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.
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