rather to say, all the great planets, confine their movements to a
certain zone around the heavens. This zone extends some way on
either side of that line called the ecliptic in which the earth
pursues its journey around the sun. It was therefore to be inferred
that the new planet need not be sought for outside this zone. It is
obvious that this consideration at once reduces the area to be
scrutinized to a small fraction of the entire heavens. But even
within the zone thus defined there are many thousands of stars. It
would seem a hopeless task to detect the new planet unless some
further limitation to its position could be assigned.

It was accordingly suggested to Le Verrier that he should endeavour
to discover in what particular part of the strip of the celestial
sphere which we have indicated the search for the unknown planet
should be instituted. The materials available to the mathematician
for the solution of this problem were to be derived solely from the
discrepancies between the calculated places in which Uranus should be
found, taking into account the known causes of disturbance, and the
actual places in which observation had shown the planet to exist.
Here was indeed an unprecedented problem, and one of extraordinary
difficulty. Le Verrier, however, faced it, and, to the astonishment
of the world, succeeded in carrying it through to a brilliant
solution. We cannot here attempt to enter into any account of the
mathematical investigations that were necessary. All that we can do
is to give a general indication of the method which had to be
adopted.

Let us suppose that a planet is revolving outside Uranus, at a
distance which is suggested by the several distances at which the
other planets are dispersed around the sun. Let us assume that this