From the _sun's semi-diameter_, as given in the nautical almanack, 3"
have been subtracted. In the almanacks of the years comprehending our
observations, the semi-diameter was stated from Mayer's tables, which
gave it 3" too great; owing to the imperfection of the telescope with
which Mayer observed.

The semi-diameters of the sun and moon being less in the vertical, than
in the horizontal direction, on account of the differences in the
refraction, they have been reduced proportionally to these differences
and to the angles at the points of contact in measuring the distance.
This correction is called _contraction of the semi-diameter_.

Before using the _moon's horizontal parallax_ in the nautical almanack,
where it is calculated for the equator, it has been corrected (printed as
'diminished', and corrected in the errata) by a number of seconds
depending upon the latitude of the place, and upon this assumed position:
that the earth is a regular spheroid, whose polar axis is to the
equatorial axis, as 320 to 321. This, and the preceding correction are
unnecessary, unless where great exactness may be required.

The _refraction_ of the heavenly bodies given in the tables, being
calculated for a mean height of 50 deg. 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 interpola