This is especially so when we remember what a point there is to work on, for the whole system reasoned about, though it may be larger than our own, is at such a distance that it appears, literally and exactly, far smaller to the eye than the point of the finest sewing-needle; and it is a course of accurate reasoning, and reasoning alone, on the character of the observed changing brightness of this point, which has not only shown the existence of some great dark satellite, but indicated its size, its distance from its sun, its time of revolution, the inclination of its orbit, and still more. The existence of dark invisible bodies in space, then, is in one case at least demonstrated, and in this instance the dark body is of enormous size; for, to illustrate by our own solar system, we should probably have to represent it in imagination by a planet or swarm of planetoids hundreds of times the size of Jupiter, and (it may be added) whirling around the sun at less than a tenth the distance of Mercury. Of a wholly different class of variables are those which have till lately only been known at intervals of centuries, like that new star Tycho saw in 1572. I infer from numerous inquiries that there is such a prevalent popular notion that the “Star of Bethlehem” may be expected to show itself again at about the present time, that perhaps I may be excused for answering these questions in the present connection. In the first place, the idea is not a new, but a very old one, going back to the time of Tycho himself, who disputed the alleged identity of his star with that which appeared to the shepherds at the Nativity. The evidence relied on is, that bright stars are said to have appeared in this constellation repeatedly at intervals of from three hundred and eight to three hundred and nineteen years (though even this is uncertain); and as the mean of these numbers is about three hundred and fourteen, which again is about one-fifth of 1572 (the then number of years from the birth of Christ), it has been suggested, in support of the old notion, that the Star of Bethlehem might have been a variable, shining out every three hundred and fourteen or three hundred and fifteen years, whose fifth return would fall in with the appearance that Tycho saw, and whose _sixth_ return would come in 1886 or 1887. This is all there is about it, and there is nothing like evidence, either that this was the star seen by the Wise Men, or that it is to be seen again by us. On the other hand, nothing in our knowledge, or rather in our ignorance, authorizes us to say positively it cannot come again; and it may be stated for the benefit of those who like to believe in its speedy return, that if it does come, it will make its appearance some night in the northern constellation of Cassiopeia’s chair, the position originally determined by Tycho at its last appearance, being twenty-eight degrees and thirteen minutes from the pole, and twenty-six minutes in right ascension.