it, and predicted
that it would return to perihelion in seventy-five or seventy-six years.
On referring to past records he discovered that a great comet appeared
in 1607, which pursued a path similar to the one traced out for his
comet, another was seen in 1531, and one in 1456. Halley perceived that
the intervals between those dates corresponded to a period of about
seventy-six years, the time which he calculated would be required for
his comet to complete a revolution of its orbit. He therefore had no
hesitation in predicting that the comet would appear again in 1758.
Halley knew that he would not be alive to witness the event, and alludes
to it in the following sentence: 'Wherefore if it should return
according to our prediction about the year 1758, impartial posterity
will not refuse to acknowledge that this was first discovered by an
Englishman.' As the time approached when the comet should be drawing
near to our system, much interest was excited among astronomers, who
would have an opportunity afforded them of testing the accuracy of
Halley's prediction. An eminent French mathematician named Clairaut
computed anew, by a method rather different to that adopted by Halley,
the retarding effect of the attraction of the planets upon the speed of
the comet, and arrived at the conclusion that it would reach perihelion
about the middle of April 1759; but, owing to unknown influences--Uranus
and Neptune not having been discovered--it might be a month before or
behind the calculated time. Clairaut made this announcement on November
14, 1758. Astronomers were now intently on the look-out for the comet,
and night after night the sky was swept by telescopes in search of the
expected visitor, which for upwards of seventy years had been pursuing
its solitary path invisible to mortal eyes. But the mental vision of the
mathematician did not fail to follow this celestial object, which was
now announced as being on the confines of our system. The comet was
first observed on December 25, 1758, it soon became conspicuous in the
heavens, and reached perihelion on March 12, 1759, a month before the
time assigned to it by Clairaut but within the limit of error allowed
for unknown influences. Halley's comet returned again in 1835, and may
be expected about the year 1911. The periodic appearance of this comet
has been traced back to the year 1305.

The celebrated comet of 1680 was noted as having been the one which
afforded Newton an oppor