impelled by the air, he says that the air must impede rather than impel the body, and that "the motion of the body, separately from the mover, arises by a certain natural impression from the impetuosity (ex impetuositate) received from the mover." He adds, that in natural motions this impetuosity continually increases, by the continued action of the cause,— namely, the propension of going to the place assigned it by nature; and that thus the velocity increases as the body moves from the beginning of its path. This statement shows a clearness of conception with regard to the cause of accelerated motion, which Galileo himself was long in acquiring.

Though Benedetti was thus on the way to the first law of motion, that all motion is uniform and rectilinear except so far as it is affected by extraneous forces, this law was not likely to be either generally conceived or satisfactorily proved, till the other laws of motion, by which the action of forces is regulated, had come into view. Hence, though a partial apprehension of this principle had preceded the discovery of the laws of motion, we must place the establishment of it in the period when those laws were detected and established, the period of Galileo and his followers.

CHAPTER II.

INDUCTIVE EPOCH OF GALILEO.

DISCOVERY OF THE

LAWS OF MOTION IN SIMPLE CASES.

Sect. 1.-Establishment of the First Law of Motion.

AFTER mathematicians had begun to doubt or reject the authority of Aristotle, they were still some time in coming to the conclusion, that the distinction of natural and violent motions was altogether untenable; that the velocity of a body in motion increased or diminished in consequence of the action of causes, not of any property of the motion itself;-and that the apparently universal fact, of bodies going slower and slower, as if by their own disposition, till they finally stopped, from which motions had been called violent, arose from the action of external obstacles not immediately obvious, as the friction and the resistance of the air, when a ball runs on the ground, and the action of gravity, when it is thrown upwards. But the truth to which they were at last led, was, that such causes would account for all the diminution of velocity which bodies experience when apparently left to themselves; and that without such causes, the motion of all bodies would go on for ever, in a straight line and with a uniform velocity.

Who first announced this law in a general form it may be difficult to point out; its exact or approximate truth was necessarily taken for granted in all complete investigations on the subject of the laws of motion of falling bodies, and of bodies projected so as to describe curves. In Galileo's first attempt to solve the problem of falling bodies, he did not carry his analysis back to the notion of force, and therefore this law does not appear. In 1604 he had an erroneous opinion on this subject; and we do not know when he was led to the true doctrine which he published in his Discorso, in 1638. In his third Dialogue he gives the instance of water in a vessel, for the purpose of showing that circular motion has a tendency to continue. And in his first Dialogue on the Copernican System' (published in 1630), he asserts circular motion alone to be naturally uniform, and retains the distinction between natural and violent motion. In the Dialogues on Mechanics, however, published in 1638, but written apparently at an earlier period, in treating of projectiles', he asserts the true law. "Mobile super planum horizontale projectum mente concipio omni secluso impedimento, jam constat ex his quæ fusius alibi dicta sunt, illius motum equabilem et perpetuum super ipso plano futurum esse, si planum in infinitum extendatur." "Conceive a moveable body upon a horizontal plane, and suppose all obstacles to motion

1 Dial. i.

P.

40.

2

p. 141.

to be removed; it is then manifest, from what has been said more at large in another place, that the body's motion will be uniform and perpetual upon the plane, if the plane be indefinitely extended." His pupil, Borelli, in 1667 (in the treatise De Vi Percussionis), states the proposition generally, that "velocity is, by its nature, uniform and perpetual;” and this opinion appears to have been, at that time, generally diffused, as we find evidence in Wallis and others. It is commonly said that Descartes was the first to state this generally. His Principia were published in 1644; but his proofs of this first law of motion are rather of a theological than of a mechanical kind. His reason for this law is, "the immutability and simplicity of the operation by which God preserves motion in matter. For he only preserves it precisely as it is in that moment in which he preserves it, taking no account of that which may have been previously." Reasoning of this abstract and à priori kind, though it may be urged in favour of true opinions after they have been inductively established, is almost equally capable of being called in on the side of error, as we have seen in the case of Aristotle's philosophy. We ought not, however, to forget that the reference to these abstract and à priori principles is an indication of the absolute universality and necessity which we look for in complete sciences, and a result of those faculties by

which such science is rendered possible, and suitable to man's intellectual nature.

The induction by which the first law of motion is established, consists, as induction consists in all cases, in conceiving clearly the law, and in perceiving the subordination of facts to it. But the law speaks of bodies not acted upon by any external force, a case which never occurs in fact; and the difficulty of the step consisted in bringing all the common cases in which motion is gradually extinguished, under the notion of the action of a retarding force. In order to do this, Hooke and others showed that, by diminishing the obvious resistances, the retardation also became less; and men were gradually led to a distinct appreciation of the resistance, friction, &c., which, in all terrestrial motions, prevent the law from being evident; and thus they at last established by experiment a law which cannot be experimentally exemplified. The natural uniformity of motion was proved by examining all kinds of cases in which it was not uniform. Men culled the abstract rule out of the concrete experiment; although the rule was, in every case, mixed with other rules, and each rule could be collected from the experiment only by supposing the others known. The perfect simplicity which we necessarily seek for in a law of nature, enables us to disentangle the complexity which this combination appears at first sight to occasion.

The first law of motion asserts that the motion of