*Lunar observations.*]

The *refraction* of the heavenly bodies given in the tables, being
calculated for a mean height of 50º of Fahrenheit's thermometer, and
29.6 inches of the barometer, it has been corrected for the difference
between these means and what was the state of the atmosphere at
the time of observation.

3rd. In reducing the apparent to the true distance, Mr. Crosley
has used the method of Joseph Mendoza de Rios, Esq., F.R.S.,
given with his *Nautical Tables*, second edition, 1809; and the tables
from which the corrections were taken and the computations made,
are those of the same valuable work.

4th. The reduced distance, found as above, has been corrected
to the spheroidal figure of the earth, according to the theory
explained in the Philosophical Transactions of the Royal Society of 1797;
and for doing which, rules are given by Mr. Mendoza with his
*Nautical Tables* of 1801. This calculation is tedious, and the correction, more especially in low latitudes, too small to be necessary in
common cases.

5th. In the nautical almanack the distances are given to every three hours, but the irregularities of the moon's motion being such as to cause some inequality in the different parts of this interval, the distance at the hour preceding, and at the hour following the time of observation, was found by interpolation from the two nearest given on each side; and having the distances at Greenwich for each hour, the observed distance can never fall more than half an hour from one of them; and the moon's inequalities do not then produce any sensible error in the corresponding time, as obtained from common proportion. The correction arising from this process is seldom so important as to be necessary in sea observations.

6th. The longitude deduced from a comparison of the true
distance at observation with the hourly distances at Greenwich, is
contained in the following tables under the head of *Longitude from Nautical Almanack*. But as it frequently happened, that the observation was not taken exactly in the place which it is intended to fix,