Monsieur Roger, hiding his satisfaction, seemed to attach no importance to this request of Miette under the assent given by Paul. Wishing to profit by the awakened curiosity of his little friend, he hastened to continue, and said,—
"Who wants to bring me a bit of cork and a glass of water?"
"I! I!" cried Miette, running.
When Miette had returned with the articles, Monsieur Roger continued:
"I told you a moment ago that if balloons and smoke and clouds do not fall, it is because they find themselves in the midst of air which is heavier than they are. I am going to try an experiment which will make you understand what I have said."
Monsieur Roger took the cork, raised his hand above his head, and opened his fingers: the cork fell.
"Is it a heavy body?" said he. "Did it fall to the ground?"
"Yes," cried Paul and Miette together.
Then Monsieur Roger placed the glass of water in front of him, took the cork, which Miette had picked up, and forced it with his finger to the bottom of the glass; then he withdrew his finger, and the cork mounted up to the surface again.
"Did you see?" asked Monsieur Roger.
"Yes," said Miss Miette.
"You remarked something?"
"Certainly: the cork would not fall, and you were obliged to force it into the water with your finger."
"And not only," continued Monsieur Roger, "it would not fall, as you say, but it even hastened to rise again as soon as it was freed from the pressure of my finger. We were wrong, then, when we said that this same cork is a heavy body?"
"Ah, I don't know," said Miette, a little confused.
"Still, we must know. Did this cork fall just now upon the ground?"
"Yes."
"Then it was a heavy body?"
"Yes."
"And now that it remains on the surface of the water, that it no longer precipitates itself towards the earth, it is no longer a heavy body?"
This time Miette knew not what to answer.
"Well, be very sure," continued Monsieur Roger, "that it is heavy. If it does not fall to the bottom of the water, it is because the water is heavier than it. The water is an obstacle to it. Nevertheless, it is attracted, like all bodies, towards the earth, or, more precisely, towards the centre of the earth."
"Towards the centre of the earth?" repeated Miette.
"Yes, towards the centre of the earth. Can Miss Miette procure for me two pieces of string and two heavy bodies,—for example, small pieces of lead?"
"String, yes; but where can I get lead?" asked Miette.
"Look in the box where I keep my fishing-tackle," said Monsieur Dalize to his daughter, "and find two sinkers there."
Miette disappeared, and came back in a moment with the articles desired. Monsieur Roger tied the little pieces of lead to the two separate strings. Then he told Miette to hold the end of one of these strings in her fingers. He himself did the same with the other string. The two strings from which the sinkers were suspended swayed to and fro for some seconds, and then stopped in a fixed position.
"Is it not evident," said Monsieur Roger, "that the direction of our strings is the same as the direction in which the force which we call weight attracts the bodies of lead? In fact, if you cut the string, the lead would go in that direction. The string which Miss Miette is holding and that which I hold myself seem to us to be parallel,—that is to say, that it seems impossible they should ever meet, however long the distance which they travel. Well, that is an error. For these two strings, if left to themselves, would meet exactly at the centre of the earth."
"Then," said Miette, "if we detach the sinkers, they would fall, and would join each other exactly at the centre of the earth?"
"Yes, if they encountered no obstacle; but they would be stopped by the resistance of the ground. They would attempt to force themselves through, and would not succeed."
"Why?"
"Why, if the ground which supports us did not resist, we would not be at this moment chatting quietly here on the surface of the earth; drawn by gravity, we would all be——"
"At the centre of the earth!" cried Miette.
"Exactly. And it might very well happen that I would not then be in a mood to explain to you the attraction of gravity."
"Yes, that is very probable," said Miss Miette, philosophically. Then she added, "If, instead of letting these bits of lead fall upon the ground, we let them fall in water?"
"Well, they would approach the centre of the earth for the entire depth of the water."
Miette had mechanically placed the sinker above the glass of water. She let it fall into it; the cork still swam above.
"Why does the lead fall to the bottom of the water, and why does the cork not fall?"
"Why," said Albert, "because lead is heavier than cork."
Miette looked at her brother, and then turned her eyes towards Monsieur Roger, as if the explanation given by Albert explained nothing, and finally she said,—
"Of course lead is heavier than cork; but why is it heavier?"
"My child, you want to know a great deal," said Madame Dalize.
"Ah, mamma, it is not my fault,—it is Paul's, who wants to know, and does not like to ask. I am obliged to ask questions in his stead."
That was true. Paul asked no questions, but he listened with attention, and his eyes seemed to approve the questions asked by his friend Miette. Monsieur Roger had observed with pleasure the conduct of his young friend, and it was for him, while he was looking at Miette, the latter continued:
"Tell us, Monsieur Roger, why is lead heavier than cork?"
"Because its density is greater," answered Monsieur Roger, seriously.
"Ah!" murmured Miette, disappointed; and, as Monsieur Roger kept silent, she added, "What is density?"
"It would take a long time to explain."
"Tell me all the same."
Monsieur Roger saw at this moment that Paul was beckoning to Miette to insist.
"Goodness!" said he, smiling at Paul; "Miss Miette was right just now. It is you that wish me to continue the questions!"
CHAPTER XIII.
WHY LEAD IS HEAVIER THAN CORK.
Monsieur Roger continued in these words:
"We say that a body has density when it is thick and packed close. We give the name of density to the quantity of matter contained in a body of a certain size.
"Let us suppose that this bit of lead has the same bulk—that is to say, that it is exactly as big—as the cork. Suppose, also, that we have a piece of gold and a piece of stone, also of the same bulk as the cork, and that we weigh each different piece in a pair of scales. We would find that cork weighs less than stone, that stone weighs less than lead, and that lead weighs less than gold. But, in order to compare these differences with each other, it has been necessary to adopt a standard of weight.
"I now return to Miss Miette's question,—'Why is lead heavier than cork?'—a question to which I had solemnly answered, 'Because its density is greater.' Miss Miette must now understand that cork, weighing four times less than water, cannot sink in water, although that process is very easy to lead, which weighs eleven times more than water. And yet," said Monsieur Roger, "the problem is not perfectly solved, and I am quite sure that Miss Miette is not entirely satisfied."
Miss Miette remained silent.
"I was not mistaken. Miss Miette is not satisfied," said Monsieur Roger; "and she is right,—for I have not really explained to her why lead is heavier than cork."
Miss Miette made a gesture, which seemed to say, "That is what I was expecting."
"I said just now," continued Monsieur Roger, "that the density of a body was the quantity of matter contained in this body in a certain bulk. Now does Miss Miette know what matter is?"
"No."
"No! Now, there is the important thing: because, in explaining to her what matter is, I will make her understand why lead is heavier than cork."
"Well, I am listening," said Miette.
And Master Paul respectfully added, in an undertone, "We are listening."
Monsieur Roger continued:
"The name of 'bodies' has been given to all objects which, in infinite variety, surround us and reveal themselves to us by the touch, taste, sight, and smell. All these bodies present distinct properties; but there are certain numbers of properties which are common to all. Those all occupy a certain space; all are expanded by heat, are contracted by cold, and can even pass from the solid to the liquid state, and from the liquid to the gaseous state. They all possess a certain amount of elasticity, a certain amount of compressibility,—in a word, there exist in all bodies common characteristics: so they have given a common name to those possessing these common properties, and called that which constitutes bodies 'matter.' Bodies are not compact, as you may imagine. They are, on the contrary, formed by the union of infinitely small particles, all equal to each other and maintained at distances that are relatively considerable by the force of attraction.
"These infinitely small particles have received the names of atoms or molecules. Imagine a pile of bullets, and remark the empty spaces left between them, and you will have a picture of the formation of bodies. I must acknowledge to you that no one has yet seen the molecules of a body. Their size is so small that no microscope can ever be made keen enough to see them. A wise man has reached this conclusion: That if you were to look at a drop of water through a magnifying instrument which made it appear as large as the whole earth, the molecules which compose this drop of water would seem hardly bigger than bits of bird-shot. Still, this conception of the formation of bodies is proved by certain properties which matter enjoys. Among these properties I must especially single out divisibility. Matter can be divided into parts so small that it is difficult to conceive of them. Gold-beaters, for instance, succeed in making gold-leaf so thin that it is necessary to place sixty thousand one on top of the other to arrive at the thickness of an inch. I will give you two other examples of 'divisibility' that are still more striking. For years, hardly losing any of its weight, a grain of musk spreads a strong odor. In a tubful of water one single drop of indigo communicates its color. The smallness of these particles of musk which strike the sense of smell and of these particles of indigo which color several quarts of water is beyond our imagination to conceive of. And these examples prove that bodies are nothing but a conglomeration of molecules. Now, if lead is heavier than cork, it is because in an equal volume it contains a far more considerable quantity of molecules, and because these molecules are themselves heavier than the molecules of cork. And now I shall stop," said Monsieur Roger, "after this long but necessary explanation. I will continue on the day when Miss Miette will present to me the famous air-pump."
"That will not be very long from now," said Miss Miette to herself.
CHAPTER XIV.
THE AIR-PUMP.
Monsieur Roger had deferred his explanations for three days. He was awaiting the air-pump which Monsieur Dalize, at Miette's desire, had decided to purchase in Paris. Monsieur Roger judged that this interruption and this rest were necessary. In this way his hearers would not be tired too soon, and their curiosity, remaining unsatisfied for the moment, would become more eager. He was not mistaken; and when a large box containing the air-pump and other objects ordered by Monsieur Roger arrived, a series of cries of astonishment came from the pretty mouth of Miss Miette. Paul Solange, however, remained calm; but Monsieur Roger knew that his interest had been really awakened. They spent the afternoon in unpacking the air-pump, and Monsieur Roger was called upon at once to explain the instrument.
"The machine," he said, "is called an air-pump because it is intended to exhaust air contained in a vase or other receptacle. To exhaust the air in a vase is to make a vacuum in that vase. You will see that this machine is composed of two cylinders, or pump-barrels, out of which there comes a tube, which opens in the centre of this disk of glass. Upon this disk we carefully place this globe of glass; and now we are going to exhaust the air contained in the globe."
"We are going to make a vacuum," said Miette.
"Exactly." And Monsieur Roger commenced to work the lever. "You will take notice," he said, "that when the lever is lowered at the left the round piece of leather placed in the cylinder on the left side is lowered, and that the bit of leather in the right-hand cylinder is raised. In the same way, when the lever is lowered at the right, it is the right-hand piece of leather which is lowered, while the piece of leather at the left is raised in its turn. These round bits of leather, whose importance is considerable, are called pistons. Each piston is hollow and opens into the air on top, while at the bottom, which communicates with that portion of the cylinder situated below the piston, there is a little hole, which is stopped by a valve. This valve is composed of a little round bit of metal, bearing on top a vertical stem, around which is rolled a spring somewhat in the shape of a coil or ringlet. The ends of this spring rest on one side on a little bit of metal, on the other on a fixed rest, pierced by a hole in which the stem of the valve can freely go up and down. When I work the lever, as I am doing now, you see that on the left side the piston lowers itself in the cylinder, and that the piston on the right is raised. Now, what is going on in the interior of each cylinder? The piston of the left, in lowering, disturbs the air contained in the cylinder,—it forces it down, it compresses it. Under this compression the coiled spring gives way, the round bit of metal is raised, and opens the little hole which puts the under part of the piston in communication with the atmosphere. The air contained in the cylinder passes in this way across the piston and disperses itself in the air which surrounds us. But the spring makes the bit of metal fall back again and closes the communication in the right-hand cylinder as soon as the piston commences to rise and the pressure of the air in the cylinder is not greater than the pressure of the atmosphere outside. Lastly, the tube which unites the cylinders to the glass globe opens at the end of each cylinder, but a little on the side. It is closed by a little cork, carried by a metal stem which traverses the whole piston. When I cause one of the pistons to lower, the piston brings the stem down with it. The cork at once comes in contact with the hole, which closes; the stem is then stopped, but the piston continues to descend by sliding over it. In the other cylinder, in which the piston is raised, it commences by raising the stem, which re-establishes communication with the glass globe; but as soon as the top of the stem comes in contact with the upper part of the cylinder, it stops and the piston glides over it and continues to rise."
"In this fashion the movements of the cork are very small, and it opens and shuts the orifice as soon as one of the pistons begins to descend and the other begins to ascend. Consequently, by working the lever for a certain space of time, I will finish by exhausting the globe of all the air which it contains."
"May I try to exhaust it?" asked Miette, timidly.
"Try your hand, Miss Miette," answered Monsieur Roger.
Miette began to work the lever of the air-pump, which she did at first very easily, but soon she stopped.
"I cannot do it any more," said she.
"Why?"
"Because it is too heavy."
"In fact, it is too heavy," said Monsieur Roger; "but tell me, what is it that is too heavy?"
Miette sought an answer.
"Oh, I do not know. It is the lever or the pistons which have become all of a sudden too heavy."
"Not at all; that is not it. Neither the lever nor the pistons can change their weight."
"Then, what is it that is so heavy?"
"Come, now! Try once more, with all your strength."
Miette endeavored to lower the right-hand side of the lever: she could not succeed.
"Why," said she, "it is, of course, the piston on the left which has become too heavy, as I cannot make it rise again."
"You are right, Miss Miette. It is the piston in the left cylinder which cannot rise; but it has not changed its weight, as I said,—only it has now to support a very considerable weight; and it is that weight which you cannot combat."
"What weight is it?" said Miette, who did not understand.
"The weight of the air."
"The weight of the air? But what air?"
"The air which is above it,—the exterior air; the air which weighs down this piston, as it weighs us down."
"Does air weigh much?"
"If you are very anxious to know, I will tell you that a wine gallon of air weighs about seventy-two grains; and as in the atmosphere—that is to say, in the mass of air which surrounds us—there is a very great number of gallons, you can imagine that it must represent a respectable number of pounds. It has been calculated, in fact, that each square inch of the surface of the soil supports a weight of air of a little more than sixteen pounds."
"But how is that?" cried Miette. "A while ago there was also a considerable quantity of air above the piston, and yet I could make it go up very easily."
"Certainly, there was above the piston the same quantity of air as now, but there was air also in the globe. Air, like gas, possesses an elastic force,—that is to say, that it constantly endeavors to distend its molecules, and presses without ceasing upon the sides of the vase which contained it, or upon the surrounding air. Now, when you began to work the lever there was still enough air in the globe to balance, through its elastic force, the air outside; and, as the piston receives an almost equal pressure of air from the atmosphere above and from the globe below, it is easily raised and lowered. But while you were working the lever you took air out of the globe, so that at last there arrived a time when so little air remained in this globe that its elastic force acted with little power upon the piston. So the piston was submitted to only one pressure,—that of the atmosphere; and, as I have just told you, the atmosphere weighs heavy enough to withstand your little strength. Still, all the air in the globe is not yet exhausted, and a stronger person, like Master Paul, for example, could still be able to conquer the resistance of the atmosphere and raise the piston."
Paul Solange could not refuse this direct invitation, and he approached the air-pump and succeeded in working the lever, though with a certain difficulty.
Meanwhile, Monsieur Roger was seeking among the physical instruments which had just arrived. He soon found a glass cylinder, whose upper opening was closed by a bit of bladder stretched taut and carefully tied upon the edges.
"Stop, Master Paul," said he: "we are going to exchange the globe for this cylinder, and you will see very readily that the air is heavy. Now take away the globe."
But, though Paul tried his best, he could not succeed in obeying this order. The globe remained firm in its place.
"That is still another proof of the weight of the air," said Monsieur Roger. "The globe is empty of air; and as there is no longer any pressure upon it except from outside,—the pressure of the atmosphere,—Master Paul is unable to raise it."
"He would be able to raise the glass," said Miss Miette, in a questioning tone, "but he cannot lift the air above it?"
"You are exactly right. But you are going to see an experiment which will prove it. First, however, it will be necessary to take away the globe. I am going to ask Miss Miette to turn this button, which is called the key of the air-pump."
Miette turned the key, and then they heard a whistling sound.
"It is the air which is entering the globe," said Monsieur Roger. "Now Master Paul can take the globe away."
That was true. When Paul took away the globe, Monsieur Roger put in its place the cylinder closed by the bit of bladder. Then he worked the handle of the machine again. As the air was withdrawn from the interior of the cylinder, the membrane was heard to crackle. Suddenly it burst, with a sort of explosion, to the great surprise of Miette and the amusement of everybody.
"What is the matter?" said Miette, eagerly.
"The matter is," answered Monsieur Roger, "that the exterior air weighed so heavily upon the membrane that it split it; and that is what I want to show you. The moment arrived when the pressure of the atmosphere was no longer counterbalanced by the elastic force of the air contained in the cylinder. Then that exhausted all the air, and the atmosphere came down with all its weight upon the membrane, which, after resisting for a little while, was torn."
"Is it true, Monsieur Roger," said Miette, "that it is with this machine that you can make smoke fall?"
"Certainly."
"Well, then, won't you show that to us?"
CHAPTER XV.
DROPS OF RAIN AND HAMMER OF WATER.
"I am very willing to show you that," answered Monsieur Roger; "but I must have a candle."
Miette ran to the kitchen and succeeded in obtaining that article which was once so common, and which is now so rare, known as a candle. Monsieur Roger lit the candle and placed it under the glass globe of the air-pump. Then he asked Paul to make a vacuum. At the end of a few minutes the candle went out. Monsieur Roger then told Paul to stop.
"Why has the candle gone out?" asked Miette.
"Because it needs air. Master Paul has just exhausted the air necessary to the combustion of the candle; but the wick still smokes, and we are going to see if the smoke which it produces will rise or fall."
Everybody approached the globe, full of curiosity.
"It falls," cried Miette, "the smoke falls."
And in fact, instead of rising in the globe, the smoke lowered slowly and heavily, and fell upon the glass disk of the air-pump.
"Well," said Monsieur Roger, "you see that I was right. In a vacuum smoke falls: it falls because it no longer finds itself in the midst of air which is heavier than it and forms an obstacle to its fall. In the same way the cloud in the sky above the château would fall if we could exhaust the air which is between it and us."
"I am very glad that we cannot," cried Miette.
"And why are you very glad?" asked Madame Dalize.
"Because, mamma, I don't wish any rain to fall."
"Does Miss Miette think, then," said Monsieur Roger, "that if the cloud fell rain would fall?"
"Certainly," answered Miss Miette, with a certain amount of logic. "When the clouds fall they fall in the form of rain."
"Yes; but supposing that I should exhaust the air which is between the cloud and us, the cloud would not fall in a rain, but in a single and large mass of water."
"Why?"
"Clouds, you doubtless know, are masses of vapor from water. Now, when these vapors are sufficiently condensed to acquire a certain weight, they can no longer float in the atmosphere, and they fall in the form of rain. But they fall in rain because they have to traverse the air in order to fall to the ground. Now, the air offers such a resistance to this water that it is obliged to separate, to divide itself into small drops. If there were no air between the water and the ground, the water would not fall in drops of rain, but in a mass, like a solid body; and I am going to prove that to you, so as to convince Miss Miette."
Among the various instruments unpacked from the box, Monsieur Roger chose a round tube of glass, closed at one end, tapering, and open at the other end. He introduced into this tube a certain quantity of water so as to half fill it. Then he placed the tube above a little alcohol lamp, and made the water boil.
"Remark," said he, "how fully and completely the vapors from the water, which are formed by the influence of heat, force out the air which this tube encloses in escaping by the open end of the tube."
When Monsieur Roger judged that there no longer remained any air in the tube, he begged Monsieur Dalize to hand him the blowpipe. Monsieur Dalize then handed to his friend a little instrument of brass, which was composed of three parts,—a conical tube, furnished with a mouth, a hollow cylinder succeeding to the first tube, and a second tube, equally conical, but narrower, and placed at right angles with the hollow cylinder. This second tube ended in a very little opening.
Monsieur Roger placed his lips to the opening of the first tube, and blew, placing the little opening of the second tube in front of the flame of a candle, which Monsieur Dalize had just lit. A long and pointed tongue of fire extended itself from the flame of the candle. Monsieur Roger placed close to this tongue of fire the tapering and open end of the tube in which the water had finished boiling. The air, forced out of the blowpipe and thrust upon the flame of the candle, bore to this flame a considerable quantity of oxygen, which increased the combustion and produced a temperature high enough to soften and melt the open extremity of the tube, and so seal it hermetically.
"I have," said Monsieur Roger, "by the means which you have seen, expelled the air which was contained in this tube, and there remains in it only water. In a few moments we will make use of it. But it is good to have a comparison under your eyes. I therefore ask Miss Miette to take another tube similar to that which I hold."
"Here it is," cried Miette.
"Now I ask her to put water into it."
"I have done so."
"Lastly, I ask her to turn it over quickly, with her little hand placed against its lower side in order to prevent the water from falling upon the floor."
Miss Miette did as she was commanded. The water fell in the tube, dividing itself into drops of more or less size. It was like rain in miniature.
"The water, as you have just seen," said Monsieur Roger, "has fallen in Miss Miette's tube, dividing itself against the resistance of the air. In the tube which I hold, and in which there is no longer any air, you will see how water falls."
Monsieur Roger turned the tube over, but the water this time encountered no resistance from the air. It fell in one mass, and struck the bottom of the tube with a dry and metallic sound.
"It made a noise almost like the noise of a hammer," said Paul Solange.
"Exactly," answered Monsieur Roger. "Scientists have given this apparatus the name of the water-hammer." And looking at Miette, who in her astonishment was examining the tube without saying anything, Monsieur Roger added, smiling, "And this hammer has struck Miss Miette with surprise."
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?"