Through the Earth/Chapter XXVI
A CURIOUS PROBLEM IN ATTRACTION
"S the earth has no longer any attraction for bodies in the car," thought William, "or rather, as it can produce no change in their position in the car, it must follow that if there were any loose objects here they would be attracted toward me and follow me around wherever I went. The car itself would n't attract them, because, the car being almost spherical, the attraction would be the same on all sides, and so neutralize itself. The attraction of each side of the car is balanced by that of the opposite side, and the attraction of the floor balances that of the ceiling. It is true that the furniture on the floor would pull bodies downward, but the furniture on the ceiling would pull them upward to the same extent.
"Consequently, if there were a loose stone in the center of the car, I should be the heaviest body to attract it, and it would accordingly fall to me, whether I were above it or below it, and it would follow me around wherever I went. If there were a whole cart-load of loose pebbles in the car, they would all come clustering about me like a hive of bees. There would be no possible way to escape them, for, wherever I went, they would be obliged to follow. What a glorious time I should have swimming about the car with such a procession after me!"
Our hero was perfectly correct in saying that, now that the earth's attraction no longer influenced the position of objects in the car, they would be free to follow the attraction of other bodies. He was also correct in saying that the attraction of the car itself would be neutralized, since it was practically the same on all sides. Sir Isaac Newton himself demonstrated that if the earth were a hollow shell it would exercise no attraction whatever on bodies in the interior. Hence if people lived inside of it, gravity would no longer exist for them, and they could fly about at will from one point to another.
These facts being admitted, the necessary consequence was that all loose objects in the interior of the car would be attracted toward William. On this point there could be no dispute. But there was one little fact which he overlooked, and that oversight was enough to doom him to disappointment.
William had no pebbles in the car with which to try the experiment, but he had the jack-knife which has already been mentioned, and this would, of course, answer the purpose just as well.
Taking the knife from his pocket, he placed it in the air beside him, and then started to swim for the top of the car. When he reached the top, and turned around to look at the knife, he was overjoyed to find that it had disappeared.
"It is evidently following me," said he. But in this he was mistaken; for, looking more closely, he perceived the knife flying about through the air, but, far from coming toward him, it was going in almost the opposite direction.
"Gracious!" exclaimed our hero, after gazing at it for a few moments in open-mouthed astonishment. "What in the world can be the matter with that knife?"
Then the explanation slowly dawned on him. "I see," said he, laughing. "The wind I make in swimming blows the knife about as though it were a feather. It seems funny to think of blowing a knife about through the air, but that's certainly what I've been doing. I'll have to wait till the wind stops before I can expect my body to act as a magnet and attract the knife toward me."
William was right. It was indeed the wind made by his movements that blew the knife irregularly through the air; for after he had waited a few minutes, and the air became calm again, the knife slowly ceased its movements and came to a rest in mid-air.
"Now it's going to fall toward me," muttered our hero, under his breath, remaining perfectly still to avoid causing new currents. But, to his surprise, although he waited quite a little while after the air had become still again, the knife remained in the identical spot where it had come to rest, about six feet away from him.
"I can't understand this at all," said William, considerably puzzled. "I'm positively certain that, by the laws of physics, that knife ought to fall toward me. And yet it does n't. Of course I know that it won't fall toward me as fast as a knife usually falls to the ground, but it ought to fall toward me at some speed. The rule they taught us at school was that "the attraction of bodies is directly in proportion to their masses." That is to say, if one body weighs twice as much as another (or, more properly speaking, if it contains twice as much matter as another) it will have twice the power of attraction.
"Now I weigh a great deal less than the earth does, and consequently the knife will fall toward me a great deal more slowly than it falls toward the earth. Ah, 'now goes me a light up!' as our German professor used to say. The earth must weigh over a trillion times as much as I do, and consequently, since it would take a second for the knife to fall sixteen feet on the earth, it would take—a trillion seconds for it to fall to me. Now a trillion seconds represent many thousands of years, so that if I want to wait until the knife is attracted to me, I shall have to stay in the same spot here for thousands upon thousands of years, and I'm afraid I have n't the time to spare just at present."
William had hit the nail on the head this time, but he had greatly underestimated the time that would be required. The density of the earth is five and one half times that of water, and our planet, therefore, weighs five and one half times as much as a globe of water of the same size. The diameter of the earth being about eight thousand miles, the weight, or rather the mass, of the earth is no less than thirteen octillion pounds!
It is difficult to form any conception of this stupendous figure, but some idea of it will be obtained when we state that the earth weighed so much more than our hero that, since it would take a second for the knife to fall sixteen feet on the earth, it would take billions upon billions of years for it to fall even one ten thousandth part of an inch nearer to William!
To say that our hero was amazed at the result even of his inaccurate calculations would be to put the matter mildly. Like every other person who has had a smattering of physics, he was familiar with the fact that the attraction of bodies is proportional to their masses; but few persons stop to reflect how infinitesimal the attraction of a man really is in comparison to the attraction of the earth itself.
William, it must be confessed, was highly disappointed at this turn of affairs, for it would have been most amusing to swim around the car, with all the loose objects in it, solids as well as liquids, following around after him as a nail follows a magnet.
This being out of the question, he turned his thoughts to another matter. He had already noticed a reservoir of water fastened to the side of the car, and as his varied exercises had made him somewhat thirsty, he decided to climb up and help himself to a drink.
On the earth it would have been the simplest matter in the world to climb up to the reservoir by means of the straps, and draw off and drink a glass of water. But here in the car, where bodies had no weight, it was by no means so simple a matter as it seemed, and our hero was destined to a fresh series of experiences, more wonderful than any he had yet met with.