observers with good
instruments will usually obtain when circumstances are favourable, then
lunar observations taken in 1814 and afterwards, may be entitled to
confidence within the following limits:

From one set of distances, consisting of six independent sights, the
error in longitude may be 30' on either side; but will probably not
exceed 12'.

From six sets on one side of the moon, each set consisting as above, the
error may be 20'; but not probably more than 8'.

Twelve sets of distances, of which six on each side of the moon, are not
likely to err more than 10' from the truth; and may be expected to come
within 5'.

The error in sixty sets, taken during three or four lunations, and one
half on each side of the moon, will not, I think, be wrong more than 5';
and will most probably give the longitude exact to 1' or 2', This degree
of accuracy is far beyond what the hopes of the first proposers of the
lunar method ever extended, and even beyond what astronomers accustomed
only to fixed observatories will be disposed to credit at this time; but
in thinking it _probable_ that sixty sets of lunar distances will come
within 1' or 2' of the truth, when compared with correct tables, I
conceive myself borne out by the following facts.

In Port Lincoln, I observed an eclipse of the sun with a refracting
telescope of forty-six inches focus, and a power of about two hundred. It
was recalculated by Mr. Crosley from Delambre's and Burckhardt's tables,
the one made four and the other ten years afterwards. The longitude
deduced from the beginning differed only 1' 31.5" from that at the end,
and the mean of both only 1' 17" from _thirty_ sets of lunar distances
corrected for the errors of the tables.

The Spanish admiral D'Espinosa observed emersions of the first and second
satellites of Jupiter in 1793, at Port Jackson, and also an eclipse of
the sun which he recalculated by the tables of Burg. He deduces from
thence the longitude of Sydney Cove to be 151 deg. 12' 45"; and from
forty-four sets of lunar distances by lieutenant Flinders, it would be
151 deg. 11' 49" east.

At Port Louis in the Isle Mauritius, the Abbe de la Caille observed an
eclipse of the sun, the transit of mercury over the sun's disk, and
various occultations of Jupiter's satellites; M. d'Apres also observed
several occultations; and this place should therefore be well determined.
Its longitude in the Requisite Tables is 57 deg. 29' 15" east; and from