Through the Earth/Chapter XVI
A STRANGE EXPLANATION
"Not only do I think so, but I am absolutely sure of it."
"Why, what grounds have you for such a belief?"
"I understand your astonishment, James, for I confess I long shared your idea that the passengers in the car would retain their weight until they reached the center of the earth. The problem is a most curious one, and is very puzzling at first; but once the conditions are well understood, the explanation is quite natural."
"Well, I'm afraid that, for my part, I don't know enough about physics to understand your explanations; for none of the physical laws with which I am familiar explains how a man can lose his weight at the very surface of the earth. I suppose, though, that you have found some obscure little law, known only to scientists, which will account for your strange assumption."
"Not a bit of it, James. The law I refer to is one of which you see examples every day, and which is quite a familiar one. Have you ever seen a man riding on a street-car?"
"Well, rather! I see hundreds of them every day," replied Mr. Curtis. "But what connection is there between a man on a street-car and a man falling through the earth?"
"There is a closer connection than you would be ready to believe. Now, let us suppose that the street-car is traveling at the rate of ten miles per hour; do you know how fast the passenger himself is traveling?"
"Why, he must be traveling at the same rate—ten miles per hour, also."
"Quite true. So long as the man does n't walk toward the front or rear of the car he is necessarily traveling at the same rate as the car. Well, now, if, as you say, the man is traveling at just the same speed as the car, no matter how long he travels, will lie find himself any farther front in the car?"
"He'd find himself pushed forward when the car stopped," interposed Flora. "I've noticed that whenever a car stops suddenly I'm always thrown forward."
"Yes; but that's because you're no longer traveling at the same speed as the car. When the car stops, its speed becomes less, while yours remains the same as before. Consequently you are really traveling faster than the car for the time being, and so you tend to get ahead of it."
"Well, I understand all that," growled Mr. Curtis; "but what has this got to do with the entirely different kind of car that we are going to drop through the earth?"
"It has everything to do with the matter. At what speed do you suppose the car will be going during the first second of its fall?"
"It will fall sixteen feet during the first second, being pulled downward by the attraction of the earth."
"Correct; and how fast will the boy be falling?"
"He will be falling sixteen feet per second, too, because gravitation will pull him down just as rapidly as it does the car."
"Also correct. Well, if the boy falls sixteen feet in one second, and the car falls sixteen feet too, how much nearer will the boy be to the bottom of the car at the end of that second than he was before?"
"You don't mean to say that he would n't be any nearer to it than he was before?"
"Most certainly I do. If two people are running a race, and one goes just as fast as the other, neither of them can get ahead."
"Of course not."
"Well, it's the same thing here. The car will travel just as fast as the boy. Consequently if, at the start, the boy is five feet away from the bottom of the car, he will remain five feet away. He is falling just as fast as the bottom of the car, and so cannot get any nearer to it. If he starts in the air he will remain in the air."
"You mean to say that he will remain floating in the air?"
"But the air cannot support him. Air can only hold up very light bodies."
"Understand me. It is not the air that will support the boy. Even though there were no air whatever in the car, if the boy were half-way between the floor and ceiling when the car began to' fall, he would still remain suspended in space."
"But why is it he would n't fall?" asked Flora, not altogether able to understand the matter.
"He would fall," said the doctor; "that is to say, he would fall toward the center of the earth. But the car would be falling, too, so he would remain suspended half-way between the floor and ceiling of the car."
"I must be awfully stupid, but I don't quite understand it yet."
"Well, listen, Flora. Suppose I were to drop a stone down through my tunnel, and were immediately afterward to let another stone fall after it. Would the second stone ever catch up with the first?"
"No, of course not. The first one would be falling just as fast as the second one, and as it started before the other, the second one could never catch up with it."
"Exactly," said Dr. Giles, triumphantly. "Now, suppose I let the bottom of the car fall through the earth first, and then a second later drop William through; could he ever catch up with it?" "No, he could n't."
"Well, that's just the way it will he. I shall arrange matters so that William will start say five feet behind the bottom of the car, and he will accordingly remain five feet behind it during the entire journey. Starting after the floor, he cannot catch up with it; and the ceiling starting behind him, it cannot catch up with him; so he will remain half-way between the floor and ceiling."
"Then you mean to say," said Mr. Curtis, "that William will have absolutely no weight at all during his whole trip through the earth. Yet not long ago you told me, on the contrary, that you expected he would have weight when he arrived near the center of the earth."
"True, and I say so again."
"What!" exclaimed William, "you really believe that while I shall have no weight at the start, I shall yet have a certain amount of weight when I get near the center!"
"I most certainly do," replied the doctor.