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.