The Calcutta Review/Series 1/Number 2/Article 1

by Thomas Smith (1817-1906)

 

THE
CALCUTTA REVIEW.

Art. I.—1. History of Astronomy. With an Appendix, containing a View of the principal elements of the Indian Astronomy as contained in the Surya Siddhanta. (Library of Useful Knowledge.) London: Baldwin and Cradock.

2. The Use of the Siddhantas in the Work of Native Education. By Lancelot Wilkinson, Esq., Bombay C.S.—Ass. Res. at Bhopal, (Calcutta Asiatic Society’s Journal), 1834.

The history of science is itself a science; and one of the most interesting and important of them all. To trace the stream of discovery from its lofty well-head, to follow its various windings, mark its frequent disappearances, its rapids and its stagnancies, is a work at once of the greatest interest, the greatest importance, and the greatest difficulty. The interest of the investigation is derived from our very nature and constitution as members of the great human brotherhood; in virtue of which nothing that belongs to man ought to be indifferent to man; and least of all that which has engrossed the attention and measured the enjoyment of the most gifted of our race. The importance of the study chiefly depends upon the fact that experience is our grand guide in philosophy; and therefore it is in a great measure by a knowledge of what has been accomplished by our predecessors, and of the methods by which it has been accomplished, that we are to be guided in the direction of our own observations. The difficulty of tracing distinctly the progress of science will be well exemplified in the course of our present article, which we purpose to devote mainly to an examination of the antiquity of the Hindu Astronomy. But while the subject we have undertaken is confessedly a difficult one, we shall endeavour as far as possible to encounter the difficulty ourselves, and by divesting the subject in a great measure of technicalities, to render it accessible and even attractive, to the general reader. In fact, we shall advance very little that is original, but shall be well contented if we can so place the matter in an attractive light before our readers, as to inspire some of them with an interest in a subject from which they have probably been repelled by the technicalities that have hitherto adhered to it.

That the Hindus have amongst them a considerable amount of astronomical knowledge, is a fact which is rendered unquestionable by their power of calculating the eclipses of the sun and moon with very considerable accuracy. That for a long period they have made no advancement, but have rather retrograded in their knowledge of the principles of the science, seems almost equally certain. It therefore follows, that the science of astronomy must have been cultivated among them at an early period; and the question is as to the actual remoteness of that period. As no formal records exist of the progress of discovery among them, the determination of the important question of the antiquity of their astronomical systems must depend almost exclusively on internal evidence furnished by the systems themselves. It must, therefore, be our first course to furnish a short sketch of the form in which their systems present themselves to us at the present day.

The astronomical works of the Hindus are of two classes, viz., astronomical tables and systematic treatises. Of the former class, four sets are known to the astronomers of Europe. The first was brought from Siam by M. La Loubere, in 1687. For some time, the tables were not intelligible to any of the European astronomers, but were at last satisfactorily explained by Cassini, one of the most illustrious astronomers of his age. Though brought immediately from Siam, they are of strictly Hindu origin; for they are constructed for a meridian 18° 15’ to the westward of Siam. This meridian will very nearly coincide with the Hindu meridian of Lanka,^[1] and also with that of Benares: and thus no doubt can exist as to the Intra-Gangetic origin of the Siamese tables.^[2] The second set of tables was sent from Chrishnabouram, in the Carnatic, by the Jesuit Missionary, Du Champ, about 1750. They were thoroughly understood by Du Champ himself, who illustrated them by a set of examples and rules, which render them easily intelligible to one who is acquainted with the details of European astronomy. The third set were sent by Patouillet, another Jesuit, and are generally known as the Narsapur tables. The fourth and most important set, because both the most complete, and professedly the most ancient, were taken to Europe by M. Le Gentil, who came to India for the purpose of observing the transit of Venus, in 1769. These are known to the scientific world as the Tirvalore tables; from a small town so called on the Coromandel coast. It becomes a question of great importance as well as considerable difficulty, to determine the period at which the Tirvalore tables were constructed; as, notwithstanding considerable discrepancies between the different sets, the principles of the whole are the same; at all events it is with them that we have chiefly to do, (except in so far as the others may illustrate or explain them) as they profess to be more ancient, by a very long period, than any of the others. It will, however, be needful for us, first of all, in order that the matter may be thoroughly intelligible, to give a general idea of the mode in which such a question as the present may be determined.

If a human artist had been entrusted with the construction of the universe, it is probable that he would have made all the planets revolve round the sun, in equal periods or years, consisting of a definite number of days. Had this been the actual structure of the solar system, the calculations of astronomy would have been destitute of all interest, as of all difficulty. If the place of any planet on any day, and also the length of the common year, were known, the places of each planet for any other day would be ascertained by the simplest arithmetical operation.

But the ways of Him who made the world are not as our ways, nor His thoughts as our thoughts. He has made no two of the planets perform their revolutions in the same period. Their revolutions are indeed regular, but the regularity is a regularity of irregularities. And it is thus that astronomy becomes useful to mankind, not only for the exercise of their talents, but also as the basis of chronology;—thus it is that the heavenly bodies subserve one of the great purposes for which they were appointed by their great Creator, to be “for signs and for seasons, for days and for years.” As this is a point, a clear apprehension of which is essential to a right understanding of the whole subject, we shall illustrate it still further by a simple comparison. Suppose a common clock made with only one hand, which shall traverse the dial in an hour. Such a clock would indicate how much time had passed at any given moment from the last hour, but it would give us no means of ascertaining how many hours had passed from any given hour. But the addition of a hand, as in our ordinary household clocks, which traverses the dial in 12 or 24 hours, supplies this information. Another hand, in some clocks, shews the day of the month, and another might be added to shew the month of the year, and another still to indicate the number of years elapsed from any given era. Now the kind of clock that we have first described,—an ordinary clock with the hour hand taken off—would fitly represent a system in which all the planets should perform their revolutions in an equal number of days. In such a system the position of any planet at any time would tell us how long time had elapsed since the planets were at any point that might be assumed as the first point of their orbit; but it would afford us no means of ascertaining the number of complete revolutions that the planets had made, or, in other words, how many years had elapsed, since any given era. But in the actual universe we have a different system altogether. At no two periods during an enormously long period, certainly a much longer period than has elapsed since the creation, have the relative positions of all the planets been the same. Just as in an ordinary clock the relative positions of the two hands are the same only after intervals of 12 hours, and in a clock that has a hand for indicating the days of the month, the relative positions of the three hands will be the same only after intervals of a month’s duration. Yea, in a clock with only two hands, and each of them traversing the dial in a moderate period, the interval of what we may call relative coincidence might be very long. If, for example, the minute hand remaining as it is, the hour hand were made by a change in the works to traverse in a period that was not a multiple of the period of the other, as for example in 12 hours and a minute;—then suppose the hands to be together at 12 o’clock. After 12 hours the minute-hand will have made 12 complete revolutions, and will have returned to the place whence it set out. But the hour hand meanwhile has not completed its revolution, by one minute. After other 12 complete revolutions of the minute hand, the hour hand will be two minutes from 12 o’clock. Thus at each successive return of the minute hand to 12 o'clock it would be further and further from the other, and they would not co-incide at that point of the dial, until the hour hand having accomplished 720 complete revolutions, the minute hand should have accomplished 8652. Now any two of the heavenly bodies may be represented by such a clock as this last, for no one of them revolves in a period which is an exact multiple of the period of any other. Hence, precisely as in our supposed clock we can ascertain the number of hours elapsed since the period of the coincidence of the hands, by merely knowing the distance between the hands at any return of one of them to 12 o’clock, so by knowing the relative positions of even two of the heavenly bodies at a given time we can calculate how many revolutions they have made since any other period when their relative positions were known.

If then we knew with perfect accuracy the elements of the orbits of several of the planets, and if we knew their precise position on a certain day,—their position both relatively with regard to each other, and absolutely with regard to their places among the fixed stars—we could ascertain with precision what that day was. Now here is exactly what constitutes the difficulty in the case before us. It is evident that, if, from knowing the positions of certain planets at an unknown time, we can ascertain that time by calculation, it must be equally possible and equally easy to calculate the position of the planets for a given known time. The problem—“Given the elements of the orbits of the planets and their position at a certain unknown time, to ascertain that time”—is just the converse of the problem,—“Given the elements of the orbits of the planets, to ascertain their position at a certain known time.” Either problem is equally easy of solution. From this it must be evident to all, that we cannot safely judge of the actual age of a set of astronomical tables from the mere dates for which they furnish astronomical facts: for these facts may, for aught we know, have been not ascertained by observation, but by calculation. Our anxiety to make every step as clear as possible, must be our apology for introducing an illustrative instance of what, to very many, requires no illustration at all. Every one knows that the Nautical Almanac, published by the Lords Commissioners of the Admiralty of Great Britain, gives the position of the sun and moon and the planets for every day of the year; and every one also knows, that these positions are by the very nature of the case, calculated and not observed positions, inasmuch as the very ends of its publication require it to be in the hands of those who use it at the time when the positions are observed; and in order to this it is always published some years in advance. And if the elements of the orbits and the periods of the revolutions of the heavenly bodies were known with perfect precision, the Nautical Almanac might be published for a hundred or a thousand years in advance. In like manner, if all records of observations were utterly lost, we might still calculate almanacs for a hundred or a thousand years past. Now if the elements, on which the calculations of these Almanacs were based, were ascertained with perfect accuracy, it would be impossible for any one to discover from internal evidence, whether the Almanacs had been composed by prospective calculations before their nominal dates, by actual observations recorded at these dates, or by retrospective calculations after the nominal dates. If, however, any of the elements of the calculations had been erroneous, then the calculations would gradually diverge from the truth, and an inspection of the Almanacs, and a comparison of them either with more accurate calculations or with independent observations, would probably shew the period at which they had been calculated. It will thus be seen, that the possibility of ascertaining the age of a set of astronomical tables depends upon their deviations from perfect accuracy. With these somewhat diffuse explanations, which, however, we trust will greatly assist us in the sequel, we must now revert to the history of the Hindu Astronomical tables.

The tables of Tirvalore were brought to Europe, as we have stated, by M. LeGentil, who presented an account of them, and of the Brahmanical Astronomy, to the French Academy, in 1773. About that time, M. Bailly, a man of great ingenuity, was labouring very zealously for the support of a theory in regard to a people, that he supposed many centuries ago to have inhabited the Northern regions of the great Asiatic Continent, and whose language, manners, and philosophy he supposed to be, as it were, the parent stems of the languages, manners, and philosophy of all the nations of Asia, and mediately of all the nations of the world. Hitherto he had derived support for this theory, chiefly from the science of philology, the most accommodating certainly of all the sciences, and one who seems never to deny her aid to any theorist, who has to maintain a hypothesis in regard to the antiquities of nations! No matter how directly the various hypotheses be opposed to each other, philology, if only canvassed aright, will most complyingly give her suffrage in favor of them all. In these circumstances Le Gentil’s account of the Hindu Astronomy seemed to coincide amazingly with Bailly’s views. Here was a people possessing a record of astronomical observations made and recorded forty-seven centuries ago; observations indicating any thing rather than an infancy of astronomical science—observations which could not be taken by the people amongst whom they are preservod at this day, and the precepts connected with which, for the calculation of eclipses, are said not to be understood by any of those who daily use them. They must then have derived their records from an extraneous source, and what could that source be, save the great hyperborean nation, long since extinct, who must, therefore, have possessed a science in a state of great advancement? To one who had a theory to maintain, and who had hitherto been constrained to support it on the easily obtained and comparatively valueless foundation of philology, a much less plausible discovery than that of Le Gentil must have been invaluable. We may well conceive, that the man who has been launched forth on the stormy billows on a single plank, would not feel more relief when he found himself left above water-mark on a lofty cliff, than the theorist who found himself transferred as by a bound from the unstable element of philology, to the immoveable strong-hold of astronomy—astronomy based on observation, and reared in accordance with “mathematics, which cannot lie.” We should, however, do Bailly great wrong if we left it to be supposed, that he paid attention to the Hindu astronomy, merely from the confirmation which it seemed, on the first blush of it, to afford to his favorite hypothesis. Few men in his day—and it was the day of La Place, and LaGrange, and De Lambre, and D’Alembert, amongst his own countrymen—were, theory and hypothesis apart, better able to analyse a system of astronomy than was Bailly. In fact we believe, that had he had no such theory to support at all, he would still have given his mind to the important subject, and would probably have turned it to better account than he has done. Bailly set forth his views, in regard to the Hindu astronomy, in 1775, just two years after the publication of Le Gentil’s Memoir, in a general history of ancient astronomy.^[3] They were afterwards set forth at great length and with great clearness in a separate work devoted expressly to the subject, and the best known of all Bailly’s works, his History of the Indian astronomy.^[4] The subject is also dwelt upon, in his letters to M. Voltaire^[5] on the ancient history of Asia, and was in fact the idol of his worship, the engrossing idea of his soul, or, to use a phrase far more expressive than dignified, the hobby from which he never dismounted.

The Indian astronomy of Bailly was reviewed by Professor Playfair, in a very excellent paper read before the Royal Society of Edinburgh, in 1790, and published in their Transactions for that year.^[6] Playfair professes himself a convert to Bailly’s opinion in regard to the antiquity of the Hindu Astronomy—and while he does not implicity follow Bailly in his estimate of the relative value of the various arguments by which that antiquity is supported, he agrees with him in the conclusion as to the construction of the Tirvalore tables from actual observations made and recorded 4800 years ago. “The fact is (says he), that notwithstanding the most profound respect for the learning and abilities of the author of the Astronomie Indienne, I entered on the study of that work, not without a portion of the scepticism, which whatever is new and extraordinary in science ought to excite, and set about verifying the calculations and examining the reasonings in it with the most scrupulous attention. The result was an entire conviction of the accuracy of the one and of the solidity of the other.”—No one can even dip into the writings of Playfair without being convinced of his extraordinary powers as a Mathematician; but those who have studied them most rigorously will be most inclined to doubt the value of his great name as a voucher for the soundness of a theory like that of Bailly. Lord Bacon has remarked, that some minds are so constituted as to be peculiarly apt to perceive coincidences between things that are dissimilar, while others are as apt to fasten upon distinctions and differences between things that upon the whole resemble each other. Now we may be permitted in regard to Playfair to make the remark, that his mind had a tendency towards the former peculiarity. There was something, despite his profundity and rigidity as a geometer, that we cannot help calling poetical, in the constitution of his mind; in virtue of which we should suppose him more likely to be struck and captivated with a remarkable coincidence, than with a discrepancy, that would have struck a more common mind much more forcibly than would the coincidence. He would have been much more pleased, we believe, to construct a system himself, or to confirm a system constructed by another, than to expose and destroy a system already constructed. They who are acquainted with the history of science will not be disposed to undervalue the effect of these mental peculiarities in influencing the decision of such a man as Playfair, in regard to a subject, whose settlement must depend not upon rigid demonstration, but upon the balancing of coincidences on the one side and discrepancies on the other. We are not altogether sure either, whether the Professor’s Geological theory might not influence his mind in a way somewhat similar to that in which we have no doubt Bailly’s ethnological theory biassed his judgment. Thus, however, the matter seems to have stood, till, in 1799, Mr. Bentley laid before the Asiatic Society, and published in vol. vi. of the Asiatic Researches, a paper on “the Antiquity of the Surya Siddhanta, and the formation of the astronomical cycles therein contained.” In this paper Mr. Bentley strongly opposed the antiquity of the Hindu Astronomy, and the reality of the observations on which it professes to have been founded. Mr. Bentley’s paper was attacked in the Edinburgh Review for 1802, and he published a reply in vol. viii. of the Asiatic Researches, which was reviewed at length in the Edinburgh Review, for 1807.

We are not sure of the date of the first publication of the Systéme du Monde of La Place. The copy now before us is of the 4th edition, published in 1813. Allowing about three years for the sale of each edition, a period which we should suppose much too short, we should have the first edition published in 1799, the year in which Mr. Bentley’s memoir appeared. We may suppose, therefore, that La Place had not seen that memoir when his own work was published. In the fifth book he gives a very rapid sketch of the history of astronomy, and states his opinion as decidedly unfavorable to the claims of the Hindu Astronomy. And this is all the more remarkable, because it is by the application of his grand discovery in regard to the mutual actions of the planets upon each other, that Bailly and Playfair make out their most striking coincidences.

In 1817, De Lambre published his history of ancient astronomy,^[7] a work that will ever be the grand storehouse from which all future writers on the history of this branch of science must draw their facts. He enters at length on the discussion of the question, and decides the controversy in favor of Mr. Bentley against his brother Academician and Professor Playfair.

In 1825, Bentley published his “Historical view of the Hindu Astronomy, from the earliest dawn of that science in India to the present time.” In the preface to this work he defends his view of the antiquity of the Surya Siddhanta against the attack of the Edinburgh Review—and quotes the testimony of Dr. Maskelyne, given in a conversation with a mutual friend, in favor of his own views. It had been generally supposed that the articles in the Edinburgh Review were written by Professor Playfair, who was well known to be in the habit of contributing scientific papers to the Review at the period. Mr. Bentley states in his preface, that he had taken means to ascertain this point—“I sent Mr. Playfair (says he) a copy of my paper on the antiquity of the Surya Siddhanta, to open his eyes as to the foundation of M. Bailly’s mistake; and after the review on it came out, it being industriously fathered on Mr. Playfair, I directed inquiry to be made at Edinburgh, through some of Mr. Playfair’s most intimate friends, to ascertain from himself if he was the author of the Review. The reply was what I would have expected from a man of candor and science, that he was not the author of the review, and could not, consistently with his character, be the author of any such nonsense.” We think, indeed, there is internal evidence to prove, that Playfair was not the author of the Review in question; since the very principle on which Mr. Bentley proceeds was clearly stated long before by Playfair himself, as the only legitimate principle on which to conduct an investigation of the kind;—and this very principle is attacked in the Review. Moreover, we have every reason to believe that Playfair’s sentiments were materially influenced by the perusal of Bentley’s treaties; since we find him in 1817, writing in the Edinburgh Review, expressing himself in terms which shew that his confidence in Bailly’s theory was greatly shaken, if not altogether overthrown. We happen to be in possession of a large collection of Playfair’s manuscripts, from which we hoped to have been able to cast light, both on the disputed point of the authorship of the Review of Bentley’s paper, and generally on Playfair’s views on the subject at successive periods. In this, however, we have been disappointed. We have the original calculations employed in many of his published works, but none that are actually introduced into, or even are connected with, any of his treatises on our present subject.

It is now full time that we should dip into the subject matter of the controversy, at the history of which we have thus glanced. We find Bailly’s views nowhere more briefly and clearly stated than in his Histoire de Astronomie Ancienne, from which we shall take the liberty to translate a rather long extract.^[8]

“When we attend to the state of Astronomy among the Indians and the Chinese, we observe a profound ignorance of the causes of phenomena. Here we have the practice of observation without results; there results without observations; methods of which the most learned make use without understanding them, like foreigners who have picked up some words of a language without knowing their meaning. The use of methods, in connexion with ignorance of their principles, proves that these methods are not the work of the people who employ them: nor can we believe that they could have lost the principles had they ever known them. A people may lose recollection of certain historical facts, of certain particular and isolated doctrines; but a science forms a body of ideas which mutually preserve and defend each other. It follows then, that the Indians have been in possession of their astronomical knowledge from time immemorial. We have been recently made acquainted with the astronomical calculations of the Brahmans by an excellent paper of M. Le Gentil, of the Academy of Sciences. We there see curious methods and interesting researches. M. Le G. stayed along time in India; he spared neither time nor labor to make himself acquainted with their systems, and to put himself into a position to compare them with ours. He had the patience to become the disciple of a Brahman, who, in instructing this astronomer, who is worthy of the body to which he belongs, (the French Academy) complimented him on his aptness as a scholar.^[9] We suppose that the Indians have exsited as a people since the year 3,553 before Christ. This is the date computed from the reigns of their kings; according to their own statements their antiquity goes beyond all credibility. They say, that the world is to last 4,320,000 years, divided into four ages. The first, the age of innocence, lasted 1,728,000 years, the second 1,296,000, the third 864,000, and the fourth, the age of misfortune in which we now live is to last 432,000 years. This last they call the Kali-yug. Let us remark, that the Persians also divide the duration of the world into four ages; and it is evident that these ages of the Indians or the Persians are the origin of those of the poets. These fables are absurd; but what is remarkable is, that in 1762, when M. Le Gentil was in India, they reckoned the 4863rd year of the fourth age or Kali-yug. Never was truth mixed with falsehood, or at least fable, with a more distinct mark to direct us in separating them. The small number of years of the last age that are past, proves that it contained a real chronological epoch, which goes up to the year 3101 B.C. It would have cost them nothing to have given to this age as to the three others some millions of centuries, had they not been possessed of some historical monument, or some tradition, or rather some observation, which served them for an epoch, and which established its duration in a precise manner. It is in reality the epoch of their astronomical calculations; the date of the empire of their first kings goes back to 3,054 B.C. And yet, notwithstanding this antiquity of their astronomy, the processes which they actually employ in the calculations of eclipses have a name which in their language means new. At Benares, in Bengal, they have other methods which they call ancient. It were a matter of great curiosity to obtain and compare these. What shall be the date of these ancient processes, if the modern ones, as we think no one can doubt, go back as far as their astronomical epoch, that is, 3,101 years before Christ.”

This is the shortest enunciation of Bailly’s proposition that we have been able to find throughout his two works. Never had any cause a more ingenious advocate. His works are full of plausible arguments, and we confess we cannot help being pleased to see the way in which he makes the most stubborn materials bend to his purposes. If one kind of years for example won't do, he tries another. If the true place of a heavenly body will not suit, he takes its mean place, and vice versâ. If the Hindu tables agree with our tables, it is because both are right;—if they do not agree, it is because ours have been merely calculated backwards, and are therefore wrong; while the Hindu have been deduced from contemporary observation, and are therefore right. Thus it is ever with the theorist, however ingenuous he may be in regard to subjects unconnected with his favorite theory, if indeed any subjects can ever be unconnected in the apprehension of a thorough-going theorist with his favorite hypothesis. We shall abundantly make good this assertion ere we have done; but in the mean time we shall make a single remark on the argument contained in the passage we have quoted. We at once admit, that it appears plausible to make a distinction between those ages whose extravagant length at once points them out as purely fabulous, and that whose more moderate length, and especially the comparatively moderate length of that portion of it which has already elapsed, gives it an appearance of reality. If, then, this could not be accounted for on any other supposition preferable to that of Bailly, we should be compelled to give it up to him, and with it his whole theory. We would remark, however, that the very fact that a termination is assigned to the Kali-yug, and with it to the mundane system, naturally gives rise at the outset to a suspicion that the period is altogether a theoretical or conjectural one. And if we can find a key to the conjecture that led to the assignment of the whole duration of the Kali-yug, we shall probably have made some advance towards ascertaining the reason of its commencement being fixed at the period specified, on the supposition that it was an epoch fixed by subsequent calculations, and not by contemporaneous observation. Now of this, the most important point of all connected with the Hindu Astronomy, we have to offer an explanation at once simple, and, to our apprehension, truth-like. We submit it to the candid consideration of such as are accustomed to researches of this nature, while at the same time we shall present it in popular rather than technical phraseology.

The point of intersection of the ecliptic with the equator is not a fixed, but a variable point. In other words, the sun has not the same right ascension (or does not rise along with the same stars) in two successive years when he has no declination, (or is vertical at noon-day at a place situated on the equator). This is a familiar fact in elementary astronomy, and is known by the name of “the precession of the equinoxes.”

The amount of this precession is, according to the best modern observations, somewhat more than 50” annually; but according to the Hindu system, as stated by Bailly and all other writers on the subject, it is taken as 54”. Whether this is owing to any actual change in the amount since their epoch, or is due to errors in their observations, we shall have to consider immediately;—at present we have only to do with the fact. This precession being observed, it would naturally occur to every Astronomer to enquire into the length of the period in the course of which this point would make a complete revolution of the whole equinoctial circle. At the Hindu rate of precession this period will be immediately found to be 24,000 years, the quotient resulting from dividing the whole circle, or 360°, by 54", the assumed precession for one year. Now the duration of the Kali-yug is just 18 times this period of 24,000 years; or the Kali-yug is the period during which the equinox will have been 18 times at each point of the equinoctial circle. Why 18 should have been chosen as a multiplier rather than any other number we are notable positively to determine. It might have been chosen arbitrarily, merely on the ground that 24,000 years being too short a period to satisfy Hindu notions, some number must be chosen as a multiplier;—or it might be selected as being the greatest common measure of 360 and 54; or it might be for the following reason:—The position of the moon’s node, or the point in which her orbit cuts the ecliptic, goes round the ecliptic in a little more than 18 years, just as the intersection of the earth’s equator with the ecliptic goes round it in about 25,700 years in reality, but according to the Hindu estimate of the precession, in 24,000 years. If then the Hindu rate of precession were correct, and if the period of the revolution of the moon’s node were 18 years (instead of about 18 years and 7 months,) then if the sun and moon were in conjunction at any point in the ecliptic, they would be in conjunction again at the same point in the ecliptic, after a period of 432,000 years. We are inclined to suppose, that this is the true account of the duration of the period of the Kali-yug; but if any of our readers are staggered at the assumption, that the Hindus used a period of 18 years instead of 18 years 7 months, we shall not dogmatize on the subject, but shall only remind them that 7 months is a much less error on 18 years 7 months, than 1,700 years is on 25,700 years; the latter being about a fifteenth part, while the former is only a thirty-second part, of the whole quantity. But be the origin of the factor 18 what it may, we can scarcely doubt that the other factor, viz. 24,000, which enters into the period of the Kali-yug, is derived, as we have shewn, from the cycle of precession.

The length of the Kali-yug being thus determined, a short process would lead to the assignment of its commencement. If a point were assigned from which to measure the precession, as we measure it from the first point of Aries, the commencement of the epoch would be at once determined by dividing the distance between that first point and the actual position of the equinox at the period of observation by the annual precession, say 54”. Now it is obvious that any point might be assumed arbitrarily as the first point of the zodiac, or the astronomer might be led by some peculiar coincidence to fix upon some particular point in preference to all others. The latter was the fact in the actual case before us. On calculating backwards the position of the planets they found, that on a particular day in the month of February in the year 3102 B.C. the Sun, Moon, Saturn, Mars, Jupiter and Mercury were, not indeed in actual conjunction, but at least in the same quarter of the heavens, the greatest distance between any two of them probably not exceeding 17° or 18°. Now it was by no means an unnatural supposition, that, at the creation or beginning of a new system, all the planets should be launched forth from one point in the heavens, and left to perform their revolutions in harmony and order. A general conjunction of all the planets was, therefore, assumed as the commencement of the epoch: no general conjunction was actually found, on calculation; but in February of 3102 B.C. was an approach to it. It is true that at this period Venus was in a different quarter of the heavens, being about 62° in longitude apart from Saturn; but what theorist would allow a single planet to stand in the way of the establishment of so grand an epoch? Not, certainly, the framers of the Hindu Astronomy; and accordingly they did determine, that at the commencement of the Kali-yug all the planets were in conjunction in the first point of the zodiac; and thus was the famous epoch fixed. All this is perfectly consistent with what we know of human nature; especially does it accord with what we know of the Hindu character, and most ofall perhaps is it in accordance with the character of the Hindu philosophers. But take the other supposition, that the epoch was determined by actual observation, and then the removal of Venus to a position 60° distant from that which she occupied before the observer’s eye is an exceedingly awkward piece of work. This M. Bailly and Professor Playfair are compelled to admit, and fairly give up the point, though we must say, that we do not think either the one or the other attaches sufficient weight to the admission. An extract from the Astronomie Indienne will, we think, justify this opinion.

“The Indians say, that at the commencement of the Kali-yug there was a conjunction of all the planets. Their tables in fact indicate this conjunction; and ours shew that it may really have occurred. Jupiter and Mercury were in precisely the same degree of the ecliptic. Mars was distant 8°, and Saturn 17°. It follows, that, about this period, or 15 days after the Kali-yug and in proportion as the sun advanced in the zodiac, the Indians saw four planets successively emerge from his rays; first Saturn, then Mars, then Jupiter and Mercury, and these planets were all seen within a short distance of each other. Although Venus was not along with them, the taste for the marvellous led them to record a general conjunction of the whole. The testimony of the Brahmans is thus in accordance with our tables; and this testimony, resulting from tradition, must be founded on actual observation.”

It seems quite unnecessary to show, that the admissions which M. Bailly is here compelled to make, completely vitiate his whole theory in regard to the Hindu tables. The testimony must, he says, be founded on actual observation; and yet in regard to the brightest and most easily observed of all the planets, he admits that the testimony regarding it is absolutely false to an extent for which no mere error of observation can possible account. Either there was a general conjunction, and the testimony of the Indian tables is true; or there was not a general conjunction, and the testimony is false: but, by Bailly’s own shewing, there was not a general conjunction, and therefore the testimony is false. In a matter of this kind it will not do to say, that the testimony is approximately true, except in regard to the position of Venus; the indication afforded by this false testimony of the want of veracity in the witnesses, neutralizes the value that might be attached to their depositions in regard to the places of those planets whose positions were nearer to those which they assign to them. De Lambre disposes of this subject in a few lines. The sarcastic tone which unfortunately runs through his whole discussion of Bailly’s arguments is here much less out of place than in many other parts; for here Bailly certainly lays himself open to it.

“Another proof which is no better than the last (says M. De L.). The Indians say, that at this epoch all the planets were in conjunction. This would be a further reason for supposing that they have determined it by calculation, in order to make all the heavenly bodies set out from one and the same point. Bailly says further that the conjunction is possible, that our tables gave it to within 17°. It appears then, that either our tables or those of the Indians contain errors of 17°! Venus alone was not found with the rest. The taste for the marvellous led them to record a general conjunction of the whole! Here are astronomers very scrupulous and very worthy of confidence! It is just as we have seen among the Chinese.”

We might claim a right to hold this single point as decisive of the whole question; but we can afford to take low ground in this discussion; we shall, therefore, try the value of some of the other arguments on which the admirers of the Hindu astronomy rest its claims to antiquity and truthfulness.

The position of the equinoxes at the period to which we have so often referred, is one of the most important points in the whole question. We have already stated incidentally that the ecliptic, or apparent path of the sun in the heavens, does not cut the plane of the earth’s equator in two successive years in the same point; but that if the sun come to the north of that plane in any year at a particular point among the fixed stars, it will come to the north of the same plane next year at the distance of about 50” 1/3 from that point. The point at which the sun cuts the plane of the equator is called the equinoctial point, because then the day is equal to the night all over the world, and the season at which this occurs is called the equinox. As then the sun, after leaving the equinoctial point, reaches it again before he has accomplished a complete revolution in respect of the fixed stars, the period between two vernal equinoxes is consequently less than a sidereal year in the proportion that 359° 59’ 9” 2/3 is less than 360° or a complete revolution. This phenomenon is called the precession of the Equinoxes. It will be observed, that all that we have said amounts just to this, that the relative positions of the equinoxes and fixed stars, do not remain constant; but it is evidently indifferent for all purposes of practical astronomy, whether we regard the equinox as a fixed point and the stars as moving at a slow rate by a proper motion, or consider the stars as absolutely fixed and the equinox as moving at the rate we have stated. The former course is adopted by European Astronomers, and the vernal equinox is regarded as a fixed point in the heavens, from which the Eastward or Westward distance of every heavenly body is reckoned, precisely as the longitudes of places on the earth are reckoned from an arbitralily assumed first meridian. In order to ascertain the reality of an epoch, it would appear, that a good criterion would be the recorded position of the equinox among the fixed stars at the epoch, or, which amounts to the same thing, the longitude of any star or stars reckoned from the equinox. If the rate of precession were known with perfect accuracy,—from the observed longitude of a star at the present time, we could deduce its longitude for any period however remote by the simplest arithmetical process. Suppose then a set of tables placed before us regarding which there was suspicion that they had been constructed by calculation at a much later period than their pretended epoch, then if, with a perfectly accurate knowledge of the rate of precession, we found that the tables disagreed widely with our calculations, we should at once be justified in rejecting them. If, however, they agreed nearly, then we should be reduced to one of two inferences,—either that the epoch was determined by actual observation, or that the subsequent observers had known the rate as well as we, and had performed substantially the same operation upon their observations, that we had performed on ours. But all who know even the first elements of astronomy are aware, that scarcely any element, such as the rate of precession, is constant and invariable. Almost all such quantities are irregular, though, as we have already said, regularly irregular. We are not, therefore, to expect that we can ascertain the longitude of a star with perfect precision for a very remote period; still we can approximate to it with tolerable certainty. If for example we wished to ascertain the longitude of a star at the commencement of the Christian era, we should just have to subtract from its present longitude the product of 1844 by 50” 1/3; but an error of a tenth part of a second in the annual rate of precession would produce an error of 184”, or 3’ 4” in the longitude of the star at the commencement of our era. Now it is a fact, that the Hindu Astronomers make the annual precession 54”, or about 3” 2/3 more than the truth. Hence in calculating back from any epoch of observation to another 1800 years before it, they would make an error amounting to about 110’ or 1° 50’; while in calculating from A.D. 600 to B.C. 3102 the error would amount to 3° 46’ 14”. Here then, it would appear, is a test; provided that the tables, which relate exclusively to the sun, moon, and planets, contain any indication of the longitude of the fixed stars, or of the position among them of the vernal equinox at the commencement of the Kali-yug.

Now it so happens, that Le Gentil brought from India a diagram or delineation of the Indian Zodiac. This diagram places the vernal equinox 40’ behind the star Aldebaran. Now calculating from the position of this star in 1750, and making the rate of precession 50” 1/3 annually, M. Bailly finds by the simple process we have described that it ought to have been 1° 32’ before the equinox; this, therefore, gives an error of 52’ in the Hindu place of the equinox. But La Grange has shewn that the precession is subject to a small secular variation, in consequence of which the position of Aldebaran in 3101 B.C. would be not 1° 32’ before the equinox, but 13’ behind it. The position of the star, therefore, according to Le Gentil’s diagram is 40’ before the equinox, and its position at the same period according to the corrected rate of precession is 13’ behind it. The error of the Hindu assignment, therefore, assuming the rate of precession as corrected to be perfectly accurate, is 53’, not an inconsiderable error certainly, but one much smaller than would have resulted from calculating back from A.D. 600 at the annual rate of 54”. Hence Bailly concludes that the epoch is a real one. “This argument, (says Prof. Playfair,) carries with it a great deal of force: and even were it the only one we had to produce, it would render it in a high degree probable that the Indian Zodiac was as old as the Calyougham (Kali-yug).”

We fully agree with the learned professor, that this is a very strong argument, and if it either stood alone, or in connection with but one or two slight errors, it might be held decisive of the question. But the very same principle that would lead us to overlook a slight error in the midst of much important truth, and would not permit us, were such the state of the case, to decide against the reality of the epoch, seems to require of us in the opposite case to look upon a single truth in the midst of much error as only a somewhat remarkable coincidence. There is, indeed, a charity in regard to philosophical as well as moral subjects, which ought to lead us in general to put the best interpretation upon phenomena that they will admit of; but when such a coincidence of truth appears in the midst of such errors as we have shewn, and have yet to shew, in regard to the ascertainment of the Kali-yug, we cannot think it inconsistent with philosophic charity to inquire whether it may not be accounted for in any other way than on the supposition, which the numerous errors seem so decisively to contradict, that of actual observations at the period of the Kali-yug. We would, accordingly, suggest a method of accounting for the coincidence, without dogmatizing upon it. The Hindu rate of precession, as we have repeatedly stated, is erroneous. The error is not very great, yet it is so considerable, that its accumulation during a considerable number of years of continuous observation would inevitably betray its existence. Now suppose, that such a course of observation were conducted during three or four centuries, say for example the first four centuries from the Christian era. Suppose that at the beginning of this period rude tables existed, calculated back to the period of the Kali-yug on the supposition of an erroneous precession, and forward to the year 499 A.D. so as to give the longitude of the first point of the moveable zodiac, or the beginning of the constellation Aries, to be nothing at this latter epoch, The observations that we have supposed would sufficiently shew the erroneousness of the rate of precession formerly in use, and a simple operation would shew what was the correct position of the equinoctial point at the Kali-yug; another equally simple operation would shew what rate of precession would reconcile the erroneous determination of the equinox for the year 499, with the true one now ascertained for the year—3102. The distance of the equinoctial points for these two periods being 54°, and the elapsed time being 3600 years, the rate required would be at once found to be 54”. The position of the equinox for the remote period being thus rectified, the erroneous determination of the comparatively modern period, and also the erroneous rate of precession by means of which the rectification was effected, have been unfortunately retained; and accordingly the tables, as they now exist, make the vernal equinox coincide with the first point of the constellation Aries in the year 3600 of the Kali-yug, or 499 of the Christian era, whereas they were at that period about 4° 1/3 apart. This is no doubt only a supposition, and our scientific readers will, of course, value it according to their own judgments; but in estimating it let it be remembered, that it satisfactorily accounts for the error in the rate of precession, which otherwise it were scarcely possible to account for. Observations at considerably distant periods are needful to determine the precession with even an approach to accuracy; but we cannot conceive that a recorded observation at the period of the Kali-yug, of half the accuracy that Bailly assigns to those that he supposes to have been then made and recorded, compared with a moderately accurate one some centuries after, should not have given it with more accuracy than as we find it in the Hindu system. When even Hipparchus, by his own observation and such traditionary fragments as he could collect from the rude observations of his predecessors, was able to ascertain it with such accuracy that we make use of his rate even now, with only the small correction of La Grange and La Place, we cannot conceive that the many astronomers who, we know, lived among the Hindus from the Christian era down to the fifteenth century, could have concurred in admitting an error which in 600 years would amount to 34’ on the position of every one of the heavenly bodies. We, therefore, can think no supposition more natural, than that this error was introduced to neutralize a previous error, and not discarded when the end for which it was introduced was accomplished.

The “Library of useful knowledge” treatise, whose title stands at the head of our article, sets aside this argument of Bailly by the assertion, that “this position of the colures for the Calyougham (Kali-yug) is merely a calculation of Bailly and Le Gentil, the Indian tables only giving us the longitude of the equinox 3600 years after the Calyougham; whence the astronomers just mentioned have deduced its position for the year 3102 B.C.” We cannot, however, avail ourselves of this refutation, because, while it is true that the tables only give the place of the equinox for 499 A.D. the diagram which we have mentioned does give it for the Kali-yug. It is true we are nowhere told whether Le Gentil received this diagram from the Hindu Pandits, or whether he constructed it himself; but at all events it is accurately constructed from the tables, with the position they assign to the equinox in 499 A.D. and the rate of precession which we know that the tables employ. Candour, therefore, not only constrains us to reject the argument thus furnished us, but also to vindicate the character of Bailly from the charge of bad faith contained by implication in the passage we have quoted. The vernal equinox at the period 499 A.D., or 3600 years after the Kali-yug, is given as coinciding with the first point of the moveable zodiac; now at the rate of 54” of annual precession, the first point of the moveable zodiac must have advanced 54° in 3600 years, and consequently at the period of the Kali-yug must have been 54° behind the equinox; nor is it of much consequence that this is not actually stated in the tables. Thus much, we think candour requires us to say in regard to the honesty of him whose theory we are controverting; and we trust we should have said it even if we had had much more need than we have of such methods of getting rid of his arguments, as that employed in the work from which we have just quoted.

The next point that we shall take up is the position of the sun and moon at the epoch in question. We have already stated, that according to the Hindu system, the sun, moon and all the planets were then in the first point of the moveable zodiac, and we have shewn that in regard to the planets this was not by any means the fact. We shall now make it appear, that according to M. Bailly’s own shewing, this was not the fact even in regard to the sun and moon. The recorded statement, be it remembered, is, that at the midnight between the 17th and 18th of February in the year 3102 B.C. the sun and moon were in the first point of the moveable zodiac; and as we have seen that at this period they made the beginning of the zodiac 54° in advance of the vernal equinox, the longitude of the sun and moon was, according to our mode of expression 306°, or the difference between 54° and 360°. Now Lacaille’s tables give the longitude of the sun at this time 301° 5’ 57”; this, by the application of La Grange’s correction of 1° 45' 22”, becomes 302° 51’ 19”. The error, therefore, is 3° 8’ 41”. This any one would suppose, is a sufficiently staggering error; but what will stagger a theorist like M. Bailly? He gets out of the difficulty by supposing, that the longitude of the sun, as given in the Indian tables for this epoch, is not the mean longitude, as is given in all other tables, but the true or apparent longitude, differing from the mean by the equation of the sun’s centre,^[10] which for that period is 2° 21' 47”. This, being to be substracted from the apparent longitude, gives the mean longitude 303° 38’ 13”, which differs from that given by Lacaille’s tables with La Grange’s correction, by 46’ 54”. It is not a little amusing to see the manner in which Bailly extricates himself from this difficulty. We shall translate the passage, as finely illustrating how much may be made by a clever advocate of the very worst cause.

“There is a reason which appears to have induced them to depart from the usage, and violate the rule, which require that an epoch be placed in a mean longitude. It is that this epoch (the entrance of the sun into the moveable zodiac) is the rule of the Indian solar times. It is the beginning of their year. This commencement ought to be true; this time ought to be sensible, (apparent) and consequently fixed by the true entrance of the sun into the moveable zodiac. However, it ought to be observed that the Indians, whether by mistake or otherwise, make use of this true longitude of 206° as a mean longitude; and we have already a proof of it, since we have seen that the Indians of Siam, of Chrisnabouram (Krishnapur) and of Narsapur, always reckon their longitudes from this as the first point of their zodiac, applying to it the correction of the equation of the centre. Undoubtedly those who chose this position of the sun for an epoch were some ignorant persons who did not know that a true position cannot become an epoch until it is corrected and reduced to the mean longitude.”

Was it Cato of Utica, or which of the sages was it, who said that no folly could be conceived which could not be matched from the writings of the philosophers? A man finds a longitude given without any distinction in a table where all the longitudes are, as in all other tables where the contrary is not mentioned, mean longitudes. He finds this longitude, the most important one in the whole tables, because the foundation of all the rest, uniformly treated in the tables themselves as a mean longitude; but he finds a reason for not believing that it is so, and what is that reason? It was necessary forsooth, that the commencement of the year should be marked by the actual apparent entrance of the sun into the zodiac! One would suppose from this, that all the people of India stand every year with their eyes riveted to their transit instruments in order that each one may determine for himself the precise moment at which he ought to begin his new-year’s-day solemnities! The fact is, that no man can ascertain by observation the true place of the sun, who cannot instantly add or subtract the equation of his centre, and thereby find the mean place. But independently of this, there cannot possibly be a more gratuitous assumption than that of Bailly. He might just as well have made any other assumption whatever; as for example that the longitude given was not meant to be the longitude for that particular time, but for a time, three days and some hours later. This would have suited his purpose just as well, and would have been just as warrantable an assumption as the other. Thus there is nothing whatsoever that may not be proved; thus there is no distinction whatsoever between truth and error.

But how, it will be asked, does Professor Playfair treat this assumption? It is pretty evident that, like his countryman’s crow, he felt more than he has expressed.

“Bailly (says he), thinks it reasonable to suppose, that this was not the mean place of the sun, as the nature of astronomical tables requires, but the true place, differing from the mean by the equation of the sun’s centre at that time. This, it must be confessed, is the mark of greatest unskilfulness that we meet with in the construction of these tables. Supposing it however to be the case, &c.”

Again, having stated Bailly’s argument, he says:—

“This agreement is near enough to afford a strong proof of the reality of the ancient epoch, if it were not for the difficulty that remains about considering the sun’s place as the true rather than the mean: and for that reason, I am unwilling that any stress should be laid on this argument.”

Were it not worth considering whether the argument would not bear a good deal of stress in the opposite direction? whether in fact it do not conclusively shew that the epoch of the Kali-yug is a merely imaginary one, formed on the mere assumption of a general conjunction of the sun, moon, and planets in the first point of the moveable zodiac,—a conjunction which never took place, save in the fancy of those who will generalize phenomena, and skip, as Lord Bacon hath it, per saltum et volatum, to the most general axioms.

The position assigned to the moon agrees more nearly with its actual place, as calculated by the aid of our modern astronomy: but then, unfortunately, we cannot repose implicit confidence on our astronomy, even in its present highly advanced state, in reference to the position of the moon at so very distant a period as that in question.

The moon’s motion is by far the most complicated one with which astronomers have to do: and although we may decide with confidence as to its position a few centuries ago, no astronomer possessed of true philosophic caution will dogmatize as to its position 48 or 50 centuries backward or forward. The comparison between the Hindu record and the modern calculation may however be stated thus: The moon’s mean longitude, as calculated from Mayer’s tables, on the supposition, that the moon’s rate of motion has been always the same as at the beginning of last century is 300° 51’ 16”. But in consequence of the mutual attractions of the planets, and the disturbances thereby introduced into their orbits and motions, the moon is subject to a small acceleration, encreasing, according to Mayer’s supposition, in proportion to the squares of the times. The amount of this acceleration in the course of a century at present is about 9”. Hence in 48 centuries it will amount to 5° 45’ 36” (the Square of 48 Multiplied by 9”.) This quantity then being added to the moon’s longitude makes it 306° 36’ 52”. But according to the Hindu tables it was 306°; the difference therefore is only 36’ 52”. Now we have only to repeat, that the correction of the moon’s place by Mayer’s theory, however accurate for moderately distant periods, is not to be depended upon for a period of 48 centuries. In fact La Place’s corrections would give a result completely different. This argument, therefore, though from the very nature of the case it cannot be refuted, is completely neutralized. It is, however, to be considered, that La Place’s correction, being founded on a theory which is unquestionably sound, is to be regarded as more likely to be correct than that of Mayer, which is merely empirical. But upon this argument we do not desire to lay much ‘stress,’ being satisfied with merely setting Bailly’s argument aside, without attempting to turn it against its employers.^[11]

The next argument is that derived from the moon’s mean motion. ‘This, it is evident from what has just been said, ought to have been slower, or, which is the same thing, a lunar month ought to have been longer than as we now find it. Accordingly the Hindu tables do make the moon’s mean motion slower than we find it at present. But in regard to the amount of the retardation, the tables do not at all agree with each other, those of Krishnapur differing from those of Tirvalore to the extent of 3° 2’ 10” in stating the moon’s motion for 16,00,984 days from the commencement of the Kali-yug. Now Playfair shews, that, the former give the motion very near the truth as ascertained by Mayer’s formula, and moderately near it as ascertained by that of La Place. The Tirvalore tables, on the other hand, make the retardation too little by upwards of 3°. This, therefore, indicates, that their origin is later than that of the Krishnapur tables; but these latter do not profess to be older than the 7th century of our era, and hence it appears—either that the Tirvalore tables have been constructed at a period subsequent to the seventh century, and thus the argument of Bailly and Playfair is refuted,—or else that our knowledge of the various disturbances of the moon’s motion is not yet sufiiciently accurate to enable us to calculate with perfect accuracy its rate of motion 5,000 years ago: and thus the argument which on the other supposition was refuted, is on this supposition neutralized. But independently of this altogether, we cannot admit that the mean motion, though it should be accurate to a tenth part of a second in 5,000 years, can furnish any argument for the reality of the epoch separate from and additional to that derived from the assignment of its place at the commencement of the epoch. The mean motion of a heavenly body is found by dividing the distance between its position at any two periods remote from each other by the length of time elapsed between the periods. Now we do not think of questioning that the Hindus might make observations on the place of the moon at the end of the 16,00,984 days, that is, A.D. 1282. The accuracy, therefore, of the determination of the mean motion, is inseparably connected with the accuracy of the determination of the moon’s place at the Kali-yug. If the latter be accurate the former must be accurate too. To derive separate arguments, therefore, from these two quantities as if they were independent of each other, is wholly unallowable. Yet this is done both by Bailly and Playfair. Since then the mean motion depends upon the moon’s place at this period, and since we have seen that either this place is falsely assigned by the Hindus, or else that our astronomy is not accurate enough to test its determination within several degrees, it follows, just as before, that the mean motion must either be erroneous, or that we have no means of accurately ascertaining whether it be so or no. And thus we reach the same dilemma as before, a refutation or a neutralization of Bailly’s argument.

The length of the tropical year, or the period that elapses between the sun’s leaving the equinox and his return to it, is subject to a small secular variation which attains its maximum in a period of many thousand years, and then again diminishes. Now La Grange has shewn, that the length of the year 3102 B.C. was 40” 1/2 greater than that of the year 1700 A.D. The true length of the tropical year was, therefore at the former period. 365d. 5h. 49’ 29” 1/2. The Hindu tables make it 365d. 5h. 50’ 35.” The difference is 1’ 5” 1/2. Now the whole difference between any two tropical years cannot exceed 3’ 40”, and hence the error is very nearly as great as possible, the utmost ‘limit of error’ being one half of 3’ 40”, or 1’ 50”. Bailly supposes, that this length of the year must have been ascertained by a course of observations continued for a long period before the Kali-yug. But this supposition Playfair shews to be inadmissible, inasmuch as the length of the tropical year had attained its maximum just about the very period of the Kali-yug; so that while in 3102 B.C. it was 40” 1/2 longer than at present, it was in 5500 B.C. if the earth then existed at all, only 29” longer than at present. This argument, therefore, is not only set aside but refuted.

Nearly similar remarks apply to the other arguments adduced by Bailly and adopted by Playfair, especially those in reference to the obliquity of the ecliptic, and the equation of the sun’s centre. The former A.D. 1700, was 23° 28’ 41”, to which is to be added 22’ 32” in order to give the correct obliquity for 3102 B.C. This gives it 23° 51’ 13”. The Hindus give it 24°. This Bailly considers as an indication that the obliquity was determined at a period 1200 years before the Kali-yug. Is it not far more likely that it was merely assumedin exact degrees? Truly we deem so. The division of the circle into degrees is the work of man for his own convenience. But the Author of nature requires no such artificial aid to assist Him in His operations; and when we find any quantity such as this stated in even degrees, we may almost certainly conclude that it is a bare assumption.

With respect to the mean motions of the planets, it is perfectly evident from what we have seen as to the errors in the determination of their positions at the Kali-yug, that there can be no soundness in the determination of their mean motions. The position of Venus. for example, being 60° from the truth, that error must be swallowed up in the course of as many revolutions as take place between that epoch, and an epoch of actual observation. We accordingly find, that there is no truth in the ascertainment of these motions. This is admitted by the advocates of the reality of the epoch, except with respect to Jupiter and Saturn. We believe that we could shew, that the argument deduced from these is not sound; but we have not sufficient confidence in our standard of reference, and therefore we hold simply that no conclusion can be drawn. The disturbing influences of these two planets were scarcely known at the period when Bailly wrote. The calculation of these influences was the achievement which has bound up the name of La Place with that of Newton: and any arguments founded on data from which these influences were either excluded, or in which they were merely guessed at, can be of no value.

If any of our readers have had patience enough to accompany us thus far, we feel that it would be an abuse of their kindness to lead them now to the more intricate arguments which we have as yct left untouched. We have not indeed exhausted the subject, but have stated, and we trust answered, such of Bailly’s arguments as we could render most intelligible to ordinary readers. Certainly we have not kept back any for fear of their leading to results contrary to those which we have endeavoured to establish. Indeed there would be no logical unfairness in passing over any arguments which we might not be able to set aside; for it is evident, that, in a matter of this kind, we have a right to expect that all the particulars of the state of the heavens, at the period in question, should be stated within such a degree of accuracy as might be supposed compatible with the means of observation of so early astronomers; and a few obvious errors would be sufficient to set aside the reality of the pretended observations, even if there were co-incidences for which we could not account. It is, however, a fact, that those arguments which we have not answered are just as little sound as those which we have answered. And now we shall sum up this branch of our subject by translating the judgment of one, whom, if such matters were to be decided by authority, the astronomical world would by acclamation have chosen as arbiter in the matter,—the author of the ''Mecanique Celeste''—

“ The origin of astronomy in Persia and in India, as among all other nations, is lost in the obscurity of the first period of their history. The Indian tables indicate an astronomy in a state of considerable advancement, but every thing leads us to believe that they are not of high antiquity. And here it is with pain that I differ from the opinion of an illustrious and unfortunate friend, whose death, the subject of endless grief and regret, is a fearful instance of the inconstancy of popular favor.^[12] After having rendered his life honourable by his labors, useful to science and the human race, as well as by his virtues and a noble character, he fell a victim to the most bloody tyranny, opposing the calmness and dignity of integrity to the outrages of a people who had idolized him. The Indian tables have two principal epochs, which go back, the one to the year 3102 before our era and the other to 1419 (of our era.) These epochs are connected together by the motions of the sun, moon and planets in such a way, that, setting out from the positions which the tables assign to these bodies at the second epoch, and calculating back to the first by means of the tables, we find the general conjunction which they suppose at this epoch. The celebrated philosopher of whom I have just spoken, Bailly, has sought to establish in his Treatise on the Indian Astronomy, that this first epoch was founded on observations. Notwithstanding his proofs, set forth with that clearness which he knew how to spread over the most abstruse subjects, I regard it as very probable that the epoch was imagined in order to give a common origin in the zodiac to the motions of the heavenly bodies. Our latest astronomical tables, brought to considerable perfection by the comparison of theory with a vast number of most accurate observations, do not allow us to admit the conjunction supposed in the Indian tables. Indeed they shew us in this respect differences far greater than any errors of which they may be susceptible. In truth, some elements of the Indian Astronomy could only have the amount which they assign to them at an enormously long period before our era: for example, in order to find their equation of the sun’s centre we must go back to 6000 years before that era. But independently of the errors of their determinations, it should be observed that they have considered the inequalities (irregularities in the motions) of the sun and moon only in relation to eclipses, in which the annual equation of the moon is added to the equation of the sun’s centre, and encreases it by a quantity nearly equal to the difference of its true value. Several elements, such as the equations of the centres of Jupiter and Mars, are very different in the Indian tables from what they ought to have been at the commencement of their epoch. The ensemble of the tables, and especially the impossibility of the general conjunction which they suppose, prove that they have been constructed, or at least corrected, in modern times. This conclusion is further borne out by the mean motions which they assign to the moon as referred to her perigee, her nodes and the sun, which being more rapid than as given by Ptolemy, prove that the tables containing them are subsequent to that astronomer; for we have seen that these motions are subject to an acceleration from age to age.”

To this deliverance of the greatest astronomer of his age, we may add a testimony, which for our present purpose is scarcely less, if not even more, weighty. It is that of Professor Playfair himself, writing in the Edinburgh Review in 1817, nearly 20 years later than the date of the memoir which has occupied so much of our attention in this article. We quote it with all the more pleasure that it both shews, in a very striking light, the candour and ingenuousness of our countryman, and also coincides with some of the views which we had expressed before the article in which it occurs came under our notice.^[13]

“When the astronomical tables of India first became known in Europe, the extraordinary light which they appeared to cast on the history and antiquity of the East made every where a great impression; and men engaged with eagerness in a study promising that mixture of historical and scientific research, which is, of all others, the most attractive. The ardour with which they entered on this pursuit, the novelty of the objects, and the surprise excited, may have led them further, in some instances, than the nature of the evidence when scrupulously examined, authorised them to proceed. Among those who were perhaps in a certain degree under the influence of this fascination, was the illustrious Historian of Astronomy, whom his talents, his virtues and his misfortunes have all combined to immortalize. Bailly, who, in his enquiries into the origin of astronomy in the West, had constantly found himself stopped and unable to proceed, on account of the impenetrable obscurity that involves the antiquities of that quarter of the world, was willing to indulge a hope, that the light which seemed now rising in the east was to dispel the obscurity he had so often complained of, and to discover the secrets contained in the antient history of the most antient of the sciences. He therefore entered with great ardour on the study of the Eastern Astronomy; on the exposition of its principles, and on the examination and defence of its accuracy; displaying in all this, the usual resources of his ingenuity, his knowledge and his eloquence.

“A more minute examination, however, instituted by our countrymen on the spot, led them to doubt of the pretensions to high antiquity that they found in the astronomical books of the Hindus, and enabled them to detect errors into which the French Astronomer had been betrayed, sometimes from the want of local knowledge, often from too much confidence in his informers, and occasionally, no doubt, from that spirit of system from which the men of greatest wisdom and genius find it most difficult to defend themselves, The tide of opinion now began to set the contrary way: the recentness, and the inaccuracy of the Indian tables, were maintained no less keenly, and by much more objectionable reasonings, than their antiquity and correctness, had formerly been.

“Among those who have lately taken up this argument, one of the most learned and skilful astronomers in Europe, M. De Lambre, is particularly distinguished. In a work just published, he has made an elaborate attack on the facts, the reasonings, the calculations of the Astronomie Orientale, and has treated the author with a severity and harshness, to which, from a brother academician, the memory of Bailly should hardly have been exposed. His main argument is drawn from this fact, that the data are nowhere quoted, from which the Indian tables were computed, and that there is no record, nor even any tradition of regular astronomical observations having been made by the Hindus. The truth of this assertion, as far as our present information goes, cannot be denied, and is certainly not very easy to be reconciled with the supposition that the Indian astronomy is as original and as antient as it pretends to be.”

Thus then the antiquity of the Hindu astronomy is virtually abandoned by its most skilful, and withal most ingenuous, advocate. And with it fall the arguments that were once attempted to be based upon it to the prejudice of the authenticity of the chronology and history of the sacred writings. It is a most striking fact that thus have perished all the arguments that have been so zealousy deduced from every source against the truth of these wondrous and blessed records. There is scarcely a branch of science that has not at one time or other been enlisted in the service of infidelity; yet have they all in due time returned to their due allegiance, and delighted to take their places in due rank under the banner of their kindred but superior truth; for revealed truth is at once akin to all other truth, and superior to all other; and as the clansman is most honored who is nearest to his kinsman chief, so is it one of the grandest aspects of science that she presents when she appears as the willing satellite of the heavenly revelation. If there be amongst those who may accompany us in these inquiries any whose misfortune it has been to have had doubts infused into their minds regarding the truth, or regarding the infinite value, of the holy scriptures, let them ponder well the fate of all the attempts that have been made from time to time to set aside their authority. The enemies of the Bible, or rather the enemies of the human race, have spared no pains, and left no arguments unused, by which they could hope to shake the confidence of men in the reality of those astounding discoveries that are contained in the book of God; and how far they have succeeded in depriving some of hope in life, and peace in death, we cannot fully tell; but the authority of the scriptures has been but the more convincingly established by the failure of every attempt that has been made to everthrow it. The evil is this—an evil not as it regards the Bible, but as it affects the interests of man—that it is a very easy matter for virulent infidels to appeal to such men as Bailly and Playfair as having proved that there were men living on the earth and observing the heavens 6,000 years before the Christian era, or 2,000 years before the period when the Bible assures us that God created the heavens and the earth; and thousands can hear and understand and be injured by the statement of the conclusion, who have neither the ability nor the inclination to estimate the accuracy of the premises or the legitimacy of the inference. In this view we trust our present article will not be wholly valueless, by exhibiting the real state of the case in a more simple and popular manner than it has ever been exhibited before.

Having thus shewn the inadmissibility of the claims set up on behalf of the Hindu astronomy to an extravagant antiquity, it may be expected that we should enter more directly into a consideration of the actual period of its construction. This however we do not purpose at present. We shall only state generally, that Mr. Bentley has shewn, by arguments that approach as nearly to demonstration as the subject admits of, that the Surya Siddhanta, which is confessedly the origin of the Hindu tables, was written between A.D. 1,000 and A.D. 1,200. The principle on which he proceeds is the simplest possible, and is virtually that which we already illustrated by the supposition of a clock, whose hands should revolve in periods of which one was not a multiple of the other. It may be safely granted as a first principle in the inquiry, that if there be a time when the positions assigned to the heavenly bodies is nearer the truth than those assigned to them at any other period either before or after, that time is the period of the construction of the tables. If there were but one or even two bodies, this principle would not apply; for it is evident that in such a case an error in the position of the body at the time of observation might be swallowed up by an error in the opposite direction in the mean motion, and thus the period of least error, or of no error, might be far distant from, either before or after, the period of actual observation. But such a compensation of errors cannot take place coincidently in the positions of nine or ten heavenly bodies. The amount of probability opposed to such a coincidence is altogether overwhelming, and hence it is impossible for any one to doubt the applicability of Bentley’s mode to the ascertainment of the antiquity of the Surya Siddhanta and the tables constructed according to its rules. Now without going into the details of the application of the principle, we shall merely state, that the period of least error in regard to almost all the elements of the planetary astronomy falls within the two centuries that we have mentioned: and hence the extreme antiquity that can be allowed to the tables does not exceed nine or ten centuries. We may observe, that Playfair laid down precisely the principle on which Bentley has proceeded, in the memoir to which we have so often alluded. We therefore cannot believe, that Playfair was the author of the attack on Bentley’s principle in the ''Edinburgh Review'' of July 1807: but that Mr. Bentley’s friend was right in reporting Playfair’s opinion that that attack was nonsensical. In fact, as we have said, the principle employed by Bentley was stated by Playfair himself long before, and it is highly probable that if he had had the tables actually before him, and had not known them only from Bailly’s account of them, he would have himself applied the principle, and have anticipated Bentley in the determination of their antiquity.

The astronomical system contained in the Surya Siddhanta, is virtually the system of Ptolemy, although we cannot agree with the arguments of DeLambre, who labors strenuously to prove that it was derived either from him or from Ulugh Beg. According to their system the earth is placed as the centre of the system, and around it revolve the Moon, Mercury, Venus, the Sun, Mars, Jupiter and Saturn. The irregularities in the motion of the sun and moon, now universally known and acknowledged to be the effect of the eccentricity of the earth’s and moon’s orbits, are accounted for on the supposition that the sun and moon move in epicycles whose centres revolve in circles. The chief, and almost the sole object of the Hindu astronomy, is the calculation of eclipses. This is accomplished with considerable accuracy by a very tedious but very ingenious process, the rationale of which is not understood by any of the modern Jyotishis, who have therefore been fitly styled machines for calculating eclipses. Examples of the method employed, are given by Bailly from Du Champ, and have been copied into various English works.

And now we come to the consideration of a question of much practical importance in relation to the Hindu astronomy. The late Mr. Wilkinson, an excellent man, as we understand, and one whom we desire to honor as having been both sincerely and intelligently interested in the improvement of this country and its people, a few years ago agitated a question as to the employment of the Siddhantas in the work of native education, as containing a sufficient amount of truth to refute and shew the absurdity of the Puranic system of astronomy, geography, and chronology; and as being more likely to find acceptance among the people than the European astronomy.

The Puranic system is such a mass of absurdity and monstrous folly, that we should be willing to listen very favorably to any proposal that should promise to drive it out of the minds of the people. Of all the “idols of the theatre” from which the true Baconian finds it needful to cleanse the minds of those whom he would lead to the worship of truth, none assuredly was ever more monstrous than this. Like some of the material idols before which the Hindus bow down, it seems formed with the special view of defying all verisimilitude, and showing the extent to which a corrupt imagination can proceed in the conception of monstrosity. And then it is so closely bound up with the religious and social system of the Hindus, that its dispersion could scarcely fail, to a good extent, to shake their confidence in these systems, and emancipate their minds from a tyranny under which their fathers have groaned for ages, and by the influence of which all that is manly and pure and lovely is banished from the land. But while we should deem it a great boon to have this “idol” smashed into fragments, and the fragments ground to powder, we can scarcely agree with Mr. Wilkinson as to the instrument by which the iconoclastic process is to be accomplished.

The Puranic system rests upon authority, an authority deemed divine. Mr. Wilkinson considers, that it is to be dislodged by an appeal to another authority, which, however high in the estimation of the Hindus, can never be so high as that which is opposed to it. Even then if we wished to indoctrinate men into philosophy by the argument of authority, we could find none sufficiently high for our purpose in the present case. But if we had such authority, we apprehend that we should defeat our main purpose by using it. It is the grand advantage of our European science, as an engine of education, that it calls for free and independent investigation. The Siddhantic astronomy, on the other hand, is just as dogmatic as the Puranic. We take not up with the utilitarian and materialistic theories that are supposed to distinguish the age in which we live, and to exert an influence over the character of some of our educational schemes; but we are thoroughly convinced that it is by actual measurement and actual inspection, by the measuring-rod, the theodolite and the telescope, that the Puranic idol is to be demolished. When we come to the Hindu and say,—“This is true, for Baraha and Bhaskar Acharya have said it”—he meets us with an answer which is logically correct and unanswerable, “This other is true, for hosts of Pundits, as learned as these, have said it.” It would be just the same if we came with an ipse dixit of Newton or La Place or La Grange. But in introducing the European astronomy, we come with no human authority, but with the authority of the very God of truth, and show His signature and His seal impressed upon the book of the universe. We shew in a solar eclipse the moon actually interposed between the earth and the sun, whereas the Puranic system declares that the sun is between the earth and the moon; and so in a hundred other instances we give not authority, but direct and visible proof to overthrow the Puranic system. To oppose one human authority to another, is not in any case consistent with sound views of the mode of inculcating truth; to oppose a lower authority to a higher, is necessarily futile and vain. We presume no advocate of native education would have us take advantage of the claims of the Siddhantas to divine inspiration; and therefore we argue upon the supposition that we are to urge natives to the study of them merely on the ground that they are the productions of their own Pandits.

But Mr. Wilkinson, while he admits that multitudes of Hindus at the presidencies will consent to be taught astronomy according to the true or European system, maintains that the people generally, throughout India, will not even listen to a statement of its doctrines. Supposing this latter statement to be correct, we venture to assert, that the Siddhantic system will not, in any degree, avail to rid us of the difficulty. The Siddhantas, as they exist, are utterly unfit for educational purposes. The only way in which they could possibly be rendered available for such purposes, would be by a thorough new-moulding. Subject them to this, and you deprive them of their only recommendation. You make them your own, whereas the only thing in their favor that has ever been alleged, is that they are the works of Hindu Pandits. The choice then is not really between the Siddhantas and European treatises, but between European treatises based on the Siddhantic system,—which is erroneous and excecdingly complicated,—and European treatises in accordance with the European system, which is both simple and true.

But Mr. Wilkinson assures us, that he has succeeded in introducing the Shiddhantic system in one case with very satisfactory results. Now, that Mr. Wilkinson might succeed in imparting a considerable knowledge of astronomy to a set of students who held some Siddhantic treatise in their hands, we do not doubt, any more than we doubt that he might have taught them astronomy, while they held a book which told them that the moon was made of green cheese, and the stars of the clippings of the old moons; but that he would have communicated less knowledge, had his scholars had no book in their hands at all, we do doubt; and that he might have communicated more, had they had one of our good elementary treatises on astronomy as a text-book, we firmly believe. In fact, with such men as Mr. Wilkinson for teachers, the character of the text-book is of comparatively little moment; but in devising a scheme for the education of the people—the 120,000,000 at least, of India, we shall be grievously wrong in our calculations if we reckon upon having a ten-thousandth part of the agents in carrying it into execution at all like him.

It is indeed the part of a skilful and intelligent instructor to illustrate the one system by a comparison with the other; to compare the principles, the processes and the results; and, by every method in his power, to inculcate and recommend truth, and especially to cultivate and develope those faculties by which truth may be investigated. And for this, amongst many other reasons, we earnestly join in the wish expressed by Mr. Wilkinson that a precise and accurate knowledge of the Siddhantas and of their system were more easily attainable than it has hitherto been. We believe that this end will be ultimately gained through the help of those natives who are now receiving a liberal education in accordance with the European system.—We would hold it out to such of them as have the ability and the taste, as an object of laudable ambition, to make themselves thoroughly acquainted with the system of the more enlightened of their Fathers;—acquainted with them not as the almanac-makers and astrologers of the present day are acquainted with them, who use their rules and precepts for the calculations of eclipses and the construction of horoscopes, as an irrational parrot repeats the words that it has been taught, or rather as the inanimate machine performs its revolutions in obedience to the power that propels it; but to study the systems in their principles, as they have been taught to study the European systems. The labors of Colebrooke, and Davies, and Bentley have marked out the path, and set an example of the spirit in which their researches should be prosecuted. It would give us sincere pleasure to find some of the more gifted of those sons of India who have enjoyed the privileges of a European education, thus rendering back to Europe information regarding a subject of which her philosophers are even now comparatively in ignorance.

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After this paper was written, and almost the whole of it had passed through the Press, we received the Asiatic Society’s Journal for June 1844, containing a translation into Latin of the astronomical portion of one of the Siddhantas, the Siddhanta Siromani of Bhaskar Acharya. The Translator, Dr. E. Roer, of this city, is entitled to the best thanks of all who are interested in the Hindu Astronomy for this work, which as it left his hands, has evidently been well executed, but which has since then suffered sadly at the hands of the printers. A careful perusal of this article has confirmed our previous conviction, that the Siddhantas are utterly unfit for educational purposes, even if they were free from philosophical and religious falsehood, which is very far from being the case. We are very glad that Dr. Roer has begun to translate such works, and we trust he will go on. The more the Hindu system in all its parts—religious, scientific, political, social and domestic,—is known, the more hope there is of good being effected.

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1. It is not exactly ascertained what is meant by the meridian of Lanka. This, as is well known, is the name usually given to the island of Ceylon. But the accuracy of the Indian tables is far too great to admit of the supposition of so much vagueness as would be implied in speaking of the meridian of a large island. The most probable supposition seems to be that the first meridian was that which bisected Ceylon.
2. May not the fact of the Siamese possessing and making use of the Hindu Astronomical tables indicate something in regard to the intercourse that subsisted at an early period between India and the Eastern Peninsula?
3. Histoire de l’Astronomie Ancienne, depuis son origine, jusqu’à l’etablissement de l’ ecole d’ Alexandrie.—Par M. Bailly, &c. Paris, 1775.
4. Histoire de l’ Astronomie Indienne et Orientale. Ouvrage que peut servir de suite à l’ Histoire de l’ Astronomie Ancienne.—Par M. Bailly, &c. Paris 1787.
5. Of this work we possess only an English translation, and are not aware of the date of its original publication.
6. Reprinted in Playfair’s Works, vol. iii. Edinburgh, 1822.
7. Histoire de l'Astronomie Ancienne, Paris, 1817.
8. Throughout this article we translate such extracts as we find it necessary to make from French Authors. This we do, chiefly for the convenience of our native readers, whom we should be glad to interest in this subject.
9. Our Indian readers know, somewhat better them M. Bailly could possibly do, the value of the compliments bestowed by a Pandit on his Saheb!
10. The true place of a heavenly body is, of course, the place where it actually is seen in the heavens. The mean place is the place that it would occupy if it performed its revolution in a circle and at a uniform rate. The difference between these is its equation, which is to be added or subtracted according as the true position of the body is before or behind its mean place.
11. We find the place of the moon by calculating from La Place’s formula to be 307° 35’ 56”, which differs by 1° 35’ from the Hindu position. This is certainly much nearer the truth than the positions found from Mayer’s rate, and made use of by Bailly and Playfair. For La Place’s formula see the Systeme du Monde p. 232, or Maddy’s Astronomy p. 283. Playfair in another part of his essay mentions La Place’s formula as being more accurate than Mayer’s. Why did he not then employ it here?
12. Bailly was one of the most zealous promoters of the French revolution. He was chosen president of the Tiers etat and of the National Assembly, and was appointed Mayor of Paris. In the discharge of the duties of this office he was obliged to employ forcible measures to repress the mad violence of the men by whose acclamations he was raised to it. He was, consequently, denounced as an enemy to the republic, and condemned to die the death of a traitor. His brutal murderers studiously protracted and encreased his sufferings, till he was released from all earthly suffering by the guillotine. Writers of all parties seem to give Bailly the character of being an amiable man, and a man of much integrity.—Ep. C. R.
13. The article is a Review of Colebrooke’s Translation of the Arithmetical and Algebraical works of Brahmaguptu and Bhascara. The review itself bears sufficient testimony to its authorship; but if there were any doubt as to this point, we find it quoted as the work of Playfair in the article on Algebra in the seventh edition of the Encyclopedia Britannica, written by the late Professor Wallace, the intimate friend of Playfair.