1456, 1380, and 1305. It is true, he noticed, that the intervals
varied by a year and a-half, and the inclination of the orbit to the
ecliptic diminished with successive apparitions. But he knew from
previous calculations that this might easily be due to planetary
perturbations. Finally, he arrived at the conclusion that all of these
comets were identical, travelling in an ellipse so elongated that the
part where the comet was seen seemed to be part of a parabolic
orbit. He then predicted its return at the end of 1758 or beginning of
1759, when he should be dead; but, as he said, "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."[3] [_Synopsis Astronomiae Cometicae_, 1749.]

Once again Halley's suggestion became an inspiration for the
mathematical astronomer. Clairaut, assisted by Lalande, found that
Saturn would retard the comet 100 days, Jupiter 518 days, and
predicted its return to perihelion on April 13th, 1759. In his
communication to the French Academy, he said that a comet travelling
into such distant regions might be exposed to the influence of forces
totally unknown, and "even of some planet too far removed from the sun
to be ever perceived."

The excitement of astronomers towards the end of 1758 became intense;
and the honour of first catching sight of the traveller fell to an
amateur in Saxony, George Palitsch, on Christmas Day, 1758. It reached
perihelion on March 13th, 1759.

This fact was a startling confirmation of the Newtonian theory,
because it was a new kind of calculation of perturbations, and also it
added a new member to the solar system, and gave a prospect of adding