[626] J’ai souvent averti que par la lumière je n’entendois pas tant le mouvement que cette inclination ou propension que ces petits corps ont à se mouvoir, et que ce que je dirois du mouvement, pour être plus aisément entendu, se devoit rapporter à cette propension; d’où il est manifeste qua selon moi l’on ne doit entendre autre chose par les couleurs que les différentes variétés qui arrivent en ces propensions. Vol. vii., p. 193.
36. Such, in a few words, is the famous Cartesian theory, which, fallen in esteem as it now is, stood its ground on the continent of Europe, for nearly a century, till the simplicity of the Newtonian system, and, above all, its conformity to the reality of things, gained an undisputed predominance. Besides the arbitrary suppositions of Descartes, and the various objections that were raised against the absolute plenum of space and other parts of his theory, it has been urged that his vortices are not reconcilable, according to the laws of motion in fluids, with the relation, ascertained by Kepler, between the periods and distances of the planets; nor does it appear why the sun should be in the focus, rather than in the centre of their orbits. Yet, within a few years it has seemed not impossible, that a part of his bold conjectures will enter once more with soberer steps into the schools of philosophy. His doctrine as to the nature of light, improved as it was by Huygens, is daily gaining ground over that of Newton; that of a subtle æther pervading space, which in fact is nearly the same thing, is becoming a favourite speculation, if we are not yet to call it an established truth; and the affirmative of a problem, which an eminent writer has started, whether this æther has a vorticose motion round the sun, would not leave us very far from the philosophy it has been so long our custom to turn into ridicule.
Transits of Mercury and Venus. 37. The passage of Mercury over the sun was witnessed by Gassendi in 1631. This phenomenon, though it excited great interest in that age, from its having been previously announced, so as to furnish a test of astronomical accuracy, recurs too frequently to be now considered as of high importance. The transit of Venus is much more rare. It occurred on December 4, 1639, and was then only seen by Horrox, a young Englishman of extraordinary mathematical genius. There is reason to ascribe an invention of great importance, though not perhaps of extreme difficulty, that of the micrometer, to Horrox.
Laws of Mechanics. 38. The satellites of Jupiter and the phases of Venus are not so glorious in the scutcheon of Galileo as his discovery of the true principles of mechanics. These, as we have seen in the former volume, were very imperfectly known till he appeared; nor had the additions to that science since the time of Archimedes been important. The treatise of Galileo, Della Scienza Mecanica, has been said, I know not on what authority, to have been written in 1592. It was not published, however, till 1634, and then only in a French translation by Mersenne, the original not appearing till 1649. This is chiefly confined to statics, or the doctrine of equilibrium; |Statics of Galileo.| it was in his dialogues on motion, Della Nuova Scienza, published in 1638, that he developed his great principles of the science of dynamics, the moving forces of bodies. Galileo was induced to write his treatise on mechanics, as he tells us, in consequence of the fruitless attempts he witnessed in engineers to raise weights by a small force, “as if with their machines they could cheat nature, whose instinct as it were by fundamental law is that no resistance can be overcome except by a superior force.” But as one man may raise a weight to the height of a foot by dividing it into equal portions, commensurate to his power, which many men could not raise at once, so a weight, which raises another greater than itself, may be considered as doing so by successive instalments of force, during each of which it traverses as much space as a corresponding portion of the larger weight. Hence the velocity, of which space uniformly traversed in a given time is the measure, is inversely as the masses of the weights; and thus the equilibrium of the straight lever is maintained, when the weights are inversely as their distance from the fulcrum. As this equilibrium of unequal weights depends on the velocities they would have if set in motion, its law has been called the principle of virtual velocities. No theorem has been of more important utility to mankind. It is one of those great truths of science, which combating and conquering enemies from opposite quarters, prejudice and empiricism, justify the name of philosophy against both classes. The waste of labour and expense in machinery would have been incalculably greater in modern times, could we imagine this law of nature not to have been discovered; and as their misapplication prevents their employment in a proper direction, we owe in fact to Galileo the immense effect which a right application of it has produced. It is possible, that Galileo was ignorant of the demonstration given by Stevinus of the law of equilibrium in the inclined plane. His own is different; but he seems only to consider the case when the direction of the force is parallel to that of the plane.
His Dynamics. 39. Still less was known of the principles of dynamics than of those of statics, till Galileo came to investigate them. The acceleration of falling bodies, whether perpendicularly or on inclined planes, was evident; but in what ratio this took place, no one had succeeded in determining, though many had offered conjectures. He showed that the velocity acquired was proportional to the time from the commencement of falling. This might now be demonstrated from the laws of motion; but Galileo, who did not perhaps distinctly know them, made use of experiment. He then proved by reasoning that the spaces traversed in falling were as the squares of the times or velocities; that their increments in equal times were as the uneven numbers, 1, 3, 5, 7, and so forth; and that the whole space was half what would have been traversed uniformly from the beginning with the final velocity. These are the great laws of accelerated and retarded motion, from which Galileo deduced most important theorems. He showed that the time in which bodies roll down the length of inclined planes is equal to that in which they would fall down the height, and in different planes is proportionate to the height; and that their acquired velocity is in the same ratios. In some propositions he was deceived; but the science of dynamics owes more to Galileo than to any one philosopher. The motion of projectiles had never been understood; he showed it to be parabolic; and in this he not only necessarily made use of a principle of vast extent, that of compound motion, which, though it is clearly mentioned in one passage by Aristotle[627] and may probably be implied in the mechanical reasonings of others, does not seem to have been explicitly laid down by modern writers, but must have seen the principle of curvilinear deflection by forces acting in infinitely small portions of time. The ratio between the times of vibration in pendulums of unequal length, had early attracted Galileo’s attention. But he did not reach the geometrical exactness of which this subject is capable.[628] He developed a new principle as to the resistance of solids to the fracture of their parts, which, though Descartes as usual treated it with scorn, is now established in philosophy. “One forms, however,” says Playfair, “a very imperfect idea of this philosopher from considering the discoveries and inventions, numerous and splendid as they are, of which he was the undisputed author. It is by following his reasonings, and by pursuing the train of his thoughts, in his own elegant, though somewhat diffuse exposition of them, that we become acquainted with the fertility of his genius, with the sagacity, penetration, and comprehensiveness of his mind. The service which he rendered to real knowledge is to be estimated not only from the truths which he discovered, but from the errors which he detected; not merely from the sound principles which he established, but from the pernicious idols which he overthrew. Of all the writers who have lived in an age which was yet only emerging from ignorance and barbarism, Galileo has most entirely the tone of true philosophy, and is most free from any contamination of the times, in taste, sentiment, and opinion.”[629]
[627] Drinkwater’s Life of Galileo, p. 80.
[628] Fabroni.
[629] Preliminary Dissertation to Encyclop. Britain.
Mechanics of Descartes. 40. Descartes, who left nothing in philosophy untouched, turned his acute mind to the science of mechanics, sometimes with signal credit, sometimes very unsuccessfully. He reduced all statics to one principle, that it requires as much force to raise a body to a given height, as to raise a body of double weight to half the height. This is the theorem of virtual velocities in another form. In many respects he displays a jealousy of Galileo, and an unwillingness to acknowledge his discoveries, which puts himself often in the wrong. “I believe,” he says, “that the velocity of very heavy bodies which do not move very quickly in descending increases nearly in a duplicate ratio; but I deny that this is exact, and I believe that the contrary is the case when the movement is very rapid.”[630] This recourse to the air’s resistance, a circumstance of which Galileo was well aware, in order to diminish the credit of a mathematical theorem, is unworthy of Descartes; but it occurs more than once in his letters. He maintained also, against the theory of Galileo, that bodies do not begin to move with an infinitely small velocity, but have a certain degree of motion at the first instance, which is afterwards accelerated.[631] In this too, as he meant to extend his theory to falling bodies, the consent of philosophers has decided the question against him. It was a corollary from these notions that he denies the increments of spaces to be according to the progression of uneven numbers.[632] Nor would he allow that the velocity of a body augments its force, though it is a concomitant.[633]
[630] Œuvres de Descartes, vol. viii., p. 24.