¹⁰—to them the most outstanding natural event in the year. Very probably from them the Jews derived the custom of dating their year also from the autumnal equinox. To this day the Jewish civil year commences with the month Tisri. But ever since the deliverance from Egypt the ecclesiastical year of the Jews has commenced at the vernal equinox with the month Nisan.

THE MONTH

The time of the moon's sidereal revolution is 27 days, 7 hours, 43 minutes, 11.5 seconds. But here again there is a difference between the sidereal revolution and the apparent interval between two successive full moons. The latter, called by astronomers “the synodical period,” is the only period which can be made use of in ordinary human affairs. The actual time of the moon's synodical period is 29 days, 12 hours, 44 minutes, 2.8 seconds.

In the earliest times the length of the lunation was taken at 30 days. This is the length of a month in the biblical account of the Flood, but at a later date all the Mediterranean peoples arrived at the length of 29[frac12] days, and this has been taken as the standard length of a month by Jews, Greeks, and Latins.

The moon's revolution does not affect life so intimately as the motions of our own earth, but still, and perhaps partly as a consequence of its detachment, it has been very much in favour as a measure of time. The moon with its various phases so conspicuous in the heavens serves as a universal natural clock, and the length of the lunation is admirably fitted to supply the practical need for an intermediate unit between the day and the year. The moon's phases are more easily observed by primitive peoples than the positions of the stars or the still more difficult observation of equinoxes or solstices. According to Mommsen¹¹ the day and the month being determined by direct observation, not by cyclical calculation, were therefore the earliest time units.

II

THE THREE POSSIBLE FORMS OF CALENDAR

It might be possible to preserve a record of the passage of time by enumerating days in constant succession from some real or imaginary starting point. This, though very inconvenient, might be sufficient for the registration of past events, but it would be useless for what is after all one main object of a calendar, namely, to record beforehand the date of future recurring events.

A calendar is an attempt to establish fixed relations between the day, the month and the year. The variations in the forms which calendars have taken are principally due to the fact that neither the month nor the year is an exact multiple of the day; nor is the year an exact multiple of the month. As a result of this there are three possible forms of a calendar: (1) a solar calendar—that is to say, one which adheres to the true length of the year, but gives an arbitrary length to the month, irrespective of the length of the lunation; (2) a lunar calendar, in which lunar month-lengths are adhered to, but the length of the year is arbitrary; (3) a luni-solar, in which an endeavour is made to observe the true length of both the month and the year, and to adjust their inequalities by means of what are called intercalations.

Notwithstanding its greater complexity, many important calendars of antiquity were of a luni-solar character. In almost every case they took the length of the lunation at 29[frac12] days, and employed months of 29 and 30 days alternately, thus giving a lunar twelve-month of 354 days, which they sought to harmonise with the solar year by the introduction at various intervals of intercalary or additional months. A good example of such a luni-solar calendar is the Jewish. Of a purely lunar calendar the outstanding example is the Mahometan; and of a purely solar calendar the capital instance is the Julian. The observation of the moon's phases being easier than that of the stars, and moonlight being specially serviceable for religious festivals, it is found that luni-solar calendars have a pre-eminently sacral or religious origin.¹² On the other hand, the observation of the stars arose amidst sailors and travellers over plains. Hence a sidereal or solar calendar has a distinctively secular, nautical and commercial reference.

III

THE GREEK CALENDAR

The Greek Calendar was luni-solar from a very early date, and several attempts were made to establish a satisfactory concordance.

According to Macrobius¹³ the normal Greek year was a lunar twelve-month of 354 days. Knowing that the solar year comprises 365[frac14] days they added 11[frac14] x 8 = 90 days every eight years. This intercalation was divided into three embolismic months of 30 days. The eight-year cycle was known as the Octaëteris.

There are traces of several variations in this cycle, but the great triumph of Greek chronometry was the discovery by Meton, in or about 432 b.c., that 19 solar years contained 235 lunations. It is understood that Meton took 365[frac14] days as the length of the year. On that assumption, and taking the exact astronomical length of the lunation, the equation is as follows:

19 Julian years of 365[frac14] days = 6939 days, 18 hours.
235 lunations of 29 days, 12 hours, 44 minutes, 2 seconds = 6939 days,
16 hours, 31 minutes

As 19 twelve-months amount to 228 months, Meton intercalated seven embolismic months in his cycle. According to Petavius and most authorities, these were introduced in the 3rd, 6th, 8th, 11th, 14th, 17th and 19th years. (Bond gives the seven years which immediately precede these, but no doubt Petavius is correct.¹⁴)

A Metonic cycle, then, is a cycle of 19 solar years, containing in the 1st, 2nd, 4th, 5th, 7th, 9th, 10th, 12th, 13th, 15th, 16th and 18th years, 12 lunar months of 29 and 30 days alternately, and in the other seven years 13 months of similar length, the odd or embolismic month having in the case of six years 30 days and in the case of the last year 29.

Of the 228 normal months one-half or 114 were full months of 30 days, and 114 short or cave months of 29 days. Of the embolismic months six were of 30 days and one of 29. Thus we have:

114 + 6 = 120 x 30 = 3600 days
114 + 1 = 115 x 29 = 3335 days
                                                                                                                                                                                                                  _________
                                                                                                                                                                                                                  6935 days

showing a deficiency of five days from 6940, which—according to Censorinus—was the length of the cycle. It is probable that these 4[frac34] or 5 deficient days were made up by adding another day to one of the cave months every fourth year—thus anticipating, though for a different reason, the intercalary device of the Julian Calendar. According to Mr Woolhouse, the cycle in practice contained:

                                                                                                                                                      125 months of 30 days = 3750
and                                                                                                                         110 months of 29 days = 3190
                                                                                                                                                                                                                                                                                                                                                                                                      ____
                                                                                                                                                                                                                                                                                                                                                                                                      6940

High honours were conferred on Meton and Euctemon, the authors of this calendar, and their names are said to have been inscribed in letters of gold on the Temple of Minerva at Athens. At any rate the years of the cycle were numbered successively from 1 to 19, and these numbers as employed to designate in series each particular year were, and have ever since been, called and known as the Golden Numbers. In the middle ages the number applicable to any one year was frequently called the Prime. The cycle was then sometimes called the cycle of the Moon.¹⁵

The Metonic cycle is said to have been enacted on 16th July 433 b.c., and the first year of the first cycle ran from that date. It has long been regarded as the masterpiece of Grecian chronology, and has influenced luni-solar adjustments ever since. Whether it was independently discovered by Meton, or received by him from the east, cannot now be ascertained, but there is evidence that the value of a cycle of 19 years as a luni-solar adjustment was known to the Chinese. It is stated by Dr Hales¹⁶ that in 2269 b.c. two Chinese astronomers, named Hi and Ho, reformed the calendar, and adjusted the solar year of 365 days to the lunar by intercalating seven months in 19 years.

A disturbing element in the cycle was the fact that the number of leap years which it contained was not a constant quantity. To obviate this inequality Calippus of Cyzicus in the following century proposed a cycle of 19 x 4 = 76 years, in which period the number of leap years is always 19, and this improved cycle was substituted in Greece for the Metonic about 330 b.c. But throughout the Christian Era the cycle of 19 years has remained the favourite. There are traces of other cycles in early Greece, notably one of 25 years, but none of these is of sufficient importance to detain us.

It should be noted here that the Greek month was divided into three decades of ten or nine days each.

IV

THE LATIN CALENDAR

The calendars of modern Europe having descended from the Roman, it is necessary to describe its origin and development.

According to Macrobius and Censorinus, the original Roman year contained 10 months, and comprised 304 days. Of these:

6, viz. April, June, Sextilis,
September, November, December, each 30 days = 180
4, viz. March, May, Quintilis, October,
each 31 days = 124
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ___
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      304

This original year began with 1st March, as is proved (says Macrobius) by the names of the six last months.

These writers say that Numa introduced January and February. Scaliger¹⁷ and Hales¹⁸ dispute the above statement as to a 10-month year, and hold that the year always contained 12 months.¹⁹ The original ten-month year is repeatedly affirmed by Ovid in his Fasti. The poet, with the characteristic obsession of a decimalist, advances various fanciful reasons for its adoption. Plutarch, however, in his Life of Numa, states that the Roman year during the reign of Romulus contained 360 days and that the lengths of the months, which he evidently believed to be 12 in number, were very irregular. In his Roman Questions he affirms that some were of opinion that the Roman year at first consisted of 10 months, some of which contained more than 30 days. Eutropius, probably with truth, states that prior to Numa the Roman year was confused and without regular division. Even Macrobius refers to two innominate months which, he says, “patiebantur absumi.”

According to both Macrobius and Censorinus the two additional months were formally incorporated in the calendar by Numa. They state that he added 50 days to the year, raising its length to 354 days, and that he then deducted one day from each of the six months of 30 days, reducing these to 29-day months. These 56 days thus made available he divided between January and February, but in deference to the superstitious dislike of even numbers which prevailed amongst the Romans, he added a day to January, thus raising the total length of the year to 355 days, and ensuring an odd number to each month except February, which was left with an even number—partly because it was devoted to the Infernal Gods—and partly because, by so doing, Numa ensured that the number of days in the year should be uneven.

To equalise these twelve months with the tropical year, Numa is said to have employed the Greek octennial intercalation, or, according to Plutarch, a dieteris or biennial cycle. A further correction was rendered necessary in consequence of Numa's raising the lunar twelve-month to 355 days. According to Livy (1, 19) a complete correction was provided for in a cycle of 24 years.²⁰

Notwithstanding the antiquity and authority of the writers who furnish the foregoing account, it is probably very largely conjectural. According to Ovid, the decemvirs, who were appointed about 452 b.c. (shortly before the time when the Metonic cycle was introduced), made certain corrections in the then existing calendar, and restored the commencement of the year to 1st March, the date in use prior to Numa's reform. It seems not improbable that they also introduced the other adjustments, particularly the adoption of the biennial intercalation or dieteris, consisting of the insertion of an extra month of 22 and 23 days alternately. This intercalary month, which Plutarch attributes to Numa, was well known to the Romans under the name of Mercedonius. At any rate a somewhat irregular scheme of intercalation was still required, and being in the hands of the Pontifices, whose methods and reasons were kept strictly secret, negligence, ignorance, and still more—corruption, led to great irregularities and a resulting dislocation and uncertainty in the Roman Calendar.

It is to be noted, however, that these uncertainties did not extend to the divisions of the months, and the enumeration of the days of each month. A highly practical scheme for the regulation of these details was early established, and survived, without alteration, all subsequent reforms of the Roman Calendar. Its principles will be described after the Julian reform has been explained.

V

THE JULIAN REFORM

Such was the state of matters when Julius Caesar with the help of Sosigenes, an Alexandrian astronomer,²¹ undertook his immortal reform. We must briefly recount the oft-told tale. His proposals partake in a high degree of the comprehensive simplicity which is a usual feature of works of genius, and which often obscures to the common-place mind the real greatness of the conception. The cardinal feature of the Julian reform was the adoption of the solar year of 365 days, 6 hours as the fundamental unit, and the abandonment of all attempt to adapt either the months or the twelve-month to the length of the lunation. It is now believed that the Julian reform was in principle a reproduction of a reform of the Egyptian Calendar enacted 238 b.c.; possibly designed by the Greek astronomer Eudoxus.

Many of the Roman festivals necessarily bore a relation to the seasons, and Caesar, therefore, deemed it desirable to restore the dates of the dislocated calendar, at least approximately, to their original position with reference to the tropical year. The sins of the intercalators appear to have been principally sins of omission, with the result that calendar dates anticipated the natural events with which they were properly associated; or, vice versa, the natural Ephemerides fell on a later calendrial date than that properly appropriated to them. Thus, for example, we find Cicero, four years before Caesar's third consulate, dating the vernal equinox on the ides of May, although that Ephemeris, if the intercalation had been maintained, should have fallen on or about the 23rd of March.

Caesar's first step was to correct this dislocation. He extended the then current year 708 a.u.c., 46 b.c., to an exceptional length. In that year after February he intercalated the usual Mercedonius of 23 days. The length of January being 29 days and February 28, this gave a quarter of 80 days. Then between November and December he intercalated two months of 34 and 33 days. This extraordinary year of 445 days ended just about where the Roman year would have done if the intercalations had been regularly observed. This year was known as the year of confusion, although Macrobius more fittingly called it the last year of confusion. The reformed year which followed was of course 709 a.u.c. or 45 b.c.

The above is the account of the year of confusion given by Censorinus, and confirmed by Macrobius.²² The account of Suetonius in his life of Julius Caesar, chap. 40, though very brief is quite consonant with these so far as it condescends on detail. Dion Cassius (XLIII) gives the length of this year as 422 days and is followed by Petavius. He makes the intercalation 67 days, thus excluding Mercedonius.

Caesar's second step was to enact that the normal length of the year should be 365 days, with one additional day intercalated after 24th February every fourth year to complete the 365[frac14] days, which was then believed to be the true length of the tropical year. The lengths of the twelve months were fixed so as to exhaust amongst themselves the whole extent of the year thus settled. These lengths, with the probable exception to be immediately mentioned, are the very lengths which have ever since prevailed. Caesar boldly abandoned all attempts to maintain a coincidence between the month and the lunation. The calendars of all or nearly all other nations had hitherto obstinately striven to maintain a luni-solar concordance. Caesar cut the gordian knot, and the Julian Calendar was and is the one great example of a purely solar calendar.

Thus with the single exception of leap day all need for intercalations disappeared, Caesar's experience of the evils of irregular and capricious intercalations having convinced him of the necessity of reducing the intercalations to a minimum.

In 44 b.c., the second year of the Julian Calendar, the name Quintilis was altered to July in honour of its founder, and Augustus subsequently, in the year 8 b.c., persuaded the Senate to alter the name of Sextilis to August. Similar attempts by one or two subsequent emperors to attach their name to one or two of the subsequent months failed to take effect.

Doubts have been suggested as to the exact lengths assigned by Julius Caesar to the several months. Some writers say that under his calendar the month-lengths were 31 and 30 alternately, with the exception of February, which had 29 days in common years and 30 days in leap years. They add that when the name of Sextilis was changed to August, the crafty emperor, desiring that the month named after him should escape the ill-luck which the Romans so constantly associated with even numbers, took a day from February and added it to August, and that then, to avoid an uninterrupted succession of three long months, he reversed the lengths of the four following months, September to December.

This story is inconsistent with the definite statements of Macrobius and Censorinus, but so far at least as regards the transfer of a day February to August, it is not improbable. It seems quite possible that those two writers, giving only a brief summary of the reform, had not deemed it necessary to refer specially to such a minor subsequent change, or that, writing as they did after the lapse of a considerable time, they had overlooked it. Macrobius indeed hints that some change in the Julian scheme was made by Augustus. The rubric of chapter 14, book 1 of the Saturnalia is as follows: “Quem in modum primum Julius deinde Augustus Caesares annum correxerint.” In the text of the said chapter he says:

Martio Majo Quintili Octobri servavit (Julius) pristinum statum; quod satis pleno erant numero; id est dierum singulorum tricenorumque ideo et septimanas habent nonas sicut Numa constituit quia nihil in his Julius mutavit sed Januarius Sextilis December, quibus Caesar binos dies addidit licet tricenos singulos habere post Caesarem coeperint.

In La Chiave del Calendaro, a rare and learned essay by Hugolini Martelli, Bishop of Glandeves, published in 1583 con licentia degli superiori, page 130, a table of the Julian months is given in which February has 29 and Sextilis 30, and on page 148 occurs the following sentence: “Caesar Augustus diem unum detraxit Februario et suo Augusto donavit.” Scaliger²³ writes as follows:

Cum autem Septem fuerint cavi menses in anno Romano Januarius Aprilis Junius Sextilis September November December quorum quinque singuli dies reliquis autem duobus bini additi sunt a Caesare.

The two months to which Caesar added two days each he states to have been January and December. It follows that the other five were raised to 30 days only.

Scaliger also²⁴ describes and reproduces a calendar “in saxum incisum a Romae repertum.” In this calendar August has xxxdays, February xxiix, which apparently meant 28, as to November are given xxxi.

On the whole the probability seems to incline in favour of the view that Caesar would have been likely to maintain the lengths of the months as near as possible to the average or standard of 30 days, and further would not have favoured a monthly syllabus, which he could not have failed to notice involved a serious and quite avoidable inequality in the length of the two half-years. For these reasons we have little hesitation in accepting the traditional story and in ascribing this obvious blot in the Julian Calendar to the selfish craft of Augustus.

A singular mistake disturbed the first operation of the Julian Calendar. The Pontifices interpreted the instruction to intercalate one day every fourth year in accordance with the usual Roman method of enumeration, by which the number enumerated was inclusive both of the day from and the day of which the computation extended. They, therefore, intercalated a leap day every third year. This continued for 36 years, during which 12 in place of 9 days had been intercalated. This error was corrected by a provision that the 12 years from 9 b.c. to 3 a.d. should be common years.²⁵ Thus after the expiry of 48 years from the original introduction of the Julian Calendar the normal system was finally brought into operation. It may be noted, however, that chronologers have not recorded this error but have treated the leap years as having succeeded one another regularly from the start.

Julius Caesar prescribed the intercalation of a 366th day to be made after the feast of Terminalia on 23rd February of every fourth year. The 24th February was, by the Roman method, the sixth day before the Kalends of March. This day was to be duplicated. The intercalated day was regarded as a part of the 24th, it was hence that it received the name of bissextus or bissextilis.²⁶.According to the theory of the Julian Calendar there are only 365 days in a leap year, but one of them, namely the 24th February, comprises two natural days in one civil day. The intercalated day was treated as a mere punctum temporis. A person born on that day had his birthday annually on 24th February. Many subtle legal discussions took place under the Empire and during the middle ages as to the effect of these provisions. Very curious as are some of the questions raised, it seems unnecessary to refer to them here.

As the week was no part of the Roman Calendar, at least until the reign of Constantine, it seems unlikely that these provisions in any way interrupted the regular succession of week days where these were observed, although this is not quite so certain as some suppose. At any rate such an interruption does not seem to have been the result of the important English statute, De Anno bissextili, passed in 21 Henry III, 1236, by which it was provided that “the day of the leap year and the day before should be holden for one day.”

VI

MONTH AND DAY IN THE ROMAN CALENDAR

Such, then, was the simple framework of the Julian Calendar. As an instrument of dating it required also the use of some rule for the enumeration of each single day. The method already for a long time in use for this purpose was continued without disturbance.

Three days in each month were taken as fixed points for enumeration—the Kalends, the Nones and the Ides. The Kalends was in every case the first day of the month. In the four months, March, May, July and October, which from the earliest times and throughout the whole length of Roman history had been pleni, i.e. full length months of 31 days, the Nones were the 7th and the Ides the 15th of the month.

In the case of the other eight months the Nones were the 5th and the Ides the 13th day reckoning from the first day onwards. Dates were determined by enumerating from these days backwards. The days of any month subsequent to the Ides were enumerated by computation backwards from the Kalends of the following month. Dates between the Ides and Nones were similarly computed backwards from the Ides, and days between the Nones and Kalends backwards from the Nones. In every case, following the Roman method, both the day from and the day to which the computation was made were enumerated. The day immediately preceding any of these three fixed points was called Pridie, the day before that was the third day from the fixed point and so on.

The days of the month were also distinguished as fasti and nefasti. Dies fasti were days on which the courts were open—business days as we should say. Dies nefasti the reverse. Any additional days added to the months by Caesar were declared to be fasti. No additional dies nefasti nor dies comitiales (i.e. days when public assemblies might be convened) were instituted by him. These must be distinguished from feriae or dies festi—religious festivals or holy days.

Where the lengths of the months were altered Caesar provided that the additional days should be held to be added at the end of the month,²⁷ thus securing that no interruption should take place in the dates of religious festivals. Thus if the third day from the Ides of any month was one of the feriae or festi and if that day was the 16th before the Kalends of the following month, still the religious observance was preserved intact on the third from the Ides, although that day might now become the 17th or 18th before the following Kalends.

The method of backward enumeration seems to us awkward simply because it is unfamiliar, and its use of course required that the exact number of days in each month should be constantly memorised. This obstacle to slovenly thinking (which was always distasteful to the resolute intellect of the Roman) being overcome, the Julian Calendar as an instrument for recording dates both past and future was the most nearly perfect which the world has ever seen—indeed, but for the one fact of its slow secular dislocation with reference to the tropical year, it was practically perfect. It furnished the government and the people of Rome with the immeasurable boon of a perpetual calendar. The programme of future work of each individual, of each city, of each institution, of the army, of the law courts and of the whole State could be definitely fixed and made available; could be at any moment inspected, referred to and understood. These programmes under this calendar were ready for instant use, remained unchanged until altered, were capable at any moment of being altered to meet altered requirements, or to be more perfectly adapted to the exigencies which experience discovered. Without this simple and perfect instrument it would have been impossible to organise the widespread activities of the Roman empire. The Julian Calendar made that organisation possible, and enabled the rulers of the empire, without steam or electricity, to arrange and administer the orderly government of their many scattered provinces and dominions with a certainty and regularity which have never since been realised.

Very different is the state of matters under the modern European calendar. The observance of week days and the occurrence of Sundays and other movable holidays without any fixed correspondence to the dates of the calendar absolutely prevents the adoption of any fixed working plans. Every year, on 1st January, the whole scheme or system of engagements is overthrown. All gradual, steady improvement of social administration or commercial arrangements is impossible, and the progress so constant and so remarkable in science and the mechanical arts finds no counterpart in the unprogressive confusion which characterises social and administrative arrangements.

The Julian Calendar was not so well suited to serve the other main purpose for which the calendar is required, namely, the measurement of equal intervals of time. The lengths of the months approximated sufficiently to the standard length of 30 days, but the sub-divisions of the months were too unequal for practical use. We are not well acquainted with the methods employed by the Romans for the measurement of intervals. There are frequent references to a period of eight days, known as the nundinae, said to have been introduced by Servius Tullius, the eighth day having apparently been a market day without religious significance. Probably, however, the fact that the calendar was perpetual enabled equal intervals to be arranged without serious inconvenience.

VII

THE GREGORIAN CALENDAR

We have seen that the Julian year is 11 minutes, 14 seconds longer than the tropical or natural year—consequently the dates of natural periodic events, and in particular of the equinoxes and solstices, fell annually 11 minutes earlier in the Julian Calendar. This was unsatisfactory. In the course of centuries the seasons would gradually have moved backwards to an earlier calendar date. The difference, however, was so small and the change so very gradual that little practical inconvenience resulted. The discrepancy was chiefly noticed in connection with the observance of Easter. As will be explained later on, the date of Easter, owing to its original derivation from the Passover festival, depended upon the occurrence of the first full moon happening after the vernal equinox.

In 325 a.d. the General Council of Nicea decreed that the celebration of Easter should be uniform throughout the Christian Church. The Decree does not appear to have contained any definite reference to the date of the vernal equinox, but that date was certainly assumed by the framers of the Easter Tables to have been the 21st of March, although in 325 a.d. the equinox actually fell on the evening of the 20th. It may be noted that apart from the excess of 11 minutes in the length of the Julian year there are other causes of variation in the date of the equinox. The fact that the assumed excess of six hours over the even period of 365 days is accumulated and added as one day every fourth year entails an oscillation of the date of the equinox, which might be avoided by an alteration in the years when the intercalary day is introduced.

As time went on, however, the calendar date of the vernal equinox fell constantly earlier. This led to much difficulty and dispute as to the proper date for the observation of the great festival. If the first full moon after 21st March was adhered to it gradually moved further away from the true date of the equinox. In course of ages, as one writer pointed out, the date of the equinox would coincide with the preceding Christmas; and the 21st March would have moved forward towards the summer solstice.

The matter was brought before General Councils several times. At length the 19th General Council, commonly called The Council of Trent, which assembled in 1545 and continued its sittings for 18 years, authorised the Pope to take the matter in hand. The calendar date of the vernal equinox had by that time receded to the 11th March. Soon after, Giovanni di Novara submitted a proposal to Pope Julius II. After the death of Julius the search for a solution was continued by Leo X, who invited the heads of the Italian Academies, and certain individuals who had studied the subject, to submit proposals. Amongst those submitted was a Treatise by Paul, Bishop of Fossombrone, entitled De recta pàschae celebratione, another De Aetatum computatione et dierum anticipatione, by Basilio Lappi, and one entitled De kalendarii correctione, by Antonius Dulciatus. Leo by a letter still extant invited the co-operation of Henry VIII.

When Gregory XIII became Pope in 1572, he found these and other proposals awaiting him. The plan which his advisers favoured most was designed by a Neapolitan physician named Aloysius Lilius. In 1577 the Pope communicated this proposal to the Christian princes and learned academies, and appointed a commission of mathematicians and chronologers to consider it. Finally, on receiving a favourable report, he issued a Bull dated 24th February, 1582, by which the new calendar was promulgated.

That Bull contained two principal provisions:

(1) In order to restore the date of the vernal equinox to the xii Kal. April (21st March) the day which the Nicene Council adopted as the date of its assumed occurrence in 325 a.d. 10 days were to be omitted from the calendar of 1582, the day following the 4th of October being declared to be the 15th. The days from iii Nones to Pridie Ides were omitted.

(2) In order to maintain in future a more exact correspondence between the tropical and the calendar year it was provided that three out of every four centurial years should be common years, instead of leap years as under the Julian Calendar; those centurial years only which were divisible by 400 without remainder being retained as leap years.

Further (3) the use of the Epacts designed by Lilius was also enjoined in place of the Tables of Golden Numbers, and (4) the necessary adjustment of the Dominical Letters was provided for.

The year 1582 was the initial year of the Gregorian Calendar, which was at once adopted by the various countries which recognised the spiritual authority of Rome. France adopted the new style in December, 1582. Switzerland, the Catholic Netherlands and the Catholic States of the Empire in 1583. The Protestant States for a considerable time refused to follow. In 1699, however, chiefly at the instigation of the philosopher Leibniz, the Protestant States of Germany came into line.

In Great Britain the new style was not adopted until the passing of the Calendar New Style Act (1750), under which Act it came into operation in 1752. In consequence of the fact that the year 1700 was a leap year under the Julian Calendar, but not under the Gregorian, the disparity by that time amounted to 11 days, and it was accordingly found necessary to provide that the day following the 2nd of September, 1752, should be called the 14th of that month. Opportunity was taken at the same time to fix the official date of the commencement of the year in England at 1st January, the date which had been taken as the commencement of the year under the Gregorian Calendar, and which had already by a Decree of the Privy Council been adopted in Scotland in 1600. Up till 1752 in England the official date of the new year had continued to be the 25th of March.

These facts must be kept in mind when dealing with English dates prior to 1752—dates between 1st January and 25th March being frequently referred to both of the alternative years—although it should be noted that in intercalating the 366th day in the month of February, England, even before 1752, had treated the year as commencing on 1st January—the February of the intercalation having been the February of the year divisible by 4, on the assumption that the years were reckoned from 1st January.

For some time the change produced considerable discontent in England, and riotous crowds assembled to the cry of “Give us back our eleven days.”

The countries which officially profess allegiance to the Greek or Eastern Church have continued to employ the Julian Calendar up to the present day; and have only recently adopted the Gregorian.

However justifiable the correction of the Julian Calendar may have been, there is no doubt that the change was productive of much confusion, which has persisted almost to our day. Customs dependent on the calendar become deeply embedded in the national life, and in Scotland, for example, the adjustment of the half-yearly terms to the new dates was only partially effected. Termly payments of money gave little trouble, but termly engagements of servants, especially in the rural districts, and termly occupations of houses and farms continued to be regulated by the old calendar dates almost up to the present day.

It is important, therefore, to ascertain the cause of this confusion. Had the Gregorian reform been confined to ensuring that for the future the disparity between the tropical and the calendar years should be removed by the omission of leap day from three out of every four centurial years no confusion could have arisen. The trouble was entirely due to the fact that Pope Gregory XIII determined to make the correction draw back to the date of the Nicene Council in 325 a.d. It was for that reason only that the omission of the 10 days in October, 1582, and of the 11 days in September, 1752, was required. Had the consequences been foreseen, there seems little doubt that the reform would have been confined to the future. The inconveniences of a retrospective correction have long been recognised by students of the calendar.²⁸

The Gregorian adjustment is not absolutely correct. The error of the Gregorian Calendar in 10,000 tropical years is 2 days, 14 hours, 24 minutes. Sir John Herschel²⁹ suggested a further correction, to be effected by providing that the leap day should be excluded from years divisible by 4000 without remainder.

A curious instance of the persistence of the old style is to be found in the date of the financial year of the British Exchequer. Prior to 1752 that year officially commenced on 25th March. In order to ensure that it should always comprise a complete year the commencement of the financial year was altered to the 5th April. In the year 1800, owing to the omission of a leap day observed by the Julian Calendar, the commencement of the financial year was moved forward one day to 6th April, and 5th April became the last day of the preceding year. In 1900, however, this pedantic correction was overlooked, and the financial year is still held to terminate on 5th April, which is about the most inconvenient date imaginable, as it so often happens that the Easter celebration occurs just about that time—indeed one result is that about one-half of the British financial years include two Easters and about one-half contain no Easter date. It would surely be a very simple matter to make the financial year commence with 1st March, in which case the Easter interruption would always occur during the course of the first quarter, causing comparatively little inconvenience, whilst any disturbance due to the incidence of the odd leap day at the end of every fourth February would be entirely relieved.

VIII

OTHER CALENDARS

Many other calendars besides the Julian and the Gregorian have been, and some still are, employed in certain countries. We do not propose to give any account of these except in so far as they may illustrate some relevant calendrial problem.

We therefore pass the Chinese Calendar, interesting though it be, merely remarking that it is luni-solar, containing months of 29 and 30 days alternately, balanced by an intercalation not unlike the Jewish.

We also make no further reference to the Chaldean and Egyptian Calendars, containing features which undoubtedly suggest a common origin and which display a remarkable degree of accuracy in the knowledge which their framers possessed of the astronomical data on which a calendar is based. Nor is it within the scope of our design to say anything of the early Indian Calendars nor of the interesting Mexican Calendar with its 18 months of 20 days.

THE JEWISH CALENDAR

Of calendars still operative the Jewish can claim the most ancient unbroken lineage. It is an excellent example of a luni-solar calendar. The months are of 29 and 30 days alternately. The equalising intercalary month is introduced usually every third year. Now and ever since the adjustments made by Rabbi Hillel II in 358 a.d. the intercalations are made in the 3rd, 6th, 8th, 11th, 14th, 17th and 19th years. The intercalary month is introduced after the month Adar at the end of the ecclesiastical year and is called Veadar.

The original Jewish year commenced with the month Tisri, at the autumnal equinox—a fact which suggests an Egyptian origin. This is still the commencement of the civil year; the ecclesiastical year begins with the month Nisan six months earlier at the vernal equinox. Veader is intercalated immediately before Nisan. Further, to enable the luni-solar adjustment to be maintained as nearly accurate as possible the Jewish Calendar recognises three different lengths for the year whether normal or embolismic. There are common years of 354 or 384 days, perfect years of 355 or 385 days and imperfect years of 353 or 383 days as the case may be.

It has been alleged that the use of the intercalary month cannot be traced earlier than the date of the establishment of the Metonic cycle by the Greeks. This, however, is uncertain. The use of the 19-year cycle can be traced in various countries at a very early date, and it is impossible to say where it first originated, or whether, as seems likely, it may have been independently discovered in more places than one.

At any rate it is certain that the Jewish months always commenced with or very nearly with the new moon and the effect of the intercalations is to ensure that the lunation corresponding to the month Nisan is always that during which the vernal equinox occurs, although of course as the intercalation is not made annually it inevitably happens that the commencement of Nisan does not coincide with the date of the vernal equinox, only that the vernal equinox always falls sometime whilst that lunation is in progress.

THE MAHOMETAN CALENDAR

A luni-solar calendar with lunar months and an intercalation somewhat similar to the Jewish was familiar to the Arabs in the time of Mahomet. That remarkable man was not a philosopher and certainly not what we should call a man of science, but he seems to have been possessed by a singular intuition of reality which is reflected in many of his civil and ecclesiastical institutions. Like so many other men of keen perceptions Mahomet recognised the immense importance of the calendar in the working of the social machine, and the Mahometan Calendar which he introduced bears the impress of his extraordinary character. It seems probable that he found the established system of intercalations disturbed by abuse and corruption, just as was the case in Rome before the Julian reform. He therefore absolutely suppressed the use of the intercalary month, alleging that twelve was the number of months according to the ordinance of God, and that a thirteen-month year was contrary to the divine appointment.³⁰ Ever since its institution the Mahometan Calendar has been purely lunar—the one outstanding example of such a calendar in actual use. Under it the day and the moon's period are the only natural units. The extreme simplicity of such a rule may largely compensate for its entire failure to maintain a fixed relation with the seasons of the year. Such a calendar is probably only possible in lands where the difference of the seasons is not so marked as it is in more temperate regions. The call it imposed on his followers to ignore the law of Nature in their regulation of their time-scheme may be regarded as an item in the ascetic appeal which Islam makes to its devotees.

THE FRENCH REPUBLICAN CALENDAR

The short-lived Revolutionary Calendar of the French Convention was instituted on 24th November, 1793, and only survived until 31st December, 1805. This calendar has little historical or scientific importance, but the attempt is not without instruction.

The Convention commenced their new era with the autumnal equinox of the year in which the republic was founded, viz. 22nd September, 1792. It was decided that the autumnal equinox should thereafter be the commencement of the civil year which was divided into 12 months of 30 days each, with five supernumerary days at the end of each year. The week was abolished and the month divided into three decades of 10 days each.

This calendar claimed to be founded on a purely scientific basis, but like most scientific reforms introduced by politicians unacquainted with science and impatient of practical tests, it bears marks of haste and superficiality, and also of a total disregard of the advantages of continuity. Its chief features were strangely archaic. The adoption of the autumnal equinox as the commencing date of the year, though made for a different reason, was a reversion to the rule of the ancient Egyptians who were influenced by the fact that the Nile flood was then at its height. The addition of five intercalary days at the end of the year was a reproduction of the ancient Chaldean plan and was detrimental to the value of the calendar, both as an instrument of dating and as a means of measuring out equal intervals of time. The division of the month into three decades was also a revival of a feature of the old Greek Calendar. No consideration seems to have been given to the question of suitability for practical use, and even if the enemies of the Revolution had not been in any haste to abolish it we may doubt whether its use would have been permanently established after the revolutionary fever had abated. At any rate, for the purposes of historical study it would have been necessary to maintain the concurrent use of a dating system which maintained continuity with the past—to break with which was probably one of the main objects of the promoters of the Revolutionary Calendar.

Notes

1. De Bell. Gall. VI, 18.

2. Germania.

3. Saturnalia, I, 3.

4. Herodotus, I, 32.

5. Life of Numa.

6. This view is supported by Herodotus II, 4, and Nilsson, op. cit. p. 279.

7. The 365-day year appeared at Babylon from Egypt after the overthrow of the Assyrian empire by Nabonassar; but Chaldea subsequently developed a luni-solar, Egypt a solar calendar.

8. See p. 41, postea.

9. Hist. Rome, vol. IV, p. 586.

10. Herodotus, II, 19.

11. Hist. Rome, vol. I, ch. xv.

12. Nilsson, Primitive Time Reckoning, pp. 217, 343, 358, etc.

13. Saturnalia, I, 13.

14. See Table of Perpetual Lunar Almanac, pp. 66, 67; also p. 65 for the natural intervals.

15. L'Art de vérifier les dates.

16. A New Analysis of Chronology, vol. I, p. 37.

17. De Emendatione Temporum, p. 172.

18. Op. cit. p. 43.

19. Mommsen refers to the ten-month year as the earliest, but without adducing proof. He admits that the duo-decimal division was adopted very early.

20. Or according to some manuscripts 20 years.

21. Pliny, Nat. Hist. XIII, 25.

22. Saturnalia, 1, 13, 14. Macrobius gives its length as 443 days.

23. Op. cit. p. 440.

24. Op. cit. p. 232.

25. Pliny, Nat. Hist. XIII, 25.

26. This term implies a 28-day February, but was not coined before the Augustan correction.

27. Macrobius, Saturnalia, 1, 14.

28. See Brinkley's Elements of Astronomy, p. 262.

29. Treatise on Astronomy, ch. XIII, § 632.

30. Koran, chap. 9. Sale's transl. p. 153. See also Nilsson, op. cit. p. 252.