It is a remarkable, not to say wonderful, fact, that in ancient times the Pythagoreans held the same system of the universe which modern astronomy teaches, though, perhaps, they were not acquainted with the mathematic calculations of its distances. But still more surprising is it, that while they were thus perfectly acquainted with the number of the planets, and even arranged them in the same order that they are placed by modern astronomers, they admitted into their system two stars which we have not. One of these, as the sun of the gods [_Geister-sonne_],[23] they placed high above the visible sun. The latter, which they named the “counter-earth,” (αντἱχθν) was placed directly opposite to the real earth. It would seem, therefore, that they regarded these two bodies as the invisible centers of the whole sidereal universe, and, as it were, the choir-leaders or _choragi_ of the apparently orderless and scattered host of heaven. Are these two stars now extinct? or is their light too pure and ethereal to penetrate our dense and thickened atmosphere; or, like so much besides, was it little else than a still surviving tradition from the primitive world? This, however, must ever remain conjectural. As for the fact itself, that the Pythagoreans did so teach, and understood by these names, not merely figurative symbols, but real stars, has been placed beyond doubt by modern investigations into the Pythagorean doctrines. At any rate, their knowledge of these stars must have been acquired by some other means than the telescope of modern astronomy, with which, in fact, they were not acquainted, and nothing but some new observation or phenomenon in the sidereal heavens can ever throw light on this matter. And who shall say that even our present astronomical science shall not advance still further, and that it has not closed too soon, and been in all too great a haste to sum up its doubtless most elaborate and complicated calculations?