Lunar observations.} APPENDIX. 
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 observa- 
tions of the moon at Greenwich, and that the errors preceding and 
following are so extremely irregular, that no accuracy could be ex- 
pected 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 com- 
paring them ; and some sea officers who boast of their having never 
been out more than g', 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 is', and might be more than' 
30' wrong. 
In the nautical almanacks for 1814 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 
