ted 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 the
computation of our ephemeris was started, in the year 1849, there were
no tables which could be regarded as really satisfactory in use. In the
British Nautical Almanac the places of the moon were derived from the
tables of Burckhardt published in the year 1812. You will understand,
in a case like this, no observations subsequent to the issue of the
tables are made use of; the place of the moon of any day, hour, and
minute of Greenwich time, mean time, was precisely what Burckhardt
would have computed nearly a half a century before. Of the tables of
the larger planets the latest were those of Bouvard, published in 1812,
while the places of Venus were from tables published by Lindenau in
1810. Of course such tables did not possess astronomical accuracy. At
that time, in the case of the moon, completely new tables were
constructed from the results reached by Professor Airy in his reduction
of the Greenwich observations of the moon from 1750 to 1830. These were
constructed under the direction of Professor Pierce and represented the
places of the moon wi