of new methods of computation. His tables of the moon are those
now used for predicting the places of the moon in all the
ephemerides of the world.

The only successful attempt to prepare systematic tables for all
the large planets is that completed by Le Verrier just before his
death; but he used only a small fraction of the material at his
disposal, and did not employ the modern methods, confining himself
wholly to those invented by his countrymen about the beginning of
the present century. For him Jacobi and Hansen had lived in vain.

The great difficulty which besets the subject arises from the fact
that mathematical processes alone will not give us the position of
a planet, there being seven unknown quantities for each planet
which must be determined by observations. A planet, for instance,
may move in any ellipse whatever, having the sun in one focus, and
it is impossible to tell what ellipse it is, except from
observation. The mean motion of a planet, or its period of
revolution, can only be determined by a long series of
observations, greater accuracy being obtained the longer the
observations are continued. Before the time of Bradley, who
commenced work at the Greenwich Observatory about 1750, the
observations were so far from accurate that they are now of no use
whatever, unless in exceptional cases. Even Bradley's observations
are in many cases far less accurate than those made now. In
consequence, we have not heretofore had a sufficiently extended
series of observations to form an entirely satisfactory theory of
the celestial motions.

As a consequence of the several difficulties and drawbacks, when