Part 32

"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."