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 twenty-seven sets of distances taken whilst a prisoner there, I made it, when corrected for the errors of the tables, 57 deg. 29’ 57” east.

In appreciating the degrees of accuracy to which a small or larger number of lunar distances may be expected to give the longitude, I suppose the observer to be moderately well practised, his sextant or circle, and time keeper to be good, and his calculations to be carefully made; and it is also supposed, that the distances in the nautical almanack are perfectly correct.  As, however, there may still be some errors, notwithstanding the science and the labour employed to obviate them, it cannot be too much recommended to sea officers to preserve all the data of their observations; more especially of such as may be used in fixing the longitudes of places but little, or imperfectly known.  The observations may then be recalculated, if requisite; the corrections found to be necessary may be applied; and the observer may have the satisfaction of forwarding the progress of geography and navigation, after having contributed to the safety of the ship, and benefit of the particular service in which he may happen to have been engaged.