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fome choice; and, if they are wife—if they liften to their own beft interefts, and are refolved not to raife up another conqueror, they will be fatisfied with leaving things as they fhall then find them, and allowing each of the new ftates which may at that time be in cxiftence under the r;rote&ion of France, to retain its rank and independence, as if it had from the beginning formed parts of the European commonwealth,—fatisfied with the termination of its dependence upon the parent ftate. The counfels which England will at that juncture be ready to give, againft her own beft interefts and thole of her allies, will be hftened to or rejected, in proportion as the vcfults of her paft operations (hall have failed or fucceeded in teaching the Continent wifdom.

Art. XII. On the Hindbo Systems of Astronomy, and their Con- nexion with History in Ancient and Modern Times. By J. Bentley, Esq. From the 8th Volume of the Asiatic Researches. Calcutta, 1805.

Of the new objects which India has offered to the curiofity of the Weftern world, none have appeared more worthy of attention than the remains of aftronomical fcience. Thefe fragments,—preferved in a country where the means of acquiring fuch knowledge is no longer to be found; the peculiarity, and at the fame time the accuracy of the methods they employ; the mixture of fable and extravagance introduced even in- the rules of trigonometrical calculation, form altogether an enigma which the antiquary and the philofopher muft be equally defirous to refolve. The philofopher, indeed, will be much interefted in the inquiry,by confidering that the darknefs which covers the hiftory and the chronology of the Eaft, is likely to be difpelled, at leai'l in fome' quarters, by the light which may be ftruck out from the analyfis of thefe extraordinary fragments, Aftronomy, more than any other portion of human knowledge, is capable of having its hiftory traced by reafoning from principles, when other documents are wanting. As the object of that fcience is fo far immutable, that it always prefents either the fame face, or a face that varies according to fixed laws; it is evident, that when we know the aftronomical fyftem of any nation, we muft be enabled to judge with fome accuracy of its ftate of refinement, and of general information. We are acquainted with the original; and therefore, from knowing the copy, we can guefs with tolerable exactnefs at the lkill of the painter. Befidcs, it often happens, that there is in the picture certain data from which its age may be deduced;

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the time required to the compofition of the work may be afcertained; and even the place on the earth's furface where the obfervations were made, may be difcovered in the fyftem to which they have given rife.

The aftronomy of the Orientals, therefore, could not fail to excite the curiofity of men of fcience in Europe, as foon as it became known to them. The firft intelligence of it was received by means of M. La Loubere, the ambaffador of Lewis XIV. to the King of Siam, who brought with him from that country a manufcript containing tables and rules for calculating the places of the fun and moon. This fragment, though obfcure and imperfect, was explained by the celebrated Dominic Caffini, into whofe hands it was put, and who bore teftimony both to its accuracy, and to its great diffimilitude to any of the fyftems of aftronomy that had previoufly been heard of in Europe. After that time, two other fets of aftronomical tables were fent to Paris by the. French miffionaries in Hindoftan; but they feem to have lain unnoticed in the royal library till the return of Mr Le Gentil from India, where he had been to obferve the tranfit of Venus in 1769. This aftronomer returned poffeffed of another fet of tables, and inftrudted by a learned Brahmen in the Indian methods of calculation. M. Bailly, proceeding on these data, dedicated an entire volume to the elucidation of the Indian aftronomy.

On the inftitution of the Asiatic Society, the aftronomy of the Eaft naturally became an object of attention. Several papers illuftrating different parts of the monuments of that fcience, have appeared in the Aftatic Refearches, particularly a paper by Mr Davis, and two others by Mr Bentley, one in the fixth, and another (the particular object of this review) in the 8th volume of the fame work.

The notion concerning the antiquity of the Indian aftronomy which M. Bailly endeavoured to eftablifh, was, that it reached back to a very remote period, earlier than any other of the records of profane hiftory, and upwards of 3000 years before the Chriftian era. This opinion was very prevalent among the learned in Europe, when Mr Bentley published the firft of the papers above referred to, where he endeavoured to fhow, that the argument of M. Bailly was ill founded, and proceeded on an entire ignorance of the principles of the Indian aftronomy. The paper before us is directed to the fame object, and contains alfo fome ftri£tures on an article in our review, where fome of the arguments contained in the former paper were fliown, as we imagined, to be inconclufive. .

Our intention, at prefent, is to confider the antiquity of the Indian tables, purely as an aftronomical queftion, and without

reference reference to any other matter in the hiftory or mythology of Hindoftan. It is the nature of aftronomical tables, as has already been remarked, to involve in themfelves evidence by which their antiquity may generally be afcertained, at leaft within certain limits. This fort of internal evidence, is the firft thing to be confidered, and is evidently a fubject which ought to be difcuffed as much as poffible on its own merits, and without the introduction of extraneous circumftances. *

With this view, we fhall now take the liberty of examining Mr Bciitley's papers, on principles purely aftronomical. We fhall endeavour to point out what we conceive to be the fallacy of the aftronomical argument contained in them; to fhow, that whatever be the age of the books in which the aftronomy of India is now contained, the aftronomy itlelf is probably of an antiquity not inferior to what has juft been mentioned; but that, neverthelefs, we fliould abftain from any abfolute conclufion on either fide, till the whole of the evidence is laid before the public.

In the fixth volume of the Afiatic Refearches, Mr Bentley treats of the antiquity of the SuRya Siddhsnta, a work that profefles to have been received by divine revelation about 2,i64,899 years ago. The extravagance of this pretenfion requires no refutation; but Mr Bentley endeavours to fhow, that the age of it docs not exceed a few hundred years. We do not however propofe, at this time, to enter into the cjueftion of the age of the Surya Siddhanta, or of any other book, but into that of the aftronomy contained in thofe books; taking our information from the fcience itfelf, and confining our attention, as Mr Bentley has alfo done, to the mean motions of the heavenly bodies as laid down in the Indian tables.

Mr Bentley fays, Afiatic Refearches, vol. vi. p. 537.

'Mjufieur Biiilly, in the year i787, puhlifhed al Pari", a whole quarto volume on the fubjeft of the Indian aftronomy; and Mr Playfair, in the year i 7H9, publifhtd a paper on the fame fuhjcct in the Edinburgh Trantactions. The principles, hbwever, of the Hindoo fyfterri.s of aftronomy, being unknown to thefe gentlemen, and differing widely in many refpefts from that of the European.., the coiiclufions drawn by them refpttting the antiquity of the feveral aftronomical tables mentioned by i\l. Bailly, appear now to be altogether unfounded. Indeed, the materials Which M. Bailly had collected, were infufficient! to enable him to form a juft idea of the principles of the Hindoo fyftems;' which being mollly artificial, his method of invelligation (from, the quantity of the mean annual motions, Sic. of the planet!, though otherwife perfectly juft), became altogether inapplicable; fo niuch fo, that the ta;blts.of Trivalore,' which he had fuppofed were as old as the commencement of the prefent Cali-yug, at leaft, were actually written

Vol. x. No. 20. G g and and dated about the year 4383 of the Cali-yug. or yi6 years ago; and the mean annual mot'ons «f the planets given in that work, were, on the principles of thr Hindoo ajlronomy, calculated to give the portions of the planets in the heavens, at that time, as near, at lead, as the author could determine by obfervarion. However, in order to do away thefe deluflons, 1 fhall, before i proceed to the inveftigation of the antiquity of the Surya Siddhanta, explain, in as fimple a manner as poffible, the principles upon which the Hindoo fyftems are founded, and the manner in which they are formed.'

The charge here brought againil M. Bailly is, without doubt, a vf.ry heavy one, and affecls his character deeply as an aftronomer and a man of fcienoe. To have had a fet of aftronomical fables put into his hands, and not to have been able to difcover their principles, or the fuppofitions on which they were calculated, might:indeed involve no reproach at all. Their form might be fo enigmatical, they might be fo imperfect, and of fo little extent, as not to afford data for the required determination. But if fuch were the cafe, the aftronomer muft at leaft be fenfible of thefe defeats. He muft know whether he underftood the matter before him or not. This is what a man, not to fay of fcience, but of common fenfe, could not but perceive; and if M. Bailly has really written a quarto volume on a fubject. which he did not underftand,—if he has treated of it at fo much length, and deduced from it fo many confequences, it will be very difficult to reconcile his conduct with the ability and modefty by which he is ufually thought to have been diftinguifhed. We fhall beg leave to confider, therefore, how far this charge is well founded, and whether thofe refults which Mr Bentley intends to do away, are really the delufions which he fuppofes them to be.

The mean motion of any of the planets, or the angle which, at a medium, it defcribes in a given portion of time, is deduced from two determinations of its place, feparated by a confiderable interval of time from one another. The more accurate the obfervations, and the greater the length of time between them, the more exact will be the mean motion derived from this comparifon. The length of the interval, even if the obfervations are not very exact, may fo far compenfate their inaccuracy, as to give great precifion to the refult. If, for example, we were to determine the length of the folar year, and if the obfervations compared were made at the interval of 2000 years, then, though the error in thefe obfervations Ihould amount to fix hours, or a quarter of a day, the determination of the length of the year would nevertheLefs be exact to the 2ooodth part of fix hours, or to ten feconds nearly. It is thus that time adds

to to the accuracy of aftronomical determinations, and is capable of doing fo indefinitely; on which account, fuch determinations might continually approximate to the truth, in as much at leaft as regards the mean motions, even were no improvement to take place in the inftruments or methods of obfervation. The im-. provements in thefe laft have no other effect than to render the approximation more rapid.

It is chiefly to this effect of time, in giving a value to obfervations, that we are to afcribe the progreffive accuracy m the tables of the planetary motions. Thus, Ptolemy was enabled to give thofe motions more accurately than Hipparchus; the Arabs more accurately than Ptolemy; Tycho than the Arabs; and the modern aftronomers much more exactly than any of their predeceffors. With regard to the latter, it is true that great improvements in aftronomical inftruments have taken place; but, even independently of the fuperior accuracy derived from this fource, the mere lapfe of time would have produced a near approach to the fame refults.

This is the natural progrefs of aftronomical improvement, and is the infeparable concomitant of the antiquity of fcience. In the Indian aftronomy, there appears to he a contrivance calculated fomewhat to retard and derange this natural progrefs; and it is on this contrivance, and the effect of it, that Mr Bentley lays fo much ftrefs, in the account of what he calls the artificial systems of the Indian aftronomy.

The contrivance referred to is thisThe Indian aftronomers, having firft determined the mean motion of the fun or any of the1 planets, from two or more obfervations made and compared as iuppofcd above, have from thence gone back by calculation to fome fictitious epocha connected with their mythological fyitem, which, in all their future calculations, they choofe to affume as an obfervation actually made, and as the ftandurd with which other obfervations are afterwards to be compared. The effect of this fiction muft be, to prevent the knowledge of the mean motions from improving and becoming more perfe£t in the progrefg -of time, in fo confiderable a degree as it has done in the agronomy which has dcfcended from the Greeks, through the Arabs, ro the nations of modern Europe.

This retardation of improvement, and the continuance of the science nearly yj the same state for a succession of ages, are the only possible effects that could result from the practice here re* ferred to. This may be made evident by a very sample instance. Suppose that the motion of the sun were reckoned at J60° in '365 days 6 hours, as in the Julian calendar, and that the instant in a cer

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