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

by Worthington Hooker

187. Course of Bodies Thrown into the Air.—It results from the principle that I have illustrated that when any body, as a stone, is thrown, as we say, straight upward, it does not, in reality, go up or come down perpendicularly. If it did it would come down at a great distance from us. Suppose it takes two seconds for it to go up and to reach the ground. If we are at the equator, in that two seconds we move from the point where we threw up the stone nearly 3000 feet eastward, and therefore if the stone rose and fell perpendicularly it would fall 3000 feet westward of us. Why, instead of this, does it fall at our feet? Because that when thrown into the air it has not only the upward motion given by the hand, but also the forward motion of the earth. It is a case similar to that of the rider in Fig. 127, the horse representing the surface of the earth and the rider the stone. For the same reason a man on board of a steamboat, though it move fifteen miles an hour, tosses up his ball or orange and catches it as well as if he were on land. This he could not do if both he and his orange did not have the same forward motion that the boat does. So, also, if a man fall from a mast-head he reaches the deck at the foot of the mast when the vessel is sailing rapidly, just as he would if it were lying still at the wharf. If he did not by inertia retain the forward motion which he had in common with the vessel he would fall at some distance behind the mast.

188. The Earth and the Atmosphere.—The air being held to the earth by attraction, § 151, it has a motion in common with the earth. It revolves with the earth just as the tire of a wheel revolves with the wheel. This being so, our winds are nothing but slight variations of this constant rapid whirl of the aerial coating of the earth. If the atmosphere were suddenly to stop whirling round with the earth we should move through it with a velocity of 1500 feet a second; and the destructive effect upon us would be the same as it would were the earth standing still while the air moved over its surface with this fearful velocity. A wise man, not reflecting that the atmosphere moved with the earth, proposed rising in a balloon, and waiting till the country to which he wished to go should be passing under him.

189. Motion and Rest.—Though we use the term rest in opposition to motion, it is obvious from some of the illustrations given that rest is merely a relative term, for not a particle of matter in the universe is at rest. Though when we are sitting still we call ourselves at rest, we are moving every hour, by the revolution of the earth on its axis, 1000 miles eastward, and 68,000 miles in our annual journey round the sun. Why, then, are we so insensible to these rapid motions? It is partly because the motions are so uniform, but chiefly because all things around us, our houses, trees, and even the atmosphere, are moving along with us. If we were moving along alone, even at a slow rate, while all these objects were standing still, we should be conscious of our motion, as we are when, as we ride along in a carriage, we see the objects at the road-side not moving along with us.

190. A Comparison.—The above can be made more clear and impressive by a familiar comparison. A man on board of a steamboat, by confining his attention to things within the boat, may, after a while, be almost unconscious of the boat's moving, if the water be smooth, though the boat may be going at the rate of fifteen miles an hour. If he be reading in the cabin he will think as little of his motion as he would were he reading in his parlor at home. If he should be blindfolded, and turned around a few times, it would be impossible for him to tell the direction in which the boat is going. Now it is with a man on the earth as it is with the man in the boat. He is unconscious of the motion of the earth for the same reason that the man in the boat is unconscious of the boat's motion. All objects around him are moving along with him, as the objects around the man in the cabin of the boat are moving along with him. We can carry the parallel farther. While the man sits in the cabin he knows not how fast the boat moves, nor even whether it moves at all. He must look out to decide this, and even then he may not be able to tell whether the boat moves, or whether he merely sees the water running by it. We often are actually deceived in this respect. A steamboat struggling against wind and wave may appear to those on board to be advancing when it is really stationary, or even when it is losing ground. So when we look at the sun we know not whether it is the sun or the earth that is moving. Mere vision, without reasoning on the subject, leads one to think that it is the sun that moves. For the same reason, if a child should be placed in a carriage for the first time without seeing the horses, but with its eyes fixed on objects at the road-side, he would probably think that all the fences and trees and rocks and houses are in motion.

191. Absolute and Relative Motion.—The motion of a body is said to be absolute when it is considered without relation to the position of any other body. Its motion is said to be relative when it is moving with respect to some other body. Absolute rest is unknown, for no body in the universe is known to be without motion. But a body may be relatively at rest, that is, in a fixed relative position to other bodies. Every body is in a state of absolute motion, and yet it may be in a state of relative rest. All objects that appear to us to be at rest have a very rapid absolute motion. They appear to be at rest merely because they have the same rapidity and direction of absolute motion that we have ourselves. And all the motions which are apparent to the eye are only slight differences in the common absolute motions, of which, though they are so exceedingly rapid, we are entirely unconscious. Thus, if I stand still, and another at my side walks at the rate of three miles an hour eastward, we both of us have a common absolute motion of 1000 miles in every hour, and he merely adds three miles to his thousand—I move 1000 miles, and he 1003. So if I sit still in my parlor, and my friend travels eastward at the rate of 20 miles an hour, I move every hour 1000 miles, and he 1020. And if he travel westward at this rate he really travels slower than I do—he has an absolute motion eastward of 980 miles, and I of 1000. At the same time we are both whirling on in our annual journey around the sun at the rate of 68,000 miles an hour.

192. Obstacles to Motion.—As motion is naturally disposed to continue (§ 49 and § 184), whenever it is stopped it does not spend itself, but is stopped by obstacles. The principal of these obstacles are: gravitation; the resistance of opposing substances—solids, liquids, and gases; and friction. When a stone is thrown into the air its upward motion is gradually destroyed by the attraction of the earth and the resistance of the air. Observe, now, why it descends. It is from the action of one of the causes which arrested its upward flight—the attraction of the earth. In its descent it is retarded by the resistance of the air, as it was in its ascent. This retardation is very obvious in the case of substances which present a large surface to the air, as a feather. A small piece of lead will outweigh many feathers, and therefore, as its quantity of matter is so much greater in proportion to its surface than that of a feather, it will fall to the ground much more quickly. That this is owing wholly to the resistance of the air can be proved with the air-pump.

Fig. 128.

Suppose that you have a tall receiver, Fig. 128, on the air-pump, and a piece of lead and a feather are placed at its upper part in such a way that they can be made to fall at the same instant. Exhaust the air, and then let them fall. They will go down side by side, as represented by the figure, and reach the bottom of the receiver at the same time, because there is no air there to resist the progress of the feather. The toy called the water-hammer illustrates the same thing. When water falls through the air the resistance of the air tends to separate its particles, as we see in the falling of water thrown up by a fountain. In the water-hammer, which is a closed tube containing a little water and no air, when the water is made to fall from one end to the other, as there is no air to divide it, it falls as one mass, and gives a sharp sound like the blow of a hammer. An instrument essentially like this can be made with a thin glass flask. Put a little water in it, and, after heating it to boiling over a spirit-lamp, cork the flask tightly, and then leave the water to cool. As all the space above the water was filled with steam when the flask was corked, it is a vacuum now that the steam is condensed.

193. Relation of Bulk to the Resistance of Liquids and Gases.—You have already seen, in § 192, that the more surface a body has in proportion to its weight the greater is the resistance of the air to its motion. This truth, which applies to liquids as well as to airs or gaseous substances, explains the fact that small bodies meet with proportionately more resistance than large ones. The body B, Fig. 129, you see is made up of eight cubes of the size of the cube a, that is, it has eight times the quantity of matter that a has. Now if B were moving through air or water, any of its sides pushing the water before it would meet with only four times the resistance that a side of a would, for its surface is only four times as large, and yet the body is eight times as large as a. And the greater the difference of size the greater is the difference of resistance. If B were a cube twenty-seven times as large as a it would meet with only nine times as much resistance. You see here the reason that shells and cannon-balls can be thrown much farther than bullets and small shot. The sportsman does not throw away his shot by foolishly aiming at birds at great distances, and yet shells and large cannon-balls can be thrown the distance of several miles. The difference is not in the degree of velocity which the powder produces, but in the resistance of the air. It is for the same reason that rain falls with greater rapidity than drizzling mist.