The effect of such a spectacle largely depends upon its rarity; but since the telescope has been applied to the sounding of the heavens, it has been found that the appearance of comets is by no means an unusual occurrence. If so few comets, comparatively, are seen, it is because most of them are telescopic objects, and are therefore invisible to the naked eye. Most of the telescopic comets are not only too faint to be perceived by the unaided eye, but are insignificant objects, even when observed through the largest telescopes. It was Kepler's opinion that comets are as numerous in the sky as fishes are in the ocean. Undoubtedly the number of these bodies must be great, considering that we can only see them when they come into the neighborhood of the Earth, and that many even here remain invisible, or at least pass unperceived. That many of them have passed unperceived heretofore, is proved by the fact that the number of those observed becomes greater every year, with the increase of the number of instruments used in their search. The number of comets observed with the naked eye during historic times is nearly 600, and that of telescopic comets, which, of course, all belong to the last few centuries, is more than 200, so that we have a total number of about 800 comets of which records have been kept. From theoretical considerations, Lambert and Arago estimated their entire number at several millions, but such speculations have generally no real value, since they cannot be established on a firm basis. Comets remain visible for more or less time, according to their size and the nature and position of their orbits, but in general, the large ones can be followed with the telescope for several months after they have become invisible to the naked eye. The comet of 1861, for example, remained telescopically visible for a year, and that of 1811, for 17 months after disappearing from ordinary sight. While a comet remains visible, it appears to revolve daily about us like the stars in general; but it also moves among the constellations, and from this movement its orbit may be computed like that of a planet. From the apparent diurnal motion of a comet with the heavens, result the changes of position which it seems to undergo in the course of a night. The direction of the head and tail of a comet, of course, has only changed in regard to the horizon, but not in regard to the sky, in which they occupy very nearly the same position throughout a given night, and even for many nights in succession.