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ministration, according to Plowden, in Beresford's ridinghouse, Sandys's Prevot, the Old Custom-house, the Royal Exchange, some of the barracks, and other places in Dublin, there were daily, hourly, notorious exhibitions of these torturings.' | During his administration, Sir Judkin had his indemnity bill; and, if we mistake not, his title and his pension. We know of no specch or document in which, at that day, he reprobated the doctrine of his colleague. Yet even he now condemns torture ; and he does not tell us that this is a new opinion.

The enemy of torture in 1798, is a friend of Catholic emancipation now. He hated torture then, but he hated exclusion from office more. He is a friend to the Catholics, but he is more friendly to his Secretaryship. As he went into office with the defender of a practice which he condemned as wicked and unjustifiable, * so he stays in office with Lord Eldon, who says, that the measures proposed in favour of the Catholics,' go to the very vitals of the constitution of this Protestant country.' (Lords' Debates, May 12, 1817).

But though these fellow-ministers do not quarrel about this question, it is sufliciently important to merit all the attention of this nation. There is no time so fit for settling it as the present; and we have the words of all parties, of friends and enemies to emancipation, that until it be finally set at rest, the Empire will never be at peace. We have seen the present system--we know it by its fruits. Shall we pass the sentence of perpetual exclusion on a people growing in numbers and relative wealth, and wait till we are plunged into another war with such a drawback from our power, or till we have tried the fortune of another rebellion ? Even at this time, the Government of Ireland.deems it necessary to its security, to have a law by which persons absent from their homes in proclaimed districts, between sun-set and sun-rise, may be transported by a

| Plowden, Vol. II. p. 695. * We do not know whether Lord Castlereagh makes the same reservations as Sir R. Musgrave, who says, “ Many severe animadver*sions have been made on a practice which took place in Ireland a • short time previous to and during the rebellion, of whipping per• sons notoriously disaffected, for the purpose of extorting evidence

from them. Whoever considers it abstractedly, must of course • condemn it as obviously repugnant to the letter of the law, the be

nign principles of our constitution, and those of justice and humanity; • BUT I am convinced that such persons as dispassionately consider • the existing circumstances, &c. will readily admit them to be, if not

an excuse, at least an ample extenuation of that practice.' Vol. II! p. 478.

bench of magistrates, without jury trial. Are laws like this, and the discontents which give rise to them, the substantial blessings' which the people of Ireland are to enjoy for ever? --Shall we madly attempt to render permanent a system which, while it degrades and exasperates the many, is dangerous even to the few; which contains the principle of self-destruction in its cruel. ty,– invidiosum-imbecillum-detestabile--caducum ?'

Art. VII. Algebra, with Arithmetic and Mensuration, from the

Sanscrit of BRAHMEGUPTA and BHASCARA. Translated by Henry THOMAS COLEBROOKE, Esq. F. R. S. &c. London, Murray, Albemarle Street, 1817. A MONG .the fragments of Eastern science, with which the bd learning and zeal of our countrymen in India have enriched the literature of the West, none perhaps were ever more deserving of attention than those in the volume just announced, namely, four different treatises, in Sanscrit Verse, on the Arithmetic, Algebra and Geometry, of Hindostan. Two of these, the Lilavati and Vija Ganita, are the works of BHASCARA ACHARYA ; the first on Arithmetic, the second on Algebra. The other two books are still more antient, and were composed by a mathematician of the name of BRAHMEGUPTA. These, like most of the mathematical writings of the Hindus, make parts of systems of astronomy; the first two being the introduction to the Siddhanta Siromani of BHASCARA, and the other two forming the twelfth and eighteenth chapters of the BrahmaSiddhanta, an astronomical work by BRAHMEGUPTA.

Beside these original pieces, the volume contains a dissertation by the translator, fuil of learned and judicious research, on the early History of Algebra, so far as it can be traced in

I There were frequent allusions made in the debate on Me Brougham's motion, at the close of last Session, to a trial, in which Judkin Fitzgerald was a party, and defended himself in person, by avowing the practice of torture, and glorying in it : But we have not been able to procure a perusal of the report ; and the debate is not fully given in the Parliamentary Register. For the same reason, we have been prevented from referring to the various affidavits read by different members in that debate; and sworn to by men who had been tortured themselves, and had seen others tortured. One of these is said in the reports to have been first flogged, and then rubbed with gunpowder to make the wounds smart, and then flogged again before the excruciating torment of the rubbing had subsided.

India, Arabia and Greece. From the ample store of scientific and literary information which he appears to combine in a singular degree, he has also added some notes on a collateral subject, the introduction and progress of Algebra among the Italians; and if this digression be a departure from the rules of strict method, it is one for which, on account of the valuable information it affords, we feel very grateful to the author.

The time when BHASCARA wrote is fixed with great preci. sion, by his own testimony, and by corresponding circumstances, to a date that answers to about the year 1150 of the Christian era. The age of BRAHMEGUPTA is considerably more remote, and his works are extremely rare. The industry and zeal of the translator have, however, put him iu possession of a copy of them, in some respects imperfect, but in which the two chapters just quoted are fortunately complete. The age in which he lived, is fixed, with great probability, from a variety of concurring circumstances, and particularly from the position which he assigns, in his Astronomy, to the solstitial points, to the sixth, or the beginning of the seventh century of the Christian era, and antecedent, therefore, to the first dawn of the sciences in Arabia. At the same time, it is observed, that even BRAHMEGUPTA's treatise is not by any means the earliest work known to have been written in India on the subject of Algebra. GANESA, the most eminent of the scholiasts of BHASCARA, quotes a passage from ARYABHATTA on the subject of Algebra, containing the very relined artifice for the solution of indeterminate problems, which is known in Sanscrit by the name of Cuttaca. ARYA-BHATTA is indeed regarded by the Indians as the most antient uninspired writer on the science of Astronomy; and, by a variety of arguments, which Mr COLEBROOKE's intimate acquaintance with the literature and the history of that country has furnished, he makes it appear, that this algebraist wrote as far back as the fifth century of the Christian era, and perhaps in an earlier age. Hence it follows, that he is nearly as an.. tient as the Grecian algebraist DIOPHANTUS, supposed, on the authority of ABULFARAJ, to have flourished in the time of the Emperor JULIAN, or about the year 360 P. C. MR COLEBROOKE goes on to remark, that, admitting the Hindu and Alexandrian authors to be nearly equally antient, it must be conceded, in favour of the former, that he was the more advanced in the science, since he appears to have been in possession of the resolution of equations involving several unknown quantities, which it is not clear, nor fairly presumable, that DIOPHANTUS knew; and also of a general method of resolving

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indeterminate problems of at least the first degree, to the knowledge of which it is certain that the Greek algebraist had not attained.

Mr COLEBROOKE seems willing to stop here, without carrying back the origin of the Algebra of the Hindus to a more remote period. We must observe, however, that though no precise, or even traditionary knowledge, concerning that science, can be carried to a more remote age, it is impossible to doubt of its baving existed long before, and having passed by many steps to the condition it bad then attained. It is very generally acknowledged, that DIOPHANTUS cannot have been himself the inventor of all the rules and methods which he delivers. Much less is ARYABHATTA to be held the sole inventor of a system that was still more perfect than that of Diophantus. Indeed, before an author could think of embodying a treatise of Algebra in the heart of a system of Astronomy, and turning the researches of the one science to the purposes of the other, both must be in such a state of advancement, as the lapse of several ages, and many repeated efforts of invention, were required to produce.

The genuineness of the text from which these translations are made, is established with the greatest certainty by numerous commentaries in Sanscrit, besides a Persian version. These commentaries comprise a perpetual gloss, in which every passage of the original is noticed and interpreted. A careful collation of several of them, with three copies of tbe original work, has been made by the learned translator: The differences are mentioned in the notes, and appear to be of little importance. The series of commentators or scholiasts who have illustrated these four works by their annotations, goes back to a considerable distance, and comes down to a period much later than the common opinions or prejudices concerning Hindu literature would incline us to believe. Mr COLEBROOKE tells us, that the oldest commentary of an ascertained date that has come into his hands, appears, from an astronomical computation which it contains, to have been written about the year 1420 of our era. The next to this, in antiquity and importance, is dated in 1460, 1463 Saca ; that is, A. D, 1538, 1541. GaNESA, a distinguished astronomer, is the author of a commentary on the Siddhanta Siromani, of which the Lilavati is a part; and his work bears a date that corresponds to A. D. 1545. It comprises a copious exposition of the text, with demonstrations of the rules, and has been used, Mr COLEBROOKE tells us, throughout the translation, as the best interpreter of the original. A commentary on the Vija Ganita, bearing the date of 1602, contaiņs a full exposition of the sense, with complete demonstrations

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