"But before I proceed farther it may be proper to take notice, that since the time when I gave their lordships an account of the near agreement of Mr. Professor Mayer's lunar tables with the observations that had been then made at the Royal Observatory, I have compared several others, which concurred to prove that the difference between the observed and computed places nowhere amounted to more than about one minute and a half; and I find that the difference (small as it is) may yet be diminished by making alterations in some of the equations, whose true quantity could not be determined without proper observations; after making the needful corrections it appeared, by the comparison of above eleven hundred observations taken here since the new instruments were fixed up, that the difference did nowhere amount to more than a minute: it may therefore be reasonably concluded, that so far as it will depend upon the lunar tables the true longitude of a ship at sea may in all cases be found within about half a degree, and generally much nearer."