CHAPTER XVII.

WHY THE MOON DOES NOT FALL.

Next evening Monsieur Roger, as well as his friend Monsieur Dalize, seemed to have forgotten completely that there was such a thing as physical science. He sat in a corner and chatted about this thing and that with Monsieur and Madame Dalize. Still, the air-pump was there, and the children touched it, looked at it, and examined the different portions of it.

At last there was a conversation in a low tone between Paul and Miette, and in the midst of the whispering were heard these words, clearly pronounced by the lips of Miette,--

"Ask him yourself."

Then Monsieur Roger heard Paul answer,--

"No, I don't dare to."

Miette then came forward towards her friend Roger, and said to him, without any hesitation,--

"Paul asks that you will explain to him about the tower?"

Monsieur Roger remained a moment without understanding, then a light struck him, and he said,--

"Ah! Master Paul wants me to explain to him how I learned the height of the tower Heurtebize?"

"That is it," said Miette.

Paul Solange made an affirmative sign by a respectful movement of the head.

"But," said Monsieur Roger, responding to this sign, "it is physical science, my dear Master Paul,--physical science, you know; and, goodness, I was so much afraid of boring you that both I and Monsieur Dalize had resolved never to approach this subject."

"Still, sir," said Paul, "all that you have said and shown to us was on account of the tower of Heurtebize, and you promised me----"

"That is true," said Monsieur Dalize; "and if you promised, you must keep your word. So explain to Paul how you have been able, without moving, to learn the exact height of that famous tower."

"Come, then, I obey," answered Monsieur Roger.

And, addressing himself to Paul, he said,--

"You will remember that at the beginning of this conversation on gravity I took a little stone and let it fall from my full height. It produced a very feeble shock; but I made you remark that if it were to fall from a greater height the shock would be violent enough to break it."

"Yes," said Paul, "I remember."

"Then, of course, you understand that the violence of the shock of a body against a fixed obstacle depends upon the rate of speed this body possessed at the moment when it encountered the obstacle. The higher the distance from which the body falls, the more violent is the shock,--for its swiftness is greater. Now, the speed of a falling body becomes greater and greater the longer it continues to fall; and, consequently, in falling faster and faster it will traverse a greater and greater space in a given interval of time. In studying the fall of a body we find that in one second it traverses a space of sixteen feet and one inch. In falling for two seconds it traverses----"

"Twice the number of feet," said Miette, with a self-satisfied air.

"Why, no," said Paul; "because it falls faster during the second second, and in consequence travels a greater distance."

"Master Paul is right," replied Monsieur Roger. "It has been found that in falling for two seconds a body falls sixteen feet and one inch multiplied by twice two,--that is to say, sixty-four feet and four inches. In falling three seconds a body traverses sixteen feet and one inch multiplied by three times three,--that is to say, by nine. In falling four seconds it traverses sixteen feet and one inch multiplied by four times four,--that is to say, by sixteen; and so on. This law of falling bodies which learned men have discovered teaches us that in order to calculate the space traversed by a body in a certain number of seconds it is necessary to multiply sixteen feet and one inch by the arithmetical square of that number of seconds. And Master Paul must know, besides, that the square of a number is the product obtained by multiplying this number by itself."

Paul bent his head.

"And now you must also know," continued Monsieur Roger, "how I could calculate the height of the tower of Heurtebize. The stone which you let fall, according to my watch, took two seconds before it reached the soil. The calculation which I had to make was easy, was it not?"

"Yes, sir: it was necessary to multiply sixteen feet and one inch by two times two,--which gives about sixty-four feet and four inches as the height of the tower."

"You are right, and, as you may judge, it was not a very difficult problem."

"Yes," added Monsieur Dalize; "but it was interesting to know why the apple fell, and you have taught us."

"That is true," cried Miette; "only you have forgotten to tell us why the moon does not fall."

"I have not forgotten," said Monsieur Roger; "but I wished to avoid speaking of the attraction of the universe. However, as Miette obliges me, I shall speak. You see that all earthly bodies are subject to a force which has been called gravity, or weight. Now, gravity can also be called attraction. By the word attraction is meant, in fact, the force which makes all bodies come mutually together and adhere together, unless they are separated by some other force. This gravity or attraction which the terrestrial mass exerts upon the objects placed on its surface is felt above the soil to a height that cannot be measured. Learned men have, therefore, been led to suppose that this gravity or attraction extended beyond the limits which we can reach; that it acted upon the stars themselves, only decreasing as they are farther off. This supposition allows it to be believed that all the stars are of similar phenomena, that there is a gravity or attraction on their surface, and that this gravity or attraction acts upon all other celestial bodies. With this frame of thought in his mind, Newton at last came to believe that all bodies attract each other by the force of gravity, that their movements are determined by the force which they exert mutually upon one another, and that the system of the universe is regulated by a single force,--gravity, or attraction."

"But that does not explain to us why the moon does not fall," said Monsieur Dalize.

Monsieur Roger looked at his friend.

"So you also," said he, smiling,--"you also are trying to puzzle me?"

"Of course I am; but I am only repeating the question whose answer Miette is still awaiting."

"Yes," said Miette, "I am waiting. Why does not the moon fall?"

"Well, the moon does not fall because it is launched into space with so great a force that it traverses nearly four-fifths of a mile a second."

Miette ran to open the door of the vestibule. The park was bathed in the mild light of a splendid moon.

"Is it of that moon that you are speaking,--the moon which turns around us?"

"Certainly, as we have no other moon."

"And it turns as swiftly as you say?"

"Why, yes. And do you know why it turns around us, a prisoner of that earth from which it seeks continually to fly in a straight line? It is because----"

Monsieur Roger stopped suddenly, with an embarrassed air.

"What is the matter?" asked Miette.

"Why, I am afraid I have put myself in a very difficult position."

"Why?"

"I have just undertaken to tell you why the moon does not fall. Is not that true?"

"Yes."

"Well, I am obliged to tell you that it does fall."

"Ah, that is another matter!" cried Miette.

"Yes, it is another matter, as you say; and it is necessary that I should speak to you of that other matter. Without that how can I make you believe that the moon does not fall and that it does fall?"

"That would not be easy," said Miss Miette.

"Well, then, imagine a ball shot by a cannon. This ball would go forever in a straight line and with the same swiftness if it were not subject to gravity, to the attraction of the earth. This attraction forces the ball to lower itself little by little below the straight line to approach the earth. At last the time comes when the force of attraction conquers the force which shot the ball, and the latter falls to the earth. This example of the ball may be applied to the moon, which would go forever in a straight line if it were not subject to the attraction of the earth. It shoots in a straight line, ready to flee away from us; but suddenly the attraction of the earth makes itself felt. Then the moon bends downward to approach us, and the straight line which it had been ready to traverse is changed to the arc of a circle. Again the moon endeavors to depart in a straight line, but the attraction is felt again, and brings near to us our unfaithful satellite. The same phenomenon goes on forever, and the straight path which the moon intended to follow becomes a circular one. It falls in every instance towards us, but it falls with exactly the same swiftness as that with which it seeks to get away from us. Consequently it remains always at the same distance. The attraction which prevents the moon from running away may be likened to a string tied to the claws of a cockchafer. The cockchafer flies, seeking to free itself; the string pulls it back towards the child's finger; and very often the circular flight which the insect takes around the finger which holds it represents exactly the circular flight of the moon around the earth."

"But," said Miette, "is there no danger that the moon may fall some time?"

"If the moon had been closer to the earth it would have fallen long ago; but it is more than two hundred and thirty-eight thousand miles away, and, as I have told you, if attraction or gravity acts upon the planets, it loses its power in proportion to the distance at which they are. The same attraction which forces the moon to turn around the earth obliges the earth and the planets to turn around the sun; and the sun itself is not immovable. It flies through space like all the other stars, bearing us in its train, subject also to universal attraction."

Monsieur Roger stopped a moment, then he said,--

"And it is this great law of universal attraction, this law which governs the universe, that Newton discovered when he asked himself, 'Why does the apple fall?'"

"Still, as for me," said Miette, "I should not have had that idea at all; I should have said quietly to myself, 'The apple fell because it was ripe.'"