tion 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, this longitude is reduced to
that place by the application of the difference shown by the time keepers
to have existed between the two situations. In ascertaining this
difference, the rates of going allowed to the time keepers are generally
those found at the place which is to be fixed; whether applied to
observations taken before arriving, or after quitting that place. This,
however, could be done only at those stations where rates had been
observed; at the intermediate points, where the result of lunar distances
is given principally as an object of comparison with the time keepers,
the rates allowed in the reduction are those found at the station
previously quitted; but then the difference of longitude is corrected by
the quantity consequent on the following supposition: that the time
keepers altered their rates from those at the previous, to those at the
following station, in a ratio augmenting in arithmetic progression. The
difference of longitude, thus corrected when necessary, is given under
the head of _Reduction by time keepers_; and the longitudes reduced by it
to the place intended to be fixed, are taken to be of equal authority
with those resulting from observations made in the place itself.

7th. But these longitudes, whether reduced to, or observed in, the place
to be fixed, still require a correction which is of more importance than
any of those before mentioned. The theories of the solar and lunar
motions not having reached such a degree of perfection as to accord
perfectly with actual observation at Greenwich, the distances calculated
from those theories and given in the almanack become subject to some
error; and consequently so do the longitudes deduced from them. The
quantiti