the table of errors kept in the Observatory, Mr. Crosley has calculated the corresponding effects on the longitude, and proportioned them to the time when our observations were taken.  The combined effect of the two errors forms a correction to the longitudes obtained from the sun and moon; but when the moon was observed with a star, then the moon’s error alone gives the correction.  But it has sometimes happened, that there were many days interval between the observations of the moon at Greenwich, and that the errors preceding and following are so extremely irregular, that no accuracy could be expected in reducing them by proportion; in these unfortunate cases, that part of the error belonging to the moon has been taken absolute, such as it was found on the day nearest to the time of observation; but the sun’s error is always from proportion.  These corrections, with the interval in the Greenwich observations of the moon, are given under their proper heads.

8th.  The longitudes thus computed, reduced to the intended point, and corrected, are placed under each other; and the mean of the whole is taken to be the true longitude of that point, unless in certain cases where it is otherwise expressed.  The mean is also given of the longitudes uncorrected for the errors of the sun and moon’s places, that the reader may have an opportunity of comparing them; and some sea officers who boast of their having never been out more than 5’, or at most 10’, may deduce from the column of corrections in the different tables, that their lunar observations could not be entitled to so much confidence as they wish to suppose; since, allowing every degree of perfection to themselves and their instruments, they would probably be 12’, and might be more than 30’ wrong.

In the nautical almanacks for 1811 and 1815, the distances are computed from the new tables of Burg for the moon, and of Delambre for the sun; and it is to be hoped that the necessity of correcting for errors in the distances at Greenwich will have ceased, or be at least greatly diminished.  Should the computed places of the sun and moon be happily found to agree with actual observation, and supposing that our results may be taken as the average of what practised 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’.