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,
and the catalogue would by that entry be wrong. The thing to do,
therefore, was to examine all the catalogues for errors, to see whether
the stars entered there actually existed, or whether any were missing.
If a wrong entry were discovered, it might of course have been due to
some clerical error, though that is hardly probable considering the care
spent in making these records, or it might have been a tailless comet,