Two boats were despatched this morning, under Mr. Usborne's command, to examine the eastern part of what I think may be named very properly Useless Bay. This would have been my duty, had I not unfortunately been taken ill in the evening of the preceding day: the symptoms were violent headache, and a disordered state of the stomach, caused, the surgeon says, by the oppressive and overpowering heat which we have experienced for the last few days, and the general effects of which seem more distressing to the ship's company than is often experienced under a higher range of the thermometer; the deprivation of all power, or energy, is one of its most unpleasant consequences. I am inclined to think that one reason for its great and wearying effect upon most of us--indeed, more or less, all are suffering from it--is that there is hardly any variation in temperature during the whole twenty-four hours: it sometimes does not amount to more than two or three degrees. Captain Wickham and the surgeon visited an inlet near the ship to-day, which had indeed been looked into, but not explored before. They proceeded to the south-west for about three miles, through a very tortuous channel, dry in many parts at low-water, thickly studded with mangrove bushes, over and through which the tide made its way at high-water, giving to that part of the country the appearance of an extensive morass. A slightly elevated table-topped range of land was seen from time to time, some eight or nine miles to the south-east, but in its highest elevation did not reach 200 feet. The apparent width of the inlet in no way diminished so far as the exploring party examined it; and this fact, coupled with the general character of the country hereabouts, induces me to suppose that the periodical return of the spring tide, floods the greater part of the coast between the sea shore and the base of the range I have alluded to. Vampires of a very large kind were here met with, the furthest south we had seen them. MIAGO ON SHORE. Miago had accompanied this party on shore, though he evidently showed no great devotion to the deed. They said he watched everything, aye, every bush, with the most scrutinizing gaze: his head appeared to turn upon a pivot, so constantly was it in motion, with all that restless watchfulness for which the savage is ever remarkable. The heat to-day either exceeded an average, or else perhaps, as an invalid, I noticed it more closely: On shore, it was 98 degrees in the shade. On board, it was 90 degrees in the shade. Pulling off in the boats 118. During the day, it fluctuated, between 88 and 94. A breeze from seaward blew the greater part of each night from West-South-West, hauling round to south in the morning. January 20. Our noon observation to-day enabled us to fix the latitude of Cape Villaret 18 degrees 18 minutes 50 seconds, which precisely agrees with that assigned to it by Captain King. MR. USBORNE WOUNDED.