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 asphysical science. He sat in a corner and chatted about this thing andthat with Monsieur and Madame Dalize. Still, the air-pump was there, andthe children touched it, looked at it, and examined the differentportions 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, clearlypronounced 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 lightstruck him, and he said,--
"Ah! Master Paul wants me to explain to him how I learned the height ofthe tower Heurtebize?"
"That is it," said Miette.
Paul Solange made an affirmative sign by a respectful movement of thehead.
"But," said Monsieur Roger, responding to this sign, "it is physicalscience, my dear Master Paul,--physical science, you know; and,goodness, I was so much afraid of boring you that both I and MonsieurDalize had resolved never to approach this subject."
"Still, sir," said Paul, "all that you have said and shown to us was onaccount of the tower of Heurtebize, and you promised me----"
"That is true," said Monsieur Dalize; "and if you promised, you mustkeep your word. So explain to Paul how you have been able, withoutmoving, 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 gravityI took a little stone and let it fall from my full height. It produced avery feeble shock; but I made you remark that if it were to fall from agreater 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 abody against a fixed obstacle depends upon the rate of speed this bodypossessed at the moment when it encountered the obstacle. The higher thedistance from which the body falls, the more violent is the shock,--forits swiftness is greater. Now, the speed of a falling body becomesgreater and greater the longer it continues to fall; and, consequently,in falling faster and faster it will traverse a greater and greaterspace in a given interval of time. In studying the fall of a body wefind that in one second it traverses a space of sixteen feet and oneinch. 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 thatin falling for two seconds a body falls sixteen feet and one inchmultiplied by twice two,--that is to say, sixty-four feet and fourinches. In falling three seconds a body traverses sixteen feet and oneinch multiplied by three times three,--that is to say, by nine. Infalling four seconds it traverses sixteen feet and one inch multipliedby four times four,--that is to say, by sixteen; and so on. This law offalling bodies which learned men have discovered teaches us that inorder to calculate the space traversed by a body in a certain number ofseconds it is necessary to multiply sixteen feet and one inch by thearithmetical square of that number of seconds. And Master Paul mustknow, besides, that the square of a number is the product obtained bymultiplying this number by itself."
Paul bent his head.
"And now you must also know," continued Monsieur Roger, "how I couldcalculate the height of the tower of Heurtebize. The stone which you letfall, according to my watch, took two seconds before it reached thesoil. 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 twotimes two,--which gives about sixty-four feet and four inches as theheight of the tower."
"You are right, and, as you may judge, it was not a very difficultproblem."
"Yes," added Monsieur Dalize; "but it was interesting to know why theapple fell, and you have taught us."
"That is true," cried Miette; "only you have forgotten to tell us whythe moon does not fall."
"I have not forgotten," said Monsieur Roger; "but I wished to avoidspeaking of the attraction of the universe. However, as Miette obligesme, I shall speak. You see that all earthly bodies are subject to aforce which has been called gravity, or weight. Now, gravity can also becalled attraction. By the word attraction is meant, in fact, the forcewhich makes all bodies come mutually together and adhere together,unless they are separated by some other force. This gravity orattraction which the terrestrial mass exerts upon the objects placed onits surface is felt above the soil to a height that cannot be measured.Learned men have, therefore, been led to suppose that this gravity orattraction extended beyond the limits which we can reach; that it actedupon the stars themselves, only decreasing as they are farther off. Thissupposition allows it to be believed that all the stars are of similarphenomena, that there is a gravity or attraction on their surface, andthat this gravity or attraction acts upon all other celestial bodies.With this frame of thought in his mind, Newton at last came to believethat all bodies attract each other by the force of gravity, that theirmovements are determined by the force which they exert mutually upon oneanother, and that the system of the universe is regulated by a singleforce,--gravity, or attraction."
"But that does not explain to us why the moon does not fall," saidMonsieur 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 answerMiette 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 sogreat 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 themild light of a splendid moon.
"Is it of that moon that you are speaking,--the moon which turns aroundus?"
"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 thatearth from which it seeks continually to fly in a straight line? It isbecause----"
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 notthat 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 Ishould speak to you of that other matter. Without that how can I makeyou 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 foreverin a straight line and with the same swiftness if it were not subject togravity, to the attraction of the earth. This attraction forces the ballto lower itself little by little below the straight line to approach theearth. At last the time comes when the force of attraction conquers theforce which shot the ball, and the latter falls to the earth. Thisexample of the ball may be applied to the moon, which would go foreverin a straight line if it were not subject to the attraction of theearth. It shoots in a straight line, ready to flee away from us; b
utsuddenly the attraction of the earth makes itself felt. Then the moonbends downward to approach us, and the straight line which it had beenready to traverse is changed to the arc of a circle. Again the moonendeavors to depart in a straight line, but the attraction is feltagain, and brings near to us our unfaithful satellite. The samephenomenon goes on forever, and the straight path which the moonintended to follow becomes a circular one. It falls in every instancetowards us, but it falls with exactly the same swiftness as that withwhich it seeks to get away from us. Consequently it remains always atthe same distance. The attraction which prevents the moon from runningaway may be likened to a string tied to the claws of a cockchafer. Thecockchafer flies, seeking to free itself; the string pulls it backtowards the child's finger; and very often the circular flight which theinsect takes around the finger which holds it represents exactly thecircular flight of the moon around the earth."
"But," said Miette, "is there no danger that the moon may fall sometime?"
"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. Thesame attraction which forces the moon to turn around the earth obligesthe earth and the planets to turn around the sun; and the sun itself isnot immovable. It flies through space like all the other stars, bearingus 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 whichgoverns the universe, that Newton discovered when he asked himself, 'Whydoes the apple fall?'"
"Still, as for me," said Miette, "I should not have had that idea atall; I should have said quietly to myself, 'The apple fell because itwas ripe.'"