to the ground? And is not this tendency the
actual cause which, like an invisible string,
retains the moon in her orbit round the earth?"
How fully Newton, answered the question will
be told immediately.

Galileo, studying the motion of bodies falling
to the ground, discovered that weight invariably
produces on them the same effects in the same
time, whatever be their condition of repose or
movement. In the case of a body projected in
any direction, weight causes it to descend from
the position it would occupy at any moment in
consequence solely of its velocity, by precisely
the distance it would have fallen during the
same interval of time, if simply allowed to
drop.

A cannon-ball shot out horizontally would,
if it had no weight, continue to move forward
in a straight line for an indefinite distance; but
in consequence of its weight, it gradually sinks
below the level of its original direction; and
the distance through which it sinks below the
straight line which, without weight, would have
been its course, is precisely the distance through
which it would have fallen if allowed to drop
from its starting-point without receiving any
impulse.

These very clear and simple principles apply
directly to the case of the moon. At every
instant of her course round the earth, she may
be compared to a cannon-ball shot out
horizontally. Instead of moving in a straight line
indefinitely forward, she declines from it little
by little to approach the earth, thus describing
an arc, or portion, of her almost circular orbit.
She is consequently every instant falling
towards the earth; and the space through which
she falls in a given time can be calculated, as
with the cannon-ball. Newton, therefore, was
able to estimate how far the moon falls towards
the earth in a second of time.* By comparing
the result thus obtained with the distance
through which bodies fall in a second of time
at the surface of the earth, he thought to find
out whether those two similar effects are to be
attributed to one and the same cause.

* M. Delaunay teaches us how to calculate the
distance through which the moon falls in a second.
The reader will probably be content with the result,
which may perhaps surprise him by its smallness,
being no more than one millimètre and a third—
not the tenth of an inch.

But a grave consideration here arises.
Although observations made on the tops of buildings
and the summits of mountains indicated no
slackening of the speed of falling bodies, that is,
no diminution of the intensity of weight, it
was probable that at distances like that which
separates the moon from the earth, the force of
weight might diminish with the increase of
distance. But what was the law of this diminution?
It was necessary to discover it, in order
to ascertain whether the incessant dragging
down of the moon towards the earth is due to
the very same force of weight whose effects we
are constantly witnessing around us. The
consequences of the conclusion thus reached, were
enormous.

Newton rightly thought that if it is the weight
of the moon which compels her to move in the
almost circular orbit which she describes round
the earth, the planets also ought to be drawn
to the sun by weight analogous to that which
draws the moon towards the earth; so that
the weight of one body towards another more
or less distant from it, would assume an universal
character.

Now, Kepler, comparing amongst themselves
the movements of the different planets round
the sun, had discovered that the squares of the
times of revolution are proportional to the cubes
of their mean distances from the sun. It is
possible, moreover, to calculate for each of the
planets (as already indicated for the moon) the
distance which it falls towards the sun in a
second of time. Following that course and
keeping Kepler's law in mind, Newton
ascertained that the weight urging the planets
towards the sun, diminishes its intensity in
proportion as their distance increases; that it
becomes four times, nine times, sixteen times
smaller, when a planet's distance from the sun
is twice, three times, and four times greater;
in other words, that the weight urging a planet
towards the sun varies inversely as the square
of the planet's distance from the central
luminary.

Applying this result to the earth, Newton
calculated that if the cause which makes the
moon revolve in a nearly circular orbit round
the earth be identical with the force of weight
which makes bodies near the earth's surface
fall to the ground, the intensity of this cause at
the distance of the moon (sixty times the length
of the earth's radius) ought to be three thousand
six hundred times weaker (the square of
sixty) than it is at the surface of the earth.
Since, therefore, bodies at the surface of the
earth traverse a certain number of feet during
the first second of their fall, the moon during
every second of her course ought to fall a
distance three thousand six hundred times less—
that is, about the twentieth of an inch.

It now remained to calculate the distance the
moon actually does fall towards the earth in a
second of time, in order to see whether this
quantity be really the twentieth of an inch.
Newton knew that the radius of the moon's
orbit is sixty times as long as the radius of the
earth, but at the date when he endeavoured to
compare weight at the surface of the earth with
the force which keeps the moon in her orbit,
the radius of the terrestrial globe was not
ascertained with sufficient exactness. The result did
not completely answer his expectations; he
made the distance fallen through by the moon
in a second to be a little less than the twentieth
of an inch. But, although the difference was
so small, he thought it sufficient to prevent his
concluding that the two forces were identical.
Fortunately the cause which checked his
progress was removed shortly afterwards.

This memorable attempt to establish the