an island of a moderate height within it,
nearly in the same direction, bearing west half north. I entered the
passage with a strong stream running to the westward and found it about a
quarter of a mile broad, with every appearance of deep water.

On the outside the reef inclined to the north-east for a few miles, and
from thence to the north-west: on the south side of the entrance it
inclined to the south-south-west as far as I could see it, and I
conjecture that a similar passage to this which we now entered may be
found near the breakers that I first discovered which are 23 miles south
of this channel.

I did not recollect what latitude Providential channel* lies in, but I
considered it to be within a few miles of this, which is situate in 12
degrees 51 minutes south latitude.

(*Footnote. Providential Channel is laid down by Captain Cook in 12
degrees 34 minutes south, longitude 143 degrees 33 minutes east.)

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 north-west, 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 degrees 46
minutes south, whence the foregoing situations may be considered as
determined with some exactness. The island first seen bore
west-south-west five leagues. This, which I have called the island
Direction, will in fair weather always show the channel, from which it
bears due west, and may be seen as soon as the reefs from a ship's
masthead: it lies in the latitude of 12 degrees 51 minutes south. 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, in which case there would be
little risk even if the wind was directly on the shore.

My longitude made by dead reckoning from the island Tofoa to our passage
through the reef is 40 degrees 10 minutes west. 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 degree 9 minutes.

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.