Vaidika Kala Mapana (वैदिककालमापनम्)

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The day, called vāsara or ahan in the vedic literature, was reckoned from sunrise to sunrise. The variability of its length was known. The Ṛgveda (8. 48. 7) invoking Somarāja says: “O Somarāja, prolong thou our lives just as the Sun increases the length of the days.” Six days were taken to form a ṣaḍaha (six-day week); 5 ṣaḍahas, a month; and 12 months, a year. As to the names of the six days of a ṣaḍaha, there is no reference in the vedic literature. However, the six-day week was later replaced by the present seven day week (saptāha) which had attained popularity and was in general use at the time of composition of the Atharva-jyautiṣa.

The duration of daylight, reckoned from sunrise to sunset, was divided into two parts called pūrvāhṇa (forenoon) and aparāhṇa (afternoon), three parts called, pūrvāhṇa, madhyāhna, and aparāhṇa, four parts called pūrvāhṇa madhyāhna, aparāhṇa and sāyāhna,4 and five parts called prātaḥ, saṅgava, madhyāhna, aparāhṇa, and sāyāhna (Śatapatha-brāhmaṇa, 2. 2. 3. 9). The days and nights were also divided into 15 parts each, and these parts were called muhūrta. The muhūrtas falling during the days of the light and dark fortnights as well as those falling during the nights of the light and dark fortnights were given specific names (Taittirīya-brāhmaṇa, 3. 10. 1. 1–3). The fifteen days and nights of the light fortnight as well as the fifteen days and nights of the dark fortnight were also assigned special names (Taittirīya-brāhmaṇa, 3. 10. 1. 1–3; 3. 10. 10. 2).

On the analogy of a civil day, a lunar day was also sometimes reckoned from one moonrise to the next and the name tithi was given to it (Aitareyabrāhmaṇa, 32. 10). The use of the term tithi in the sense in which it is used now occurs in the Vedāṅga-jyautiṣa (Ārca-jyautiṣa, 20, 21, 31; Yājuṣa-jyautiṣa, 20–23, 25, 26). It does not occur in the vedic saṃhitās and brāhmaṇas, but there are reasons to believe that tithis were used even in those times.

The year, generally called by the terms samā, vatsara, and hāyana in the vedic literature, was seasonal or tropical and was measured from one winter solstice to the next, but in due course it was used in the sense of a sidereal year. In the early stages, therefore, the names of the seasons were used as synonyms of a year. The Kauṣītaki-brāhmaṇa (19. 3) gives an interesting account of how the year-long sacrifice was commenced at one winter solstice and continued until the next winter solstice: “On the new moon of Māgha he (the Sun) rests, being about to turn northwards. They (the priests) also rest, being about to sacrifice with the introductory Atirātra. Thus, for the first time, they (the priests) obtain him (the Sun). On him they lay hold with the Caturviṃśa rite; that is why the laying hold rite has that name. He (the Sun) goes north for six months; him they (the priests) follow with six day rites in continuation. Having gone north for six months, he (the Sun) stands still, being about to turn southwards. They (the priests) also rest, being about to sacrifice with the Viṣuvanta (summer solstice) day. Thus, for the second time, they obtain him (the Sun). He (the Sun) goes south for six months; they (the priests) follow him with six day rites in reverse order. Having gone south for six months, he (the Sun) stands still, being about to turn north; and they (the priests) also rest, being about to sacrifice with the Mahāvrata day. Thus, they (the priests) obtain him (the Sun) for the third time”.

The Taittirīya-brāhmaṇa (3. 9. 22) calls the year “the day of the gods”, the gods being supposed to reside at the north pole.

The year was supposed to consist of six seasons and each season of two (solar) months. The relation between the seasons and months was as shown in Table 1.

Two (solar) months commencing with the winter solstice were called Śiśira; the next two months, Vasanta; and so on. Sometimes Śiśira and Hemanta were treated as one season and the number of seasons was taken as five (Aitareyabrāhmaṇa, 1. 1; Taittirīya-brāhmaṇa, 2. 7. 10)

The lunar or synodic month was measured from full moon to full moon or from new moon to new moon (Taittirīya-saṃhitā, 7. 5. 6. 1) as is the case even now. The names Caitra etc. based on the nakṣatras in which the Moon becomes full do not occur in the early saṃhitās and brāhmaṇas but such terms as phalgunī-pūrnamāsī, citrā-pūrnamāsī, etc. are found to occur in the Taittirīyasaṃhitā (7. 4. 8). They occur in the Saṅkhāyana and Tāṇḍya-brāhmaṇas, the Vedāṅga-jyautiṣa, and the Kalpa-sūtras.5 Twelve lunar months constituted a lunar year. In order to preserve correspondence between lunar and solar years, intercalary months were inserted at regular intervals. Mention of the intercalary month is made in the Ṛgveda (1. 25. 8), but how it was arrived at and where in the scheme of months it was introduced in that time is not known. The Vedāṅga-jyautiṣa prescribes insertion of an intercalary month after every 30 lunar months (Yājuṣa-jyautiṣa, 37). Thus, a year sometimes contained 12 lunar months and sometimes 13 lunar months. The Taittirīya-saṃhitā (5. 6. 7) refers to 12 as well as 13 months of a year and calls the thirteenth (intercalary) month by the names saṃsarpa and aṃhaspati (1. 4. 14). The Vājasaneyī-saṃhitā (7. 30; 22. 31) calls the intercalary month on one occasion by the name aṃhasaspati and on another by the name malimluca (22. 30). In later works the synodic month with two saṃkrantis is called aṃhaspati, the synodic month without any saṃkrānti, occurring before it, is called saṃsarpa, and the synodic month without any saṃkrānti occurring after it is called adhimāsa (intercalary month, Tantrasaṃgraha i. 8)

Originally the lunar (or synodic) months Caitra etc. were named after the nakṣatras occupied by the Moon at the time of full moon. But in due course they were linked with the solar months. Thus, the lunar month (reckoned from one new moon to the next) in which the Sun entered the sign Aries was called Caitra or Madhu; that in which the Sun entered the sign Taurus was called Vaiśākha or Mādhava; and so on. The lunar month in which the Sun did not enter a new sign was treated as an intercalary month.

Periods bigger than a year are also met with in the vedic literature. They were called yuga. One such yuga consisted of 5 solar years. The five constituent years of this yuga were called saṃvatsara, parivatsara, idāvatsara, anuvatsara and idvatsara. The Ṛgveda (7. 103. 7–8) mentions two of these, viz. saṃvatsara and parivatsara. The Taittirīya-saṃhitā (5. 5. 7. 1–3), the Vājasaneyi-saṃhitā (27. 45; 30. 16), and the Taittirīya-brāhmaṇa (3. 4. 11; 3. 10. 4), mention all the five names, with some alteration. The Taittirīyasaṃhitā calls them saṃvatsara, parivatsara, idāvatsara, iduvatsara, and vatsara; the Vājasaneyi-saṃhitā, saṃvatsara, parivatsara, idāvatsara, idvatsara, and vatsara, and the Taittirīya-brāhmaṇa saṃvatsara, parivatsara, idāvatsara, idvatsara, and vatsara respectively. The names Kṛta, Tretā, Dvāpara, and Kali which are used in later astronomy as the names of longer yugas are also used in the vedic literature to indicate different grades, each inferior to the preceding. But Dvāpara, as a unit of time, is found to be used in the Gopatha-brāhmaṇa (1. 1. 28).

The earliest work which exclusively deals with vedic astronomy is the Vedāṅga- jyautiṣa. It is available in two recensions, Ārca-jyautisa and Yājuṣajyautiṣa. Both the recensions are essentially the same; a majority of the verses occurring in them being identical. The date of this work is controversial, but the situation of the Sun and Moon at the beginning of the yuga of five years mentioned in this work, according to T. S. Kuppanna Sastry, existed about 1150 bc or about 1370 bc, according as the first point of nakṣatra Śraviṣṭhā stated there means the first point of the nakṣatra-segment Śraviṣṭhā or the nakṣatra-group Śraviṣṭhā (Sastry 1984, 3, p. 13). This work defines jyotiṣa (astronomy) as the science of time-determination and deals with months, years, muhūrtas, rising nakṣatras, new moons, full moons, days, seasons, and solstices. It states rules to determine the nakṣatra occupied by the Sun or Moon, the time of the Sun’s or Moon’s entry into a nakṣatra, the duration of the Sun’s or Moon’s stay in a nakṣatra, the number of new moons or full moons that occurred since the beginning of the yuga, the position of the Sun or Moon at the end of a new moon or full moon day or tithi, and similar other things. It gives also the measure of the water-clock, which was used to measure time, and tells when an intercalary month was to be added or a tithi was to be omitted. In short, it gives all necessary information needed by the vedic priest to predict times for the vedic sacrifices and other religious observances.

The five-year yuga of the Vedāṅga-jyautiṣa contained 61 civil, 62 lunar, and 67 sidereal months. The year consisted of 366 civil days which were reckoned from sunrise to sunrise. After every thirty lunar months one intercalary month was inserted to bring about concordance between solar and lunar years. Similarly, to equate the number of tithis and civil days in the yuga of five solar years, the thirty full moon tithis which ended between sunrise and midday were omitted. There were six seasons of equal duration in every year, each new season beginning after every 61 days. Besides tithis and nakṣatras, the yoga called Vyatīpāta was also in use.

The five-year yuga was taken to commence at the winter solstice occurring at the beginning of the first tithi of the light half of the month Māgha. Since the Sun and Moon were supposed to occupy the same position at the beginning of each subsequent yuga and all happenings in one yuga were supposed to be repeated in the subsequent yugas in the same way, the calendar constructed on the basis of the Vedāṅga-jyautiṣa was meant to serve for a long time.

The Vedāṅga-jyautiṣa astronomy suffered from two main defects. Since there are actually 1826.2819 days in a yuga of five solar (sidereal) years and not 1830 as stated in the Vedāṅga-jyautiṣa, therefore if one yuga was taken to commence at a winter solstice the next one commenced about four days later than the next winter solstice and not at the next winter solstice. Similarly, since there are actually 1830.8961 days in a period of 62 lunar months and not 1830 as stated in the Vedāṅga-jyautiṣa, therefore there was a deficit of about one tithi in the yuga of five solar years. These discrepancies must have been rectified but we do not know when and how this was done.

There is one more work on jyotiṣa belonging to the later vedic period. It is known as Atharva-jyautiṣa. This work describes the muhūrtas, tithis, karaṇas, nakṣatras, and week days, and prescribes the deeds that should be performed in them. The names of the lords of the week days stated in this work viz. Āditya (Sun), Soma (Moon), Bhauma (the son of Earth), Bṛhaspati, Bhārgava (the son of Bhṛgu), and Śanaiścara (the slow-moving planet), are undoubtedly of Indian origin and must have been in use in India from very early times.6