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The Astronomical Observatories of Jai Singh c15.s1.t3: Greek Astronomy in India

The Astronomical Observatories of Jai Singh c15.s1.t3

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English

Greek Astronomy in India

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67. Varāha Mihira and others, about A.D. 550, made popular new ideas borrowed from the west: they remodelled the Hindu astronomical system on Greek lines. Varāha Mihira’s astrological works contain numerous Greek technical terms and show, unmistakably, Greek influence. His great astronomical work, the Pañchasiddhāntikā, consists of summaries of the Paitāmaha, Vāsisṭha, Romaka, Pauliśa¹ and Saura Siddhāntas. “The Siddhānta made by Pauliśa is accurate, near to it is the Siddhānta proclaimed by Romaka, more accurate is Sāvitra and the two remaining ones are far from the truth.” The summary of the Paitāmaha Siddhānta exhibits the teaching of the Vedānga stage but adds the epoch of 2 Śaka (=A. D. 80). The Vāsisṭha Siddhānta appears to represent the transition stage. It alters the longest day rule and introduces shadow calculations, and the lagna or ‘rising sign’ notion; while the other three introduce, unequivocally, the Greek teaching. The main characteristics of the Romaka Siddhānta are—

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¹ Albirūni writes (i, 153): “Paulisa-siddhānta, so called from Paulisa the Greek, from the city of Samtra, which I suppose to be Alexandria.”

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(a) A cycle of 2850=19×150 years, perhaps based on the Metonic cycle.

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(b) A year of 365ᵈ 5ʰ 55ᵐ 12ˢ, which is exactly the tropical year of Hipparchus.

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(c) The epoch of 427 Śaka (=A.D. 505).

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(d) Omission of mention of epicycles.

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In the Pauliśa Siddhānta the following points are noteworthy:—

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(a) A year of 365ᵈ 6ʰ 12ᵐ.

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(b) A special rule for finding the place of the moon.

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(c) Very rough rules for eclipses.

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(d) Differences in longitudes between Avanti (Ujjain) and Vārāṇasī (Benares) and Yavana (Alexandria) are given.

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(e) A table of sines agreeing with Ptolemy’s table of chords.

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68. The Sūrya Siddhānta is probably the best known astronomical work of the Hindus. The several sections of the accepted text² relate to—

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² Varāha Mihira’s summary of this work differs in some details from the text now in use, but not essentially, e.g., the length of the sidereal year in the two works is: Old Sūrya Siddhānta 365ᵈ 6ʰ 12ᵐ 36ˢ. Modern Sūrya Siddhānta 365ᵈ 6ʰ 12ᵐ 36·56ˢ. The text now accepted possibly dates from about A.D. 1100, while the earlier limit for the original Sūrya Siddhānta is about A.D. 400.

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1. The mean motions of the planets.

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2. The true places of the planets.

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3. The gnomon.

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4. Eclipses.³ 5. Planetary conjunctions.
6. Asterisms.
7. Heliacal risings and settings.¹
8. Instruments.
9. Time. Cosmogony.
10. Astrology.

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³ That subject which is the greatest mystery, which perplexes the minds of writers of astronomical works.” (P.S. i, 5.)

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¹ For some historical account of this topic see Bouché-Leclercq, *L'Astrologie grecque*, p. 111f.

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69(a). The topics dealt with in most of the later Hindu works are fundamentally the same as those of the Sūrya Siddhānta, and the following notes apply, fairly generally, to all these works. The earth is considered as a fixed unsupported sphere, round which the other heavenly bodies revolve.² Its diameter is given as 1,600 yojanas, and the distance of the moon as 51,570 yojanas, or roughly the same relative distance as Ptolemy gives (61 1/4 radii of the earth). The distances of the other planets are calculated on the assumption that they move with equal velocities. The equation of the centre of a planet is calculated by assuming epicycles, but an apparently indigenous notion is introduced by making the epicycle oval. Ptolemy's theory of the equant is omitted, and certain other improvements of Ptolemy, relating to the moon and Mercury, are also omitted. The precession of the equinoxes is explained as a sort of libration, within limits of 27 degrees east and west of a fixed position, at a rate of 54 seconds a year; and the obliquity is generally reckoned at 24 degrees.

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² Āryabhaṭa attempted to revive the theory of Heraclitus that it was the earth's own rotation that produced the apparent motions of the heavenly bodies; but he was condemned as unorthodox, and the view has never been accepted by Hindu astronomers generally.

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The Greek names of the signs of the zodiac were adapted, and the seven day week introduced; many Greek astrological terms and some Greek mathematical terms were adopted without change. Some of the old cosmological notions, that did not interfere with the new ideas, were retained. The Greek teaching was, indeed, accepted as a whole—but the evidence points to the curious fact, that the Greek astronomy introduced is that of a period preceding Ptolemy, although Ptolemy lived in the second century of our era, and the Hindu-Greek astronomical works did not appear earlier than A.D. 400.

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69(b). One of the most notable features of Hindu astronomy of this period is the employment of immense cycles. To express the planetary elements in integral numbers the astronomers assumed an artificial epoch of general conjunction, and a period of recurring conjunctions. The last general conjunction was supposed to be at 3102 B.C., and the cycle or yuga of recurring conjunction is supposed to consist of 4,320,000 years.³ The planetary elements are expressed in terms of this cycle as follows:—

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³ The number 4,320,000=20×60³ is suggestive of Babylonian influence. See also J. Adam, *The Nuptial Number of Plato*.

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| Planet. | Revolutions. | Planet. | Revolutions. |
| Sun | 4,320,000 | Saturn | 146,568 |
| Mercury . . . . . . | 17,937,060 | Moon : Sidereal revolutions | 57,753,336 |
| Venus . . . . . . | 7,022,376 | " Synodic " | 53,433,336 |
| Mars . . . . . . | 2,296,832 | " Revolution of apsis | 488,203 |
| Jupiter . . . . . . | 364,220 | " " , node | 232,233⁴ |

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⁴ As Whitney points out all these numbers except the last two are divisible by four and this seems to indicate that the last two were later additions.

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There was, of course, no general conjunction at 3102 B.C., which period was arrived at by calculating backwards, according to the rules. Bentley assumed that, at that particular time when the calculation was made, the positions of the planets were known with some accuracy: he then calculated, according to the *Sūrya Siddhānta* rules, the positions of the planets at several periods, and found them most correct for A.D. 1091, and concluded that the elements were fixed and the work composed towards the end of the eleventh century.¹

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¹ For further details see my *Hindu Astronomy*. Bentley's general argument is quite sound, but he must not be accepted as reliable on all points.

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