CHAPTER XVI.
AMUSING PHYSICS
Hearing Monsieur Roger's jest, Miette raised her head, and said,—
"Yes, it is very curious to see water fall like that, in a single mass; and, besides, it fell quicker than the water in my tube."
"Of course: because it did not encounter the resistance of the air. This resistance is very easy to prove; and if Miss Miette will give me a sheet of any kind of paper–"
Miss Miette looked at Monsieur Roger, seeming to be slightly nettled,—not by the errand, but by something else.
Then she went in search of a sheet of letter-paper, which she brought back to Monsieur Roger. He raised his hand and dropped the paper. Instead of falling directly towards the earth, as a piece of lead or stone would do, it floated downward from the right to the left, gently balanced, and impeded in its fall by the evident resistance of the air. When this bit of paper had at last reached the ground, Monsieur Roger picked it up, saying,—
"I am going to squeeze this bit of paper in such a way as to make it a paper ball; and I am going to let this paper ball fall from the same height as I did the leaf."
The paper ball fell directly in a straight line upon the floor.
"And yet it was the same sheet," said he, "which has fallen so fast. The matter submitted to the action of gravity remains the same; there can be no doubt on that point. Therefore, if the sheet of paper falls more quickly when it is rolled up into a ball, it is certainly because it meets with less resistance from the air; and if it meets with less resistance, it is because under this form of a ball it presents only a small surface, which allows it easily to displace the air in order to pass."
"That is so," said Miss Miette, with a certainty which made every one smile.
Miette, astonished at the effect which she had thus produced, looked at her friend Paul, who remained silent, but very attentive.
"Well, Paul," said she, "is not that certain?"
"Yes," answered Paul.
"Hold," returned Monsieur Roger. "I am going to show you an example still more convincing of the resistance of the air,—only I must have a pair of scissors; and if Miss Miette will have the kindness to–"
Miss Miette looked again at Monsieur Roger with a singular air. None the less, she ran off in search of the scissors. Then Monsieur Roger pulled from his pocket a coin, and with the aid of the scissors cut a round bit of paper, a little smaller than the coin. That done, he placed the circular bit of paper flat upon the coin, in such a manner that it did not overlap, and asked Miss Miette to take the coin between her thumb and her finger.
"Now," said he, "let it all fall."
Miette opened her fingers, and the coin upon which he had placed the bit of paper fell. Coin and paper reached the ground at the same time.
"Why," asked Monsieur Roger, "does the paper reach the ground as soon as the coin?"
And as Miette hesitated to answer, Monsieur Roger continued:
"Because the fall of the bit of paper was not interfered with by the resistance of the air."
"Of course," cried Miette, "it is the coin which opened the way. The paper was preserved by the coin from the resistance of the air."
"Exactly so," said Monsieur Roger; "and these simple experiments have led scientists to ask if in doing away entirely with the resistance of the air it would not be possible to abolish the differences which may be observed between the falling of various bodies,—for instance, the paper and the coin, a hair and a bit of lead. And they have decided that in a vacuum—that is to say, when the resistance of the air is abolished—the paper and the coin, the hair and the lead would fall with exactly the same swiftness; all of them would traverse the same space in the same time."
"The hair falls as fast as lead," said Miette, in a tone which seemed to imply, "I would like to see that."
Monsieur Roger understood the thought of Miette, and answered by saying,—
"Well, I am going to show you that."
He chose a long tube of glass, closed by bits of metal, one of which had a stop-cock. He put in this tube the coin, the round bit of paper, a bit of lead, and a strand of hair from Miss Miette's head. Then he fastened the tube by one of its ends upon the disk of the air-pump and worked the pistons. As soon as he thought that the vacuum had been made, he closed the stop-cock of the tube, to prevent the exterior air from entering. He withdrew the tube from the machine, held it vertically, then turned it briskly upsidedown. Everybody saw that the paper, the coin, the hair, and the lead all arrived at the same time at the bottom of the tube. The experiment was conclusive. Then Monsieur Roger opened the stop-cock and allowed the air to enter into the tube. Again he turned the tube upsidedown: the coin and the bit of lead arrived almost together at the bottom of the tube, but the paper, and especially the strand of hair, found much difficulty on the way and arrived at the bottom much later.
"Why, how amusing that is!" cried Miette; "as amusing as anything I know. I don't understand why Paul wishes to have nothing to do with physical science."
But Miette was mistaken this time, for Paul was now very anxious to learn more.
"Very well," said Monsieur Roger, "as all this has not wearied you, I am, in order to end to-day, going to make another experiment which will not be a bit tiresome, and which, without any scientific apparatus, without any air-pump, will demonstrate to you for the last time the existence of the pressure, of the weight of the atmosphere."
Monsieur Roger stopped and looked at Miette, whose good temper he was again going to put to the test. Then he said,—
"I need a carafe and a hard egg; and if Miss Miette will only be kind enough to–"
This time Miette seemed still more uneasy than ever, more embarrassed, more uncomfortable; still, she fled rapidly towards the kitchen. During her absence, Monsieur Roger said to Madame Dalize,—
"Miette seems to think that I trouble her a little too often."
"That is not what is annoying her, I am certain," replied Madame Dalize; "but I do not understand the true cause. Let us wait."
At this moment Miette returned, with the carafe in one hand, the hard-boiled egg (it was not boiled very hard, however) in the other. Monsieur Roger took the shell off the egg and placed the egg thus deprived of its shell upon the empty carafe, somewhat after the manner of a stopper or cork.
"What I want to do," said he, "is to make this egg enter the carafe."
"Very well," said Miette; "all you have to do is to push from above: you will force the egg down."
"Oh, but nobody must touch it. It must not be a hand that forces it down, but by weight from above. No, the atmosphere must do this."
Monsieur Roger took off the egg, and lit a bit of paper, which he threw into the empty carafe.
"In order to burn," said he, "this paper is obliged to absorb the oxygen of the air in the carafe,—that is to say, it makes a partial vacuum." When the paper had burned for some moments, Monsieur Roger replaced the egg upon the carafe's neck, very much in the manner you would place a close-fitting ground-glass stopper in the neck of a bottle, and immediately they saw the egg lengthen, penetrate into the neck of the carafe, and at last fall to the bottom. "There," said he, "is atmospheric pressure clearly demonstrated. When a partial vacuum had been made in the carafe,—that is to say, when there was not enough air in it to counterbalance or resist the pressure of the exterior air,—this exterior air pressed with all its weight upon the egg and forced it down in very much the same way as Miss Miette wished me to do just now with my hand."
In saying these last words, Monsieur Roger looked towards Miette.
"By the way," he said, "I must apologize to you, Miss Miette, for having sent you on so many errands. I thought I saw that it annoyed you a little bit."
Miss Miette raised her eyes with much surprise to Monsieur Roger.
"But that was not it at all," said she.
"Well, what was it?" asked Monsieur Roger.
And Miette replied timidly, yet sweetly,—
"Why, I only thought that you might stop calling me Miss. If you please, I would like to be one of your very good friends."
"Oh, yes; with very great pleasure, my dear little Miette," cried Monsieur Roger, much moved by this touching and kindly delicacy of feeling, and opening his arms to the pretty and obliging little child of his friends.
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.'"
CHAPTER XVIII.
A MYSTERIOUS RESEMBLANCE
The days passed by at the château 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 album.
"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.
An hour later, Monsieur Roger, in his walk, saw at the turning of a pathway lined by young chestnut-trees a scene which brought a smile to his lips. Two camp-stools were placed in front of each other, some distance apart; upon one of these camp-stools Paul was seated, his album and his pencil between his hands; on the other camp-stool was Miss Miette, posing for a portrait. Monsieur Roger approached.
When Miette saw him, she sat up, and, crossing her little arms, cried, with pretended anger,—
"I told you so: he is going to sketch me."
"Oh, Miette," said Paul, softly, "you have spoiled the pose."
Miette turned towards Paul, and, seeing that she had made him angry, returned to her former attitude without saying a word. Monsieur Roger looked at Miette, so pretty, so restless by disposition, now forcing herself to sit quietly, with an expression of determination upon her face that was half serious and half laughing. Then he cast his eyes upon Paul's album, but at that moment Paul was scratching over with his pencil the sketch which he had begun.
"Never," said he, discouraged, "never shall I be able to catch her likeness."
"That is not astonishing," replied Monsieur Roger. "I was struck at once with the change in her face. Miette in posing does not resemble herself any longer."
"That is true, sir; but why is it?"
"Why, because it is possible that it does not amuse her very much."
Miette began to laugh. Monsieur Roger had guessed aright.
"Oh, stay like that!" cried Paul, seeing Miette's face lighten up with gayety.
"I will remain like this on one condition."
"And what is that?"
"That our friend Roger will remain also with us. I shall have some one to whom I can talk, and you, Paul, will make your sketch at your ease."
"That is understood," said Monsieur Roger, seating himself upon a bank of stones beside the children. At first he lent a rather listless ear to Miette's words, for he was thinking of something else, and he only uttered a word or two in answer, which, however, allowed the little girl to think that she was being listened to. His eyes had travelled from the model to the artist. Since his arrival at Sainte-Gemme Paul's face had slightly changed: his hair, which had been cut short at school, had lengthened, and now fell over his forehead, shading the top of his face and giving him an expression that was slightly feminine; his large eyes, with long, black lashes, went from Miette to the sketch-book with a grave attention which the presence of a third party did not trouble at all. Roger's looks had rested upon Paul, full of that sympathy which the boy had inspired in him the first time he had seen him; but, instead of looking elsewhere at the end of a few minutes, his eyes were riveted upon Paul's face. He eagerly examined every feature of that face, which had suddenly been revealed to him under a new aspect. He had become very pale, and his hands trembled slightly. Miette perceived this sudden change, and, full of uneasiness, cried out,—
"Why, what is the matter?"
Recalled to himself by this exclamation, Monsieur Roger shook his head, passed his hand over his eyes, and answered, striving to smile,—
"Why, there is nothing the matter with me, my dear, except a slight dizziness, caused by the sun no doubt. Don't be uneasy about me. I am going back home."
And Monsieur Roger left them at a rapid pace, cutting across the pathway to get out of sight of the children. He walked like a crazy man; his eyes were wild, his brain full of a strange and impossible idea. When he had reached the other end of the park, sure of being alone, sure of not being seen, he stopped; but then he felt weak, and he allowed himself to fall upon the grass. For a long time he remained motionless, plunged in thought. At last he got up, murmuring,—
"Why, that is impossible. I was a fool."
He was himself again. He had thought over everything, he had weighed everything, and he persuaded himself that he had been the plaything of a singular hallucination. Still reasoning, still talking to himself, he took no notice of where he was going. Suddenly he perceived that he was returning to the spot which he had left. He stopped, and heard the voice of Miette in the distance; then he approached as softly as was possible, walking on tiptoe and avoiding the gravel and the falling leaves. One wish filled his heart,—to see Paul again without being seen. He walked through the woods towards the side whence the voice had made itself heard. The voice of Miette, now very close, said,—
"Let's see, Paul. Is it finished?"
"Yes," answered Paul; "only two minutes more. And this time, thanks to Monsieur Roger, it will be something like you."
Monsieur Roger, hidden behind branches and leaves, came nearer, redoubling his precautions. At last, through an opening in the foliage he perceived Paul Solange. He looked at him with profound attention until the lad, having started off with Miette, was some distance away. When the two children had disappeared, Monsieur Roger took the shaded path he had been following and went towards the château. He walked slowly, his head bent down, his mind a prey to mysterious thoughts. He had seen Paul again, and had studied his face, this time appealing to all his coolness, to all his reasoning power. And now a violent, unconquerable emotion bound him. In vain he tried in his sincerity to believe in a too happy and weak illusion, in a too ardent desire, realized only in his imagination. No, he was forced to admit that what he had just beheld had been seen with the eyes of a reasoning and thinking man whose brain was clear and whose mind was not disordered. However, this thought which had taken possession of him, this overwhelming idea of happiness, was it even admissible? And Monsieur Roger, striving to return to the reality, murmured,—
"It is folly! it is folly!"
Was it not in fact folly which had led him suddenly to recognize in the features of Paul Solange those of Madame Roger La Morlière? Was it not folly to have noticed a mysterious, surprising, and extraordinary resemblance between the face of Paul Solange and the sweet one of her who had been the mother of George? Yes, it was madness, it was impossible. Yet, in spite of all, Monsieur Roger said to himself, deep down in his heart,—
"If it were my son?"