were other than a single star.

The errors of Uranus, though small, were enormously greater than other
things which had certainly been observed; there was an unmistakable
discrepancy between theory and observation. Some cause was evidently at
work on this distant planet, causing it to disagree with its motion as
calculated according to the law of gravitation. If the law of
gravitation held exactly at so great a distance from the sun, there must
be some perturbing force acting on it besides all the known forces that
had been fully taken into account. Could it be an outer planet? The
question occurred to several, and one or two tried to solve the problem,
but were soon stopped by the tremendous difficulties of calculation.

The ordinary problem of perturbation is difficult enough: Given a
disturbing planet in such and such a position, to find the perturbations
it produces. This was the problem that Laplace worked out in the
_Mécanique Céleste_.

But the inverse problem--given the perturbations, to find the planet
that causes them--such a problem had never yet been attacked, and by
only a few had its possibility been conceived. Friedrich Bessel made
preparations for solving this mystery in 1840, but he was prevented by
fatal illness.

In 1841 the difficulties of the problem presented by these residual
perturbations of Uranus excited the imagination of a young student, an
undergraduate of Cambridge--John Couch Adams by name--and he determined
to make a study of them as soon as he was through his _tripos_. In
January, 1843, he was graduated as senior wrangler, and shortly
afterward he set to work. In less than two years he reached a definite