the centre of the earth. As this power is not found to suffer any sensible
diminution at the greatest distance from the earth's centre to which we can
reach--being as powerful at the tops of the highest mountains as at the
bottom of the deepest mines--he conceived it highly probable that it must
extend much further than was usually supposed. No sooner had this happy
conjecture occurred to his mind than he considered what would be the effect
of its extending as far as the moon. That her motion must be influenced
by such a power he did not for a moment doubt; and a little reflection
convinced him that it might be sufficient for retaining that luminary in
her orbit round the earth.

Though the force of gravity suffers no sensible diminution at those small
distances from the earth's centre at which we can place ourselves, yet he
thought it very possible that, at the distance of the moon, it might differ
much in strength from what it is on the earth. In order to form some
estimate of the degree of its diminution, he considered that, if the moon
be retained in her orbit by the force of gravity, the primary planets must
also be carried round the sun by the same power; and by comparing the
periods of the different planets with their distances from the sun he found
that, if they were retained in their orbits by any power like gravity, its
force must decrease in the duplicate proportion, or as the squares of their
distances from the sun. In drawing this conclusion, he supposed the planets
to move in orbits perfectly circular, and having the sun in their centre.
Having thus obtained the law of the force by which the planets were drawn
to the sun, his next object was to ascertain if such a force emanating from
the earth, and directed to the moon, was sufficient, when diminished in the
duplicate ratio of the distance, to retain her in her orbit.

In performing this calculation it was necessary to compare the space
through which heavy bodies fall in a second at a given distance from the