On the 31st of May, we left Ascension, and steered to the northward with a fine gale at S.E. by E. I had a great desire to visit the island of St Matthew, to settle its situation; but as I found the wind would not let me fetch it, I steered for the island of Fernando de Noronha on the coast of Brazil, in order to determine its longitude, as I could not find this had yet been done. Perhaps I should have performed a more acceptable service to navigation, if I had gone in search of the island of St Paul, and those shoals which are said to lie near the equator, and about the meridian of 20° W.; as neither their situation nor existence are well known. The truth is, I was unwilling to prolong the passage in searching for what I was not sure to find; nor was I willing to give up every object, which might tend to the improvement of navigation or geography, for the sake of getting home a week or a fortnight sooner. It is but seldom that opportunities of this kind offer; and when they do, they are too often neglected. In our passage to Fernando de Noronha, we had steady fresh gales between the S.E. and E.S.E., attended with fair and clear weather; and as we had the advantage of the moon, a day or night did not pass without making lunar observations for determining our longitude. In this run, the variation of the compass gradually decreased from 11° W., which it was at Ascension., to 1° W., which we found off Fernando de Noronha. This was the mean result of two compasses, one of which gave 1° 37', and the other 23' W.