2. It is exerted every way from the center of the attracting body in right-lined directions.

3. It is directly proportional to the quantity of matter in the attracting bodies.

4. It decreases in strength, as the squares of the distances from the center increase.

From the first of these laws we learn, that there is no such thing as absolute levity, or any body indued with the property of lightness, or want of gravity. All bodies, on which we can make any experiments, have the property of gravity; and it would be absurd to suppose that there were others destitute of it, especially if their motions and other affections were the same that they must necessarily be, on the supposition of their being possessed of this property. Whether the particles of light, which appear to be matter, are indued with this property, we cannot tell; as we cannot collect them together in sufficient quantities for the discovery.

From the second law we see the reason, why all heavy bodies fall to the earth in right lines perpendicular to its surface.

From the third law we learn, that there is not an absolute plenum in nature, as the Cartesians affirmed; but that there must be some vacuities, or spaces void of all matter, in the composition of natural bodies. For, if the gravity or weight of bodies be proportional to their quantities of matter, there must be much less matter in a cubic inch of cork than one of lead, as it is much lighter, and therefore in its composition there must be vacuities, or spaces void of all matter.

From the same third law we see the reason, why all bodies fall equally fast in vacuo; the attraction of the earth being always proportional to the quantity of

matter in the falling body. If one body contain an hundred times the quantity of matter that is in another, the earth will exert an hundred times more force upon it, than upon the other, and therefore will bring it down in the same time and with the same velocity. This may be easily apprehended by conceiving the larger body to be divided into an hundred parts, each equal to the smaller body: the attraction of the earth on each of these parts is equal to its influence on the smaller body; and their union or separation can neither increase nor diminish the earth's action upon them.

From the fourth law we learn, that if the earth were a hollow sphere, a heavy body would be perfectly at rest, when placed any where within it, being equally attracted in contrary directions. The particle C, fig. 1. placed any where within the hollow sphere ABDE, is attracted with a force proportional to the number of particles in the bases of the cones AB and DE, or the areas of these bases; which areas are as the squares of the distances from C respectively, as is evident from the third law, above mentioned. And by the fourth law, the particle C is attracted in a contrary direction, with a force, which is inversely as the squares of the distances. But the direct and inverse ratios of the distances or squares of the distances, when compounded together, make a ratio of equality. Therefore the body C, being equally attracted in contrary directions, must rest indifferently in any part of the hollow sphere; for what is demonstrated of the point C is equally true of any other.

A body placed on the surface of two spheres of equal density, but unequal diameters, would be attracted by them with forces proportional to the said diameters. Let the two spheres be represented by A and B, fig. 2.

their diameters by D and d, and the attractive forces of the spheres by F and f: then, by the fourth law, the attractive forces are as the squares of the distances, or double distances from the center, inversely; that is 1 1

F:f:: But, by the third law, these forces are : D2' d2

directly as the quantities of matter in the spheres, which are as the cubes of their diameters; that is, F:f:: D3: d3. and by compounding these ratios, we D3 d3 have F: f:: :D: d; that is, the attractive forces

of the spheres are directly as their diameters. Q.E.D. Hence if the earth were of the same density through. out, and perforated through the center, the gravity of a body descending through it would continually diminish as it approached the center; because in every point of its descent, it might be considered as on the surface of a sphere, whose diameter is double the distance from the center; and the parts behind being only a concave shell, which attracts equally in all directions, can no way affect the descent of the body. Yet it would acquire such a velocity at the center as would be sufficient to carry it up to the surface on the other side, if all resistance of the air be removed. Hence it would continue to vibrate in this perforation, without ceasing.

N. B. The weight of a body depends both on its bulk or magnitude, and its density, or the compactness of its parts; therefore when neither are given, W

W=MD. Hence M=, and D=

W

Μ'

MOTION IN GENERAL.

As all motion in bodies depends on the principle of attraction, whose general laws we have explained, we now proceed to consider the various affections and species of motion.

MOTION is the translation of a body from one part of space to another, and may be considered under different views, either as absolute or relative, equable or accelerated. Absolute motion is the change of absolute place, but relative motion is the change of relative place, when compared with some other place or body. A person on board of a vessel at sea is absolutely in motion, although he may be relatively at rest, with respect to other objects in the same vessel. When a body in motion passes over equal spaces in equal times, the motion is said to be equable; but if the spaces passed over in equal portions of time, be unequal the motion is said to be accelerated or retarded, according as the spaces increase or decrease. If the increase or decrease be equal in equal portions of time, the motion is said to be equably accelerated or retarded. Equable motion is generated by a single impulse, as the motion given to a ball by the action of gunpowder; but accelerated or retarded motion depends upon the continued action, or constant exertion of the moving force every instant. Thus the motion of a falling body is continually accelerated by the attractive force of the earth; which acting upon it every moment, and communicating equal increments of velocity in equal times, the motion is thereby equably accelerated. For the same reason, the motion of a body, projected perpendicularly upwards,

is equably retarded; and if the resistance of the air be neglected, the velocity of the ascent and descent of the body in any given point, must be constantly the same, as also the whole times of the ascent and descent; since the attractive force of the earth generates or destroys equal quantities of the motion in equal times.

The general laws of all motion are reduced by Sir Isaac Newton to these three.

1. As a body at rest continues at rest until it be put in motion by some external force, this motion will continue until it be altered by some external force.

2. The motion produced is always in the direction of the moving force, and invariably proportional to it. 3. When one body acts upon another, its action is equalled by the contrary reaction of the other. Or, action and reaction are equal and contrary.

The first of these laws depends upon the vis inertiæ of bodies, or the resistance they give to all change of situation or condition, whether of motion or rest. Daily observation convinces us, that any body, which we once see at rest, never puts itself in motion, but continues always in the same place, till removed by some power applied: and when in motion, having no power within itself either to generate or destroy its motion, the motion continues after the moving force ceases to act: and if it continue in motion but a single moment after the moving power leaves it, there can be no reason assigned, why it should stop without some external force.

This shows us the reason why the planetary motions are so long continued, by the influence of the projectile force, which first set these worlds in motion, through spaces void of all resistance.