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Bharatiya Jyotihshastra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s2.t4: Pitāmaha Siddhānta

Bhāratīya Jyotiḥśāstra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s2.t4

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English

Pitāmaha Siddhānta

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The Subject matter

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The basic principles underlying the Pitāmaha Siddhānta have been given in the 12th chapter of the Pañcasiddhāntikā. That chapter contains only five āryās (couplets). Nowhere else in the Pañcasiddhāntikā is found anything about this Siddhānta. The first two of the five couplets run thus :—

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रविशशिनो: पंच युगं वर्षाणि पितामहोपदिष्टानि ।। अधिमासस्त्रिंशद्भिर्मासैरवमस्त्रिषष्ट्याह्नां ।।
दूनं शकेन्द्रकालं पंचभिरुद्ध्य शेषवर्षाणि ।। युगं माघसितार्थं कुर्याद्युगुणस्तदन्युदयात् २ ।।

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“According to the teaching of Pitāmaha, five years constitute a yuga of the sun and the moon. The adhimāsas occur after thirty months and an omitted lunar day (avam) once in sixty three days. Lessen the time of the Śaka King by two and divide the remainder by five ; with the remaining years find the ahargaṇa, counting from the first day of the light half of Māgha. The Ahargaṇa thus found begins with sunrise”.

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The fifth couplet describes the method of calculating the length of the day :—

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द्विघ्नं शशिरस (६१) भवतं † द्वादशहीनं दिवसमानं ।।

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† The word ‘hinam’ in this couplet is incorrect ; the proper word must be ‘yuktam’. The first half of the couplet is incorrect and has not, therefore, been given here, but it means nothing more than that has been given above within brackets.

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“Multiplying (the number of days elapsed after winter solstice or the number of days to go before the end of the ayana beginning with summer-solstice) by 2 divide by 61. Add 12 (muhūrtas) to the quotient, and the result will be the length of the day”.

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∗ The author copied out the couplets from the Pañcasiddhāntikā, exactly as they are written in his book. Dr. Thibaut has introduced new readings in the next and he has accepted at places only such of them which were considered suitable.

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This verse and the following, describing the method of calculating the nakṣatra, and stating that the nakṣatra should be counted from the Dhaniṣṭhā onward, show that the Pitāmaha Siddhānta has some similarity with the Vedāṅga Jyotiṣa system.

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Date of Compilation

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The method followed by Varāhamihira in explaining the Pitāmaha Siddhānta involves Śaka era but it has been used simply to calculate the ‘ahargaṇa’. The methods attributed to other Siddhāntas also direct one to calculate the ‘ahargaṇa’ from Śaka 427. Just as this does not imply that the Siddhāntas were compiled (by Varāhamihira himself), in Śaka 427, it cannot be taken to imply that the Pitāmaha Siddhānta was compiled after the beginning of Śaka era. It is evident from its similarity with the Vedāṅga Jyotiṣa system that it must have been more ancient than the beginning of Śaka era. There are, however, no means to fix up the date of its compilation.

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Āryabhaṭa I has, in the beginning of *Daśagītikā* written the following benedictory verse :—

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प्रणिपत्यैकमनेकं कं सत्यां देवतां परं ब्रह्म ।। आर्यभटस्त्रीणि गदति गणितं कालक्रियां गोलं ।।१।।

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“After saluting the Pitāmaha (kam) who is manifold and one at the same time, the god of truth and the Parabrahma, Āryabhaṭa describes the three subjects viz. mathematics, method of calculating time and the celestial spheree and in his last couplet he observes,

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आर्यभटीयं नाम्ना पूर्वं स्वायंभुवं सदा सदसत् ।।

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“The science known as the Āryabhaṭīya is the same as the science originaly expounded by Brahmā himself”.

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This shows that the Pitāmaha Siddhānta must have been compiled long before Āryabhaṭa lived (i.e. Śaka 421)

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Brahmagupta (Śaka 550) , in his Siddhānta, observes,

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ब्रह्मोक्तं ग्रहगणितं महता कालेन यत्खिलीभूतं ।।३भिर्धृतं स्फुटं तत् जिष्णुसुतब्रह्मगुप्तेन ।।२।।

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“The calculation of planets’ places as propounded by Brahmā has, become disjointed on account of (lapse of) long time ; Brahmagupta, the son of Jiṣṇu, is describing the same in clearer terms”.

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There are three Brahma Siddhāntas available at present. One is the Brahma Siddhānta by Brahmagupta, the second, the Brahma Siddhānta mentioned in Śakalya Saṃhitā and the third that included in Viṣṇudharmottara tarapurāṇa. In the Author’s view, to be explained later, the Viṣṇudharmottara and the Śakalyokta Brahma Siddhāntas are not older than the Brahmagupta’s time, but compiled much later. The basic principles, propounded by the Śakalya Brahma Siddhānta, even it be more ancient than Brahmagupta, are exactly the same as those propounded by the modern Sūrya-Siddhānta. It may as well be said to be in current use and not antiquated or disjointed ; and it will be shown further that the Viṣṇudharmottara Brahma Siddhānta is not similar to the Brahmagupta Siddhānta. This shows that the Brahma Siddhānta to which Brahmagupta has referred as containing mathematics explained by Brahmā, must have been different from the Brahma Siddhāntas of Śakalya Saṃhitā and Viṣṇudharmottarapurāṇa and it must be the same as the Pitāmaha Siddhānta of the Pañcasiddhāntikā. The Vedāṅga Jyotiṣa does not deal with the calculation of planets other than the sun and the moon; and the Pitāmaha Siddhānta of the Pañcasiddhāntikā also describes the calculations of the sun and the moon only. Varāhamihira has given the calculations of all planets in the case of only the Sūrya-Siddhānta out of the five Siddhāntas and mentions nothing about the planetary calculations contained in the Pitāmaha Siddhānta. It must have, however, contained the calculations of planets as remarked by Brahmagupta, and Varāhamihira appears to have omitted it, on finding that it did not agree with the actual observed places on account of lapse of time. A Pitāmaha Siddhānta, different from the one described in the Pañcasiddhāntikā, does not appear to have ever existed before Brahmagupta. The words “planetary calculations given by Brahmā” occurring in Brahmagupta’s work must certainly be referring to the Pitāmaha Siddhānta of the Pañcasiddhāntikā, and the remark, “a long time has elapsed” also refers to the same Pitāmaha Siddhānta. It follows, therefore, that it must have been compiled long before the Śaka era.

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Āryabhaṭa and Brahmagupta appear to have expressed veneration for the Pitāmaha Siddhānta only as a formality, because their siddhāntas and the Pitāmaha Siddhānta of the Pañcasiddhāntikā have nothing in common. It has already been pointed out in the course of the study of the Vedāṅga Jyotiṣa that Brahmagupta has openly found fault with the five-year Yuga system. Still, these arguments in no way affect the inference that there existed a Siddhānta known as the Pitāmaha Siddhānta before these two astronomers lived.

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The System

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The Pañcasiddhāntikā gives in the beginning two couplets relating to the Pitāmaha Siddhānta, the first of which contains the expression,

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अधिमासस्त्रिंशद्विमसैः

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meaning, “an intercalary month to be reckoned after 30 months”. It has been shown in the study of Vedāṅga Jyotiṣa that the adoption of an intercalary month after 30 months causes a grave error; but this very couplet has been cited by Bhaṭṭotpala in his commentary on Vṛhatsaṃhitā in connection with the verse “ekaikamabdeṣu” in Chapter 8. The reading there is “adhimāso dwyagnisamāisaiḥ” which means that an intercalary month is to be reckoned after 32 months. Again the same couplet is found in the commentary (Chapter I) by Mahādeo on Śrīpati’s Ratnamālā and it also gives “adhimāso dwyagnisamāiḥ” as the reading. It is strange that there is room for confusion due to doubtful readings at such an important place.

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If it be assumed that Utpala and Mahādeo changed the original reading viz. “triṃśatbhirmāsaiḥ”, why should they have substituted “dwyagnisamāiḥ” as the reading? The intercalary month occurs after more than 32½ months, and hence, they could have as well substituted some words meaning 32½ or 33. It appears, therefore, that “dwyagnisamāiḥ” must have been the original reading. According to the Vedāṅga Jyotiṣa one day (tithi) is suppressed after 62 days, while the above couplet mentions the suppression of one day as occuring after 63 days (tithis). This shows that the Vedāṅga Jyotiṣa and the Pitāmaha Siddhānta are not similar to each other completely, and this also lends an additional support to the view that “dwyagnisamaiḥ” must have been the original reading.

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The number of intercalary months in 8 years comes to be 3 at the rate of one intercalary month in 32 months. This gives 99 as the number of lunar months in 8 years and 2970 as the number of tithis (lunar days); and 47 1/6 lunar days will be suppressed during this number of tithis at the rate of one suppressed tithi per 63 lunar days. Hence, 8 years will be equal to 2922 6/7 sāvana days or one year will be equivalent to 365 days and 21 3/4 ghaṭis. This measure of a year is more accurate than that found in the Vedāṅga Jyotiṣa.

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The Pitāmaha Siddhānta existed before Āryabhaṭa, Varāhamihira, and Brahmagupta. As it had fallen into disuse in their times it is evident that it must have beer compiled long before them. It is similar to the Vedāṅga Jyotiṣa but differs from it much. Brahmagupta’s statement shows that it (the Pitāmaha Siddhānta) contained the calculations of Mars and other planets, which is not given in the Vedāṅga Jyotiṣa. It proves that a more accurate work known as the Pitāmaha Siddhānta was compiled sometime after the Vedāṅga Jyotiṣa and this is an important fact. If it were known how the places of Mars and other planets used to be calculated according to the Pitāmaha Siddhānta, it would have been found very useful in tracing the growth of Indian astornomy; but we have almost no hopes of obtaining the Pitāmaha Siddhānta now in its original form.

Cites (8)