n 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 m