Venus gives 860 years, and Mars 140, which is evidently too little. For Jupiter, Saturn, and the sun Mr. Bentley makes use of new equations. The aphelion of Mars gives 641 years. The sidereal year 736. The whole brought together stand thus : From the moon's apogee... 605 Years. node........... 580 which being divided by 10, the number of results, in order to get the mean, gives 731 years nearly for the age of the Surya Siddhanta, which differs but five years from the age determined by the length of the year only. Mr. Bentley says, that independent of all calculations, it is known from the Hindoo books by whom the Surya Siddhanta was written, and when. In the commentary on the Bhasvoti, it is declared that Varaha was the author of the work. Now, the Bhasvoti was written in the year 1021 of saka, by one Sotanund, a pupil of Varaha, and under whose directions he wrote his commentary. Varaha must then have been alive, or a short time before. This agrees as nearly as possible with the age above deduced; for the Bhasvoti, in the year 1799, the time when Mr. Bentley made his computations, was exactly 700 years old. It is extremely probable that the name of Varaha must have been to the Surya Siddhanta when it was first written; but that after his death, priestcraft found means to alter it, and to introduce the absurd story of Meya or Moya having received it through divine revelation at the conclusion of the satya yug. Indeed, according to Bentley, a number of other astronomical works were then framed for the purpose of deception, some were pretended to be delivered from the mouth of one or other of their deities, as the Brama Siddhanta, Vishnu Siddhanta, and the works of Siva, com monly called Tantros. Others were pretended to have been received through revelation, as the Soma Siddhanta; while others again were imputed to sages who lived in the remotest periods of antiquity, as Varishta Siddhanta, and other Siddhantas, to the number of about eighteen altogether, including the Surya Siddhanta. These are now called the eighteen original shasters of astronomy, although there be not above three or four of them original. M. Delambre says that the system explained in Mr. Bentley's memoir is so simple and reasonable, that it might have been found without the aid of the Indian books; but when it appears to be the result of a careful examination of them, it seems to be placed beyond all doubt. On the whole, it appears that the Hindoo astronomy is entirely different from ours. If there be any resemblances, they have arisen out of the nature of the science, or from what the Indians have borrowed from the Arabians, who were instructed by the Greeks, rather than from any thing borrowed from the Indians by the Arabians, or by the Greeks. The enigmatic methods of the Indians were never known to the Greeks, and indeed have only been explained of late years; so that the Greeks have taken nothing in astronomy from the Indians, unless perhaps the constellations; this, however, has not by any means been proved. As to the mathematical doctrines in the astronomy of the Greeks, they were their own; and they have demonstrated them, while the Indians have proved nothing. It cannot even be shown that the Indians have ever observed, nor are there any recorded original observations of which the date is certain. It is remarkable that the Indians, who could compute eclipses, and who now announce them in their almanacs, have not recorded even one as having been actually observed; while the Chinese, less skilful calculators, and yet less geometers, have long recorded them in their annals. We have been told of their spheres and their gnomons; but the gnomons of India appear to have served merely as sundials, and to determine the latitude of a place. It is surprising that we have never heard of the solstitial shadow, and but rarely of the equinoctial shadow: that the Surya Siddhanta only slightly mentions the armillary sphere, which served to divide the zodiac into nacshatras; that we find only in the commentary some imperfect indications, but no actual observations. Their armillary sphere, with a terrestrial globe in its centre, and all their planetary orbits, resemble the furniture of a cabinet rather than instruments intended for real observations. With their obliquity of 24°, their ignorance of refraction, the errors which they would no doubt make on the altitude of the pole, it is not easy to see how they could find with any accuracy the longitude and latitude of the stars. They have only designated twentyseven, that is, one in each nacshatra, and their positions are only given in degrees. We believe enough has been now said on the Indian astronomy. The opinions which we have followed are those of Sir William Jones, Messrs. Davis, Bentley, and Colebrooke, as delivered in the Asiatic Researches, and which have been adopted by Delambre, a high authority in the history of astronomy. On a subject which has been so much contested, it will no doubt be highly satisfactory to have also the opinion of the celebrated Laplace, the author of the Mécanique Céleste. He says, "The Indian tables suppose an astronomy considerably advanced; but all tends to produce a belief that it is not of high antiquity. Here I differ, with much regret, from the opinion of an illustrious and unfortunate friend. The Indian tables have two principal epochs, one 3102 years before our era, the other 1491. These epochs are connected by the motions of the sun, the moon, and the planets, in such a manner, that departing from the position which the Indian tables assign to the stars, at the second epoch, and returning to the first, by means of these tables we find the general conjunction which is supposed at that epoch. The celebrated philosopher to whom I have alluded (Bailly), has sought to establish in his Indian Astronomy that this first epoch was founded on observations; but, notwithstanding his proofs, exhibited with that clearness which he knew so well how to spread over the most abstract subject, I consider it as very probable that it has been imagined in order to give a common origin in the zodiac to the celestial motions. Our latest astronomical tables, improved by a comparison of theory with a great number of very precise observations, do not allow to admit the supposed conjunction in the Indian tables. They even present differences much greater than the errors of which they are susceptible. Indeed, some elements of the Indian astronomy could only have the magnitude assigned to them a long time before our era. For example, it would be necessary to go back 6000 years to give the equation of the sun's centre the value it has in the tables; but, independently of the errors of their determinations, it must be observed that they have considered the inequalities of the sun and moon only in relation to eclipses, in which the annual equation of the moon unites with the equation of the sun's centre, and increases it by a quantity nearly equal to the difference of its true value from that of the Indians. Several elements, such as the equations of the centre of Jupiter and Mars, are very different in the Indian tables from what they ought to be at the first epoch. The whole structure of the tables, and especially the impossibility of the conjunction which they suppose, prove that they have been formed, or at least rectified, in modern times." CHAPTER XIV. Hindoo Mathematics. Division of the Circumference of the Circle-Ratio of the Diameter to the Circumference-Tables of Sines and Versed Sines-Mathematical Treatises--Account of the Origin of the 'Lilavati-Its ContentsKnowledge of Algebra. THERE is another subject of inquiry intimately connected with the astronomy of India; this is their knowledge of the mathematical sciences. Here there is not so much room for the exercise of that disposition to exaggeration in respect of dates which so eminently distinguishes their astronomical systems. It is true, that part of their geometry, which is contained in the Surya Siddhanta, which professes to have been a revelation delivered four millions of years ago in the golden age of the Indian mythologists, when man was incomparably better than he is at present, when his stature exceeded twenty-one cubits, and his life extended to ten thousand years, is involved in the absurdity of a pretension to antiquity which outrages all probability; yet this is not any part of the doctrines themselves: setting aside what is fabulous, there yet remains sufficient to give the subject high interest as a most important feature in the history of the pure mathematics. In the Surya Siddhanta, notwithstanding the mass of fable and absurdity which it contains, there is a very rational system of trigonometry. This has been made the subject of a memoir by the late Professor Playfair, in the fourth volume of the Edinburgh Philosophical Transactions; and although it be evidently written with a belief of the truth of Bailly's visionary system deeply impressed on his mind, yet, leaving out of view the question of absolute antiquity, it will be read with all the interest which that elegant writer has never failed to excite, even when the reader is not disposed to agree with him in opinion. We have already noticed that the Indians divided the circumference of a circle into 360 equal parts, each of which was again subdivided into sixty, and so on. The same division was followed by the Greek mathematicians. This coincidence is remarkable, because it has no dependence on the nature of the circle, and is a matter purely conventional. It is probable both nations took the number 360 as the supposed number of days in a solar year, which might be the first approximation of the early astronomers to its true value. The Chinese divide the circle into 365 parts and onefourth, which can have no other origin than the sun's annual motion. The next thing to be mentioned is also a matter of arbitrary arrangement, but one in which the Bramins follow a mode peculiar to themselves. They express the radius of a circle in parts of the circumference. In this they are quite singular. Ptolemy and the Greek mathematicians supposed the radius to be divided into sixty equal parts, without seeking in this division to express any relation between the radius and the circumference. The Hindoo mathematicians have but one measure and one unit for both, viz. a minute of a degree, or one of those parts of which the circumference contains 21,600, and they reckon that the radius contains 3438. This is as great a degree of accuracy as can be obtained without taking in smaller divisions than minutes, or sixtieths of a degree. It is true to the nearest |