From an observation of the sun’s upper and lower limbs in an artificial horizon, the latitude was 21 deg. 50’ 18”, and the ship bore from thence S. 68 deg.  E. two miles and a half; the latitude of the ship should therefore have been 21 deg. 51’ 14”; but a meridian altitude observed to the north by lieutenant Flinders, gave 21 deg. 49’ 54”; and I believe that altitudes from the sea horizon can never be depended on nearer than to one minute, on account of the variability of the horizontal refraction.  From this cause it was that, when possible, we commonly observed the latitude on board the ship both to the north and south, taking the sun’s altitude one way and his supplement the other, and the mean of the two results was considered to be true; separately, they often differed 1’, 2’, and even 3’, and sometimes they agreed.  The observation to the north most commonly gave the least south latitude, but not always, nor was there any regular coincidence between the results and the heights of the barometer or thermometer; though in general, the more hazy the weather, the greater were the differences.  At this time, the wind was light from the eastward and weather hazy; the thermometer stood at 72 deg., and barometer at 30.15 inches.

At two o’clock we got under way to go up Broad Sound, it being then near low water.  After steering south-east one mile, the depth rapidly diminished and we tacked; but the ship was set upon a bank of sand, where she hung five minutes and then swung off.  I afterwards steered nearer to the shore, in deeper water; and at dusk the anchor was dropped in 5 fathoms, sandy bottom, between the Flat Isles and the main, West Hill bearing N. 35 deg.  W. three leagues; the master sounded towards the coast, which was five miles off, and found the deepest water to be on that side.  In the morning [FRIDAY 10 SEPTEMBER 1802] the wind had shifted to south, and we beat up in a channel formed by the Flat Isles and the shoals attached to them, on one side, and the shelving banks from the main coast, on the other.  We had the assistance of a strong flood tide till eleven o’clock; at which time the anchor was let go, one mile from the north end of the 4th Flat Island.

I landed immediately, with the botanists; and at the south-east end of the island, which is a little elevated, took bearings and the meridian altitude of both limbs of the sun from an artificial horizon.  The latitude deduced was 22 deg. 8’ 33”; and the ship bearing N. 19 deg. 30’ W., two miles, it should have been for her, 22 deg. 6’ 40”; but lieutenant Flinders’ observation to the north gave 22 deg. 5’ 19”, or 1’ 21” less, nearly as on the preceding day; and it was ascertained that the difference arose neither from the eye nor the instrument.  Amongst the bearings were,

West Hill, the top, N. 16 deg. 40’ W.
Northumberland Isles. the peak marked ‘h’, N. 25 15 E.
Long Island, extreme of the north point, N. 73 35 E.
Upper Head, on the west shore up Broad Sound, S. 39 55 E.