Three leagues to the north-west of Montgomery's westernmost island are COCKELL'S ISLES, two in number, low and flat, but of small size. A reef extends for more than five miles to the westward, and it was not thought improbable that it might be connected with the reefs that extend to the westward of Montgomery Islands. The centre of the largest island is in 15 degrees 48 minutes South, and 124 degrees 4 minutes East. To the North-East of Cockell's Islands the flood-tide sets to the south; but to the westward with great strength to the South-East, and, at an anchorage ten miles to the eastward of Macleay Isles, the tide rose and fell thirty-six feet, the moon being twenty-one days old. Cockell's Islands are twenty miles from the land to the south; and in this interval, but within four leagues from the shore, are several small rocky islets, on one of which there is a remarkable lump; nearer the shore are two islands, which have a more fertile and verdant appearance than any other part near them: these form the western extremity of COLLIER'S BAY. MACLEAY ISLES lie in a North by West direction, and are eight miles in extent; the principal and highest island is near the south end of the group; those to the northward are small and straggling. The centre of the highest is in latitude 15 degrees 57 minutes, and longitude 123 degrees 42 minutes. CAFFARELLI ISLAND was seen by the French. Its summit is in latitude 16 degrees 2 minutes 25 seconds, and longitude 123 degrees 18 minutes 35 seconds. It is the north-westernmost of a range of islands, extending in the direction of North 60 degrees West; among which Cleft Island, so named from a remarkable cleft or chasm near its north end, and DAMPIER'S MONUMENT, are conspicuous: the latter is a high lump. This range is separated from one of a similar nature, and extending in a like direction to the eastward, by a strait from three to four miles wide, and from fifteen to twenty deep. Fourteen miles North 68 degrees West from the summit of Caffarelli Island is BRUE REEF, a circular patch of rocks of about a mile in diameter; three miles to the north-east of which we had irregular soundings, between thirty-eight and forty-five fathoms on a rocky bottom. The reef is in 15 degrees 57 minutes South, and 123 degrees 4 minutes 45 seconds East.