The light-coloured water off the latter, we knew indicated the reef discovered by the brig Tigris, belonging to the Indian navy, which in company with the New South Wales colonial schooner, Isabella, was returning from rescuing the survivors of the Charles Eaton, from the natives of Murray Island. When half a mile from the North-East side, in 22 fathoms rocky bottom, Cape Croker, bearing South 29 degrees East six miles; we steered out, keeping at the same distance round this patch of light water in twenty and twenty-one fathoms, seven or eight miles from the Cape, which bore when over what appeared the shoalest part, South 42 degrees East. This conclusion I afterwards found, on meeting Captain Stanley, to be correct, as that bearing led over the part of the reef he struck on in H.M.S. Britomart. But being on the inner part he was distant only three miles from Cape Croker, whilst the outer edge of the reef I believe to be seven miles from it on the same bearing. In hauling up to the southward, round the North-West extreme of the discoloured water, the soundings were as follows, 17, 12, and 19 fathoms, with rocky bottom. The Cape bore when in the least depth South 58 degrees East nine miles. We were fortunate in having such good means of determining the longitude of Cape Croker, by observation of a twilight star when in the meridian, and others with the sun soon afterwards. These both agreeing, place the Cape 27 1/4 miles east of Port Essington, instead of 20, as it is laid down in the chart. This discovery is of vital importance to ships proceeding to Port Essington; we were therefore glad of so good an opportunity for rectifying the error. PORT ESSINGTON. Expectation was on tip-toe as we were fast approaching Port Essington, feeling naturally anxious to see what progress had been made at the new settlement, and to learn the fate of the expedition. There was, however, nothing striking in the first appearance of the land, a low woody shore; the most remarkable object being a sandy islet, with a tree in its centre, about a mile east of Point Smith, the eastern point of Port Essington: Vashon Head forming the western.