th far greater accuracy than the older tables of
Burckhardt. For the larger planets corrections were applied to the
older tables to make them more nearly represent observations before new
ones were constructed. These corrections, however, have not proved
satisfactory, not being founded on sufficiently thorough
investigations. Indeed, the operation of correcting tables by
observation, as we would correct the dead-reckoning of a ship, is a
makeshift, the result of which must always be somewhat uncertain, and
it tends to destroy that unity which is an essential element of the
astronomical ephemeris designed for permanent future use. The result of
introducing them, while no doubt an improvement on the old tables, has
not been all that should be desired. The general lack of unity in the
tables hitherto employed is such that I can only state what has been
done by mentioning each planet in detail.

For Mercury, new tables were constructed by Professor Winlock, from
formulae published by Le Verrier in 1846. These tables have, however,
been deviating from the true motion of the planet, owing to the motion
of the perihelion of Mercury, subsequently discovered by Le Verrier
himself. They are now much less accurate than the newer tables
published by Le Verrier ten years later.

Of Venus new tables were constructed by Mr. Hill in 1872. They are more
accurate than any others, being founded on later data than those of Le
Verrier, and are therefore satisfactory so far as accuracy of
prediction is concerned.

The place of Mars, Jupiter, and Saturn are still computed from the old
tables, with certain necessary corrections to make them better
represent observations.

The places of Uranus and Neptune are derived from new tables which will
probably be sufficiently accurate for some time to come.

For the moon, Pierce's tables have been employed up to the year 1882
inclusive. Commencing with the ephemeris for the year 1883, Hansen's
tables are introduced with corrections to the mean longitude founded on
two centuries of observation.

With so great a lack of uniformity, and in the absence of any existing
tables which have any other element of unity than that of being the
work of the same authors, it is extremely desirable that we should be
able to compute astronomical ephemerides from a single uniform and
consistent set of astronomical data. I hope, in the course of years, to
render this possible.

When our ephemeris was first commen