orbits are very elongated; and, instead of being nearly circular, they take the elliptical form.  In consequence of the nature of these orbits, the same comet may approach very near the Sun, and afterwards travel from it to immense distances.  Thus, the period of the Comet of 1680 has been estimated at three thousand years.  It approaches the Sun, so as to be nearer to it than our Moon is to us, whilst it recedes to a distance 853 times greater than the distance of the Earth from the Sun.  On the 17th of December, 1680, it was at its perihelion—­that is, at its greatest proximity to the Sun; it is now continuing its path beyond the Neptunian orbit.  Its velocity varies according to its distance from the solar body.  At its perihelion it travels thousands of leagues per minute; at its aphelion it does not pass over more than a few yards.  Its proximity to the Sun in its passage near that body caused Newton to think that it received a heat twenty-eight thousand times greater than that we experience at the summer solstice; and that this heat being two thousand times greater than that of red-hot iron, an iron globe of the same dimensions would be fifty thousand years entirely losing its heat.  Newton added that in the end comets will approach so near the Sun that they will not be able to escape the preponderance of its attraction, and that they will fall one after the other into this brilliant body, thus keeping up the heat which it perpetually pours out into space.  Such is the deplorable end assigned to comets by the author of the “Principia,” an end which makes De la Bretonne say to Retif:  “An immense comet, already larger than Jupiter, was again increased in its path by being blended with six other dying comets.  Thus displaced from its ordinary route by these slight shocks, it did not pursue its true elliptical orbit; so that the unfortunate thing was precipitated into the devouring centre of the Sun.”  “It is said,” added he, “that the poor comet, thus burned alive, sent forth dreadful cries!”

[Illustration:  A COMET]

It will be interesting, then, in a double point of view, to follow a comet in its different passages in sight of the Earth.  Let us take the most important in astronomical history—­the one whose orbit has been calculated by Edmund Halley, and which was named after him.  It was in 1682 that this comet appeared in its greatest brilliancy, accompanied with a tail which did not measure less than thirty-two millions of miles.  By the observation of the path which it described in the heavens, and the time it occupied in describing it, this astronomer calculated its orbit, and recognized that the comet was the same as that which was admired in 1531 and 1607, and which ought to have reappeared in 1759.  Never did scientific prediction excite a more lively interest.  The comet returned at the appointed time; and on the 12th of March, 1759, reached its perihelion.  Since the year 12 before the Christian era, it had presented itself twenty-four times to the Earth.  It was principally from the astronomical annals of China that it was possible to follow it up to this period.