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 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 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, 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 passages 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 Dôme 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. 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 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. 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 command—such as “Clermont, at the foot of the Puy de Dôme”—and 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 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 assured 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. 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 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 assault 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 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.”