In a valley to the left of the slope by which we ascended the peak, were noticed several very remarkable, low and spreading trees, with a dark green foliage, and leaves large, ovate, and obtuse. The branches, from which, when broken, a milky juice exuded, were thick and glossy, of an ash colour; at their extremity they were thin, with long pendulous stems, supporting a bell-shaped flower, of a rich crimson hue; these hung in great profusion, and contrasting with the surrounding dark green verdure, presented a very beautiful and striking appearance. The diameter of the trunk of the largest tree was 20 inches, and the height 25 feet. Lieutenant Emery painted a most faithful representation of one of them, by means of which we found on our arrival at Port Essington, that neither the professional nor amateur botanists, had any knowledge of it. To them and to ourselves it was alike perfectly new. CAPTAIN COOK. On the preceding evening I had refreshed my memory by reading Cook's account of his visit to the same spot, and was thus able minutely to follow in the footsteps of the immortal navigator. There is an inexpressible charm in thus treading in the track of the mighty dead, and my feelings on attaining the summit of the peak, where the foot of the white man, had perhaps but once before rested, will easily be understood. Below to the eastward stretched a vast expanse of water, broken at the distance of about eight miles, by a long narrow line of detached reefs, on which there ran a white crest of foaming breakers, marking the outer edge of the Great Barrier, a name which few seamen could hear with indifference when in its vicinity. If I felt emotions of delight, on first perceiving the extent of a danger so justly dreaded, how much stronger must have been the feelings of Captain Cook, when from the same spot years before, he saw by a gap in the line of broken water, there was a chance of his once more gaining the open sea, after being confined to the eastern shores of the Australian continent, for a distance of 750 miles. Though the dangers of this inner channel had proved so nearly fatal to his ship, the truth of the homely adage, which describes all as happening for the best, was here fully borne out, as the very fact of his position enabled Captain Cook to make considerable discoveries along the coast--just as by the mishap on Endeavour Reef, the presence of a river was made apparent, and some slight knowledge of the aborigines obtained, as well as numerous facts illustrative of the natural and vegetable productions of the locality. PROVIDENCE CHANNEL.