TO READERS AND CORRESPONDENTS.

The letter from Col. Putnam to Gen. Dearborn, arrived too late for this number. It shall certainly have an early insertion.

An obituary notice from Boston is in the same predicament. We should greatly prefer a biography.

An Index to this volume accompanies this number. The Proceedings of Congress are to be placed at the end of the book; or they may be reserved for a separate volume.

There are few names in the history of our literature, which will redound more to its honour, than that of the author of the learned and ingenious Essay on Grammar; and yet in passing through the ordeal of public criticism, it has been his fate, too often, to fall into the hands of the most shallow of the fraternity. His Hebrew Grammar was reviewed in a Boston Journal with much parade of learning, and a sufficient demonstration that the writer had entirely mistaken the object of the author. We have already noticed two articles purporting to be reviews of the Essay on Grammar, and we think our readers will agree with us, that if their authors had understood what they pretended to discuss, they would not have written the worse. One of these critics soon discovered that he should get beyond his depth, if he "followed the author through his Essay," and he prudently shut it up for the amusement of baiting Mr. Hamilton, Mr. Dufief, and Mr. Varin. The first of these gentlemen, however, turned upon his assailant, and it is affirmed, that the critic was terribly gored. Not intimidated by this warning, another critic has entered the lists against the Grammar; and be comes, like his predecessors, unprepared for the contest. He pleads the narrow limits of the grounds which he himself has selected; and though a voluntary combatant, he presses old Time into his service, to prove that if he had not been so hasty, he might have made “a more regular appearance." The Remarks of this critic, confessedly so imperfect, conclude in the following words: "On the whole, we believe that no elementary work on Grammar was ever offered with so little claim to public patronage, and so replete with palpable errors and failures." This decisive sentence is issued from the same place, at which we understand there is a machine, by which the principles of grammar are said to be taught. If, from this circumstance, we may be allowed to infer, that the mechanic and the critic are one person, we can learn from Gil Blas how to value his judgment. "Heaven be praised, I carry on my profession in a plain honest manner. I am the only old-clothes-man who has any morality about him."

By such rude and indecent attacks the learned are confined to their closets, while sciolists usurp the laurels. Hence it is that we have taken so much notice of writers of comparative insignificance, who presume to investigate the character of one whose attainments have reached the most enviable heights of erudition, and whose labours are offer ed to his country with intentions the most pure and honourable. It is our duty to rescue learning from the assaults of ignorance; and the motives of the wise from the flippancy of the vain. On this subject we may appeal with confidence not only to the understanding but to the social relations. If we cannot reward Enceladus and Palamon we may defend them against false science and pompous nonsense.

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VOL. V.

THE PORT
PORT FOLIO.

FOURTH SERIES.

CONDUCTED BY OLIVER OLDSCHOOL, ESQ.

Various; that the mind

Of desultory man, studious of change

And pleased with novelty, may be indulged.-COWPER.

A DISCOURSE ON THE LIFE AND WRITINGS OF BLAISE

PASCAL.

FROM THE FRENCH OF BOSSUT.

(Concluded from page 276.)

PASCAL was nearly three years engaged in this controversy. It delayed, to a later period than he could have wished, the commencement of a great work, which he had meditated for many years, on the evidences of religion. He had, at various times, committed to paper some unconnected thoughts, comprehended within the plan of this work, and in 1658 he seriously undertook the prosecution of it, but his health from that moment suffered such frequent and violent attacks, that he was never able to com. plete it, and all that now remains consists of some imperfect frag.

ments.

He was first seized with an excruciating disorder of the teeth, which almost deprived him of rest. While he was lying in one of his long fits of sleepless agony, some problems relating to the cycloid occurred to his mind, and excited anew his genius for the mathematics. He had long since renounced the pursuit of all knowledge merely human; but the great beauty of these problems, and the

necessity of some powerful exertion to divert the sense of his sufferings, engaged him in an investigation which he carried to such a length, that the discoveries to which he was led are ranked, even at this day, among the highest attainments of the human mind.

The curve, usually denominated a cycloid, is well known to geometers. It is the line described in the air by the motion of a pin in the circumference of a carriage wheel. It is not known, and it is in itself of little importance to know, by whom the generation of this curve was first observed. It is certain, however, that the French were the first to develop its properties. Roberval, in 1637, demonstrated that the area of the common cycloid is three times that of its generating circle. Shortly after, he determined the solid described by the revolution of the cycloid on its base, and, what was a much greater achievement for the science of that day, the solid described by the revolution of the same curve on the diameter of its generating circle. Torricelli, in a work printed in 1644, gave to the world most of these problems as his own; but in France it was asserted that the Italian geometer had found the demonstrations of Roberval among the papers of Galileo, to whom they had been sent by Beaugrand some years before; and Pascal, in his History of the Cycloid, charges Torricelli with the plagiarism in direct and positive terms. I have attentively examined the evidence upon which this charge is founded, and cannot help thinking that Pascal has made it somewhat rashly. There is great rea son to believe that Torricelli had in truth made the discoveries to which he laid claim, ignorant of the fact that Roberval had anticipated him by several years. A problem of another kind, relating to the same curve, was resolved by Descartes, Fermat, and Roberval; they gave the method of drawing tangents to it.

Roberval and Torricelli had determined the measure of the cy. cloid and of its solids of revolution in a very ingenious manner, but their solutions had the defect of being too limited, and applicable only to the particular cases then under their consideration. The problems required to be treated in a general and uniform manner; the investigation was to be carried farther and embraced other problems; the length of the curve and its centre of gravity, the centre of gravity of the complete solid, half solid, and quarter solid of revolution, whether described on the base or the axis

of the curve-all these were still to be determined. The investigation required the use of a new analysis, or at least a new application of principles already known. In a period of less than eight days, during which he was suffering under a most painful disease, Pascal invented a method which embraced all the problems which have just been indicated. This method was founded on the summation of certain series, the elements of which he had given at the end of his treatise on the Arithmetical Triangle. From this invention to the differential and integral calculus was but a single step; and there is much reason to presume that if Pascal had been able to prosecute his mathematical inquiries, the glory of the invention of those calculi would never have belonged to Leibnitz and Newton.

The duke de Roannez, to whom, among other friends, Pascal had communicated his reflections and the results to which they had led him, conceived the design of making them subservient to the interests of religion. Pascal afforded an incontestible proof that the character of an humble Christian might be united with that of a mathematician of the highest order. To make his example, however, operate with the more striking effect, his friends determined, instead of publishing his investigations, at once to the world, to propose the problems of the cycloid in the first place as prize questions. They reasoned thus: though they may receive a solution from other mathematicians, their great difficulty will at least be discovered and acknowledged; science will be a gainer, and Pascal, as the original inventor, will still be intitled to the praise of having advanced its progress. If, on the contrary, mathematicians should fail to accomplish the solution of the problems, the infidel must abandon his objections to the proofs of religion; for why should he be allowed to be more difficult in relation to those proofs than a man profoundly skilled in a science resting altogether in demonstration, and who had accomplished in that science what all other men had failed to attain?

Accordingly, in the month of June, 1658, a scheme was made public; in which it was proposed to find the measure and the centre of gravity of any segment whatever of the cycloid; and the dimensions and centre of gravity of the solids, half solids, and quarter solids, formed by the revolution of the segment both on the absciss and the ordinate. As the solutions, however, might in

volve processes which, if given at full length, in every case, would consume too much time and labour, the candidates were enly required to furnish applications of their several methods to some particular and remarkable cases, such, for instance, as that in which the absciss is equal to the radius or to the diameter of the generating circle. Forty pistoles was the prize offered for the solution of the first problem, and twenty pistoles for that of the second. The most celebrated mathematicians then resident in Paris were selected to examine the pieces of the candidates. The pieces under the attestation of a public notary, were to be transmitted, before the first of October following, to M. de Carcavi, one of the judges, with whom the prizes were deposited. Pascal, for the purpose of concealment, assumed the signature of A. Dettonville.*

This scheme drew the attention of mathematicians again to the cycloid, which they had begun in some degree to neglect. Huyghens squared the segment included between the summit of the curve and the ordinate corresponding to half the radius of the generating circle. Slusius, canon of the cathedral of Liege, invented a new and very ingenious method of measuring the area of the curve. Sir Christopher Wren, an English geometer and architect, whose eminent genius is sufficiently attested by the church of St. Paul at London, showed that every arc of the cycloid, commencing at the summit of the curve, is twice the corresponding chord of the generating circle: he also determined the centre of gravity of the cycloidal arc, and the superficies of its solids of revolution. Both Fermat and Roberval, upon the mere enunciation of Wren's theorems, immediately produced demonstrations of them. All these investigations, however, though very beautiful in themselves, did not completely answer what was required. Neither were they communicated by their authors with any intention of having them put in competition. Two geometers only, having treated all the problems announced in the scheme, thought themselves intitled to claim the prizes. One was father Lallouère, a Jesuit of Toulouse, who enjoyed some reputation as a mathe

* AMOS DETTONVILLE, an anagram from LOUIS DE MONTALTE, the name under which Pascal had published his Provincial Letters.