reof very far toward its completion. It unfolded the
mechanical theory of universal gravitation upon the principle that all
bodies tend to approach each other with forces directly as their masses,
and inversely as the squares of their distances.

[Sidenote: Propounds the theory of universal gravitation.] To the force
producing this tendency of bodies to approach each other the designation
of attraction of gravitation, or gravity, is given. All heavy bodies
fall to the earth in such a way that the direction of their movement is
toward its centre. Newton proved that this is the direction in which
they must necessarily move under the influence of an attraction of every
one of the particles of which the earth is composed, the attraction of a
sphere taking effect as if all its particles were concentrated in its
centre.

[Sidenote: Preparation for Newton.] Galileo had already examined the
manner in which gravity acts upon bodies as an accelerating force, and
had determined the connexion between the spaces of descent and the
times. He illustrated such facts experimentally by the use of inclined
planes, by the aid of which the velocity may be conveniently diminished
without otherwise changing the nature of the result. He had also
demonstrated that the earth's attraction acts equally on all bodies.
This he proved by inclosing various substances in hollow spheres, and
showing that, when they were suspended by strings of equal length and
made to vibrate, the time of oscillation was the same for all. On the
invention of the air-pump, a more popular demonstration of the same fact
was given by the experiment proving that a gold coin and a feather fall
equally swiftly in an exhausted receiver. Galileo had also proved, by
experiments on the leaning tower of Pisa, that the velocity of falling
bodies is independent of their weight. It was for these experiments that
he was expelled from that city.

[Sidenote: Extension of attraction or gravity.] Up to the time of Newton
there were only very vague ideas that the earth's attraction extended to
any considerable distance. Newton was led to his discovery by reflecting
that at all altitudes accessible to man, gravity appears to be
undiminished, and that, therefore, it may possibly extend as far as the
moon, and actually be the force which deflects her from a rectilinear
path, and makes her revolve in an orbit round the earth. Admitting the
truth of the law of the inverse squares, it is easy t