One of the great uses of artificial education would be, to spread the knowledge of the English tongue. The men the best acquainted with Ireland, Mr Grattan, Mr Wakefield, and others, concur in observing, that a deeper shade of barbarity accompanies, throughout Ireland, a total unacquaintance with the language of a civilized people. Even this circumstance, however, derives its malignity from the pestilent habits of Ireland in general. Diversity of language is, no doubt, an unhappy circumstance. But in the Highlands of Scotland, and in Wales, it has not given occasion to such complaints.

When one hears of schemes for the instruction of the Irish, and considers, that in many parishes of Ireland not a man understands English, and in a great proportion of parishes, very few, and that there is scarcely one of the clergymen of the Established Protestant Church, who knows any thing of the Irish language-and probably not one who ever preached or prayed in it, it is impossible not to be struck with the pains which that Church has bestowed upon the religious instruction of that people. The Church of Scotland, however, provided somewhat differently for the instruction of her Celtic flocks. No minister can be ordained to a parish in the Highlands, who cannot speak the language of the natives, and who is not bound to perform divine service in it once every Sunday. The bible is translated into that language, and the children are taught to read it in their schools. This is true pastoral care. In a letter from the Bishop of Limerick to Mr Wakefield, which he has published in his recent work, that prelate says, he had found parishes in his diocese which had never even seen a Protestant minister.' Yet there would the tythe be collected--and naturally with more severity, than when the clergyman resided, and could not withdraw his any hardships which severity might produce. The grand concluding remark is,-that improvement is the natural tendency of human beings themselves. All that legislators have to do, is to remove obstructions: and it is melancholy to think, that, owing to obstructions which may be removed, mankind are, in so many situations, stationary in wretchedness.

eye from

ART. VI. BIJA GANNITA, or the Algebra of the Hindus. By EDWARD STRACHEY, of the East-India Company's Bengal Civil Establishment. London, 1813.

THE

HE mere name of a work on Algebra, translated from the
Sanscrit, is sufficient to excite the most lively interest in

all who take any concern in the history of human knowledge. The Bijă Gănnită is understood in India to be the work of BHASKARA ACHARYA, a Hindu mathematician and astronomer, who lived about the end of the 12th century of the Christian era; and who, beside this book on Algebra, has left behind him other mathematical treatises, particularly the Lilavati, on Arithmetic and practical Geometry. From a work which he composed on Astronomical Calculation, which has also been preserved, it appears, that Bhascara wrote about the year 1105 of the astronomical era of Salibahn. This era began in the 83d of the Christian era; so that the preceding date answers to the year of Christ 1188. Col. Colebrooke (Asiat. R. vol. 9.) has given the time of his birth (1063 Saca), or 1141 after Christ.

These books, written originally in Sanscrit, had the highest reputation in the East, and were translated into different languages. The Lilavati was translated by the order of the Emperor Akbar into Persian, on account, as FYZEE, the translator, says, of the rare and wonderful arts of calculation and mensuration which it contained. The Bija Gannita was also translated into Persian in the year 1634; and it is from the Persian that Mr Strachey has made the English translation, with which he has now favoured the public. The idea thus given of the original work, is certainly less perfect than if the translation had been made from the Sanscrit; but, in a matter where authentic information is so difficult to be obtained, we must be satisfied with what can be procured, though it may not be in all respects what we would wish. Mr STRACHEY appears to have great merit in the double capacity of a translator and commentator; and it adds not a little to the value of his communication, that it is accompanied with notes by Mr. DAVIS, who is known to be deeply versed in Oriental science, from his papers on the Indian Astronomy. That gentleman, who is master of the Sanscrit, had been fortunate enough to procure a copy of the Bija Gannita in the original, out of which he made several extracts, and has added to them some notes and illustrations. Though these notes are evidently written only for the author's own use, they convey a great deal of information, and assist in distinguishing the original Hindu composition from the interpolations of the Persian translator.

Mr Strachey had also the use of a translation of the Bija Gannita from the Persian, by the late Mr REUBEN BURROW, which is now in the possession of Mr DALBY, of the Military School at High Wicombe: this, however, is less valuable than might have been expected from one so well acquainted with

the mathematical sciences. It is a fair copy of the Persian translation, with the English of each word written above the Persian, and, as it now stands, is not, it may be supposed, very easily understood.

It appears from Mr Davis's notes, that the references to Euclid's Elements, of which there are some in the Persian translation, are mere interpolations, not to be found in the original. It appears also, that the Hindu mathematicians have a particu lar notation, which is entirely wanting in the Persian, where the algebraic process is always expressed in words. These are the sources of the information now communicated to the public, and the conclusions to which they lead, cannot but form a very interesting article in the history of Oriental science.

The work of the Hindu algebraist consists of an Introduction and five Books: The Introduction contains the rules for the algebraic computations, addition, subtraction, &c. applied first to known, then to unknown quantities, and to surds. There are, besides this, still making a part of the Introduction, two chapters on Indeterminate Problems of the first and second degree. Of the five Books that follow, the first treats of Simple Equations; the second of Quadratic; the third on Indeterminate Problems of the first Degree; the fourth of those of the second Degree; the fifth of Products. :

The work is said to have been written with a view to astronomy. A passage is quoted by Mr Davis, where Bhascara says, it would be as absurd for a person ignorant of algebra to write upon astronomy, as for one ignorant of grammar to write poetry.

Bliascara himself does not assume any character but that of a compiler, who was composing an elementary treatise from materials that already existed.

Though we are highly gratified by any thing that throws light on the ancient science of the East, and think ourselves much indebted to Mr STRACHEY for. what he has done toward the elucidation of a subject so curious and interesting, we feel it necessary to remark, that the manner in which this translation and commentary are given, is not the most happily conceived. The work consists partly of a literal translation, partly of an abstract, and partly of the translator's own remarks. These are not always sufficiently distinguished, and never in the marked manner which was necessary. The literal translation is marked by inverted commas; the part, Mr Strachey says, that consists of his own remarks, will appear by the context and all the rest is abstract. It is plain, that this last dis tinction is not sufficiently precise; and that the first, though

tolerably clear, is not marked with the force which the difference requires. Indeed, the error in this respect begins from the title page: The BIJA GANNITA, &c.-By Edward Strachey. A title could not be better contrived for repressing, by its conclusion, the curiosity excited by its commencement; and a modern name following, in the place of the author's, after a title that is ancient, and was meant to be considered as such, is a solecism which we know not how any editor could commit. Perhaps Mr Strachey found it difficult to express his triple character of translator, abstracter, and commentator, with the conciseness required in a title page. The work might have been called, The BIJA GANNITA, &c. abridged; with Extracts and Notes by, &c. This would not, perhaps, have formed an elegant title page; but it would have been a tolerably exact description of the book.

In the account we are to give, we shall begin with what relates to the Notation of the Hindu Algebra; next the Rules, and, lastly, the Problems, to the solution of which the rules are applied. This exposition will naturally lead to the question concerning the antiquity and originality of the Hindu Algebra. In this notation, letters are used to denote quantities in the same manner as with us. The addition of quantities is denoted by placed between them; thus ab, is a + b. They have also a mark for negative quantities, which consists of a point over the letter: a is a, and a || b || x, is a + b. r. The relation between positive and negative quantities, is illustrated by a reference to possession and debt, the same as with us; and it must naturally be so, whenever the operations of a calculus in which the magnitude of the quantities is not expressed by the symbols denoting them, forces on the computer the convenient fiction of a quantity possessing the power of destroying other quantities.

The product of quantities into one another, is expressed by writing the letters close to one another, ab, abc, being the products of a into b; and of a into b and into c. When there is a numeral coefficient, it is written, not before the letters as with us, but after them; thus it is not Sab, but ab3. The Hindus, who write from left to right as we do, and the Persians, who write in the opposite direction, appear to give the same position to the coefficients. A surd is called carni; in the Per sian translation, this word follows the number that it relates to, thus: 5 carni, signifies the square root of 5. Whether, in the Sanscrit, there be any sign equivalent to our radical sign, does not appear.

Letters are used to denote the quantities both known and un

known. When there is but one unknown quantity, it is denominated the thing. It is remarkable, that at the introduction of algebra into Europe, this was the language employed. In Italian, the first of the western languages in which algebraic treatises were composed, the unknown quantity was called cosa; whence, as Dr H. remarks, algebra was called the Cossic art. But the most singular thing in the Hindu notation is, that when there are more unknown quantities than one, they call them colours; and speak of the multiplication, the addition of colours, &c. The third book of the Bija has its subject announced thus, explaining how many colours may be equal to one another. This is the language always used, both in the Sanscrit original, and in the Persian translation. Five letters are given by Mr DAVIS, as they also are by Dr HUTTON, which are used for denoting the unknown quantities; and we regret that we cannot copy them, as they are from types struck on purpose. Mr WILKINS has observed that they are the initials of words denoting colour: The first is på, the initial of panta, pale or white; the second ka, the initial of kală, black; the third ni, of nilă, blue, &c. This seems very enigmatical; and we have not found, in what is said by Mr Strachey, Mr Davis, or Dr Hutton, any conjecture concerning the analogy which must have suggested this extraordinary nomenclature. It so happens, however, that accident has put it in our power to offer what seems to us a very satisfactory explanation of it.

A friend of ours, who has devoted a good deal of time to the study of the mathematical sciences, and particularly of Algebra, for his own amusement, and for the instruction of the young people about him, contrived long since a kind of palpable Algebra, which employed counters to express and resolve equations; performing with them the real operations of addition, subtraction, &c. of which those on the conventional characters of Arithmetic or Algebra, are only indications. In this way it was easy to express the known quantities, which were all of one kind:-numbers and counters, sufficient to do this, would always be at hand. But the expression of the unknown quantities was often much more inconvenient. If there was but one unknown quantity, one kind of counter indeed would suffice, though there might be a necessity for many of the same kind, because if there was 3 x or 5 x to be expressed, this could only be done by repeating the thing which answered to x, 3 or 5 times. The embarrassment was much greater when there were several unknown quantities; for then counters of different kinds, and a considerable number of each kind, must be procured.

The pieces of money that one usually carries about him, are