bit, causes a small annual displacement known as
_aberration_.

Now it is easy to see that any uncertainty in the application of these
corrections saps the very foundations of exact astronomy. Extremely
minute quantities, it is true, are concerned; but the life and progress
of modern celestial science depends upon the sure recognition of
extremely minute quantities. In the early years of the nineteenth
century, however, no uniform system of "reduction" (so the complete
correction of observational results is termed) had been established.
Much was left to the individual caprice of observers, who selected for
the several "elements" of reduction such values as seemed best to
themselves. Hence arose much hurtful confusion, tending to hinder united
action and mar the usefulness of laborious researches. For this state of
things, Bessel, by the exercise of consummate diligence, sagacity, and
patience, provided an entirely satisfactory remedy.

His first step was an elaborate investigation of the precious series of
observations made by Bradley at Greenwich from 1750 until his death in
1762. The catalogue of 3,222 stars which he extracted from them gave the
earliest example of the systematic reduction on a uniform plan of such a
body of work. It is difficult, without entering into details out of
place in a volume like the present, to convey an idea of the arduous
nature of this task. It involved the formation of a theory of the errors
of each of Bradley's instruments, and a difficult and delicate inquiry
into the true value of each correction to be applied, before the entries
in the Greenwich journals could be developed into a finished and
authentic catalogue. Although completed in 1813, it was not until five
years later that the results appeared with the proud, but not
inappropriate title of _Fundamenta Astronomiae_. The eminent value of the
work consisted in this, that by providing a mass of entirely reliable
information as to the state of the heavens at the epoch 1755, it threw
back the beginning of _exact_ astronomy almost half a century. By
comparison with Piazzi's catalogues the amount of precession was more
accurately determined, the proper motions of a considerable number of
stars became known with certainty, and definite prediction--the
certificate of initiation into the secrets of Nature--at last became
possible as regards the places of the stars. Bessel's final improvements
in the methods of reduction were published i