Notwithstanding these differences between the elements of the orbits of the comets and those of the planets, the fact that each has the Sun in one focus indicates that the body moving in it is a member of the solar system, either for the time, or permanently, according to the nature of its orbit.
A distinction may accordingly be made between the comets which are permanent members of our solar system and those which are only accidental or temporary visitors. Those moving in elliptical orbits around the Sun, like the planets, and therefore having a determinate period of revolution, from which the time of their successive returns may be predicted, are permanent members of our system, and are called periodic comets. All comets moving in parabolical or hyperbolical curves, are only temporary members of the solar system, being apparently strangers who have been diverted from their courses by some disturbing influence. No comet is classed as periodical which does not follow a perceptibly elliptical orbit. Any comet passing around the Sun at the mean distance of the Earth from this body, with a velocity of 26 miles per second, will fly off into infinite space, to return to us no more.
The time of revolution of the different periodic comets thus far observed varies greatly, as do also the distances to which they recede from the Sun at aphelion. Whilst the period of revolution of Encke's comet, the shortest thus far known, is only 3½ years, that of the comet of 1844, II., is 102,000 years; and whilst the orbit of the first is comprised within the orbit of Jupiter, that of the last extends to a distance equal to 147 times the distance of Neptune from the Sun. But so vast an orbit cannot be accurately determined from the imperfect data at our disposal.
The periodic comets are usually divided into two classes. The comets whose orbits are within the orbit of Neptune are called interior comets, while those whose orbits extend beyond that of Neptune are called exterior comets. The known interior periodic comets are twelve in number, while, including all the cases in which there is some slight evidence of elliptic motion, the number of exterior comets observed is six or seven times as great. The periodic comets of short period are very interesting objects, inasmuch as by their successive returns they afford an opportunity to calculate their motions and to observe the physical changes which they undergo in their intervals of absence.
From observation of the periodic comets, it has been learned that the same comet never presents twice the same physical appearance at its different returns, its size, shape and brilliancy varying so greatly that a comet can never be identified by its physical characters alone. It is only when its elements have been calculated, and are found to agree with those of a cometary orbit previously known, that the two comets can be identified one with the other. There are reasons to believe that, in general, comets decrease in brightness and size at each of their successive returns, and that they are also continually losing some of their matter as they traverse their orbits.
When very far away from us, all comets appear nearly alike, consisting of a faint nebulosity, of varying dimensions. When a comet first appears in the depths of space, and travels towards the Sun, it generally resembles a faint, uniformly luminous nebulosity, either circular or slightly elongated in form. As it approaches nearer to the Sun, a slight condensation of light appears towards its centre, and as it draws still nearer, it becomes brighter and brighter, and in condensing forms a kind of diffused luminous nucleus. At the same time that the comet acquires this concentration of light, the nebulosity gradually becomes elongated in the direction of the Sun. These effects generally go on increasing so long as the comet is approaching the Sun; the condensation of light sometimes forms a bright nucleus, comparable to a very brilliant star, while the elongation becomes an immense appendage or tail. When the comet has passed its perihelion and recedes from the Sun, the inverse phenomena are observed; the comet, decreasing in brightness, gradually loses its nucleus and tail, resumes its nebulous aspect, and finally vanishes in space, to appear again in due course, if it chance to be a periodic comet. While all comets become brighter in approaching the Sun, they do not all, however, develop a large tail, some of them showing only a slight elongation.
When a comet is first discovered with the telescope at a great distance from the Sun, it is difficult to predict whether it will become visible to the naked eye, or will remain a telescopic object, as it is only in approaching the Sun that these singular bodies acquire their full development. Thus, Donati's comet, whose tail became so conspicuous an object at its full appearance in 1858, remained two months after its discovery by the telescope without any indication of a tail. The comet of Halley, which before and after its return in 1759, remained five years inside of the orbit of Saturn, showed not the least trace of its presence during the greater part of this time. Nothing but calculation could then indicate the position in the sky of this invisible object, which was so prominent when it approached the Sun.
Another curious phenomenon exhibited by comets, and first noticed by Valz, is that in approaching the Sun the nebulosity composing these bodies contracts, instead of dilating, as would be naturally supposed from the greater amount of solar heat which they must then receive. In receding from the Sun, on the contrary, they expand gradually. As comets approach the Sun, the tail and nucleus are developed, while the nebulosity originally constituting these comets contracts, as if its material had been partly consumed in this development. In a certain sense it may be said that the comets are partly created by the Sun; in more exact terms, the changes of form which they undergo are induced by the Sun's action upon them at different distances and under varying conditions. Moreover, they are rendered visible by its influence, without which they would pass unperceived in our sky. When a comet disappears from view, it is not because its apparent diameter is so much reduced by the distance that it vanishes, but rather on account of the diminution of its light, both that which it receives from the Sun, and its own light; these bodies being in some degree self-luminous, as will be shown below.
The large comets, such as can be seen with the naked eye, always show the following characteristics, on examination with the telescope. A condensation of light resembling a diffused star forms the brightest part of the comet, this condensation being situated towards the extremity the nearest to the Sun. It is this starlike object which is called the nucleus. The nucleus seems to be entirely enclosed in a luminous vapory envelope of the same general texture, called the coma. This envelope, which is quite variable in brightness and form, is brightest next to the nucleus, and gradually fades away as it recedes from it. The nucleus and the coma, considered as a whole, constitute the head of a comet. From the head of a comet proceeds a long trail of pale nebulous light, which usually grows wider, but fainter, as it recedes from the nucleus, and insensibly vanishes in the sky. This delicate appendage, or tail, as it is commonly called, varies very much in size and shape, not only in different comets, but in the very same comet, at different times. Its direction is generally opposite to that of the Sun from the head of the comet.
The nuclei vary very much in brightness, in size and in shape; and while in some telescopic comets they are either absent or barely distinguishable as a small condensation of light, in bright comets they may become plainly visible to the naked eye, and they sometimes even surpass in brightness the most brilliant stars of the heavens. But whatever may be the size of cometary nuclei, they are subject to sudden and rapid changes, and vary from day to day. Sometimes they appear exceedingly brilliant and sharply outlined, while at other times they are so dim and diffused that they are hardly distinguishable from the coma of which they seem then to form a part.