arrived at the proof of the fact, that the sum of all the angles of a triangle is equal to two right angles, which is the thirty-second proposition of the first book of Euclid. The young geometer had just attained this point, when his father surprized him, deeply occupied in the prohibited study. But he was himself no less as tonished than his son, when, on examining into the nature of his occupation, he ascertained the conclusion to which he had come; and on inquiring how he arrived at it, the child pointed out several other principles which he had previously ascertained, and at length stated the first principles which he had gathered for himself in the way of axioms and definitions.

To control, after this, such evident manifestations of superior mathematical genius, was quite out of the question. Every advantage was afforded to him, of which he eagerly availed himself. At twelve years of age, he read through the Elements of Euclid, without feeling the need of any explanation from teachers; and at sixteen, he composed a treatise on Conic Sections, which was considered to possess very extraordinary merit. He attained rapidly to a very high degree of knowledge and of celebrity as a Mathematician; and before the age of nineteen, he invented the famous Arithmetical Machine which bears his name, and by which, through the instrumentality of a mechanical movement, somewhat similar to a watch, any numerical calculation might be performed. The main difficulty in Arithmetic lies in finding the mode of arriving at the desired result. This must ever be a

purely mental operation; but the object of this instrument was, that in all those numerical operations where the course to be pursued was fixed and certain, a mechanical process might relieve the mind from the monotonous and wearisome labour of the mere detail of calculation. Pascal's invention succeeded; but it was found too cumbrous for general use.

About this time, Stephen Pascal was appointed the Intendant of Rouen, to which place he removed his family. He remained there seven years; and during that period, his son diligently pursued his studies, although it was quite evident that his severe application had already affected his health, and marked him with the symptoms of decline.

Here his ardent mind, which had been turned during his retirement to the study of Physics, occupied itself with one of the most striking phenomena of the natural world, and did not rest till he had elicited a satisfactory explanation of it. This phenomenon was that in a pump, in which the piston played at a distance of more than thirty-two feet above the reservoir that supplied it, the water rose to the height of thirty-two feet, and no farther. On this question, Galileo had been consulted; and the explanation of this fact which was offered by him was, that the water rose to a certain height in the pipe, because nature abhorred a vacuum; but that the force by which she resisted a vacuum was limited, and that beyond a height of thirty-two feet, it ceased to act. This answer, however, was not even then satisfactory; and within a

short period of that time, Torricelli, the disciple of Galileo, ascertained, by a series of experiments, that the cause of this ascent of the water in fountains and pumps, was the pressure of the weight of the atmosphere upon the surface of the reservoir. At this juncture, however, Torricelli died; but Pascal, to whom the result of his experiments had been communicated by Mr Mersenne, through Mr Petit, the Intendant of Fortifications at Rouen, having repeated the experiments of Torricelli, verified their results, and completely refuted the popular notion of the abhorrence of a vacuum. And in the year 1647, in a small tract dedicated to his father, he published the account of these experiments.

It does not however appear, that, at this time, he had arrived at a satisfactory solution of the phenomenon in question, he had done little more than ascertained that it could not arise from the cause to which it had been attributed, according to the popular doctrine of the day, and that the notion of nature's abhorrence of a vacuum, had no foundation in fact. Pascal therefore followed out his inquiries most perseveringly; and in the year 1653, he wrote two pamphlets, one on the equilibrium of fluids, and another on the weight of the atmosphere; in which, by a series of satisfactory experiments, he completely established that doctrine on the subject, which is now universally received. The most important and original of these experiments were those which shewed that the rise of the water, or the mercury in the tube, varied in proportion to

the height above the level of the sea, of the place where the experiment was tried. Many attempts have been made to rob Pascal of the merit of these discoveries, but they have altogether failed. It was however to be regretted, that the two latter tracts were not printed till 1663, the year following his death.

At the time, however, when M. Pascal issued his first tract on this subject, his health had manifestly given way before the severity of his studies; and at the close of the year 1647, he had an attack of paralysis, which deprived him, in a great measure, of the use of his limbs. He returned to Paris, and resided there with his father and sister, and, for some time, relaxed from study, and took several journies by way of recreation. But in the year 1651, he lost his father; and in 1653, his sister Jacqueline, in the fulfilment of a wish which she had long cherished, joined the sisterhood of Port Royal; and being thus left alone at Paris, for his other sister and M. Perier then resided at Clermont, he returned without restraint to those habits of severe and excessive study which must, in a short time, had they not been interrupted, have brought him to the grave. But his friends interfered, and their advice, seconded by the severity of his bodily afflictions, constrained him for a time to lay aside his studies, and to mingle more than he had done with general society. Here he gradually regained his spirits, acquired a fresh relish for the fascinations of life, and began even to think of marriage. But an event which occurred about this time, and

which we shall have occasion afterwards to mention, dissipated all these thoughts, and gave an entirely new colour to his whole life, and tended especially to induce him to consecrate his splendid talents to the noblest of all employments,-the service of God.

There is reason to suppose, that the paralytic attack that Pascal experienced in the year 1647, first led him to the serious consideration of the subject of religion. He read, at that time, some few devotional books, and the effect which they produced upon his mind, was a clear conviction of the truth of the Christian religion, and of the propriety of its high requirements. He saw that it enjoined upon men the necessity of living for God, and of making Him the supreme object of their attention and love; and so strong was his conviction of this, that he determined about that time to renounce the studies to which, up to that period, he had so eagerly applied himself, and thenceforth, to devote the powers of his mind to that subject of supreme interest, which Jesus Christ has declared to be the one thing needful.

It is evident that the resolution then formed, did materially influence M. Pascal's whole character and habits, and that gradually he gave an increased attention to the subject of religion. Still there is reason to suppose, that the state of his mind underwent some material variations in this respect, and that, for several years, he was not altogether so entirely devoted to religious topics, nor so cordially separated from irreligious society, as he afterwards considered to be neces