Part 2 (1/2)

Descartes, however, in his retirement at Stockholm, plainly cherished the impression that Roberval's 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 Pascal's experiments on the Puy de Dome 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 a.s.sured 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 pa.s.sions of his friend_.”

{42a}

That letter was immediately communicated to Pascal by Carcavi, who was his intimate a.s.sociate no less than Roberval. But it seems to have elicited no reply. Bossut {42b} says that he despised it. On the other hand, Descartes's biographer and eulogist, Baillet, blames Pascal for having carefully kept out of view Descartes's name in all the accounts of his discoveries; and produces an array of pa.s.sages from Descartes's 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 Descartes's 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 Dome from the time that he published his first researches. {43b} It was not, indeed, till about six weeks after Descartes's visit, or on the 15th December 1647, that he communicated with M. Perier 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 Descartes's 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. Descartes's name is not mentioned in his correspondence with M. Perier, 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 command-such as ”Clermont, at the foot of the Puy de Dome”-and by some person, such as M. Perier, 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 doubt-unless 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, 1649-that he was greatly interested in hearing of the success of the experiments, having two years before besought Pascal to make them, and a.s.sured him of success-because 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 ”Nature's abhorrence of a vacuum.”

”I do not think it allowable,” he says in his letter to M. Perier, ”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 philosophy-not 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 Descartes's 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 a.s.sault on the value of his own work, as an exaggerated estimate by the other of his share in that work.

Pascal's 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.

”Pascal's treatise on the weight of the whole ma.s.s of air forms the basis of the modern science of Pneumatics. In order to prove that the ma.s.s 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 Dome. 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. .h.i.therto ascribed to the horror of a vacuum, arise from the weight of the ma.s.s 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 ma.s.s 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 ent.i.tle him to a high rank amongst the greatest mathematicians of the age. Of these, his 'Traite du Triangle Arithmetique,' 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.”

Pascal's 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 problems-a method founded upon the summation of certain series, of which he had given the elements in his writings accompanying his 'Traite du Triangle Arithmetique.' 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 antic.i.p.ated 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 ill.u.s.trious example that the highest mathematical genius and the humblest Christian piety might be united; but in order to give _eclat_ 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 Pascal's a.s.sumed name as the writer of the 'Provincial Letters.'

Huyghens, Sluzsius, a canon of the Cathedral of Liege, and Wren, the architect of St Paul's, sent in partial solutions of the problems-those of Wren especially attracting the interest of both Fermat and Roberval.

But Wallis, of Oxford, and Lallouere, a Jesuit of Toulouse, were the only two compet.i.tors 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 Pascal's 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 Lallouere, in the treatises which they published,-which did not, however, appear till after Pascal's,-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 pa.s.sion 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.

Pascal's 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, a.s.sociated with the very last months of his life.

Amongst the letters of Madame Perier, there is one of date March 24, 1662, addressed to M. Arnauld de Pompone {50}-a nephew of the great Arnauld-in which she gives a lively description of the success of an experiment ”dans l'affaire 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 public-”carrosses a cinq sols,” as they were called-is attributed to Pascal. It is certain that the privilege of running ”carrosses a cinq sols” was granted to Pascal's friend, the Duc de Roannez, and to other n.o.blemen, by royal patent, in January 1662,-and that the experiment, as described by Madame Perier, 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 year's profits in order to provide for the poor at Blois; {51} and a note from his own hand, appended to his sister's 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.

Pascal's 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 Descartes's 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 brother's illness.” He appears to have given him very sound advice, which, unfortunately, Pascal did not follow-”to 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. etienne Pascal's 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 latter's 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 Mere Angelique, 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 father's consent and approval. The brother at this time strongly sympathised with her aspirations, and favoured them. On the father's arrival in Paris, the design of his daughter was imparted to him. He was greatly surprised and moved by the proposition-pleased, on the one hand, by his daughter's 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 sister's 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 Perier; {54a} and the unpleasantness which arose out of this event appears also implied in Jacqueline's 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 Perier 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 Pascal's 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 amus.e.m.e.nts could not harm him. So he set himself on the world.” When this definite change in Pascal's 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 Dome (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 a.s.sociations to her connected with that neighbourhood.

Of Pascal's 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 Flechier, describing his stay at Clermont in 1665 and 1666, a few years after Pascal's death. In these Memoirs, Flechier 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 Pascal's more religious admirers have even been scandalised by it, and have tried to show that it could not refer to the author of the 'Pensees.' M.