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Bharatiya Jyotihshastra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s2.t7: Puliśa Siddhānta

Bhāratīya Jyotiḥśāstra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s2.t7

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Puliśa Siddhānta

v2.c12.s2.t7.1

A large part of the Pañcasiddhāntikā is devoted to the Puliśa Siddhānta. It is stated in the 10th couplet of the first Chapter that Romaka’s ‘ahargaṇa’ is very nearly equal to that of the Puliśa Siddhānta. Then follows the calculation of the place of the luminaries etc. and of the eclipses of the sun and the moon.

v2.c12.s2.t7.2

It has not at all been stated what the motions and places of Mars and other planets are according to the Puliśa Siddhānta; but the last couplet states that “the planets have thus been described according to the Puliśa Siddhānta” and which shows that about 16 ‘āryās’ in the end mention something from Puliśa Siddhānta about their direct and retrograde motions, and the rise and set of planets.

v2.c12.s2.t7.3

The elements pertaining to the Puliśa Siddhānta are found to be as follows :

v2.c12.s2.t7.4

खार्क (१२०) घ्नेग्निहुताशन (३३) मपास्य रूपाग्निवसुहुताशकृतैः (४३८३१) ।। हृत्वा क्रमादिनेशो मध्यः... ।। १४ ।। अष्टगुणे दिनराशौ रूपेंद्रियशीतरश्मिभि (१५१) भंक्ते ।। लब्धा राहोरंशा भगणसमाश्च क्षिपेलिप्ताः ।। ४१ ।। वृश्चिकभागा राहोः षड्विंशतिरेकलिप्तिकागुप्ताः ।। ४२ ।।

v2.c12.s2.t7.5

“(14) Multiply the ahargaṇa by 120, deduct 33, and divide by 43831 the result is the mean longitude of the sun in due order. (41) Multiply the ahargaṇa by 8 and divide the product by 151; the quotient indicates the degrees of Rāhu (i.e. the moon’s ascending node) to which as many minutes have to be added, as there are complete revolutions. (42) This is a stanzas stating certain correction to be applied to the place of the moon’s node as found according to the above rule. Apparently 25 minutes have to be deducted from that place. We do not know what is meant by “Vṛścika-bhāgā Rāhoḥ”.

v2.c12.s2.t7.6

These couplets are found in the chapter following the one consisting of the first 25 āryās, and they form part of the passages attributed to the Puliśa Siddhānta. The elements derived from these āryās are as follows :—

v2.c12.s2.t7.7

| The measure of the year | . | 365d 15gh 30pal |
| Number of Sāvana days in one Mahāyuga | . | 1577916000 |
| No. of revolutions of Rāhu | . | 232227 65703915/67946855 |
| Period of Rāhu’s one revolution | . | 6794d 41gh 18pal |

v2.c12.s2.t7.8

This gives for the measure of the year a figure different from that of other Siddhāntas. Similarly, the period of the revolution of Rāhu (the moon’s ascending node) is also somewhat different.

v2.c12.s2.t7.9

The Pañcasiddhāntikā mentions other things from the Puliśa Siddhānta which include the question of true places of the sun and the moon. It describes the method of finding ‘carakhaṇḍas’ (groups of ascensional differences) from the ‘palabhā’ (the noon shadow on equinoctial day), and calculating therefrom the length of the day; terrestrial longitudes too have been considered.

v2.c12.s2.t7.10

The method of calculating the tithi and nakṣatra is similar to one of the present day. It includes the explanation of the ‘karaṇas’ and ‘Mahāpātas’ (or the parallels of the declination of the sun and the moon). The question of eclipses is also considered and the method is almost similar to that of other modern Siddhāntas. The study of the direct and retrograde motions of planets is similar to that described in the work entitled Khaṇḍakhādya. The study ‘cara’ (ascensional difference) quotes the following couplet.

v2.c12.s2.t7.11

यवनाच्चरजा नाड्यः सप्ता (७) वंत्यास्विभाग (१/३) संयुक्ताः ॥ वाराणस्यां त्रिकृतिः (६) साधनम्यत्र वक्ष्यामि ॥

v2.c12.s2.t7.12

“The Yavana mentions 7gh 20pal. as the ‘cara’ for Ujjayinī and 9 ghaṭis for Vārāṇasī. The method of calculating it, is described elsewhere”.

v2.c12.s2.t7.13

The word mentions, as in Vedāṅga Jyotiṣa, dinamānavṛddhi, or the increase in the length of a day at the end of Udagayana as compared with that at the end of the Dakṣiṇāyana. According to the sayana almanac, the minimum and the maximum length of the day at Ujjayinī are 26gh. 26pal. and 33gh. 34 pal. respectively; that is, the difference between the two amounts to 7gh. 8p. According to the Grahalāghava these values are 26gh. 21p. and 33gh. 39p respectively and the difference is equal to 7gh. 18p. These have been calculated by assuming 5-8 as the palabhā for Ujjayinī. Pandit Bāpūdeva śāstri gives in his almanac, the maximum length of the day at Vārāṇasī to be 33gh. 56p. and the minimum length as 26gh. 4HP. The difference between the two comes to be 7gh. 52p. This has been calculated on the basis of 5-40 as the palabhā at Vārāṇasī. Assuming this very value for Vārāṇasī, the Grahalāghava calculation shows 8gh. 4pal. as the difference between the two lengths. Assuming 6-15 as the palabhā, one gets a difference of about 9 ghaṭis on the basis of Puliśa’s ‘Carakhaṇḍa’ as given by the Pañcasiddhāntikā.

v2.c12.s2.t7.14

The third couplet in the Pañcasiddhāntikā shows that Lāṭadeva has written a commentary on the Paulīśa Siddhānta.

v2.c12.s2.t7.15

The author has neither seen nor heard of any Puliśa Siddhānta of any kind being available at present. Utpala has incidentally quoted about 35 couplets from the Puliśa Siddhānta as authority in his commentary on the Bṛhatsaṃhitā. They contain the number of revolutions and other important elements given by the Puliśa Siddhānta. Those couplets as collected in one place are, therefore, quoted below :—

v2.c12.s2.t7.16

अष्टाचत्वारिंशत्पादविहीनाः क्रमात् कृतादीनां ॥ अंशास्ते शतगुणिता ग्रह्तुल्ययुगं तदेकत्वं ॥

v2.c12.s2.t7.17

(The meaning is not quite clear)

v2.c12.s2.t7.18

“The number of years* in a Kṛta yuga is obtained by multiplying 48 by 100 and that in the successive Yugas is obtained after multiplying 100 the “number 48 diminished by its quarter (i.e. 12) successively”.

v2.c12.s2.t7.19

This is a unit (ekatvam) to start with in the case of each kind of ‘planetery’ yugas.

v2.c12.s2.t7.20

[*Footnote by the translator :— Although the text quotes ‘aṃśaḥ’ as the word, the manuscript, which I could see by the kind permission of the local Scindia Institute, gives the word “abdaḥ”, and the explanation therein shows that the Mahāyuga (which was rendered as the ‘divine yuga’ by the later astronomers) consisted of (4800+3600+2400+1200=12,000 years). According to the prevailing system, the year was of 4 kinds and consisted of 4 kinds of months, each of 30 days of the corresponding denomination].

v2.c12.s2.t7.21

सावनमकृतं १५५२००००० चांद्रं सूर्येंदसंगमान् दिनीकृत्य (१६०३००००८०) ।। सौरं भूदिनराशि: १५७७९१७८०० शशिभगणदिनानि १७३२६०००८० नाक्षत्रं ।।

v2.c12.s2.t7.22

“The natural yuga is termed ‘sāvana’ (civil). That which is reckoned after calculating number of days in the joint revolutions of the sun and the moon as Cāndra (Lunar); the Saurā or solar (yuga) is “the heap” of solar days; and the number of days in the revolution of the moon constitutes a Nakṣatra (sidereal) yuga”.

v2.c12.s2.t7.23

परिवर्तैरयुतगुणद्वित्रिकृतै (४३२००००) भास्करो युगं भुंक्ते ।। रसदहनहुतवहानलशरमन्यद्रीशवचंद्र: (५७७५३३३६) ।।

v2.c12.s2.t7.24

“The sun completes 4320000 revolutions in one yuga, while the moon makes 57753336 revolutions (in the same period)”.

v2.c12.s2.t7.25

अधिमासका: षडग्नित्रिकदहनछिद्रशररूपा: (१५९३३३६) ।। भगणांतरशेषं यत् समागमास्ते द्वयोर्गृहयो: ।। तिथिलोपा: खवसुद्विकदसाष्टशून्यशरपक्ष: (२५०८२२८०) ।।

v2.c12.s2.t7.26

“The intercalary months (adhimāsas) in a yuga amount to 1593336. The number of luni-solar conjunctions is equal to the difference between the bhagaṇas of the sun and the moon. The number of suppressed tithis is 25082280”.

v2.c12.s2.t7.27

दसार्थबाणतिथयो लक्षहता: (१५५२०००००) सावनेन ते दिवसा: ।। विषया (?) ष्टौ ऋचतुष्कं विश्व…षोडश चांद्रमानेन ।। वसुसप्तरूपनवमुनिनगतिय: शतगुणाश्च (१५७७९१७८००) सौरेण ।। आक्षैण खाष्टक्षत्रयरसदसगुणनिल (?) शशांका: (१७३२६०००८०) ।।

v2.c12.s2.t7.28

“The measure of the Sāvana yuga is 1555200000 days, that of Lunar yuga is 1603000080, of Solar yuga is 1577917800 and of Sidereal yuga is 1732600080.”

v2.c12.s2.t7.29

षद्‌ प्राणास्तु विनाडी, तत्षष्ट्या नाडिका, दिनं षष्ट्या ।। एतासां तंत्रिंशन्मासस्तद्वैशभिरब्द: ।।

v2.c12.s2.t7.30

“Six ‘praṇas’ make a ‘vināḍī’, sixty vināḍīs make a nāḍikā (or ghaṭikā), sixty nāḍikās make a day; thirty such days make a month and twelve months make a year.”

v2.c12.s2.t7.31

षष्ट्यातु तत्पराणां विकला, तत्षष्टिरपि कला, तासां ।। षष्ट्यांशस्ते त्रिंशद्राशिस्ते द्वादश भचक्रं ।।

v2.c12.s2.t7.32

“Sixty ‘tatpars’ make a ‘Vikalā’, sixty ‘vikalās’ make a ‘kalā’ (minute), sixty ‘kalās’ make an ‘aṃśa’ (degree), thirty degrees make a rāśi (sign) and twelve rāśis make a ‘Bhacakra’ (Zodiacal circuit).”

v2.c12.s2.t7.33

चांद्रै: सावनवियुतै: प्रचय (४७८०००८०) स्तैरपचयोर्कदिनै: (२५०८२२८०) युगवत्सरै: प्रयच्छति यदिमानचतुष्टयं किमेकेन ।। यदवाप्तं ते दिवसा विज्ञेया: साबनादीनां ।। “We get the number of suppressed days with the help of the number of solar days in the yuga and the difference (47800080) between the measures of the lunar and sāvana yugas. When all the four results can be obtained by means of the above figures, where is the need of remembering the results individually ? Whatever results we thus obtain, indicate the number of days in the Sāvana and other kinds of Yugas.”

v2.c12.s2.t7.34

वेदाशिवसुरसांतरलोचनदस्रं (२२६६८२४) खनिसूनुः ॥ अंबरगगनवियन्मुनिगुणविवरगेंदुभिः (१७४३७०००) शशिसुतस्य ॥ आकाशलोचनेक्षणसमुद्रषटकानलै (३६४२२०) जीवः ॥ अष्टवसुहुतवहानल (?) यमखनगै (७०२२३८८) भर्ग्वस्यापि ॥ कृतरसशर्तुमनुभिः (१४६५६४) सौरो; बुधभागर्वौ दिवाकरवत् ॥

v2.c12.s2.t7.35

“These verses give the number of revolutions which each planet makes in a yuga. Mars makes 2296824 ; Mercury’s epicycle 17937000 ; Jupiter; 364220; Venus’s epicycle, 7022388 ; Saturn 146564 ; Mercury and Venus make revolutions equal to those of the Sun. “Atha kakṣāmānāni”:—Now are given the lengths of the orbits of planets :—

v2.c12.s2.t7.36

अथकक्षामानानि-आकाशशून्यतिथिगुणदहनसमुद्रुधार्कशुक्राणां (४३३१५००) इंदोः सहस्रगुणितैः समुद्रनेत्राग्निभिश्च (३२४०००) स्यात् ॥ भूसूनुर्मुनिरामिछद्रतुसमुद्रशिशुसृभिः (८१४६९३७) ॥ रुद्रयमाग्रिचतुष्क्योमशांकै (१०४३२११) बुधोच्चस्य ॥ जीवस्य वेदष्टकस्वरविषयनगामिश्रीतकिरणायैः (५१३७५७६४) ॥ शुक्रोच्चस्य यमानलष्टकसमुद्रतुंरसद्रैः (२६६४६३२) ॥ भगणोर्कजस्य नवशिखिमुनींदुनगष्टकमुनिसूर्यैः (१२७६७१७३६) रिवखवियन्नवसुनवविषयेक्षण (२५६८४००१२) योजनर्भकक्षयाः ॥

v2.c12.s2.t7.37

“The lengths of planetary orbits in yojanas (i.e. 8 miles) are as follows :— Mercury, Venus and the Sun, 4331500 ; Moon, 324000 ; Mars, 8146937 ; Mercury’s aphelion, 1043211 ; Jupiter 51375764 ; Aphelion of Venus 2664632 ; Saturn 127671739 ; Zodiac 259890012”.

v2.c12.s2.t7.38

इष्टग्रहकक्षाम्यो यलब्धं चंद्रकक्षया भक्त्वा ॥ ता मध्यमा ग्रहाणां सौरादीनां कलाश्चंद्राः ॥ पंचदशाहतयोजनसंख्या तत्सगुणार्धविष्कंभः ॥ मोजनकर्णार्धस्यायोजनकर्णविधिना वा ॥

v2.c12.s2.t7.39

“Whatever is obtained after dividing the planet’s orbital length by the moon’s orbital length, is to be known as the planet’s mean distance in lunar-minutes of arc. When this number is multiplied by 15, it gives the semi-diameter of the planet’s orbit, which represents the planet’s geocentric distance. This can otherwise be calculated from the geocentric radius of the orbit of the heavens (i.e. that of the celestial sphere).”

v2.c12.s2.t7.40

वसुमुनिगुणांतराष्टकष्टकै (६८६३७८) दिननाथशुकसौम्यानां ॥ द्वादशलषद्केंद्रियशशांकभूतै (५१५६६) रजनिकर्तुः ॥

v2.c12.s2.t7.41

दस्त्राब्धिषट्करसनलोचनचंद्रै (१२६६४२) खनिसूनोः ॥ रूपाग्निशन्यषट्काष्टिसंमितः (१६६२३१) स्यादुच्चस्य ॥ अष्टकवसुरसमुनिशशांकवसुभिसु (८१७६६८८) जीवस्य ॥ वसुवसुशून्याष्टद्विकवेदै (४२८०८८) रपि भार्गवोच्चस्य ॥ एकार्णवार्थनवशशिदहनखदस्रै (२०३१९५४१) रविसुतस्य ॥ त्रिवसुरसद्विरसानलशशिवेदै (४१३६२६८३) राक्षपरिधकर्णार्ध ॥

v2.c12.s2.t7.42

"The semidiameters of planetary orbits in yojanas are given below :— 689378 of the Sun, Venus and Mercury, 51566 of the Moon ; 1296642 of Mars, 166231 of Mercury’s aphelion ; 8176688 of Jupiter, 428088 of Venus’s aphelion, 20319541 of Saturn and 41362683 of the Zodiacal belt”.

v2.c12.s2.t7.43

वृत्ता चक्रवदनिस्तमस्पारे विनिर्मिता धात्रा ॥ पंचमहाभूतमेया तन्मध्ये मेरुरमराणां तस्योपरि ध्रुवः खे न द्वंद्वं पवनरश्मिमिश्चक्रं ॥ पवनाक्षिप्तं भानामुदयास्तमयं परिभ्रमति । सर्वैजयिन उदकस्था दक्षिणदिक्स्थो जयी शुक्रः ॥

v2.c12.s2.t7.44

"Beyond darkness has been created by God Brahmā, this earth, round like wheel, was made up of five main elements. In its centre stands the mountain Meru, the abode of gods, and the pole occupies a place in the sky just above it. The wheel of stars, being propelled by wind, and creating rises and sets, revolves, as if pulled by ‘reins’ of wind. (The words ‘na dwandwan’ are not clear). All planets when occupying the north give success and only Venus, when in the south gives success.”

v2.c12.s2.t7.45

Although the Pañcasiddhāntikā does not explicitly state that the Pulisa Siddhānta in it postulated the Yugādi system, it appears from the couplets, which mention the intercalary months and suppressed tithis, that it did not postulate the Yuga system. Moreover Brahmagupta has blamed only Romaka on that account. This tends to show that the Pulisa Siddhānta of the Pañcasiddhāntikā did probably contain the description of the yuga-system. The Pulisa’s statement as quoted by Utpala includes it. The ‘sāvana māna’ (i.e. civil measure) alluded to in the statement is termed as ‘solar’ in other works, and the solar measures in the former are termed sāvana by the latter. The measures of ‘bhagaṇas’ etc., as quoted by Utpala from the Pulisa Siddhānta, taking the meanings of the words ‘sāvana’ etc. as given by other works are given below :—

v2.c12.s2.t7.46

| Revolutions of stars | . | 1582237800 |
| Revolutions of the sun | . | 4320000 |
| Sāvana days | . | 1577917800 |
| Revolutions of the moon | . | 57753336 |
| Revolutions of Moon’s apogee (from Beruṇi) | . | 488219 |
| Revolutions of Moon’s asc. node (from Beruṇi) | . | 232226 |
| Revolutions of Mars | . | 2296824 |
| Revolutions of Mercury’s epicycle | . | 17937000* |
| Revolutions of Jupiter | . | 364220 |

v2.c12.s2.t7.47

*This is the number of the planets’ conjunctions with the Sun.

v2.c12.s2.t7.48

Revolutions of Venus’s epicycle . . . . . . 7022388 Revolutions of Saturn . . . . . . . . 146564 Civil Months . . . . . . . . . . 51840000 Intercalary months . . . . . . . . . 1593336 Lunar months . . . . . . . . . . 53433336 Tithis . . . . . 1603000080 Suppressed days . . . . . . . . . . 25082280 The Length of a year . . . . . . . . 365ᵈ-15ᵍʰ-31ᵖ-30ᵛᵖ

v2.c12.s2.t7.49

This shows that the length of the year as given by the Pulisa Siddhānta of the Pañcasiddhāntikā and the Pulisa Siddhānta of Utpala are different. This means that the Pulisa Siddhānta of the Pañcasiddhāntikā is quite different from the Pulisa Siddhānta of Utpala. One more surprising fact is that Utpala himself has given the sentence as an ‘extract’ from the original Pulisa Siddhānta :-

v2.c12.s2.t7.50

खखाष्टमुनिरामादिवनेत्राष्टशररात्रिप्राः (१५८२२३७८००) ।।

भानां चतुर्युगेनैते परिवर्ताः प्रकीर्तिताः ।।

v2.c12.s2.t7.51

“The number of revolutions of the stars in one Caturyuga (Mahāyuga) is 1582237800.”

v2.c12.s2.t7.52

It gives the number of revolutions of nakṣatras in a Mahāyuga. This tallies with the one mentioned in the couplets quoted above. Even then, Utpala has mentioned this as a quotation from the original Pulisa Siddhānta, and it is composed in the Anuṣṭup meter. This shows that there existed at the time of Utpala (śaka 888) two Pulisa Siddhāntas which were different from the one belonging to the Pañcasiddhāntikā group. Hence, the number of Pulisa Siddhāntas comes to be three. The first two couplets of the last 2½, out of those quoted by Utpala, describes the Universe in the manner in which it is found described in the modern Sūrya Siddhānta and other Siddhāntas; the last half couplet refers to the conjunctions of planets. This shows that the Pulisa Siddhānta, composed in the Āryāmetre and existing in Utpala’s time, must have been a complete work like other Siddhāntas. Similarly, the Pulisa Siddhānta belonging to the Pañcasiddhāntikā group also appears to have been a complete work from the detailed information cited from it above.

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The numbers of revolutions and other elements in the Pulisa Siddhānta as quoted by Utpala, exactly tally with those of the Sūrya Siddhānta belonging to the Pañcasiddhāntikā and given on a subsequent page. Similarly, all the measures, excepting the number of civil days and the numbers depending upon it, such as suppressed tithis etc. and the revolutions of Mercury and Jupiter agree with those given by First Āryabhaṭa.

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Albiruṇī, the famous Muslim scholar and traveller, who had come to India with Mahmud of Ghazni, and stayed here from 1017 to 1030 A.D. and studied Indian sciences, particularly, the science of astronomy very critically remarks that the Pulisa-Siddhānta was compiled by Paulus-ul-Yunani or Paulus, the Greek, which means that the Hindus compiled it with the help of his work. Weber says that Albiruṇī could get in India only the Brahmagupta and the Pulisa Siddhāntas and none others.

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Albiruni’s statement cannot be further considered unless it is known as to which of the three Pulisa Siddhāntas referred to above was obtained by him and unless it is possible to see which of the three Siddhāntas agree with the work of Paulus Greek, if it be available at all now, so far as the elements are concerned. Weber observes : “ A work of Paulus Alexandricus is available at present ; but it is not devoted to astronomy but to astrology, and hence, the elements given by the Pulisa Siddhānta do not tally with those given by it. It, however, contains some of the technical terms pertaining to the Hindu astronomy”. But Weber’s remark does not make it clear what terms have been used and in what contest. It seems, the work of Paulus on astronomy is not available now, and it would not be correct to draw any inference without obtaining the actual work.

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References to the Pulisa Siddhānta have occurred at three or four places in the Brahma Siddhānta mentioned by Sākalya which shows that the Pulisa Siddhānta existed at the time of its compilation, but which Pulisa Siddhānta it was, cannot be said. The commentary on Brahma Siddhānta by Prthūdaka (Saka 900) gives a couplet preceded by the words “desāntararekhāca paulise pathyate” (meaning, the subject of terrestrial longitudes is to be read from Paulisa*). This shows that there existed in his time a Pulisa Siddhānta compiled in Āryā-metre.

Cites (9)