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PASCAL

BY PRINCIPAL TULLOCH

WILLIAM BLACKWOOD AND SONS EDINBURGH AND LONDON 1878.REPRINT, 1882

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PREFATORY NOTE.

The translations in this volume are chiefly my own; but I have also taken expressions and sentences freely from othersand especially from Dr MCrie, in his translation of the Provincial Letterswhen they seemed to convey well the sense of the original. It would be impossible to distinguish in all cases between what is my own and what I have borrowed. The Provincial Letters have been translated at least four times into English. The translation of Dr MCrie, published in 1846, is the most spirited. The Pensées were translated by the Rev. Edward Craig, A.M. Oxon., in 1825, following the French edition of 1819, which again followed that of Bossut in 1779. A new translation, both of the Letters and Pensées, by George Pearce, Esq.the latter after the restored text of M. Faugèreappeared in 1849 and 1850.

J. T.



CONTENTS.

CHAP. PAGE

INTRODUCTION 1

I. PASCALS FAMILY AND YOUTH 5

II. PASCALS SCIENTIFIC DISCOVERIES 25

III. PASCAL IN THE WORLD 52

IV. PORT ROYAL AND PASCALS LATER YEARS 74

V. THE PROVINCIAL LETTERS 103

VI. THE PENSÉES 157

INTRODUCTION.

There are few names which have become more classical in modern literature than that of Blaise Pascal. There is hardly any name more famous at once in literature, science, and religion. Cut off at the early age of thirty-ninethe fatal age of geniushe had long before attained pre-eminent distinction as a geometer and discoverer in physical science; while the rumour of his genius as the author of the Provincial Letters, and as one of the chiefs of a notable school of religious thought, had spread far and wide. His writings continue to be studied for the perfection of their style and the vitality of their substance. As a writer, he belongs to no school, and is admired simply for his greatness by Encyclopedist and Romanticist, by Catholic and Protestant alike,by men like Voltaire and Condorcet and Sainte-Beuve, no less than by men like Bossuet, Vinet, and Neander. His Pensées have been carefully restored, and re-edited with minute and loving faithfulness in our time by editors of such opposite tastes and tendencies as M. Prosper Faugère, M. Havet, and M. Victor Rochet. Cousin considered it one of the glories of his long intellectual career that he had first led the way to the remarkable restoration of Pascals remains. Of all the illustrious names which group themselves around Port Royal, it is Pascal alone, and Racinewho was more its pupil, but less its representativewhose genius can be said to survive, and to invest it with an undying lustre.

Pascals early death, the reserve of his friends under the assaults which the Provincial Letters provoked, and his very fame, as a writer, have served in some degree to obscure his personality. To many a modern reader he is little else than a great name. The man is hidden away behind the author of the Pensées, or the defender of Port Royal. Some might even say that his writings are now more admired than studied. They have been so long the subject of eulogy that their classical character is taken for granted, and the reader of the present day is content to look at them from a respectful distance rather than spontaneously study them for himself. There may be some truth in this view. Pascal is certainly, like many other great writers, far more widely known than he is understood or appreciated. The old, which are still the common, editions of the Pensées, have also given a certain commonplace to his reputation. It were certainly a worthy task to set him more clearly before our age both as a man and as a writer.

It is no easy task, however, to do this; and to tell the full story of Pascals life is no longer possible. Its records, numerous as they are, are incomplete; all fail more or less at an interesting point of his career. They leave much unexplained; and the most familiar confidences of his sisters and niece, who have preserved many interesting details regarding him, have not entirely removed the veil from certain aspects of his character. The well-known life by Madame Périer, his elder sister, is of course the chief authentic source of his biography. It was written shortly after his death, although not published for some time later; and nothing can be more lively, graphic, and yet dignified, than its portraiture of his youthful precocity, and, again, of the devotions and austerities of his later years. But it leaves many gaps unsupplied. Like other memoirs of the kind, it is written from a somewhat conventional point of view. No one, as M. Havet says, was nearer to him in all senses of the expression, or could have given a more true and complete account of all the incidents in his life; but she was not only his sister, but his enthusiastic friend and admirer, in whose eyes he was at once a genius and a sainta man of God, called to a great mission. It was from a consciousness of this mission, and the full glory of his religious fame, that she looked back upon all his life; and the lines in which she draws it are coloured, in consequence, too gravely and monotonously. Certain particulars she drops out of sight altogether. These are to be found scattered here and there, sometimes in his own letters, more frequently in the letters of his younger sister, Jacqueline, and in a supplementary memoir, written by his niece, Marguerite Périer, all of which have been carefully published in our time, and made accessible to any reader. {3} The researches of M. Cousin, M. Faugère, and M. Havet, the curious and interesting monograph of M. Lélut, {4a} have thrown light on various points; while the copious portraiture of Sainte-Beuve {4b} has given to the whole an animation and a desultory charm which no English pen need strive to imitate.

My only hope, as my aim, will be in this little volume to set before the English reader perhaps a more full and connected account of the life and writings of Pascal than has yet appeared in our language, freely availing myself of all the sources I have indicated. And if long and loving familiarity with a subjectan intimacy often renewed both with the Provincial Letters and the Penséesform any qualification for such a task, I may be allowed to possess it. It is now nearly thirty years since the study of Neander first drew me to the study of Pascal; and I ventured, with the confidence of youth, to draw from the Pensées, which had then recently appeared in the new and admirable edition of M. Faugère, the outlines of a Christian Philosophy. {4c} I shall venture on no such ambition within the bounds of this volume; but I trust I may be able to bring together the story of Pascals life, controversy, and thought in such a manner as to lead others to the study of a writer truly great in the imperishable grandeur and elevation of his ideas, no less than in the exquisite finish and graces of his style.



CHAPTER I. PASCALS FAMILY AND YOUTH.

Blaise Pascal was born at Clermont-Ferrand on the 19th June 1623. He belonged to an old Auvergne family, Louis XI. having ennobled one of its members for administrative services as early as 1478, although no use was made of the title, at least in the seventeenth century. The family cherished with more pride its ancient connection with the legal or Parliamentary institutions of their country. {5} Pascals grandfather, Martin Pascal, was treasurer of France; and his father, Étienne, after completing his legal studies in Paris, acquired the position of Second President of the Court of Aides at Clermont. In the year 1618 he married Antoinette Begon, who became the mother of four children, of whom three survived and became distinguished. Madame Pascal died in 1626 or 1628; {6a} and two years afterwards (in 1630) Étienne Pascal abandoned his professional duties, and came to Paris, in order that he might devote himself to the education of his children.

Soon after the Pascal family settled in Paris, their character and endowments seem to have attracted a widespread interest. If not superior to the Arnaulds, they were no less remarkable. They did not escape the penetrating eye of Richelieu, who, as he looked upon the father with his son, then fifteen years of age, and his two daughters, was so struck by their beauty that he exclaimed, without waiting for their formal introduction to him, that he would like to make something great of them. {6b} Étienne Pascal was a man not only of official capacity, but of keen intellectual instincts and aspirations. He shared eagerly in the scientific enthusiasm of his time. A letter by him addressed to the Jesuit Noël shows that the vein of satire, half pleasant, half severe, which reached such perfection in the famous Letters of his son, was not unknown to the father. The careful and systematic education which he gave to his son would alone have stamped him as a man of remarkable intelligence.

Gilberte, Pascals elder sister and biographer, exerted an influence upon his character only second to that of his father. She married her cousin, M. Périer, also of a Parliamentary family, and Counsellor of the Court of Aides at Clermont. She was alike beautiful and accomplished, a student of mathematics, philosophy, and history. {7} For a time she shared in the enjoyments of the world, like other persons of her age and condition; but the same impulses of religious enthusiasm which animated the rest of her family led to her practical abandonment of the world while still young. The memoirs which she composed, both of her brother and sister, and her letters, all indicate a high intelligence and a mingled dignity, sweetness, and restraint of character, which made her their best counsellor and friend.

The younger sister, Jacqueline, has been made a special study by M. Cousin amongst the Illustrious Women of the Seventeenth Century. She was beautiful as her sister, and a child of genius like her brother. She began to compose verses at the age of eight, and in her eleventh year assisted in the composition and the acting of a comedy in five acts, which was a subject of universal talk in Paris. Her powers, both as an actor and a verse-maker, made a wonderful reputation at the time, which, as we shall see, was highly serviceable to her after. Her verses, it must be confessed, are somewhat artificial and hollow; but her letters, and, more remarkable than either her verses or her letters, her Thoughts on the Mystery of the Death of Christ, are in some respects very fine, and might even claim a place beside some of those of her brother. They are equally elevated in tone, and pervaded by the same subtle, penetrating, radiant mysticism, the same rapture of self-sacrificing aspiration, though lacking the glow of inward fire and exquisite charm of style which marked the author of the Pensées. Noble-minded and full of genius, she was yet without his depth and power of feeling, or his skill and finish as an author. In 1646 she came, along with her brother, and greatly through his influence, strongly under the power of religion; and in 1652, after her fathers death, she renounced the world, and became one of the Sisters of Port Royal. She died amidst the persecution of the Sisters in 1661, a year before her brother.

In Paris the elder Pascal became a centre of men of congenial intellectual tastes with himself, and his house a sort of rendezvous for the mathematicians and the physicists of the time. Among them were Descartes, Gassendi, Mersenne, Roberval, Carcavi, and Le Pailleur; and from the frequent reunion of these men is said to have sprung the Academy of Sciences founded in 1666. It is interesting to notice that it was into this same society that Hobbes was introduced on his first and second visits to France, when he accompanied the future Duke of Devonshire there as tutor. With Father Mersenne and Gassendi especially he formed a warm friendship, which sheds an interest over his life. Possibly in some of these reunions the author of the Leviathan may have encountered the young Pascal, and joined in the half admiration and half incredulity which his wonderful powers had begun to excite.

There never certainly was a more singular story of youthful precocity than that which Madame Périer has given of her brother, accustomed as we have become to such stories in the lives of eminent men. Detecting the remarkable powers of the boy, his father had formed very definite resolutions as to his education. His chief maxim, Madame Périer says, was always to keep the boy above his work. And for this reason he did not wish him to learn Latin till he was twelve years of age, when he might easily acquire it. In the meantime, he sought to give him a general idea of grammarof its rules, and the exceptions to which these rules are liableand so to fit him to take up the study of any language with intelligence and facility. He endeavoured further to direct his sons attention to the more marked phenomena of nature, and such explanations as he could give of them. But here the sons perception outstripped the fathers power of explanation. He wished to know the reason of everything; and when his fathers statements did not appear to him to give the reason, he was far from satisfied.

For he had always an admirable perspicacity in discerning what was false; and it may be said that in everything and always truth was the sole object of his mind. From his childhood he could only yield to what seemed to him evidently true; and when others spoke of good reasons, he tried to find them for himself. He never quitted a subject until he had found some explanation which satisfied him.

Once, among other occasions, he was so interested in the fact that the sound emitted by a plate lying on a table when struck, suddenly ceased on the plate being touched by the hand, that he made an inquiry into sound in general, and drew so many conclusions that he embodied them in a well-reasoned treatise. At this time he was only twelve years of age.

At the same age he gave still more astonishing evidence of his precocious scientific capacities. His father, perceiving his strong scientific bent, and desirous that he should first of all acquaint himself with languages before the absorption of the severer, but more engrossing, study seized him, had withdrawn from his sight all mathematical books, and carefully avoided the subject in the presence of his son when his friends were present. This, as might be expected, only quickened the curiosity of the boy, who frequently begged his father to teach him mathematics, and the father promised to do so as a reward when he knew Latin and Greek, which he was then learning. Piqued by this resistance, the boy asked one day, What mathematical science was, and of what it treated? He was told that its aim was to make figures correctly, and to find their right relations or proportions to one another. He began, says his sister, to meditate during his play-hours on the information thus communicated to him.

And being alone in a room where he was accustomed to amuse himself, he took a piece of charcoal and drew figures upon the boards, trying, for example, to make a circle perfectly round, a triangle of which the sides and angles were equal, and similar figures. He succeeded in his task, and then endeavoured to determine the proportion of the figures, although so careful had his father been in hiding from him all knowledge of the kind, that he did not even know the names of the figures. He made names for himself, then definitions, then axioms, and finally demonstrations; and in this way had pushed his researches as far as the thirty-second proposition of the first book of Euclid. {10}

At this point a surprise visit of his father arrested him in his task, although so absorbed was he in it, that he did not at first recognise his fathers presence. The older Pascal, having satisfied himself of the astonishing achievement which the youthful mathematician had worked out for himself in solitude, ran with tears of joy to communicate the fact to his friend M. le Pailleur. It was agreed betwixt them that such an aptitude for science should no longer be balked, and the lad was furnished with the means of pursuing his mathematical studies. Before he had completed his sixteenth year he had written the famous treatise on Conic Sections which excited the mingled incredulity and astonishment of Descartes. {11}

The happiness of Pascals home was suddenly interrupted by an unforeseen calamity. On coming to Paris, his father had invested his savings in bonds upon the Hotel de Ville. The Government, impoverished by wars and extravagance, reduced the value of these revenues, with the result of creating discontent and calling forth expostulation from the disappointed annuitants. Some of them met together, and, among others, Étienne Pascal, and gave such vent to their feelings as to alarm the Government. Richelieu took summary means of asserting his authority and silencing the disturbers. The meeting was denounced as seditious, and a warrant issued to arrest the offenders and throw them into the Bastille. Étienne Pascal, having become apprised of the hostile designs of the Cardinal, contrived to conceal himself at first in Paris, and afterwards took refuge in the solitude of his native district. His children were left without his care, and plunged in the greatest sorrow. At intervals, indeed, he contrived to see them in secret, and is said even to have nursed Jacqueline through a severe attack of the smallpox, which impaired her hitherto remarkable beauty. But all the pleasant companionship which he had enjoyed as their instructor, and the centre of a group of intellectual friends, was at an end. He could only visit his home by stealth.

At this crisis (February 1639) Richelieu took a fancy to have Scudérys tragi-comedy of LAmour Tyrannique acted before him by young girls. The Court lady who undertook the management of the piece appealed to Jacqueline Pascal, whose accomplishments as a girl-actor were well known, to assist in its performance. She was then thirteen years of age. The elder sister, who, in the enforced absence of the father, was acting as the head of the family, replied, with feeling, that they did not owe any favour to M. le Cardinal, who had not acted kindly towards them. The request, however, was pressed, in the hope that some good might come out of the affair to the family, and Jacqueline was allowed to appear. The result was all that could be anticipated. The Cardinal, charmed by the grace and accomplishment of her acting, received her cordially when she ventured to approach him with a petition on behalf of her father, thrown into a form of verses similar to many which she had already composed. The verses have been preserved with her other pieces, and have been thus rendered:{12}

O marvel not, Armand, the great, the wise, If I have failed to please thine ear, thine eyes; My sorrowing spirit, torn by countless fears, Each sound forbiddeth save the voice of tears. With power to please thee wouldst thou me inspire? Recall from exile now my hapless sire.

She has herself described, in an interesting letter to her father, {13} the whole incident, and the result of her intercession. Having told how the Cardinal had been previously well prepared, and had the true state of the case explained in reference to her father, who appears to have been in no degree to blame in the agitation which called forth the displeasure of the Government, she says that

M. le Cardinal appeared to take great pleasure in the representation, especially when I spoke. He laughed very much, as did the whole company. When the comedy was finished, I descended from the theatre with the design of speaking to Madame dAiguillon [the same lady who had already interested herself in the business]. But as the Cardinal seemed about to leave, I approached him directly, and recited to him the verses I send you. He received them with extraordinary affection and caresses more than you can imagine; for at first, when I approached, he cried, Voilà la petite Pascal! Then he embraced me and kissed me, and while I said my verses he continued to hold me in his arms, and kissed me each moment with great satisfaction. And then when I was done he said, Yes; I grant to you all that you ask; write to your father that he may return with safety. Thereupon Madame dAiguillon approached, and addressed the Cardinal. It is truly well, sir, that you do something for this man. I have heard him spoken of as a thoroughly honest and learned man, and it is a pity he should remain unemployed. Then he has a son who is very learned in mathematics, although as yet only fifteen years of age. The Cardinal assured me once more that I might tell you to return in all safety; and as he seemed in such good humour, I asked him further that you might be allowed yourself to pay your thanks and respects to his Eminence. He said you would be welcome; and then, with other discourse, repeated, Tell your father, when he returns, to come and see me. This he said three or four times. After this, as Madame dAiguillon was going away, my sister went forward to salute her. She received her with many caresses, and inquired for our brother, whom she said she wished to see. It was this that led to his introduction to the Duchess, who paid him many compliments on his scientific attainments. We were then conducted to a room, where we had a magnificent collation of dried sweetmeats, fruits, lemonade, and such things. Here the Duchess renewed her caresses in a manner you will hardly believe. In short, I cannot tell how much honour I received, for I am obliged to write as succinctly as possible. I am greatly obliged to M. de Moudroy for all the trouble he has taken, and I beg you will be so good as write to him by the first post to thank him, for he well deserves it. As for me, I esteem myself extremely happy to have in any way assisted in a result which must give you satisfaction.

This letter was written from Paris on the 4th April 1639, when Jacqueline Pascal was therefore only fourteen years of age. It is in all respects a remarkable and interesting production, both for the glimpse it gives of the great Cardinal in his hours of ease, and its revelation of Jacquelines own character,her dramatic cleverness, her firmness and wisdom in assailing the Cardinal with her prepared verses at the right moment, her self-conscious importance as the chief actor of such a scene, and all the same, her girlish enjoyment of the sweetmeats provided for her. It is a pleasant enough picture; and it deserves especially to be noticed how prominently the scientific reputation of her brother, only two years older than herself, is already recognised.

The sequel was all that could have been desired. The father hastened, at the summons of his daughter, to pay his respects to Richelieu, who gave him a welcome reception. I know all your merit, he said. I restore you to your children, and commend them to you. I desire to do something considerable for you. Within two years Étienne Pascal was, in consequence, appointed Intendant of Rouen, where he settled with his family in 1641. Disturbances had arisen in Normandy at this time in connection with the payment of taxes, and the Government, believing that the Parliament at Rouen had not acted with sufficient vigour, took the matter into their own hands, and sent their officers to collect the revenues of the province. {15} Étienne Pascals character and previous labours in this capacity, no less than his restoration to the Cardinals favour, pointed him out as a man specially fitted for this work, which in the circumstances was not unattended with danger. The work in itself was also harassing and troublesome; and the youthful Pascal, anxious to assist his father, had busied himself in the invention of a machine for performing arithmetical calculations, which made a great sensation at the time. Ingenious as the machine was, it came to little, as we shall see in the next chapter, which will be devoted to a brief account of Pascals scientific discoveries. In the meantime it will be better to confine ourselves to the thread of his personal history up to the important epoch which is known as his first conversion.

Settled at Rouen, he pursued his studies with unremitting devotion, and with only too little regard for his health. His elder sister, who might have won him occasionally to lighter pursuits, was married to her cousin M. Périer in 1641, and two years afterwards went with him to Clermont, where her husband was appointed a Counsellor in the Court of Aides. Jacqueline was absorbed in her own poetical studies, which received a special impetus from the friendship of Corneille, who had returned at this time to his native town. The illustrious dramatist speedily sought out the Pascal family, and became one of their most intimate associates. A prize being given every year for the best copy of verses on the Conception of the Virgin, it was awarded to certain verses of Jacquelines for the year 1640. When the announcement of the result was made she was absent, but a friend of the family rose and returned thanks in verse in the name of the youthful poetessPour une jeune muse absente. The friend was Corneille, whose impromptu lines on the occasion, along with those of Jacqueline, are still preserved. {16} Neither have much poetic merit, but they recall an interesting incident.

A bright atmosphere of intellectual emulation and cheerful prospects surrounds the family at this time. But all the while it is evident, from Madame Périers account, that her brother was injuring his health greatly in his undue assiduity in his scientific pursuits. The attempts to perfect the construction of his arithmetical machine seem especially to have worn out his delicate frame, and to have laid the foundation of the nervous prostration from which he more or less suffered all his life afterwards. From the age of eighteen, she says in a significant passage that her brother hardly ever passed a day without pain. In the intermissions of his sufferings, however, his spirit was such that he was constantly bent on some new discovery. {17}

In the beginning of 1646 an accident happened which had important consequences both to Pascal and his sisters. Étienne Pascal fell upon the ice and severely sprained his foot. During his confinement he was attended by two brothers who had acquired repute in the treatment of such injuries. They were gentlemen of family in the neighbourhood, who had devoted themselves to medicine and anatomy from benevolent instincts and the love of these studies. Both were disciples of a clergyman at Rouville, who was an enthusiastic pietist and friend of St Cyran. Crowds flocked to hear Pastor Guillebert whenever he preached, and many were stirred by his eloquence to devote themselves to pious and philanthropical labours. One of the brothers under this inspiring guidance built a hospital at the end of his park, and gave his children to the service of the Church in various capacities. The other brother, who had no children, provided beds in the hospital and attended the sick poor.

The character and conversation of these men made a deep impression upon the Pascal family. Hitherto esteemed pious, they had not yet made religion an anxious concern in their lives. Madame Périer says expressly of her brother that he had been preserved by the special protection of God from all youthful vices, and, what was still more remarkable in the case of a mind of such strength and pride, he had never yielded to any libertinism of thought, but had always limited his curiosity to natural inquiries. He attributed, according to her statement, this religious sobriety of mind to the instructions and example of his father, who had a great respect for religion, and who had impressed upon him from his infancy the maxim, that whatever is the object of faith cannot be the object of reason, and still less the subject of it. He had seen, in his father, the combination of scientific attainment with a strong reasoning power, and the maxim therefore fell with weight from his lips. And so, when he listened to the discourses of free-thinkers, young as he was

He remained unmoved by them, and simply looked upon them as men who had adopted the false principle that the human reason is above everything, and who know nothing of the real nature of faith; so that this spirit, so great and inquisitive, which searched so carefully for the reason of everything, was at the same time submissive as a child to all the truths of religion, and this submissive simplicity predominated in him through his whole life. {18}

This is a significant extract in more ways than one. In the meantime we quote it as indicating the religious atmosphere of Pascals home, and the pious temper which marked him from the first. But as yet religion had not taken hold of him with an absorbing enthusiasm. It had its place in his thoughts, and this a deeply respectful place; but now, about his twenty-third year, in communication with the two friends we have mentioned, and under the same influence which had moved them so deeply, it began to lay hold of him more powerfully. He and his father and sisters read eagerly the books of St Cyran, and of Jansen, the Bishop of Ypres, whose name became so conspicuous in connection with Port Royal. A discourse by the latter on The Reformation of the Inward Man, and also Arnaulds Manual on Frequent Communion, are supposed to have specially impressed him. In the language of his sister

Providence led him to the study of such pious writings while he was not yet twenty-four years of age; and God so enlightened him by this course of reading, that he came to realise that the Christian religion obliges us to live only for God, and to have no other object besides Him. So clear and necessary appeared this truth to him, that he gave up for a time all his researches, renounced all other knowledge, and applied himself alone to the one thing needful spoken of by our Lord.

This event is spoken of by Pascals biographers as his first conversion, and it appears to have been attended not only with a zealous consecration of his own powers to the service of religion, but moreover, as often happens in the case of youthful enthusiasm, with a warm determination against all who seemed to him to be acting at variance with the true faith. Although, as his sister says, he had made no special study of scholastic theology, he was not ignorant of the judgments of the Church against the heresies invented by human subtlety. All indications of heretical opinion excited his indignation, and God gave him at this time an opportunity of testifying his zeal on behalf of religion. She then adds in illustration the following story:

There was at Rouen at this time a man who taught a new philosophy which attracted the curious. My brother, pressed by two of his young friends, accompanied them to hear this man; but they were greatly surprised when they found, in conversation with him, that he drew consequences from his philosophy at variance with the decisions of the Church. He sought to prove by his arguments that the body of Jesus Christ was not formed of the blood of the Holy Virgin, but of some other matter specially created, and several other like subjects. They pointed out to him his error, but he remained firm in his opinions. Thereupon, taking into consideration how dangerous it was to leave the instruction of youth in the hands of a man with such erroneous opinions, they resolved, after previously informing him of their intention, to denounce him if he continued in his errors. So it happened; for he despised their advice, and in such a manner, as to leave them no alternative but to denounce him to M. du Bellay, {20} who was then discharging episcopal functions in the diocese of Rouen for the Archbishop. M. du Bellay sent for the man, and having interrogated him, was deceived by an equivocal confession of faith which he wrote and subscribed. Otherwise he made little account of the affair as reported by the three young men. However, when they saw the confession of faith, they at once recognised its defects, and entered into communication with the Archbishop himself, who, having examined into the matter, saw its gravity, and sent in writing a special order to M. du Bellay to make the man retract all the points of which he was accused, and to receive nothing from him except by communication of his accusers. The order was carried out, and the result was that he appeared in the council of the Archbishop and renounced all his errorsit may be said sincerely, for he never showed any anger towards those who had engaged in the affair, so as to lead one to suppose that he had been himself deceived by the false conclusions which he had drawn from false principles. It was made plain that his accusers had no design of injuring him, but only of undeceiving him, and so preventing him from seducing the young, who were incapable of distinguishing the true from the false in such subtle questions.

This story reflects somewhat doubtfully on Pascals fairness and good sense, even as told by Madame Périer. But it has not been left in the vagueness in which it stands in her narrative. M. Cousin published for the first time full details regarding it in the volume by which he may be said to have initiated the new researches into the life and writings of Pascal. These details, which fill more than forty pages of appendix to M. Cousins volume, {21} are no longer of any interest in themselves; but they enable us to understand more clearly the conduct of Pascal and his two friends. Unhappily they deepen rather than lighten the shade which the story throws upon Pascals intemperate zeal. The name of the accused teacher was Jacques Forton, a Capucin monk, known as the Père St Ange. He taught no new philosophy; but he had communicated to Pascal or his friends, in private conversation specially desired by them, certain theological opinions which he had espoused. These, as given in the statement of the case signed by Pascal and his two friends, mainly concern such abstruse subjects as the relation of reason and faith, and the possibility of demonstrating the doctrine of the Trinity as the source of all other knowledge. The curious question as to the constitution of the body of Jesus occupies only a subordinate place. The monk, as shown in the whole proceedings, was evidently more of a speculative dreamer than a heretica man fond of disputation about matters beyond his comprehension. It is mentioned by the three youthful zealots, in the récit bearing their signature, that as they were about to part with him, after the accustomed civilities, he was careful to let them know that he advanced the points in dispute, not as dogmas, but merely as propositions or thoughts for discussion, the fruit of his own reasonings.

There is no reason to doubt that Pascals conduct on this occasion arose entirely from honest zeal. He thought religion compromised by the strange reasonings which he had heard. There is as little doubt, however, that his zeal outran his discretion. He showed a determination to pursue the matter amounting to persecution. The worthy priest had evidently no intention of promulgating heresy; for he is glad, when called upon, of an opportunity of proving his orthodoxy. With this view he produced, side by side with the articles of accusation, passages from a former volume of his which had been printed with official sanction. Pascal still demurred, even with this evidence before him. A second declaration was obtained from the priest, and the bishop refused to go further. The sympathies of the community were evidently against the youthful zealots; and finally Pascals father, convinced that enough had been done to vindicate the truth, successfully interposed as mediator. {23a}

Pascals health about this period appears to have undergone a change for the worse. He suffered from excessive headache and great internal heat and pain. A singular characteristic of his malady was his inability to swallow water unless it was heated, and even then only drop by drop. He was the subject, also, of a remarkable paralytic seizure thus described by his niece:

He fell, she says, into a very extraordinary state, as the result of his great application to his scientific studies; for the senses (les esprits) having mounted strongly to the brain, he became in a manner paralysed from the waist downwards. His legs and feet grew cold as marble; and they were obliged every day to put on socks soaked in brandy in order to try and restore heat in his feet. At the same time the physician interdicted him from all study. {23b}

M. Lélut {23c} explains at length this attack of Pascals as a well-known form of dynamical paralysis, of a similar nature with hypochondria and hysteria, proceeding from a disordered state of the nervous affections, the result of overwork acting upon a delicate organisation. The result is temporary, as distinguished from the paralysis arising from organic lesion, but indicates a highly susceptible constitution, the ready prey of melancholy and imaginative exaggeration, to which, in M. Léluts opinion, Pascal was more or less liable during the remaining years of his life.



CHAPTER II. PASCALS SCIENTIFIC DISCOVERIES.

Pascals scientific studies may be said to have begun with the remarkable incident of his youth already related, when he elaborated for himself, in a solitary chamber without books, thirty-two propositions of the first book of Euclid. On the other hand, these studies may be said to have extended to his closing years, when (in 1658 and 1659) he reverted to the abstruser mathematics, and made the cycloid a subject of special thought. But his scientific labours were in the main concentrated in the eight or ten years of his life which followed the removal of the family to Rouen. It will be convenient, therefore, to notice these labours and discoveries in a single chapter here, which will, at the same time, carry on the main history of his life during these years. All that can be expected from the present writer is a slight sketch of this part of the subject, which indeed is all that would be interesting to the general reader.

At the age of sixteen Pascal had already acquired a scientific reputation. He is spoken of by the Duchess dAiguillon, in the interview with Richelieu in which she pleaded the cause of the exiled father, as very learned in mathematics; and when his sister presented him after the dramatic representation on that occasion, the Duchess gave him great commendation for his scientific attainments. {26a} When allowed by his father to pursue the natural bent of his genius, he made extraordinary progress. He was still only twelve years of age, but Euclids Elements, as soon as put into his hands, were mastered by him without any explanation. By-and-by he began to take an active part in the scientific discussions which took place at his fathers house; and his achievement in Conic Sections has been already narrated.

Descartess incredulity was not without reason; but there is no room to doubt the fact. The little treatise, Pour les Coniques, still survives. It bears the date of 1640, and occupies only six pages. {26b} After a very clear statement of his subject, the writer modestly concludes:

We have several other problems and theorems, and several consequences deducible from the preceding; but the mistrust which I have of my slight experience and capacity does not permit me to advance more till my present effort has passed the examination of able men who may oblige me by looking at it. Afterwards, if they think it has sufficient merit to be continued, we shall endeavour to push our studies as far as God will give the power to conduct them.

It is interesting to notice the beginning of relations betwixt Descartes and Pascal, considering the jealousy that afterwards arose betwixt them. There is something of this feeling from the first in the older philosopher, who was now in the forty-fourth year of his age, and in the full zenith of his great reputation. He appears to have been greatly fascinated by Pascals peculiar powers; but the men were of too marked individuality of character, and too divergent in intellectual sympathy and personal aspiration, to appreciate each other fully.

Pascals next achievement was the invention of an arithmetical machine, chiefly prompted by a desire to assist his father in his official duties at Rouen. He has given us no description of this machine from his own pen. In the Avis addressed to all whose curiosity was excited by it, he excuses himself from this task by the natural remark that such a description would be useless without entering into a number of technical details unintelligible to the general reader; and that an actual inspection of it, combined with a brief vivâ voce explanation, would be far more satisfactory than any lengthened account in writing. There is an elaborate description, however, of the machine, by Diderot, in the first volume of the Encyclopédie, which is reprinted in the collection of Pascals scientific works. Pascals main difficulties occurred, not in connection with the invention itself, which he seems to have very soon perfected according to his own conception, but with the construction of the instrument after he had mentally worked it out in all its details. These difficulties proved so great, and so many imperfect specimens of the instrument were made, that, in order to secure both his reputation and his interest, he acquired in 1649 a special privilége du Roi, which confined the manufacture of the machine to himself, and such workmen as he should employ and sanction. All others, of whatever quality and condition, were prohibited from making it, or causing it to be made, or selling it. But neither these precautions nor the merits of the invention itself, which were admitted by all competent judges, were of avail to make the instrument a practical success. Many men of mathematical and mechanical genius in different countries have applied themselves to the same task. The celebrated Leibnitz is said to have constructed a machine excelling Pascals in ingenuity and power. In our own time, Mr Babbages wonderful achievement in the same direction attracted wide attention, and has been lavishly eulogised by Sir David Brewster and others:

While all previous contrivances, says Sir David, {28a} performed only particular arithmetical operations, under a sort of copartnery between the man and the machine, the extraordinary invention of Mr Babbage actually substitutes mechanism in the place of man. A problem is given to the machine, and it solves it by computing a long series of numbers following some given law. In this manner it calculates astronomical, logarithmic, and navigation tables, as well as tables of the powers and products of numbers. It can integrate, too, innumerable equations of finite differences; and, in addition to these functions, it does its work cheaply and quickly; it corrects whatever errors are accidentally committed, and it prints all its calculations.

Notwithstanding this brilliant picture, the great expense and the complications involved in the construction of such an instrument have seriously interfered with its success. It is said that Mr Babbages machine, much more his marvellous analytic engine, have never yet been properly constructed. {28b}

Pascal fortunately turned his thoughts into a new and more fruitful channel. We have now to contemplate him as one of an illustrious band associated in a great discovery in physical science. Before his time considerable progress had been made towards a knowledge of atmospheric pressure. Galileo and his pupil Torricelli had both been busy with the subject. To Pascal, however, remains the glory of carrying successfully to a conclusion the suggestion of Torricelli, and of verifying the results which he had indicated. Here, as in almost all such discoveries, it is found that different minds have been actively pursuing the same or similar lines of thought and observation, and controversy has arisen as to the exact merits of each; but Pascal has himself so candidly explained {29a} how far he was indebted to his great Italian predecessors, and how far he made original experiments of his own, that both his relation to them and his own work stand clearly apparent.

It had been found by the engineers engaged in the construction of fountains for Cosmo dei Medici in Florence that they could not raise water in an ordinary pump more than thirty-two feet above the reservoir. The water, having reached this height, would rise no higher. Galileo was appealed to for a solution of the difficulty. {29b} Imbued with the ancient notion that Nature abhors a vacuum, and that this was, as then prevalently believed, the explanation of the water following the elevation of the piston in the pump, the philosopher replied in effect that there were limits to the action of this principle, and that Natures abhorrence of a vacuum did not extend beyond thirty-two feet. He was himself, it need hardly be said, dissatisfied with such a reply, and accordingly he invited his pupil, Torricelli, to investigate the subject. The latter very soon found that the weight of the water was concerned in the result. He made experiments with a heavier fluidmercuryand ascertained that a column of mercury enclosed in a tube three feet in length hermetically sealed at the lower end, and closed with the finger at the top, on being inserted in a basin of the same liquid and the finger withdrawn, stood at a height of about 28 inches in the basin. As the specific gravities of water and mercury were in the ratio of 32 feet and 28 inches, he was led to the conclusion that the water in the pump and the mercury in the tube at these respective heights exerted the same pressure on the same base, and that both were of course counterbalanced by a determinate force. But what was this force? He had learned from Galileo that the air was a heavy fluid, and he was carried, therefore, directly to the further conclusion that the weight of the atmosphere was the counteracting cause in both cases; in the one, pressing upon the reservoir from which the water was drawnand in the other, on the surrounding mercury in the basin. He published his experiments and researches in 1645, but dying soon afterwards, his conclusions remained unverified.

The fame of Torricellis experiments had reached Paris as early as 1644, before their formal publication. Some one, Pascal says, had communicated them to Father Mersenneboth a religious and scientific intimate, as we have already seen, of the Pascal family. Mersenne had tried the experiments for himself, at first without success, but soon with better fortune, after he had been to Rome and had learned more fully about them. The news of these having reached Rouen in 1646, where I then was, says Pascal, {31} I made the Italian experiment, founding on Mersennes account, with great success. I repeated it several times, and in this manner satisfying myself of its accuracy, I drew certain conclusions from it, for the proof of which I made new and very different experiments in presence of four or five hundred people of all sorts, and amongst others, five or six Jesuit fathers of the College of Rouen. When his experiments became known in Paris, he adds, they were confounded with those which had been made in Italy, and the result was that some attributed to him a credit which was not his due, while others, by a contrary injustice, were disposed to take away the credit of what he had really done.

It was with the view of placing the matter in a clear light, and vindicating his own share in the train of experiments which had been made, that he published in 1647 his Nouvelles Expériences touchant le Vide, the first of his hydrostatical treatises. He was at pains to explain the distinction betwixt his own experiments and those which had been made in Italy; and not content with this, he added in express words, in an avis au lecteur, that he was not the inventor of the original experiment, but that it had been made in Italy four years before. So little, indeed, did Pascal borrow directly from Torricelli, or seek to appropriate the fruits of his researches, that he was as yet ignorant of the explanation which the Italian had suggested of the phenomenon so fully established. He saw, of course, that the old maxim of Nature abhorring a vacuum had no solid foundation; but he tried to account for the vacuum above the water and the mercury by such a supposition as the following:

That it contained no portion of either of these fluids, or of any matter appreciable by the senses; that all bodies have a repugnance to separate from a state of continuity, and admit a vacuum between them; that this repugnance is not greater for a large vacuum than a small one; that its measure is a column of water about 32 feet in height, and that beyond this limit a great or small vacuum is formed above the water with the same facility, provided that no foreign obstacle interfere to prevent it.

Pascals treatise, while still retaining so much of the old traditional physics, was made an object of lively attack by the Jesuit Rector of the College of Paris, Stephen Noël. Pascal replied to him at first directly; and then in answer to a second attackand so far also in answer to a treatise by the Jesuit, entitled Le Plein du Vide, published in 1648he made a more elaborate statement in a letter addressed to M. le Pailleur, and in a further letter addressed to Father Noël in the same year. There can hardly be any doubt that this was the commencement of Pascals hostile relations with the Jesuits. On their part, they failed not to remember in after years, and in a more serious struggle, that he was an old enemy; whilst he on his part probably drew something of the contemptuous scorn which he poured upon them from the recollection of their obstinate ignorance in matters of science.

Meanwhile, in defending himself from the attacks of ignorance, Pascal did not fail to open his own mind to fuller scientific light. As soon as the explanation of Torricelli was communicated to him, he accepted it without hesitation, and resolved to carry out a further series of experiments with the view of verifying this explanation, and of banishing for ever the scholastic nonsense of Natures abhorrence of a vacuum. If the weight of the air was really the cause which sustained the height of the mercury in the Torricellian tube, he saw at once that this height would vary at different elevations, according to the varying degree of atmospheric pressure at these elevations. He proceeded accordingly to test the result; but the higher levels around Rouen were too insignificant to enable him to draw any decisive inference. Accordingly, he communicated with his brother-in-law in Auvergne with the view of having an adequate experiment made during an ascent of the Puy de Dôme, which rises in the neighbourhood of Clermont to a height of about 3000 feet. The state of his own health prevented him from conducting the experiment personally, and M. Périer was detained by professional avocations from undertaking it immediately. But at length, in September 1648, the experiment was carried out successfully, and the results communicated to Pascal. I cannot do better than quote the account of this important event as rendered by an eminent scientific authority, {33} from M. Périers own recital of the facts in his letter to Pascal:

On the morning of Saturday, the 19th September, the day fixed for the interesting observation, the weather was unsettled; but about five oclock the summit of the Puy de Dôme began to appear through the clouds, and Périer resolved to proceed with the experiment. The leading characters in Clermont, whether ecclesiastics or laymen, had taken a deep interest in the subject, and had requested Périer to give them notice of his plans. He accordingly summoned his friends, and at eight in the morning there assembled in the garden of the Pères Minimes, about a league below the town, M. Bannier, of the Pères Minimes; M. Mosnier, canon of the cathedral church; along with MM. la Ville and Begon, counsellors of the Court of Aides, and M. la Porte, doctor and professor of medicine in Clermont. These five individuals were not only distinguished in their respective professions, but also by their scientific acquirements; and M. Périer expresses his delight at having been on this occasion associated with them. M. Périer began the experiment by pouring into a vessel 16 lb. of quicksilver, which he had rectified during the three preceding days. He then took two glass tubes, four feet long, of the same bore, and hermetically sealed at one end and open at the other; and making the ordinary experiment of a vacuum with both, he found that the mercury stood in each of them at the same level and at the height of 26 inches 3½ lines. This experiment was repeated twice, with the same result. One of these glass tubes, with the mercury standing in it, was left under the care of M. Chastin, one of the Religious of the House, who undertook to observe and mark any changes in it that might take place during the day; and the party already named set out with the other tube for the summit of the Puy de Dôme, about 500 toises (a toise is about six feet in length) above their first station. Before arriving there, they found that the mercury stood at the height of 23 inches and 2 linesno less than 3 inches and 1½ line lower than it stood at the Minimes. The party were struck with admiration and astonishment at this result; and so great was their surprise that they resolved to repeat the experiment under various forms. The glass tube, or the barometer, as we may call it, was placed in various positions on the summit of the mountainsometimes in the small chapel which is there; sometimes in an exposed and sometimes in a sheltered position; sometimes when the wind blew, and sometimes when it was calm; sometimes in rain, and sometimes in a fog: and under all these various influences, which fortunately took place during the same day, the quicksilver stood at the same height of 23 inches 2 lines. During their descent of the mountain they repeated the experiment at Lafon-de-lArbre, an intermediate station, nearer the Minimes than the summit of the Puy, and they found the mercury to stand at the height of 25 inchesa result with which the party was greatly pleased, as indicating the relation between the height of the mercury and the height of the station. Upon reaching the Minimes, they found that the mercury had not changed its height, notwithstanding the inconstancy of the weather, which had been alternately clear, windy, rainy, and foggy. M. Périer repeated the experiments with both the glass tubes, and found the height of the mercury to be still 26 inches 3½ lines. On the following morning M. de la Marc, priest of the Oratory, to whom M. Périer had mentioned the preceding results, proposed to have the experiment repeated at the top and bottom of the towers of Notre Dame in Clermont. He accordingly yielded to his request, and found the difference to be 2 lines. Upon comparing these observations, M. Périer obtained the following results, showing the changes in the altitude of the mercurial column corresponding to certain differences of altitude of position:

Difference of altitude. Changes in the height of the mercury.

Toises. Lines.

500 37½

150 15½

27 2½

7 ½

When Pascal received these results, all the difficulties were removed; and perceiving from the two last observations in the preceding table that 20 toises, or about 120 feet, produce a change of 2 lines, and 7 toises, or 42 feet, a change of ½ a line, he made the observation at the top and bottom of the tower of St Jacques de la Boucherie, which was about 24 or 25 toises, or about 150 feet high, and he found a difference of more than 2 lines in the mercurial column; and in a private house 90 steps high he found a difference of ½ a line. . . . After this important experiment was made, Pascal intimated to M. Périer that different states of the weather would occasion differences in the barometer, according as it was cold, hot, dry, or moist; and in order to put this opinion to the test of experiment, M. Périer instituted a series of observations, which he continued from the beginning of 1649 till March 1651. Corresponding observations were made at the same time at Paris and at Stockholm by the French ambassador, M. Chanut, and Descartes; and from these it appeared that the mercury rises in weather which is cold, cloudy, and damp, and falls when the weather is hot and dry, and during rain and snow, but still with such irregularities that no general rule could be established. At Clermont the difference between the highest and the lowest state of the mercury was 1 inch 3½ lines; at Paris the same; and at Stockholm 2 inches 2½ lines.

From the account here presented of these researches, there is no difficulty in determining the exact credit due to Pascal on the one hand, and his Italian predecessors on the other. He completed what they had begun, and verified what they had indicated. As the Abbé Bossut has expressed it, Galileo proved that air was a heavy fluid; Torricelli conceived that its weight was the cause of the suspension of the water in a pump and the mercury in a tube. Pascal demonstrated that this was the fact. No one was more anxious than Pascal himself that Torricelli should be acknowledged as the real discoverer of the principle which it was left to him to establish by the test of experiment. He claimed, however, his own definite share in the discovery, both as having carried on a series of independent experiments, and as having converted what he himself calls the conjecture of Torricelli into an established fact. It was painful to him, therefore, to have this share denied, and even open accusations made against him that he had appropriated, without acknowledgment, the results of Torricellis researches. This accusation was made in certain theses of philosophy maintained in the Jesuit College of Montferrand in 1651, and dedicated to Pascals own friend, M. de Ribeyre, first president at the Court of Aides at Clermont. Pascals name was not indeed mentioned in these theses; but there could be no doubt of the allusion made to certain persons loving novelty who claimed to be the inventors of a definite experiment of which Torricelli was the real author. It was this accusation which drew from Pascal his letter to M. Ribeyre, bearing the date of 12th July of the same year, in which he has described, with admirable lucidity and temper, his relations to the whole subject. In this letter he distinctly says that the Italian experiments were known in France from the year 1644; that they were repeated in France by several persons in several places during 1646; that he himself had made, as we have already seen, definite experiments in 1647, and published the results in the same year; and that he had then not mentioned the name of Torricelli, because, while he knew that the experiments were made in Italy four years before, he did not then know that the experimenter was Torricelli; but that so soon as he learned this factwhich he and his friends were so eager to know, that they sent a special letter of inquiry to Romehe was ravished with the idea that the experimenter was so illustrious a genius, whose mathematical writings, already well known, surpassed those of all antiquity. He says, in conclusion, that it was only in the same year (1647), after the publication of his own researches, that he learned the very fine thought of Torricelli concerning the cause of all the effects which had been attributed to the horror of a vacuum. But as this was only a conjecture as yet unverified, he then, with the view of ascertaining the truth or falsehood of it, conceived the plan of the experiments carried out by M. Périer at the top and the foot of the Puy de Dôme. It is true, sir, he adds, and I say it boldly, that this series of experiments was my own invention; and therefore I may say that the new knowledge thus acquired is entirely due to me.

To this letter M. Ribeyre made a satisfactory and touching reply. He expresses disapproval of the allusion of the Jesuit father, but as the discourse was otherwise free from offence, he was willing to attribute it to a pardonable emulation among savants, rather than to any intention of assailing Pascal. He makes, in short, the best excuse he can for the Jesuit, and hastens to assure Pascal that his reputation needed no justification:

Your candour and your sincerity are too well known to admit any belief that you could do anything inconsistent with the virtuous profession apparent in all your actions and manner. I honour and revere your virtue more than your science; and as in both the one and the other you equal the most famous of the age, do not think it strange if, adding to the common esteem which all have of you, a friendship contracted many years ago with your father, I subscribe myself yours, etc.

But Pascal had to sustain suspicion and attack in a quarter more formidable than that of the Jesuit fathers at Montferrand. We have already spoken of the rather unhappy commencement of relations between him and Descartes. Farther on we get a more pleasant glimpse of these relations, in a letter from Jacqueline Pascal to Madame Périer, dated 25th September 1647, and apparently shortly after Pascal had retired to Paris, along with his younger sister, leaving their father for some time still at Rouen. This letter is so interesting, both in its bearing on the question which arose between Descartes and Pascal, and in itself, as giving the only account we have of personal intercourse between these two illustrious men, that we present it almost entire:

I have delayed writing to you, Jacqueline says, addressing her sister, {39a} because I wished to tell to you at length of the interview of M. Descartes and my brother, and I had no leisure yesterday to say that on the evening of Sunday last M. Habert {39b} came, accompanied by M. de Montigny, a gentleman of Brittany, with the view of letting me know, in the absence of my brother, who was at church, that M. Descartes, his compatriot and good friend, had expressed a strong desire to see my brother, for the sake of the great esteem in which both he and my father were everywhere held, and that he begged to be allowed to wait upon him next day at nine oclock in the morning, if this would not inconvenience him, whom he knew to be an invalid. When M. de Montigny proposed this, I felt hindered from giving a definite answer, because I knew that my brother was reluctant to force himself to conversation, especially in the morning. Nevertheless, I did not think it right to refuse, so we arranged that he should come at half-past ten next day. Along with M. Habert and M. de Montigny there were also a young man in the dress of a priest, whom I did not know, M. de Montignys son, and two or three other young people. M. de Roberval, whom my brother had informed of the intended visit, was also present. After some civilities, talk fell upon the instrument [probably that which Pascal had used in the experiments], which was very much admired, while M. de Roberval showed it. Then they spoke of the idea of a vacuum; and M. Descartes, on hearing of the experiments, and being asked what he thought was within the tube (dans la seringue), said with great seriousness that it was some subtle matter, to which my brother replied what he could. M. Roberval, believing that my brother had difficulty in speaking, took up the reply to M. Descartes with some heat, yet with perfect civility. M. Descartes answered with some harshness that he would talk to my brother as much as he wished, because he spoke with reason, but not to any one who spoke with prejudice. Thereupon, finding from his watch it was mid-day, he rose, being engaged to dine at the Faubourg Saint Germain. M. Roberval also rose, in such a way that M. Descartes conducted him to a carriage, where the two were alone, and battled at one another more strongly than playfully, as M. Roberval, who returned here after dinner, told us. . . . I have forgotten to tell you that M. Descartes, annoyed at seeing so little of my brother, promised to return next day at eight oclock. . . . He desired this, partly to consult regarding my brothers illness, as to which, however, he did not communicate anything of importance, only he counselled him to remain in bed every day as long as he could till he was tired, and to take plenty of soup. They spoke of many other things, for he was here till eleven oclock, but I cannot tell you more particularly what they said, as I was not present on this occasion. We were prevented during the whole day from making him take his early bath. He had found it give him a little headache, but that was because he had taken it too late; and I believe the bleeding at the foot on Sunday had done him good, for on Monday he conversed freely and strongly all dayin the morning with M. Descartes, and after dinner with M. de Roberval, with whom he argued for a long time on many things, both belonging to theology and physics, and yet he took no further harm than perspiring much, and slept rather sound during the night.

The revelations of this letter are very curious. The respectful desire of Descartes, already so distinguished, to make Pascals acquaintance, and to enter into conversation with him; his resentment of Robervals interference, and their earnest altercation, prolonged in the carriage after leaving Pascals house; the evidently serious character of Pascals maladies, and the watchful attention of his sister. It is clear through all that Descartes had been busily occupied with the same physical problems as Pascal, and that he was somewhat jealous of the results towards which Pascal and his friends were tending. Evidently there was a certain measure of unfriendliness between Roberval and Descartes. I am unable, however, to see any traces of a coterie surrounding Pascal and inimical to Descartes, as M. Cousin suggests. {41} If such a coterie existed at this time in Paris, of which the hasty and jealous Roberval was the centre, and which delighted in abusing Descartes, and attacking him on all sides, Jacquelines frank and lively letter seems enough to show that while Roberval was Pascals friend and Descartess disputant, there was nothing in the meantime between Descartes and Pascal but courteous friendliness and a cordial feeling of mutual respect.

Descartes, however, in his retirement at Stockholm, plainly cherished the impression that Robervals intimacy with Pascal prevented the latter from doing full justice to his scientific position and suggestions; and having as yet heard nothing, in June 1649, of the special results of Pascals experiments on the Puy de Dôme in the preceding year, he wrote to his friend Carcavi to let him know about these.

I pray you, let me know of the success of an experiment which Pascal is said to have made on the mountains of Auvergne. . . . I had the right to expect this of him rather than of you, because it was I who advised him two years ago to make the experiment, and who assured him that, although I had not made it, I had no doubt of its success. But as he is the friend of M. Roberval, who professes not to be mine, I have some reason to think he follows the passions of his friend. {42a}

That letter was immediately communicated to Pascal by Carcavi, who was his intimate associate no less than Roberval. But it seems to have elicited no reply. Bossut {42b} says that he despised it. On the other hand, Descartess biographer and eulogist, Baillet, blames Pascal for having carefully kept out of view Descartess name in all the accounts of his discoveries; and produces an array of passages from Descartess letters, showing plainly that his mind was in the line of discovery finally verified by the experiments in Auvergne. {43a} It may be granted beyond doubt this was the case. It would ill become any admirer of Pascal to detract from the glory of Descartes. But it must be held no less firmly, that in the personal question raised by Descartess letter, the balance of evidence is all in favour of Pascal. There are no indications that the two men ever met save on the occasion so frankly described by his sister Jacqueline. Before this Pascal had not only been busy with the subject, but says distinctly that he had meditated the experiment finally made on the Puy de Dôme from the time that he published his first researches. {43b} It was not, indeed, till about six weeks after Descartess visit, or on the 15th December 1647, that he communicated with M. Périer regarding these experiments, and his earnest desire that they should be made; and it was not till the following September, or about a year after Descartess visit, that they were actually made. But it is incredible that Pascal could have written as he did if he had really, for the first time, been indebted to Descartes for the suggestion. Descartess name is not mentioned in his correspondence with M. Périer, nor in any of his writings on the subject; and the delay in making the experiments is sufficiently explained by the facts stated by himself, that they could only be made effectually at some place of greater elevation than he could commandsuch as Clermont, at the foot of the Puy de Dômeand by some person, such as M. Périer, on whose knowledge and accuracy he could rely. If we add to this the force of the statement already quoted from his letter to M. Ribeyre, four years afterwards, or in 1651, that he claimed the experiments as entirely his own invention, and that he did so boldly, the case seems put beyond all doubtunless we are to suppose the author of the Provincial Letters and the Thoughts capable of wilful suppression of the truth. On the other hand, it is unnecessary to attribute to Descartes anything beyond a mistaken opinion of the value of certain statements which he had no doubt made to Pascal, and possibly some confusion of memory. And that this is not an unwarranted view appears from what he says in a subsequent letter to M. Carcavi, on the 17th August of the same year, 1649that he was greatly interested in hearing of the success of the experiments, having two years before besought Pascal to make them, and assured him of successbecause the supposed explanation was one, he adds, entirely consistent with the principles of my philosophy, apart from which he [Pascal], would not have thought of it, his own opinion being quite contrary. {44} This may or may not be true. Pascal certainly held as long as he could to the old maxim of Natures abhorrence of a vacuum. I do not think it allowable, he says in his letter to M. Périer, to depart lightly from maxims handed down to us by antiquity, unless compelled by invincible proofs. But the notions of Descartes on the subject of a vacuum were at least as confused as those originally held by Pascal. {45a} It is absurd, therefore, to suppose that the latter could have been indebted to the principles of the Cartesian philosophynot to say that this is a very different suggestion from that of the former letter, that Descartes himself had advised the experiment to be made. Evidently the older philosopher wrote under vague and somewhat inflated ideas of the value of his labours and his conversation with Pascal; while the latter, again, absorbed in his own thoughts on the subject, and unconscious that he had received any special impulse from Descartes or his philosophy, naturally made no mention of his name. His silence when Descartess accusation was communicated to him indicates the same somewhat lofty reserve and confidence in the independence of his own researches, rather than any contempt. He felt too sure of his position to think of defending himself, or of repelling what he no doubt regarded as not so much a deliberate assault on the value of his own work, as an exaggerated estimate by the other of his share in that work.

Pascals researches regarding atmospheric pressure conducted him gradually to the examination of the general laws of the equilibrium of fluids. {45b} It had been already determined that the pressure of a fluid on its base is as the product of the base multiplied by the height of the fluid, and that all fluids press equally on all sides of the vessels enclosing them. But it still remained to determine exactly the measure of the pressure, in order to deduce the general conditions of equilibrium. With the view of ascertaining this, Pascal made two unequal apertures in a vessel filled with fluid, and enclosed on all sides. He then applied two pistons to these apertures, pressed by forces proportional to the respective apertures, and the fluid remained in equilibrio. Having established this truth by two methods equally ingenious and satisfactory, he deduced from it the different cases of the equilibrium of fluids, and particularly with solid bodies, compressible and incompressible, when either partly or wholly immersed in them.

But the most remarkable part of his treatise on the Equilibrium of Fluids, continues Sir David Brewster, from whose exposition we quote, {46a} and one which of itself would have immortalised him, is his application of the general principle to the construction of what he calls the mechanical machine for multiplying forces, {46b}an effect which, he says, may be produced to any extent we choose, as one may by means of this machine raise a weight of any magnitude. This new machine is the Hydrostatic Press, first introduced by our celebrated countryman, Mr Bramah.

Pascals treatise on the weight of the whole mass of air forms the basis of the modern science of Pneumatics. In order to prove that the mass of air presses by its weight on all the bodies which it surrounds, and also that it is elastic and compressible, a balloon half filled with air was carried to the top of the Puy de Dôme. It gradually inflated itself as it ascended, and when it reached the summit it was quite full and swollen, as if fresh air had been blown into it; or what is the same thing, it swelled in proportion as the weight of the column of air which pressed upon it diminished. When again brought down, it became more and more flaccid, and, when it reached the bottom, it resumed its original condition. In the nine chapters of which the treatise consists, he shows that all the phenomena or effects hitherto ascribed to the horror of a vacuum, arise from the weight of the mass of air; and after explaining the variable pressure of the atmosphere in different localities, and in its different states, and the rise of the water in pumps, he calculates that the whole mass of air round our globe weighs 8,983,889,440,000,000,000 French pounds.

Having thus completed his researches respecting elastic and incompressible fluids, Pascal seems to have resumed with a fatal enthusiasm his mathematical studies: but, unfortunately for science, several of the works which he composed have been lost. Others, however, have been preserved, which entitle him to a high rank amongst the greatest mathematicians of the age. Of these, his Traité du Triangle Arithmétique, his Tractatus de Numericis Ordinibus, and his Problemata de Cycloide, are the chief. By means of the Arithmetical Triangle, an invention equally ingenious and original, he succeeded in solving a number of theorems which it would have been difficult to demonstrate in any other way, and in finding the coefficients of different terms of a binomial raised to an even and positive power. The same principles enabled him to lay the foundation of the doctrine of probabilities, an important branch of mathematical science, which Huyghens, a few years afterwards, improved, and which the Marquis la Place and M. Poisson have so greatly extended. These treatises, with the exception of that on the Cycloid, were composed and printed in the year 1654, but were not published till 1668, after the death of the author.

Pascals discoveries as to the cycloid belong to a later period of his life, after he had long forsaken the scientific studies which engrossed him at this time, and had become an inmate of Port Royal. But, as we have already said, it is well to complete our view of his scientific labours in a single chapter.

During an access of severe toothache which, in 1658, deprived him of sleep, his thoughts fastened on certain problems connected with the cycloid. Fermat, Roberval, and Torricelli had all been occupied with the subject, and made some definite progress in ascertaining its properties. But much still remained to be done, and especially to resolve the problems connected with it in a general and uniform manner. Pascal, says Bossut, devised within eight days, and in the midst of cruel sufferings, a method which embraced all the problemsa method founded upon the summation of certain series, of which he had given the elements in his writings accompanying his Traité du Triangle Arithmétique. From this discovery there was only a step to that of the Differential and Integral Calculus; and it may be confidently presumed that, if Pascal had proceeded with his mathematical studies, he would have anticipated Leibnitz and Newton in the glory of their great invention.

Having communicated the result of his geometrical meditation to the Duc de Roannez and some of his other religious friends, they conceived the design of making it subservient to the triumph of religion. Pascal himself was an illustrious example that the highest mathematical genius and the humblest Christian piety might be united; but in order to give éclat to such an example, his friends proposed to propound publicly the questions solved by the great Port Royalist in his moments of suffering, and to offer prizes for the best solutions given of them. This they did in June 1658. A programme was published making the offer of prizes of forty and twenty pistoles, for the best determination of the area and the centre of gravity of any segment of the cycloid, and the dimensions and centres of gravity of solids and half and quarter solids which the same curve would generate by revolving round an abscissa and an ordinate. The programme was put forth in the name of Amos Dettonville, the anagram of Pascals assumed name as the writer of the Provincial Letters. Huyghens, Sluzsius, a canon of the Cathedral of Liège, and Wren, the architect of St Pauls, sent in partial solutions of the problemsthose of Wren especially attracting the interest of both Fermat and Roberval. But Wallis, of Oxford, and Lallouère, a Jesuit of Toulouse, were the only two competitors who treated all the problems proposed. It was held that they had not completely succeeded in solving them; and Dettonville published his own solution in an elaborate letter addressed to M. Carcavi, and in a treatise on the subject. Carcavi was an old friend of Pascals father as well as of himself; and being a lawyer as well as a mathematician, the arrangement of the affair seems to have been intrusted to him. This did not save him, however, from attacks by the disappointed candidates, who accused him of unfairness; and Leibnitz has given his decision that both Wallis and Lallouère, in the treatises which they published,which did not, however, appear till after Pascals,had succeeded in solving the problems. Upon such a point we cannot pretend to judge; but it may be safely said that the design of the Duc de Roannez was hardly realised in the issue. It was sufficiently proved, indeed, that Pascal, in the midst of all his austerities and devotional exercises, was the same Pascal who had held his own both with Descartes and with the Jesuits. But the life of thought which survived in him no sooner touched the outer world of intellectual ambition, than it flamed forth into something of the passion of controversy which his pen had already kindled in another direction. Religion is best vindicated, not in the strifes of science, but by the beauty of its own activities.

Pascals labours on the cycloid may be said to bring to a close his scientific career. There is still one invention, however, of a very practical kind, associated with the very last months of his life. Amongst the letters of Madame Périer, there is one of date March 24, 1662, addressed to M. Arnauld de Pompone {50}a nephew of the great Arnauldin which she gives a lively description of the success of an experiment dans laffaire des carrosses. The affair was nothing less than the trial on certain routes in Paris of what is now known as an omnibus; and the idea of such conveyances for the publiccarrosses à cinq sols, as they were calledis attributed to Pascal. It is certain that the privilege of running carrosses à cinq sols was granted to Pascals friend, the Duc de Roannez, and to other noblemen, by royal patent, in January 1662,and that the experiment, as described by Madame Périer, was made with great success in the following March, and that Pascal had an active interest in the undertaking. His sister tells that he had mortgaged his share of its first years profits in order to provide for the poor at Blois; {51} and a note from his own hand, appended to his sisters letter, shows with what eagerness he entered into the affair and hailed its success. It is singular to connect the name of Pascal, and that, too, during the last sad months of his life, with so world-wide a commonplace as the omnibus.



CHAPTER III. PASCAL IN THE WORLD.

Pascals health, we have seen, was very delicate. His labours to perfect his arithmetical machine had seriously impaired it. The attack of partial paralysis, described by his niece, seems to have taken place in the early summer of 1647. As soon as he was able, he removed to Paris, where we find him settled with his younger sister in September of the same year. It was on the twenty-fifth of this month that Jacqueline writes from Paris of Descartess memorable visits. One of the motives of his change of residence was no doubt to consult the best physicians of the day; and Descartes, who, amongst his other numerous gifts, had some skill in medicine, made his second visit to him partly as a physician. He came in part, says Jacqueline, to consult as to my brothers illness. He appears to have given him very sound advice, which, unfortunately, Pascal did not followto lie in bed as much as he could, and take strong soup. On the contrary, he was bled, bathed, and purged, after the usual medical routine of the time, apparently without any good effects, or any alleviation of his sufferings.

The father also returned to Paris in May 1648. The Provincial Parliament, with regained authority, had exacted the recall of the Intendants appointed by the Court. Étienne Pascals services were remunerated by the dignity of a Counsellor of State, and he was set at liberty to rejoin his children. It was at this period that the struggle took place betwixt father and daughter as to the latters determination to choose a religious life. Encouraged by her brother after his access of zeal at Rouen, Jacqueline was gradually more and more drawn towards piety. After their settlement in Paris they went frequently together to the Church of Port Royal de Paris, to listen to the sermons of M. Singlin, whose touching pictures of the beauty and perfection of the Christian life awoke in the youthful enthusiast the desire of entering Port Royal. She opened personal communications with the sainted head of the House, the Mère Angélique, and also with M. Singlin, who recognised in her all the marks of a true vocation, but who would not allow her to proceed further without her fathers consent and approval. The brother at this time strongly sympathised with her aspirations, and favoured them. On the fathers arrival in Paris, the design of his daughter was imparted to him. He was greatly surprised and moved by the propositionpleased, on the one hand, by his daughters devotion, and yet deeply wounded by the idea of parting with her. He took time for consideration, and at length made up his mind that it was impossible to give his consent. Not only so, but he strongly blamed his son, who had broken the matter to him, for encouraging his sisters design without first ascertaining whether it would be agreeable to himself, and he seems for the time to have felt so much distrust in them both, that he instructed an old domestic, who had been with them from their youth, to watch over their actions. This is the narrative of Madame Périer; {54a} and the unpleasantness which arose out of this event appears also implied in Jacquelines letter to her sister in the spring of the same year. {54b}

In 1649 the Pascal family left Paris for Auvergne, and seem to have remained there for about a year and a half. Madame Périer says nothing of this visit, so far as her brother is concerned, beyond the fact that he accompanied Jacqueline and her father. The likelihood, however, is, that the visit was in some degree prompted by a regard for Pascals health. He had made in Paris some progress towards recovery, notwithstanding the severity of his treatment. But he was still far from well, and it was judged necessary, in order to re-establish him entirely, that he should abandon every sort of mental occupation, and seek, as much as he could, opportunities of amusing himself. Her brother, she adds, was very reluctant to take this advice, because he saw its danger. At length, however, he yielded, considering himself obliged to do all he could to restore his health, and because he thought that trivial amusements could not harm him. So he set himself on the world. When this definite change in Pascals life began is left uncertain, but there are indications that he had largely abandoned his studies in 1649 and the following year. During these years there is nothing from his pen. The interval between the recital of the experiments on the Puy de Dôme (1648), and his letter to M. Ribeyre, 12th July 1651, is blank in any record of scientific or literary labour. This is not conclusive, of course, that he was idle; but taken in connection with the remarks of his sister, and the retirement to Auvergne, it suggests that the family may have sought there, in rural isolation and domestic reunion, the means of entirely withdrawing Pascal from his severer studies, and the scientific companions who were constantly prompting them in Paris. It may be, also, that the father sought the means of withdrawing Jacqueline from the neighbourhood of Port Royal, and from the equally exciting associations to her connected with that neighbourhood.

Of Pascals life at this time in Auvergne we know nothing, or next to nothing. There is, indeed, a single trace, of which the most has been made, in the Memoirs of Fléchier, describing his stay at Clermont in 1665 and 1666, a few years after Pascals death. In these Memoirs, Fléchier relates an anecdote of a young lady who was the Sappho of the country, and greatly beloved by all the beaux esprits of the time. Amongst others, M. Pascal, who had then acquired so much reputation, and another savant, were continually with this belle savante. It is difficult to know what to make of this vague if piquant anecdote. Some of Pascals more religious admirers have even been scandalised by it, and have tried to show that it could not refer to the author of the Pensées. M. Cousin and other parties have emphasised it too much. {55} There seems no reason to doubt that the anecdote relates to the younger Pascalit cannot reasonably be supposed to relate to his father. Nor is there any ground to suppose that Pascal was less likely to be interested in a beautiful and accomplished demoiselle than any other young man of his age. On the contrary, there is some reason to think him at this time peculiarly susceptible to the charms of female companionship. The passing glimpse which the story gives of his occupations in Auvergne, and the comparative brightness and leisure in which it seems to set his life for a little, are pleasing. It suggests the idea that the change to the country had worked successfully, and that with rest and retirement from Paris his health had greatly benefited.