about it; and I want you to observe it very carefully. You see," he
says, "that the small end of the magnet attracts the point of the
needle. But if I try it now upon the other end of the needle, where the
eye is, it will _repel_ that, just as the large end of the magnet repels
the point."
He tried it, and the result was just as he had said. And he repeated the
experiment in a great many ways, and they always found that the large
end of the magnet would draw the eye of the needle towards it, and drive
the point away; and the small end of the magnet would draw the point of
the needle, and drive the eye away. This proved, as Rollo's father said,
some great difference between the magnetisms of the two ends. "And you
see," he added, "that it is a difference in _kind_, not merely a
difference in _degree_."
"But one thing seems strange to me," said Rollo's mother, "and that is,
that both ends of the magnet don't attract the point of the needle, just
as both of them attracted the nail."
"And the sand," said Rollo.
"Yes," added his mother. "When you brought both ends of the magnet, one
after the other, to the nail, they both attracted it."
"And so they did the needle which hung down by the thread," said Jonas.
"Yes," said Rollo's mother; "but now this needle, that is floating upon
the water, is half attracted, and half repelled."
"The reason is," said Rollo's father, "that the needle, that is floating
upon the water, is a magnet itself, and has two magnetic poles; but the
sand, and the nail and the needle that Jonas held up by the thread, were
not magnets. They were only common pieces of iron and steel."
"Why, father," said Rollo, "that was the very same needle; you laid it
away upon the corner of the table."
"Yes," said his father; "but it was not a magnet _then_."
"When?" asked Rollo.
"Why, when Jonas held it up by the thread."
"And is it a magnet now?"
"Yes," said his father. "We will see if it is not."
So he took the needle off from the float, and put it upon the paper. He
then sprinkled a little sand over it, from the sand-box, and, upon
taking it up, they all saw that there was a little tuft of black sand
both upon the point and at the eye, showing that it was magnetic at both
ends.
"It became magnetic," said Rollo's father, "only by being touched by the
bar magnet; and that was the reason why I put it away by itself as soon
as it had touched the bar. I did not want to have it mixed with the
other needles, which had not been touched, and which, of course, were
not magnetic. Now, if I take one of the needles which has not been
touched, and put it upon the float, you will see that both ends of it
will be attracted by both ends of the bar."
So he placed away the magnetized needle upon the corner of the table
again, and took another one, and placed it very carefully upon the
float. Then he brought down one end of Jonas's magnet very near the
point of the needle. It attracted it. Then he brought it down very near
the eye of the needle. It attracted the eye too. Then he turned the
magnet, and tried the other end, and he found that that end also would
attract both the eye and the point of the needle.
"Try the magnetized needle, and see if that will attract it too," said
Rollo's mother.
Then Rollo's father took the magnetized needle from the corner again,
and brought the two ends of that, one after another, near to the ends of
the needle upon the float. It attracted them just as Jonas's magnet had
done, only a great deal more feebly.
"So, you see that this needle is really a little magnet, just like
Jonas's great one."
"Only there is no proof that it has the two different kinds of magnetism
in the two ends," said Rollo's mother.
"We can easily show that," said his father. He asked Dorothy to get
another saucer full of water, while he prepared another float. Then he
put the magnetized needle upon the new float, leaving the unmagnetized
one upon the old float. They both looked almost precisely alike, each
upon its own little disc of cork in its saucer of water.
"There," said he, "you cannot see any difference between them; but there
is a great deal of difference between them; for one is only a common
needle of steel, but the other has its two extremities magnetic in
opposite ways."
To prove this, Rollo's father brought one end of the bar to the _point_
of the magnetized needle, and the point was repelled. He brought it then
to the _eye_ of the same needle, and it attracted it. Then he brought
the same end of the bar, first to the point, and then to the eye of the
unmagnetic needle, and it attracted them both; so it was evident that
there was a considerable difference, in reality, between the condition
of the two, though there was no difference in external appearance.
"Now you see, from all this," added Rollo's father, "that when a magnet
touches a piece of steel, like a needle, it immediately makes it a
magnet itself; that is, it makes the two ends magnetic, one having one
kind of magnetism, and the other the other kind; and then, if you take
two magnets, and bring those two poles which have the same magnetism
together, they repel one another; and if you bring those together which
have different magnetisms, they attract each other."
"How do you know that they are the same magnetisms that repel, and
different that attract?" said Rollo's mother.
"I will show you," said his father.
Then he took the needles that he had used off from their floats, and
laid them away. He took next two new needles, exactly of a size, and he
held them together between his thumb and finger, with the eyes
projecting together. Then he rubbed them once or twice upon the end of
Jonas's magnet, saying,
"There, you see I use both of these needles alike. Of course the eyes
have both the same magnetisms. Now you will find that when I put one of
them upon the float, and then bring the eyes together, they will repel
each other; but an eye and a point will attract. So two points will
repel."
"But you have not magnetized the points," said Rollo's mother.
"Yes," said his father. "When we magnetize one end, the other end
becomes magnetized, itself, in the contrary way."
So he put one of the needles upon the float, and then brought the eye of
the other down very near to its eye. It was repelled, as he had said it
would be. He then brought the two points together, and they were
repelled. But if he brought an eye towards a point, or a point towards
an eye, they were attracted.
"This is the end of my lecture," said he, "for to-night."
"O, father," said Rollo, "a little more."
"No more to-night, only to recapitulate," said he.
"Recapitulate? what is that?"
"Why, tell you, briefly, the substance of what I have explained, so that
you may remember it."
"Well, father," said Rollo.
"In the first place, a magnet has a peculiar and mysterious attractive
power for iron, residing in its two extremities, which are called _its
poles;_ and the power which resides in one extremity is, in some way or
other, opposite in its nature to that of the other extremity. Each of
these poles repels a pole like itself, and attracts one different from
itself, in any other magnet."
Poor Nathan could not understand this grave, philosophical disquisition
very well, and he began to get pretty sleepy. He had, however, been
somewhat amused, during the greater part of the time, in seeing the
corks float about upon the water, with the needles upon them. So his
father took the needles off, and let him have the two floats in one of
the saucers to play with, a few minutes, while Dorothy put the other
things away. He asked her to put all the things away together, so that
they could get them ready the next evening, and then he said that
perhaps he would give them another lecture.
INTELLECTUAL PHILOSOPHY
Rollo's father gave one or two other lectures upon magnetism, in the
course of which Rollo found out a good deal about the subject; and,
having learned from his father's explanations that any magnet, when
balanced freely, would point to the north and south, that is, one end to
the north and the other to the south, he determined to try the
experiment. He accordingly poised a needle carefully upon a cork, as his
father had done in his lecture, and put it in a basin of water upon the
platform. But he did not succeed very well. The needle would always
swing round, and turn its point towards the garden gate; but Rollo knew
very well that the garden gate was not north from the platform. He
remembered that the North Star was over the barn, for he and Jonas had
noticed it particularly when they had made the dial. The needle,
therefore, ought to have pointed towards the barn, according to his
father's lecture; but it would not. Rollo took up a straw, and pushed
the point of the needle round, and said, "Point there! point there, I
tell you!" But all in vain. The needle would not heed either his pushing
or his commands; but, as soon as he let it go, it would immediately
swing back into its old position, where it pointed towards the garden
gate.
Rollo was just about giving up in despair, when he saw his sister Mary
coming in from the garden gate, with a book under her arm.
"O Mary," said he, "what shall I do? My needle won't point right."
"Why, what is the matter with it?" said Mary.
"It will point over towards the garden," said Rollo; "look."
So Mary came up, and looked at his needle. She saw that it was pointing
towards the garden gate.
"Now I'll push it away," said Rollo, "and you will see that it comes
directly back again."
So he took up his straw, and pushed the point of the needle away. The
cork moved, turning round rapidly, until at length it swung away
towards one side of the basin, and then suddenly drifted up against the
side, and stuck there.
"That's another plague," said Rollo. "It will run up to the side of the
basin, and stick there."
"What makes it?" said Mary.
"I don't know," said Rollo.
Mary sat down upon the platform, and examined the needle and the surface
of the water very carefully. She observed that the water was heaped up a
little against the side of the basin, all around. She asked Rollo to
observe it.
"Yes," said he, "and the needle and cork run right up that ridge of
water."
"And the bubbles too," said Mary.
Mary pointed, when she said this, to several little bubbles which were
adhering closely to the side of the basin, in another place.
She took up a little straw, and pushed away some of the bubbles from the
side of the basin, and then gently moved them back again until they were
pretty near, and observed that they would immediately rush up against
the side again. She did not understand this phenomenon, especially as
the water was raised a little along the edge by the side of the basin,
so that the bubbles and the needle actually appeared to rush up hill.
After examining this for some time, Mary moved the cork float, with the
needle upon it, back into the middle of the basin, and then left it to
itself. It slowly moved around until it pointed to the garden gate, as
it had done before.
"Now what is the reason?" said Rollo; "that isn't north."
Mary looked upon it very attentively for a few minutes in silence, and
then said, suddenly,
"O, I see."
"What?" said Rollo.
She did not answer, but pointed down to the platform by the side of the
basin.
Rollo looked where she pointed, and saw the hammer lying there. He had
had it to play with a short time before, and, when he brought the basin
of water, he had laid it down by his side.
"What?" said Rollo.
"The hammer attracts the needle," replied Mary.
"The hammer?" said Rollo.
"Yes," replied Mary. "Don't you know that iron attracts the needle, and
it will not point to the north if there is any iron near to draw it
away?"
Rollo was just going to take the hammer up, but Mary stopped him,
saying,
"Wait a moment. Let me take it away slowly, and see the effect."
So Mary told Rollo to watch the needle, while she carefully drew the
hammer away.
Rollo did so. He and Mary both watched the needle. It was pointing
pretty nearly toward the hammer, and when Mary gently moved the hammer
away, the needle, released from the influence which the iron exerted
upon it, slowly moved back towards the direction of the barn, that is,
the direction of a north and south line, which is called the meridian.
"It's going back! it's going back!" said Rollo.
Mary said nothing, but watched it carefully. The needle swung beyond the
direction of the meridian a little way, and then came slowly back
again. So it continued vibrating from one side to the other, though to a
less and less distance every time. Finally, it came to a state of rest;
but it was not then, however, exactly in the meridian.
"What makes it swing so, back and forth?" said Rollo.
"I don't know exactly," said Mary. "I suppose the force that it moves
with, carries it a little beyond, and then it is drawn back again, and
that makes the oscillations."
"Oscillations?" said Rollo, inquiringly.
"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 title 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 principally 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.
"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."
"Very well," said Rollo, "we will; and then we shall see that the big
one will vibrate the quickest."
"Let us think, first, what other circumstances there are, that it may
depend upon."
"I can't think of any thing else," said Rollo.
"Why, there is the nature of the body which we suspend. A piece of cork
may oscillate differently from a piece of stone."
"Yes," said Rollo, "it will oscillate slower."
"We must not decide," said Mary, "in our own minds, before we try the
experiment. We must leave our minds free to observe the facts, and wait
until we make the experiment, before we come to any conclusion, or else
we shall not be good experimenters."
"Why not?" said Rollo.
"Because," said Mary, "when persons make up their minds beforehand what
the facts will be, they are very apt not to observe fairly. So good
observers or experimenters always take care to keep their minds free and
unbiassed."
"Well," said Rollo, "and what else is there that the oscillations may
depend upon?"
"The length of the string," replied Mary.
"O yes," said Rollo, "it may depend upon that."
"Let us see," continued Mary. "There are three experiments we have
already proposed; a large and a small pebble; a pebble and a cork; a
long and a short string; and now there is one more,--a long and short
arc."
"How?" said Rollo.
"Why, if I draw up the weight, which forms the pendulum, pretty high, it
will swing back and forth through a long arc. But if I move it only a
little way, it will swing through only a short arc, and _that_ may make
a difference in the length of the vibrations."
"Well," said Rollo, "and now let us try."
"First, let us see whether we have got all the apparatus we want. Here
are strings and pebbles,--only we want a cork."
"I'll go and get one," said Rollo.
So Rollo went off towards the house to get the cork. In a few minutes he
came back, saying,
"I have got the cork. Now how shall we begin?"
"First," replied Mary, "we will try what effect the weight of the pebble
will have upon the oscillations."
"Very well," said Rollo.
"Now, in order to test that," added Mary, "we must take two pebble
stones, of different sizes, and hang them together, by strings of the
same kind, and of the same length; and then we must set them a-going
exactly together, and then watch the oscillations. You see that as they
will be alike in every respect, excepting the size of the pebble stones,
whatever difference there is in the mode of vibration will probably be
caused by the difference in the size of the stones."
"Is that the way they do it?" said Rollo.
"Yes," replied Mary. "Whenever we want to know what effect any one
circumstance produces, in such a case, we always arrange two experiments,
making them very different in respect to the circumstance which we wish
to examine, and as nearly alike as possible in all other respects."
"I think that is a very good way," said Rollo.
"Yes," replied Mary, "I think it is an excellent way."