father entered the apartment; but so absorbed in thought was this young geometer, that the astonished father remained some time unperceived by him. It would be difficult to say, which experienced the greater surprise, the son at being thus discovered by his father, after the express prohibition he had received to give no attention to such subjects, or the father, at seeing his son in the midst of all these diagrams. But the astonishment of the father was still greater, when, on asking him what he was doing, he announced to him as the truth he was proving, the thirty-second proposition of the first book of Euclid! Upon his father's enquiring what had led him to think of this truth, he told him it was a certain other truth he had discovered; and having asked the same question in regard to this, he received answer, that it was from another truth still; and thus retracing his processes, step by step, and explaining them constantly by the names round and bar, the boy arrived at his definitions and axioms. His father, amazed at the greatness and power of his genius, left him without saying a word, and went directly to the house of his intimate friend, Le Pailleur. On arriving there, he stood some time motionless, like one entranced. Le Pailleur, seeing this, and noticing that he shed tears, was alarmed, and entreated him no longer to conceal from him the cause of his sorrow. "I weep not for sorrow," said he, "but for joy. You know the care I have taken, that my son should give no attention to Geometry, lest it should divert him from his other studies; and yet, listen to what he has done." He then related to him what he had just witnessed, whereof it might be said in a certain sense, the boy had invented Geometry. Le Pailleur was not less astonished than the father, and thought it not right any longer to hold this young mind in captivity. From this time no further restraint was put upon the boy's genius. Euclid's "Elements" were given him for his hours of recreation, and he read the book by himself, without need of explanation, before he was thirteen years old. He was now permitted to attend regularly those weekly meetings of the learned men of Paris, from which he had formerly been excluded. He took an active part in their discussions, and soon attained a distinguished rank among them, not only by the judgment he passed upon scientific principles introduced by others, but by questions and principles which he himself brought forward. There were often brought before the society, propositions sent from Italy, Germany, and other foreign countries, and, upon all these, they were as careful to get his opinions, as that of any other member; for, by the keenness of his perceptions, he often detected errors which were overlooked by others. To estimate aright the wonderful progress he was now making in mathematical science, it must be remembered, that he devoted only his hours of recreation to these pursuits, for he continued to follow strictly the rules which his father had at first laid down for his study of the languages. Yet he took such delight in these investigations, and applied himself to them with so much energy, that, when he was but sixteen years old, he composed a short treatise upon Conic Sections. This was considered a prodigy of genius, showing him superior in geometrical science to any one since the time of Archimedes. It astonished Descartes himself, who persisted in maintaining, that it was the work of Pascal's instructors, as he could not believe it to be the production of a boy of sixteen. Etienne Pascal was now one of the happiest of fathers. He saw his son moving with giant strides in the career of science, which he regarded as the most noble exercise of the human mind. His daughters afforded him no less satisfaction. In them, beauty of person was united with superiority of mind, and they began to be distinguished in those fashionable circles in which they occasionally appeared. But all this domestic happiness, as well as the studies of young Blaise, was now interrupted by misfortune. "The father incurred the resentment of Richelieu, by offering some opposition to an arbitrary plan for cutting short the income attached to the Hôtel de Ville. An order was made out for committing him to the Bastile; but, obtaining seasonable notice of it, he fled from Paris, and concealed himself in his native province of Auvergne. A singular circumstance aided the talents and filial piety of his children, to which he was at last indebted for restoration from exile. The cardinal, it is well known, had a passion for dramatic performances, and even wrote a play himself, which was quite bad enough to be worthy of a prime-minister. He took a fancy about this time, that a tragi-comedy by Scudéri, called 'L' Amour Tyrannique,' should be represented in his presence by a party of young girls. The Duchess d'Aiguillon, who had charge of the affair, selected Jacqueline Pascal, then about thirteen years old, the younger sister of Blaise, to be one of the performers. The permission of the elder sister, afterwards Madame Perier, who was at the head of the family during the absence of the father, was asked; but she coldly answered, that they did not consider themselves under any great obligation at that time to please the cardinal. The duchess persisted in her request, and hinted that the pardon of the father might reward them for compliance. They yielded to this suggestion, and the representation took place on the third of April, 1639. Jacqueline acted her part like a little fairy, and her grace and spirit quite captivated the spectators, and excited all the good feelings of Richelieu. It had been arranged, she should approach the minister at the close of the piece, and recite some verses, pleading for the restoration of her father.* She did so with a degree of simplicity and earnestness that delighted the cardinal, who embraced her as soon as she had finished, and exclaimed, 'Yes, my child, I grant all that ask for; you write to your father, that he may immediately return with safety.' The kind duchess then spoke with strong commendation of the merits of the family, and added, pointing to Blaise, who was standing near, 'There is the son, who is but fifteen years old, and is already a distinguished mathematician.""† As a result of the scene just described, Pascal's father was immediately recalled from banishment; and, in accordance with a *The following is the petition recited by the successful little actress, which we will not rob of its grace and beauty by translating. Ne vous étonnez pas, incomparable Armand, De l'esprit et du corps, de la voix et du geste. ↑ North American Review, April, 1845. request of Jacqueline, that her father might be permitted to come in person to thank the cardinal for his kindness, he hastened, with his three children, to appear before him, and was received in the kindest and most flattering manner. Two years after this, in 1641, the elder Pascal was appointed by Richelieu to an honorable and lucrative office in the government of Rome. Thither he removed his family, and the same year, Gilberte, his eldest daughter, was married to M. Perier. The numerous accounts and calculations that were necessary in his father's official business, were confided to young Pascal. But he, weary of the tedious arithmetical processes he was obliged to go over, day after day, was led to seek some mechanical means of executing the work. After two years of intense application, not only to invent the instrument, but to make it intelligible to the workmen employed in its construction, he produced the celebrated Arithmetical Machine which bears his name. This was a wonderful production for a youth of nineteen. Leibnitz viewed it with admiration, and spent some time in improving and simplifying it; and recently in England, Mr. Babbage, availing himself of the ingenious contrivance of this young Frenchman, has constructed his famous Mathematical Machine, whose object is to solve the most complicated problems, and calculate the motions of the stars, and the return of eclipses. Pascal's machine consists of a kind of frame-work, supporting several parallel bars, each having two series of numbers inscribed upon it. By a combination of wheels and pinions, these bars are made to revolve upon their axes, and after the machine is set for a particular process, the numbers forming the result appear through the opening in the face of the instrument. Not only does it execute all the lower processes of arithmetic with quickness and certainty, but also some of the more complex and difficult operations. The Arithmetical Triangle, sometime afterwards invented by Pascal, gives the coefficient of a binomial raised to any power denoted by an integer; it was used to facilitate the calculations in the theories of combinations and probabilities. Pascal's discoveries in mathematical science, were conspicuous and important enough to attract the attention and envy of Descartes, who, at this period, arrogated to himself the whole province of pure mathematics. His discoveries concerning the theory of the cycloid, must be regarded as almost miraculous achievements of the geometry of his time. The calculation of chances owes its earliest development, and the establishment of some of its most important principles, to the genius of Pascal. When about twenty-three years of age, physical science offered to his enquiring mind a phenomenon, his solution of which affords still more remarkable proof of the premature vigor of his intellect. The workmen of the Duke of Florence, observing that water would not rise in a pump to the height of more than thirty-two feet, consulted Galileo as to the cause of this seeming caprice. He, imbued with the opinion, then commonly received, of nature's abhorrence of a vacuum, replied that the water did indeed rise from this cause to a certain height, but that this power had a limited sphere, and beyond thirty-two feet, it ceased to act. But Galileo was not satisfied with his own explanation thus hastily given to the workmen; and as he was advanced in age, and exhausted by his long continued labors, he charged Torricelli, his disciple, to examine the question more thoroughly. Torricelli suspected that the ascent of water in a pump was owing to the pressure of the air upon the surface of the reservoir. He made several experiments upon the subject, but was not able to establish the truth of his supposition; although it explained the fact, it did not exclude other hypotheses to account for the phenomenon. It therefore remained to be proved, that the weight of the atmosphere was the only possible cause of it. Just at this time, Torricelli died; but Pascal, to whom the result of his experiments had been communicated, in 1646 repeated them with some variations. He used tubes of great length, and thus proved that nature did not dread a large vacuum any more than a small one. He was not yet acquainted with the explanation Torricelli had given, but, guided by his own reflections, he came to the conclusion, that the doctrine of nature's repugnance to a vacuum was false. The results of his experiments, and the arguments founded upon them, he published in 1647, in a little book, entitled, “New Experiments respecting a Vacuum.” This work was attacked by many authors. To a severe criticism by Noel, a Jesuit, then rector of the College of Paris, Pascal replied |