outer planet has started on its course, in a prescribed path, and
that it has a certain mass. It will, of course, disturb the motion
of Uranus, and in consequence of that disturbance Uranus will follow
a path the nature of which can be determined by calculation. It
will, however, generally be found that the path so ascertained does
not tally with the actual path which observations have indicated for
Uranus. This demonstrates that the assumed circumstances of the
unknown planet must be in some respects erroneous, and the astronomer
commences afresh with an amended orbit. At last after many trials,
Le Verrier ascertained that, by assuming a certain size, shape, and
position for the unknown Planet's orbit, and a certain value for the
mass of the hypothetical body, it would be possible to account for
the observed disturbances of Uranus. Gradually it became clear to
the perception of this consummate mathematician, not only that the
difficulties in the movements of Uranus could be thus explained, but
that no other explanation need be sought for. It accordingly
appeared that a planet possessing the mass which he had assigned, and
moving in the orbit which his calculations had indicated, must indeed
exist, though no eye had ever beheld any such body. Here was,
indeed, an astonishing result. The mathematician sitting at his
desk, by studying the observations which had been supplied to him of
one planet, is able to discover the existence of another planet, and
even to assign the very position which it must occupy, ere ever the
telescope is invoked for its discovery.

Thus it was that the calculations of Le Verrier narrowed greatly the
area to be scrutinised in the telescopic search which was presently
to be instituted. It was already known, as we have just pointed out,
that the planet must lie somewhere on the ecliptic. The French
mathematician had now further indicated the spot on the ecliptic at