[Chap. I.]
Of the LAWS of MOTION.
HAVING thus explained Sir Isaac Newton’s method of reasoning in philosophy, I shall now proceed to my intended account of his discoveries. These are contained in two treatises. In one of them, the Mathematical principles of natural philosophy, his chief design is to shew by what laws the heavenly motions are regulated; in the other, his Optics, he discourses of the nature of light and colours, and of the action between light and bodies. This second treatise is wholly confined to the subject of light: except some conjectures proposed at the end concerning other parts of nature, which lie hitherto more concealed. In the other treatise our author was obliged to smooth the way to his principal intention, by explaining many things of a more general nature: for even some of the most simple properties of matter were scarce well established at that time. We may therefore reduce Sir Isaac Newton’s doctrine under three general heads; and I shall accordingly divide my account into three books. In the first I shall speak of what he has delivered concerning the motion of bodies, without regard to any particular system of matter; in the second I shall treat of the heavenly motions; and the third shall be employed upon light.
2. In the first part of my design, we must begin with an account of the general laws of motion.
3. These laws are some universal affections and properties of matter drawn from experience, which are made use of as axioms and evident principles in all our arguings upon the motion of bodies. For as it is the custom of geometers to assume in their demonstrations some propositions, without exhibiting the proof of them; so in philosophy, all our reasoning must be built upon some properties of matter, first admitted as principles whereon to argue. In geometry these axioms are thus assumed, on account of their being so evident as to make any proof in form needless. But in philosophy no properties of bodies can be in this manner received for self-evident; since it has been observed above, that we can conclude nothing concerning matter by any reasonings upon its nature and essence, but that we owe all the knowledge, we have thereof, to experience. Yet when our observations on matter have inform’d us of some of its properties, we may securely reason upon them in our farther inquiries into nature. And these laws of motion, of which I am here to speak, are found so universally to belong to bodies, that there is no motion known, which is not regulated by them. These are by Sir Isaac Newton reduced to three[43].
[4.] The first law is, that all bodies have such an indifference to rest, or motion, that if once at rest they remain so, till disturbed by some power acting upon them: but if once put in motion, they persist in it; continuing to move right forwards perpetually, after the power, which gave the motion, is removed; and also preserving the same degree of velocity or quickness, as was first communicated, not stopping or remitting their course, till interrupted or otherwise disturbed by some new power impressed.
[5.] The second law of motion is, that the alteration of the state of any body, whether from rest to motion, or from motion to rest, or from one degree of motion to another, is always proportional to the force impressed. A body at rest, when acted upon by any power, yields to that power, moving in the same line, in which the power applied is directed; and moves with a less or greater degree of velocity, according to the degree of the power; so that twice the power shall communicate a double velocity, and three times the power a threefold velocity. If the body be moving, and the power impressed act upon the body in the direction of its motion, the body shall receive an addition to its motion, as great as the motion, into which that power would have put it from a state of rest; but if the power impressed upon a moving body act directly opposite to its former motion, that power shall then take away from the body’s motion, as much as in the other case it would have added to it. Lastly, if the power be impressed obliquely, there will arise an oblique motion differing more or less from the former direction, according as the new impression is greater or less. For example, if the body A (in fig. 1.) be moving in the direction A B, and when it is at the point A, a power be impressed upon it in the direction A C, the body shall from henceforth neither move in its first direction A B, nor in the direction of the adventitious power, but shall take a course as A D between them: and if the power last impressed be just equal to that, which first gave to the body its motion; the line A D shall pass in the middle between A B and A C, dividing the angle under B A C into two equal parts; but if the power last impressed be greater than the first, the line A D shall incline most to A C; whereas if the last impression be less than the first, the line A D shall incline most to A B. To be more particular, the situation of the line A D is always to be determined after this manner. Let A E be the space, which the body would have moved through in the line A B during any certain portion of time; provided that body, when at A, had received no second impulse. Suppose likewise, that A F is the part of the line A C, through which the body would have moved during an equal portion of time, if it had been at rest in A, when it received the impulse in the direction A C: then if from E be drawn a line parallel to, or equidistant from A C, and from F another line parallel to A B, those two lines will meet in the line A D.
[6.] The third and last of these laws of motion is, that when any body acts upon another, the action of that body upon the other is equalled by the contrary reaction of that other body upon the first.
7. These laws of motion are abundantly confirmed by this, that all the deductions made from them, in relation to the motion of bodies, how complicated soever, are found to agree perfectly with observation. This shall be shewn more at large in the next chapter. But before we proceed to so diffusive a proof; I chuse here to point out those appearances of bodies, whereby the laws of motion are first suggested to us.