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{{ToBeEdited}}The culture of astronomy in vedic times was motivated by the need of fixing time for the various religious sacrifices which were performed at different times in different seasons.
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Vaidika Kala Mapana (Samskrit: वैदिककालमापनम्) refers to the various divisions of [[Kala (कालः)|time]] discussed in [[Vaidika Vangmaya (वैदिकवाङ्मयम्)|Vedic literature]].
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== परिचयः ॥ Introduction ==
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People of the vedic times engaged seriously in the performance of [[Yajna (यज्ञः)|yajnas]] at specific times prescribed by the shastras. Thus, it was necessary to have accurate knowledge of the science of time so that the times prescribed for performing the various vedic yajnas could be correctly predicted well in advance. Thus, it was essential to study the natural divisions of time caused by the motion of the [[Surya (सूर्यः)|Sun]] and Moon, such as days, months, seasons, and years, with special attention to the study of the times of occurrence of new moons, full moons, equinoxes, and solstices that is included under the purview of the science of Astronomy. Therefore, Astronomy in the vedic times, was essentially the science of time-determination that was motivated by the need to fix time for the various yajnas that were performed at different times in different seasons.<ref name=":1">Kolachana, Aditya & Mahesh, Kaluva & Ramasubramanian, K.. (2019). Main characteristics and achievements of ancient Indian astronomy in historical perspective. 10.1007/978-981-13-7326-8_24. </ref>
  
The Kauṣītaki-brāhmaṇa records  the occurrence of the winter solstice on the new moon day of Māgha.2 (2Kauṣītaki-brāhmaṇa, xi. 3.)
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In fact, this is the definition of astronomy given in [[Vedanga Jyotisha (वेदाङ्गज्योतिषम्)|Vedanga Jyotisha]], the earliest available work dealing exclusively with astronomy that gives all necessary information needed by the vedic hota to predict times for the vedic yajnas and other observances.<ref name=":1" /><ref name=":2">K. S. Shukla, [https://www.insa.nic.in/writereaddata/UpLoadedFiles/IJHS/Vol04_1And2_11_KSShukla.pdf Astronomy in ancient and medieval India], Indian Journal of History of Science, Vol.4, Nos. 1-2 (1969), pp.99-106.</ref>
  
It is also stated there that the year ended with the full moon at the Pūrva-Phālgunī,3 (3Ibid, v. 1.) and that the spring commenced one day after the new moon of Caitra.(4Ibid, xix. 3.)
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However, the Vedic literature also has references to astronomical events and observations. For eg. The Kaushitaki brahmana states that the year ended with the full moon at the Purva Phalguni.<ref name=":2" /> <blockquote>मुखम् वा एतत् संवत्सरस्य यत् फाल्गुनी पौर्णमासी । मुखम् उत्तरे फल्गू । पुच्छम् पूर्वे । तद् यथा प्रवृत्तस्य अन्तौ समेतौ स्याताम् । एवम् एव एतौ संवत्सरस्य अन्तौ समेतौ ।5.1<ref>Kaushitaki brahmana, [https://sa.wikisource.org/wiki/%E0%A4%95%E0%A5%8C%E0%A4%B7%E0%A5%80%E0%A4%A4%E0%A4%95%E0%A4%BF%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%A3%E0%A4%AE%E0%A5%8D/%E0%A4%85%E0%A4%A7%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AF%E0%A4%83_%E0%A5%A6%E0%A5%AB Adhyaya 5].</ref></blockquote><blockquote>''mukham vā etat saṁvatsarasya yat phālgunī paurṇamāsī । mukham uttare phalgū । puccham pūrve । tad yathā pravr̥ttasya antau sametau syātām । evam eva etau saṁvatsarasya antau sametau ।5.1''</blockquote>Thus, ancient Indian astronomy may be classified into two main categories:
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# Vedic astronomy
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# Post-vedic astronomy.  
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Vedic astronomy is the astronomy of the vedic period, i.e., the astronomy found in the vedic [[Samhita (संहिता)|samhitas]], [[Brahmana (ब्राह्मणम्)|brahmanas]] and allied literature.<ref name=":1" /> And that is elaborated in this article below.
  
This shows that the beginning of the year under the amānta reckoning synchronised with the beginning of the seasons.
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== Day in Vedic Literature ==
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The day, in vedic literature was called Vasara (वासरः) or ahan (अहन्). And was reckoned from sunrise to sunrise. The variability of its length was known. For, the Rgveda invoking Somaraja says, <blockquote>''“O Somaraja, prolong thou our lives just as the Sun increases the length of the days.”<ref name=":1" />''</blockquote><blockquote>सोम राजन्प्र ण आयूंषि तारीरहानीव सूर्यो वासराणि ॥७॥<ref>Rgveda, Mandala 8, [https://sa.wikisource.org/wiki/%E0%A4%8B%E0%A4%97%E0%A5%8D%E0%A4%B5%E0%A5%87%E0%A4%A6%E0%A4%83_%E0%A4%B8%E0%A5%82%E0%A4%95%E0%A5%8D%E0%A4%A4%E0%A4%82_%E0%A5%AE.%E0%A5%AA%E0%A5%AE Sukta 48].</ref></blockquote><blockquote>''soma rājanpra ṇa āyūṁṣi tārīrahānīva sūryo vāsarāṇi ॥7॥''</blockquote>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.<ref name=":1" /><blockquote>तदाहुर्यद्दर्शपूर्णमासयोरुपवसति न ह वा अव्रतस्य देवा हविरश्नन्ति तस्मादुपवसत्युत मे देवा हविरश्नीयुरिति। पूर्वां पौर्णमासीमुपवसेदिति पैङ्ग्यमुत्तरामिति कौषीतकं या पूर्वा पौर्णमासी साऽनुमतिर्योत्तरा सा राका। या पूर्वाऽमावास्या सा सिनीवाली योत्तरा सा कुहूः। यां पर्यस्तमियादभ्युदियादिति सा तिथिः.....॥7.11॥ (Aitareya brahmana 32.10)<ref>Aitareya brahmana, [https://sa.wikisource.org/wiki/%E0%A4%90%E0%A4%A4%E0%A4%B0%E0%A5%87%E0%A4%AF_%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%A3%E0%A4%AE%E0%A5%8D/%E0%A4%AA%E0%A4%9E%E0%A5%8D%E0%A4%9A%E0%A4%BF%E0%A4%95%E0%A4%BE_%E0%A5%AD_(%E0%A4%B8%E0%A4%AA%E0%A5%8D%E0%A4%A4%E0%A4%AE_%E0%A4%AA%E0%A4%9E%E0%A5%8D%E0%A4%9A%E0%A4%BF%E0%A4%95%E0%A4%BE) Panchika 7].</ref></blockquote><blockquote>''tadāhuryaddarśapūrṇamāsayorupavasati na ha vā avratasya devā haviraśnanti tasmādupavasatyuta me devā haviraśnīyuriti। pūrvāṁ paurṇamāsīmupavasediti paiṅgyamuttarāmiti kauṣītakaṁ yā pūrvā paurṇamāsī sā'numatiryottarā sā rākā। yā pūrvā'māvāsyā sā sinīvālī yottarā sā kuhūḥ। yāṁ paryastamiyādabhyudiyāditi sā tithiḥ.....॥7.11॥''</blockquote>However, the term tithi in the sense in which it is used now occurs in the Vedanga Jyotisha. It does not occur in the vedic samhitas and brahmanas, but there are reasons to believe that tithis were used even in those times.<ref name=":1" />
  
The year of vedic astronomy seems to have been a tropical one. The months were lunar and measured from full moon to full moon and also from new moon to new moon. There is evidence to show that to make the lunar year correspond to the solar year 12 days were intercalated after every lunar year and one month was dropped after every 40 years.5 (5Law, N. N., Age of the Ṛgveda, pp. 20, 28–29.) At a later stage this correspondence was established by evolving a cycle of five solar years with 62 lunar months. This cycle was called a yuga.
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=== Divisions of a Day<ref name=":1" /> ===
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The duration of daylight, reckoned from sunrise to sunset, was variously divided into,
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# Two parts called Purvahna (forenoon) and Aparahna (afternoon)
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# Three parts called Purvahna, Madhyahna, and Aparahna.  
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# Four parts called Purvahna, Madhyahna, Aparahna and Sayahna
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# Five parts called Pratah, Sangava, Madhyahna, Aparahna, and Sayahna
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The names of these five parts occur together in the Shatapatha brahmana,<blockquote>आदित्यस्त्वेव सर्व ऋतवः । यदैवोदेत्यथ वसन्तो यदा संगवोऽथ ग्रीष्मो यदा मध्यन्दिनोऽथ वर्षा यदापराह्णोऽथ शरद्यदैवास्तमेत्यथ हेमन्तस्तस्मादु मध्यंन्दिन एवादधीत तर्हि ह्येषोऽस्य लोकस्य नेदिष्ठं भवति तन्नेदिष्ठादेवैनमेतन्मध्यान्निर्मिमीते - २.२.३.९<ref>Shatapatha brahmana, Kanda 2, Adhyaya 2, [https://sa.wikisource.org/wiki/%E0%A4%B6%E0%A4%A4%E0%A4%AA%E0%A4%A5%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%A3%E0%A4%AE%E0%A5%8D/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%AE%E0%A5%8D_%E0%A5%A8/%E0%A4%85%E0%A4%A7%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AF%E0%A4%83_%E0%A5%A8/%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%A3_%E0%A5%A9 Brahmana 3].</ref></blockquote><blockquote>''ādityastveva sarva r̥tavaḥ । yadaivodetyatha vasanto yadā saṁgavo'tha grīṣmo yadā madhyandino'tha varṣā yadāparāhṇo'tha śaradyadaivāstametyatha hemantastasmādu madhyaṁndina evādadhīta tarhi hyeṣo'sya lokasya nediṣṭhaṁ bhavati tannediṣṭhādevainametanmadhyānnirmimīte''</blockquote>While the first three words ie. Pratah, Sangava and Madhyahna occur in Rgveda (Mandala 5), <blockquote>उता यातं संगवे प्रातरह्नो मध्यंदिन उदिता सूर्यस्य । दिवा नक्तमवसा शंतमेन नेदानीं पीतिरश्विना ततान ॥३॥<ref>Rgveda, Mandala 5, [https://sa.wikisource.org/wiki/%E0%A4%8B%E0%A4%97%E0%A5%8D%E0%A4%B5%E0%A5%87%E0%A4%A6%E0%A4%83_%E0%A4%B8%E0%A5%82%E0%A4%95%E0%A5%8D%E0%A4%A4%E0%A4%82_%E0%A5%AB.%E0%A5%AD%E0%A5%AC Sukta 76].</ref></blockquote><blockquote>''utā yātaṁ saṁgave prātarahno madhyaṁdina uditā sūryasya । divā naktamavasā śaṁtamena nedānīṁ pītiraśvinā tatāna ॥3॥''</blockquote>The term Saya (evening) occurs in Rgveda (Mandala 8 and 10),  <blockquote>मो ष्वद्य दुर्हणावान्सायं करदारे अस्मत् । अश्रीर इव जामाता ॥२०॥<ref>Rgveda, Mandala 8, [https://sa.wikisource.org/wiki/%E0%A4%8B%E0%A4%97%E0%A5%8D%E0%A4%B5%E0%A5%87%E0%A4%A6%E0%A4%83_%E0%A4%B8%E0%A5%82%E0%A4%95%E0%A5%8D%E0%A4%A4%E0%A4%82_%E0%A5%AE.%E0%A5%A8 Sukta 2].</ref></blockquote><blockquote>उत गाव इवादन्त्युत वेश्मेव दृश्यते । उतो अरण्यानिः सायं शकटीरिव सर्जति ॥३॥<ref>Rgveda, Mandala 10, [https://sa.wikisource.org/wiki/%E0%A4%8B%E0%A4%97%E0%A5%8D%E0%A4%B5%E0%A5%87%E0%A4%A6%E0%A4%83_%E0%A4%B8%E0%A5%82%E0%A4%95%E0%A5%8D%E0%A4%A4%E0%A4%82_%E0%A5%A7%E0%A5%A6.%E0%A5%A7%E0%A5%AA%E0%A5%AC Sukta 146].</ref></blockquote><blockquote>''mo ṣvadya durhaṇāvānsāyaṁ karadāre asmat । aśrīra iva jāmātā ॥20॥''</blockquote><blockquote>''uta gāva ivādantyuta veśmeva dr̥śyate । uto araṇyāniḥ sāyaṁ śakaṭīriva sarjati ॥3॥''</blockquote>The days and nights were also divided into 15 parts each called as muhurta. According to Taittiriya brahmana (3. 10. 1. 1–3), the muhurtas falling during the days and nights of the shukla and krshna pakshas (fortnights) were respectively given specific names.<ref name=":0">Taittiriya brahmana, Kanda 3, [https://sa.wikisource.org/wiki/%E0%A4%A4%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%B0%E0%A5%80%E0%A4%AF%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%A3%E0%A4%AE%E0%A5%8D_(%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%83)/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%83_%E0%A5%A9/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%95%E0%A4%83_%E0%A5%A7%E0%A5%A6 Prapathaka 10].</ref>
  
The Vedāṅgajyotiṣa is the earliest Hindu work dealing exclusively with astronomy. The Vedāṅgajyotiṣa has come down to us in two recensions, viz. the Ṛgvedic recension (called Ārca-jyotiṣa) and the Yajurvedic recension (called Yājuṣa-jyotiṣa). Both the recensions are thus practically the same and give an account of months, years, days and day-divisions, nakṣatras, new moons and full moons, solstices, and seasons occurring in the cycle of five solar years.  
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The Taittiriya brahmana (3. 10. 1. 1–3; 3. 10. 10. 2)<ref name=":0" /> also assigns specific names to the fifteen days and nights of the shukla as well as krshna pakshas.
  
lay down rules for determining
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However, by the time of the Kautiliya Arthashastra, the day and night came to be divided into eight parts each.<blockquote>नालिकाभिरहरष्टधा रात्रिं च विभजेत् । छाया-प्रमाणेन वा ।। ०१.१९.०६ ।।<ref>Arthashastra, Adhikarana 1, [https://sa.wikisource.org/wiki/%E0%A4%85%E0%A4%B0%E0%A5%8D%E0%A4%A5%E0%A4%B6%E0%A4%BE%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A5%8D/%E0%A4%85%E0%A4%A7%E0%A4%BF%E0%A4%95%E0%A4%B0%E0%A4%A3%E0%A4%AE%E0%A5%8D_%E0%A5%A7/%E0%A4%85%E0%A4%A7%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AF%E0%A4%83_%E0%A5%A7%E0%A5%AF Adhyaya 19].</ref></blockquote><blockquote>''nālikābhiraharaṣṭadhā rātriṁ ca vibhajet । chāyā-pramāṇena vā ।। 01.19.06 ।।''</blockquote>
  
(i) the beginning of a season, (vi) the length of a day.<ref>K. S. Shukla, [https://www.insa.nic.in/writereaddata/UpLoadedFiles/IJHS/Vol04_1And2_11_KSShukla.pdf Astronomy in ancient and medieval India], Indian Journal of History of Science, Vol.4, Nos. 1-2 (1969), pp.99-106.</ref>
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== Week in Vedic Literature ==
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In vedic literature, six days were taken to form a week that was called a Shadaha. 5 shadahas made a month and 12 months, a year. As to the names of the six days of a shadaha, there is no reference in the vedic literature. However, this six-day week was later replaced by the present seven day week (called saptaha) which had attained popularity and was in general use at the time of composition of the Atharva Jyotisha - a work on Jyotisha belonging to the later vedic period.<ref name=":1" /><ref name=":5" />
  
Ancient Indian astronomy may be classified into two main categories:  
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== Months in Vedic Literature ==
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In vedic astronomy, months were lunar or synodic and were measured from full moon to full moon and also from new moon to new moon<ref name=":2" /> as mentioned in the Taittiriya samhita (7.5.6.1)<ref name=":1" /><ref>Taittiriya Samhita, Kanda 7, [https://sa.wikisource.org/wiki/%E0%A4%A4%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%B0%E0%A5%80%E0%A4%AF%E0%A4%B8%E0%A4%82%E0%A4%B9%E0%A4%BF%E0%A4%A4%E0%A4%BE(%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%B0%E0%A4%83)/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%AE%E0%A5%8D_%E0%A5%AD/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%95%E0%A4%83_%E0%A5%AB Prapathaka 5].</ref> Originally, these months were named as Chaitra etc. based on the [[Nakshatras (नक्षत्राणि)|nakshatras]] occupied by the Moon at the time of full moon. And these names do not occur in the early samhitas and brahmanas. They are known to occur in Taittiriya samhita, Shankhayana/Kaushitaki, and Tandya brahmanas, Ashvalayana grhyasutra, Archa and Yajusha jyotisha. Some of the occurrences are as follows:<ref name=":1" />
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* The terms Phalguni purnamasi, Chitra purnamasi, etc. are found in the Taittiriya samhita (7. 4. 8).<ref>Taittiriya Samhita, Kanda 7, [https://sa.wikisource.org/wiki/%E0%A4%A4%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%B0%E0%A5%80%E0%A4%AF%E0%A4%B8%E0%A4%82%E0%A4%B9%E0%A4%BF%E0%A4%A4%E0%A4%BE(%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%B0%E0%A4%83)/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%AE%E0%A5%8D_%E0%A5%AD/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%95%E0%A4%83_%E0%A5%AA Prapathaka 4].</ref>
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* The term Magha is mentioned in Shankhayana/Kaushitaki brahmana (19. 3)
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<blockquote>स वै माघस्य अमावास्यायाम् उपवसत्य् उदन्न् आवर्त्स्यन् ।<ref name=":3" />''sa vai māghasya amāvāsyāyām upavasaty udann āvartsyan ।''</blockquote>
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* The term Phalguna occurs in Tandya brahmana (5. 9. 7–12)
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* The terms Margashirsha and Shravana occurs in the Ashvalayana grhyasutra 2. 3. 1 and 3. 5. 2 respectively.
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<blockquote>मार्गशीर्ष्यां प्रत्यवरोहणं चतुर्दश्याम् १ | ''mārgaśīrṣyāṁ pratyavarohaṇaṁ caturdaśyām 1 |''</blockquote><blockquote>ओषधीनां प्रादुर्भावे श्रवणेन श्रावणस्य २ |<ref>[https://sa.wikisource.org/wiki/%E0%A4%86%E0%A4%B6%E0%A5%8D%E0%A4%B5%E0%A4%B2%E0%A4%BE%E0%A4%AF%E0%A4%A8%E0%A4%97%E0%A5%83%E0%A4%B9%E0%A5%8D%E0%A4%AF%E0%A4%B8%E0%A5%82%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A5%8D Ashvalayana Grhyasutra]</ref> ''oṣadhīnāṁ prādurbhāve śravaṇena śrāvaṇasya 2 |''</blockquote>
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* While the terms Shravana, Magha and Pausha also occur in Archa jyotisha (5, 6, 32 and 34) and Yajusha jyotisha (5, 6, and 7)
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However, in due course the lunar months 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 Chaitra or Madhu; that in which the Sun entered the sign Taurus was called Vaishakha or Madhava; and so on. And the lunar month in which the Sun did not enter a new sign was treated as an intercalary month.
  
(1) the vedic astronomy and
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Twelve such lunar months constituted a lunar year.<ref name=":1" />
  
(2) the post vedic astronomy.  
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== Year in Vedic Literature ==
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In the vedic literature, the year, generally called by the terms sama, vatsara, and hayana, was measured from one winter solstice to the next. However, in due course, it was used in the sense of a sidereal year.<ref name=":1" /><ref name=":2" /> In fact, the Kaushitaki brahmana (19.3) gives an interesting account of how the year-long yajna commenced at one winter solstice and continued until the next. It says, “On the new moon of Magha, the Sun rests, about to turn northwards. The hotas also rest, about to begin with the introductory Atiratra. Thus, for the first time, the hotas obtain the Sun. On him, they lay hold with the Chaturvimsha rite; that is why the laying hold rite has that name. The Sun then goes north for six months, while the hotas follow him with six day rites in continuation. Having gone north for six months, the Sun stands still, about to turn southwards. The hotas also rest, about to begin with the Vishnuvanta (summer solstice) day. Thus, for the second time, they obtain the Sun. The Sun then goes south for six months and the hotas follow him with six day rites in reverse order. Having gone south for six months, the Sun stands still, being about to turn north and the hotas also rest, about to begin with the Mahavrata day. Thus, they obtain the Sun for the third time."<ref name=":1" /><ref name=":3">Kaushitaki brahmana, [https://sa.wikisource.org/wiki/%E0%A4%95%E0%A5%8C%E0%A4%B7%E0%A5%80%E0%A4%A4%E0%A4%95%E0%A4%BF%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%A3%E0%A4%AE%E0%A5%8D/%E0%A4%85%E0%A4%A7%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AF%E0%A4%83_%E0%A5%A7%E0%A5%AF Adhyaya 19].</ref>
  
The vedic astronomy is the astronomy of the vedic period, i.e., the astronomy found in the vedic saṃhitās and brāhmaṇas and allied literature. The principal avocation of the people in the vedic times being the performance of the vedic sacrifices at the times prescribed by the śāstras, it was necessary to have accurate knowledge of the science of time so that the times prescribed for performing the various vedic sacrifices could be correctly predicted well in advance. Astronomy in those times, therefore, was essentially the science of time-determination. It centred round the Sun and Moon and its aim was to study the natural divisions of time caused by the motion of the Sun and Moon, such as days, months, seasons, and years, special attention being paid to the study of the times of occurrence of new moons, full moons, equinoxes, and solstices.<ref name=":1" />
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In this context, it is worth observing that the Taittiriya brahmana (3. 9. 22) calls the year “the day of the deities” who are supposed to reside at the north pole.<ref name=":1" /><blockquote>एकं वा एतद्देवानामहः  । यत्संवत्सरः  ।<ref>Taittiriya brahmana, Kanda 3, [https://sa.wikisource.org/wiki/%E0%A4%A4%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%B0%E0%A5%80%E0%A4%AF%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%A3%E0%A4%AE%E0%A5%8D_(%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%83)/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%83_%E0%A5%A9/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%95%E0%A4%83_%E0%A5%A6%E0%A5%AF Prapathaka 9].</ref> ''ekaṁ vā etaddevānāmahaḥ । yatsaṁvatsaraḥ ।''</blockquote>
  
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.” <blockquote>सोम राजन्प्र ण आयूंषि तारीरहानीव सूर्यो वासराणि ॥७॥<ref>Rgveda, Mandala 8, [https://sa.wikisource.org/wiki/%E0%A4%8B%E0%A4%97%E0%A5%8D%E0%A4%B5%E0%A5%87%E0%A4%A6%E0%A4%83_%E0%A4%B8%E0%A5%82%E0%A4%95%E0%A5%8D%E0%A4%A4%E0%A4%82_%E0%A5%AE.%E0%A5%AA%E0%A5%AE Sukta 48].</ref></blockquote>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.
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=== Seasons<ref name=":1" /> ===
 
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The year of vedic astronomy seems to have been a seasonal or tropical one. Therefore, in the early stages, the names of the seasons were used as synonyms of a year. The year consisted of six seasons and each season lasted for a duration of two solar months. The two solar months commencing with the winter solstice were called Shishira; the next two months, Vasanta; and so on. According to the Aitareya brahmana (1.1) and Taittiriya brahmana (2.7.10), sometimes Shishira and Hemanta were treated as one season and the number of seasons was taken as five.<blockquote>''द्वा''दश मासाः पञ्चर्तवो हेमन्तशिशिरयोः समासेन तावान्संवत्सरः |<ref>Aitareya brahmana, [https://sa.wikisource.org/wiki/%E0%A4%90%E0%A4%A4%E0%A4%B0%E0%A5%87%E0%A4%AF_%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%A3%E0%A4%AE%E0%A5%8D/%E0%A4%AA%E0%A4%9E%E0%A5%8D%E0%A4%9A%E0%A4%BF%E0%A4%95%E0%A4%BE_%E0%A5%A7_(%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%A5%E0%A4%AE_%E0%A4%AA%E0%A4%9E%E0%A5%8D%E0%A4%9A%E0%A4%BF%E0%A4%95%E0%A4%BE) Panchika 1].</ref>''dvādaśa māsāḥ pañcartavō hēmantaśiśirayōḥ samāsēna tāvānsaṁvatsaraḥ |''</blockquote><blockquote>पञ्च वा ऋतवः संवत्सरः ऋतुष्वेव संवत्सरे प्रतितिष्ठति ।<ref>Taittiriya brahmana, Kanda 2, [https://sa.wikisource.org/wiki/%E0%A4%A4%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%B0%E0%A5%80%E0%A4%AF%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%A3%E0%A4%AE%E0%A5%8D_(%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%83)/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%83_%E0%A5%A8/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%95%E0%A4%83_%E0%A5%A6%E0%A5%AD Prapathaka 7].</ref>''pañca vā r̥tavaḥ saṁvatsaraḥ । r̥tuṣvēva saṁvatsarē pratitiṣṭhati ।''</blockquote>The relation between the seasons and months was as follows:
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). <blockquote>आदित्यस्त्वेव सर्व ऋतवः । यदैवोदेत्यथ वसन्तो यदा संगवोऽथ ग्रीष्मो यदा मध्यन्दिनोऽथ वर्षा यदापराह्णोऽथ शरद्यदैवास्तमेत्यथ हेमन्तस्तस्मादु मध्यंन्दिन एवादधीत तर्हि ह्येषोऽस्य लोकस्य नेदिष्ठं भवति तन्नेदिष्ठादेवैनमेतन्मध्यान्निर्मिमीते - २.२.३.[९]<ref>Shatapatha brahmana, Kanda 2, Adhyaya 2, [https://sa.wikisource.org/wiki/%E0%A4%B6%E0%A4%A4%E0%A4%AA%E0%A4%A5%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%A3%E0%A4%AE%E0%A5%8D/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%AE%E0%A5%8D_%E0%A5%A8/%E0%A4%85%E0%A4%A7%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AF%E0%A4%83_%E0%A5%A8/%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%A3_%E0%A5%A9 Brahmana 3].</ref></blockquote>Of these names the first three occur in Ṛgveda, 5. 76. 3; <blockquote>उता यातं संगवे प्रातरह्नो मध्यंदिन उदिता सूर्यस्य । दिवा नक्तमवसा शंतमेन नेदानीं पीतिरश्विना ततान ॥३॥<ref>Rgveda, Mandala 5, [https://sa.wikisource.org/wiki/%E0%A4%8B%E0%A4%97%E0%A5%8D%E0%A4%B5%E0%A5%87%E0%A4%A6%E0%A4%83_%E0%A4%B8%E0%A5%82%E0%A4%95%E0%A5%8D%E0%A4%A4%E0%A4%82_%E0%A5%AB.%E0%A5%AD%E0%A5%AC Sukta 76].</ref></blockquote>and sāyam (evening) occurs in Ṛgveda, 8. 2. 20;  <blockquote>मो ष्वद्य दुर्हणावान्सायं करदारे अस्मत् । अश्रीर इव जामाता ॥२०॥<ref>Rgveda, Mandala 8, [https://sa.wikisource.org/wiki/%E0%A4%8B%E0%A4%97%E0%A5%8D%E0%A4%B5%E0%A5%87%E0%A4%A6%E0%A4%83_%E0%A4%B8%E0%A5%82%E0%A4%95%E0%A5%8D%E0%A4%A4%E0%A4%82_%E0%A5%AE.%E0%A5%A8 Sukta 2].</ref></blockquote>10. 146. 3, 40.<blockquote>उत गाव इवादन्त्युत वेश्मेव दृश्यते । उतो अरण्यानिः सायं शकटीरिव सर्जति ॥३॥<ref>Rgveda, Mandala 10, [https://sa.wikisource.org/wiki/%E0%A4%8B%E0%A4%97%E0%A5%8D%E0%A4%B5%E0%A5%87%E0%A4%A6%E0%A4%83_%E0%A4%B8%E0%A5%82%E0%A4%95%E0%A5%8D%E0%A4%A4%E0%A4%82_%E0%A5%A7%E0%A5%A6.%E0%A5%A7%E0%A5%AA%E0%A5%AC Sukta 146].</ref></blockquote>Kauṭilya (Arthaśāstra, 1.19), Dakṣa, and Kātyāyana divided the day and night each into eight parts.<blockquote>नालिकाभिरहरष्टधा रात्रिं च विभजेत् । छाया-प्रमाणेन वा ।। ०१.१९.०६ ।।<ref>Arthashastra, Adhikarana 1, [https://sa.wikisource.org/wiki/%E0%A4%85%E0%A4%B0%E0%A5%8D%E0%A4%A5%E0%A4%B6%E0%A4%BE%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A5%8D/%E0%A4%85%E0%A4%A7%E0%A4%BF%E0%A4%95%E0%A4%B0%E0%A4%A3%E0%A4%AE%E0%A5%8D_%E0%A5%A7/%E0%A4%85%E0%A4%A7%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AF%E0%A4%83_%E0%A5%A7%E0%A5%AF Adhyaya 19].</ref></blockquote>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).<ref name=":0">Taittiriya brahmana, Kanda 3, [https://sa.wikisource.org/wiki/%E0%A4%A4%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%B0%E0%A5%80%E0%A4%AF%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%A3%E0%A4%AE%E0%A5%8D_(%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%83)/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%83_%E0%A5%A9/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%95%E0%A4%83_%E0%A5%A7%E0%A5%A6 Prapathaka 10].</ref>
 
 
 
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). <blockquote>तदाहुर्यद्दर्शपूर्णमासयोरुपवसति न ह वा अव्रतस्य देवा हविरश्नन्ति तस्मादुपवसत्युत मे देवा हविरश्नीयुरिति। पूर्वां पौर्णमासीमुपवसेदिति पैङ्ग्यमुत्तरामिति कौषीतकं या पूर्वा पौर्णमासी साऽनुमतिर्योत्तरा सा राका। या पूर्वाऽमावास्या सा सिनीवाली योत्तरा सा कुहूः। यां पर्यस्तमियादभ्युदियादिति सा तिथिः। पूर्वां पौर्णमासीमुपवसेदनिर्ज्ञाय पुरस्तादमावास्यायां चन्द्रमसं यदुपैति यद्यजते तेन सोमं क्रीणन्ति तेनोत्तरामुपवसेदुत्तराणि ह वै सोमो यजते सोममनु दैवतमेतद्वै देवसोमं यच्चन्द्रमास्तस्मादुत्तरामुपवसेत्॥7.11॥ (32.10) (134)<ref>Aitareya brahmana, [https://sa.wikisource.org/wiki/%E0%A4%90%E0%A4%A4%E0%A4%B0%E0%A5%87%E0%A4%AF_%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%A3%E0%A4%AE%E0%A5%8D/%E0%A4%AA%E0%A4%9E%E0%A5%8D%E0%A4%9A%E0%A4%BF%E0%A4%95%E0%A4%BE_%E0%A5%AD_(%E0%A4%B8%E0%A4%AA%E0%A5%8D%E0%A4%A4%E0%A4%AE_%E0%A4%AA%E0%A4%9E%E0%A5%8D%E0%A4%9A%E0%A4%BF%E0%A4%95%E0%A4%BE) Panchika 7].</ref></blockquote>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.<blockquote>अमुं तैः  । अनवरुद्धो वा एतस्य संवत्सर इत्याहुः ।  य इतेतश्चातुर्मास्यानि संवत्सरं प्रयुङ्क्त इति  ।  एतावान्वै संवत्सरः  यच्चातुर्मास्यानि  ।  यदेते चातुर्मास्याः पशव आलभ्यन्ते  । प्रत्यक्षमेव तैः संवत्सरं यजमानोऽवरुन्धे ।  वि वा एष प्रजया पशुभिरृध्यते  ।  यः संवत्सरं प्रयुङ्क्ते  संवत्सरः सुवर्गो लोकः  २<ref>Taittiriya brahmana, Kanda 3, [https://sa.wikisource.org/wiki/%E0%A4%A4%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%B0%E0%A5%80%E0%A4%AF%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%A3%E0%A4%AE%E0%A5%8D_(%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%83)/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%83_%E0%A5%A9/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%95%E0%A4%83_%E0%A5%A6%E0%A5%AF Prapathaka 9].</ref></blockquote>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.
 
 
{| class="wikitable"
 
{| class="wikitable"
|+Relation between Vedic seasons and months<ref name=":1" />
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|+Relation between Vedic seasons and months
 
!Seasons
 
!Seasons
 
!Months
 
!Months
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12. Tapasya
 
12. Tapasya
 
|}
 
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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<ref>Aitareya brahmana, [https://sa.wikisource.org/wiki/%E0%A4%90%E0%A4%A4%E0%A4%B0%E0%A5%87%E0%A4%AF_%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%A3%E0%A4%AE%E0%A5%8D/%E0%A4%AA%E0%A4%9E%E0%A5%8D%E0%A4%9A%E0%A4%BF%E0%A4%95%E0%A4%BE_%E0%A5%A7_(%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%A5%E0%A4%AE_%E0%A4%AA%E0%A4%9E%E0%A5%8D%E0%A4%9A%E0%A4%BF%E0%A4%95%E0%A4%BE) Panchika 1].</ref>; Taittirīya-brāhmaṇa, 2. 7. 10<ref>Taittiriya brahmana, Kanda 2, [https://sa.wikisource.org/wiki/%E0%A4%A4%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%B0%E0%A5%80%E0%A4%AF%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%A3%E0%A4%AE%E0%A5%8D_(%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%83)/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%83_%E0%A5%A8/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%95%E0%A4%83_%E0%A5%A6%E0%A5%AD Prapathaka 7].</ref>)
 
 
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<ref>Taittiriya Samhita, Kanda 7, [https://sa.wikisource.org/wiki/%E0%A4%A4%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%B0%E0%A5%80%E0%A4%AF%E0%A4%B8%E0%A4%82%E0%A4%B9%E0%A4%BF%E0%A4%A4%E0%A4%BE(%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%B0%E0%A4%83)/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%AE%E0%A5%8D_%E0%A5%AD/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%95%E0%A4%83_%E0%A5%AB Prapathaka 5].</ref>) 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).<ref>Taittiriya Samhita, Kanda 7, [https://sa.wikisource.org/wiki/%E0%A4%A4%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%B0%E0%A5%80%E0%A4%AF%E0%A4%B8%E0%A4%82%E0%A4%B9%E0%A4%BF%E0%A4%A4%E0%A4%BE(%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%B0%E0%A4%83)/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%AE%E0%A5%8D_%E0%A5%AD/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%95%E0%A4%83_%E0%A5%AA Prapathaka 4].</ref>
 
 
They occur in the Saṅkhāyana and Tāṇḍya-brāhmaṇas, the Vedāṅga-jyautiṣa, and the Kalpa-sūtras.5
 
 
5Māgha is mentioned in Sāṅkhāyana-brāhmaṇa (= Kauṣītaki-brāhmaṇa) 19. 3;
 
 
Phālguna in Tāṇḍya-brāhmaṇa, 5. 9. 7–12;
 
 
and Srāvana, Māgha and Pauṣa in Ārca-jyautiṣa, 5, 6, 32, and 34 and Yājuṣa-jyautiṣa 5, 6, and 7;
 
 
and Mārgaśīrṣa and Śrāvana in Āśvalāyanagṛhyasūtra, 2. 3. 1 and 3. 5. 2 respectively.<blockquote>मार्गशीर्ष्यां प्रत्यवरोहणं चतुर्दश्याम् १</blockquote><blockquote>ओषधीनां प्रादुर्भावे श्रवणेन श्रावणस्य २<ref>[https://sa.wikisource.org/wiki/%E0%A4%86%E0%A4%B6%E0%A5%8D%E0%A4%B5%E0%A4%B2%E0%A4%BE%E0%A4%AF%E0%A4%A8%E0%A4%97%E0%A5%83%E0%A4%B9%E0%A5%8D%E0%A4%AF%E0%A4%B8%E0%A5%82%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A5%8D Ashvalayana Grhyasutra]</ref></blockquote>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. <blockquote>वेद मासो धृतव्रतो द्वादश प्रजावतः । वेदा य उपजायते ॥८॥<ref>Rgveda, Mandala 1, [https://sa.wikisource.org/wiki/%E0%A4%8B%E0%A4%97%E0%A5%8D%E0%A4%B5%E0%A5%87%E0%A4%A6%E0%A4%83_%E0%A4%B8%E0%A5%82%E0%A4%95%E0%A5%8D%E0%A4%A4%E0%A4%82_%E0%A5%A7.%E0%A5%A8%E0%A5%AB Sukta 25].</ref></blockquote>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<ref>Taittiriya Samhita, Kanda 5, [https://sa.wikisource.org/wiki/%E0%A4%A4%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%B0%E0%A5%80%E0%A4%AF%E0%A4%B8%E0%A4%82%E0%A4%B9%E0%A4%BF%E0%A4%A4%E0%A4%BE(%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%B0%E0%A4%83)/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%AE%E0%A5%8D_%E0%A5%AB/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%95%E0%A4%83_%E0%A5%AC Prapathaka 6]. </ref>) 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).<blockquote>1.4.14 अनुवाक 14 ऋतुग्रहाः</blockquote><blockquote>1 मधुश् च माधवश् च शुक्रश् च शुचिश् च नभश् च नभस्यश् चेषश् चोर्जश् च सहश् च सहस्यश् च तपश् च तपस्यश् च । उपयामगृहीतो ऽसि सꣳसर्पो ऽसि । अꣳहस्पत्याय त्वा ॥<ref>Taittiriya Samhita, Kanda 1, [https://sa.wikisource.org/wiki/%E0%A4%A4%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%B0%E0%A5%80%E0%A4%AF%E0%A4%B8%E0%A4%82%E0%A4%B9%E0%A4%BF%E0%A4%A4%E0%A4%BE(%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%B0%E0%A4%83)/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%AE%E0%A5%8D_%E0%A5%A7/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%95%E0%A4%83_%E0%A5%AA Prapathaka 4].</ref> </blockquote>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. <blockquote>ब्राह्मणासो अतिरात्रे न सोमे सरो न पूर्णमभितो वदन्तः । संवत्सरस्य तदहः परि ष्ठ यन्मण्डूकाः प्रावृषीणं बभूव ॥७॥</blockquote><blockquote>ब्राह्मणासः सोमिनो वाचमक्रत ब्रह्म कृण्वन्तः परिवत्सरीणम् । अध्वर्यवो घर्मिणः सिष्विदाना आविर्भवन्ति गुह्या न के चित् ॥८॥<ref>Rgveda, Mandala 7, [https://sa.wikisource.org/wiki/%E0%A4%8B%E0%A4%97%E0%A5%8D%E0%A4%B5%E0%A5%87%E0%A4%A6%E0%A4%83_%E0%A4%B8%E0%A5%82%E0%A4%95%E0%A5%8D%E0%A4%A4%E0%A4%82_%E0%A5%AD.%E0%A5%A7%E0%A5%A6%E0%A5%A9 Sukta 103].</ref></blockquote>The Taittirīya-saṃhitā (5. 5. 7. 1–3)<ref>Taittiriya Samhita, Kanda 5, [https://sa.wikisource.org/wiki/%E0%A4%A4%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%B0%E0%A5%80%E0%A4%AF%E0%A4%B8%E0%A4%82%E0%A4%B9%E0%A4%BF%E0%A4%A4%E0%A4%BE(%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%B0%E0%A4%83)/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%AE%E0%A5%8D_%E0%A5%AB/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%95%E0%A4%83_%E0%A5%AB Prapathaka 5].</ref>, 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. <blockquote>यम्यै यमसूम् । अथर्वभ्योऽवतोकाम् । संवत्सराय पर्यारिणीम् । परिवत्सरायाविजाताम् । इदावत्सरायापस्कद्वरीम् । इद्वत्सरायातीत्वरीम् । वत्सराय विजर्जराम् । सर्वंत्सराय पलिक्नीम् । वनाय वनपम् । अन्यतोऽरण्याय दावपम् १<ref>Taittiriya brahmana, Kanda 3, [https://sa.wikisource.org/wiki/%E0%A4%A4%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%B0%E0%A5%80%E0%A4%AF%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%A3%E0%A4%AE%E0%A5%8D_(%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%83)/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%83_%E0%A5%A9/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%95%E0%A4%83_%E0%A5%A6%E0%A5%AA Prapathaka 4].</ref></blockquote><blockquote>संवत्सरोऽसि परिवत्सरोऽसि । इदावत्सरोऽसीदुवत्सरोऽसि । इद्वत्सरोऽसि वत्सरोऽसि ।<ref name=":0" /></blockquote>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).<blockquote>1.1.28 असमीक्ष्यप्रवल्हितानि श्रूयन्ते द्वापरादाव् ऋषीणाम् एकदेशो दोषपतिर् इह चिन्ताम् आपेदे त्रिभिः सोमः पातव्यः समाप्तम् इव भवति...</blockquote>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).  
+
=== Lunar and Solar Year ===
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Just as there were Lunar months and Solar months, there was also the concept of a Lunar year and a Solar year. And in order to preserve correspondence between lunar and solar years, intercalary months were inserted at regular intervals. It is said that, the mention of the intercalary month is made in the Rgveda (1. 25. 8<ref>Rgveda, Mandala 1, [https://sa.wikisource.org/wiki/%E0%A4%8B%E0%A4%97%E0%A5%8D%E0%A4%B5%E0%A5%87%E0%A4%A6%E0%A4%83_%E0%A4%B8%E0%A5%82%E0%A4%95%E0%A5%8D%E0%A4%A4%E0%A4%82_%E0%A5%A7.%E0%A5%A8%E0%A5%AB Sukta 25].</ref>), but how it was arrived at and where in the scheme of months it was introduced in that time is not known.<ref name=":1" /> Prof K. S. Shukla mentions that there is evidence to show that to make the lunar year correspond to the solar year, 12 days were intercalated after every lunar year and one month was dropped after every 40 years.<ref name=":2" />
  
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.
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The Taittiriya samhita (5. 6. 7<ref>Taittiriya Samhita, Kanda 5, [https://sa.wikisource.org/wiki/%E0%A4%A4%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%B0%E0%A5%80%E0%A4%AF%E0%A4%B8%E0%A4%82%E0%A4%B9%E0%A4%BF%E0%A4%A4%E0%A4%BE(%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%B0%E0%A4%83)/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%AE%E0%A5%8D_%E0%A5%AB/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%95%E0%A4%83_%E0%A5%AC Prapathaka 6]. </ref>) refers to 12 as well as 13 months of a year and calls the thirteenth (intercalary) month by the names Samsarpa and Amhaspati (1. 4. 14).<blockquote>1 मधुश् च माधवश् च शुक्रश् च शुचिश् च नभश् च नभस्यश् चेषश् चोर्जश् च सहश् च सहस्यश् च तपश् च तपस्यश् च । उपयामगृहीतो ऽसि सꣳसर्पो ऽसि । अꣳहस्पत्याय त्वा ॥<ref>Taittiriya Samhita, Kanda 1, [https://sa.wikisource.org/wiki/%E0%A4%A4%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%B0%E0%A5%80%E0%A4%AF%E0%A4%B8%E0%A4%82%E0%A4%B9%E0%A4%BF%E0%A4%A4%E0%A4%BE(%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%B0%E0%A4%83)/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%AE%E0%A5%8D_%E0%A5%A7/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%95%E0%A4%83_%E0%A5%AA Prapathaka 4].</ref></blockquote><blockquote>''1 madhuś ca mādhavaś ca śukraś ca śuciś ca nabhaś ca nabhasyaś cēṣaś cōrjaś ca sahaś ca sahasyaś ca tapaś ca tapasyaś ca । upayāmagr̥hītō 'si saꣳsarpō 'si । aꣳhaspatyāya tvā ॥''</blockquote>While the Vajasaneyi samhita (7. 30; 22. 31) calls the intercalary month on one occasion by the name Amhasaspati and on another by the name malimlucha (22. 30). <blockquote>उपयामगृहीतो स्य् अꣳहसस्पतये त्वा ॥7. 30||<ref>Shukla Yajurveda, [https://sa.wikisource.org/wiki/%E0%A4%B6%E0%A5%81%E0%A4%95%E0%A5%8D%E0%A4%B2%E0%A4%AF%E0%A4%9C%E0%A5%81%E0%A4%B0%E0%A5%8D%E0%A4%B5%E0%A5%87%E0%A4%A6%E0%A4%83/%E0%A4%85%E0%A4%A7%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AF%E0%A4%83_%E0%A5%A6%E0%A5%AD Adhyaya 7].</ref> ''upayāmagr̥hītō sy aꣳhasaspatayē tvā ॥7. 30||''</blockquote><blockquote>तपस्याय स्वाहाꣳहसस्पतये स्वाहा ॥22. 31||<ref name=":4">Shukla Yajurveda, [https://sa.wikisource.org/wiki/%E0%A4%B6%E0%A5%81%E0%A4%95%E0%A5%8D%E0%A4%B2%E0%A4%AF%E0%A4%9C%E0%A5%81%E0%A4%B0%E0%A5%8D%E0%A4%B5%E0%A5%87%E0%A4%A6%E0%A4%83/%E0%A4%85%E0%A4%A7%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AF%E0%A4%83_%E0%A5%A8%E0%A5%A8 Adhyaya 22].</ref> ''tapasyāya svāhāꣳhasaspatayē svāhā ॥22. 31||''</blockquote><blockquote>मलिम्लुचाय स्वाहा ||22. 30||<ref name=":4" /> ''malimlucāya svāhā ||22. 30||''</blockquote>While, according to later works (Tantrasamgraha), Amhaspati referred to the synodic month with two samkrantis, the synodic month without any Samkranti, occurring before it, is called Samsarpa and the synodic month without any Samkranti occurring after it is called Adhimasa (intercalary month).<ref name=":1" />
  
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.
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Thus, a year sometimes contained 12 lunar months and sometimes 13 lunar months. By the time of the Vedanga jyotisha, insertion of an intercalary month after every 30 lunar months was prescribed (Yajusha jyotisha 37). Then, at a later stage the correspondence between the lunar and  solar year was established by evolving a cycle of five solar years with 62 lunar months. And this cycle was called a yuga.<ref name=":2" /> According to the Vedanga Jyotisha, an ordinary yuga consisted of 1,830 days. And an intercalary month was added at half the yuga and another at the end of the yuga.<ref name=":5">Subhash Kak (2000), [http://www.ece.lsu.edu/kak/ast.pdf Astonomy and its Role in Vedic Culture], Chapter 23 in Science and Civilization in India, Vol.1, The Dawn of Indian Civilization, Part 1, edited by G. P. Pande, Delhi: ICPR/Munshiram Manoharlal, pp. 507-524.</ref>
  
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.
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== Yuga in Vedic Literature ==
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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 Samvatsara, Parivatsara, Idavatsara, Anuvatsara and Idvatsara.<ref name=":1" />
  
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.
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Two of these names viz. Samvatsara and Parivatsara find mention in the Rgveda (7. 103. 7–8),<blockquote>ब्राह्मणासो अतिरात्रे न सोमे सरो न पूर्णमभितो वदन्तः । संवत्सरस्य तदहः परि ष्ठ यन्मण्डूकाः प्रावृषीणं बभूव ॥७॥</blockquote><blockquote>ब्राह्मणासः सोमिनो वाचमक्रत ब्रह्म कृण्वन्तः परिवत्सरीणम् । अध्वर्यवो घर्मिणः सिष्विदाना आविर्भवन्ति गुह्या न के चित् ॥८॥<ref>Rgveda, Mandala 7, [https://sa.wikisource.org/wiki/%E0%A4%8B%E0%A4%97%E0%A5%8D%E0%A4%B5%E0%A5%87%E0%A4%A6%E0%A4%83_%E0%A4%B8%E0%A5%82%E0%A4%95%E0%A5%8D%E0%A4%A4%E0%A4%82_%E0%A5%AD.%E0%A5%A7%E0%A5%A6%E0%A5%A9 Sukta 103].</ref></blockquote><blockquote>''brāhmaṇāsō atirātrē na sōmē sarō na pūrṇamabhitō vadantaḥ । saṁvatsarasya tadahaḥ pari ṣṭha yanmaṇḍūkāḥ prāvr̥ṣīṇaṁ babhūva ॥7॥''</blockquote><blockquote>''brāhmaṇāsaḥ sōminō vācamakrata brahma kr̥ṇvantaḥ parivatsarīṇam । adhvaryavō gharmiṇaḥ siṣvidānā āvirbhavanti guhyā na kē cit ॥8॥''</blockquote>While the Taittiriya samhita, the Vajasaneyi samhita and the Taittiriya brahmana (3. 4. 11 and 3. 10. 4) mention all the five names, with some alteration.<ref name=":1" />
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* The Taittiriya samhita (5. 5. 7. 3–4)<ref>Taittiriya Samhita, Kanda 5, [https://sa.wikisource.org/wiki/%E0%A4%A4%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%B0%E0%A5%80%E0%A4%AF%E0%A4%B8%E0%A4%82%E0%A4%B9%E0%A4%BF%E0%A4%A4%E0%A4%BE(%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%B0%E0%A4%83)/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%AE%E0%A5%8D_%E0%A5%AB/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%95%E0%A4%83_%E0%A5%AB Prapathaka 5].</ref> calls them Samvatsara, Parivatsara, Idavatsara, Iduvatsara and Vatsara.
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* The Vajasaneyi samhita (27. 45 and 30. 15) calls them Samvatsara, Parivatsara, Idavatsara, Idvatsara and Vatsara.
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<blockquote>संवत्सरो ऽसि परिवत्सरोऽसीदावत्सरो ऽसीद्वत्सरो ऽसि वत्सरो ऽसि ।27. 45|<ref>Shukla Yajurveda, [https://sa.wikisource.org/wiki/%E0%A4%B6%E0%A5%81%E0%A4%95%E0%A5%8D%E0%A4%B2%E0%A4%AF%E0%A4%9C%E0%A5%81%E0%A4%B0%E0%A5%8D%E0%A4%B5%E0%A5%87%E0%A4%A6%E0%A4%83/%E0%A4%85%E0%A4%A7%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AF%E0%A4%83_%E0%A5%A8%E0%A5%AD Adhyaya 27].</ref></blockquote><blockquote>यमाय यमसूम् अथर्वभ्यो ऽवतोकाꣳ संवत्सराय पर्यायिणीं परिवत्सरायाविजाताम् इदावत्सरायातीत्वरीम् इद्वत्सरायातिष्कद्वरीं वत्सराय विजर्जराꣳ संवत्सराय पलिक्नीम् ऋभुभ्यो ऽजिनसंधꣳ साध्येभ्यश् चर्मम्नम् ॥30. 15||<ref>Shukla Yajurveda, [https://sa.wikisource.org/wiki/%E0%A4%B6%E0%A5%81%E0%A4%95%E0%A5%8D%E0%A4%B2%E0%A4%AF%E0%A4%9C%E0%A5%81%E0%A4%B0%E0%A5%8D%E0%A4%B5%E0%A5%87%E0%A4%A6%E0%A4%83/%E0%A4%85%E0%A4%A7%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AF%E0%A4%83_%E0%A5%A9%E0%A5%A6 Adhyaya 30].</ref></blockquote><blockquote>''saṁvatsarō 'si parivatsarō'sīdāvatsarō 'sīdvatsarō 'si vatsarō 'si ।27. 45|''</blockquote><blockquote>''yamāya yamasūm atharvabhyō 'vatōkāꣳ saṁvatsarāya paryāyiṇīṁ parivatsarāyāvijātām idāvatsarāyātītvarīm idvatsarāyātiṣkadvarīṁ vatsarāya vijarjarāꣳ saṁvatsarāya paliknīm r̥bhubhyō 'jinasaṁdhaꣳ sādhyēbhyaś carmamnam ॥30. 15||''</blockquote>
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* The Taittiriya brahmana (3. 4. 11 and 3. 10. 4) calls them Samvatsara, Parivatsara, Idavatsara, Idvatsara and Vatsara.
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<blockquote>यम्यै यमसूम् । अथर्वभ्योऽवतोकाम् । संवत्सराय पर्यारिणीम् । परिवत्सरायाविजाताम् । इदावत्सरायापस्कद्वरीम् । इद्वत्सरायातीत्वरीम् । वत्सराय विजर्जराम् । सर्वंत्सराय पलिक्नीम् । वनाय वनपम् । अन्यतोऽरण्याय दावपम् १<ref>Taittiriya brahmana, Kanda 3, [https://sa.wikisource.org/wiki/%E0%A4%A4%E0%A5%88%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%B0%E0%A5%80%E0%A4%AF%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%A3%E0%A4%AE%E0%A5%8D_(%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%83)/%E0%A4%95%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%83_%E0%A5%A9/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%95%E0%A4%83_%E0%A5%A6%E0%A5%AA Prapathaka 4].</ref></blockquote><blockquote>संवत्सरोऽसि परिवत्सरोऽसि । इदावत्सरोऽसीदुवत्सरोऽसि । इद्वत्सरोऽसि वत्सरोऽसि ।<ref name=":0" /></blockquote><blockquote>''yamyai yamasūm । atharvabhyō'vatōkām । saṁvatsarāya paryāriṇīm । parivatsarāyāvijātām । idāvatsarāyāpaskadvarīm । idvatsarāyātītvarīm । vatsarāya vijarjarām । sarvaṁtsarāya paliknīm । vanāya vanapam । anyatō'raṇyāya dāvapam 1''</blockquote><blockquote>''saṁvatsarō'si parivatsarō'si । idāvatsarō'sīduvatsarō'si । idvatsarō'si vatsarō'si ।''</blockquote>There are allusions to yugas, meant as an age also, in the Vedas. The names Krta, Treta, Dvapara and Kali which are used in later astronomy as the names of longer yugas find mention in the vedic literature as well.<ref name=":5" /><ref name=":1" />
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* The Shadvimsha Brahmana (5.6) mentions the names Krta, Kharva, Dvapara and Pushya for the four ages that later came to be acknowledged by the names Krta, Treta, Dvapara and Kali.
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* In the Aitareya Brahmana (7.15.4) Kali, Dvapara, Treta and Krta are compared to a man lying down, moving, rising, and walking.<ref name=":5" />
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* It is also understood that the four yugas indicated different grades; each inferior to the preceding.<ref name=":1" /> In order from Krta to Kali, each yuga represents a decline in morality, piety, strength, knowledge, truthfulness and happiness.<ref name=":5" />
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* While Dvapara, as a unit of time, is found to be used in the Gopatha-brahmana (1. 1. 28).
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<blockquote>असमीक्ष्यप्रवल्हितानि श्रूयन्ते द्वापरादाव् ऋषीणाम् एकदेशो दोषपतिर् इह चिन्ताम् आपेदे त्रिभिः सोमः पातव्यः समाप्तम् इव भवति...<ref>Gopatha brahmana, [https://sa.wikisource.org/wiki/%E0%A4%97%E0%A5%8B%E0%A4%AA%E0%A4%A5_%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%A3%E0%A4%AE%E0%A5%8D/%E0%A4%AD%E0%A4%BE%E0%A4%97%E0%A4%83_%E0%A5%A7_(%E0%A4%AA%E0%A5%82%E0%A4%B0%E0%A5%8D%E0%A4%B5%E0%A4%AD%E0%A4%BE%E0%A4%97%E0%A4%83)/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AA%E0%A4%BE%E0%A4%A0%E0%A4%95%E0%A4%83_%E0%A5%A7 Prapathaka 1].</ref></blockquote><blockquote>''asamīkṣyapravalhitāni śrūyantē dvāparādāv r̥ṣīṇām ēkadēśō dōṣapatir iha cintām āpēdē tribhiḥ sōmaḥ pātavyaḥ samāptam iva bhavati...''</blockquote>
  
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<ref name=":1">Kolachana, Aditya & Mahesh, Kaluva & Ramasubramanian, K.. (2019). Main characteristics and achievements of ancient Indian astronomy in historical perspective. 10.1007/978-981-13-7326-8_24. </ref>
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== Reconciliations in the Vedanga Jyotisha ==
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The Vedic literature does have scattered references to many terms that help in understanding the division of time during the vedic times. However, it is the Vedanga jyotisha, the earliest available work dedicated to the field of Astronomy that mentions in detail about the divisions of time that finally evolved from the vedic period. Some facts of note from the Vedanga jyotisha are as follows:
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#According to the Vedanga Jyotisha, each yuga was taken to begin with the asterism Shravishtha and the synodic month of Magha, the solar month Tapas and the bright fortnight (parvan), and the northward course of the sun and the moon.<ref name=":5" />
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# The five-year yuga of the Vedanga Jyotisha contained 61 civil, 62 lunar, and 67 sidereal months wherein the year consisted of 366 civil days which were reckoned from sunrise to sunrise or 372 tithis.<ref name=":1" /><ref name=":5" /> 
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# Thus, after every thirty lunar months one intercalary month was inserted to bring about concordance between solar and lunar years. 
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# 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. 
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# There were six seasons of equal duration in every year, each new season beginning after every 61 days.<ref name=":1" /> 
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#The moon is conjoined with each asterism 67 times during a yuga. And the sun stays in each asterism for 13 5/9 days.<ref name=":5" />
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# Besides tithis and nakshatras, the yoga called Vyatipata was also in use.  
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It is also to be noted that the five-year yuga was taken to commence at the winter solstice occurring at the beginning of the first tithi of the Shukla paksha of the month Magha. 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 Vedanga Jyotisha was meant to serve for a long time. And this 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.<ref name=":1" />
  
 
== References ==
 
== References ==
 
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[[Category:Vedas]]
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[[Category:Vedangas]]
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[[Category:Shastras]]

Latest revision as of 08:02, 29 April 2020

Vaidika Kala Mapana (Samskrit: वैदिककालमापनम्) refers to the various divisions of time discussed in Vedic literature.

परिचयः ॥ Introduction

People of the vedic times engaged seriously in the performance of yajnas at specific times prescribed by the shastras. Thus, it was necessary to have accurate knowledge of the science of time so that the times prescribed for performing the various vedic yajnas could be correctly predicted well in advance. Thus, it was essential to study the natural divisions of time caused by the motion of the Sun and Moon, such as days, months, seasons, and years, with special attention to the study of the times of occurrence of new moons, full moons, equinoxes, and solstices that is included under the purview of the science of Astronomy. Therefore, Astronomy in the vedic times, was essentially the science of time-determination that was motivated by the need to fix time for the various yajnas that were performed at different times in different seasons.[1]

In fact, this is the definition of astronomy given in Vedanga Jyotisha, the earliest available work dealing exclusively with astronomy that gives all necessary information needed by the vedic hota to predict times for the vedic yajnas and other observances.[1][2]

However, the Vedic literature also has references to astronomical events and observations. For eg. The Kaushitaki brahmana states that the year ended with the full moon at the Purva Phalguni.[2]

मुखम् वा एतत् संवत्सरस्य यत् फाल्गुनी पौर्णमासी । मुखम् उत्तरे फल्गू । पुच्छम् पूर्वे । तद् यथा प्रवृत्तस्य अन्तौ समेतौ स्याताम् । एवम् एव एतौ संवत्सरस्य अन्तौ समेतौ ।5.1[3]

mukham vā etat saṁvatsarasya yat phālgunī paurṇamāsī । mukham uttare phalgū । puccham pūrve । tad yathā pravr̥ttasya antau sametau syātām । evam eva etau saṁvatsarasya antau sametau ।5.1

Thus, ancient Indian astronomy may be classified into two main categories:

  1. Vedic astronomy
  2. Post-vedic astronomy.

Vedic astronomy is the astronomy of the vedic period, i.e., the astronomy found in the vedic samhitas, brahmanas and allied literature.[1] And that is elaborated in this article below.

Day in Vedic Literature

The day, in vedic literature was called Vasara (वासरः) or ahan (अहन्). And was reckoned from sunrise to sunrise. The variability of its length was known. For, the Rgveda invoking Somaraja says,

“O Somaraja, prolong thou our lives just as the Sun increases the length of the days.”[1]

सोम राजन्प्र ण आयूंषि तारीरहानीव सूर्यो वासराणि ॥७॥[4]

soma rājanpra ṇa āyūṁṣi tārīrahānīva sūryo vāsarāṇi ॥7॥

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.[1]

तदाहुर्यद्दर्शपूर्णमासयोरुपवसति न ह वा अव्रतस्य देवा हविरश्नन्ति तस्मादुपवसत्युत मे देवा हविरश्नीयुरिति। पूर्वां पौर्णमासीमुपवसेदिति पैङ्ग्यमुत्तरामिति कौषीतकं या पूर्वा पौर्णमासी साऽनुमतिर्योत्तरा सा राका। या पूर्वाऽमावास्या सा सिनीवाली योत्तरा सा कुहूः। यां पर्यस्तमियादभ्युदियादिति सा तिथिः.....॥7.11॥ (Aitareya brahmana 32.10)[5]

tadāhuryaddarśapūrṇamāsayorupavasati na ha vā avratasya devā haviraśnanti tasmādupavasatyuta me devā haviraśnīyuriti। pūrvāṁ paurṇamāsīmupavasediti paiṅgyamuttarāmiti kauṣītakaṁ yā pūrvā paurṇamāsī sā'numatiryottarā sā rākā। yā pūrvā'māvāsyā sā sinīvālī yottarā sā kuhūḥ। yāṁ paryastamiyādabhyudiyāditi sā tithiḥ.....॥7.11॥

However, the term tithi in the sense in which it is used now occurs in the Vedanga Jyotisha. It does not occur in the vedic samhitas and brahmanas, but there are reasons to believe that tithis were used even in those times.[1]

Divisions of a Day[1]

The duration of daylight, reckoned from sunrise to sunset, was variously divided into,

  1. Two parts called Purvahna (forenoon) and Aparahna (afternoon)
  2. Three parts called Purvahna, Madhyahna, and Aparahna.
  3. Four parts called Purvahna, Madhyahna, Aparahna and Sayahna
  4. Five parts called Pratah, Sangava, Madhyahna, Aparahna, and Sayahna

The names of these five parts occur together in the Shatapatha brahmana,

आदित्यस्त्वेव सर्व ऋतवः । यदैवोदेत्यथ वसन्तो यदा संगवोऽथ ग्रीष्मो यदा मध्यन्दिनोऽथ वर्षा यदापराह्णोऽथ शरद्यदैवास्तमेत्यथ हेमन्तस्तस्मादु मध्यंन्दिन एवादधीत तर्हि ह्येषोऽस्य लोकस्य नेदिष्ठं भवति तन्नेदिष्ठादेवैनमेतन्मध्यान्निर्मिमीते - २.२.३.९[6]

ādityastveva sarva r̥tavaḥ । yadaivodetyatha vasanto yadā saṁgavo'tha grīṣmo yadā madhyandino'tha varṣā yadāparāhṇo'tha śaradyadaivāstametyatha hemantastasmādu madhyaṁndina evādadhīta tarhi hyeṣo'sya lokasya nediṣṭhaṁ bhavati tannediṣṭhādevainametanmadhyānnirmimīte

While the first three words ie. Pratah, Sangava and Madhyahna occur in Rgveda (Mandala 5),

उता यातं संगवे प्रातरह्नो मध्यंदिन उदिता सूर्यस्य । दिवा नक्तमवसा शंतमेन नेदानीं पीतिरश्विना ततान ॥३॥[7]

utā yātaṁ saṁgave prātarahno madhyaṁdina uditā sūryasya । divā naktamavasā śaṁtamena nedānīṁ pītiraśvinā tatāna ॥3॥

The term Saya (evening) occurs in Rgveda (Mandala 8 and 10),

मो ष्वद्य दुर्हणावान्सायं करदारे अस्मत् । अश्रीर इव जामाता ॥२०॥[8]

उत गाव इवादन्त्युत वेश्मेव दृश्यते । उतो अरण्यानिः सायं शकटीरिव सर्जति ॥३॥[9]

mo ṣvadya durhaṇāvānsāyaṁ karadāre asmat । aśrīra iva jāmātā ॥20॥

uta gāva ivādantyuta veśmeva dr̥śyate । uto araṇyāniḥ sāyaṁ śakaṭīriva sarjati ॥3॥

The days and nights were also divided into 15 parts each called as muhurta. According to Taittiriya brahmana (3. 10. 1. 1–3), the muhurtas falling during the days and nights of the shukla and krshna pakshas (fortnights) were respectively given specific names.[10]

The Taittiriya brahmana (3. 10. 1. 1–3; 3. 10. 10. 2)[10] also assigns specific names to the fifteen days and nights of the shukla as well as krshna pakshas.

However, by the time of the Kautiliya Arthashastra, the day and night came to be divided into eight parts each.

नालिकाभिरहरष्टधा रात्रिं च विभजेत् । छाया-प्रमाणेन वा ।। ०१.१९.०६ ।।[11]

nālikābhiraharaṣṭadhā rātriṁ ca vibhajet । chāyā-pramāṇena vā ।। 01.19.06 ।।

Week in Vedic Literature

In vedic literature, six days were taken to form a week that was called a Shadaha. 5 shadahas made a month and 12 months, a year. As to the names of the six days of a shadaha, there is no reference in the vedic literature. However, this six-day week was later replaced by the present seven day week (called saptaha) which had attained popularity and was in general use at the time of composition of the Atharva Jyotisha - a work on Jyotisha belonging to the later vedic period.[1][12]

Months in Vedic Literature

In vedic astronomy, months were lunar or synodic and were measured from full moon to full moon and also from new moon to new moon[2] as mentioned in the Taittiriya samhita (7.5.6.1)[1][13] Originally, these months were named as Chaitra etc. based on the nakshatras occupied by the Moon at the time of full moon. And these names do not occur in the early samhitas and brahmanas. They are known to occur in Taittiriya samhita, Shankhayana/Kaushitaki, and Tandya brahmanas, Ashvalayana grhyasutra, Archa and Yajusha jyotisha. Some of the occurrences are as follows:[1]

  • The terms Phalguni purnamasi, Chitra purnamasi, etc. are found in the Taittiriya samhita (7. 4. 8).[14]
  • The term Magha is mentioned in Shankhayana/Kaushitaki brahmana (19. 3)

स वै माघस्य अमावास्यायाम् उपवसत्य् उदन्न् आवर्त्स्यन् ।[15]sa vai māghasya amāvāsyāyām upavasaty udann āvartsyan ।

  • The term Phalguna occurs in Tandya brahmana (5. 9. 7–12)
  • The terms Margashirsha and Shravana occurs in the Ashvalayana grhyasutra 2. 3. 1 and 3. 5. 2 respectively.

मार्गशीर्ष्यां प्रत्यवरोहणं चतुर्दश्याम् १ | mārgaśīrṣyāṁ pratyavarohaṇaṁ caturdaśyām 1 |

ओषधीनां प्रादुर्भावे श्रवणेन श्रावणस्य २ |[16] oṣadhīnāṁ prādurbhāve śravaṇena śrāvaṇasya 2 |

  • While the terms Shravana, Magha and Pausha also occur in Archa jyotisha (5, 6, 32 and 34) and Yajusha jyotisha (5, 6, and 7)

However, in due course the lunar months 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 Chaitra or Madhu; that in which the Sun entered the sign Taurus was called Vaishakha or Madhava; and so on. And the lunar month in which the Sun did not enter a new sign was treated as an intercalary month.

Twelve such lunar months constituted a lunar year.[1]

Year in Vedic Literature

In the vedic literature, the year, generally called by the terms sama, vatsara, and hayana, was measured from one winter solstice to the next. However, in due course, it was used in the sense of a sidereal year.[1][2] In fact, the Kaushitaki brahmana (19.3) gives an interesting account of how the year-long yajna commenced at one winter solstice and continued until the next. It says, “On the new moon of Magha, the Sun rests, about to turn northwards. The hotas also rest, about to begin with the introductory Atiratra. Thus, for the first time, the hotas obtain the Sun. On him, they lay hold with the Chaturvimsha rite; that is why the laying hold rite has that name. The Sun then goes north for six months, while the hotas follow him with six day rites in continuation. Having gone north for six months, the Sun stands still, about to turn southwards. The hotas also rest, about to begin with the Vishnuvanta (summer solstice) day. Thus, for the second time, they obtain the Sun. The Sun then goes south for six months and the hotas follow him with six day rites in reverse order. Having gone south for six months, the Sun stands still, being about to turn north and the hotas also rest, about to begin with the Mahavrata day. Thus, they obtain the Sun for the third time."[1][15]

In this context, it is worth observing that the Taittiriya brahmana (3. 9. 22) calls the year “the day of the deities” who are supposed to reside at the north pole.[1]

एकं वा एतद्देवानामहः  । यत्संवत्सरः  ।[17] ekaṁ vā etaddevānāmahaḥ । yatsaṁvatsaraḥ ।

Seasons[1]

The year of vedic astronomy seems to have been a seasonal or tropical one. Therefore, in the early stages, the names of the seasons were used as synonyms of a year. The year consisted of six seasons and each season lasted for a duration of two solar months. The two solar months commencing with the winter solstice were called Shishira; the next two months, Vasanta; and so on. According to the Aitareya brahmana (1.1) and Taittiriya brahmana (2.7.10), sometimes Shishira and Hemanta were treated as one season and the number of seasons was taken as five.

द्वादश मासाः पञ्चर्तवो हेमन्तशिशिरयोः समासेन तावान्संवत्सरः |[18]dvādaśa māsāḥ pañcartavō hēmantaśiśirayōḥ samāsēna tāvānsaṁvatsaraḥ |

पञ्च वा ऋतवः संवत्सरः । ऋतुष्वेव संवत्सरे प्रतितिष्ठति ।[19]pañca vā r̥tavaḥ saṁvatsaraḥ । r̥tuṣvēva saṁvatsarē pratitiṣṭhati ।

The relation between the seasons and months was as follows:

Relation between Vedic seasons and months
Seasons Months
  1. Vasanta (Spring)
  1. Madhu
  2. Madhava
2. Grishma (Summer) 3. Shukra

4. Shuchi

3. Varsha (Rainy) 5. Nabhas

6. Nabhasya

4. Sharada (Autumn) 7. Isha

8. Urja

5. Hemanta (Winter) 9. Sahas

10. Sahasya

6. Shishira (Chilly Winter) 11. Tapas

12. Tapasya

Lunar and Solar Year

Just as there were Lunar months and Solar months, there was also the concept of a Lunar year and a Solar year. And in order to preserve correspondence between lunar and solar years, intercalary months were inserted at regular intervals. It is said that, the mention of the intercalary month is made in the Rgveda (1. 25. 8[20]), but how it was arrived at and where in the scheme of months it was introduced in that time is not known.[1] Prof K. S. Shukla mentions that there is evidence to show that to make the lunar year correspond to the solar year, 12 days were intercalated after every lunar year and one month was dropped after every 40 years.[2]

The Taittiriya samhita (5. 6. 7[21]) refers to 12 as well as 13 months of a year and calls the thirteenth (intercalary) month by the names Samsarpa and Amhaspati (1. 4. 14).

1 मधुश् च माधवश् च शुक्रश् च शुचिश् च नभश् च नभस्यश् चेषश् चोर्जश् च सहश् च सहस्यश् च तपश् च तपस्यश् च । उपयामगृहीतो ऽसि सꣳसर्पो ऽसि । अꣳहस्पत्याय त्वा ॥[22]

1 madhuś ca mādhavaś ca śukraś ca śuciś ca nabhaś ca nabhasyaś cēṣaś cōrjaś ca sahaś ca sahasyaś ca tapaś ca tapasyaś ca । upayāmagr̥hītō 'si saꣳsarpō 'si । aꣳhaspatyāya tvā ॥

While the Vajasaneyi samhita (7. 30; 22. 31) calls the intercalary month on one occasion by the name Amhasaspati and on another by the name malimlucha (22. 30).

उपयामगृहीतो स्य् अꣳहसस्पतये त्वा ॥7. 30||[23] upayāmagr̥hītō sy aꣳhasaspatayē tvā ॥7. 30||

तपस्याय स्वाहाꣳहसस्पतये स्वाहा ॥22. 31||[24] tapasyāya svāhāꣳhasaspatayē svāhā ॥22. 31||

मलिम्लुचाय स्वाहा ||22. 30||[24] malimlucāya svāhā ||22. 30||

While, according to later works (Tantrasamgraha), Amhaspati referred to the synodic month with two samkrantis, the synodic month without any Samkranti, occurring before it, is called Samsarpa and the synodic month without any Samkranti occurring after it is called Adhimasa (intercalary month).[1]

Thus, a year sometimes contained 12 lunar months and sometimes 13 lunar months. By the time of the Vedanga jyotisha, insertion of an intercalary month after every 30 lunar months was prescribed (Yajusha jyotisha 37). Then, at a later stage the correspondence between the lunar and solar year was established by evolving a cycle of five solar years with 62 lunar months. And this cycle was called a yuga.[2] According to the Vedanga Jyotisha, an ordinary yuga consisted of 1,830 days. And an intercalary month was added at half the yuga and another at the end of the yuga.[12]

Yuga in Vedic Literature

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 Samvatsara, Parivatsara, Idavatsara, Anuvatsara and Idvatsara.[1]

Two of these names viz. Samvatsara and Parivatsara find mention in the Rgveda (7. 103. 7–8),

ब्राह्मणासो अतिरात्रे न सोमे सरो न पूर्णमभितो वदन्तः । संवत्सरस्य तदहः परि ष्ठ यन्मण्डूकाः प्रावृषीणं बभूव ॥७॥

ब्राह्मणासः सोमिनो वाचमक्रत ब्रह्म कृण्वन्तः परिवत्सरीणम् । अध्वर्यवो घर्मिणः सिष्विदाना आविर्भवन्ति गुह्या न के चित् ॥८॥[25]

brāhmaṇāsō atirātrē na sōmē sarō na pūrṇamabhitō vadantaḥ । saṁvatsarasya tadahaḥ pari ṣṭha yanmaṇḍūkāḥ prāvr̥ṣīṇaṁ babhūva ॥7॥

brāhmaṇāsaḥ sōminō vācamakrata brahma kr̥ṇvantaḥ parivatsarīṇam । adhvaryavō gharmiṇaḥ siṣvidānā āvirbhavanti guhyā na kē cit ॥8॥

While the Taittiriya samhita, the Vajasaneyi samhita and the Taittiriya brahmana (3. 4. 11 and 3. 10. 4) mention all the five names, with some alteration.[1]

  • The Taittiriya samhita (5. 5. 7. 3–4)[26] calls them Samvatsara, Parivatsara, Idavatsara, Iduvatsara and Vatsara.
  • The Vajasaneyi samhita (27. 45 and 30. 15) calls them Samvatsara, Parivatsara, Idavatsara, Idvatsara and Vatsara.

संवत्सरो ऽसि परिवत्सरोऽसीदावत्सरो ऽसीद्वत्सरो ऽसि वत्सरो ऽसि ।27. 45|[27]

यमाय यमसूम् अथर्वभ्यो ऽवतोकाꣳ संवत्सराय पर्यायिणीं परिवत्सरायाविजाताम् इदावत्सरायातीत्वरीम् इद्वत्सरायातिष्कद्वरीं वत्सराय विजर्जराꣳ संवत्सराय पलिक्नीम् ऋभुभ्यो ऽजिनसंधꣳ साध्येभ्यश् चर्मम्नम् ॥30. 15||[28]

saṁvatsarō 'si parivatsarō'sīdāvatsarō 'sīdvatsarō 'si vatsarō 'si ।27. 45|

yamāya yamasūm atharvabhyō 'vatōkāꣳ saṁvatsarāya paryāyiṇīṁ parivatsarāyāvijātām idāvatsarāyātītvarīm idvatsarāyātiṣkadvarīṁ vatsarāya vijarjarāꣳ saṁvatsarāya paliknīm r̥bhubhyō 'jinasaṁdhaꣳ sādhyēbhyaś carmamnam ॥30. 15||

  • The Taittiriya brahmana (3. 4. 11 and 3. 10. 4) calls them Samvatsara, Parivatsara, Idavatsara, Idvatsara and Vatsara.

यम्यै यमसूम् । अथर्वभ्योऽवतोकाम् । संवत्सराय पर्यारिणीम् । परिवत्सरायाविजाताम् । इदावत्सरायापस्कद्वरीम् । इद्वत्सरायातीत्वरीम् । वत्सराय विजर्जराम् । सर्वंत्सराय पलिक्नीम् । वनाय वनपम् । अन्यतोऽरण्याय दावपम् १[29]

संवत्सरोऽसि परिवत्सरोऽसि । इदावत्सरोऽसीदुवत्सरोऽसि । इद्वत्सरोऽसि वत्सरोऽसि ।[10]

yamyai yamasūm । atharvabhyō'vatōkām । saṁvatsarāya paryāriṇīm । parivatsarāyāvijātām । idāvatsarāyāpaskadvarīm । idvatsarāyātītvarīm । vatsarāya vijarjarām । sarvaṁtsarāya paliknīm । vanāya vanapam । anyatō'raṇyāya dāvapam 1

saṁvatsarō'si parivatsarō'si । idāvatsarō'sīduvatsarō'si । idvatsarō'si vatsarō'si ।

There are allusions to yugas, meant as an age also, in the Vedas. The names Krta, Treta, Dvapara and Kali which are used in later astronomy as the names of longer yugas find mention in the vedic literature as well.[12][1]

  • The Shadvimsha Brahmana (5.6) mentions the names Krta, Kharva, Dvapara and Pushya for the four ages that later came to be acknowledged by the names Krta, Treta, Dvapara and Kali.
  • In the Aitareya Brahmana (7.15.4) Kali, Dvapara, Treta and Krta are compared to a man lying down, moving, rising, and walking.[12]
  • It is also understood that the four yugas indicated different grades; each inferior to the preceding.[1] In order from Krta to Kali, each yuga represents a decline in morality, piety, strength, knowledge, truthfulness and happiness.[12]
  • While Dvapara, as a unit of time, is found to be used in the Gopatha-brahmana (1. 1. 28).

असमीक्ष्यप्रवल्हितानि श्रूयन्ते द्वापरादाव् ऋषीणाम् एकदेशो दोषपतिर् इह चिन्ताम् आपेदे त्रिभिः सोमः पातव्यः समाप्तम् इव भवति...[30]

asamīkṣyapravalhitāni śrūyantē dvāparādāv r̥ṣīṇām ēkadēśō dōṣapatir iha cintām āpēdē tribhiḥ sōmaḥ pātavyaḥ samāptam iva bhavati...

Reconciliations in the Vedanga Jyotisha

The Vedic literature does have scattered references to many terms that help in understanding the division of time during the vedic times. However, it is the Vedanga jyotisha, the earliest available work dedicated to the field of Astronomy that mentions in detail about the divisions of time that finally evolved from the vedic period. Some facts of note from the Vedanga jyotisha are as follows:

  1. According to the Vedanga Jyotisha, each yuga was taken to begin with the asterism Shravishtha and the synodic month of Magha, the solar month Tapas and the bright fortnight (parvan), and the northward course of the sun and the moon.[12]
  2. The five-year yuga of the Vedanga Jyotisha contained 61 civil, 62 lunar, and 67 sidereal months wherein the year consisted of 366 civil days which were reckoned from sunrise to sunrise or 372 tithis.[1][12]
  3. Thus, after every thirty lunar months one intercalary month was inserted to bring about concordance between solar and lunar years.
  4. 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.
  5. There were six seasons of equal duration in every year, each new season beginning after every 61 days.[1]
  6. The moon is conjoined with each asterism 67 times during a yuga. And the sun stays in each asterism for 13 5/9 days.[12]
  7. Besides tithis and nakshatras, the yoga called Vyatipata was also in use.

It is also to be noted that the five-year yuga was taken to commence at the winter solstice occurring at the beginning of the first tithi of the Shukla paksha of the month Magha. 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 Vedanga Jyotisha was meant to serve for a long time. And this 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.[1]

References

  1. 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.20 1.21 1.22 1.23 Kolachana, Aditya & Mahesh, Kaluva & Ramasubramanian, K.. (2019). Main characteristics and achievements of ancient Indian astronomy in historical perspective. 10.1007/978-981-13-7326-8_24.
  2. 2.0 2.1 2.2 2.3 2.4 2.5 K. S. Shukla, Astronomy in ancient and medieval India, Indian Journal of History of Science, Vol.4, Nos. 1-2 (1969), pp.99-106.
  3. Kaushitaki brahmana, Adhyaya 5.
  4. Rgveda, Mandala 8, Sukta 48.
  5. Aitareya brahmana, Panchika 7.
  6. Shatapatha brahmana, Kanda 2, Adhyaya 2, Brahmana 3.
  7. Rgveda, Mandala 5, Sukta 76.
  8. Rgveda, Mandala 8, Sukta 2.
  9. Rgveda, Mandala 10, Sukta 146.
  10. 10.0 10.1 10.2 Taittiriya brahmana, Kanda 3, Prapathaka 10.
  11. Arthashastra, Adhikarana 1, Adhyaya 19.
  12. 12.0 12.1 12.2 12.3 12.4 12.5 12.6 12.7 Subhash Kak (2000), Astonomy and its Role in Vedic Culture, Chapter 23 in Science and Civilization in India, Vol.1, The Dawn of Indian Civilization, Part 1, edited by G. P. Pande, Delhi: ICPR/Munshiram Manoharlal, pp. 507-524.
  13. Taittiriya Samhita, Kanda 7, Prapathaka 5.
  14. Taittiriya Samhita, Kanda 7, Prapathaka 4.
  15. 15.0 15.1 Kaushitaki brahmana, Adhyaya 19.
  16. Ashvalayana Grhyasutra
  17. Taittiriya brahmana, Kanda 3, Prapathaka 9.
  18. Aitareya brahmana, Panchika 1.
  19. Taittiriya brahmana, Kanda 2, Prapathaka 7.
  20. Rgveda, Mandala 1, Sukta 25.
  21. Taittiriya Samhita, Kanda 5, Prapathaka 6.
  22. Taittiriya Samhita, Kanda 1, Prapathaka 4.
  23. Shukla Yajurveda, Adhyaya 7.
  24. 24.0 24.1 Shukla Yajurveda, Adhyaya 22.
  25. Rgveda, Mandala 7, Sukta 103.
  26. Taittiriya Samhita, Kanda 5, Prapathaka 5.
  27. Shukla Yajurveda, Adhyaya 27.
  28. Shukla Yajurveda, Adhyaya 30.
  29. Taittiriya brahmana, Kanda 3, Prapathaka 4.
  30. Gopatha brahmana, Prapathaka 1.