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
almost 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 with some certainty, though
with only rough accuracy. And many other phenomena were capable of
prediction by accumulated experience. We have seen, for instance (coming
to later times), how a gap between Mars and Jupiter caused a missing
planet to be suspected and looked for, and to be found in a hundred
pieces. We have seen, also, how 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 get burnt--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, on 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 pre-eminently among the verified
predictions of science, and the circumstances surrounding it are of
singular interest.

* * * * *

In 1781, Sir William Herschel discovered the planet Uranus. Now you know
that three distinct observations suffice to determine the orbit of a
planet completely, and that 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. (See p. 298.) Directly Uranus was
found, therefore, 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