Fig. 22.
Fig. 23.
80. Attraction Toward the Earth's Centre.—All bodies are attracted toward the centre of the earth. This is because the earth is globular, as may be made clear by Fig. 22. Let the circle represent the earth, and a a body attracted by it. The lines drawn from the body to the earth represent the attractive force exerted by the earth upon the body. It is obvious from these that there is as much attraction on the one side of the line drawn from the body to the earth's centre as there is on the other. The attractive force, then, of the earth as a whole is exerted upon the body in the direction of this middle line. It tends to draw it, therefore, toward the centre. If, therefore, a weight be suspended by a string, the line of the string continued would go to the centre of the earth. This being so, it is clear that two weights suspended by two strings do not hang perfectly parallel to each other. The difference is so slight in an ordinary pair of scales that it can not in any way be perceived. But if it were possible to suspend in the heavens a beam so long as to stretch over a large extent of the earth's circumference, as represented in Fig. 23, the scales attached to it would be very far from hanging parallel to each other. Substances suspended in different parts of the globe are hanging in different directions, and those which are hung up by our fellow-men on the opposite side of the earth, are hanging directly toward us.
Fig. 24.
81. Up and Down.—All falling bodies fall toward the centre of the earth, and the same remarks can be made on this point that I have made in relation to suspended weights. Up and down are merely relative terms—up being from the centre of the earth, and down toward it. As the earth moves round on its axis, the same line of direction which we call upward at one time is downward at another. This may be illustrated on Fig. 24. Let the circle represent the circumference of the earth. In the daily revolution we pass over this whole circle. If we are at D at noon, we are at E at six o'clock, and at F at midnight. If, therefore, the ball A be dropped from some height at noon, the line in which it falls will be at right angles to a line in which it will fall if you drop it from the same height at six o'clock; for this height will have moved in this time from A to B. If it be dropped from the same height at midnight its line of direction will be directly opposite to what it was twelve hours before; for the height will have moved in that time to C.
It is not always true that falling bodies tend exactly toward the centre of the earth. It is nothing in the centre that attracts them, but it is the substance of the whole earth; and as this is irregular in its density and form, the attraction will be irregular also. Thus it is found by accurate experimenting that a plumb line suspended in the neighborhood of a mountain is so attracted by it that it will not hang exactly parallel with another suspended at some distance from the mountain. The difference is not, however, enough in any case to have any practical bearing.
82. Weight.—I have said before (§ 52) that what we call weight is not a property of matter, but merely the result of a property, the attraction of gravity. This I will now illustrate. If two bodies are falling to the earth, and one of them contains ten times as many particles of matter as the other, ten times as much force of gravity is required, and is actually exerted, to bring it to the ground. This will appear plain to you if you bear in mind that a body does not come to the ground because there is nothing to keep it there, but because it is drawn down by the force of attraction, and then compare this force to any other force, as, for example, that of muscular action. If you draw toward you two weights, one of which is twenty times as heavy as the other, or, in other words, has twenty times the quantity of matter that the other has, you must exert twenty times as much strength on the former as you do on the latter. Just so it is with the force of attraction. The earth attracts or draws toward itself a body having twenty times the quantity of matter that another has with twenty times the amount of force. And the first body will have twenty times the weight of the other, for it will make twenty times the pressure upon any thing that resists the force with which the earth draws it toward itself. Weight, then, is the amount of the pressure occasioned by the attraction existing between the earth and the body weighed. If you place a substance in one side of a pair of scales, it goes down because of the attraction between it and the earth. By placing weights in the other side until the scales are balanced, you find how much is needed to counteract the downward pressure caused by the attraction of the substance and the earth for each other; or, in other words, you find out how much it weighs. In doing this you use certain standard weights; that is, certain quantities of matter which have been agreed upon by mankind, and are called by certain names, as pounds, ounces, etc. When a spring is used in weighing, the spring has been tried by these standard weights, and its scale has been marked accordingly.