and the revolution which Galileo and Descartes had prepared, was rapidly tending to its consummation. Involved in the general movement, Stephen Pascal applied himself to the study of geometry and physics. Similarity of taste and pursuits connected him with Pere Mersenne, Roberval, Carcavi, le Pailleur, and other men of science of that period. They met from time to time at their own houses, for the purpose of conversing on those general subjects of sciences in which they were engaged, or of discussing such occasional topics as might be suggested in the course of debate. They maintained a regular correspondence with other men of science in the various provinces of France as well as in foreign countries; and thus were speedily informed of all the discoveries which were made in the mathematics, or in natural philosophy. This little society constituted a sort of academy, animated by no spirit but that of friendship and mutual confidence, and acknowledging no other tie of connexion. It was the origin of the academy of sciences, which afterwards (1666) was regularly established under the seal of the royal authority.

Blaise Pascal was sometimes admitted to the meetings of the philosophers at his father's house. He listened to their conversation with the most eager attention. He was extremely curious to learn the causes of the various phenomena of nature. It is related that at the age of eleven years he composed a little treatise on sounds, in which he undertook to explain why, when a dish is struck with a knife, the sound ceases on the application of the hand. His father, fearing that this strong predilection for science might obstruct the acquisition of the languages, which were then considered as the most material part of education, came to a determination, in which his friends concurred, to avoid the introduction of mathematical and philosophical discussions in the presence of the boy. This determination grieved him severely. To quiet his mind, he was told, that when he should have arrived at a suitable age, after finishing his course of Latin and Greek, he should be allowed to commence the study of geometry. In the mean time, it was thought sufficient to inform him, that it was a science which treated of magnitudes, or the length, breadth and thickness of bodies; and that it taught us, moreover, the relations which dif

ferent figures have to each other, and the manner of describing

them.

This vague and general hint, extorted by the importunate curiosity of a child, was a ray of light which excited into life and energy the germ of his mathematical talent. From that moment he was incapable of rest. He was resolved to acquire a knowledge of a science, withheld from him with so much mystery, and contemptuously believed to be beyond the reach of his powers. During the hours allotted to recreation, he shut himself up in a retired chamber, where he employed himself in tracing on the floor, with a piece of charcoal, triangles, parallelograms, circles and other figures, of none of which did he know even the names. He examined the positions of the lines and sides, observed the manner in which they met, and compared the figures with each other; founding his investigations on definitions and axioms entirely his own, and formed for the occasion. Proceeding from one step to another, he arrived at the discovery that the sum of the three angles of every triangle must be measured by half the circumference of a circle, or, in other words, that it is equal to two right angles; which is precisely the thirty-second proposition of the first book of Euclid. He was employed on this theorem when he was one day surprised in his study by his father, who, understanding the nature of his son's pursuits and the successful progress he had made in them, was so overcome with admiration and tenderness that he stood for some moments incapable of speech or motion. As soon as he recovered himself, he ran to his friend le Pailleur to relate to him the discovery which he had made.

It is proper to mention that doubts have been thrown over this part of the life of Pascal. Such an achievement has been considered by some as altogether impossible, and the story, therefore, a mere fabrication. Others admit that it may be true, but can discover in it nothing very extraordinary. If the matter, however, is examined with candour, it will appear, that the fact is supported by evidence too powerful to be resisted; and as to the achievement itself, it cannot be denied that it displays a genius and depth of mind, which, in so young a child, is of very rare

1

Be that as it may, the decided taste of young Pascal was now no longer opposed, and he was permitted to pursue at will the study of geometry. At the age of twelve, Euclid's Elements were put into his hands, and he mastered them without requiring the least explanation or assistance. In a short time he was qualified to make no mean figure among the philosophers, and his productions, among the rest, were read at their meetings. Before he was sixteen years of age he composed a little treatise on conic sections, which was at that time regarded as a work of prodigious depth and ingenuity.

Stephen Pascal was the happiest of fathers. He beheld his son advancing, with great strides, in the career of those sciences which he regarded as the noblest exercise of the human mind. His daughters gave him no less satisfaction. To the graces of person and manners they united amaturity of understanding uncommon at their age, and in the society, in which they had just began to appear, were already the objects of distinguished regard. All this happiness was disturbed by one of those events which human prudence can neither foresee nor prevent.

In the month of December, 1638, the government, impoverished by a long succession of wars and the continual plunder of the finances, levied a tax on the rents of the Hotel-de-ville at Paris. This mode of raising money for the state is now allowed to be one of the least oppressive that can be resorted to; but it excited at that time a violent clamour among the proprietors of the rents, and was even the occasion of some public meetings, which were denounced as seditious. Stephen Pascal was accused of being one of the chief promoters of these disturbances; and the charge, though in truth entirely unfounded, derived some appearance of probability, from the circumstance of his having, on his arrival at Paris, invested the chief part of his fortune in the stock of the Hotel-de-ville. No sooner was the accusation made, than a terrible minister, whose tyrannical temper was roused into fury by the least opposition, issued an order for the arrest of Pascal, and his confinement in the Bastile. Informed, however, of his danger, he contrived, for some time, to conceal himself, and then secretly escaped into Auvergne.

It is not difficult to imagine the grief of the children at this separation; or the painful feelings of the father himself, in being thus forced to abandon them at an age when they most required his paternal care. If men in power can thus, without proof and without examination, indulge themselves in the practice of violence and injustice, and yet retain any sentiment of remorse, they must experience occasional moments of very bitter reflection.

Calumny soon exhausted its power; and here it is impossible not to remark how strangely the events of human life are sometimes connected. The cardinal de Richelieu had conceived the fancy of having l'Amour tyrannique, a dramatic piece of Scudéry, played for his amusement by young ladies. The business of getting up the piece was committed to the duchess d'Aiguillon, who requested that Jacqueline Pascal, then about thirteen years of age, might be permitted to take a part in the performance. To this request, Gilberte, the elder sister of Jacqueline, and in the absence of her father the head of the family, proudly answered: the cardinal thinks too little of what will gratify us, to expect that we can take any trouble to gratify him. The duchess insisted, and intimated that the recal of Stephen Pascal might be the reward of compliance. The matter was submitted to the friends of the family, and it was decided that Jacqueline should be permitted to accept the part which had been reserved for her. The piece was performed on the 3d of April, 1639. Jacqueline gave to her performance so much grace and propriety that all who beheld her, and particularly the cardinal, manifested a high degree of delight. She skilfully took advantage of this moment of excited feeling, and, after the play was ended, advancing towards the cardinal, addressed to him a little petition in verse for the return of her father. The cardinal, taking her in his arms, and, as she herself relates in a letter written to her father on the following day, interrupting her every moment with his kisses and caresses, told her she should have all that she asked. "Write to your father, and inform him that he may return with perfect safety." The duchess d'Aiguillon then spoke in high terms of the character of Stephen Pascal. She declared him to be an excellent and very learned man, and regretted that his talents were not employed for the public benefit. "And here is his son," said she, pointing to Blaise Pascal," who,

though but fifteen years of age, is already a great mathematician." Jacqueline, encouraged by the success of her first application, told the cardinal that she had one favour still to ask of him. "Name it, my child," said he, "and you shall be gratified; to such loveliness it is impossible to deny any thing." "It is, that your highness will permit my father to thank you personally for your goodness towards us." "I wish to see him," said the cardinal; "let him come, and bring his family with him.”

Without a moment's delay, an order was despatched for Stephen Pascal's immediate return. As soon as he arrived in Paris he took with him his three children and repaired directly to Ruel, the residence of the cardinal, where he was received in the most flattering manner. "I am made acquainted with your great merit," said he; "I restore you to your children, and recommend them to you as worthy of your regard. I shall not forget them."

Two years after this period, in 1641, Stephen Pascal was associated with M. de Paris, the master of requests, in the government of Rouen. For seven successive years he discharged the important duties of this station, with an ability and a disinterestedness which were equally applauded by the province and the court. He had taken all his family with him to Rouen, and the same year (1641) gave his daughter, Gilberte, in marriage to M. Perier, who had acquired some distinction by the ability with which he had executed a commission from the government in Normandy, and who afterwards purchased the situation of a counsellor in the court of aids at Clermont-Ferrand.

Blaise Pascal was already reputed a first rate geometer, and he enjoyed the rare advantage of an unrestrained indulgence of his inclination for science; but he enjoyed it at the expense of health, and perhaps also of life. He was hardly nineteen years of age when he invented the famous arithmetical machine which bears his name. We all know the importance of arithmetical calculations, not only in the ordinary business of life, but in what are called the practical branches of the mathematics; where, after an analysis has furnished the solution of any problem, the values of the quantities involved in it are still to be expressed in numbers. But when a rule is once ascertained, the calculations of particular cases under it, being all performed in the same way,