An introductory text-book of logic - Mellone, Sydney - Rare Books at ...

298
THE THEORY OF INDUCTION
(/.*., the radius of the earth) ; and, squaring
these num
bers, the inverse proportion would be that of the spaces
fallen through in one second by the moon, and by a
body
at the surface of the earth. If this calculated
result agreed with the result actually observed, his con
jecture would be verified ; and the very same force of
gravity which causes bodies to fall near the earth, would
be that which causes the moon to fall, or, in other
words, to be deflected from a rectilinear course, and to
describe her orbit round the earth." In this calculation
Newton took for the radius of the earth the length which
at that time (about 1666) was considered accurate, and
the result did not verify his conjecture ; there was a
difference of two feet per second between the actual and
the calculated deflection of the moon. This small dis
crepancy was large enough, in Newton s opinion, to show
that his cherished hypothesis could not account for the
facts ; and he dismissed the subject from his thoughts
for some time. But in 1682 the radius of the earth had
been more accurately calculated. Newton substituted
the new value in his former proportion, and "having
proceeded a little way in the calculation, was utterly
unable to carry it on, from the overpowering excitement
of its anticipated termination ; and he requested a friend
to finish it for him." The result was that the moon s
deflection, as calculated from his hypothesis, agreed with
the deflection calculated from observation. This great
result sufficed as a clue to the whole mechanism of the
planetary system, and afterwards of the universe. New
ton proceeded to show, by his unrivalled powers of
mathematical calculation, that Kepler s Laws are a ne
cessary consequence of the Law of Gravitation. If we
have bodies freely revolving round a common centre
of force, which attracts them with a "pull" varying