The dikoveries of this great man concerning motion drew the attention of philoso phers more readily, from the circumstance that the astronomical theories of Copernicus had directed their attention to the same subject. It had become evident, that the great point in dispute between his system and the Ptolemaic must be finally decided by an ap peal to the nature of motion and its laws. The great argument to which the friends of the latter system naturally had recourse was the impossibility, as it seemed to them to be, _ of the swift motion of the earth being able to without the perception, nay, even without the destruction, of its inhabitants. It was natural for the followers of Copernicus to reply, that it was not certain that these two things were. incompatible ; that there were many cases in which it appeared, that the motion common to a whole system of bodies did not affect the motion of those bodies relatively to one another ; that the question must be more deeply inquired into ; and that, without this, the evidence on opposite sides could not be fairly and accurately compared. Thus it was, at a very fortunate moment, that Galileo made his discoveries in Mechanics, as they were rendered more interesting by those which, at that very time, he himself was making in Astronomy. The sys tem of Copernicus had, in this manner, an influence on the theory of motion, and, of course, on all the parts of natural philosophy. The inertia of matter, or; the ten. deny of body, when put in motion, to preserve the quantity and direction of that ma . tion, after the cause which impressed it has ceased to act, is a principle which might still have been unknown, if it had not been forced upon us by the discovery of the motion of the earth.
The first addition which was made to the mechanical discoveries of Galileo was by Torricelli, in a treatise De Motu Gravium naturaliter descendentium et projectorum.` To this ingenious man we are indebted for the discovery of a remarkable property of the centre of gravity, and a general principle with respect to the equilibrium of bodios. It is this : If there be any number of heavy bodies connected together, and so circum stanced, that by their motion their centre of gravity can neither ascend nor descend, these bodies will remain at rest. This proposition often furnishes the means of resolving very difficult questions in mechanics.
Descartei, whose name is so great in philosophy and mathematics, has also a place in the history of mechanical discovery. With regard to the action of machines, he laid down the same principle which Galileo had established,--that an equal effort is neces nary to give to a weight a certain velocity, as to give to double the weight the half of that velocity, and so on in proportion, the effect being always measured by the weight tiplied into the velocity which it receives. He could hardly be ignorant that this propo • sition had been already stated by Galileo, but he has made no mention of it. He, indeed, always affected a disrespect for the reasonings and opinions of the Italian philosopher, which has done him no credit in the eyes of posterity.
The theory of motion, however, has in some points been considerably indebted to Des cartes. Though the reasonings of Galileo certainly involve the knowledge of the disposi tion which matter has to preserve its condition either of rest or of rectilineal and uniform motion, the first distinct enunciation of this law is found in the writings of the French philosopher. It is, however, there represented, not as mere inactivity, or indifference,
but as a real force, which' bodies exert in order to preserve their state of rest or of mo tion, and this inaccuracy affects some of the reasonings concerning their action on one another.
Descartes, however, argued very justly, that all motion being naturally rectilineal, when a body moves in a curve, this must arise from some constraint, or some force urging it in a direction different from that of the first impulse, and that if this cause were removed at any time, the motion would become rectilineal, and would be in the direction of a tan gent, to the curve at the point where the deflecting force ceased to act. ' Lastly, He taught that the quantity of motion in the universe remains always the same.
The reasoning by which he supported the first and second of these propositions is not very convincing, and though he might have appealed to experience for the truth of both, it was not in the spirit of his philosophy to take that method of demonstrating its principles. His argument was, that motion is a state of body, and that body or matter cannot change its own state. This was his demonstration of the first proposition, from which the second followed necessarily.
The evidence produced for the third, or the preservation of the same quantity of motion in the universe, is founded on the immutability of the Divine nature, and is an instance of the intolerable presumption which se often distinguished the reasonings of this philosopher. Though the immutability of the Divine nature will readily be ad mitted, it remains to be shown, that the continuance of the same quantity of motion in the universe is a consequence of it. This, indeed, cannot be shown, for that quantity, in the sense in which Descartes understood it, is so far from being preserved uniform, that it varies continually from one instant to another. It is nevertheless true, that the quantity of motion in the universe, when rightly estimated, is invariable, that is, when reduced to the direction of three axes at right angles to one another, and when oppo site motions are supposed to have opposite signs. This is a truth now perfectly under. stood, and is a corollary to the equality of action and reaction, in consequence of which; whatever motion is communicated in one direction, either lost in that direction, or generated in the opposite. This, however, is quite different from the proposition of Descartes, and if expressed in his language, would assert, not that the sum, but that the difference of the -opposite motions in the universe remains constantly the same. When he proceeds, by help of the principle which he had thus mistaken, to determine the laws of the collision of bodies, his conclusions are almost all false, and have, indeed, such a want of consistency and analogy with one another, as ought, in the eyes of a mathematician, to have appeared .the most decisive indications of error. How this escaped the penetration of a man well acquainted with the harmony of geometrical truths, and the gradual transitions by which they always pass into one another, is not easily explained, and perhaps, of all his errors, is the least consistent with the powerful and systematic genius which he is.so. well known to have possessed.