NEWTON AND MOTION
"How is it that you are able to make these great discoveries?" was once
asked of Sir Isaac Newton, _facile princeps_ of all philosophers, and
the discoverer of the great law of universal gravitation.
"By perpetually thinking about them," was Newton's terse and
illuminating reply. He had set for himself the definite problem of
Kepler's laws: why is it that they are true, and is there not some
single, general law that will embody all the circumstances of the
planetary motions?
Newton was born in 1643, the year after the death of Galileo. He had a
thorough training in the mathematics of his day, and addressed himself
first to an investigation and definite formulation of the general laws
of motion, which he found to be three in number, and which he was able
to put in very simple terms. The first one is: Any body, once it is set
in motion, will continue to move forward in a straight line with a
uniform velocity forever, provided it is acted upon by no force
whatever. In other words, a state of motion is as natural as a state of
rest (rest in relation to things everywhere adjacent) in which we find
all things in general.
Here on earth where gravity itself pulls all objects downward toward the
earth, and where resistance of the air tends to hold a moving body back
and bring it to rest, and where friction from contact with whatever
material substance may be in its path is perpetually tending to
neutralize all motion--with all three of these forces always at work to
stop a moving body, the truth of this first and fundamental law of
motion was not apparent on the surface.
Till Galileo's time everyone had made the mistake of supposing that some
force or other must be acting continually on every moving body to keep
it in motion. Ptolemy, Copernicus, Kepler, Leonardo da Vinci--all failed
to see the truth of this law which Newton developed in the immortal
_Principia_. And at the present day it is not always easy to accept at
first, although the progress of mechanical science, by reducing friction
and resistance, has produced machines in which motion of large masses
may be kept up indefinitely with the application of only the merest
minimum of force.
Once a planet is set in motion round the sun, it would go on forever
through frictionless, non-resistant space; but there must be a central
force, as Huygens saw clearly, to hold it in its orbit. Otherwise it
would at any moment take the direction of a tangent to the orbit. Here
is where Newton's second law of motion comes in, and he formulated it
with great definiteness. When any force acts on a moving body, its
deviation from a straight line will be in the direction of the force
applied and proportional to that force.
In accord with this law, Newton first began to inquire whether the force
of attraction here on earth, which everyone commonly recognizes as
gravity, drawing all things down toward the center of the earth, might
not extend upward indefinitely. It is found in operation on the summits
of mountain peaks, and the clouds above them and the rain falling from
them are obviously drawn downward by the same force. May it not extend
outward into space, even as far as the moon?
This was an audacious question, but Newton not only asked, but tried to
answer it in the year 1665, when he was only twenty-three. On the
surface of the earth this attraction is strong enough to draw a falling
body downward through a vertical space of sixteen feet in a second of
time. What ought it to be at the distance of the moon. The distance of
the moon in Newton's time was better known in terms of the earth's size
than was the size of the earth itself: the earth's radius was known to
be one-sixtieth of the moon's distance, but the earth's diameter was
thought to be something under 7,000 miles, so that Newton's first
calculations were most disappointing, and he laid them aside for nearly
twenty years.
Meanwhile the French astronomers led by Picard had measured the earth
anew, and showed it to be nearly 8,000 miles in diameter. As soon as
Newton learned of this, he revised his calculations, and found that by
the law of the inverse square the moon, in one second, should fall away
from a tangent to its orbit one thirty-six hundredth of sixteen feet.
This accorded exactly with his original supposition that the earth's
attraction extended to the moon. So he concluded that the force which
makes a stone fall, or an apple, as the story goes, is the same force
that holds the moon in its orbit, and that this force diminishes in the
exact proportion that the square of the distance from the earth's center
increases. The moon, indeed, becomes a falling body; only, as Kingdon
Clifford puts it: "She is going so fast and is so far off that she falls
quite around to the other side of the earth, instead of hitting it; and
so goes on forever."
[Illustration: NICHOLAS COPERNICUS]
[Illustration: GALILEO GALILEI]
[Illustration: JOHANN KEPLER]
[Illustration: SIR ISAAC NEWTON]
Newton goes on in the _Principia_ to explain the extension of
gravitation to the other bodies of the solar system beyond the earth and
moon. Clearly the same gravitation that holds the moon in its orbit
round the earth, must extend outward from the sun also, and hold all the
planets in their orbits centered about him. Newton demonstrates by
calculation based on Kepler's third law that (1) the forces drawing the
planets toward the sun are inversely as the squares of their mean
distances from him; and (2) if the force be constantly directed toward
the sun, the radius vector in an elliptic orbit must pass over equal
areas in equal times.