"Yes. They call this swinging back and forth, _oscillating_; and each movement is an oscillation."
"Is that the name of it?" said Rollo.
"Yes," said Mary. "When you tie a little stone to a string, and hold the upper end of the string still, and let the stone swing back and forth, it makes oscillations."
"I mean to try it," said Rollo.
"Yes," said Mary; "and I will help you by and by, after I have studied my philosophy lesson."
"Your philosophy lesson?" asked Rollo. "Have you got a philosophy lesson to get?"
"Yes," said Mary, "in that great book."
So Rollo took up Mary"s book, which she had laid down upon the platform near Rollo"s apparatus. He found that the t.i.tle of it was "Intellectual Philosophy."
"Intellectual Philosophy?" said Rollo; "and what sort of philosophy is _intellectual_ philosophy?"
"It is the philosophy of the _mind_," replied Mary. "It explains to us about the thoughts and feelings of our minds."
"Are there any _experiments_ in intellectual philosophy?" asked Rollo.
"Yes," said Mary, "we can try experiments in intellectual philosophy."
"What experiments?" said Rollo.
"Why, there is a question whether we always dream when we are asleep."
"_I_ do," said Rollo, "every night."
"Yes, but perhaps not all night long."
"Yes, I do," said Rollo. "I have good long dreams."
"But," replied Mary, "you may dream several hours in the night, so as to remember good long dreams in the morning, and yet perhaps you might have been, for some time, perfectly sound asleep, so as not to have any dreams in your mind at all. Some persons think we dream all the time when we are asleep, and others think we don"t dream all the time. Now we might contrive some experiments to decide the question."
"How?" said Rollo.
"Why, you and I might agree to wake each other up several times, from a sound sleep, and then, if we were dreaming at that time, we should probably remember it."
"Well," said Rollo, "let us try it."
"That would be an experiment in intellectual philosophy," said Mary.
Rollo determined to try the experiment; and then he took Mary"s book, and asked her where her lesson was that day. She found the place, and Rollo read a little. He could not understand it very well, and so he concluded that he would rather have Mary go and study her lesson, and then come down and help him make the experiments of oscillation.
Mary accordingly took her book and went in, and left Rollo at his play.
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 princ.i.p.ally 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.