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== Week in Vedic Literature ==

== 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.<ref name=":1" />

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" />

== Months in Vedic Literature ==

== Months in Vedic Literature ==

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>  

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>  

== Yuga in Vedic Literature<ref name=":1" /> ==

== 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.

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" />

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.  

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" />

* 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.  

* 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.  

* The Vajasaneyi samhita (27. 45 and 30. 15) calls them Samvatsara, Parivatsara, Idavatsara, Idvatsara and Vatsara.  

* The Vajasaneyi samhita (27. 45 and 30. 15) calls them Samvatsara, Parivatsara, Idavatsara, Idvatsara and Vatsara.  

<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>

<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>

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

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

<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>The names Krta, Treta, Dvapara and Kali which are used in later astronomy as the names of longer yugas are also used in the vedic literature. However they indicated different grades; each inferior to the preceding. But Dvapara, as a unit of time, is found to be used in the Gopatha-brahmana (1. 1. 28). <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>

<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" />

* 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" />

* 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" />

* While Dvapara, as a unit of time, is found to be used in the Gopatha-brahmana (1. 1. 28).  

<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>

== Reconciliations in the Vedanga Jyotisha ==

== 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:

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:

# 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.   

# After every thirty lunar months one intercalary month was inserted to bring about concordance between solar and lunar years.   

# 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" />  

# Thus, 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.   

# 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.<ref name=":1" />   

# There were six seasons of equal duration in every year, each new season beginning after every 61 days.<ref name=":1" />