Having cleared Clarence Strait, and found it to be perfectly navigable with common precaution (which in a slight degree enhanced the value of the discovery of the Adelaide) our course was directed for a bay to the southward, which Captain King had not examined. A very refreshing cool north-westerly seabreeze* had just succeeded a short calm. Passing four miles from the western extremity of the Vernon Isles, we had irregular soundings of ten and seven fathoms. The ripplings and discoloured water are a warning that they should be approached with caution on this side. (*Footnote. The seabreeze prevailing from the westward through Clarence Strait, the passage to Port Essington from the westward, during the easterly monsoon, might be more easily made by passing through it, instead of working along the north side of Melville Island.) The mouth of a considerable inlet came in sight at the head of a bay as we advanced towards it, steering South by East. This opening began to appear of consequence as we drew near, although the singularly gradual decrease in the soundings, on a sandy bottom materially diminished the probability of its being the mouth of a river. Still, when we anchored as near as we could approach, there remained a hope of its being so. HOPE INLET. SHOAL BAY. September 8. Early in the morning Mr. Forsyth and myself started to explore the opening. We soon discovered that it was nothing more than a shallow creek at low-water. The tide here rising twenty feet, gave it the important appearance it had yesterday evening. A tall clump of naked trees was conspicuous at the east entrance point, towering above the insipid mangrove shore. We gave it the name of Hope Inlet, to commemorate the feelings it excited on its first discovery. From the south point of Clarence Strait it is distant eleven miles, and the bay in which it lies, from the shallow-water at the head of it, was called Shoal Bay. The boat being provisioned for four days, we pushed on to explore another opening above fifteen miles to the westward. The seabreeze setting in early, we did not reach it till after dark, when we landed for observations at a cliffy projection near the eastern entrance point: this we found to be composed of a kind of pipeclay, mixed with calcareous matter. We had some difficulty in landing, and then in scrambling up the cliffs by the light of a lantern. If any of the watchful natives happened at the time to be on the lookout, they must have stood fixed with astonishment at beholding such strange persons, who at such a time of night, with no ostensible object were visiting their shores. EXPLORE A NEW OPENING. September 9.