Mr. Brodie, Commander of the brig Alert, in October, 1817, saw A REEF extending for a considerable distance in a North-East and South-West direction. The Alert ran along the reef for twenty-five miles: about the centre Mr. Brodie saw two sand islets in latitude 17 degrees 2 minutes, and longitude 151 degrees 49 minutes. LIHOU'S SHOAL, probably a part of the above reefs seen by Lieutenant Vine and from the Alert, lies in latitude 17 degrees 25 minutes, and longitude 151 degrees 45 minutes: it is forty-six miles in length, and lies North-North-East and South-South-West. A very extensive RANGE OF SHOALS and ISLETS was seen by M. Tregrosse, of the French brig Les Trois Freres, in company with the brig Jessie, in 1821, according to the subjoined account. On the 19th June, the two brigs in company fell in with a range of reefs, terminated to the eastward by two sandy islets, the easternmost of which is in 151 degrees 47 minutes (149 degrees 27 minutes East of Paris); the vessels hauled to the wind immediately, but finding they could not pass to windward, bore up, and ran along the shoal from eight a.m. to four p.m., at the distance of a league and a half. Altogether they counted seven islets, three of which were covered with shrubs, and the whole connected by a reef, on the edge of which the sea broke heavily: they were called GOVERNOR FARQUHAR'S GROUP: the westernmost islet is in 17 degrees 39 minutes, and 151 degrees 27 minutes (149 degrees 7 minutes East of Paris) and appeared to terminate the group. As it was near sunset, the vessels hauled to the wind for the night, and at daylight bore up on a north course: soon afterwards they saw an islet West-North-West; they, however, continued to steer North until eight o'clock, and then, having run nine miles, saw another island North-North-East. On attempting to steer between the isles, they were found to be connected, and having sounded in eleven fathoms, the vessels bore up, and steered between the westernmost islet and two extensive reefs, through a passage five or six miles wide, that appeared to be clear. The westernmost islet is in 17 degrees 42 minutes South, and 150 degrees 43 minutes East (148 degrees 23 minutes East of Paris) and the westernmost reef, in 17 degrees 44 minutes South, and 150 degrees 32 minutes East (148 degrees 12 minutes East of Paris). A space of ten or twelve leagues between Governor Farquhar's Group and that seen the preceding day was passed in the night, and probably may contain other reefs. The last group was named TREGROSSE'S ISLETS. NORTH COAST. The ALERT struck on a shoal to the westward of Torres Strait in 1817; it seemed to be about two hundred fathoms in length, and about fifty yards broad: it is in latitude 9 degrees 52 minutes, and longitude 140 degrees 50 minutes.