Here follow the lunar observations by Mr Wales, for ascertaining the longitude of these islands, reduced by the watch to Port Sandwich in Mallicollo, and Port Resolution in Tanna.

Port Sandwich, ( Mean of 10 sets of ob. before 167 deg. 56’ 33” 1/4 ) E.
                 ( 2 ditto, at 168 2 37 1/2 ) long
                 ( 20 ditto, after 167 52 57 )
                 ( ----------------
                 ( Mean of those means, 167 57 22 3/4

Port Resolution, ( Mean of 20 sets of ob. before 169 37 35 ) E.
                 ( 5 ditto, at 169 48 48 ) long
                 ( 20 ditto, after 169 47 22 1/2 )
                 ( ----------------
                 ( Mean of these means, 169 44 33

It is necessary to observe, that each set of observations, consisting of between six and ten observed distances of the sun and moon, or moon and stars, the whole number amounts to several hundreds; and these have been reduced by means of the watch to all the islands; so that the longitude of each is as well ascertained as that of the two ports above-mentioned.  As a proof of this I shall only observe, that the longitude of the two ports, as pointed out by the watch and by the observations, did not differ two miles.  This also shews what degree of accuracy these observations are capable of, when multiplied to a considerable number, made with different instruments, and with the sun and stars, or both sides of the moon.  By this last method, the errors which may be either in the instruments or lunar tables, destroy one another, and likewise those which may arise from the observer himself; for some men may observe closer than others.  If we consider the number of observations that may be obtained in the course of a month (if the weather is favourable,) we shall perhaps find this method of finding the longitude of places as accurate as most others; at least it is the most easy, and attended with the least expence to the observer.  Every ship that goes to foreign parts is, or maybe, supplied with a sufficient number of quadrants at a small expence; I mean good ones, proper for making these observations.  For the difference of the price between a good and a bad one, I apprehend, can never be an object with an officer.  The most expensive article, and what is in some measure necessary in order to arrive at the utmost accuracy, is a good watch; but for common use, and where that strict accuracy is not required, this may be dispensed with.  I have observed before, in this journal, that this method of finding the longitude is not so difficult but that any man, with proper application, and a little practice, may soon learn to make these observations as well as the astronomers themselves.  I have seldom known any material difference between the observations made by Mr Wales, and those made by the officers at the same time.