Any study of the Indian tradition of science has to start with linguistics. This is so not only because Linguistics is the earliest of Indian sciences to have been rigorously systematised; but also because this systematisation became the paradigm example for all other sciences of India.
Like all sciences and arts of the Indian tradition, Linguistics finds its first expression In the Vedas. For most of the Indian sciences, already by the Vedic period, the basic elements i of study arid the basic categories through which these are to be studied had been [established, preliminary data for the operation of these sciences had been collected and rough systematisation had been achieved. Thus, for the science of Linguistics, In the siksha and pfatiakhya texts associated with the various Vedas, we find a settled complete list of phonemes appropriately classified into vowels, semi-vowels, sibilants and the five groups of five consonants, all beautifully arranged according to the place of. articulation which moves systematically from the throat to the lips. In fact phonetics and phonology are taken for granted by all authorities on etymology (nlrukta) and grammar (vyakarana) including Yaska and Panini. In the pratisakhya literature one also finds the morpho-phonemic (sandhi) rules and much of the methodology basic to the later grammatical literature.
The Indian science of Linguistics finds its rigorous systematisation in Panini's Ashtadhyayl. The date of this text, like that of much of the early Indian literature, is yet to settled with any certainty.' But surely the Ashtadhyayl Is not of a date later than 500 BC*. In the Ashtadhyayl, Panini achieves a complete charaterisatton of the Sanskrit language as spoken at hisrtime. and also manages to specify the way it deviated from the Sanskrit of the Vedas. Given a list of the root words of the Sanskrit language (dhatupatha) and using the sutras of Panini it is possible to generate all possible correct utterances in Sanskrit. This is of course the main thrust of the generative grammars of today that seek to achieve a purely grammatical description of language through a formalized set of derivational strings. It is understandable, that till such attempts were made in the West in the recent past, the Paninian sutras to the Western scholars looked like nothing but some artificial and abstruse formulations with little content,
Patan ali (c 1stC BC) in his ma or commentary on the Ashtadhyayi, the Mahabhashya, gives an elaborate rationale for the Paninian exercise. According to the Mahabhashya the purpose of grammer is to give an exposition of all correct utterances in the language.
The dates mentioned here are those based on Western scholarship. An Indigenous Indian dating and chronology in this as in all other matters has yet to be established.
obvious way to do this is to enumerate all correct utterances Individually. This is how the celestial teacher Brihaspati would have taught the science of language to the celestial student, Indra. However for ordinary mortals, not having access to celestial time-scales this method can apparently not be of much use. Therefore according to the Mahabhashya It Is necessary to lay down general rules (Otsarga sutras) with a wide application so that with a comparatively small effort men can learn larger and larger collections of valid utterances. What fails to fit in this set of general rules should than be encompassed in exceptional rules (apavada sutras), and so on.
In providing this characterisation of the science of grammer Patan ali laid his finger on perhaps the most essential feature of the Indian scientific effort. Science in India seems to start with the assumption that truth resides in the real world with all its diversity and complexity. Thus for the Linguist what is ultimately true is the language as spoken by the people in all their diverse expressions. As Patanjali emphasises, valid utterances are not manufactured by the Linguist, but are already established by the practice In the world. Nobody goes to a linguist asking for valid utterances, the way one goes to a potter asking for pots. Linguists do make generalisations about the language as spoken In the world. But these generalisations are not the truth behind or above the reality. These are not the Idealisation according to which reality is to be tailored. On the other hand what is ideal is the real, and some part of the real always escapes our idealisation of it. There are always exceptions. It is the business of the scientist to formulate these generalisations, but also at the same time to be always attuned to the reality, to always be conscious of the exceptional nature of each specific instance. This attitude, as we shall have occasion to see, seems to permeate all Indian science and makes ft an exercise quite different from the scientific enterprise of the West.
In the tradition of Linguistics after the period of Mahabhashya the ma or attempt of the grammarians seems to be to provide refinements and simplifications of Paninl. In this period a number of Sanskrit grammars are written. One of them, Slddhanta Kaumudi (c 1600) became eminently successful, perhaps because of its simplicity. These attempts continue till the 19th century. Another form of study that became popular amongst the grammarians is what may be called the philosophical semantics, wherein one starts with an utterance and by analysing ft into its basic grammatical components tries to fix and characterise its meaning. This, of course, is the ma or application for which grammer is intended in the first place.
Other Indian language grammers were written using Panian framework as the basis. In fact these grammers are not fully formalised grammars In the sense of Panini. Instead what is attempted is to start with the Paninian apparatus and specify the transfer rules from Sanskrit as also the specific morpho-phonemlc rules (sandhi). for the language under consideration. Such grammers for various Prakrit languages of the North and also the South Indian languages continued to be written till the 18th century, so much so that in the 16th century Krishnadas wrote a grammer for the Persian language, Parasi Prakash, styled on the grammers of the Prakrit languages.
Among the sciences of the Indian tradition Astronomy and Mathematics also occupy an important place. Indian mathematics rinds Its early beginnings In the famous Shulva Sutras of the L Vedfc times. Purportedly written to facilitate the accurate construction of various types! of sacriflcfa! attars of the Vedic ritual, these sutras fay down the basic geometrical properties of plane figures like the triangte, the tectangfe, the rhombus, and the circle. Basic categories of the Indian astronomical tradition were also already established In the various Vedanga yotfsha texts.
Rigorous systematisatlon of Indian astronomy however begins with Aryabhata (b.476 AD). His Aryabhatiya is a concise text of 121 aphoristic verses containing separate sections on the basic astronomical definitions and parameters; basic mathematical procedures in arithmetic, geometry, algebra and trigonometry; methods of determining mean and true positions of the planets at any given time; and description of the motions of sun, moon and the planets along with computation of the solar and lunar eclipses. After Aryabhata one comes across a long series of Illustrious astronomers with their equally illustrious texts, many of which gave rise to a host of commentaries and refinements by later astronomers and became the cornerstones of flourishing schools of astronomy and mathematics. Some of the well known names belonging to the Indian tradition are those of Varahamihira (d.578 AD), Brahmagupta (b.598 AD), Bhaskara I (b.629 AD), Lalla (C.Sth C AD), Mun ala (932 AD), Srlpatl (1039 AD), Bhaskara II (b.1114 AD), Madhava (c.14th C AD), Parameshwara (c.15th C AD), Nilakantha (c,16th C AD), yeshthadeva (c.16th C AD), Ganesha Daiva na (c.l6th C AD) and a host of others. The tradition continued and thrived right upto the late eighteenth century, and in regions like Kerala, original work in the Indian tradition continued to appear till much later.
The most striking feature of this long tradition of Indian mathematics and astronomy Is the efficacy with which the Indians seem to be handling and solving rather complicated problems. Thus In Mathematics the Indians already in Shulva sutras know all the basic theorems of plane geometry. Around this time they also develop a sophisticated theory of numbers including the concepts of zero, and negative numbers. They also seem to hava arrived at simple algorithms for all basic arithmetical operations by using the place-value notation.
Thus by the time of Aryabhatiya the Indians have all basic mathematical concepts and procedures that are today taught at the high school level. By the 10th or 11th century they are able to solve sophisticated problems in algebra such as second order Piophantine equations. By the 14th century Infinite series for sine and cosine functions are written down in trigonometry. High levels of approximations of and recognition of Its irrational character are also achieved by the same time.
The reason for this success of the Indian mathematicians lies perhaps In the explicitly algorithmic and computational nature of Indian mathematics. The ob ective of the Indian mathematician was not to find ultimate axiomatic truths In mathematics but to find methods of solving specific problems that may arise in the astronomical or other contexts. For this purpose the Indian mathematicians were prepared to set up simple algorithms that may give only approximate solutions to the problem at hand, and to evolve theories of error and recursive procedures so that the approximations may be kept In check. This algorithmic methodology persisted In the Indian mathematical consciousness till recently so that Ramanu an in the twentieth century seems to be chalking up his impressive mathematical discoveries perhaps through the use of this traditional Indian methodology.
The same pragmatic concern to be able to calculate the positions of the various planets and eclipses of the sun and the moon reasonably accurately, informs the efforts of the Indian astronomers. And in this they turned out to be eminently successful. In their calculations Indians often take the beginning of the Kaliyuga in the year 3102 before Christ as their starting point, and the so-called Siddhanta texts deal with a much larger period consisting of 43,20,000 years called a Mahayuga or sometimes even a period 1000 times the above, which is called a Kalpa. In spite of dealing wfth such long time periods the Indian astronomers were able to keep their techniques fairly simple and their parameters fairly well refined so that even towards the end of the eighteenth century and early parts of nineteenth, when the active astronomical tradition had become dormant In large parts of India, European astronomers art able to locate Brahmins in South India, who could calculate for them the details of the current eclipses to an accuracy comparable to, and often better than the best calculations of Europe of the time.
The reasons for the simplicity and accuracy of the Indian astronomical techniques are again to be found in the pragmatic attitude of the Indians towards the sciences. The Indian astronomers were in the business to calculate and to compute; but not to form pictures of the heavens as they ought to be In reality. Indian astronomers do use some geometrical models but these are supposed to be nothing more than artifacts necessary to perform their calculations (see Appendix). It is obvious that the astronomical parameters obtained using such artifacts will get out of tune with reality sooner or later and the calculations made with such parameters will start deviating from actual positions of the planets. Indian astronomers are aware of this and were quite willing to take up the onerous task of continuously observing the skies, continuously checking their computations against observations and repeatedly read justing their parameters so as to make their calculations accord with reality. Thus the sixteenth century astronomer Nilakantha Somasutvan, finding a contemporary commentator lamenting about the different times given in different Siddhantas and the computed times differing from the actual ones, exhorts:
O faiht-hearted, there is nothing to be despaired of... one has to realise that five Siddhantas had been correct at a particular time. Therefore one has to search for a Siddhanta that does not show discord with the actual observation at the present time. Such accordance has to be ascertained by observers during times of eclipses, etc. When Siddhantas show discord observations should be made with the use of instruments and correct number of revolutions etc., found, and a new Siddhanta enunciated".
A little later yesthadeva In his Drikkarana tells how from Aryabhata to the present day the astronomers have ad usted the parameters to accord wfth observations and how he too Is doing the same fob for his times and he ends wfth the statement that 'henceforth too the deviations that occur should be carefully observed and revisions effected'.
The third major science of the classical tradition Is Ayurveda, the science of life. Like Linguistics and Astronomy this too finds Fts early expression In the Vedas, especially the Athrvaveda in which a large amount of early medicinal lore is collected. Systematisation of Ayurveda takes place during the period 5th century BC and 5th century AD in the Charaka Samhita, Susfiruta Samhlta and the Ashtanga Sangraha, the so called Srihaf-frayee texts, which are still popular today. This is followed by a long period of Intense activity during which attempts are made to refine the theory and practice of medicine, and to bring more and more Information Into the stream of systematic medicine. This process of accretion of Information and refinement of practice continued right upto the beginning of the nineteenth century.
Like in Linguistics and Astronomy the remarkable feature of Indian tradition of medicine Is its pragamatic ettftude towards scientific theorlzation. The Ayurvedic texts while providing a theoretical framework through which the problem of finding an appropriate cure for a particular patient must be approached, never tire of reminding the practitioner that he "must be constantly observant of all the specific features that a particular case presents. In fact for Charaka Samhita the most desirable intellectual accomplishment of a doctor Is that of possessing Yukti; the Yukti is the capacity of the trained intellect that manages to see the course'of action through the complexity of phenomena wfth their multiple causes.
The attitude of Ayurveda towards theoretical generlisations is very clearly brought out in a revealing verse of Sushruta Samhita. While describing the theoretical qualities of a substance through which its medicinal properties are to be determined, the text comes up with the warning that the wise physician should never raise theoretical arguments about the properties of a drug when they are already known and established in tradition based on actual practice, because afterall a thousand reasons will not make the drugs of the ambastha group perform laxative functions'. Therefore the physician must rely on what Is established in tradition based on actual practice, rather then acting exclusively on his theoretical reasoning. This attitude towards theory gives the Ayurvedic texts a refreshing openness and a surprising keenness of observation. Nothing that may have any effect on the problem of health seems to escape the observation of the physicians. One finds the physicians worrying about the differing aspects of the seasons, the soils, the waters and so on. And In the therapeutic sections they bring into use all their theoretical understanding and all the folk practices that nave been proved to be efficacious in tradition.
This pragmatic attitude towards scientific theorlzation made the doing of science In India a rather painstaking business. The Indian scientists not having the luxury of reducing the reality of the world to that encompassed by their theories of the time, had to be continuously aware of the world in fts complete complexity, and had to continuously refine and simplify their procedures In order to operate successfully in this complex world.
That they were able to do this systematically In a number of fields over a long period of over 2000 years Is a measure of their Ingenuity and Industry. Thus one can only marvel at the stupendousness of the task of encapsulating the whole of Sanskrit language as it was spoken in 4000 aphoristic rules. Equally remarkable is the effort of the astronomer-mathematicians to repeatedly refine their parameters to fit the observations so that ever since Aryabhata the Indians always had access to reasonably accurate information about the motions of the heavens. But the astronomer-mathematicians also simplified their computations to an extent that learned Brahmins In their innumerable locales could also compute all the astronomical information that mattered to the residents. The effort of Indian physicians also falls in the same class. They were not only able to painstakingly acquire and systematize within their theoretical framework all the information about drugs and diseases that was current amongst the people in diverse areas, but were also able to simplify their theories sufficiently so that much of the Ayurvedic science became the folklore of health known in all families. The fact that the Indian scientists given their theoretical attitude had to be necessarily open to the world around them perhaps ensured that the folk and the science had to remain in a symbiotic relation with each other.
Besides Linguistics, Astronomy and Mathematics, and Medicine, Indians also developed the sciences of matter (Padartha Sastra), metallurgy (Rasa Sastra), architecture (Vasfu Sastra), music (Sangita Sastra) etc. To all,of these sciences they brought their peculiarly Indian mode of careful but tentative generalisations and continuous keen observation.
The pragmatic attitude of conceptual sophistication and operational simplicity that we have noticed amongst the sciences of India seems also to have informed the Indian technologies. A systematic history of the traditional Indian technologies is yet to be written. Therefore one has to rely largely on the accounts of European travellers and administrators who observed and wrote about the Indian practices during the early phase of European conquest of India.
The major technological endeavor of India was of course in the field of agriculture. Col. Alexander Walker writing In the early nineteenth century seems to have been amazed at the keen interest that ordinary Indians showed in everything connected with agriculture. He is also greatly impressed by the care with which the Indian cultivators tended their fields, so that to him the fields of Malabar and Gu arat seem more like carefully laid out gardens. This care is coupled with an intimate knowledge of the soils, the seasons and seeds. The Indians seemed to have mastered techniques of rotation of crops, irrigation, manuring, and selection of seeds etc., from very early times. These techniques had been so well studied and so optimized to the peculiar conditions of each area that John Voeicker, the Consulting Chemist to the Royal Agricultural society, sent to India towards the end of the nineteenth century to suggest ways of improving Indian agriculture through the use of chemistry, could recommend little by way of technological changes. He was of the opinion that if only the traditional facilities of water and manure could be ensured the farmers of India could obtain the best possible yields. As for suggesting improvements he seemed to have feit that It was much easier to propose Improvements In English agriculture, than to make really valuable suggestions for that of India. Another expert of early twentieth century ohn Kenny, remarks in the same vein that he did not consider It wise to suggest seed selection In a land where 4000 different sorts of paddy are grown In one province alone and carefully differentiated according to their qualities and land suitable for them'.
The Implements of the Indian cultivator often seemed rough and primitive to the occasional observer. However It was soon realised that these implements were fully adapted to the particular conditions In which they operated and even in the late nineteenth century nothing could be suggested by way of their Improvement. In fact an early experiment during the later half of the eighteenth century to introduce the heavy English plough near Salsette on the West coast had proved a total disaster. In 1795 Cap. Thos Holcott reported on the sophistication of the Indian drill plough widely used in the Andhra region. The drill plough till then was considered a 'modem' European invention.
With their simple but sophisticated Implements and their meticulous techniques of agriculture, the Indian farmers were able to obtain impressive yields. It was reported that In early nineteenth century in the Allahabad region the produce of an acre of land amounted to over 55 Bushels per harvest while that in England around the same time was only abut 20 Bushels. Since the Indian farmer In this region usually produced two crops a year, the annual yield of each acre may be taken as over 110 Bushels at this time. The productivity of Indian agriculture, however, declined very rapidly during the nineteenth century. But even in the 1890's lands which had access to irrigation and manure yielded harvests comparable to those In England, and larger than the harvests obtained those days In Europe, USA and Australia.
The Indian technical Ingenuity in evolving simple techniques that are sophisticated enough to take advantage of the full complexity of the local situation, and then meshing these local techniques into a large impressive system can be best seen in the tank irrigation system of South India. It seems that the whole of South India was dotted with these tanks. A British expert writing in the 1850's estimated the total number of such tanks in the Madras Presidency to be over 50,000. Another estimate Indicates that In the eighteenth century there were more than 38,000 tanks In the region which later constituted the Mysore state. The state had an area of around 29,500 square miles. It is, therefore, fair estimate that there were over a lakh tanks in whole of South India. From what is known of the political circumstances of the time It Is clear that these tanks were constructed and maintained by local effort. However, together they formed a closely knit whole so that the outflow from the one at a higher level supplied the one at a lower level, and so on. This chain of tanks was so complete and Interrelated within itself that the British engineers of the nineteenth century felt that it would have been Impossible to add another tank to the chain
The Indian genius for performing vast tasks through simple, small and dispersed techniques is seen even better in the case of metallurgy. Early European observers noticed the Indians using small furnaces for smelting and refining iron and making steel. Scores of seventeenth, eighteenth and early nineteenth century accounts of Indian manufacture of Iron and steel are available, and these pertain to perhaps a hundred districts spread all over India. The smelting furnaces described in these accounts seem to be of quite rough construction from the outside. However, the observers noticed that the Internal proportions and various angles needed to be rather exact, and there were cases where the furnace had to be demolished and reconstructed to correct some minor error in the angle of blast, or In some internal proportion. Yet these sophisticated furnaces were routinely constructed by the Indian iron-smiths in a matter of hours without the help of any very complicated instruments.
These furnaces worked quite efficiently by the standard of those times. Thus, according to one detailed account, two units of charcoal were sufficient to produce one unit of crude iron in these furnaces. Processes of refining iron and steel making were also equally efficient. Steel was prepared by direct carbonisation of Iron in closed crucibles in which green leaves, wood and charcoal were all put together. This process seemed mysterious to the British observers, since a process of direct conversion was discovered in Europe only in the 1820's. Even then, observers were often surprised at the quickness with which steel was made in the Indian furnaces, the process taking a few hours compared to many days taken in the corresponding European processes.
The simplicity of these Indian techniques should be seen In the context of the fact that Indian iron and steel had been renowned for their qualities for centuries past. All over India one can find scattered Iron pillars and girders of very high quality, especially as regards corrosion resistance. Indian steel has an equally distinguished record of maintaining excellent quality, and even in the late eighteenth century an expert In Britain when presented with a sample of Indian steel noted that it was 'excellently adapted for the purpose of fine cutlery, and particularly for all edged instruments used for surgical purposes'.
It is worth remarking that with their small and dispersed furnaces which produced perhaps half a ton of iron during a week's operation,Indians were capable of producing a rather large amount of Iron and steel. According to some nineteenth century enumerations there were hundreds of such furnaces operating In certain districts and taluks. On the basis of this information tt has been estimated that the total number of furnaces throughout India In the later part of the eighteenth century could have been over 10,000 and these furnaces together had the potential to produce some 2 lakh tonnes of Iron annually.
A survey of Indian technologies cannot be complete without some discussion of textiles, the great industrial enterprise of pre-Brttish India. Upto 1800 India was the world's leading producer and exporter of textiles. Yet this production was almost entirely based on techniques that could be operated at the level of the Individual or the family. Spinning of yam was an activity In which perhaps whole of India participated According to an observer from Manchester, Arno Pearse, who in 1930 visited India to study its cotton
Industry, there were probably 5 crore spinning wheels (Charkhas) Intermittently at work even then. And this simple small wheel was so efficient that till the early decades of the nineteenth century a widowed mother could still maintain a whole family In reasonable manner by spinning on the charkha for a few hours a day. Weaving was a relatively more specialised activity. However, the number of those belonging to the weaver castes was smaller In comparison only to those from the cultivating castes. Early nineteenth century data for certain districts of South India indicate that each district had around 20,000 looms. Amo Pearse in 1930 estimated the number of handlooms operating In India to be In the vicinity of 20 lakhs.
There were vast regions of India which specialised In specific types of fabrics. Each of these areas developed techniques of weaving, bleaching, dyeing and painting etc., that were Indigenous to the region, and also had Its own characteristic designs, motifs and symbols. For [example, in Western India alone, Slron In Rajasthan and Burhanpur In Khandesh were ma or centers of cotton painting; cheap printed cottons came from Ahmedabad; wotlens including the extra-ordinary Cashmfre Shawls were produced In Kashmir; true silks were worked as Patolas at Patan In Gu arat and so on.
These dispersed and diverse techniques were so optimised that textile produced in Britain through the post-Industrial revolution British technology could hardly match the Indian textiles In quality or price. Till the early nineteenth century, mSI produced fabric had to be protected from Indian competition by the Imposition of duties of 70 to 80 per cent on the cottons and silks Imported from India or, by positive prohibition. As the historian H.W.Wilson notes, without such prohibitory duties and decrees, the mBIs of Paisley and Manchester would have been stopped in their outset and could scarcely, have been again set In motion even by the power of steam',
The Indians had developed their locality-specific techniques not only In agriculture, irrigation, metallurgy and textiles, but also in diverse other areas like buHding and construction, sculpture, pottery, making of glass, and even luxuries like making of tee etc. That Is perhaps why most historians of pre-Britlsh India are agreed that India of that time was not only an agricultural, but also an Industrial society.
Appendix: Computations in Indian Astronomy
To get a flavour of the Indian way of doing Astronomy and Mathematics, ft may be Instructive to look at the way they make particular Astronomical calculations like for example the calculation of the longitudes of the grahas (the sun, the moon and the various planets) at any given time. The following are the essential steps:
1. The Indian Astronomers first compute the ahargana or the total number of mean solar days elapsed from the chosen epoch till the given date, specified as such and such Sakabda (Saka year) masa (lunar month) and tithi (lunar day). For this, they first compute the number of adhikamasas (Intercalary lunar months) elapsed since the epoch tHI the beginning of the current Saka year. From this the number of tlthis elapsed since the epoch till the given date Is calculated. Then the number of kshayahas (omitted lunar days) from the epoch are computed and this, when subtracted from the number of tithls, gives . the ahargana for the given date. The computation of the number of adhikamasas and kshyahas is based on specified basic astronomical parameters, such as the mean motions of the sun and the moon.
2. From the computed ahargana, the mean longitudes (madhyama graha) of the sun, the moon and planets are calculated using the specified values of mean (daily) motions of these grahas.
3. To take care of the irregular motion of the grahas a series of corrections are applied to the madhyama graha mean longitude to get sphuta graha the true longitude. For the case of planets the basic corrections are the manda karma and the slghra karma. For the (outer) planets - Mars, upitar and Saturn - the manda karma is roughly the equation of centre which takes care of the non-circular orbit, and the sighra karma converts the corrected heliocentric longitudes Into the corrected geocentric longitudes. The basic form of the manda and sighra corrections are obtained from a geometric epicyclic (or eccentric) model and involves the mean motions of the apsides (mandoccha and sighroccha) and the circumferences (pttanda paridhi and sighra parldhi) of the epicycles, as the basic parameters. However, what every text of Indian astronomy prescribes Is a series of manda and sighra type of corrections performed iteratively till the results show a convergence to desired accuracy. The actual steps involved in this sequence of corrections depend on the particular planet and also varies from one school of astronomy to another. This procedure seems to enable the Indian astronomers achieve much better fit with observations than those achieved in other ancient traditions of astronomy which operate with Ideal geometrical models of planetary motion involving epicycles, equants, etc. This sequence of operations is what enables the Indian astronomers to Incorporate for Instance some of the higher order corrections to the equation of centre which In modern astronomy are calculated using the Keplerian orbits, etc.
4. The above planetary position is as observed at the time of sunrise (or midnight in some schools of Indian astronomy) at the Indian zero meridian passing through U aln. The desantara correction is applied to calculate the planetary position at sunrise at places on a different meridian.
5. Finally, the planetary position at any given time of the day or night is calculated from mat at sunrise (or midnight) by using the so called sphutagati or the true daily motion of the planet. This calculation also Involves the knowledge of the latitude of the place. Further it is necessary to know whether the planet Is In retrograde motion by computing the so called sighragati phaia. In computing these gatls or velocities, various formulae which are obtained by procedures which tantamount to differentiation of the expressions for the sighra and manda corrections, are used.
The basic astronomical parameters Involved In the above calculation are the mean motions of [the sun, the moon and the various planets, their upsides, and the circumferences of the manda and sighra epicycles, etc. These have to be determined on the basis of 'careful observations made over long periods. Each text of Indian astronomy gives the values for these parameters current at Its time.
Further Reading Material
1. Sirisa Chandra Vasu: The Ashtadhyayl of Panini, Edited and Translated Into English, 2 vols. Allahabad 1891 (Reprint Delhi 1962).
2. Kashlnatf Vasudev Abhayankar: Patan ali's Vyakarana Mahabhashya; Ahnlkas 1,2, Edited and Translated Into English, Poona 1967.
3. TA. Saraswatl Arfima: Geometry in Ancient and Medieval India, Delhi 1979.
i4. B. Datta and A.N. Singh: A History of Hindu Mathematics, Parts 1 and 2, Bombay 1962; Part 3 revised by K.S.Shukia, ind. our. History of Science 18 (1983).
5. KV.Sarma and B.V.Subbarayyappa: A Source Book of Indian Astronomy, Bombay 1985.
6. D. Arka Somaya i: Indian Astronomy, Dharwar 1971.
7. Charka Samhita: Edited with English, Gu aratl and Hindi Translations, 6 vols, amnagar 1949.
8. Kun alal Bhishagratna: Susruta Samhita, Edited and Translated into English, Varanasl 1963.
9. Dharampa : Indian Science and Technology in the Eighteenth Century, New Delhi 1971 (Reprint, New Delhi 1983). ]
10. Claude Alvares: Homo Faber, Delhi 1979.
11. Madras Group: Indian Agriculture at the Turn of the Century, PPST Bulletin No.4, Nov. 1982. ;