# Popular Science Monthly/Volume 27/August 1885/Curiosities of Time-Reckoning

First published in French as "Le calendrier chez les différents peuples" in Revue Scientifique, 11 April 1885.
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* CURIOSITIES OF TIME-RECKONING.
By M. L. BARRE.
THE natural unities for the measurement of time are three, and are afforded by the rotation of the earth upon its axis, the revolution of the moon around the earth, and the revolution of the earth around the sun; of which the mean values respectively are 24 hours; 29 days, 12 hours, 44 minutes, 2*9 seconds; and 365·2422 days. These numbers are incommensurable and wholly independent of one another. But men have tried to connect them from the most remote ages, and have devised the lunar-solar year, the duration of which is related to the movements of the sun and the moon. Although this system may appear complicated, it is in reality quite simple, for the sun and moon spare man the trouble of calculating the days, while the years and months write themselves in large characters in the appearance of the sky and of vegetation.
The lunar-solar year thus having its origin in Nature, is found in the most ancient form of the Jewish calendar. The Israelite year was so regulated that the feast of the Passover was celebrated on the fourteenth day of the first month, when the barley to be offered in sacrifice was ripe at the full moon. This marked the first month of the year, named Nisan, and served as the point of departure for the twelve usual months. But, if the ripening of the barley did not occur during the fortnight following the end of the year, another month was intercalated, and the new year began with the next new moon. If we desire an exact and rigorous measure, this form of year is simply confusing. The Jews have years of twelve lunar months, of twenty-nine or thirty days, to which is added a thirteenth month, when the year is embolismic; and they might contain 353, 354, 355, 383, 384, or 385 days. The Jewish calendar also included a period of nineteen solar years, or a lunar cycle of 235 months. The years date from the creation of the world, which is fixed by the Jews at October 7th, b. c. 3761.
The Chinese month begins with the new moon; the first month when the sun enters Pisces, the second when it enters Aries, etc. But if the sun does not enter a new sign of the zodiac with the new month, an additional month is introduced, which is given the same name as the preceding one, with a distinctive sign. The months are of twenty-nine and thirty days, but there is no absolute rule for their succession, nor for the place of the supplementary month, nor for the intercalation of complementary years; and, as the beginnings of the months and the years are calculated from the movements of the celestial bodies, the whole year is uncertain and changeable. In the difficulty of ascertaining from what tables the ancient Chinese calculated their astronomical elements, there would be great uncertainty in ​compating a Chinese date with the corresponding date of any other chronology, were it not that the learned from the most ancient times have used a cycle of sixty days in much the same manner as we use our week of seven days, without regard to the movements of the sun and the moon. This calendar has become of prime necessity for fixing the year in which a particular day may have fallen; and the preparation of it is considered a matter of such importance that it is confided to an imperial mathematical tribunal, and, when the work is completed, it is ceremoniously presented to the members of the imperial family and the chief personages of the government.
The Chinese years are designated by two numbers. The first, the official number, indicates the number of the years of the reign of the emperor, and is variable; the second pertains to a cycle of sixty years, of which each year has a special name. In all Eastern Asia, the system employed for the designation of the years is based upon the combination of the name of ten, kan, with one of the denominations of twelve, chi. The cycle formed by a combination of this character may be found in Japan, Manchooria, Mongolia, and Thibet. The Aztec cycle of fifty-two years, formed of two smaller cycles of four and thirteen years, led Humboldt to suggest that Asiatic ideas might have penetrated to Mexico. Sometimes, but rarely, the Asiatics count by cycles of twelve years, each of which has the name of an animal.
The lunar-solar year of the Hindoos was based on a sidereal solar year of which the twelve months, of unequal length, had a duration exactly defined. The solar month Chaîtra consisted of 30 days, 20 hours, 21 minutes, 2 seconds, and 36 thirds, the day being divided into sixty hours. The year began with the new moon preceding the beginning of the solar year. When two lunar months began within the same solar month, the first one was intercalated. If no lunar month began in the course of a particular solar month, the year lost an ordinary month, but two intermediate months were added. Every Hindoo month has a particular name, and the new moons, which serve to fix the beginnings of the months and the years, are calculated with so great precision that it is much more easy to identify an ancient date in India than in China. But some difficulties arise out of the use of different systems in ancient times, and also from the fact that the Hindoo day is the thirtieth part of the lunar month, which consists of twenty-nine days and a half, and is consequently shorter than the natural day.
The computation of the years begins with zero, the first year counting as 0, the second as 1, and so on. Each year bears a particular name appertaining to a cycle of sixty years, which is, however, different from the Chinese cycle, and is based on the course of the planet Jupiter, which performs its revolution in 11·86 years, or, in round numbers, twelve years. The Hindoo cycle is therefore equivalent to five Jovian revolutions and 7/10 of a year ($10\cdot 86\ {\text{years}}\times 5=59\cdot 30\ {\text{years}}$); in three ​periods of sixty years we have to omit two years, one in the first cycle, and the other in the third; but in thirty cycles we have to omit $0\cdot 7\ {\text{year}}\times 30=21\ {\text{years}}$, while the preceding correction has omitted only twenty years; so a new suppression of a year has to be performed in each series of thirty cycles.
The Hindoos also employed ages in the computation of time, and these, too, divided into periods of different durations. The present age is the kali yuga, or the age of iron; 4,985 years of it have already passed, but its total duration is supposed to be 432,000 years. The succession of the ages, counting back, is given as follows:
Fourth age—Kali yuga, age of iron, or of woe (the present age), to be of 432,000 years. Third age—Dvapara yuga, 864,000 years. Second age—Treta yuga, or age of silver, 1,296,000 years. First age—Krita yuga, age of gold, or of innocence, 1,728,000 years.
These four ages form the maha yuga, or great age, of 4,320,000 years. The length of a patriarchate is seventy-one maha yugas, or 306,720,000 years, to which is added a twilight period of 1,728,000 years, making in all 308,448,000 years. Fourteen of these patriarchates, augmented by a dawn of 1,728,000 years, gives 4,320,000,000 years, which form a kalpa, or the æon of the Hindoo chronology.
A kalpa is only a day in the life of Brahma, whose nights are also of the same duration. Now, Brahma lives a hundred years of three hundred and sixty days and three hundred and sixty nights. The present epoch is the kali yuga of the twenty-seventh grand age of the seventh patriarchate of the first æon of the second half of the life of Brahma, who is now in his 155,521,972,848,985th spring. Yet the whole life of Brahma is only a little longer than a single wink of Siva's eye!
The Greeks employed first two years of 12 months each consisting of 30 days, and a third year of 13 months, giving an average of 370 days to the year; then the cycle of 19 lunar years, with seven months intercalated in each cycle to obtain 19 solar years. The months were of 29 and 30 days, and the time was calculated by Olympiads, of four years each. Afterward, Calippus introduced the cycle of Méton, 433 years b. c., shorter than the 19 solar years, in consequence of the suppression of a day every 76 years. The era of the Olympiads goes back to b. c. 776, at which time Corœbus obtained the prize in the race, from and after which date the names of the victors were inscribed on the official registers.
The ancient Egyptians reckoned at first 12 months of 30 days, or 360 days; but they afterward added five supplementary days. The years were counted from the accession of the kings; and the canon of Ptolemy is a chronological table giving the changes of the reigns. The same form of year was formerly in use among the Persians, with the difference that they added the five supplementary days to the eighth month instead of to the twelfth. Their months had particular ​names, and their years were counted from the accession of Yesdegerd I, a. d. 399; an epoch which is still employed by the Persians in some parts of India. Five thousand years ago, the heliacal rising of Sirius announced to the Egyptians an event of prime importance to them—the overflow of the Nile. They honored the watchful constellation that includes this star with the name of "The Dog," and worshiped it under the title of Anubis. Their year consisting of 365 days, they remarked that the phenomenon took place later, at the rate of a day every four years, so that after 1,461 years of 365 days (or 1,460 years of 3651/4 days) the heliacal risings took place in the original order, after having successively occurred at very different days and hours. This period of 1,461 Egyptian years was called the Sothic period, or the period of the dog. After b. c. 25, the Egyptian year contained 3651/4 days, or nearly the real value of the year. This was called the Alexandrian year. The Copts still employ it, but begin their reckoning from Martyr's day in the reign of Diocletian, August 29th, a. d. 284, while the Alexandrian era began with the battle of Actium, September 2d, b. c. 31. Three Egyptian years included 12 months of 30 days each followed by five epagomenous days; while the fourth or following year had a sixth epagomenous day.
The Roman year consisted of 304 days under Romulus, 355 under Numa, and 366 on the intercalation of the month Mercedonius. The irregularities of their calendar were so great that the pontifices were charged with the duty of regulating the number of days in the intercalated month. Unfortunately, some of the less scrupulous of these functionaries fell into a way of "doctoring" the year so as to make it longer when their friends, or shorter when their enemies, were in office! The corruption was carried out so recklessly that the feast of the Autumnalia was made to come in the spring, and the festival of Ceres, the goddess of the harvest, was celebrated in the middle of the winter! Julius Cæsar put an end to this disorder by introducing the year of 3651/4 days, and gave to the months such numbers of days as made the intercalation of the epagomens unnecessary. The 366th day of the fourth year was added to the month of February, which then had 29 days, and as this caused the sixth day of the kalends to be counted twice (bis sexto calendarum), the name of bissextile was given to this year. This reform took place in the year 708 of Rome (46 b. c.), which year Julius Cæsar ordered to consist of 445 days, so as to make the civil year and the tropical year agree. Hence that year was called the year of confusion. Cæsar's calendar is the basis of the calendar which, further corrected by Pope Gregory XIII, is now in use among the Western nations.
The Mexican year was a peculiar form of the year of 3651/4 days. It included 18 months of 20 days each, to which were added five supplementary days; and, after 52 years, 13 new days made up out of the neglected quarters of days.
​The ancient Irish year was curiously formed. The unit being the week of seven days, they computed 12 months of 30 days each, to which they added four supplementary days to give an even number of weeks, and then every six or seven years they added a week, so that the years might be of 52 or 53 weeks.
The last essay in reforming the calendar was made during the French Revolution, partly with the object of introducing the decimal system into the calculation of time, and partly to eliminate everything relating to the Roman Catholic or any other religion. The months, of thirty days each, were given names, generally typical of some peculiar feature characterizing them. They were divided into three periods of ten days, or decades, to take the place of the weeks, with six intercalated days (five in leap-years) at the end of the last month. The intercalation was not periodic, but was based on exact astronomical calculations. This calendar was used for thirteen years, beginning with the proclamation of the republic, on the 22d of September, 1792.
In the lunar year, the months are alternately of 29 and of 30 days, the moon's synodical revolution taking place in about 29 days. The lunar cycle of the Mohammedans comprises a period of thirty lunar years, during which the seasons begin at all times of the year. If a Turkish festival now falls in the middle of the winter, it will, fifteen years hence, be celebrated in the summer.—Translated for the Popular Science Monthly from the Revue Scientifique.