Being now happily within the reefs, and in smooth water, I endeavoured to keep near them to try for fish; but the tide set us to the N W; I therefore bore away in that direction, and, having promised to land on the first convenient spot we could find, all our past hardships seemed already to be forgotten. At noon I had a good observation, by which our latitude was 12 deg. 46' S, whence the foregoing situations may be considered as determined with some exactness. The island first seen bore W S W five leagues. This, which I have called the island Direction, will in fair weather always shew the channel, from which it bears due W, and may be seen as soon as the reefs, from a ship's mast-head: it lies in the latitude of 12 deg. 51' S. These, however, are marks too small for a ship to hit, unless it can hereafter be ascertained that passages through the reef are numerous along the coast, which I am inclined to think they are, and then there would be little risk if the wind was not directly on the shore. My longitude, made by dead reckoning, from the island Tofoa to our passage through the reef, is 40 deg. 10' W. Providential channel, I imagine, must lie very nearly under the same meridian with our passage; by which it appears we had out-run our reckoning 1 deg. 9'. We now returned God thanks for his gracious protection, and with much content took our miserable allowance of a 25th of a pound of bread, and a quarter of a pint of water, for dinner. [Sidenote: Friday 29.] Friday, May the 29th. Moderate breezes and fine weather, wind E S E. [Sidenote: 1789. MAY 29.]