Rollo's Experiments

“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.