egrees one way or the other, it might
easily have been off the map; in which case, it is probable that the
search would not have been successful, or at any rate that success would
have been delayed.

[Illustration: V.--CORNER OF THE BERLIN MAP, BY THE USE OF WHICH GALLE
FOUND NEPTUNE.]

[Sidenote: Every one made mistakes.]

Thus, it is a most remarkable feature of the discovery of Neptune that
mistakes were made by almost every one concerned, however eminent. Airy
made a mistake in regarding the question of the Radius Vector as of
fundamental importance; Sir J. Herschel was wrong in describing an
elementary method which he considered might have found the planet;
Professor Peirce was wrong in supposing that the actual and the supposed
planet were essentially different in their action on Uranus; Le Verrier
was wrong in assigning limits outside which it was not necessary to look
when the actual planet was outside them; Adams was more or less wrong in
thinking that the eccentricity of the new planet could be found from the
material already at disposal of man. Both Adams and Le Verrier gave far
too much importance to Bode's Law.

To review a piece of history of this kind and note the mistakes of such
men is certainly comforting, and need not in any way lessen our
admiration. In the case of the investigators themselves, much may be set
down to excitement in the presence of a possible discovery. Professor
Sampson has provided us with a small but typical instance of this fact.
When Adams had carried through all his computations for finding Neptune,
and was approaching the actual place of the planet, he, "who could carry
through fabulous computations without error," for the first time wrote
down a wrong figure. The mistake was corrected upon the MS., "probably as
soon as made," but no doubt betrays the excitement which the great worker
could not repress at this critical moment. There is a tradition that,
similarly, when the mighty Newton was approaching the completion of his
calculations to verify the Law of Gravitation, his excitement was so great
that he was compelled to assign to a friend the task of finishing them.

Finally, we may remark how the history of the discovery of Neptune again
illustrates the difficulty of formulating any general principles for
guiding scientific work. Sometimes it is well to follow the slightest
clue, however imperfectly understood; at other times we shall do better to
refuse such guidance.