I have now some great discoveries to talk to you about, which were made
by Sir Isaac Newton. He was not an astronomer who looked much through
a telescope, though he made many remarkable experiments. He used to
sit in his study and think, and then he used to draw figures with his
pencil, and make long calculations. At last he was able to give answers
to the questions: What is the reason why the planet moves in an
ellipse? Why should it move in this curve rather than in any other? Why
should this ellipse be so placed that the sun lies at one of the foci?
If the planet had run uniformly round its course, Newton would have
found his task an impossible one. But I have already explained that
the motion is not uniform. I described how the planet hurried along
with extra speed at certain parts of its path; how it lingered at
other parts; how, in fact, it never preserved the same rate for even a
single minute during the whole journey. Kepler had shown how to make a
time-table for the whole journey. In fact, just as a captain on a long
voyage keeps a record of each day’s run, and shows how to-day he makes
170 miles, and to-morrow perhaps 200, and the next day 210, while the
day after he may fall back to 120, so Kepler gave rules by which the
log of a planet in its voyage round the sun might be so faithfully kept
that every day’s run would be accurately recorded.
When Newton commenced his work, one of the first questions he had to
consider was the following: Suppose that a great globe like a planet,
or a small globe like a marble, or an irregular body like an ordinary
stone, were to be thrown into space, and were then to be left to follow
its course without any force whatever acting upon it, where would it go
to?
You may say, at once, that a body under such circumstances will
presently fall down to the ground; and so, of course, it will, if it be
near the earth. I am not, however, talking of anything near the earth;
I want you to imagine a body far off in the depths of space, among the
stars. Such a body need not necessarily fall down here, for you see the
moon does not fall, and the sun does not.
If you were at a great distance from our globe and from all other large
globes--so far, indeed, that their attractions were imperceptible--you
could try the experiment that I wish now to describe. Throw a stone
as hard as ever you can, and what will happen? Of course, when you do
it down here, it moves in a pretty curve through the air, and tumbles
to the ground; but away in open space, what will the stone do? There
will be no such motion as up or down, as we ordinarily understand it;
for though the earth, no doubt, will lie in one particular direction
at a great distance, yet there will be other bodies just as large in
other directions; and there is no reason why the stone should move
towards one of these rather than to another; in fact, if they are all
far enough, as the stars are from us, their attractions will be quite
inappreciable. There is, therefore, not the slightest reason why the
stone should swerve to one side more than to another. There is no more
reason why it should turn to the right than why it should turn to the
left. Nor could you throw the stone so as to make it follow a curved
path. You can, of course, make it describe a curve while it remains in
your hand, but the moment the stone has left your hand, it proceeds on
its journey by a law over which you have no control. As the direction
cannot be changed towards one side more than towards the other, the
stone must simply follow a straight line from the very moment when it
is released from your hand.
The speed with which the stone is started will also not change. You
might at first think that it would gradually abate, and ultimately
cease. No doubt a stone thrown along the road will behave in this way,
but that is because the stone rubs against the ground. If you throw
a stone across a sheet of ice, then it will run a very long distance
before it stops, and all the time it will be moving in a straight line.
In this case there is but little loss by rubbing against the ice,
because it is so smooth. Thus we see that if the path be exceedingly
smooth, the body will run a long way before it stops. Think of the
distance a railway train will run if, while travelling at full speed
along a level line, the steam is turned off.
These illustrations all show that if you let a body alone, after having
once started it, and do not try to pull it this way or that way, and
do not make it rub against things, that body will move on continually
in a straight line, and will keep up a uniform speed. We can apply
this reasoning to a stone out in space. It would certainly move in a
straight line, and would go on and on forever, without losing any of
its pace.
I need hardly tell you that no one has ever been able to try this
experiment. In the first place, we reside upon the surface of the
earth, and we have no means of ascending into those elevated regions
where the stone is supposed to be projected. There is also another
difficulty which we cannot entirely avoid, and that arises from the
resistance of the air. All movements down here are impeded because
the body has to force its way through the air; and in doing so it
invariably loses some of its speed. Out in open space there is, of
course, no air, and no loss of speed can therefore arise from this
cause.
[Illustration: FIG. 57.--The Humming-top.]
There are, however, several actual experiments by which we can assure
ourselves of the general truth. Set a humming-top spinning (Fig. 57);
it gradually comes to rest, partly because of the rubbing of its point
on the table, and partly because it has to force its way through the
air. In fact, the hum of the top that you hear is only produced at the
expense of its motion. Supposing I use a much heavier top; if I set it
spinning it will keep up for many minutes, because its weight gives it
a better store of power wherewith to overcome the resistance of the
air. I remember hearing a story about Professor Clerk-Maxwell. He had,
when at Cambridge, invented one of these large and heavy tops, which
would spin for a long time. One evening the top was left spinning on a
plate in his room when his friends took their departure, and no doubt
it came to rest in due time. Early the next morning, Professor Maxwell,
hearing the same friends coming up to his rooms again, jumped out of
bed, set the top spinning, and then got back to bed, and pretended to
be asleep. He thus astounded his friends, who, of course, imagined that
the top must have been spinning all the night long!
If we spin a top under the receiver of an air pump (Fig. 58), it will
keep up its motion for a very much longer time after the air has been
exhausted than it would in ordinary circumstances. Such experiments
prove that the motion of a body will not of itself naturally die out,
and that if we could only keep away the interfering forces altogether,
the motion would continue indefinitely with unabated speed. What I have
been endeavoring to illustrate is called the first law of motion. It is
written thus:--
“_Every body continues in its state of rest or of uniform motion in a
straight line, except in so far as it may be compelled by impressed
forces to change that state._”
[Illustration: FIG. 58.--To illustrate the First Law of Motion.]
I would recommend you to learn this by heart. I can assure you it is
quite as well worth knowing as those rules in the Latin Grammar with
which many of you, I have no doubt, are acquainted. The best proof
of the first law of motion is derived, not from any experiments, but
from astronomy. We make many calculations about the movements of the
sun, the moon, the stars, and then we venture on predictions, and
we find those predictions verified. Thus we had a transit of Venus
across the sun in 1882, and every astronomer knew that this was going
to occur, and many went to the ends of the earth so that they might
see it favorably. Their anticipations were realized; they always are.
Astronomers make no mistakes in these matters. They know that there
will be another transit of Venus in the year 2004, but not sooner. The
calculations by which these accurate prophecies are made involve this
first law of motion; and as we find that such prophecies are always
fulfilled, we know that the first law of motion must be true also.
Newton knew that if a planet were merely left alone in space, it would
continue to move on forever in a straight line. But Kepler had shown
that the planet did not move in a straight line, but that it described
an ellipse. One conclusion was obvious. There must be some force acting
upon the planet which pulls it away from the straight line it would
otherwise pursue. We may, for the sake of illustration, imagine this
force to be applied by a rope attached to the planet so that at every
moment it is dragged by some unseen hand. To find the direction this
rope must have, we take the law of Kepler, which explains the rules
according to which the planet varies its speed. I cannot enter into
the question fully, as it would be too difficult for us to discuss
now. I should have to talk a great deal more about mathematics than
would be convenient just at present; but I think you can all understand
the result to which Newton was led. He showed that the rope must always
be directed towards the sun. In other words, suppose that there was
no sun, but that in the place which it occupied there was a strong
enough giant constantly pulling away at the planet, then we should find
that the speed of the planet would alter just in the way it actually
does. Thus we learn that some force must reside in the sun by which
the planet is drawn, and this force is exerted, although there is no
visible bond between the sun and the planet.
There is another fact to be learned about the sun’s attraction, and
this time we obtain it by knowing the shape of the curve followed by
the planet. The laws by which the planet’s speed is regulated prove
that the force emanates from the sun. We shall now learn much more when
we take into account that the path of the planet is an ellipse, of
which the sun lies at the focus. Nothing has been said as yet regarding
the magnitude of the pull which is being exerted by the sun. Is that
pull to be always the same, or is it to be greater at some times than
at other times? Newton showed that no ellipse other than a circle
could be described, if the pull from the sun were always the same. Its
magnitude must be continually changed, and the nearer the planet lies
to the sun, the more vehement is the pull it receives. Newton laid down
the exact law by which the force on the planet at any one place in
its path could be compared with the force at any other position. Let
us suppose that the planet is in a certain position, and that it then
passes into a second position, which is twice as far from the sun. The
pull upon the planet at the shorter distance is not only greater than
the pull at the longer distance, but it is actually four times as much.
Stating this result a little more generally, we assert, in the language
of astronomers, that the _attraction varies inversely as the square of
the distance_. If this law were departed from, then I do not say that
it would be impossible for the planet to revolve around the sun in some
fashion, but the motion would not be performed in an ellipse described
around the sun in the focus.
You see how very instructive are the laws which Kepler discovered.
From the first of them we were able to infer that the sun attracts the
planets; from the second, we have learned how the magnitude of the
attracting force varies.
The true importance of these great discoveries will be manifest when
we compare them with what we have already learned with regard to the
movements of the moon. As the moon revolves around the earth it is held
by the earth’s attraction, and the moon follows a path which, though
nearly a circle, is really an ellipse. This orbit is described around
the earth just as the earth describes its path around the sun. That
law by which a stone falls to the ground in consequence of the earth’s
attraction is merely an illustration of a great general principle.
Every body in the whole universe attracts every other body.
Think of two weights lying on the table. They no doubt attract each
other, but the force is an extremely small one--so small, indeed, that
you could not measure it by any ordinary appliance. One or both of the
attracting masses must be enormously big if their mutual gravitation is
to be readily appreciable. The attraction of the earth on a stone is
a considerable force, because the earth is so large, even though the
stone may be small. Imagine a pair of colossal solid iron cannon-balls,
each 53 yards in diameter, and weighing about 417,000 tons. Suppose
these two globes were placed a mile apart, the pull of one of them on
the other by gravitation would be just a pound weight. Notwithstanding
the size of these masses, the hand of a child could prevent any motion
of one ball by the attraction of the other. If, however, they were
quite free to move, and there was absolutely no friction, the balls
would begin to draw together; at first they would creep so slowly that
the motion would hardly be noticed. The pace would no doubt continue to
improve slowly, but still not less than three or four days must elapse
before they will have come together.
By the kindness of Professor Dewar, I am enabled to exhibit a
contrivance with which we can illustrate the motion of a planet around
the sun. Here is a long wire suspended from the roof of this theatre,
and attached to its lower end is an iron ball, made hollow for the sake
of lightness. When I draw the ball aside, it swings to and fro with
the regularity of a great pendulum. But when I place a powerful magnet
in its neighborhood (Fig. 59), you see that as soon as the ball gets
near the magnet it is violently drawn to one side, and follows a curved
path. This magnet may be taken to represent the sun, while the ball is
like our earth, or any other planet, which would move in a straight
line were it not for the attraction of the sun which draws the body
aside.
[Illustration: FIG. 59.--The Effect of Attraction.]