seem nearly
insoluble, it has been solved, and solved with some approach to
accuracy; being done by the help of observations of certain other
bodies. The bodies by whose help this difficult problem has been
attacked and resolved are comets. What are comets?

I must tell you that the scientific world is not entirely and completely
decided on the structure of comets. There are many floating ideas on the
subject, and some certain knowledge. But the subject is still, in many
respects, an open one, and the ideas I propose to advocate you will
accept for no more than they are worth, viz. as worthy to be compared
with other and different views.

Up to the time of Newton, the nature of comets was entirely unknown.
They were regarded with superstitious awe as fiery portents, and were
supposed to be connected with the death of some king, or with some
national catastrophe.

Even so late as the first edition of the _Principia_ the problem of
comets was unsolved, and their theory is not given; but between the
first and the second editions a large comet appeared, in 1680, and
Newton speculated on its appearance and behaviour. It rushed down very
close to the sun, spun half round him very quickly, and then receded
from him again. If it were a material substance, to which the law of
gravitation applied, it must be moving in a conic section with the sun
in one focus, and its radius vector must sweep out equal areas in equal
times. Examining the record of its positions made at observatories, he
found its observed path quite accordant with theory; and the motion of
comets was from that time understood. Up to that time no one had
attempted to calculate an orbit for a comet. They had been thought
irregular and lawless bodies. Now they were recognized as perfectly
obedient to the law of gravitation, and revolving round the sun like
everything else--as members, in fact, of our solar system, though not
necessarily permanent members.

But the orbit of a comet is very different from a planetary one. The
excentricity of its orbit is enormous--in other words, it is either a
very elongated ellipse or a parabola. The comet of 1680, Newton found
to move in an orbit so nearly a parabola that the time of describing it
must be reckoned in hundreds of years at the least. It is now thought
possible that it may not be quite a parabola, but an ellipse so
elongated that it will not return till 2255. Until that date arrives,
however, uncertainty will pr