The wind was at S. by E. in the morning, and we steered northward after the brig, in order to fall in with the reefs and prosecute our search for an opening; in an hour they were visible, and we passed along their west side at the distance of a mile. Before nine o'clock the brig made signal for having only 17 fathoms, other reefs were discovered in the north-west, and the course was altered to pass within them. At eleven we rounded their west end; and at noon were in latitude 20° 38' 58", and from the bearing of the Cumberland Isle _k_, in longitude 150° 1' east. We were now obliged to steer westward again, having reefs at the distance of two miles, from N. E. by E., to N. W. by W.; and seeing that they extended onward, and the breeze was fresh, I hauled up for the Cumberland Island marked _l_, the largest yet seen, with the intention of anchoring there for the night. The tide carried us too far to leeward, but we fetched a lesser island, _l2_, seven miles to the north; and came to, in 17 fathoms grey sand, one mile from a beach on its north-west side, and half a mile from the reef which surrounds the island. SATURDAY 16 OCTOBER 1802 Early in the morning I landed with a party of the gentlemen, and scrambled through a thick brush and over lumps of rock, to the highest part near the north end of the island. Hazy weather much contracted my view; but several new Cumberland Islands were visible, making up the number to fifteen, of which the greater part had not been seen by captain Cook. Amongst the bearings taken with a theodolite, were those of 'k' and 'k2', which had been set from No. 4 of the Percy Isles. 'k', the extremes, bore S. 48° 30' to 46° 40' E. 'k2', S. 36 50 to 33 40 E. Ship at anchor, dist. one mile, N. 64 0 W. From these bearings and the several latitudes, I ascertained the difference of longitude made from Upper Head to the ship, to be 12' 37" west.