But though we may be convinced from the facts of gravitation that these meteoric stones, and all other bodies flying through space near our solar system, must be constrained by the sun to obey Kepler's laws, and fly round it in some regular elliptic or hyperbolic orbit, what chance have we of determining that orbit? At first sight, a very poor chance, for we never see them except for the instant when they splash into our atmosphere; and for them that instant is instant death. It is unlikely that any escape that ordeal, and even if they do, their career and orbit are effectually changed. Henceforward they must become attendants on the earth. They may drop on to its surface, or they may duck out of our atmosphere again, and revolve round us unseen in the clear space between earth and moon. Nevertheless, although the problem of determining the original orbit of any given set of shooting-stars before it struck us would 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.