All material bodies have weight. By the weight of a body we understand it is that force by which it tends to approach the center of the earth; this force is inversely proportional to the square of the distances of the body to the earth's center; consequently, the weight of a body is variable. The falling body tends towards the center of the earth, because it is attracted by every particle of the earth, not because the particles at the center have a greater attraction than any other particles. This same would be true if the earth were a hollow sphere.

There is no material body which is exempt from the earth's attraction. If some objects, like smoke or a balloon, seem not to be attracted, it is only because they are immersed in the air, which is a fluid heavier than themselves. In like manner, a cork plunged in water immediately rises to the top, not be cause it is not attracted by the earth, but because the water is more attracted than itself, and therefore displaces the cork. In a vacuum the lightest objects fall with the velocity of metallic bodies.

Weight is the measure of the force of gravity. When we say that a body weighs 10 lbs., we mean that the earth attracts it that amount.

Each atom which composes a body has weight, and the weight of the mass is the sum of the weights of all its atoms. If the particles composing a body had no mutual cohesion, each particle would obey the force of gravity independently of the others; but, being connected by

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colesion, the several forces acting upon the particles are compounded so as to produce a single force which is the resultant of all these separate forces. This resultant is a force acting vertically downward and equal to the sum of all the forces affecting the particles severally The weight of a body at the center

of the earth is nothing, because the attraction is equal in every direction.

The weight of a body varies on different portions of the surface of the earth. It will be least at the equator, on account of the bulging form of our globe; a body here is further removed from the entire mass and more removed from the center of attraction, also because centrifugal force is strongest at the equator. It will be greatest at the poles because the oblateness of the earth brings a body nearer to the mass thus causing greater force of attraction. Furthermore, there is no centrifugal force at those points. These variations, however, would in weighing machines, effect only spring balances. In lever scales, the weights used would be

come heavier or lighter in the same proportion as the body to be weighed.

Since the attraction of the earth is toward the center, all falling bodies move in a direct line toward that point. This line is called the vertical or plumb line. All plumb-lines point toward the center of the earth.

If a body be suspended from a fixed point it will not remain at rest unless the resultant of the weights of all its particles passes through that point. Hence, if we suspend a body by a string, and allow it to come to rest, the resultant of the weights of all its particles will be in the direction of the string.

If the same body be suspended successively from a number of different points, the resultant of the weights of the particles of the body will be found to have as many different positions, but all these resultants will intersect each other at a common point. This may be easily verified by taking a solid body or some material which is easily perforated. The experiment is most conveniently performed with a flat, thin plate of metal or some other solid substance. This common

point through which the resultant of the gravity of the particles always passes, is called the center of gravity.

A line drawn vertically through the center of gravity of a body is called the line of direction. At the center of gravity a body will remain at rest in any position in which it may be placed; for the resultant of the weights of all its particles is in the direction of a vertical line passing through the center of gravity. and this resultant will be supported when the center of gravity is supported.

We may define the center of gravity of a body to be that point about which, if supported, all the parts of a body, (acted upon only by the force of gravity) balance each other.

The common center of gravity of two bodies may be found from the following principle.

Two weights, A and B, acting at the extremeties of an inflexible rod, will be in equilibrium about a given point C when their distances from that point are inversely as those weights. This point of support is the center of gravity of the two weights.

FOR EXAMPLE: If the weight A be 14 ounces and B 7 ounces, and if the length of the arm AF is 7 inches, then, in order that the two weights may be in equilibrium, BF must be 14 inches.

FIG. NO. 1.

There are three different positions in which the center of gravity may be supported: First, the prop may be applied directly to the center itself; in which

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case the body will rest in any position, as in the common wheel. This is called indifferent equilibrium. Second - The point of support may be above the center of gravity; in which case, if we deviate the body from this position, it will always tend to return to it; and it will not rest until the center of gravity is ver