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 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