History of Dharmashastra (Ancient and Mediaeval Religious and Civil Law in India) v6.c82.631
History of Dharmaśāstra (Ancient and Mediaeval Religious and Civil Law in India) v6.c82.631
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v6.c82.631.1
Among all nations the fundamental periods of time are the same, viz. the day, the month and the year (consisting of seasons). The years are the constituents of eras that are vital for chronology and history. Though the fundamental periods of time are the same, there are variations in the arrangement of days to form months and years, about the sub-divisions of the day, about the commencement of the day, about the divisions of the year among seasons and months, about the number of days in each month and in the year and about various kinds of months. The great time measurers are the Sun and the Moon. The day is due to the revolution of the earth round its axis. The month is mainly a lunar phenomenon and the year is due to the apparent motion of the Sun (but in reality it is due to the revolution of the earth round the sun). The tropical year is the time of the passage of the Sun from one vernal equinox to the next. The latter is shorter than the sidereal year (i. e. the time between the two successive arrivals of the Sun at the same fixed star) by about 20 minutes as the vernal equinox point shifts to the west at the rate of about 50 seconds per year.⁹⁸⁷ A modern calendar mentions the current year (by some era), the month and the day of the month and generally the week-day, besides several other matters of religious and social interest. The eras and accurate knowledge of the length of the year and the month came to man rather late.
v6.c82.631.2
The synodic month is a little over 29½ days, while the tropical year is a little less than 365¼ days. These are incommensurable periods. For ordinary life and calendars whole days are required; besides, the starting of the year and the month must be properly defined and must correspond to seasons and some era-must be used. These are the requirements of a calendar which has to be used for civil and religious purposes The complexity of calendars is due mainly to the incommensurability of the above two astronomical periods. The Moslems solved it by ignoring the length of the tropical year and holding fast by the Moon as the measurer of time. They had a purely lunar year. The result was that the Moslems' year was of 354 days and that in about 33 years all their festivals travelled through all the months of the year. On the other hand, the ancient Egyptians ignored the moon as the measurer of time and their year was of 365 days (12 months of 30 days each plus five epagomenal, i. e. additional days). Their priests stuck to this system for 3000 years, they had no leap years or intercalary months. Most ancient peoples including Indians followed a luni-solar calendar and tried to adjust the lunar months to the solar year by the system of intercalary months. It has been seen above (p. 489 note 710) that even the Ṛgveda speaks of an additional month (in I. 25 8) but how it was arrived at and where in the scheme of months it was introduced we do not know.
v6.c82.631.3
We know that the Vedāṅgajyotiṣa⁹⁸⁸ added two months in five years. The people of those ancient times had to solve the problem of adjusting the reckoning of the months by the moon and the years by the sun. People wanted to know in advance when the Full Moon or New Moon on which many ancient festivals were celebrated may be expected, when to expect monsoon or winter, when to prepare ground for sowing and when to sow. Sacrifices had to be in spring and other seasons, as also on New Moon and Full Moon. The lunar year of 354 days was less by about 11 days than the solar year. Therefore, the seasons would shift back if the lunar year-alone were observed. Hence intercalary months were introduced by several nations. The Greeks had the 'Octaeteris' (eight years cycle), that contained 99 months of which three were intercalary, viz. in the 3rd, 5th and 8th years Then was introduced the Metonic cycle of 19 years in which occurred seven intercalary months (19 × 12 plus 7 = 235). Olmstead (in American Journal of Semitic Languages, vol. 55 for 1938) says at p. 116 that the cycle of intercalation in Babylon was of eight years and that it was followed by the Greeks Fotherigham (in Journal of Hellenistic studies, vol 39 p 179) says that intercalation in Babylon was irregular till 528 B. C. and in Greece it was unsystematic in the 5th and 4th centuries B. C. Vide also C. R. C. Report pp. 175-176.