The explanation by Newton of the observed facts of the motion of the moon, the way he accounted for precession and nutation and for the tides; the way in which Laplace explained every detail of the planetary motions—­these achievements may seem to the professional astronomer equally, if not more, striking and wonderful; but of the facts to be explained in these cases the general public is necessarily more or less ignorant, and so no beauty or thoroughness of treatment appeals to it or excites its imagination.  But to predict in the solitude of the study, with no weapons other than pen, ink, and paper, an unknown and enormously distant world, to calculate its orbit when as yet it had never been seen, and to be able to say to a practical astronomer, “Point your telescope in such a direction at such a time, and you will see a new planet hitherto unknown to man”—­this must always appeal to the imagination with dramatic intensity, and must awaken some interest in the dullest.

Prediction is no novelty in science; and in astronomy least of all is it a novelty.  Thousands of years ago Thales, and others whose very names we have forgotten, could predict eclipses, but not without a certain degree of inaccuracy.  And many other phenomena were capable of prediction by accumulated experience.  A gap between Mars and Jupiter caused a missing planet to be suspected and looked for, and to be found in a hundred pieces.  The abnormal proper-motion of Sirius suggested to Bessel the existence of an unseen companion.  And these last instances seem to approach very near the same class of prediction as that of the discovery of Neptune.  Wherein, then, lies the difference?  How comes it that some classes of prediction—­such as that if you put your finger in fire it will be burned—­are childishly easy and commonplace, while others excite in the keenest intellects the highest feelings of admiration?  Mainly, the difference lies, first, in the grounds on which the prediction is based; second, in the difficulty of the investigation whereby it is accomplished; third, in the completeness and the accuracy with which it can be verified.  In all these points, the discovery of Neptune stands out as one among the many verified predictions of science, and the circumstances surrounding it are of singular interest.

Three distinct observations suffice to determine the orbit of a planet completely, but it is well to have the three observations as far apart as possible so as to minimize the effects of minute but necessary errors of observation.  When Uranus was found old records of stellar observations were ransacked with the object of discovering whether it had ever been unwittingly seen before.  If seen, it had been thought, of course, to be a star—­for it shines like a star of the sixth magnitude, and can therefore be just seen without a telescope if one knows precisely where to look for it and if one has good sight—­but if it had been seen and catalogued as a star it would have moved from its place,