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GRAVITATION
I. Gravitation at the Surface of the Earth.
IT is a matter of universal experience all over the earth that a heavy body tends to fall to the ground. Let us inquire into this in the first place by taking such a general view of the phenomenon as would be presented to an imaginary spectator who was sufficiently removed from the earth to be able to take a general view. Fig. 1 represents a section of the earth by a plane which is drawn through its centre 0. Then, the earth being sufficiently near a sphere for our purpose, we may regard the section PQRS as a circle, where the points P, Q, It, S are the intersections of the lines OA, OB, OC, OD with the surface of the earth. If a stone be dropped from a point A above the surface of the earth, it will fall to the ground at P. The spectator would also notice that, if a stone were dropped from B or C or D, it would fall upon the ground at the points Q, R, S re spectively. From A the stone would appear to fall downwards, from C it appears to move up wards, from B the spectator would see the stone moving to the left, while from D it appears
to move to the right. One feature of these motions could not fail to be noticed: they all tend to the centre of the earth. The spectator might therefore sum up his experi ence in the following statement : A body dropped from a point above the surface of the earth always falls in a straight line ivhich is directed to wards the centre of the earth.
§ 1. Attraction.—The familiar instance of the action of a magnet upon a piece of iron will suffice to illustrate what is meant by the word attraction. In virtue of certain properties possessed by the iron and the magnet, they are drawn together. The magnet draws the iron, arid the iron draws the magnet This particular kind of attraction is of a very special character, Thus, for example, the magnet appears to have no appreciable influence on a piece of wood or a sheet of paper, and has indeed no considerable influence on any known substance except iron. By the attraction of gravitation, every body attracts every other body, whatever be the materials of which each is composed. In this we see a wide difference between the attractions of gravitation and that form of attraction which is known as magnetic attraction. Nor is the contrast between the intensities of these two different attractions less striking. The keeper of a magnet is drawn to the magnet by two different forces of attraction. The first of these is the gravitative attraction, which, so far as we know at present, would be equally exerted, whether the magnetism were present or not. The second is the magnetic attraction. The latter is enormously greater than the former ; in fact, under ordinary circumstances as to intensity and dimensions, the intensity of the attraction of gravitation will not be nearly so much as a millionth part of the magnetic attrac tion. The intensity of the attraction of gravitation is indeed so small that, with one conspicuous exception, we can only become aware of its existence by refined and elaborate in quiries. That any two objects for example, two books lying on the table do actually attract each other, there can be no doubt whatever ; but the intensity of this is so small that the attractive force cannot overcome the friction of the table, and consequently we do not find that the books are drawn together. It has, however, been found that the in tensity of the attraction of gravitation between two masses is directly proportional to the product of those masses. Hence though the force is so small as to be almost inappreciable between two bodies of moderate dimensions, yet when the masses of the two bodies, or of even one of them, are enormously great, the intensity of the force will be sufficiently large to be readily discernible. In this way it is that the existence of the attraction of gravitation has been made known to us, and is, in fact, identified with our daily experience, indeed, with our actual existence. The mass of the earth is so enormous that the attraction of gravitation which, exists between it and an object near the surface is readily appreciable. It is this attraction of gravitation bstween the earth and any object which constitutes that force which is referred to when we speak of the weight of the body. It is the attraction of gravitation which causes bodies to fall to the surface of the earth ; and it is easy to show that the facts already presented with respect to the direction in which a falling body moves are readily explained by the supposition that the motions are due to an attractive influence exerted by the earth, or, to speak more correctly, to a mutual attraction subsisting between the earth and the body. Let be the centre of the earth, supposed to be a sphere, and let A be the position of a body above its surface. Then, when the body is released, the attraction must evi dently cause the body to move along the line OA. The line OA, in fact, is directed along a diameter of the sphere, and there is really no reason why the stone should move to one side of the line more than to another. We thus see that attraction would always tend to draw objects in a direction pointing towards the centre of the. earth. The observed facts are therefore explained by the supposition that the earth possesses a power of attraction.
§ 2. Movement of a Falling Body.—Our knowledge of the force of gravitation being ultimately founded on observation and experiment, it will be convenient at this point to de scribe the experiments by which a knowledge of the laws of motion of a falling body may be ascertained. We shall first describe these experiments, and then we shall discuss the laws to which we are conducted by their aid.
A beginner is apt to be surprised when he is told that a heavy body and a light body will fall to the ground in the same time if let drop from the same height. Yet nothing can be easier than to prove this important fact experimentally. Take a piece of cork in one hand and a bullet in the other, and drop these two objects at the same moment from the same height. They will reach the ground together. Nor will the results be different if we try a stone and a piece of wood. If, however, one of the objects were a feather and the other were a stone, then no doubt the latter would reach the ground long before the former. But this arises from a cause quite different from gravity. It is the resistance of the air which retards the motion of the feather. Even the stone is retarded to a certain extent by the resistance of the air; but the feather, on account of its greater surface in proportion to its mass, is much more retarded. If we could get rid of the influence of the air, the stone and the feather would be found to fall to the ground in the same time. This can actually be verified by performing the experiment (or a similar one) in a space from which the greater portion of the air has been withdrawn by the aid of an air-pump. But the same thing can also be shown in a much more simple manner.
