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borrowed their science from any other nation? In answer to the first of these questions, Mr. Bentley has published two very interesting memoirs in the sixth and eighth volumes of the Asiatic Researches. In these, his endeavour is to show, as well from internal evidence as positive historical testimony, that the age of the Surya Siddhanta may be referred to somewhere about 1000 years after the Christian era. This he concludes, from the very reasonable supposition, that whatever be the real date of the tables in question, the errors on the places of the sun, moon, and planets for that time, (as deduced from the tables,) will be less than for any other; as we cannot but imagine that any astronomer, whatever mistakes he might make in giving the positions of the heavenly bodies, for past or future times, would wish to represent faithfully the state of the heavens which he himself observed. Mr. Bentley proceeds then to find when the errors we have above-mentioned are the least in the Surya Siddhanta; and this he shows pretty clearly to have been the case about ten centuries after Christ. If we exclude from our consideration the place of Mercury, the positions of the lunar apogee and nodes, the solar apogee, and the aphelion of Mars, as being imaginary points, and therefore more difficult to be fixed in an imperfect state of astronomy; and if we deduce the age of the Surya Siddhanta from the positions of the Moon, Venus,

Mars, Jupiter, and Saturn, we shall find for this date respectively, the years A. D. 1040, 940, 1460, 924, and 994 . Taking the mean of these five, we get A.D. 1071; if we leave out Mars, we obtain A.D. 977. From the whole of the data to be found in the Surya Siddhanta, Mr. Bentley finds A.D. 1036. The general accordance of these results seems sufficiently satisfactory .

However, the Surya Siddhanta is not the oldest system of astronomy to be found among the Indians. Mr. Bentley has examined the tables of BrahmaGupta; and, by an analysis exactly similar to that just described, has been led to fix their age about the year 536 A.D. Indeed, it appears that BrahmaGupta was preceded by other astronomers, and particularly by one named Aryabhatta, deserving of notice here, as having advocated the doctrine of the earth's diurnal revolution on its axis. This opinion, it seems, was rejected by subsequent philosophers among the Hindoos, which will scarcely excite our surprise, when we consider that it shared the same fate in the west. Having been embraced by Philolaus, Anaximander, and Aristarchus, it was controverted by Ptolemy, and had fallen into complete oblivion, when revived by the immortal Copernicus. These doctrines of Aryabhatta render it a very interesting point to determine his age, that we may ascertain whether he borrowed this philosophical idea from the sages of Greece, or whether

Table of the Errors in the Surya Siddhanta with respect to the places of the Planets, &c., at the undermentioned periods.

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However, the historical part of Mr. Bentley's argument seems open to objections, which have been urged by Mr. Colebrooke in the 12th volume of the Asiatic Researches. Mr. Bentley affirms, that an astronomer named Varaha-mihira was the author of the Surya Siddhanta, and that he is known to have lived somewhere about 1000 A.D. But it appears that it is by no means proved that Varaha was the anthor of the Surya Siddhanta; indeed, it is quoted by himself in a way which seems clearly to show that it was not his composition (a.) And another difficulty arises here, for Mr. Bentley, by reasoning entirely analogous to that just explained with regard to the Surya Siddhanta, is led to the conclusion that an ancient system of astronomy, composed by an author called Brahma-Gupta, may be referred to the year 536 A.D. (b) Now, Brahma-Gupta, in a work of acknowledged authenticity, quotes by name Varaha (c.) which circumstance corroborates the inference that Varaha could not have been the author of the Surya Siddhanta.

Asiatic Researches, vol. vi. p. 581. This date agrees pretty well with that attributed to BrahmaGupta by the Hindoos themselves.-V. Asiat. Res., vol. xii. Addit. Ib. vol. xii. p. 227.

(a) Asiatic Researches, vol, xil. p. 221. Calcutta. (b) Ib. vol. vi, p. 581, (c) Ib. vol. xii. p. 221.

Pythagoras, who was undoubtedly well the tropics, the difference between the

versed in the learning of the east, borrowed it himself from the Indians. But at present we have not sufficient data to decide this question, which is worthy of all the attention of Sanserit scholars *. The age of the tables of Brahma-Gupta, as fixed by Mr. Bentley, decides one question, by showing that the Indian astronomy was not originally borrowed from the Arabs. The tables in question were composed about 500 years after Christ. We shall see that the Arabs did not begin to cultivate astronomy till a century or two later. It is much more difficult to ascertain whether the Indians were indebted to the Greeks for any of their principal determinations; and, on this point, different opinions seem to be entertained by those who are best qualified to judge in such matters. Mr. Davis, and Delambre, think the Hindoo methods of calculation essentially different from the Grecian; and this circumstance has been much insisted upon by Playfair. The limits of this treatise will not allow us to go into a detailed examination of these methods; we must be contented with selecting some of the most striking instances of originality.

One of these is the method given in the tables of Chrisnabouram, to find the time of the sun's continuance above the horizon, or what we call the diurnal arc, for any given day. On the day of the equinox, observe the length of the shadow of the gnomon, which is to be divided into parts, each equal to ‚th of the length of the gnomon; one-third of this measure is the number of minutes by which the day at the end of the first month after the equinox exceeds twelve hours: four-fifths of this excess is the increase of the day during the second month; and one-third of it the increase of the day during the third month. This rule involves the supposition, that

supposition of the Brahmins and the exact formula will be so inconsiderable as to be safely neglected. In higher latitudes, this difference will increase pretty rapidly, and soon becomes a very appreciable quantity*. It is then pretty clear that this rule of the Brahmins must have had its origin in a tropical country, and in all probability in the Indian peninsula in which it is found. The Indian methods for the calculation of eclipses which have been explained at length by Le Gentilt, and Mr. Davis, are extremely curious, and bear certainly the appearance of originality. But for these we must refer to the author just mentioned; we shall only remark, in passing, that these methods show a knowledge of the celebrated property of the right-angled triangle, which tradition informs us that Pythagoras (who, it may be remarked, had travelled much in the east) first made known in Greece. The Indians demonstrate this propositions in a very singular way, which partakes more of the nature of algebraic reasoning than of pure geometry. Indeed, they seem to have been singularly attached to the study of algebra, in which they made great progress; and of which they were, very probably, the

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the sun's declination being given, the in Indian minutes of time, and neglecting all the

ratio between the ascensional difference,

terms after the first.

(that is, the arc measuring the increase of the day at any place,) and the tan

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gent of the latitude, is constant. Now The Indian rule is 2 x = 720.
this is not rigorously true, for the con-
stant ratio in question exists between the


or a 256.


sine of the ascensional difference and the v. Bailly, p. 32; and Edin. Trans. vol. ii., p. 172. tangent of the latitude. But between

The length of the sidereal year, as fixed by Aryabhatta, is 365 days 6 hours 12 minutes and 30 seconds.-Asiat. Res., vol. xii. p. 249. This is the quantity adopted in most of the Indian tables. Some of them, however, make it 36, instead of 30 seconds.

Astron. Ancienne, vol, i. p. 478.

Mem. Acad. des Sciences for 1772, Part II.

p. 221.

Asiat. Research., vol. ii. p. 273. Delamb., Ast. Anc., vol. i. p. 471.

The 47th, 1st Book of Euclid's Elements. I The Hindoos have been particularly successful in their methods for the solution of indeterminate problems; in this respect they have not been equalled in Europe till the latter half of the 18th. century.


Their methods for calculating the ascensional differences prove that they were in possession of the principal theorems of spherical trigonometry; their tables of sines, which are given for every 3 throughout the quadrant, may be regarded as a mathematical curiosity.

On the other hand, the system on which the Indians calculate the inequalities of the sun, moon, and planets, presents some remarkable coincidences with that imagined by the Greeks for the same purpose. On reference to a subsequent part of this treatise, it will be seen, that Hipparchus explained the principal inequality of the sun, and of the moon, by supposing each of these planets to revolve round the earth in a circle, the centre of which was at some distance from this last body; and thus the motion, though really uniform round the centre, appeared unequal as seen from the earth. Hipparchus also proposed another theory, which leads to the same results as that just mentioned; he supposed the sun or moon to revolve in a small circle, called the epicycle, the centre of which revolved uniformly round the earth; and he proved the virtual identity of the two hypotheses. It is remarkable enough that both these sys tems are made use of by the Indian astronomers; and it is equally remarkable that they appear to be ignorant of the modifications of these theories, which Ptolemy was obliged to make in the case of the moon and the planet Mercury. They have indeed felt the necessity of some modifications in these cases, but theirs consist in giving an oval form as well to the eccentric as to the planet's epicycle. The method of Ptolemy, which is very different, will be explained when we come to speak of the astronomers of Alexandria.

Sir W. Jones has affirmed that it is very improbable the Indians should have borrowed anything from the Greeks, as the pride of the Brahmins leads them to

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despise foreign nations in general, and the Greeks in particular. They have a proverb, says he, that no base creature can be lower than a Yavan; which term he explains to mean an Ionian or Greek*. But Mr. Colebrooke has quoted a very curious passage from Varahamihira, one of the earliest astronomers of India, who speaks with applause of the proficiency of the Yavans in astronomy. "The Yavans," says he, 66 are barbarians; but this science is well established among them, and they are revered like holy sages." About the age of Varaha-mihira there seems to be some uncertainty, Mr. Bentley fixing it at about 1000 B.C.: while others make him more than five hundred years older; but whenever we suppose him to have lived, this acknowledgment of an acquaintance with the science of the West goes far to confirm the ideas of those who consider the Hindoo astronomy as derived from the Greek.


The Chaldeans.

IF we may credit Porphyry, quoted by Simplicius §, Callisthenes transmitted to Aristotle a series of observations made at (Babylon during a period of 1903 years preceding the capture of that city by Alexander. This would carry back the origin of astronomy in Chaldæa to at least 2234 years before the birth of Christ. It is certainly an argument of some strength against the correctness of this statement, that Ptolemy, who has founded his theory of the moon partly upon Chaldæan observations, quotes none anterior to the year 720 B.C.; but this fact is not perhaps so decisive as it at first appears. It is impossible now to say whether or not Ptolemy had access to the whole of the observations in question; whether any had been lost in the interval-not an inconsiderable one-between himself and Callisthenes; or lastly, whether the superior accuracy of the more modern observations made him prefer them ||. The eclipses recorded by Ptolemy are

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given in a rough way, yet they are of singular interest, as with them begins, at least for the western nations, the long train of observation and discovery that has brought the science to its present perfection.

A striking proof of the acquirements of the Chaldæans is to be found in their knowledge of the period of 65854 days, in which the moon makes 223 revolutions with regard to the sun, 239 with regard to the apsides of her orbit, and 241 with regard to her nodes. This is attributed to them by Geminus: Ptolemy § refers it simply to the "ancient mathematicians.' The accuracy of this period is very great, and its utility no less in calculating the recurrence of eclipses. Indeed, there can be little doubt that it was by means of this period, or one very analogous to it, that they were able to predict these phenomena in the case of the moon; for, according to Diodorus Siculus ||, they did not attempt such predictions for eclipses of the sun. This is natural enough; it is sufficiently obvious to those who have any acquaintance with the science, that the calculation of the former is far more easy, the parallax not entering into it. The author just quoted also tells us that they attached great importance to the theory of the planets, which bodies they observed with care, and more par ticularly Saturn. In fact we find in Ptolemy several such observations. Their zodiac was divided into twelve signs**: the extra-zodiacal constellations were twenty-four in number, twelve in each hemisphere. To this we may add from Herodotus +, that to them we owe the duodecimal division of the day. This historian attributes, at the same time,

V. Syntax., lib. iv. c. 5. The time is not given more nearly than within an hour-the quantity of the disk eclipsed is expressed in digits.

Ptolemy (Syntax. xiii. 7.), speaking of astronomical observations, informs us, that the most numerous and best have been made in Chaldæa. To this we may add a curious passage of Cleomedes, it. 6, who says, speaking of the moon being seen eclipsed, while the sun was above the horizon, that "so many eclipses of the moon having been observed and recorded, no astronomer, whether

Chaldæan or Egyptian, has ever recorded one of

this kind."

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to them the invention of the gnomon, and an instrument called polus. The former, we have already seen, was used in China from the earliest antiquity; of the last we have a very imperfect knowledge; it seems to have been destined to indicate the changes in the sun's meridian altitude towards the solstices. The divisions of time were measured by clepsydræ.

Seneca informs us that Epigenes and Apollonius Myndius, both of whom professed to have studied under the Chaldæans, ascribed to them very different opinions on the subject of comets. According to the former they were ignorant of their nature and course; while the latter, who is called by Seneca a most scientific observer of natural phenomena, states, that they classed them with the planets, and were able to determine their motions. It is certain that very philosophical ideas were entertained on the subject of comets by the Pythagoreans, who had evidently borrowed many of their doctrines from the East. Could we admit the statement of Apollonius, few things would tend more to give us a high idea of the Chaldæan astronomy.


The Egyptians.

THE Egyptians seem to have enjoyed in ancient times considerable reputation for astronomical science. It is, however, certain, that few, if any, relies of it have descended to us. It has been remarked, that the exactitude with which the Pyramids have been made to face the four cardinal points, gives us an advantageous idea of their methods of observation. However, Ptolemy and Hipparchus, who it is natural to suppose would have had access while living in the country to the Egyptian records, never quote any ancient observation made by astronomers of that nation; but, on the contrary, were forced to have recourse to the Chaldæans. the other hand, there is some respectable testimony to prove that the Egyptians were in the habit of observing celestial phenomena in general, and eclipses in particular. Diodorus Siculus + goes so far as to say, that they were able to calculate beforehand the circumstances of these latter with much exactness. Di. ogenes Laertius mentions 373 solar,

Quæst. Nat., lib. vii. c. 3. + Lib. i. § 2. In proœmio.


and 832 lunar, eclipses observed in Egypt. The testimony of this author is in itself of no great weight, and he adds the absurd circumstance, that they had been seen in an interval of 48863 years. But it is very singular that this is the proportion of the solar to the lunar eclipses visible above a given horizon within a certain time*; and such a coincidence certainly cannot be accidental. Seneca likewise informs us, that Conon, the contemporary of Archimedes, had collected all the eclipses of the sun preserved in Egypt. Lastly, we may remark, that Aristotle mentions the Babylonians and Egyptians as having recorded a great number of credible observations. To all this is to be opposed the silence of Ptolemy, and upon this point we must refer to the remarks already made when treating of the Chaldæan astronomy.

The civil year of the Egyptians was of 365 days, but they were very early acquainted with the more accurate value, 365 days. This appears from the Sothiac period of 1461 years, which brought round to the same seasons their months and festivals. For this people, among their numerous singularities, had that of not wishing to connect the civil invariably with the physical year, but to suffer it to anticipate gradually, displacing thereby all the times fixed for their religious ceremonies, till at the end of the great Sothiac period they coincided once more with their original positions. One of these periods, according to Censorinus §, began in the consulship of Antoninus and Bruttius, A.D. 139, That this was not the first period of the kind, there can be little doubt. The preceding one must have commenced, then, in the year 1322 B.C. Bailly even, relying upon some expressions of Manetho, thinks that this was preceded by another. But, as far as the tropical year is concerned, it is necessary to observe, that the Sothiac period could not have been deduced from an actual observation of the time required for a complete restitution, for the time observed would not have been 1461 years, but 1506. It has, however,

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been supposed that the Egyptians had a rural year, comprising the intervals between two heliacal risings of Sirius, and that the Sothiac period must be considered as applying to this rural, and not to the tropical year. And here we meet with a very curious coincidence ; for this rural year, as thus determined, had, for twenty or thirty centuries before the Christian era, very exactly the length of 365 days; and, consequently, the period of restitution of 1461 years would apply to it very accurately. A recent author has disputed the fact, that such a rural year was in use among the Egyptians, before the time of Hip. parchus: however, the authorities urged in its favour seem pretty satisfactory; and the coincidence above mentioned tends strongly to corroborate them. Thus it appears that the Sothiac or Canicular period had its origin when the first day of the month, Thoth, coincided with the heliacal rising of Sirius. According to Censorinus, this happened the 20th of July, A.D. 139. M. Ideler has found by calculation, that on the very same day of July, Sirius rose heliacally in the Julian years 1322 and 2782 B.C.

According to Dio Cassius, the Egyptians were the inventors of the short period of seven days, distinguished by the names of the planets, which we call week. This period, used among all the eastern nations from time immemorial, has been called, by an eminent philosopher, the most ancient monument of astronomical knowledge. It is found even among the Brahmins of India with the same denominations, and the days similarly named by them and by us correspond to the same physical portions of time. The arrangement is founded upon the ancient systems of astronomy, in which the planets were placed in the following order, beginning with the most distant from the earth; Saturn, Jupiter, Mars, the Sun, Venus, Mercury, and the Moon. The day being divided into twenty-four hours, the hours were consecrated to the planets in the order just given; and each day took its name from the hour with which it began. Thus, the first hour of the first day being dedicated to Saturn, the second would be so to Jupiter, the third to Mars, and so on; then the eighth again to Saturn, the fifteenth, and the twenty-second, so that the first hour of

Biot, Essai sur la Période Caniculaire. + Lib. xxxvii. c. 18.

La Place, Syst. du Monde, lib. v. c. 1.

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