Indian Science and Technology in the Eighteenth Century: Some Contemporary European Accounts c9: II. Remarks on the Astronomy of the Brahmins
Indian Science and Technology in the Eighteenth Century: Some Contemporary European Accounts c9
- Language
- English
II. Remarks on the Astronomy of the Brahmins
c9.1
(By John Playfair, A.M., F.R.S., Edin. (Published 1790).)
c9.2
Since the time when astronomy emerged from the obscurity of ancient fable, nothing is better known than its progress through the different nations of the earth. With the era of Nabonassar, regular observations began to be made in Chaldea; the earliest which have merited the attention of succeeding ages. The curiosity of the Greeks was, soon after, directed to the same object; and that ingenious people was the first that endeavoured to explain, or connect by theory, the various phenomena of the heavens. This work was supposed to be so fully accomplished in the Syntaxes of Ptolemy that his system, without opposition or improvement, continued, for more than five hundred years, to direct the astronomers of Egypt, Italy and Greece. After the sciences were banished from Alexandria, his writings made their way into the East, where, under the Caliphs of Bagdat, astronomy was cultivated with diligence and success. The Persian princes followed the example of those of Bagdat, borrowing besides, from Trebisond, whatever mathematical knowledge was still preserved among the ruins of the Grecian empire. The conquests of Gengis, and afterwards of Timour, though they retarded, did not stop the progress of astronomy in the East. The grandsons of these two conquerors were equally renowned for their love of science: Hulagu restored astronomy in Persia, and Ulugh-Beigh, by an effort still more singular, established it in Tartary. In the meantime, having passed with the Arabs into Spain, it likewise found, in Alphonso of Castile, both a disciple and a patron. It was carried, soon after, into the north of Europe, where, after exercising the genius of Copernicus, of Kepler, and of Newton, it has become the most perfect of all the sciences.
c9.3
2. In the progress which astronomy has thus made, through almost all the nations, from the Indus to the Atlantic, there is scarce a step which cannot be accurately traced; and it is never difficult to determine what each age, or nation received from another, or what it added to the general stock of astronomical knowledge. The various systems, that have prevailed in all these countries, are visibly connected with one another; they are all derived from one original, and would incline us to believe, that the manner in which men begin to observe the heavens, and to reason about them, is an experiment on the human race, which has been made but once.
c9.4
It is, therefore, matter of extreme curiosity to find, beyond the Indus, a system of astronomical knowledge that appears to make no part of the great body of science, which has traversed, and enlightened the other countries of the earth; a system that is in the hands of men, who follow its rules without understanding its principles, and who can give no account of its origin, except that it lays claim to an antiquity far beyond the period, to which, with us, the history of the heroic ages is supposed to extend.
c9.5
3. We owe our first knowledge of this astronomy to M. La Loubere, who, returning, in 1687, from an embassy to Siam, brought with him an extract from a Siamese manuscript, which contained tables, and rules, for calculating the places of the sun and moon.¹ The manner in which these rules were laid down, rendered the principles, on which they were founded, extremely obscure; and it required a commentator, as conversant with astronomical calculation as the celebrated Cassini, to explain the meaning of this curious fragment. After that period, two other sets of astronomical tables were sent to Paris, by the missionaries in Hindostan; but they remained unnoticed, till the return of M. Le Gentil from India, where he had been to observe the transit of Venus in 1769. This academician employed himself, during the long stay, which his zeal for science induced him to make in that country, in acquiring a knowledge of the Indian astronomy. The Brahmins thought they saw, in the business of an astronomer, the marks of a cast, that had some affinity to their own, and began to converse with M. Le Gentil, more familiarly than with other strangers. A learned Brahmin of Tirvalore, having made a visit to the French astronomer, instructed him in the methods, which he used for calculating eclipses of the sun and moon, and communicated to him the tables and rules, that are published in the Memoirs of the Academy of Sciences, for 1772. Since that time, the ingenious and eloquent author of the History of Astronomy, has dedicated an entire volume to the explanation, and comparison of these different tables, where he has deduced, from them, many interesting conclusions.² The subject indeed merited his attention; for the Indian astronomy has all the precision necessary for resolving the great questions, with respect to its own origin and antiquity, and is by no means among the number of those imperfect fragments of ancient knowledge, which can lead no further than conjecture, and which an astronomer would gladly resign to the learned researches of the antiquary, or the mythologist.
c9.6
4. It is from these sources, and chiefly from the elaborate investigations of the last mentioned work, that I have selected the materials of the paper, which I have now the honour to lay before this Society; and it is perhaps necessary that I should make some apology for presenting here, what can have so little claim to originality. The fact is, 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 always 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; and I then fancied, that, in an argument of such variety, I might perhaps do a service to others, by presenting to them, that particular view of it, which had appeared to me the most striking. Such, therefore, is the object of these remarks; they are directed to three different points: The first is to give a short account of the Indian astronomy, so far as it is known to us, from the four sets of tables above mentioned; the second, to state the principal arguments, that can be deduced from these tables, with respect to their antiquity; and the third, to form some estimate of the geometrical skill with which this astronomical system is constructed. In the first, I have followed M. Bailly closely; in the second, though I have sometimes taken a different road, I have always come to the same conclusion; having aimed at nothing so much, as to reduce the reasoning into a narrow compass, and to avoid every argument that is not purely astronomical, and independent of all hypothesis; in the third, I have treated of a question which did not fall within the plan of M. Bailly’s work, but have only entered on it at present, leaving to some future opportunity, the other discussions to which it leads.
c9.7
5. The astronomy of India, as you already perceive, is confined to one branch of the science. It gives no theory, nor even any description of the celestial phenomena, but satisfies itself with the calculation of certain changes in the heavens, particularly of the eclipses of the sun and moon, and with the rules and tables by which these calculations must be performed. The Brahmin, seating himself on the ground, and arranging his shells before him, repeats the enigmatical verses that are to guide his calculation, and from his little tablets of palm leaves, takes out the numbers that are to be employed in it. He obtains his result with wonderful certainty and expedition; but having little knowledge of the principles on which his rules are founded, and no anxiety to be better informed, he is perfectly satisfied, if, as it usually happens, the commencement and duration of the eclipse answer, within a few minutes, to his prediction. Beyond this his astronomical enquiries never extend; and his observations, when he makes any, go no farther than to determine the meridian line, or the length of the day, at the place where he observes.
c9.8
The objects, therefore, which this astronomy presents to us, are principally three. 1. Tables and rules for calculating the places of the sun and moon; 2. Tables and rules for calculating the places of the planets; 3. Rules by which the phases of eclipses are determined. Though it is chiefly to the first of these that our attention at present is to be directed, the two last will also furnish us with some useful observations.
c9.9
6. The Brahmins, like all other astronomers, have distinguished from the rest of the heavens, that portion of them, through which the sun, moon and planets continually circulate. They divide this space, which we call the Zodiac, into twenty-seven equal parts, each marked by a group of stars, or a constellation.³ This division of the Zodiac is extremely natural in the infancy of astronomical observation; because the moon completes her circle among the fixed stars, nearly in twenty-seven days, and so makes an actual division of that circle into twenty-seven equal parts. The moon too, it must be remembered, was, at that time, the only instrument, if we may say so, by which the positions of the stars on each side of her path could be ascertained; and when her own irregularities were unknown, she was, by the rapidity of her motion eastward, well adapted for this purpose. It is also to the phases of the moon, that we are to ascribe the common division of time into weeks, or portions of seven days, which seems to have prevailed almost over the whole earth.⁴ The days of the week are dedicated by the Brahmins, as by us, to the seven planets, and what is truly singular, they are arranged precisely in the same order.
c9.10
7. With the constellations, that distinguish the twenty-seven equal spaces, into which their Zodiac is divided, the astronomers of India, have connected none of those figures of animals, which are among us, of so ancient, and yet so arbitrary an origin. M. Le Gentil has given us their names, and configurations.⁵ They are formed, for the most part, of small groups of stars, such as the Pleiades or the Hyades, those belonging to the same constellation being all connected by straight lines. The first of them or that which is placed at the beginning of their Zodiac, consists of six stars, extending from the head of Aries to the foot of Andromeda, in our Zodiac, and occupying a space of about ten degrees in longitude. These constellations are far from including all the stars in the Zodiac. M. Le Gentil remarks, that those stars seem to have been selected, which are best adapted for marking out, by lines drawn between them, the places of the moon in her progress through the heavens.
c9.11
At the same time that the stars in the Zodiac are thus arranged into twenty-seven constellations, the ecliptic is divided, as with us, into twelve signs of thirty degrees each. This division is purely ideal, and is intended merely for the purpose of calculation. The names and emblems by which these signs are expressed, are nearly the same as with us;⁶ and there is nothing in the nature of things to have determined this coincidence, it must, like the arrangement of the days of the week, be the result of some ancient and unknown communication.
c9.12
8. That motion by which the fixed stars all appear to move eastward, and continually to increase their distance from the place, that the sun occupies at the vernal equinox, is known to the Brahmins, and enters into the composition of all their tables.⁷ They compute this motion to be at the rate of 54" a year; so that their *annus magnus*, or the time in which the fixed stars complete an entire revolution, is 24,000 years. This motion is too uick by somewhat less than 4" a year; an error that will not be thought great, when it is considered, that Ptolemy committed one of 14", in determining the same quantity.
c9.13
Another circumstance, which is common to all the tables, and, at the same time, peculiar to the Indian astronomy, is, that they express the longitude of the sun and moon, by their distance from the beginning of the moveable Zodiac, and not, as is usual with us, by their distance from the point of the vernal equinox. The longitude is reckoned in signs of 30°, as already mentioned, and each degree is subdivided into 60', etc. In the division of time, their arithmetic is purely sexagesimal: They divide the day into 60 hours, the hour into 60 minutes, etc.; so that their hour is 24 of our minutes, their minute 24 of our seconds, and so on.
c9.14
9. These remarks refer equally to all the tables. We are now to take notice of what is peculiar to each, beginning with those of Siam.
c9.15
In order to calculate for a given time, the place of any of the celestial bodies, three things are required. The first is, the position of the body in some past instant of time, ascertained by observation; and this instant, from which every calculation must set out, is usually called the epoch of the tables. The second requisite is, the mean rate of the planet's motion, by which is computed the arch in the heavens, that it must have described, in the interval between the epoch and the instant for which the calculation is made. By the addition of this, to the place at the epoch, we find the mean place of the planet, or the point it would have occupied in the heavens, had its motion been subject to no irregularity. The third is, the correction, on account of such irregularity, which must be added to the mean place, or subtracted from it, as circumstances require, in order to have the true place. The correction thus made is, in the language of astronomy, called an equation; and, when it arises from the eccentricity of a planet's orbit, it is called the equation of the centre.
c9.16
10. The epoch of the tables of Siam does not go back to any very remote period. M. Cassini, by an ingenious analysis of their rules, finds that it corresponds to the 21st of March, in the year 638 of our era, at 3 in the morning, on the meridian of Siam.⁸ This was the instant at which the astronomical year began, and at which both the sun and moon entered the moveable Zodiac.
c9.17
Indeed, it is to be observed, that, in all the tables, the astronomical year begins when the sun enters the moveable Zodiac, so that the beginning of this year is continually advancing with respect to the seasons, and makes the complete round of them in 24,000 years.
c9.18
From the epoch above mentioned, the mean place of the sun for any other time is deduced, on the supposition that in 800 years, there are contained 292,207 days.⁹ This supposition involves in it the length of the sydereal year, or the time that the sun takes to return to the beginning of the moveable Zodiac, and makes it consist of 365ᵈ, 6ʰ, 12′, 36″.¹⁰ From this, in order to find the tropical year, or that which regulates the seasons, we must take away 21′, 55″, as the time which the sun takes to move over the 54″, that the stars are supposed to have advanced in the year; there will remain 365ᵈ, 5ʰ, 50′, 41″, which is the length of the tropical year that is involved, not only in the tables of Siam, but likewise, very nearly, in all the rest.¹¹ This determination of the length of the year is but 1′, 53″, greater than that of De La Caille, which is a degree of accuracy beyond what is to be found in the more ancient tables of our astronomy.
c9.19
11. The next thing with which these tables present us, is a correction of the sun's mean place, which corresponds to what we call the equation of his centre, or the inequality arising from the eccentricity of his orbit, in consequence of which, he is alternately retarded and accelerated, his true place being, for one half of the year, left behind the mean, and, for the other, advanced before it. The point where the sun is placed, when his motion is slowest, we call his apogee, because his distance from the earth is then greatest; but the Indian astronomy, which is silent with respect to theory; treats this point as nothing more than what it appears to be, a point, viz. in the heavens, where the sun's motion is the slowest possible, and about 90° distant from that, where his greatest inequality takes place. This greatest inequality is here made to be 2°, 12′,¹² about 16′ greater than it is determined, by the modern astronomy of Europe. This difference is very considerable; but we shall find that it is not to be ascribed wholly to error, and that there was a time when the inequality in question was nearly of the magnitude here assigned to it. In the other points of the sun's path, this inequality is diminished, in proportion to the sine of the mean distance from the apogee, that is, nearly as in our own tables. The apogee is supposed to be 80° advanced beyond the beginning of the Zodiac, and to retain always the same position among the fixed stars, or to move forward at the same rate with them.¹³ Though this supposition is not accurate, as the apogee gains upon the stars about 10″ annually, it is much nearer the truth than the system of Ptolemy, where the sun's apogee is supposed absolutely at rest, so as continually to fall back among the fixed stars, by the whole quantity of the precession of the equinoxes.¹⁴
c9.20
12. In these tables, the motions of the moon are deduced, by certain intercalations, from a period of nineteen years, in which she makes nearly 235 revolutions; and it is curious to find at Siam, the knowledge of that cycle, of which the invention was thought to do so much honour to the Athenian astronomer Meton, and which makes so great a figure in our modern kalendars.¹⁵ The moon's apogee is supposed to have been in the beginning of the moveable Zodiac, 621 days after the epoch of the 21st of March 638, and to make an entire revolution in the heavens in the space of 3232 days.¹⁶ The first of these suppositions agrees with Mayer's tables to less than a degree, and the second differs from them only by 11ʰ, 14′, 31″; and if it be considered that the apogee is an ideal point in the heavens, which even the eyes of an astronomer cannot directly perceive, to have discovered its true motion, so nearly, argues no small correctness of observation.
c9.21
13. From the place of the apogee, thus found, the inequalities of the moon's motion, which are to reduce her mean to her true place, are next to be determined. Now, at the oppositions and conjunctions, the two greatest of the moon's inequalities, the equation of the centre and the evection, both depend on the distance from the apogee, and therefore appear but as one inequality. They also, partly, destroy one another; so that the moon is retarded or accelerated, only by their difference, which, when greatest, is according to Mayer's tables, 4°, 57', 42". The Siamese rules, which calculate only for oppositions and conjunctions, give, accordingly, but one inequality to the moon, and make it, when greatest, 4°, 56', not 2' less than the preceding. This greatest equation is applied, when the moon's mean distance from the apogee is 90°; in other situations, the equation is less, in proportion as the sine of that distance diminishes.¹⁷
c9.22
14. The Siamese MS breaks off here, and does not inform us how the astronomers of that country proceed, in the remaining parts of their calculation, which they seem to have undertaken, merely for some purpose in astrology. M. Cassini, to whom we are indebted for the explanation of these tables, observes, that they are not originally constructed for the meridian of Siam, because the rules direct to take away 3' for the sun, and 40' for the moon, (being the motion of each for 1ʰ 13'), from their longitudes calculated as above.¹⁸ The meridian of the tables is therefore 1ʰ, 13' or 18°, 15' west of Siam; and it is remarkable, that this brings us very near to the meridian of Benares, the ancient seat of Indian learning.¹⁹ The same agrees nearly with what the Hindoos call their first meridian, which passes through Ceylon and the banks of Ramanancor. We are, therefore, authorised, or rather, we are necessarily determined to conclude, that the tables of Siam came originally from Hindostan.
c9.23
15. Another set of astronomical tables, now in the possession of the Academy of Sciences, was sent to the late M. De L'Isle from Chrisnabouram, a town in the Caranatic, by Fr Du Champ, about the year 1750. Though these tables have an obvious affinity to what has already been described, they form a much more regular and extensive system of astronomical knowledge. They are fifteen in number; and include, beside the mean motions of the sun, moon and planets, the equations to the centre of the sun and moon, and two corrections for each of the planets, the one of which corresponds to its apparent, and the other to its real inequality. They are accompanied also with precepts, and examples, which Fr Du Champ received from the Brahmins of Chrisnabouram, and which he has translated into French.²⁰
c9.24
The epoch of these tables is less ancient than that of the former, and answers to the 10th of March at sunrise, in the year 1491 of our era, when the sun was just entering the moveable Zodiac, and was in conjunction with the moon; two circumstances, by which almost all the Indian eras are distinguished. The places, which they assign, at that time, to the sun and moon, agree very well with the calculations made from the tables of Mayer, and De La Caille. In their mean motions, they indeed differ somewhat from them; but as they do so equally for the sun and moon, they produce no error, in determining the relative position of these bodies, nor, of consequence, in calculating the phenomena of eclipses. The sun's apogee is here supposed to have a motion swifter than that of the fixed stars, by about 1" in nine years, which, though it falls greatly short of the truth, does credit to this astronomy, and is a strong mark of originality. The equation of the sun's centre is somewhat less here than in the tables of Siam; it is 2°, 10', 30"; the equation of the moon's centre is 5°, 47"; her path, where it intersects that of the sun, is supposed to make an angle with it of 4°, 30', and the motions, both of the apogee and node, are determined very near to the truth.
c9.25
16. Another set of tables, sent from India by Fr Patouillet, were received by M. De L'Isle, about the same time with those of Chrisnabouram. They have not the name of any particular place affixed to them; but, as they contain a rule for determining the length of the day, which answers to the latitude of 16°, 16', M. Bailly thinks it probable that they come from Narsapour.²¹
c9.26
The precepts and examples, which accompany these tables, though without any immediate reference to them, are confined to the calculation of the eclipses of the sun and moon; but the tables themselves extend to the motion of the planets, and very much resemble those of Chrisnabouram, except that they are given with less detail, and in a form much more enigmatical.²²
c9.27
The epoch of the precepts, which M. Bailly has evolved with great ingenuity, goes back no farther than the year 1569, at midnight, between the 17th and 18th of March. From this epoch, the places of the sun and moon are computed, as in the tables of Siam, with the addition of an equation, which is indeed extremely singular. It resembles that correction of the moon's motion, which was discovered by Tycho, and which is called the annual equation, because its quantity depends, not on the place of the moon, but on the place of the sun, in the ecliptic. It is every where proportional to the inequality of the sun's motion, and is nearly a tenth part of it. The tables of Narsapour make their annual equation only of the sun's: but this is not their only mistake; for they direct the equation to be added to the moon's longitude, when it ought to be subtracted from it, and vice versa. Now, it is difficult to conceive from whence the last mentioned error has arisen; for though it is not at all extraordinary, that the astronomers, who constructed these tables, should mistake the quantity of a small equation, yet it is impossible, that the same observations, which informed them of its existence, should not have determined, whether it was to be added or subtracted. It would seem, therefore, that something accidental must have occasioned this error; but however that be, an inequality in the lunar motions, that is found in no system with which the astronomers of India can have had any communication, is at least a proof of the originality of their tables.
c9.28
17. The tables, and methods, of the Brahmins of Tirvalore, are, in many respects, more singular than any that have yet been, described.²³ The solar year is divided, according to them, into twelve unequal months, each of which is the time that the sun takes to move through one sign, or 30°, of the ecliptic. Thus, Any, or June, when the sun is in the third sign, and his motion slowest, consists of 31ᵈ, 36ʰ, 38' and Margagy, or December, when he is in the ninth sign, and his motion quickest, consists only of 29ᵈ, 20ʰ, 53.²⁴ The lengths of these months, expressed in natural days, are contained in a table, which, therefore, involves in it the place of the sun’s apogee, and the equation of his centre. The former seems to be 77° from the beginning of the Zodiac, and the latter about 2°, 10', nearly as in the preceding tables. In their calculations, they also employ an astronomical day, which is different from the natural, being the time that the sun takes to move over one degree of the ecliptic; and of which days there are just 360 in a year.²⁵
c9.29
²³ [The footnote text is not present on this page.]
c9.30
18. These tables go far back into antiquity. Their epoch coincides with the famous era of the Calyougham, that is, with the beginning of the year 3102 before Christ. When the Brahmins of Tirvalore would calculate the place of the sun for a given time, they begin by reducing into days the interval between that time, and the commencement of the Calyougham, multiplying the years by 365ᵈ, 6ʰ, 12', 30"; and taking away 2ᵈ, 3ʰ, 32', 30", the astronomical epoch having begun that much later than the civil.²⁶ They next find, by means of certain divisions, when the year current began, or how many days have elapsed since the beginning of it, and then, by the table of the duration of months, they reduce these days into astronomical months, days, etc., which is the same with the signs, degrees and minutes of the sun’s longitude from the beginning of the Zodiac. The sun’s longitude, therefore, is found.
c9.31
19. Somewhat in the same manner, but by a rule still more artificial and ingenious, they deduce the place of the moon, at any given time, from her place at the beginning of the Calyougham.²⁷ This rule is so contrived, as to include at once the motions both of the moon and of her apogee, and depends on this principle, according to the very skilful interpretation of M. Bailly, that, 1,600,894 days after the above mentioned epoch, the moon was in her apogee, and 7ˢ, 2°, 0', 7", distant from the beginning of the Zodiac; that after 12,372 days, the moon was again in her apogee, with her longitude increased, 9ˢ, 27°, 48', 10″; that in 3031 days more, the moon is again in her apogee, with 11ˢ, 7°, 31′, 1″ more of longitude; and, lastly, that, after 248 days, she is again in her apogee, with 27°, 44′, 6″, more of longitude. By means of the three former numbers, they find, how far, at any given time, the moon is advanced in this period of 248 days, and by a table, expressing how long the moon takes to pass through each degree of her orbit, during that period, they find how far she is then advanced in the Zodiac.²⁸ This rule is strongly marked with all the peculiar characters of the Indian astronomy. It is remarkable for its accuracy, and still more for its ingenuity and refinement; but is not reduced withal, to its ultimate simplicity.
c9.32
20. The tables of Tirvalore, however, though they differ in form very much from those formerly described, agree with them perfectly in many of their elements. They suppose the same length of the year, the same mean motions, and the same inequalities of the sun and moon, and they are adapted nearly to the same meridian.²⁹ But a circumstance in which they seem to differ materially from the rest is, the antiquity of the epoch from which they take their date, the year 3102 before the Christian era. We must, therefore, enquire, whether this epoch is real or fictitious, that is, whether it has been determined by actual observation, or has been calculated from the modern epochs of the other tables. For it may naturally be supposed, that the Brahmins, having made observations in later times, or having borrowed from the astronomical knowledge of other nations, have imagined to themselves a fictitious epoch, coinciding with the celebrated era of the Calyougham, to which, through vanity or superstition, they have referred the places of the heavenly bodies, and have only calculated what they pretend that their ancestors observed.
c9.33
21. In doing this, however, the Brahmins must have furnished us with means, almost infallible, of detecting their imposture. It is only for astronomy, in its most perfect state, to go back to the distance of forty-six centuries, and to ascertain the situation of the heavenly bodies at so remote a period. The modern astronomy of Europe, with all the accuracy that it derives from the telescope and the pendulum, could not venture on so difficult a task, were it not assisted by the theory of gravitation, and had not the integral calculus, after a hundred years of almost continual improvement, been able, at last, to determine the disturbances in our system, which arise from the action of the planets on one another.
c9.34
Unless the corrections for these disturbances be taken into account, any system of astronomical tables, however accurate at the time of its formation, and however diligently copied from the heavens, will be found less exact for every instant, either before or after that time, and will continually diverge more and more from the truth, both for future and past ages. Indeed, this will happen, not only from the neglect of these corrections, but also from the small errors unavoidably committed, in determining the mean motions, which must accumulate with the time, and produce an effect that becomes every day more sensible, as we retire, on either side, from the instant of observation. For both these reasons, it may be established as a maxim, that, if there be given a system of astronomical tables, founded on observations of an unknown date, that date may be found, by taking the time when the tables represent the celestial motions most exactly.
c9.35
Here, therefore, we have a criterion, by which we are to judge of the pretensions of the Indian astronomy to so great antiquity. It is true, that, in applying it, we must suppose our modern astronomy, if not perfectly accurate, at least so exact as to represent the celestial motions, without any sensible error, even for a period more remote than the Calyougham; and this, considering the multitude of observations on which our astronomy is founded, the great antiquity of some of those observations, and the extreme accuracy of the rest, together with the assistance derived from the theory of physical causes, may surely be assumed as a very reasonable postulatum. We begin with the examination of the mean motions.
c9.36
22. The Brahmins place the beginning of their moveable Zodiac, at the time of their epoch, 54° before the vernal equinox, or in the longitude of 10s, 6°, according to our method of reckoning. Now, M. Le Gentil brought with him a delineation of the Indian Zodiac, from which the places of the stars in it may be ascertained with tolerable exactness.³⁰ In particular, it appears, that Aldebaran, or the first star of Taurus, is placed in the last degree of the fourth constellation, or 53°, 20', distant from the beginning or the Zodiac. Aldebaran was therefore 40' before the point of the vernal equinox, according to the Indian astronomy, in the year 3102 before Christ. But the same star, by the best modern observations, was, in the year 1750, in longitude, 2s, 6°, 17', 47"; and had it gone forward, according to the present rate of the precession of the equinoxes, 50" annually, it must have been, at the era of the Calyougham, 1°, 32', before the equinox. But this result is to be corrected, in consequence of the inequality in the precession, discovered by M. De La Grange,³¹ by the addition of 1°, 45', 22", to the longitude of Aldebaran, which gives the longitude of that star 13' from the vernal equinox, at the time of the Calyougham, agreeing, within 53', with the determination of the Indian astronomy.³²
c9.37
This agreement is the more remarkable, that the Brahmins, by their own rules for computing the motion of the fixed stars, could not have assigned this place to Aldebaran for the beginning of the Calyougham, had they calculated it from a modern observation. For as they make the motion of the fixed stars too great by more than 3" annually, if they had calculated backward from 1491, they would have placed the fixed stars less advanced by 4° or 5°, at their ancient epoch, than they have actually done. This argument 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.
c9.38
23. Let us next compare the places of the sun and moon, for the beginning of the Calyougham, as deduced from the Indian and the modern astronomy. And, first, of the sun, though, for a reason that will immediately appear, it is not to be considered as leading to any thing conclusive. M. Bailly, from a comparison of the tables of Tirvalore with those of Chrisnabouram, has determined the epoch of the former to answer to midnight, between the 17th and 18th³³ of February of the year 3102 before Christ, at which time the sun was just entering the moveable Zodiac, and was therefore in longitude 10ˢ, 6°. M. Bailly also thinks it reasonable to suppose, that this was not the mean place of the sun, as the nature of astronomical tables require, but the true place, differing from the mean, by the equation to the sun's centre at that time.³⁴ 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, the mean place of the sun, at the time of the epoch, comes out 10ˢ, 3°, 38', 13". Now, the mean longitude of the sun, from De La Caille's tables, for the same time, is 10ˢ, 1°, 5', 57", supposing the precession of the equinoxes to have been uniformly at the rate it is now, that is, 50" annually. But M. De La Grange has demonstrated, that the precession was less in former ages than in the present; and his formula gives 1°, 45', 22", to be added, on that account, to the sun's longitude already found, which makes it 10ˢ, 2°, 51', 19", not more than 47' from the radical place in the tables of Tirvalore. 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 upon this argument. The place of the moon is not liable to the same objection.
c9.39
24. The moon’s mean place, for the beginning of the Calyougham, (that is, for midnight between the 17th and 18th of February 3102, B.C. at Benares), calculated from Mayer’s tables, on the supposition that her motion has always been at the same rate as at the beginning of the present century, is 10ˢ, 0°, 51′, 16″.³⁵ But, according to the same astronomer, the moon is subject to a small, but uniform acceleration, such, that her angular motion, in any one age, is 9″ greater than in the preceding, which, in an interval of 4801 years, must have amounted to 5°, 45′, 44″. This must be added to the preceding, to give the real mean place of the moon, at the astronomical epoch of the Calyougham, which is therefore 10ˢ, 6°, 37′. Now, the same, by the tables of Tirvalore, is 10ˢ, 6°, 0′; the difference is less than two thirds of a degree, which, for so remote a period, and considering the acceleration of the moon’s motion for which no allowance could be made in an Indian calculation, is a degree of accuracy that nothing but actual observation could have produced.
c9.40
25. To confirm this conclusion, M. Bailly computes the place of the moon for the same epoch, by all the tables to which the Indian astronomers can be supposed to have ever had access.³⁶ He begins with the tables of Ptolemy; and if, by help of them, we go back from the era of Nabonassar, to the epoch of the Calyougham, taking into account the comparative length of the Egyptian and Indian years, together with the difference of meridians between Alexandria and Tirvalore, we shall find the longitude of the sun 10°, 21′, 15″ greater, and that of the moon 11°, 52′, 7″ greater than has just been found from the Indian tables.³⁷ At the same time that this shows, how difficult it is to go back, even for a lesser period than that of 3000 years, in an astronomical computation, it affords a proof, altogether demonstrative, that the Indian astronomy is not derived from that of Ptolemy.
c9.41
The tables of Ulugh Beig are more accurate than those of the Egyptian astronomer. They were constructed in a country not far from India, and but a few years earlier than 1491, the epoch of the tables of Chrisnabouram. Their date is July 4, at noon, 1437, at Samarcand; and yet they do not agree with the Indian tables, even at the above mentioned epoch of 1491.38 But, for the year 3102 before Christ, their difference from them, in the place of the sun, is 1°, 30′, and in that of the moon 6°; which, though much less than the former differences, are sufficient to show, that the tables of India are not borrowed from those of Tartary.
c9.42
The Arabians employed in their tables the mean motions of Ptolemy; the Persians did the same, both in the more ancient tables of Chrysococca, and the later ones of Nassireddin.39 It is therefore certain, that the astronomy of the Brahmins is neither derived from that of the Greeks, the Arabians, the Persians or the Tartars. This appeared so clear to Cassini, though he had only examined the tables of Siam, and knew nothing of many of the great points which distinguish the Indian astronomy from that of all other nations, that he gives it as his opinion, that these tables are neither derived from the Persian astronomy of Chrysococca, nor from the Greek astronomy of Ptolemy; the places they give at their epoch to the apogee of the sun, and or the moon, and their equation for the sun's centre, being very different from both.40
c9.43
26. But, to return to what respects the moon's acceleration; it is plain, that tables, as ancient as those of Tirvalore pretend to be, ought to make the mean motion of that planet much slower than it is at present. They do accordingly suppose, in the rule for computing the place of the moon, already described, that her motion for 4383 years, 94 days, reckoned in the moveable Zodiac from the epoch of the Calyougham, is 7s, 2°, 0′, 7″, or 9s, 7°, 45′, 1″, when referred to the fixed point of the vernal equinox. Now, the mean motion for the same interval, taken from the tables of Mayer, is greater than this, by 2°, 42′, 4″,41 which, though conformable, in general, to the notion of the moon's motion having been accelerated, falls, it must be confessed, greatly short of the quantity which Mayer has assigned to that acceleration. This, however, is not true of all the tables; for the moon's motion in 4383 years, 94 days, taken from those of Chrisnabouram, is 3°, 2′, 10″ less than in the tables of Tirvalore;42 from which it is reasonable to conclude, with M. Bailly, that the former are, in reality, more ancient than the latter, though they do not profess to be so: and hence, also, the tables of Chrisnabouram make the moon's motion less than Mayer's, for the above mentioned interval, by 5°, 44', 14", which therefore is, according to them, the quantity of the acceleration.
c9.44
27. Now, it is worthy of remark, that if the same be computed on Mayer's principles, that is, if we calculate how much the angular motion of the moon for 4383 years, 94 days, dated from the beginning of the Calyougham, must have been less than if her velocity had been all that time uniform, and the same as in the present century, we shall find it to be 5°, 43', 7", an arch which is only 1', 7", less than the former. The tables of Chrisnabouram, therefore, agree with those of Mayer, when corrected by the acceleration within 1', 7", and that for a period of more than four thousand years. From this remarkable coincidence, we may conclude, with the highest probability, that at least one set of the observations, on which those tables are founded, is not less ancient than the Calyougham; and though the possibility of their being some ages later than that epoch, is not absolutely excluded, yet it may, by strict mathematical reasoning, be inferred, that they cannot have been later than 2000 years before the Christian era.43
c9.45
28. This last is one of the few coincidences between the astronomy of India and of Europe, which their ingenious historian has left for others to observe. Indeed, since he wrote, every argument, founded on the moon's acceleration, has become more worthy of attention, and more conclusive. For that acceleration is no longer a mere empirical equation, introduced to reconcile the ancient observations with the modern, nor a fact that can only be accounted for by hypothetical causes, such as the resistance of the ether, or the time necessary for the transmission of gravity; it is a phenomenon, which M. De La Place has,44 with great ability, deduced from the principle of universal gravitation, and shown to be necessarily connected with the changes in the eccentricity of the earth's orbit, discovered by M. De La Grange; so that the acceleration of the moon is indirectly produced by the action of the planets, which alternately increasing and diminishing the said eccentricity, subjects the moon to different degrees of that force by which the sun disturbs the time of her revolution round the earth. It is therefore a periodical inequality, by which the moon's motion, in the course of ages, will be as much retarded as accelerated; but its changes are so slow, that her motion has been constantly accelerated, even for a longer period than that to which the observations of India extend.
c9.46
A formula for computing the quantity of this inequality, has been given by M. De La Place, which, though only an approximation, being derived from theory, is more accurate than that which Mayer deduced entirely from observation;45 and if it be taken instead of Mayer’s, which last, on account of its simplicity, I have employed in the preceding calculations, it will give a quantity somewhat different, though not such as to affect the general result. It makes the acceleration for 4383 years, dated from the beginning of the Calyougham, to be greater by 17', 39", than was found from Mayer’s rule, and greater consequently by 16', 32", than was deduced from the tables of Chrisnabouram. It is plain, that this coincidence is still near enough to leave the argument, that is founded on it, in possession of all its force, and to afford a strong confirmation of the accuracy of the theory, and the authenticity of the tables.
c9.47
That observations made in India, when all Europe was barbarous or uninhabited, and investigations into the most subtle effects of gravitation made in Europe, near five thousand years afterwards, should thus come in mutual support of one another, is perhaps the most striking example of the progress and vicissitude of science, which the history of mankind has yet exhibited.
c9.48
29. This, however, is not the only instance of the same kind that will occur, if, from examining the radical places and mean motions in the Indian astronomy, we proceed to consider some other of its elements, such as, the length of the year, the inequality of the sun’s motion, and the obliquity of the ecliptic, and compare them with the conclusions deduced, from the theory of gravity, by M. De La Grange. To that geometer, physical astronomy is indebted for one of the most beautiful of its discoveries, viz. that all the variations in our system are periodical; so that though every thing, almost without exception, be subject to change, it will, after a certain interval, return to the same state in which it is at present, and leave no room for the introduction of disorder, or of any irregularity that might constantly increase. Many of these periods, however, are of vast duration. A great number of ages, for instance, must elapse before the year be again exactly of the same length, or the sun’s equation of the same magnitude as at present.⁴⁶ An astronomy, therefore, which professes to be so ancient as the Indian, ought to differ considerably from ours in many of its elements. If indeed these differences are irregular, they are the effects of chance, and must be accounted errors; but if they observe the laws, which theory informs us that the variations in our system do actually observe, they must be held as the most undoubted marks of authenticity.
c9.49
⁴⁶ An astronomy, therefore, which professes to be so ancient as the Indian, ought to differ considerably from ours in many of its elements. If indeed these differences are irregular, they are the effects of chance, and must be accounted errors; but if they observe the laws, which theory informs us that the variations in our system do actually observe, they must be held as the most undoubted marks of authenticity.
c9.50
We are to examine, as M. Bailly has done, which of these takes place in the case before us.⁴⁷
c9.51
30. The tables of Tirvalore, which, as we have seen, refer their date to the beginning of the Calyougham, make the siderial year to consist of 365ᵈ, 6ʰ, 12′, 30″; and therefore the tropical of 365ᵈ, 5ʰ, 50′, 35″, which is 1′, 46″, longer than that of De La Caille.⁴⁸ Now, the tropical year was in reality longer at that time than it is at present; for though the siderial year, or the time which the earth takes to return from one point of space to the same point again, is always of the same magnitude, yet the tropical year being affected by the precession of the equinoxes, is variable by a small quantity, which never can exceed 3′, 40″, and which is subject to slow, and unequal alternations of diminution and increase. A theorem, expressing the law and the quantity of this variation, has been investigated by M. De La Grange, in the excellent memoir already mentioned;⁴⁹ and it makes the year 3102 before Christ 40½″ longer than the year at the beginning of the present century.⁵⁰ The year in the tables of Tirvalore is therefore too great by 1′, 5½″.
c9.52
31. But the determination of the year is always from a comparison of observations made at a considerable interval from one another; and, even to produce a degree of accuracy much less than what we see belongs to the tables of Tirvalore, that interval must have been of several ages. Now, says M. Bailly, if we suppose these observations to have been made in that period of 2400 years, immediately preceding the Calyougham, to which the Brahmins often refer; and if we also suppose the inequality of the precession of the equinoxes, to increase as we go back, in proportion to the square of the times, we shall find, that, at the middle of this period, or 1200 years before the beginning of the Calyougham, the length of the year was 365ᵈ, 5ʰ, 50′, 41″, almost precisely as in the tables of Tirvalore. And hence it is natural to conclude, that this determination of the solar year is as ancient as the year 1200 before the Calyougham, or 4300 before the Christian era.⁵¹
c9.53
32. In this reasoning, however, it seems impossible to acquiesce; and. M. Bailly himself does not appear to have relied on it with much confidence.52 We are not at liberty to suppose, that the precession of the equinoxes increases in the ratio above mentioned, or, which is the same, that the equinoctial points go back with a motion equably retarded. If, by M. De La Grange’s formula, we trace back, step by step, the variation of the solar year, we shall find, that about the beginning of the Calyougham, it had nearly attained the extreme point of one of those vibrations, which many centuries are required to complete; and that the year was then longer than it has ever been since, or than it had been for many ages before. It was 40½″ longer than it is at present; but, at the year 5500 before Christ, it was only 29″ longer than at present, instead of 2′, 50″, which is the result of M. Bailly’s supposition. During all the intervening period of 2400 years, the variation of the year was between these two quantities; and we cannot therefore, by any admissible supposition, reduce the error of the tables to less than 1′, 5″. The smallness of this error, though extremely favourable to the antiquity, as well as the accuracy of the Indian astronomy, is a circumstance from which a more precise conclusion can hardly be deduced.
c9.54
33. The equation of the sun’s centre is an element in the Indian astronomy, which has a more unequivocal appearance of belonging to an earlier period than the Calyougham. The maximum of that equation is fixed, in these tables, at 2°, 10′, 32″. It is at present, according to M. De La Caille, 1°, 55½′, that is, 15′ less than with the Brahmins. Now, M. De La Grange has shown, that the sun’s equation, together with the eccentricity of the earth’s orbit, on which it depends, is subject to alternate diminution and increase, and accordingly has been diminishing for many ages. In the year 3102 before our era, that equation was 2°, 6′, 28½″; less, only by 4′, than in the tables of the Brahmins. But if we suppose the Indian astronomy to be founded on observations that preceded the Calyougham, the determination of this equation will be found to be still more exact. Twelve hundred years before the commencement of that period, or about 4300 years before our era, it appears, by computing from M. De La Grange’s formula, that the equation of the sun’s centre was actually 2°, 8′, 16″; so that if the Indian astronomy be as old as that period, its error with respect to this equation is but of 2′.53
First 54 of 225 passages. Read on
Linked texts (3)
- Śvetāmbara Āgama — Ardhamāgadhī Prakrit
- Pāṭaliputra
- Kānyakubja