"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.
TRANSCRIBER'S NOTES
The following corrections have been made to the text:
Page 14: She looked on with a good deal{original omitted this word} of interest
Page 32: "What is satiety, father?"{original had a single quotation mark instead of the double one}
Page 88: Then he stirred{original had stirrred} it about with his hand
Page 122: he took hold of the flower-pot with both his hands, and slid it suddenly off of the seat.{the original had a footnote here, See Frontispiece. The frontispiece however relates to a different chapter (Pruning) and so the footnote has been removed}
Page 149: and the small end{original had and} of the magnet would draw the point of the needle