Kala (कालः) - Revision history

AnuragV at 19:12, 13 December 2023

2023-12-13T19:12:16Z

Prthvi: added video

2021-05-30T12:05:31Z

added video

Prthvi: added video

2021-05-30T09:46:06Z

added video

Fordharma: /* Current Kala */

2020-08-28T14:28:54Z

Current Kala

Fordharma: /* Current Kala */

2020-08-28T14:16:59Z

Current Kala

Ckanak93: /* Microcosmic Time Scale */ Adding content with reference

2020-04-16T12:38:14Z

Microcosmic Time Scale: Adding content with reference

Ckanak93: /* Yuga in Vedas */ Adding content with reference

2020-03-20T18:55:52Z

Yuga in Vedas: Adding content with reference

Ckanak93: /* Yuga System */ Adding content with reference

2020-03-20T16:46:29Z

Yuga System: Adding content with reference

Ckanak93: Added content with reference

2020-03-20T16:24:35Z

Added content with reference

Fordharma: /* कालमापनयन्त्राणि ॥ Instruments to measure time */

2019-06-07T04:38:55Z

कालमापनयन्त्राणि ॥ Instruments to measure time

← Older revision		Revision as of 19:12, 13 December 2023
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 |container=frame
 |description=Talk on the Theory of Four Yuga in Vedas
 }}
 == कालः सृष्टिः च ॥ Kala and Creation ==

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 Many of astronomers of ancient days had different versions of what time period constituted the yugas on the macroscopic scale of time.
+{{#evu:https://www.youtube.com/watch?v=798qvcUdLvA&feature=youtu.be
 == कालः सृष्टिः च ॥ Kala and Creation ==
 Kala as related to the Universe refers to the theories of creation, the cosmogenesis on the macroscopic scale.

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 '''Present Chaturyuga''' = Kaliyuga (4th of the Chaturyugas)
-The later time points in Kali yuga are calculated in our calendars and Panchangas. Based on the periodical natural observations such as the sunrise and sunset, new moon, full moon, and seasons, a working scale of time - consisting of day, fortnight, month and year - has been used from early times. Accurate prediction of the ending moment of tithis, sankramana (transit of sun across rasis), eclipses etc seem to have contributed in a big way to the growth of mathematics in India.
+The later time points in Kali yuga are calculated in our calendars and Panchangas. Based on the periodical natural observations such as the sunrise and sunset, new moon, full moon, and seasons, a working scale of time commonly reckoned as the present [[Kalamana (कालमानम्)]] - consisting of day, fortnight, month and year - has been used from early times. Accurate prediction of the ending moment of tithis, sankramana (transit of sun across rasis), nakshatra and rashi transits, eclipses which have been discussed in established astronomical texts show, in a big way, the growth of mathematics in India.
 === Importance of Astronomy ===

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 Currently we are in the Vaivasvata Manvantara, the seventh Manvantara of the Svetavaraha Kalpa, which is at the beginning of the second Parardha, or the fifty-first year of the current 100 year cycle of Brahma.<blockquote>अयं तु कथितः कल्पो द्वितीयस्यापि भारत । वाराह इति विख्यातो यत्रासीत् शूकरो हरिः ॥ ३६ ॥ (Bhag. Pura. 3.11.36)<ref name=":3" /></blockquote><blockquote>ayaṁ tu kathitaḥ kalpō dvitīyasyāpi bhārata । vārāha iti vikhyātō yatrāsīt śūkarō hariḥ ॥ 36 ॥ (Bhag. Pura. 3.11.36)</blockquote>Sumamary : The present Kalpa of the second Parardha is known as Varaha (pertaining to the boar) as Hari assumed the boar-form (शूकरः) in this Kalpa.
-Present Kalpa = Svetavaraha Kalpa (51 year of the 100 years of Brahma Ayuh)
+'''Present Kalpa''' = Svetavaraha Kalpa (51 year of the 100 years of Brahma Ayuh)
-Present Manvantara = Vaivasvata Manvantara (seventh of the 14 Manvantaras)
+'''Present Manvantara''' = Vaivasvata Manvantara (seventh of the 14 Manvantaras)
-Present Mahayuga = 28th (of the 71 Mahayugas)
+'''Present Mahayuga''' = 28th (of the 71 Mahayugas)
-Present Chaturyuga = Kaliyuga (4th of the Chaturyugas)
+'''Present Chaturyuga''' = Kaliyuga (4th of the Chaturyugas)
-The later time points in Kali yuga are calculated in our calendars and Panchangas. Accurate prediction of the ending moment of tithis, sankramana (transit of sun across rasis), eclipses etc seem to have contributed in a big way to the growth of mathematics in India.
+The later time points in Kali yuga are calculated in our calendars and Panchangas. Based on the periodical natural observations such as the sunrise and sunset, new moon, full moon, and seasons, a working scale of time - consisting of day, fortnight, month and year - has been used from early times. Accurate prediction of the ending moment of tithis, sankramana (transit of sun across rasis), eclipses etc seem to have contributed in a big way to the growth of mathematics in India.
 === Importance of Astronomy ===
-Vedanga Jyotisha (Yajurveda recension) clearly indicates how Jyotisha forms a part of Veda apart from highlighting the need for an accurate calendar system.<blockquote>वेदा हि यज्ञार्थमभिप्रवृत्ताः कालानुपूर्व्या विहिताश्च यज्ञाः । तस्मादिदं कालविधामशास्त्रं यो ज्योतिषं वेद स वेद यज्ञम् ॥ (Veda. Jyot. Yaju. 3)<ref name=":8" /></blockquote><blockquote>vēdā hi yajñārthamabhipravr̥ttāḥ kālānupūrvyā vihitāśca yajñāḥ । tasmādidaṁ kālavidhāmaśāstraṁ yō jyōtiṣaṁ vēda sa vēda yajñam ॥ (Veda. Jyot. Yaju. 3)</blockquote>Summary : The Vedas have indeed been revealed for the sake of performance of the Yajnas. But these yajnas are dependent on (various segments of) time. Therefor, only he who knows the lore of time. viz., Jyotisha, understands the processes of Yajnas.<ref name=":8" />
+[[Vedanga Jyotisha (वेदाङ्गज्योतिषम्)|Vedanga Jyotisha]] (Yajurveda recension) clearly indicates how Jyotisha forms a part of Veda apart from highlighting the need for an accurate calendar system.<blockquote>वेदा हि यज्ञार्थमभिप्रवृत्ताः कालानुपूर्व्या विहिताश्च यज्ञाः । तस्मादिदं कालविधामशास्त्रं यो ज्योतिषं वेद स वेद यज्ञम् ॥ (Veda. Jyot. Yaju. 3)<ref name=":8" /></blockquote><blockquote>vēdā hi yajñārthamabhipravr̥ttāḥ kālānupūrvyā vihitāśca yajñāḥ । tasmādidaṁ kālavidhāmaśāstraṁ yō jyōtiṣaṁ vēda sa vēda yajñam ॥ (Veda. Jyot. Yaju. 3)</blockquote>Summary : The Vedas have indeed been revealed for the sake of performance of the Yajnas. But these yajnas are dependent on (various segments of) time. Therefor, only he who knows the lore of time. viz., Jyotisha, understands the processes of [[Yajna (यज्ञः)|Yajnas]].<ref name=":8" />
 Given the importance of the calendrical system, Indian astronomers took it as a challenge upon themselves to prepare accurate calendars to cater to the needs of the society. Thus arose the concepts of Panchangas and the specific calculations associated with them.

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 == Microcosmic Time Scale ==
 Just as the macrocosmic Yuga system is discussed extensively in various texts, the microcosmic time scale is also widely explained in different texts and different scholars have given different measures. A few systems are discussed here below.
 === Surya Siddhanta ===

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 # अनुवत्सरः ॥ Anuvatsara
 # इद्वत्सरः ॥ Idvatsara
-This five-year cycle contains, 1830 civil days, 1835 sidereal days, 1800 saura days, 62 lunar months, 5 revolutions of the Sun, and 67 revolutions of the Moon.<ref name=":10" />
+This five-year cycle contains, 1830 civil days, 1835 sidereal days, 1800 saura days, 62 lunar months, 5 revolutions of the Sun, and 67 revolutions of the Moon.
-Yuga (युगम्) is one of the four large periods into which the basic Chaturyuga cycle is divided, it forms the basic Indian cycle of creation and destruction. Yuga Pramana is calculated in terms of Human varshas and Divya varshas. Bhagavata Purana describes the concept of time and yugas (in Divya varshas) in the following verses<blockquote>कृतं त्रेता द्वापरं च कलिश्चेति चतुर्युगम् । दिव्यैर्द्वादशभिर्वर्षैः सावधानं निरूपितम् ॥ १८ ॥ (Bhag. Pura. 3.11.18) kr̥taṁ tretā dvāparaṁ ca kaliśceti caturyugam । divyairdvādaśabhirvarṣaiḥ sāvadhānaṁ nirūpitam ॥ 18 ॥ (Bhag. Pura. 3.11.18)</blockquote><blockquote>चत्वारि त्रीणि द्वे चैकं कृतादिषु यथाक्रमम् । सङ्ख्यातानि सहस्राणि द्विगुणानि शतानि च ॥ १९ ॥ (Bhag. Pura. 3.11.19) <ref name=":3">Bhagavata Purana ([https://sa.wikisource.org/wiki/%E0%A4%B6%E0%A5%8D%E0%A4%B0%E0%A5%80%E0%A4%AE%E0%A4%A6%E0%A5%8D%E0%A4%AD%E0%A4%BE%E0%A4%97%E0%A4%B5%E0%A4%A4%E0%A4%AA%E0%A5%81%E0%A4%B0%E0%A4%BE%E0%A4%A3%E0%A4%AE%E0%A5%8D/%E0%A4%B8%E0%A5%8D%E0%A4%95%E0%A4%A8%E0%A5%8D%E0%A4%A7%E0%A4%83_%E0%A5%A9/%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%A7 Skanda 3 Adhyaya 11])</ref></blockquote><blockquote>catvāri trīṇi dvē caikaṁ kr̥tādiṣu yathākramam । saṅkhyātāni sahasrāṇi dviguṇāni śatāni ca ॥ 19 ॥ (Bhag. Pura. 3.11.19)</blockquote>Meaning : The four yugas are namely Krta, Treta, Dvapara and Kali consisting of 12,000 divya varshas, in the order of 4000, 3000, 2000, and 1000 divya years respectively.
+However, in astronomy, the epoch as well as the elements by which the mean motions were determined had to be changed from time to time, as a result of observation. But, on basic principles and theories, there was complete unanimity. Accordingly, the Hindu astronomers established an epoch when all the planets were in zero longitude. And the period from one such epoch to the next, according to Aryabhata I, is 10,80,000 years. When the Moon's apogee and the Moon's ascending node are included in the list of the planets, the above mentioned period becomes 43,20,000 years which is defined as the duration of a yuga. Thus, yuga is a period of time which begins and ends when the Sun, the Moon, Mars, Mercury, Jupiter, Venus, Saturn, the Moon's apogee, and the Moon's ascending node are in zero longitude. According to Aryabhata I, the last time this phenomenon occurred was sunrise at Lanka (a hypothetical place at the intersection of the equator and the meridian of Ujjain) on Friday, 18 February, 3102 BC. It is also noted that this yuga consists of four periods of 10,80,000 years, which are called quarter yugas and bear the names Krtayuga, Tretayuga, Dvaparayuga and Kaliyuga. And the current quarter yuga is the Kaliyuga which is assumed to have begun at the sunrise at Lanka on Friday, 18 February, 3102 BC.<ref name=":10" />
 The earliest reference to a mahayuga's division into 4 yugas is found in the Aitereya Brahmana belonging to the Rig Veda.  <blockquote>कलिः शयानो भवति संजिहानस्तु द्वापरः। उत्तिष्ठंस्त्रेता भवति कृतं सम्पद्यते चरंश् चरैवेति चरैवेति... (Aite. Brah. 7.15)<ref>Aitereya 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>kaliḥ śayānō bhavati saṁjihānastu dvāparaḥ। uttiṣṭhaṁstrētā bhavati kr̥taṁ sampadyatē caraṁś caraivēti caraivēti... (Aite. Brah. 7.15)</blockquote>Thus, the concept of four yugas is vedic in origin, although the exact measure is not mentioned we rely on the Puranas and other texts.
 === Kala in Puranas ===
-Thus even though the concept of yugas is vedic in origin, Puranas have dealt with this subject extensively. One of the 5 lakshanas of Puranas include that such texts should contain the information of Creation and Manvantaras. Thus apart from description about the scheme and number of years, Puranas also deal with many other topics. However, the macrocosmic and microcosmic time scales are varying in Puranic texts. Commonly it is the सृष्टिप्रकरणम् Srsthiprakaranam that deals with the information regarding Kalapramanas. Below is a list of Puranas and the information of Kalapramana contained therein.
+Thus even though the concept of yugas is vedic in origin, Puranas have dealt with this subject extensively. One of the 5 lakshanas of Puranas include that such texts should contain the information of Creation and Manvantaras. Thus, apart from description about the scheme and number of years, Puranas also deal with many other topics. However, the macrocosmic and microcosmic time scales are varying in Puranic texts. Commonly it is the सृष्टिप्रकरणम् Srsthiprakaranam that deals with the information regarding Kalapramanas. Below is a list of Puranas and the information of Kalapramana contained therein.
 * Brahmanda Purana (Purvabhaga)<ref>Brahmanda Purana ([https://sa.wikisource.org/wiki/%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%BE%E0%A4%A3%E0%A5%8D%E0%A4%A1%E0%A4%AA%E0%A5%81%E0%A4%B0%E0%A4%BE%E0%A4%A3%E0%A4%AE%E0%A5%8D/%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%85%E0%A4%A7%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AF%E0%A4%83_%E0%A5%A8%E0%A5%AF Purvabhaga Adhyaya 29])</ref>
 * Vishnu Purana (Prathama Amsha)<ref>Sri Vishnu Purana ([https://sa.wikisource.org/wiki/%E0%A4%B6%E0%A5%8D%E0%A4%B0%E0%A5%80%E0%A4%B5%E0%A4%BF%E0%A4%B7%E0%A5%8D%E0%A4%A3%E0%A5%81%E0%A4%AA%E0%A5%81%E0%A4%B0%E0%A4%BE%E0%A4%A3%E0%A4%AE%E0%A5%8D-%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%A5%E0%A4%AE%E0%A4%BE%E0%A4%82%E0%A4%B6%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 Amsha 1 Adhyaya 3])</ref>

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 === Yuga in Vedas ===
-Astronomical knowledge was necessary since early Rig vedic times for the day-today-life of the people seasons for sowing, rains for growth and reaping were all acquired. Direct connection of astronomy, particularly the lunar transits, are seen in the performance of monthly rites such as Darsapurnamasa and seasonal rites such as chaturmasya. Thus vedic people had knowledge required for their religious activities. The Vedic astronomers evolved a system of five years yuga. As seen in Rigveda time period of yuga was mentioned <blockquote>दीर्घतमा मामतेयो जुजुर्वान् दशमे युगे । dīrghatamā māmateyo jujurvān daśame yuge । (Rig Veda 1.158.6)<ref>Rig Veda ([http://vedicheritage.gov.in/samhitas/rigveda/shakala-samhita/rigveda-shakala-samhitas-mandal-01-sukta-158/ Mandala 1 Sukta 158])</ref></blockquote>Prof K. S. Shukla explains the evolution of the Vedic concept of a Yuga as follows:<blockquote>''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. 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.''<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></blockquote>The names of the five years of a yuga being<ref name=":0" />
+Astronomical knowledge was necessary since early Rig vedic times for the day-today-life of the people seasons for sowing, rains for growth and reaping were all acquired. Direct connection of astronomy, particularly the lunar transits, are seen in the performance of monthly rites such as Darsapurnamasa and seasonal rites such as chaturmasya. Thus vedic people had knowledge required for their religious activities. The Vedic astronomers evolved a system of five years yuga. As seen in Rigveda time period of yuga was mentioned <blockquote>दीर्घतमा मामतेयो जुजुर्वान् दशमे युगे । dīrghatamā māmateyo jujurvān daśame yuge । (Rig Veda 1.158.6)<ref>Rig Veda ([http://vedicheritage.gov.in/samhitas/rigveda/shakala-samhita/rigveda-shakala-samhitas-mandal-01-sukta-158/ Mandala 1 Sukta 158])</ref></blockquote>Prof K. S. Shukla explains the evolution of the Vedic concept of a Yuga as follows:<blockquote>''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. 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.''<ref name=":10">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></blockquote>The names of the five years of a yuga being<ref name=":0" />
 # संवत्सरः॥ Samvatsara
 # परिवत्सरः ॥ Parivatsara
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 # अनुवत्सरः ॥ Anuvatsara
 # इद्वत्सरः ॥ Idvatsara
 Yuga (युगम्) is one of the four large periods into which the basic Chaturyuga cycle is divided, it forms the basic Indian cycle of creation and destruction. Yuga Pramana is calculated in terms of Human varshas and Divya varshas. Bhagavata Purana describes the concept of time and yugas (in Divya varshas) in the following verses<blockquote>कृतं त्रेता द्वापरं च कलिश्चेति चतुर्युगम् । दिव्यैर्द्वादशभिर्वर्षैः सावधानं निरूपितम् ॥ १८ ॥ (Bhag. Pura. 3.11.18) kr̥taṁ tretā dvāparaṁ ca kaliśceti caturyugam । divyairdvādaśabhirvarṣaiḥ sāvadhānaṁ nirūpitam ॥ 18 ॥ (Bhag. Pura. 3.11.18)</blockquote><blockquote>चत्वारि त्रीणि द्वे चैकं कृतादिषु यथाक्रमम् । सङ्ख्यातानि सहस्राणि द्विगुणानि शतानि च ॥ १९ ॥ (Bhag. Pura. 3.11.19) <ref name=":3">Bhagavata Purana ([https://sa.wikisource.org/wiki/%E0%A4%B6%E0%A5%8D%E0%A4%B0%E0%A5%80%E0%A4%AE%E0%A4%A6%E0%A5%8D%E0%A4%AD%E0%A4%BE%E0%A4%97%E0%A4%B5%E0%A4%A4%E0%A4%AA%E0%A5%81%E0%A4%B0%E0%A4%BE%E0%A4%A3%E0%A4%AE%E0%A5%8D/%E0%A4%B8%E0%A5%8D%E0%A4%95%E0%A4%A8%E0%A5%8D%E0%A4%A7%E0%A4%83_%E0%A5%A9/%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%A7 Skanda 3 Adhyaya 11])</ref></blockquote><blockquote>catvāri trīṇi dvē caikaṁ kr̥tādiṣu yathākramam । saṅkhyātāni sahasrāṇi dviguṇāni śatāni ca ॥ 19 ॥ (Bhag. Pura. 3.11.19)</blockquote>Meaning : The four yugas are namely Krta, Treta, Dvapara and Kali consisting of 12,000 divya varshas, in the order of 4000, 3000, 2000, and 1000 divya years respectively.

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-Kala (Samskrit : कालः) means "time period" in a broad sense. The concept of time is explained systematically in [[Vedanga Jyotisha (वेदाङ्गज्योतिष्)|vedanga jyotisha]] (astronomy). It is significant that time has been considered both at the microcosmic and the macrocosmic levels. Various Puranas also describe Kalapramana that existed previously.
+Kala (Samskrit : कालः) means "time period" in a broad sense. The concept of time is explained systematically in [[Vedanga Jyotisha (वेदाङ्गज्योतिषम्)|vedanga jyotisha]] (astronomy). It is significant that time has been considered both at the microcosmic and the macrocosmic levels. Various Puranas also describe Kalapramana that existed previously.
 [[File:Kalachakram.png|thumb|450x450px|'''Kala Chakram. Time is depicted as a Wheel. Konark Temple in Odisha, India houses an elaborate architectural construction of the Surya's Chariot having a single wheel.''']]
 Kala is kshayakari (क्षयकारी । exhausting) or vriddi kari (वृध्दिकारी । flourishing). Firstly Kala, refers to the inexorable flow of both creation and unfolding of the universe and its subsequent destruction, in time cycles of huge dimensions. Secondly, Kala refers to the shorter and relative time periods on earth, the days and nights, paksha, masa (months), ayana (uttarayana and dakshinayana), samvatsara (year) and this leads to the bigger units of yugas which again refer back to the cycles of srishti (सृष्टिः । creation) and kshaya (क्षयः। decay) that the universe passes through.<ref name=":2">Narayanacharya, K. S. (2011). ''Veda Sanskritiya Parichaya''. Hubli:Sahitya Prakashana.</ref>Thus, Kala is usually represented as a wheel due to its cyclic nature (although linear time scales are also present).
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 On the macroscopic scale of time, the yuga system is highly evolved in the Indian Astronomy. Many important elements of planets and other parameters are given in terms of the number of revolutions in the course of a long period of time called '''yuga'''. The concept of Yugas is extensively discussed in various puranas.
-While in the [[Vedanga Jyotisha (वेदाङ्गज्योतिष्)|Vedanga Jyotisha]] the word yuga was used to mean a period of 5 years, in later works the word meant a large period of time. Yugas of large periods of time have been used to indicate the rates of motion of planets and other important points of astronomical significance. This technique enabled them to express these constants as integers, though very large, thus avoiding very inconvenient fractions.<ref name=":0">Balachandra Rao, S. (2017 Third Edition) Indian Mathematics and Astronomy. Benguluru : Bhavan's Gandhi Center of Science & Human Values</ref>
+While in the [[Vedanga Jyotisha (वेदाङ्गज्योतिषम्)|Vedanga Jyotisha,]] the word yuga was used to mean a period of 5 years, in later works the word meant a large period of time. Yugas of large periods of time have been used to indicate the rates of motion of planets and other important points of astronomical significance. This technique enabled them to express these constants as integers, though very large, thus avoiding very inconvenient fractions.<ref name=":0">Balachandra Rao, S. (2017 Third Edition) Indian Mathematics and Astronomy. Benguluru : Bhavan's Gandhi Center of Science & Human Values</ref>
 === Yuga in Vedas ===
-Astronomical knowledge was necessary since early Rig vedic times for the day-today-life of the people seasons for sowing, rains for growth and reaping were all acquired. Direct connection of astronomy, particularly the lunar transits, are seen in the performance of monthly rites such as Darsapurnamasa and seasonal rites such as chaturmasya. Thus vedic people had knowledge required for their religious activities. The Vedic astronomers evolved a system of five years yuga. As seen in Rigveda time period of yuga was mentioned <blockquote>दीर्घतमा मामतेयो जुजुर्वान् दशमे युगे । dīrghatamā māmateyo jujurvān daśame yuge । (Rig Veda 1.158.6)<ref>Rig Veda ([http://vedicheritage.gov.in/samhitas/rigveda/shakala-samhita/rigveda-shakala-samhitas-mandal-01-sukta-158/ Mandala 1 Sukta 158])</ref></blockquote>The names of the five years of a yuga being<ref name=":0" />
+Astronomical knowledge was necessary since early Rig vedic times for the day-today-life of the people seasons for sowing, rains for growth and reaping were all acquired. Direct connection of astronomy, particularly the lunar transits, are seen in the performance of monthly rites such as Darsapurnamasa and seasonal rites such as chaturmasya. Thus vedic people had knowledge required for their religious activities. The Vedic astronomers evolved a system of five years yuga. As seen in Rigveda time period of yuga was mentioned <blockquote>दीर्घतमा मामतेयो जुजुर्वान् दशमे युगे । dīrghatamā māmateyo jujurvān daśame yuge । (Rig Veda 1.158.6)<ref>Rig Veda ([http://vedicheritage.gov.in/samhitas/rigveda/shakala-samhita/rigveda-shakala-samhitas-mandal-01-sukta-158/ Mandala 1 Sukta 158])</ref></blockquote>Prof K. S. Shukla explains the evolution of the Vedic concept of a Yuga as follows:<blockquote>''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. 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.''<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></blockquote>The names of the five years of a yuga being<ref name=":0" />
 # संवत्सरः॥ Samvatsara
 # परिवत्सरः ॥ Parivatsara

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 * जलत्नलिकायन्त्रम् ॥ Star positioning instrument
 * पीठयन्त्रम् ॥ Peetha Yantra
-Astrolabes were used to know the position of stars and also calculate time in more recent years. Siddhanta Shiromani by Bhaskaracharya II extensively describes the construction of yantras for various purposes. The construction of Gola (Sidd. Shir. Yant. 3 and 4) and Ghati Yantras are given in Siddhanta Shiromani in the following sloka as an example<blockquote>घटदलरूपा घटिता घटिका ताम्री तले पृथुच्छिद्रा।  द्युनिशनिमज्जनमित्या भक्तं द्युनिशं घटीमानम्॥ सि. शि. यन्त्र.८ (Sidd. Shir. Yant. 8)</blockquote>
+Astrolabes were used to know the position of stars and also calculate time in more recent years. Siddhanta Shiromani by Bhaskaracharya II extensively describes the construction of yantras for various purposes. The construction of Gola (Sidd. Shir. Yant. 3 and 4) and Ghati Yantras are given in Siddhanta Shiromani in the following sloka as an example<blockquote>घटदलरूपा घटिता घटिका ताम्री तले पृथुच्छिद्रा।  द्युनिशनिमज्जनमित्या भक्तं द्युनिशं घटीमानम्॥ सि. शि. यन्त्र.८ (Sidd. Shir. Yant. 8)</blockquote><blockquote>ghaṭadalarūpā ghaṭitā ghaṭikā tāmrī tale pr̥thucchidrā। dyuniśanimajjanamityā bhaktaṁ dyuniśaṁ ghaṭīmānam॥ si. śi. yantra.8 (Sidd. Shir. Yant. 8)</blockquote>
 == कालस्य ईश्वररूपम् ॥ Kala's Ishvaraswarupa ==