Rollo's Experiments

OSCILLATIONS.

In about an hour, Mary came down into the yard in pursuit of Rollo, in order to try the experiments which she had proposed.

When Rollo saw her coming, he left his play, and ran to meet her.

"Well, Mary," said he, "have you come to make the oscillations?"

"Yes," said Mary. "I have brought some thread for strings, and I want you to get some pebble stones-some large, and some small ones."

Rollo went for the pebble stones, while Mary looked about for a suitable place for making the experiments. In a corner of the yard there was a bench under a tree, and the branches came down pretty low. Mary thought that this would be a good place, for she could tie her strings to these branches with the pebbles hanging down below; and she and Rollo could watch the oscillations, while seated upon the bench.

Mary took her station here, and Rollo presently appeared, with the crown of his cap half filled with pebble stones. Mary said they would do finely. She poured them out upon the bench by her side, and Rollo put his cap upon his head again.

"Now, Rollo," said she, "we will study the art of experimenting."

"No," said Rollo, "we are going to study oscillation."

"Yes," replied Mary; "the experiments are to be on oscillations; but what I want principally to teach you, is, the proper way to make experiments."

"Well," said Rollo.

Mary said no more, but she proceeded to tie a small pebble to the end of one of the long threads which she had brought out with her. Then she tied the other end of the thread to the branch of the tree, which was over her head. The pebble then hung down before them, so that both Rollo and herself could plainly see all its motions.

"The first thing," said Mary, "is to get a clear idea of the nature of the oscillation, for we must know what we are experimenting about."

So saying, Mary carefully took hold of the suspended pebble stone, and began to draw it off towards one side. She showed Rollo that, as it was confined by its string above, it must move in a curved line when she drew it away from its place, rising higher and higher the farther it was drawn away. And when she had drawn it out to a considerable distance, to one side, it was at a much higher level, than when it hung down freely in its natural position.

"Now," said Mary, "you see that if I let it go, it will descend of course as much as it can, for the earth draws it downwards."

"The earth draws it?" said Rollo.

"Yes," said Mary. "The reason why things fall is that they are attracted, or drawn down, by the earth. Now the earth draws the pebble. It would go straight towards it, if it could; but the string confines it, and so it can only go down in the same way that it came up; that is, by the curved line."

Mary then held one of her hands open at the place where the pebble had hung when it had been at liberty, and let go the pebble, which she had been holding with the other. It fell down in the curved line, or arc, as Mary had said it would, until it struck her hand, and there it stopped and remained at rest.

"What did you stop it for?" said Rollo.

"So that we could see and attend to one part of the phenomenon at a time," said Mary; "that is, the descent of the pebble. You see the attraction of the earth causes the pebble to go down if it can, and the confinement of the string prevents its going down in any other way than in that curve or arc. For the string keeps it always just its own length from the branch, and so that makes the curved line the arc of a circle."

"Yes," said Rollo, "I understand."

Then Mary drew up the pebble once or twice more, and let Rollo see it fall against her hand. Rollo observed that it was a very regular arc.

"Now we see," continued Mary, "that I hold my hand so as to stop the pebble stone at the lowest point to which it can go; for I hold it exactly under the point where the upper end of the string is fastened to the tree. Now I will take my hand away, and then let the pebble fall, and we will see what takes place."

So Mary took her hand away, and let the pebble fall freely. It descended as before through the arc, and then, by the force which it acquired in moving so far, it was propelled beyond the lowest point, and ascended in another curve, upon the other side, similar to the first. When the force was expended, it came back again; and thus it swung to and fro, several times, and at length came almost to a state of rest.

"There," said Mary, "those are the oscillations we are going to experiment upon."

"Yes," said Rollo.

"And first," said Mary, "we notice that they are regular."

So she swung the pebble again; and as it moved to and fro, she counted the oscillations aloud, beating time with her hand, down and up, thus,-

"One,-two,-three,-four," &c. Rollo perceived that they were very regular.

"Now, first we will endeavor to ascertain by our experiments," said Mary, "what the time of the vibrations depends upon."

"Well," said Rollo.

"You see," continued Mary, "it swings back and forth with a certain degree of rapidity. Now we want to know what this rapidity depends upon, and then we could make a pendulum so that it would oscillate faster or slower, just as we pleased."

"A pendulum?" asked Rollo.

"Yes," said Mary, "we call it a pendulum. Any heavy body hung in this manner, so as to swing back and forth by its weight, is called a pendulum. So that we are experimenting upon the oscillations of a pendulum."

"Yes," said Rollo, "I understand."

"Now the question which we are going to examine," said Mary, "is, what the rapidity of the vibrations depends upon."

"O, it depends upon the bigness of the pebble," said Rollo.

"How do you know?" said Mary.

"Why, of course, a bigger pebble will be heavier, and will fall quicker, and that will make it vibrate faster."

"That is reasoning about it," said Mary, "and what we want to do, now, is to experiment. Now, in order to decide it by experiment, we must try two pendulums, one with a small pebble, and the other with a large one."

"Very well," said Rollo, "we will; and then we shall see that the big one will vibrate the quickest."

"Let us think, first, what other circumstances there are, that it may depend upon."

"I can't think of any thing else," said Rollo.

"Why, there is the nature of the body which we suspend. A piece of cork may oscillate differently from a piece of stone."

"Yes," said Rollo, "it will oscillate slower."

"We must not decide," said Mary, "in our own minds, before we try the experiment. We must leave our minds free to observe the facts, and wait until we make the experiment, before we come to any conclusion, or else we shall not be good experimenters."

"Why not?" said Rollo.

"Because," said Mary, "when persons make up their minds beforehand what the facts will be, they are very apt not to observe fairly. So good observers or experimenters always take care to keep their minds free and unbiassed."

"Well," said Rollo, "and what else is there that the oscillations may depend upon?"

"The length of the string," replied Mary.

"O yes," said Rollo, "it may depend upon that."

"Let us see," continued Mary. "There are three experiments we have already proposed; a large and a small pebble; a pebble and a cork; a long and a short string; and now there is one more,-a long and short arc."

"How?" said Rollo.

"Why, if I draw up the weight, which forms the pendulum, pretty high, it will swing back and forth through a long arc. But if I move it only a little way, it will swing through only a short arc, and that may make a difference in the length of the vibrations."

"Well," said Rollo, "and now let us try."

"First, let us see whether we have got all the apparatus we want. Here are strings and pebbles,-only we want a cork."

"I'll go and get one," said Rollo.

So Rollo went off towards the house to get the cork. In a few minutes he came back, saying,

"I have got the cork. Now how shall we begin?"

"First," replied Mary, "we will try what effect the weight of the pebble will have upon the oscillations."

"Very well," said Rollo.

"Now, in order to test that," added Mary, "we must take two pebble stones, of different sizes, and hang them together, by strings of the same kind, and of the same length; and then we must set them a-going exactly together, and then watch the oscillations. You see that as they will be alike in every respect, excepting the size of the pebble stones, whatever difference there is in the mode of vibration will probably be caused by the difference in the size of the stones."

"Is that the way they do it?" said Rollo.

"Yes," replied Mary. "Whenever we want to know what effect any one circumstance produces, in such a case, we always arrange two experiments, making them very different in respect to the circumstance which we wish to examine, and as nearly alike as possible in all other respects."

"I think that is a very good way," said Rollo.

"Yes," replied Mary, "I think it is an excellent way."

While Mary was thus explaining her plan to Rollo, she was going on steadily with preparations, Rollo standing all the time by her side, looking on with great interest. Mary selected two pebbles. One was as big as a walnut, and the other about as big as an egg. She tied two of her threads to these stones, one to each, and then tied the other ends of these threads to a small branch of the tree which extended horizontally over their heads. They hung down about two feet. She took care so to adjust the strings, as to have the centres of the stones as nearly as possible on a level.

"The big one is twice as large, and so it will go twice as fast," said Rollo.

"We shall see," said Mary.

She then drew them both carefully out a little way on one side, and holding them there steadily a moment, she let them go. They immediately began to swing back and forth, together.

After a few oscillations, however, the large stone began to gain a little upon the other, and seemed to be moving faster. Presently it had gained half an oscillation, i. e. when the large one was moving forward, the small one would be coming back.

"The big one moves the fastest," said Rollo.

"Not much," said Mary.

"No," said Rollo, "not much."

"And I don't think it is owing to the difference in the bigness of the stones."

"What else can it be?" said Rollo. "They are exactly alike in all other respects."

"Not exactly," said Mary. "We have made them as nearly alike as we could, but not exactly. There may be a good many little differences that we do not observe. But if the size of the stone would cause any difference in the vibrations, I should think it would make a much greater difference, for one is twice as big as the other."

"Let us try a very big stone," said Rollo.

"Well," said Mary.

So Rollo got a stone as large as an orange, which was as heavy a one as Mary thought the thread would hold; and Mary suspended that from the branch of the tree, and then swung it in company with the two others. They all went very nearly together at first, though there was evidently a slight difference, which, in a short time, separated the oscillations, so that the stones did not keep together; while yet they each swung back and forth, in nearly the same time. Rollo and Mary both concluded, from the result of this experiment, that the size of the vibrating body did not perceptibly affect the rapidity of the vibrations.

"Now," said Mary, "we will try different lengths of string."

So she began to look over Rollo's pebbles, to find two as nearly as possible alike.

"The pebble stones must be of the same size, this time, for we want the two pendulums to be alike in all respects, except the length of the string, for that is the circumstance which we are now going to consider. We will have one string twice as long as the other."

Mary found two pebbles very nearly equal in size, and similar in shape. She tied them to two strings, making one string twice as long as the other. She suspended them as before, and then, taking hold of one with one hand, and the other with the other, she drew them out to the same distance on one side, and let them go. The short one began at once to swing back and forth very quick, while the other followed quite slowly.

"That makes a difference," said Rollo, clapping his hands.

"It goes twice as fast," said Mary.

"More than twice as fast," said Rollo, "I think."

"Let us see," said Mary.

They set them vibrating again; but they did not succeed in ascertaining whether the short one went more or less than twice as fast as the other. The two motions, so rapid and so near together, confused them. At length, Mary proposed that Rollo should count the vibrations of the long pendulum, while she counted those of the short one, and when she had got up to twenty, she said they would both stop, and then Rollo could tell how many he had got in the same time. But this plan, though apparently a very simple one, they found it somewhat difficult to put into practice. Mary's pendulum puzzled Rollo's counting, and Rollo, who could not count very well without at least whispering the numbers, puzzled Mary, and so pretty soon they gave it up.

Rollo then said that he meant to try a very short pendulum indeed, and he asked Mary to tie one up for him, not more than an inch in length. She, however, said that it would not be necessary to tie it to the branch; but, instead of that, she took hold of the string of one of the pebbles which was already hanging before them, about an inch above the pebble itself, and then set the pebble in motion; and they were both very much interested in observing how quick it vibrated to and fro.

Rollo then wanted to try a very long one, and proposed that he should climb up into the tree, and tie the end of the string to a high branch. But Mary was afraid that he would fall; and besides, she said that the pendulum would not swing clear of the branches below. She, however, immediately thought of the chamber window, and said that she would try it there. She accordingly went up into her chamber, taking a large pebble stone with her, and Rollo remained below to set the pendulum in motion, when it should be ready. Mary soon appeared at the window, and Rollo watched her while she tied her pebble to the end of a thread.

"Have you got your thread long enough?" said Rollo. "It will take a good long thread to reach away down here."

"It is a whole spool of cotton," said Mary. And, so saying, she held up in her hand the spool, to the thread of which she was tying her pebble stone.

When it was secured, she slowly let it down, until it reached Rollo's hand, which was held up from below, ready to receive it. Mary then held the thread steady above, at a little distance out from the window, while Rollo took the stone along the side of the house, three or four feet from the place where it would naturally hang. He then let it go, and it swung back very slowly.

"O, how slow!" said Rollo.

"Yes," said Mary, "it is very slow, indeed."

"I wish you had gone up to the garret window," said Rollo.

"O, this will do very well," said Mary.

Rollo determined to see how many he could count while the stone made one oscillation to and fro. He counted sixteen.

Mary then said she was tired of experimenting, and so she should not come down again. She, however, asked Rollo to set the pendulum swinging, and that then she would draw the thread in, and he could see that it would go faster and faster, the farther she drew it up, for that would make the string grow shorter and shorter.

Rollo did so; and this was the end of the experiments on oscillations.