[631] Il faut savoir, quoique Galilée et quelques autres disent au contraire, que les corps qui commencent à descendre, ou à se mouvoir en quelque façon que ce soit, ne passent point par tous les degrés de tardiveté; mais que des le premier moment ils ont certaine vitesse qui s’augmente après de beaucoup, et c’est de cette augmentation que vient la force de la percussion. viii., 181.
[632] Cette proportion d’augmentation selon les nombres impairs, 1, 3, 5, 7, &c., qui est dans Galilée et que je crois vous avoir aussi écrite autrefois, ne peut être vraie, qu’en supposant deux ou trois choses qui sont très fausses, dont l’une est que le mouvement croisse par degrés depuis le plus lent, ainsi que le songe Galilée, et l’autre que la résistance de l’air n’empêche point. Vol. ix., p. 349.
[633] Je pense que la vitesse n’est pas la cause de l’augmentation de la force, encore qu’elle l’accompagne toujours. Id. p. 356, See also vol. viii., p. 14. He was probably perplexed by the metaphysical notion of causation, which he knew not how to ascribe to mere velocity. The fact that increased velocity is a condition or antecedent of augmented force could not be doubted.
Law of motion laid down by Descartes. 41. Descartes, however, is the first who laid down the laws of motion; especially that all bodies persist in their present state of rest or uniform rectilineal motion till affected by some force. Many had thought, as the vulgar always do, that a continuance of rest was natural to bodies, but did not perceive that the same principle of inertia or inactivity was applicable to them in rectilineal motion. Whether this is deducible from theory, or depends wholly on experience, by which we ought to mean experiment, is a question we need not discuss. The fact, however, is equally certain; and hence Descartes inferred that every curvilinear deflection is produced by some controlling force, from which the body strives to escape in the direction of a tangent to the curve. The most erroneous part of his mechanical philosophy is contained in some propositions as to the collision of bodies, so palpably incompatible with obvious experience that it seems truly wonderful he could ever have adopted them. But he was led into these paradoxes by one of the arbitrary hypotheses which always governed him. He fancied it a necessary consequence from the immutability of the divine nature that there should always be the same quantity of motion in the universe; and rather than abandon this singular assumption he did not hesitate to assert, that two hard bodies striking each other in opposite directions would be reflected with no loss of velocity; and, what is still more outrageously paradoxical, that a smaller body is incapable of communicating motion to a greater; for example, that the red billiard-ball cannot put the white into motion. This manifest absurdity he endeavoured to remove by the arbitrary supposition, that when we see, as we constantly do, the reverse of his theorem take place, it is owing to the air, which, according to him, renders bodies more susceptible of motion, than they would naturally be.
Also those of compound forces. 42. Though Galileo, as well as others, must have been acquainted with the laws of the composition of moving forces, it does not appear that they had ever been so distinctly enumerated as by Descartes, in a passage of his Dioptrics.[634] That the doctrine was in some measure new may be inferred from the objections of Fermat; and Clerselier, some years afterwards, speaks of persons “not much versed in mathematics, who cannot understand an argument taken from the nature of compound motion.”[635]
[634] Vol. v., p. 18.
[635] Vol. vi., p. 508.
Other discoveries in mechanics. 43. Roberval demonstrated what seems to have been assumed by Galileo, that the forces on an oblique or crooked lever balance each other, when they are inversely as the perpendiculars drawn from the centre of motion to their direction. Fermat, more versed in geometry than physics, disputed this theorem which is now quite elementary. Descartes, in a letter to Mersenne, ungraciously testifies his agreement with it.[636] Torricelli, the most illustrious disciple of Galileo, established that when weights balance each other in all positions, their common centre of gravity does not ascend or descend, and conversely.
[636] Je suis de l’opinion, says Descartes, de ceux qui disent que pondera sunt in æquilibrio quando sunt in ratione reciproca linearum perpendicularium, &c., vol. xi., p. 357. He would not name Roberval; one of those littlenesses which appear too frequently in his letters and in all his writings. Descartes in fact could not bear to think that another, even though not an enemy, had discovered anything. In the preceding page he says: C’est une chose ridicule que de vouloir employer la raison du levier dans la poulie, ce qui est, si j’ai bonne mémoire, une imagination de Guide Ubalde. Yet this imagination is demonstrated in all our elementary books on mechanics.
In Hydrostatics and pneumatics. 44. Galileo, in a treatise entitled, Delle Cose che stanno nell’Acqua, lays down the principles of hydrostatics already established by Stevin, and among others what is called the hydrostatical paradox. Whether he was acquainted with Stevin’s writings, may be perhaps doubted; it does not appear that he mentions them. The more difficult science of hydraulics was entirely created by two disciples of Galileo, Castellio and Torricelli. It is one everywhere of high importance, and especially in Italy. The work of Castellio, Della Misura dell’Acque Correnti, and a continuation, were published at Rome, in 1628. His practical skill in hydraulics, displayed in carrying off the stagnant waters of the Arno, and in many other public works, seems to have exceeded his theoretical science. An error, into which he fell, supposing the velocity of fluids to be as the height down which they had descended, led to false results. Torricelli proved that it was as the square root of the altitude. The latter of these two was still more distinguished by his discovery of the barometer. The principle of the syphon or sucking-pump, and the impossibility of raising water in it more than about thirty-three feet, were both well known; but even Galileo had recourse to the clumsy explanation that nature limited her supposed horror of a vacuum to this altitude. It occurred to the sagacity of Torricelli that the weight of the atmospheric column pressing upon the fluid which supplied the pump was the cause of this rise above its level; and that the degree of rise was consequently the measure of that weight. That the air had weight was known, indeed, to Galileo and Descartes; and the latter not only had some notion of determining it by means of a tube filled with mercury, but in a passage which seems to have been much overlooked, distinctly suggests as one reason why water will not rise above eighteen brasses in a pump, “the weight of the water which counterbalances that of the air.”[637] Torricelli happily thought of using mercury, a fluid thirteen times heavier, instead of water, and thus invented a portable instrument by which the variations of the mercurial column might be readily observed. These he found to fluctuate between certain well known limits, and in circumstances which might justly be ascribed to the variations of atmospheric gravity. This discovery he made in 1643; and in 1648, Pascal, by his celebrated experiment on the Puy de Dome, established the theory of atmospheric pressure beyond dispute. He found a considerable difference in the height of the mercury at the bottom and the top of that mountain; and a smaller yet perceptible variation was proved on taking the barometer to the top of one of the loftiest churches in Paris.