83. =Weight not Fixed, but Variable.=--Weight does not depend alone upon the density of the body weighed, but also upon the density of the earth. For the attraction causing the pressure which we call weight is a _mutual_ attraction, and is in proportion to the quantities of matter in both the body and the earth. If, therefore, the density of the earth were increased twice, three times, or four times, the weights of all bodies would be increased in the same proportion; that is, the force with which the earth would attract them would be twice, three times, or four times as great as now. This would not be perceived by any effect on balances, for the weights and the articles weighed would be alike increased in weight. But it would be perceived in instruments that indicate the weights of bodies by their influence on a spring. These would disagree with scales and steelyards just in proportion to the increase of the earth's density. It would be perceived also in the application of muscular and other forces in raising and sustaining weights. Every stone would require twice, three times, or four times the muscular effort to raise it that it does now. 84. =Weight Varies with Distance.=--The nearer two bodies are to each other the greater is their attraction. The nearer a body is to the earth the greater is the attraction that presses it toward the earth; in other words, the greater is its weight. The force of gravity, or weight, is greatest, therefore, just at the surface of the earth, and it diminishes as we go up from the earth. As we go from the earth, the force of gravity lessens in such a proportion that it is always _inversely_ as the square of the distance from the centre of the earth. I will explain. If the distance from the centre of the earth to its surface, which is 4000 miles, be called 1, then 4000 miles from the earth would be called 2, or twice as far from the centre, and 8000 miles from the earth would be 3, and so on. The squares of these numbers would be 1, 4, 9, 16, etc. Now as weight lessens so as to be _inversely_ as the square of the distance, a body weighing a pound on the surface of the earth would weigh but a quarter of a pound at the distance of 4000 miles, and but the ninth part of a pound at 8000 miles. A body weighs less on the summit of a high mountain than it would in the valley below, because it is farther away from the great bulk of the earth, and therefore is not so strongly attracted. The difference, however, is but small. A man weighing two hundred and fifty pounds in the valley would weigh but half a pound less if on the summit of a mountain four miles high.