"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 s.p.a.ce 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 ma.s.s 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 s.p.a.ce 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 embarra.s.sed air.
"What is the matter?" asked Miette.
"Why, I am afraid I have put myself in a very difficult position."
"Why?"
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"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 c.o.c.kchafer. The c.o.c.kchafer 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 s.p.a.ce 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.""
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CHAPTER XVIII.
A MYSTERIOUS RESEMBLANCE.
The days pa.s.sed by at the chateau of Sainte-Gemme quietly and happily.
Monsieur Roger, having fulfilled his promise to give the explanation of gravity and of attraction, was careful to make no allusions to scientific matters. He thought it useful and right to let his little hearers find their own pleasures wherever they could. One afternoon he saw Miette and Paul leave the house together. Paul had two camp-stools, while Miette held her friend"s alb.u.m.
"Where are you going?" asked Monsieur Roger.
"We are going to sketch," answered Paul: "at the end of the park."
Miette put on the air of a martyr, and said to Monsieur Roger,--
"I think he is going to sketch me."
"Not at all; come along," replied Paul.
And Miette ran gayly after Paul.