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A Concise History of Science in India c6: 2 Astronomy

A Concise History of Science in India c6

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English

Contents

2 Astronomy

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Man’s interest in the heavens is perhaps as old as the beginning of his career as *homo sapiens* on this planet. This is doubtless a consequence of his erect posture which enables him to look and wonder at the sky and the various striking phenomena occurring there day by day and night by night. The sun, the moon, the vault of the sky with numerous sparkling stars, bright and dim, must have appealed to him at the dawn of his capacity to wonder at, and indulge in certain amount of speculation about them. Moreover, he was impressed by the regularity of appearance and disappearance of these objects. The sequence of day and night, the obvious connection of the sun with such alteration of light and darkness, the regular revelation of the splendour of the nightly sky, the periodic waxing and waning of the moon and the unchanging character of the stellar vault must have fired the imagination of the primitive man.

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It did not perhaps take the primitive man a long time to discover some kind of relationship between the cycle of his activities and the regularity of the heavenly phenomena. Thus were differentiated his day-time activities from the nocturnal. He noticed that his hunting seasons and, more particularly, his sowing times, when he settled down as a primitive agriculturist, depended on climatic changes or the seasons. He vaguely felt that these periodic changes were somehow connected with the most conspicuous of all heavenly bodies, the sun. In lower Egypt the periodical overflowing of the Nile was noticed to have some connection with the heliacal rising of Sirius.

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Such cycle of events in the life processes on the one hand and the regularity in the heavenly phenomena on the other inevitably led to a time sense. At the same time these suggested methods of marking and measuring time to an intelligent priestly class wherever human civilizations sprang up and had their normal course of development. This priestly class, as is well known, had a dominant role to play in human societies, with powers to regulate religious and, not infrequently, the secular life of their fellow members. Everywhere they evolved an elaborate and complicated system of rituals and sacrifices to be performed with perfect regularity in time. This naturally imposed on them the task of measuring and dividing time or, in other words, of evolving a suitable calendar and consequently of studying astronomical phenomena. This is true as much of the temple priests of Thebes, Nineveh, Sumer and Akkad as of the Brāhmaṇas of Vedic India.

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The whole corpus of the Vedic literature represents the intellectual activity of a sacerdotal caste which, by turning to account the religious instincts of a gifted and devout race, transformed a primitive worship of the powers of nature into a highly artificial system of sacrificial ceremonies. In prescribing rules for the observance of such ceremonies, the priestly leaders never tired of emphasizing the importance of carrying them out in proper times. This clearly envisaged a dependable calendar. Thus, the building of the different types of fire altars and consecration (*agnyādhāna*), or the holding of seasonal sacrifices (*cāturmāsyāni*), the full-moon sacrifices, the *soma* feast lasting a year, the yearly *sattras* and so on involved knowledge of a workable calendar and presupposed a class of priests skilled in time-reckoning.

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In the sacred literature of the Hindus, the Jainas and the Buddhists, such a skilled priest has been referred to as ‘astronomer’ and his science ‘astronomy’ (*jyotiṣa*). In the *Muṇḍaka Upaniṣad*a astronomy is included in the list of several branches of Vedic studies. The *Chāndogya Upaniṣad*b has it that Nārada, upon being interrogated by Sanat Kumāra as to the range of his knowledge, replied, ‘I have learnt the *Ṛgveda*, the *Yajurveda*, the *Sāmaveda* and the fourth the *Atharvaveda*; the *Itihāsa* and the *Purāṇa* as the fifth *Veda*; grammar, the science *par excellence*; the obsequies of Manu; the art of computation; omens; the revolutions of periods; speech; ethics; scriptures; sciences appendant on holy writings (accentuation, prosody, etc.); the abjuration of spirits; the military science; *astronomy*; snake-charming; music and mechanical arts (sciences of the demi-gods).’ In explaining the scope of astronomy, the *Vedāṅga Jyotiṣa* states: ‘The Vedas are revealed for the purpose of performing sacrificial rites; these rites are laid down in order of time. Therefore, he who is versed in astronomy, the science of the reckoning of time, knows the sacrifices.’ In the *Brāhmaṇa* literature, we come across the term *nakṣatra-darśa* meaning ‘a star gazer’ or ‘a gazer at the lunar mansions’. This term has also been used sometimes to mean an astrologer. Another term used to refer to an astronomer is *gaṇaka* which literally means ‘a calculator’ or ‘a mathematician’. The use of these two terms appears to imply the study of astronomy both from the practical (observation of stars) and theoretical (calculation) considerations.

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The Jainas also claim considerable antiquity for their interest in, and study of, astronomy. The four branches of their canonical texts include *gaṇitānuyoga* (principles of mathematics), *saṃkhyāna* (arithmetic) and *jyotiṣa* (astronomy).c Like the Brāhmaṇas, the Jainas, too, demanded of their priests great proficiency in astronomy for the proper observance of their religious ceremonies. The Buddhists did not evince much interest in astronomy due probably to the degeneration in their time of astronomy into astrology, and to the difficulty of distinguishing between the two. We find in their literature the term *nakṣatra-pāṭhaka* (a reader of stars) which refers both to an astronomer and an astrologer. Buddha referred to astronomy and astrology as low forms of arts (*tiracchāna vijjā*) and advised Buddhist monks to refrain from the study of astronomy.a This opinion, however, was modified later on and the *bhikṣus* dwelling in the woods were advised to learn the elements of astronomy.

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a *Muṇḍ. Up.*, i. 1.5.

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b *Chānd. Up.*, vii, 1–4.

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c *Bhag. Sū.*, 90; *Uttar. Sū.*, xxv. 7.8.38.

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From what has been stated above, and will appear in what follows, there is no doubt that astronomy was cultivated to a considerable extent in India in the Vedic times. The selection of a few fixed stars for the development of a system of lunar mansions, the fixation of a *sāvana* year of 360 days, based upon the variation of the length of day, the elaboration of a quinquennial cycle with intercalary months, going back to the time of the *Ṛgveda*, the idea of the four mundane ages and several other findings abundantly show their interest and proficiency in astronomy. This Brāhmaṇic interest and proficiency did not also escape the notice of foreign observers and writers, for Megasthenes found the *yuga* system flourishing in full perfection and Strabo referred to astronomy as a favourite occupation of the Brāhmaṇas.b

Astronomical Knowledge as Revealed in the Saṃhitās, Brāhmaṇas and Sūtras

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Before summarizing the astronomical information contained in this vast body of the sacred literature, a few general remarks may be made here. Of the various sacerdotal families such as those of Gṛtsamada, Viśvāmitra, Vāmadeva, Atri, Bharadvāja and Vasiṣṭha, who originated some of the oldest hymns, the family of Atri was probably distinguished for their interest in astronomy. Atri's name is frequently mentioned in connection with eclipse hymns both in the *Saṃhitās* and the *Brāhmaṇas*. The *Sāmaveda* and its *Brāhmaṇas* and *Sūtras* are full of interest from the viewpoint of calendrical astronomy because of their fuller treatment of *gavām ayana* and the *sattras* of various durations, built round the daily progress of the sun. The various recensions of the *Yajurveda* are by far the most important of this class of literature from the viewpoint of the early history of Hindu astronomy. While the *nakṣatras* are doubtless mentioned in the *Ṛgveda*, their whole series, numbering 27 or 28 and headed by *Kṛttikās*, turns up for the first time in the recensions of the *Yajurveda*. These texts are again repositories of several mythologies developed around stellar constellations. The details of *darśapūrṇamāsa*, i.e. the new- and full-moon sacrifices, the *cāturmāsya* or four-monthly sacrifices, seasons, months and month names, are here met with. The importance of the winter solstice is emphasized through the *mahāvrata* rites which are also dealt with at length in the *Brāhmaṇas* of the *Sāmaveda*. The number 10,800 used to specify the bricks required for some types of altars appears to be related to the length of the astronomical *yuga* characteristic of the later *Siddhānta-jyotiṣa* texts. The *gavām ayana* and the *sattras*, probably taken over from the *Sāmaveda* and its *Brāhmaṇas*, find lengthy treatment in these *Yajus* texts. The *Atharvaveda* offers little assistance towards our understanding of the nature and extent of the Vedic astronomy. Nevertheless, it does contain stray passages of astronomical consequence, such as the solar eclipse, the mention of *Rāhu* for the first time, intercalation with a thirteenth month and a list of 28 *nakṣatras* including *Abhijit*. Finally, its cosmogonic and theosophic hymns addressed to Goddess Earth, the glorification of the sun, and the personification of time as a primordial power have also some relevance to this study.

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a Rhys Davids, II, pp. 20 ff.; Oldenberg, *VP. Culla.*, v. 33.3.

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b Weber, p. 246.

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The *Brāhmaṇas* are systematized theological works composed for the main purpose of elucidating the sacrificial texts and explaining the origin and hidden meaning of sacrifices. Each *Saṃhitā* gave rise to a number of *Brāhmaṇas*. In this way astronomical ideas and precepts embedded in the *Saṃhitās* assumed clearer perspective through Brāhmaṇic interpretations. As the materials of the *Saṃhitās* and the *Brāhmaṇas* constitute the basis of the *sūtras*, passages in them of astronomical import have received fresh treatment and sometimes further elaboration at the hands of the *sūtrakāras*. Such is particularly the case with regard to the Vedic calendars. Although the elements and suggestions of such calendars are met with in the *Vedas* proper, different modes of year-reckoning and calendar-keeping appear clearly in the *sūtras*. The *Lāṭyāyana Śrautasūtra* and the *Nidānasūtra* of the *Sāmaveda* are particularly important for this purpose. The *Śulba-sūtras* forming part of the *Kalpasūtras*, as we shall see in the section on mathematics, are important as the oldest Indian works on geometry. Finally, we have two *Jyotiṣa-Vedāṅgas*, one in the *Yajurveda* recension containing 43 verses and the other in the *Ṛgveda* recension containing 36 verses, dealing exclusively with astronomy.

The Sun, the Moon, the Earth and Planets

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The Sun

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From the Ṛgvedic times the universe was regarded as divided into three distinct regions, the earth (*pṛthivī*), the firmament (*antarikṣa*) and the heaven (*dyaus*). Each region again had a threefold subdivision. The sun during its sojourn through the universe illuminates and sustains all these regions and their subdivisions. These ideas have been repeatedly expressed in several hymns and verses of the *Ṛgveda*, such as ‘the sun hath filled the air and earth and heaven’,a ‘Ye Gods who yonder have your home in the three lucid realms of heaven’,b and more fully elsewhere.c The ‘threefold earth’, the ‘triple sphere of light’ and similar threefold division of the intermediate region, the sky, have been further elaborated in the *Brāhmaṇas*, as witness the following passage of the *Pañcaviṃśa Brāhmaṇa*:a

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a *ṚV.*, I. 115.1.

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b *ṚV.*, I. 105.5.

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c *ṚV.*, IV., 54.2–7.

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‘Through fire, earth and plants, thereby this world is threefold: through wind, intermediate region and birds, thereby that world is threefold, which stands between; through sun, sky and stars, thereby yonder world is threefold.’

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The Ṛgvedic verses also bring out very clearly the important part played by the sun as a beneficial power in the Vedic mythology and also its various roles in nature. By its light it not only reveals the worlds, but regulates them, and sustains life on the earth. Although it illuminates the worlds, it also causes the constellations with their weak beams to pass away, like thieves, before its all-beholding rays of light.b These rays of light are seven in colour, for ‘where these seven rays are shining, thence my house and family extend’c and are often likened to the sun god’s ‘bay coloured horses, bright, changing hues, which speed round earth and heaven.’d

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As to its regulating powers in nature, it is the cause of the flowing of the floods and the winds and is the maker of time through the alteration of day and night, the twilight, month and year. Regarding day and night the *Aitareya Brāhmaṇa*e of the *Ṛgveda* states that the sun neither sets nor rises. After reaching the end of the day, it only changes about and in the process makes night below and day on the other side. After reaching the end of the night, the sun makes day below and night on the reverse side. According to another naïve interpretation, the sun was here represented as possessing a bright and a dark face; at the end of the day, the sun’s dark face was turned towards the earth making night below and the bright face upwards illuminating the stars in the upper regions of the heaven.

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The Sun's Path, the Ecliptic

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There are several references in the *Ṛgveda* and in the *Brāhmaṇas* of the later ages to the sun’s path through the heavens. Varuṇa, the chief of the Lords of natural order, has made a spacious pathway for the sun to travel.f This path called *ṛta* is easy to find. Elsewhere, it is referred to as Aryaman’s mighty path: ‘How may we pass the wicked on the path of mighty Aryaman? Mark this my woe, ye Earth and Heaven.’g The *Pañcaviṃśa Brāhmaṇa* speaks of this path as follows: ‘By means of this (rite), Aryaman gained the world. The path called Aryaman’s path is the path leading to the Gods. They who undertake this (rite) reach the path leading to the Gods.’h According to the *Śatapatha Brāhmaṇa*, ‘to Bṛhaspati belongs that upper region, and there above lies that path of Aryaman (the sun).’a These passages have been interpreted in two ways. Weber regarded Aryaman’s path as the milky way; Hillebrandt, Ludwig and others as the ecliptic. Ludwig further traced the inclination of the ecliptic to the equator in another passage of the *Ṛgveda* in which the *Ṛbhus* are described as wandering afar in their path.

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a *Pañc. Br.*, x. 1.1.

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b *ṚV.*, I. 50.2.

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c *ṚV.*, I. 105.9.

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d *ṚV.*, I. 115.3.

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e *Ait. Br.*, iii. 44.4.

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f *ṚV.*, I. 24.8.

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g *ṚV.*, I. 105.6.

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h *Pañc. Br.*, xxv. 12.2.3.4.

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From the way Aryaman’s path is described it is not immediately easy to associate it with the ecliptic, but such inference is quite possible from the knowledge of the Vedic Hindus about the sun’s annual revolution, its going northward (*uttarāyaṇa*) for half of the year and southward (*dakṣiṇāyana*) for the remaining half, the references to solstices and other related matters. Of further significance in this regard is the occurrence of such terms as *devayāna* and *pitryāna* from which Tilak attempted to derive the knowledge of equinoxes in the Vedic times and therefore of the celestial equator, the ecliptic and their inclination.b

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*The Moon*

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The moon, the next most conspicuous object in the night sky, receives such appellations as *candra*, *candramas* and *soma*. It has no light of its own, but assumes ‘the brilliancy of the sun’c or ‘is adorned with Sūrya’s arrowy beam’,d that is it shines with the borrowed light of the sun. The phases of the moon are described by saying that the moon, ‘born afresh, is new and new for ever’.e Some of its phases received special names and personifications. Thus, the day before the new moon was called *sinīvālī*, the new moon day *kuhū*, the day preceding the full moon *anumati* and the full moon day *rākā*. An allegorical description of the sun swallowing the moon on the new moon day so that it can neither be seen in the eastern nor the western sky is preserved in the *Śatapatha Brāhmaṇa*f as follows:

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‘Now the one that burns there (viz. the sun) is, assuredly, no other than Indra, and that moon is no other than Vṛtra. But the former is of a nature hostile to the latter, and for this reason, though this one (the moon, Vṛtra) had previously (to the night of new moon) risen at a great distance from him (the sun, Indra), he now swims towards him and enters into his open mouth.

‘Having swallowed him, he (the sun) rises; and that (other) one is not seen either in the east or in the west . . .

‘Having sucked him empty, he throws him out; and the latter, thus sucked out, is seen in the western sky, and again increases; he again increases to serve that (sun) as food . . .’

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The above passage sets forth the moon’s elongation from the sun, its true motion from west to east and the cause of the new and full moon.

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The interval between the consecutive new moons or full moons was seized upon at quite an early date as a natural unit of time, the month, in much the same way as it was done by the people of other culture areas, the Babylonians, the Greeks and so on. From several verses and passages stating that the year consists of 360 days and of 12 months, it appears that a month of 30 days was widely accepted in the time of the *Saṃhitās* and the *Brāhmaṇas*. The month was again divided into two natural halves, the light half (*śukla*) from new to full moon and the dark half (*kṛṣṇa*) from full to the new moon. The Ṛgvedic bard had thus no hesitation in proclaiming:a

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a *Śat. Br.*, v. 3.1.2.

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b Tilak, pp. 112 ff.

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c *ṚV.*, IX. 71.9.

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d *ṚV.*, IX. 76.4.

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e *ṚV.*, X. 85.19.

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f *Śat. Br.*, i. 6.4.18–20.

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‘Twelve are the fellies, and the wheel is single; three are the
naves. What man hath understood it?
‘Therein are set together spokes three hundred and sixty,
which in no wise can be loosened.’

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The moon’s synodic period was later on more correctly given as 29½ days. Its sidereal period lying between 27 and 28 days appears to have been correctly formulated in the days of the early *Saṃhitās* as is clear from the development of the 27 or 28 *nakṣatra* system.

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*The Solar Eclipse*

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Observation of the solar eclipse is recorded in several places in the Vedic literature in the form of the well-known Svarbhānu legend. According to its earliest Ṛgvedic version,b Svarbhānu, the *asura*, pierced the sun with darkness so completely that the bewildered inhabitants on the earth did not know where they were standing. Then Atri, with the power of his prayers, caused Svarbhānu’s magic arts to disappear and restored the sun to its brilliance. The Svarbhānu legend and Atri’s part in ending the eclipse appear in a number of places in the *Pañcaviṃśa Brāhmaṇa*, of which a typical description runs as follows:c

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‘The Daemoniac Svarbhānu struck the sun with darkness; the
Gods did not discern it (the sun hidden as it was by darkness): they
resorted to Atri; Atri repelled its darkness by the *bhāsa*. The part
of the darkness he first repelled became a black sheep, what (he repelled)
the second time (became) a silvery (sheep), what (he repelled) the third
time (became) a reddish one, and with what (arrow) he set free its
original appearance (colour), that was a white sheep.’

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The interesting feature of the above passage is the detailed observation of the change of colour in the sun’s disc during the progress of an eclipse.

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The frequent and consistent references to Atri in connection with eclipses doubtless indicate a class of Brāhmaṇa priests skilled in eclipse observations and in astronomy in general. The eclipse hymns of the *Ṛgveda* contain an expression *turīyeṇa brahmaṇā* which, according to some scholars, meant a kind of quadrant; but such interpretation is far-fetched.

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a *RV.*, I. 164.48; Eng. trans. by Griffith.

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b *RV.*, V. 40.5–9.

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c *Pañc. Br.*, vi. 6–8; Eng. trans. by Caland.

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*The Earth*

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It is difficult to say definitely if the Vedic Hindus regarded the earth as spherical. The sphericity of the earth may be implied in such casual statements as the earth is freely suspended in air,a the dawn precedes the sunriseb and the like. In the cosmogonic and theosophic hymns of the *Atharvaveda*c the earth and the heaven have been imagined as constituting two hemispheres which the Brahmacārin guards with his creative power. This and statements like the placing of fire between two receptacles or the union of two *agnis* between the two hemispheres of the world suggest terrestrial sphericity, later on accepted uniformly in Hindu astronomical texts.

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*The Planets*

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The study of planets appears in late astronomical works. The *Vedāṅga Jyotiṣa* does not mention them. But this does not mean that the Vedic Hindus were altogether unacquainted with planets. Weber did not notice the mention of planets in any texts earlier than the *Taittirīya Āraṇyaka*. In the *Maitrāyaṇī Upaniṣad*, planets (*graha*) are mentioned. In the early astronomical *saṃhitās*, planets are mentioned in the context of their astrological implications. Planet worship is established in Yājñavalkya’s law-book and is mentioned in the epics, and in the dramas of Kālidāsa and in the *Mṛcchakaṭika*. Opinion, however, differs as to whether earlier Vedic works contain any evidence of the knowledge of planets. The 7 *ādityas* mentioned in the *Ṛgveda*d were interpreted by Oldenberg as referring to the sun, the moon and the 5 planets. The number 34 used to express, in hymn X. 55.4, the lights with which Indra looks around him and, in hymn I. 162.18, the ribs of the sacrificial horse has been explained by Ludwig as referring to the sun, the moon, 5 planets and 27 *nakṣatras*.

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More convincing perhaps is the association of Bṛhaspati, Lord of Prayer, with the planet Jupiter. The *Taittirīya Brāhmaṇa* refers to the conjunction of Bṛhaspati with the *nakṣatra Tiṣya*. The planet’s first birth ‘from mighty splendour in supremest heaven’ is also referred to in the *Ṛgveda*. The *Ṛgveda* and the *Brāhmaṇas* contain the words *śukra*, *manthin* and *vena*, and attempts have been made to associate them with the planet Venus; but this interpretation has not found acceptance with all scholars.

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*Rāhu and Ketu*

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To the seven planets, including the sun and the moon, the Indians added *Rāhu* and *Ketu*, to formulate their *Rāhu-Ketu* theories of eclipses. The word *Rāhu*, in the sense of a planet, appears in the *Atharvaveda* and the *Chāndogyopaniṣad* apparently with no astronomical meaning, but in the *Yājñavalkyasmṛti* it does so in the astronomical sense. The word *Ketu* also appears in the *Atharvaveda* in the sense of any unusual or striking phenomenon such as comet, meteor or a falling star. Astronomical *saṃhitās*, however, do not mention *Ketu* as a cause of eclipse. *Rāhu* and *Ketu*, along with planets, are mentioned in the *Mahābhārata*, though *Ketu* is omitted in the *Rāmāyaṇa*. From Varāhamihira onwards, in true astronomical circles, *Rāhu* and *Ketu* meant the ascending and the descending node respectively of the moon.

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a *ṚV.*, IV. 53.3.

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b *ṚV.*, I. 123.

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c *AV.*, XI. 5.8–11.

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d *ṚV.*, IX. 114.3.

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The ingenious *Rāhu*-*Ketu* theory of eclipse travelled from India to China and appeared in a Chinese astronomical text *Chiu Chih*. This *Chiu Chih* was the Chinese version of an Indian calendrical work called *Navagraha* and its translator was the well-known Tantric-Buddhist astronomer Chhuthan Hsi-Ta who flourished at the Thang court during the first quarter of the eighth century A.D.

The Stars, the Nakṣatra System and the Lunar Zodiac

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Unlike the Babylonians or the Chinese, the ancient Indian astronomers were not particularly interested in the study of stars as such and in the preparation of star catalogues. They were primarily interested in the study of the motions of the sun and the moon with a view to developing a workable calendar. As such their interest in stars and constellations largely centred round those which lie along or near the ecliptic. By a careful selection of suitable stars and constellations they were able to provide a stellar frame of reference against which to follow and measure planetary motions. A number of ancient civilizations—the Indian, the Chinese, the West Asian and the Egyptian—developed and perfected such a stellar frame of reference to mark the path of the sun and the moon. The system came to be known as that of the *nakṣatras* among the Indians, of the *hsius* among the Chinese, of *manāzil* among the Arabs and so on.

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The origin of the Indian *nakṣatra* system has been traced to the *Ṛgveda*, where the term *nakṣatra* has been used both in the sense of stars and lunar mansions. In the former sense it appears in I. 50.2; VII. 86.1; X. 68.11 and in several hymns. The sun is also sometimes identified with stars.a In the sense of lunar mansions, at least two *nakṣatras* are clearly mentioned, namely *Maghā* (*Aghā*) and *Phalgunīs* (*Arjunīs*), as in the thirteenth verse of the sun’s bridal hymn 85 in the tenth *maṇḍala*:

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‘The bridal pomp of Sūrya, which Savitar started, moved along.
In Maghā days are oxen slain, in Arjunīs they wed the bride.’b

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Although other *nakṣatras* are not specifically named, Ludwig, Zimmer and others held that 27 *nakṣatras* were already known when the *ṛcas* were formed and included in the number 34 (the sun, the moon, 5 planets and 27 *nakṣatras*) previously referred to. Their use in the sense of lunar mansions is also stated clearly in another expression: ‘Thus Soma in the midst of all these constellations hath his place.’c *Nakṣatra list in the Vedic Saṃhitās, the Vedāṅga Jyotiṣa and in the Sūrya-siddhānta*

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a *ṚV.*, III. 54.19.

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b Eng. trans. by Griffith.

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c *ṚV.*, X. 85.2.
* *Abhijit* is, however, mentioned in the *Taittirīya Brāhmaṇa*. † In the *Vedāṅga Jyotiṣa*, the head of the *nakṣatras* is not mentioned. From the statement that solstices coincide with *Dhaniṣṭhā* and *Āśleṣa*, vernal equinox appears to coincide with *Bharaṇyaḥ* and so the list has been shown in the table starting with this *nakṣatra*.

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| No. in order | *Taitt. Sam.* (IV. 4.10) | *Maitrā. Sam.* (II. 13.20) | *Kāṭh. Sam.* (XXXLX, 13) | *Atharvaveda* | No. in order | *Vedāṅga Jyotiṣa* (18) | No. in order | *Sūrya-siddhānta* (VIII. 2–21) |
| 1. | Kṛttikās | Kṛttikās | Kṛttikās | Kṛttikās | 1. | Bharaṇyaḥ† | 1. | Aśvinī |
| 2. | Rohiṇī | Rohiṇī | Rohiṇī | Rohiṇī | 2. | Kṛttikā | 2. | Bharaṇī |
| 3. | Mṛgaśīrṣa | Invagā | Invakā | Mṛgaśiras | 3. | Rohiṇī | 3. | Kṛttikā |
| 4. | Ārdrā | Bāhu | Bāhu | Ārdrā | 4. | Mṛgaśiras | 4. | Rohiṇī |
| 5. | Punarvasū | Punarvasū | Punarvasū | Punarvasū | 5. | Ārdrā | 5. | Mṛgaśiras |
| 6. | Tiṣya | Tiṣya | Tiṣya | Puṣya | 6. | Punarvasū | 6. | Ārdrā |
| 7. | Āśreṣās | Āśleṣās | Āśleṣās | Āśleṣās | 7. | Puṣya | 7. | Punarvasu |
| 8. | Maghās | Maghās | Maghās | Maghās | 8. | Āśleṣa | 8. | Puṣya |
| 9. | Phalgunī | Phalgunīs | Phalgunīs | Pūrvā Phalgunyau | 9. | Maghā | 9. | Āśleṣā |
| 10. | Phalgunī | Phalgunīs | Uttarāḥ Phalgunīs | | 10. | Pūrvaphalgunī | 10. | Maghā |
| 11. | Hasta | Hasta | Hastau | Hasta | 11. | Uttaraphalgunī | 11. | Pūrvaphālgunī |
| 12. | Citrā | Citrā | Citrā | Citrā | 12. | Hasta | 12. | Uttaraphālgunī |
| 13. | Svāti | Niṣṭya | Niṣṭya | Svāti | 13. | Citrā | 13. | Hasta |
| 14. | Viśākhe | Viśākhe | Viśākhā | Viśākhe | 14. | Svāti | 14. | Citrā |
| 15. | Anūrādhās | Anūrādhā | Anūrādhās | Anūrādhā | 15. | Viśākhā | 15. | Svāti |
| 16. | Rohiṇī | Jyeṣṭhā | Jyeṣṭhā | Jyeṣṭhā | 16. | Anurādhā | 16. | Viśākhā |
| 17. | Vicṛtau | Mūla | Mūla | Mūla | 17. | Jyeṣṭhā | 17. | Anurādhā |
| 18. | Aṣāḍhās | Aṣāḍhās | Aṣāḍhās | Pūrva Aṣāḍhās | 18. | Mūla | 18. | Jyeṣṭhā |
| 19. | Aṣāḍhās | Aṣāḍhās | Uttarā Aṣāḍhās | Uttarā Aṣāḍhās | 19. | Pūrvāṣāḍhā | 19. | Mūla |
| 20. | * | Abhijit | — | Abhijit | 20. | Uttarāṣāḍhā | 20. | Pūrva Aṣāḍhā |
| 21. | Śroṇā | Śroṇā | Aśvattha | Śravaṇa | 21. | Śravaṇa | 21. | Uttarā Aṣāḍhā |
| 22. | Śraviṣṭhās | Śraviṣṭhās | Śraviṣṭhās | Śraviṣṭhās | 22. | Dhaniṣṭhā | 22. | Abhijit |
| 23. | Śatabhiṣaj | Śatabhiṣaj | Śatabhiṣaj | Śatabhiṣaj | 23. | Śatabhiṣaj | 23. | Śravaṇa |
| 24. | Proṣṭhapadās | Proṣṭhapadās | Proṣṭhapadā | Dvayā Proṣṭhapadā | 24. | Pūrva Bhādrapadā | 24. | Śraviṣṭhā |
| 25. | Proṣṭhapadās | Proṣṭhapadās | Uttare Proṣṭhapadās | | 25. | Uttara Bhādrapadā | 25. | Śatabhiṣaj |
| 26. | Revatī | Revatī | Revatī | Revatī | 26. | Revatī | 26. | Pūrva Bhādrapadā |
| 27. | Aśvayujau | Aśvayujau | Aśvayujau | Aśvayujau | 27. | Aśvayujau | 27. | Uttara Bhādrapadā |
| 28. | Apabharaṇīs | Bharaṇīs | Apabharaṇīs | Bharaṇyas | | | 28. | Revatī |

c6.s1.t2.9

The full list of 27 or 28 *nakṣatras* headed by *Kṛttikās* appears in the various recensions of the *Black Yajurveda* and in the *Atharvaveda*. Table 2.1 gives the full list of *nakṣatras* as found in the *Saṃhitās*, in the *Vedāṅga Jyotiṣa* and in later astronomical *siddhāntas* (the list given in the *Sūryasiddhānta* is given here).

c6.s1.t2.10

It is clear from the table that the *nakṣatra* names have remained practically the same since their formulation in the Vedic times. The *nakṣatra Abhijit* does not appear in all the lists, making the number sometimes 27 and sometimes 28. It appears only in the *Maitrāyaṇī Saṃhitā*, the *Atharvaveda*, the *Taittirīya Brāhmaṇa* and some *Siddhāntic* texts, but the star does not have associated with it any *nakṣatra* space. This *nakṣatra* space requires some clarification. The term *nakṣatra* has been used to indicate both asterisms, stars or star-groups, and any of the 27 equal divisions of the ecliptic, each distinguished by a determinant star (yoga *tārā*). Derived from *nakta-tra*, it means ‘guardian of night’, that is stars or star-groups, and in this sense the word must have been used at the beginning. Later on, *nakṣatra* meant one of the 27 equal parts, that is a space of 13° 20′ or 800′ of the ecliptic. In the *Sūrya-siddhānta* and such later astronomical works, a *nakṣatra* division of 800′ has been clearly defined, and the positions of the determinant or junction stars have been given in degrees and minutes with respect to the starting point of the *nakṣatra* concerned. These values have been given in accordance with a system of polar coordinates—the polar longitudes (*dhruvaka*) and latitudes (*śara*)—from which true longitudes and latitudes or right ascensions and declinations can be calculated for comparison with current stellar positions. Colebrooke, Burgess and Whitney and other historians of Hindu astronomy have carried out these conversions and identified Hindu *nakṣatras* with those given in modern star catalogues. Some of these identifications, the Hindu stellar configurations and the legends built round them are summarized below.

c6.s1.t2.11

*The Nakṣatras and Constellations*

c6.s1.t2.12

*Kṛttikā* is a group of 6 or 7 stars known as Pleiades; the dominant star is η Tauri (magnitude 3). According to the *Yajurveda*, this group consists of 7 stars and, according to al-Bīrūnī and other texts, of 6 stars. It corresponds to the Chinese *hsieu Mao* and the *manāzil ath-Thuraiyā*. *Rohiṇī* has been identified with Aldebaran or α Tauri (magnitude 0·9). *Mṛgaśīrṣa* figured as the ‘antelope’s head’ is a group of 3 stars, λ, φ¹ and φ² in Orion. Around *Rohiṇī* and *Mṛgaśīrṣa* developed the Prajāpati legend given in the *Aitareya* and the *Śatapatha Brāhmaṇa*. Lord Prajāpati once fell in love with his own daughter *Rohiṇī* and in the form of a deer pursued her as she was running away in the form of a female deer. Enraged at such incestous chase, the gods ordered Rudra to stop the chase, whereupon Rudra assumed the form of a hunter (*Mṛgavyādha*) and pierced Prajāpati with his arrow. The head of the antelope with the arrow sticking to it became the constellation *Mṛgaśīrṣa*.

c6.s1.t2.13

*Punarvasū* is the twin stars Castor and Pollux in the constellation of Gemini. *Puṣya* is a group of 3 to 5 faint stars in Cancri. *Āśreṣās* (or *Āśleṣās*) and *Maghā* each is a cluster of 5 to 6 stars, the former in Hydrae and the latter in Leonis. *Phalgunī* is a double-star constellation in Leo. The five-starred *Hasta*, meaning hand, is in Corvus. *Citrā* is the readily identifiable brilliant star α Virginis or Spica of the first magnitude. So also in *Niṣtyā* or *Svātī*, the brilliant α Bootis or Arcturus (magnitude 0·0). To *Viśākhā* are attached sometimes 2 and sometimes 4 stars in Librae and to *Anurādhā* 4 stars in Scorpionis. *Jyeṣṭhā* is a trio in Scorpio, of which the determinant star is Antares or α Scorpionis (magnitude 0·8).

c6.s1.t2.14

*Abhijit* (determinant α Lyrae) has no *nakṣatra* space assigned to it in the ecliptic. Its 3 stars form a triangle in Lyra. It is mentioned only in texts giving a list of 28 *nakṣatras*, but not in those giving one of 27. This might mean a later addition to, or even dropping out from, the original list and received much attention in connection with the question of origin of the *nakṣatra* system and its relationship with similar systems in other civilizations.

c6.s1.t2.15

*Śroṇā* or *Śravaṇa* (determinant α Aquilae) is a constellation of 3 stars in Aquilae; the four-starred *Dhaniṣṭhā* is in Delphinus; and *Śatabhiṣaj*, meaning ‘having one hundred physicians’, is a thickly studded cluster in Aquarii. The two *Bhādrapadās* are twin star-groups in Pegasi. *Revatī*, a group of 32 stars, has its determinant star in ζ Piscium (magnitude 5·5). The end of this *nakṣatra* (according to the *Sūrya-siddhānta*, 13° 10′ from the beginning of *Revatī* or 359° 50′ with respect to the First Point of Aries) or the beginning of *Aśvinī*, the next *nakṣatra* in Aries marked the initial point of the Hindu sphere about a.d. 572.

c6.s1.t2.16

*The Nakṣatra and Lunar Mansions of Other Nations*

c6.s1.t2.17

We have said that a number of nations of antiquity, notably the Chinese, the Arabs and the Babylonians, followed a system of lunar mansions analogous to that of the *nakṣatras*. Whether all these systems had a common origin or had developed independently became naturally enough a subject of considerable discussion and controversy. The Sinologists, the Indianists and the Assyriologists laid powerful claims on the anteriority as well as the originality of their respective systems, and not unoften suggested borrowing by other nations of the system they considered native to the culture area of their preference. But the question has still remained very much an open one.

c6.s1.t2.18

*The Hsius*

c6.s1.t2.19

The Chinese *hsius* were originally selected to mark the equator and facilitate observation of the culmination of stars.a In their system a series of circumpolar stars were keyed to equatorial stars so that, by observing the lower meridional transits of the former, those of the latter below the horizon could be readily ascertained. The declination circles passing through the selected equatorial and the corresponding circumpolar stars divided the equator into a number of unequal segments called the *hsius*. At least two of the *hsiu* stars, the Bird Star (α Hydrae) and the Fire Star (π Scorpii), have been recognized in the carvings of the oracle-bones belonging to the Shang period (1500 B.C.). The *Book of Odes* (Shih Ching) believed to have come down from the eighth or ninth century B.C. records about 8 *hsius*. The use of four quadrantal *hsius*, e.g. Fang (middle of Eastern Palace), *Hsü* (middle of Northern Palace), *Mao* (middle of Western Palace) and *Hsing* (middle of Southern Palace), is met with in the *Historical Classic* (eighth to fifth century B.C.). *The Lesser Annuary of the Hsia Dynasty* (fourth century B.C.), a kind of farmer's calendar, mentions all the four quadrantal stars plus two more, *Wei* (μ Scorpii) and *Liu* (δ Hydrae). A fuller list of *hsius*—23 out of 28—is given in the *Records of Rites of Younger Tai* (first century B.C.). The full list of 28 *hsius*, however, appears for the first time in *Huai Nan Tzu* (160 or 150 B.C.) and, more importantly, as a lunar zodiac and not as equatorial stars of earlier records.

c6.s1.t2.20

a Needham, III, pp. 242–52.

c6.s1.t2.21

Thus the full list of 28 *hsius* appeared in China several centuries later than did the *nakṣatra* list in the various recensions of the *Black Yajurveda*. As a lunar zodiac, the Chinese system did not emerge before the fourth century B.C., if not later. As to the *hsius* themselves, many of them differ importantly from the *nakṣatras*. Nine *nakṣatras* agree with the corresponding *hsius* both in regard to their determinant stars and more or less with the number of stars attached to the constellations. For 11 *nakṣatras*, the determinants are different although they belong to the same constellations. For the remaining 8 *nakṣatras* and *hsius*, the determinant stars were selected from different constellations.

c6.s1.t2.22

The Manāzil

c6.s1.t2.23

The Arabian *manāzils*, 28 in number, agree on the whole with the Indian *nakṣatras*. Their lunar zodiac is headed by *ash-Sharaṭān*, the first *manāzil* corresponding to *nakṣatra Aśvinī* which marked the point of intersection between the equator and the ecliptic about the fifth or sixth century A.D. As many as 19 *manāzils* agree with the corresponding *nakṣatras*; there are discrepancies with regard to *Ārdrā*, *Hasta*, *Svātī*, *Abhijit*, *Śroṇā*, *Śraviṣṭhā* and *Revatī* vis-à-vis the corresponding *manāzils*. Weber at one time believed that the Arabian lunar stations had been derived directly from the Indian *nakṣatras*. The recorded evidence of transmission of Indian astronomical texts, particularly the *Siddhāntas*, makes such a view attractive; but, as Filliozat (3) has pointed out, all this, even the close resemblance between the two systems, does not *ipso facto* prove an Arab borrowing from India. Long before the beginning of active Arab scientific contacts with India during the reign of the Abbāsid Caliphs, the *manāzils* found mention in the al-Qur'ān (x. 5; xxxvi. 39). The *Fihrist* records that the ancient Harranites had a custom of visiting their temples for offering sacrifices to the moon and performing other religious ceremonies on the 27th or 28th day of each month, from which Weber inferred far-fetchedly knowledge of lunar mansions among the Harranites.a Of greater consequence perhaps were his interpretations of the Hebrew word *mazzaloth* or *mazzaroth* in the Book of Job (38. 32) and Book of Kings (23. 5) to mean *manāzil* and suggestion of Chaldean origin. Derivation of the *manāzil* from an Iranian system was attempted by Leopold de Saussure.

c6.s1.t2.24

*The Question of Babylonian Origin of Lunar Mansions*

c6.s1.t2.25

Weber, Whitney and later on Hommel and other Assyriologists favoured the theory of a Babylonian origin of lunar mansions. The Babylonians, at quite an early date, developed the knowledge of constellations and its use in following the motions of the sun, the moon and planets. By about 1100 B.C. they had divided the sky into three zones of 12 sectors each, these sectors containing the names of constellations, planets and simple numbers in arithmetic progression. Moreover, they assigned 3 stars or constellations to every month, which indicates an attempt to obtain some kind of correlation of months to constellations.

c6.s1.t2.26

A true zodiacal scheme is implied in the important series of texts known as mulAPIN dated about 700 B.C., but based on older materials. These tablets give the names of about 18 constellations more or less along the ecliptic. Here are some of them: mulmul (Pleiades), mulgu4.an.na (Taurus), mulUR.GU.LA (Leo), mulab.Sín (Spica), mulPA.BIL.SAG (Sagittarius) and so on. Later texts appear either to multiply or to reduce the number of stars with a view to defining planetary positions more accurately and, in this manner, their number gradually rose to 33 or more as recorded in Babylonian ephemerides.

c6.s1.t2.27

The first attempt to construct out of 33 or 36 Babylonian normal stars a lunar zodiac composed of 24 ecliptic stars was due to Fritz Hommel of Munich.b He compared the Babylonian stars with the Arabian *manāzils*, found agreement in respect of 16 stations and concluded that the *manāzils* were based on the more ancient Babylonian scheme. On the basis of the theory of common origin, Hommel's work was taken to be an important argument in favour of the derivation of the various lunar zodiac schemes from the Babylonian. Thibaut raised a number of objections to such a view.c Between the *nakṣatras* and the Babylonian ecliptic stars, agreement has been noticed in the case of about one-third of the total number. *Mṛgaśīrṣa*, *Ārdrā*, *Āśreṣās*, *Hasta*, *Mūla*, *Abhijit* and *Śraviṣṭhās* differ completely from their opposite numbers in the Babylonian series. Even in the agreement itself there is nothing very surprising if one bears in mind that, in all these separate attempts, the task was the same, namely to select a series of conspicuous asterisms near the ecliptic. In such circumstances it is inevitable that specially bright stars such as α Tauri, β Geminorum, α Leonis, α Virginis, α Scorpionis—all of the first magnitude—

c6.s1.t2.28

a Weber, p. 248.

c6.s1.t2.29

b Hommel, pp. 592–619.

c6.s1.t2.30

c Thibaut (3), pp. 144–63.

c6.s1.t2.31

or such well-defined stars such as Pleiades, α and β Geminorum, α and β Librae should be selected.

c6.s1.t2.32

Another important objection is that the Babylonian series comprises 33 or 36 stars, whereas the *manāzil* consists of 28 and the *nakṣatra* 27 or 28 star-groups. Hommel tried to explain this by guessing that the lunar zodiacs of all nations had originally 24 stars or star-groups only, which were expanded into 27, 28 or even a larger number. The Chinese *hsius*, it is true, had 23 members at some early stage of their development, but such is not the case with either the *manāzil* or the *nakṣatra*, which from the beginning comprised of 27 or 28 stations.

c6.s1.t2.33

Thus the common origin hypothesis, with Babylon as the centre of diffusion, does not appear to rest on solid ground. The career in Babylon of a lunar zodiac proper is itself doubtful. There is no such doubt about the careers of the *nakṣatras*, the *hsius* or the *manāzils*. Whether all these systems developed independently or had a common origin or to what extent one system influenced the other still remains largely a matter of speculation.

Division of Time—Day, Month, Seasons, Vedic Luni-Solar Calendar, Solstices and Equinoxes

c6.s1.t3.1

*The Day*

c6.s1.t3.2

Both ‘day’ and ‘night’ appear as natural unit of time in the earliest literary productions of the Indians. Expressions like ‘many dawns and nights’, ‘days subdue the nights’ occur in the *Ṛgveda*. As Haug has shown, the day in the Vedic times was generally taken to start and end with the sunset. The civil or natural day from sunrise to sunrise or from mid-night to midnight has been called *sāvana* day in later astronomical works. In the *Sūrya-siddhānta*, terrestrial civil days are reckoned from sunrise to sunrise. Āryabhaṭa reckoned it both from sunrise and from mid-night at Laṅkā.

c6.s1.t3.3

Day, that is the bright half, was divided, according to the *Atharvaveda* and the *Taittirīya Brāhmaṇa*, into five parts, e.g. *udyan sūryaḥ* (rising sun), *saṃgava* (gathering of cows), *madhyaṃ-dina* (midday), *aparāhṇa* (afternoon) and *astaṃ-yan* (sunset).a Further division of the day into *muhūrtas* and still smaller units has been traced to the *Brāhmaṇa* period. According to the *Śatapatha Brāhmaṇa*,b ‘there are ten thousand and eight hundred *muhūrtas* in the year (1 day = 30 *muhūrtas*), and fifteen times as many *kṣiprus* as there are *muhūrtas*; and fifteen times as many *idāni* as there are *etarhi*; and fifteen times as many breathings as there are *idāni*’. In the *Sāṅkhyāyana Āraṇyaka*c the day is progressively subdivided into *muhūrta*, *kṣaṇa*, *kalā*, *kāṣṭhā*, *nimeṣa* and *dhvaṃsa*. Kauṭilya's *Arthaśāstra* gives *muhūrta*, *nālikā*, *kalā*, *kāṣṭhā*, *nimeṣa*, *lava* and *tuṭa* as various units of time.

c6.s1.t3.4

a *AV.*, IX. 6.45.

c6.s1.t3.5

b *Śat. Br.*, xii, 3.2.5.

c6.s1.t3.6

c *Sāṅkh. Ār.*, vii. 20.

c6.s1.t3.7

The experience of the variations of day-length with seasons must have been very ancient, but details of actual measurements and rules for calculating them at any time of the year appear rather late—about the time of the *Vedāṅga Jyotiṣa*. The increase of day-length from winter solstice to summer solstice and the corresponding decrease in the duration of the night are recorded in the *Jyotiṣa*. Here the day has 30 *muhūrtas*, the shortest day-length at the winter solstice is given as 12 *muhūrtas* and the longest at the summer solstice as 18 *muhūrtas*. The total increase in day-length in one *ayana* of 183 days (according to the *Jyotiṣa*, a year has 366 days) being 6 *muhūrtas*, the rate of increase per day is given as 2/61. Weber suspected that the rule found in the *Vedāṅga Jyotiṣa* might have been imported to India from Babylon, for the latitude of which the above statements agree. But the results are also true for latitudes of parts of north-west India and could have been obtained as well by independent observations.

c6.s1.t3.8

A ‘solar’ day (*saura-dina*) as a time unit, defined as 360th part of the year, is hinted at in the *Vedāṅga Jyotiṣa* and also given in the *Pañcasiddhāntikā*. The sidereal day, defined as the time taken by the asterisms to complete one revolution, is met with in Hindu astronomy. Garga, in enumerating different kinds of day, makes a clear distinction between a *sāvana* and a ‘solar’ day (*arka-dina*).

c6.s1.t3.9

A lunar day or *tithi* is 30th part of one lunation, that is the period in which the moon’s elongation increases by 12 degrees. A *pakṣa* or half lunation contains 15 *tithis* which are named by Sanskrit ordinals *prathamā*, *dvitīyā*, etc. The first *tithi* of either *pakṣa* is called *pratipad* and the last or the fifteenth *pūrṇimā* or *amāvāsyā* depending on whether the *pakṣa* is bright or dark. A *tithi* is a calendrical device, but has not much astronomical significance except as an artificial division of the lunation. There is no indication of its development in the period of the *saṃhitās*. It appears fully developed in the *Jyotiṣa* and in the *sūtra* literature. The *Jyotiṣa* and the *sūtras* define a *nakṣatra* day as the thirtieth part of the time required by the moon to complete one revolution through 27 asterisms.

c6.s1.t3.10

The Month

c6.s1.t3.11

The reckoning of the month by the moon and the year by the sun was widespread among the ancient civilizations. The concept of the month as a unit of time based on lunation developed in the Vedic times. The *Ṛgveda* describes the moon as ‘that which shapes the year’.a We have already referred to the riddle hymn describing the year of 360 days as a single wheel with 12 months of 30 days each. Two systems of month-reckoning, e.g. the *amānta* and the *pūrṇimānta*, were in vogue. According to the former, a month has its beginning and end with the new moon; in the latter it is with the full moon. The Greeks, the Romans and the Jews also regarded their lunar months as lasting from the first appearance of the crescent after any new moon till that of the next. Oldenburg was more favourably disposed to the *amānta* system. We also have it from al-Bīrūnī that the *amānta* month was the canonical one. At the same time the derivation of the month names from the *nakṣatras* in which full moon takes place, as also the practice of starting the year with the full moon of the month, leave hardly any doubt that the *pūrṇimānta* reckoning was equally in vogue in the time of the *Brāhmaṇas*.

c6.s1.t3.12

a *ṚV.*, X. 85.5.

c6.s1.t3.13

The names of the lunar months were derived from the *nakṣatras* in which the full moon occurred, e.g. *Phālguna*, *Caitra*, *Vaiśākha*, *Jyaiṣṭha* and so on from the *nakṣatras Phālgunī*, *Citrā*, *Viśākhā*, *Jyeṣṭhā* respectively. Another system of naming months after the seasons of the year also originated during the period of the *Saṃhitās* and the *Brāhmaṇas*. According to the *Black Yajurveda*, such seasonal or solar months are: spring months—*Madhu*, *Mādhava*; summer months—*Śukra*, *Śuci*; rain months—*Nabha*, *Nabhasya*; autumn months—*Iṣa*, *Ūrja*; Dewy or Hemanta months—*Saha*, *Sahasya*; winter months—*Tapa*, *Tapasya*. A rough correspondence of lunar and solar months with the seasons was as follows during the period in question:

c6.s1.t3.14

| *Lunar months* | *Solar months* | *Seasons* |
| *Caitra* *Vaiśākha* | .Madhu / Mādhava | Spring |
| *Jyaiṣṭha* *Āṣāḍha* | .Śukra / Śuci | Summer |
| *Śrāvaṇa* *Bhādrapada* | .Nabha / Nabhasya | Rains |
| *Āśvina* *Kārttika* | .Iṣa / Ūrja | Autumn |
| *Mārgaśira* *(Agrahāyaṇa)* *Pauṣa* | .Saha / Sahasya | Dewy |
| *Māgha* *Phālguna* | .Tapa / Tapasya | Winter |

c6.s1.t3.15

The above correspondence agrees with the statement given in the *Yajus* recensions of the *Jyotiṣa* that *Māgha* and *Tapas* (*māghastapaḥ*) begin together at the commencement of the five-yearly *yuga*. Scholars, however, differ in their opinion on the question of such correspondence. Weber thought *Phālguna* as the first month of spring. Jacobi and Tilak argued that at one time winter solstice coincided with the full moon in *Phālgunī*.

c6.s1.t3.16

*The Seasons*

c6.s1.t3.17

The mention of six seasons in the foregoing paragraph should not be taken to mean that the Vedic Hindus had distinguished them from the very beginning. The *cāturmāsya* or four-monthly sacrifices very strongly indicate that to all intents and purposes the year was originally divided into three seasons, e.g. the warm, the rainy and the cold. The corresponding sacrifices to be performed to mark the beginning of these three seasons were *Vaiśvadeva*, *Varuṇapraghāsā* and the *Sākamedha*. Very befittingly, these sacrifices are called *ṛtu mukhāni* in the *Śatapatha Brāhmaṇa*. Two further seasons were in course of time added to the three primitive ones—the autum between the rainy and the cold and the spring between the cold and the warm season. Later on or concurrently, their number was expanded into six by the inclusion of the dewy season (*hemanta* or *śiśira*). The *Śatapatha Brāhmaṇa* mentions sometimes fivea and sometimes sixb seasons in the year.

c6.s1.t3.18

*The Intercalary Month*

c6.s1.t3.19

A year of 360 days divided into 12 months of 30 days each raises difficulties in the matter of adjusting the lunar months with the seasons. In the course of a few years the months would be out of step with the seasons. To make them agree with the seasons, it is necessary either to introduce an intercalary month at regular intervals or add the difference of 5 to 6 days to one or more months. There is evidence of both these methods having been tried for purposes of such calendrical adjustments. A year occasionally having a thirteenth or additional month which is produced of itself is referred to in the *Ṛgveda*.c The *Atharvaveda* puts it more explicitly as ‘He who measures the thirteenth month, fabricated of days and nights, having thirty members—against that God, angered, in this offence.’d In the *Black Yajurveda*, the thirteenth month is called *saṃsarpa*, a creeping month, in the *Kāṭhaka*, *malimluca*, and in the *Atharvaveda*, *sanisrasa*. From various stray statements in the *Brāhmaṇas*, it is possible to infer that the Vedic Hindus recognized a lunar year of 354 days (12 × 29½), which was adjusted to the sidereal solar year of 366 days (*Vedāṅga Jyotiṣa*) either by adding 12 days each year or a thirteenth month of 30 days every 2½ years.

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