We see here the head of the comet, containing as its brightest spot what is called the nucleus, and in which the material of the comet seems to be much denser than elsewhere. Surrounding the nucleus we find certain definite layers of luminous material, the coma, or head, from 20,000 to 1,000,000 miles in diameter, from which the tail seems to stream away. This view may be regarded as that of a typical object of this class, but the varieties of structure presented by different comets are almost innumerable. In some cases we find the nucleus absent; in other cases we find the tail to be wanting. The tail is, no doubt, a conspicuous feature in those great comets which receive universal attention; but in the small telescopic objects, of which a few are generally found every year, this feature is usually absent. Not only do comets present great varieties in appearance, but even the aspect of a single object undergoes great change. The comet will sometimes increase enormously in bulk; sometimes it will diminish; sometimes it will have a large tail, or sometimes no tail at all. Measurements of a comet's size are almost futile; they may cease to be true even during the few hours in which a comet is observed in the course of a night. It is, in fact, impossible to identify a comet by any description of its personal appearance. Yet the question as to identity of a comet is often of very great consequence. We must provide means by which it can be established, entirely apart from what the comet may look like. It is now well known that several of these bodies make periodic returns. After having been invisible for a certain number of years, a comet comes into view, and again retreats into space to perform another revolution. The question then arises as to how we are to recognise the body when it does come back? The personal features of its size or brightness, the presence or absence of a tail, large or small, are fleeting characters of no value for such a purpose. Fortunately, however, the law of elliptic motion established by Kepler has suggested the means of defining the identity of a comet with absolute precision. After Newton had made his discovery of the law of gravitation, and succeeded in demonstrating that the elliptic paths of the planets around the sun were necessary consequences of that law, he was naturally tempted to apply the same reasoning to explain the movements of comets. Here, again, he met with marvellous success, and illustrated his theory by completely explaining the movements of the remarkable body which was visible from December, 1680, to March, 1681. [Illustration: Fig. 69.--The Parabolic Path of a Comet.]