Science for the School and Family, Part I. Natural Philosophy

by Worthington Hooker

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.

85. Weight Every Where.—I have spoken of weight only in relation to the earth. But there is weight in bodies every where, for there is attraction wherever there is matter. The weight of substances on the surface of different heavenly bodies varies according to the quantities of matter in those bodies. As the moon is much smaller than the earth, what weighs a pound with us would weigh much less than a pound in the moon. And as the sun is much larger than the earth, what is a pound with us would be much more than a pound there. If we knew the exact densities of the sun and the moon and the earth, as well as their size, we could estimate exactly the difference in the weights which any body would have in them; for the attraction which causes the pressure that we call weight is as the quantity of matter, and the quantity of matter depends on both density and size.

86. Cohesion, Capillary Attraction, and Gravitation the Same.—The attraction of cohesion, capillary attraction, and gravitation are only different modes of action of the same power; viz., the attraction which matter every where has for matter. At first thought it would appear that there is something peculiar in the attraction of particles when they are brought together so as to adhere. For if we take any substance, a piece of glass, for example, its particles seem to be held together by an attraction vastly stronger than that attraction which inclines different bodies to move toward each other. If you break the glass, however closely you may press the two pieces together, they will not unite again. It would seem, at first view, that there must be some peculiar arrangement of the particles which is destroyed by breaking the glass. But we can readily account for the facts in another way. The attraction between bodies of matter is the greater the nearer we bring them together. The nearer, for example, is the moon to any portion of the earth, the greater is the attraction which it exerts, as seen in the tides; and if it were much nearer to the earth than it is, our tides would prove awfully destructive. What is true of masses is also true of the particles of which they are composed. Though their attraction is comparatively feeble when at a distance from each other, it increases, not in the arithmetical but the geometrical ratio (§ 84), as they come nearer together; so that when they are exceedingly near together the attraction is very powerful. It must be remembered in regard to the pieces of broken glass that you can not bring the particles on their surfaces as near as they were before the glass was broken, for the crack does not disappear. And as the attraction is inversely as the square of the distance, a little distance must make a great difference. The particles of some substances you can bring so near together as to cause adhesion, as you saw in the case of the two bullets (§ 66). That their adhering together depends merely upon their particles being brought near to each other appears from the fact, that the smoother you make the surfaces the more strongly will they adhere. And the reason that liquids and semi-liquids adhere so readily to solid substances is, that their particles, moving freely among each other, have thus the power of arranging themselves very near to the particles of the solid. Thus, when a drop of water hangs to glass, all the particles of water in that part of the drop next to the glass touch, or rather are exceedingly near to, the particles of the glass.

87. Variety in the Results of Attraction.—It is one and the same force, then, which binds the particles of a pebble together, and makes it fall to the ground—which "moulds the tear" and "bids it trickle from its source"—which gives the earth and all the heavenly bodies their globular shape, and, in connection with another power hereafter to be noticed, makes them revolve in their orbits. How sublime the thought that this one simple principle that gives form to a drop extends its influence through the immensity of space, and so marshals "the host of heaven" that, without the least interruption or discord, they all hold on their course from year to year and from age to age! It is thus that Omnipotence makes the simplest means to produce the grandest and most multiform results.

88. Opposition Between the Modes of Attraction.—Although cohesion and gravitation are essentially the same thing, we see them continually acting in opposition to each other. Abundant illustrations might be given, but, I will cite only a few.

Fig. 25. Fig. 26.

89. Why Pitchers have Lips.—If you pour water out of a tumbler there is a struggle between the attraction of cohesion and gravitation for the mastery—the attraction of cohesion tending to make the water adhere to the tumbler, and run down its side, as in Fig. 25, and gravitation tending to make it fall straight down. But when water is poured out of a pitcher, as in Fig. 26, the lip of the pitcher acts in favor of the attraction of gravity; for the water would have to turn a very sharp corner to run down the outside of the pitcher in obedience to the attraction of cohesion. In pouring water from a tumbler, we can often, by a quick movement, throw the water, as we may say, into the hands of gravity before the attraction of cohesion can get a chance to turn it down the tumbler's side. If you can only make the water begin to run from the tumbler without going down its side there will be no difficulty; for there is an attraction of cohesion between the particles of the water, tending to make them keep together, which in this case acts against the cohesion between the water and the glass, and therefore acts in favor of gravitation. It is cohesion that forms the drop on the lip of a vial as we drop medicine—cohesion between the particles of the liquid, and cohesion between these particles and those of the glass. It is gravitation, on the other hand, that makes the drop fall, it becoming so large that the force of gravity overcomes the cohesion between the drop and the vial.

90. Size Limited by Gravity.—Were it not for the attraction of gravity there would be no limit to the size of drops of any liquid. When the drop reaches a certain size, it falls because it is so heavy; or, in other words, because with its slight cohesion the attraction of the earth brings it down. Now if this attraction could be suspended, and the attraction of cohesion left to act alone, particles of water might be added to the drop to any extent, and they would cling there. You can see the struggling between cohesion and gravitation very prettily illustrated if you watch the drops of rain on a window-pane. If two drops happen to be quite near together they unite by attraction, and then, being too large to allow of its being retained there by cohesion in opposition to gravitation, the united drop runs down. If it meet with no other drop it soon stops, because by cohesion some portion of it clings to the glass all along its track, and so at length lessens it sufficiently to allow it to remain suspended again. It is from the influence of the attraction of gravitation that different kinds of liquids furnish drops of different sizes, the heavier giving small, and the lighter large ones. Thus you can drop from a vial a larger drop of alcohol than of water, and a larger one of water than of nitric acid. You have another illustration of a similar character in the adhesion of chalk to a black-board or any surface. The chalk crayon itself can not adhere, for the attraction of the earth does not permit it. But small quantities of it can adhere for the same reason that water adheres to surfaces in small quantities. So also dust clings to sides of furniture, though a lump of dirt would not.