There is another class of Comet of which we see examples from time to time, and having seen them once shall never see again. This is because these Comets move in orbits which are not closed, and which are known as parabolic or hyperbolic orbits respectively, because derived from those sections of a cone which are called the Parabola and the Hyperbola. It must be understood that what I am now referring to is purely a matter of orbit, and that no relationship subsists between the size and physical features of a Comet and the path it pursues in space. The only sort of reservation, perhaps, to be made to this statement is, that the comets celebrated for their size and brilliancy, are often found to be revolving in elliptic orbits of great eccentricity, which means that their periods may amount to many centuries. It may be well to say something now as to what is the ordinary career of a comet, so far as visibility to us, the inhabitants of the Earth, is concerned. Though this might be illustrated by reference to the history of many comets, perhaps there is no one more suitable for the purpose than Donati’s Comet of 1858. In former times, when telescopes were few or non-existent, brilliant comets often appeared very suddenly, just as a carriage or a man does, as you turn the corner of a street. Such things even happen still: for instance, the great comet of 1861 burst upon us all at once at a day’s notice. Usually, however, now in consequence of the large size of the telescopes in use, and the great number of observers who are incessantly on the watch, comets are discovered when they are very small, because remote both from the Earth and Sun, and many weeks, or even months, it may be, before they shine forth in their ultimate splendour. Now, let us see how these statements are supported by the history of Donati’s comet in 1858. On June 2 in that year, it was first seen by Donati at Florence, as a faint nebulosity, slowly journeying northwards. June passed away, and July, and August, the comet all the while remaining invisible to the naked eye; that is to say, it first became perceptible to the naked eye on August 29, having put forth a faint tail about August 20. After the beginning of September its brilliancy rapidly increased. On September 17, the head equalled in brightness a 2nd magnitude star, the tail being 4° long. Passing its point of nearest approach to the Sun on September 29, it came nearest to the Earth on October 10; though, perhaps, its appearance a few days previously, namely on October 5, is the thing best remembered by those who saw it, because it was on that night that the comet passed over the 1st magnitude star Arcturus. For several days about this time, the comet was an object of striking beauty in the Western Heavens, during the hours immediately after sun-set. After October 10, it rapidly passed away to the Southern hemisphere, diminishing in brightness, as it did so, because receding from the Earth and the Sun.