[New York, August] 16th.ー Our General was again requested to be a spectator on the bank of the river the approaching night, with the most positive assurances that he should not be again disappointed: he accordingly went, attended as on the preceding time, and took a proper position on the bank. The night was pretty dark; they soon found that the galleys and fire-vessels were silently moving up with the tide. After some time, and almost immediately after the sentinels on board the British ships has passed the word, "all is well, " two of the fire-vessels flashkd into a blaze; the one close on the side of the Phenix, the other grappling one of the tenders. To appearance, the' flames were against the side of the Phenix; and there was much confusion on board. A numbkr of cannon were discharged into the fire-vessel in order to sink her. A number of seamen ascended, and got out on the yard-arm, supposed to clear away some grapplings. The fire-vessel was alongside, as was judged near ten minutes, when the Phenix either cut, or slipt her cable, let fall her fore-topsail, wore round, and stood up the river, being immediately veiled from the spectators, by the darkness of the night. The tender burnt down to the water's edge, and was towed to the shore by the Americans, out of which was taken, one iron six-pounder, two three-pounders, one two pounder, ten swivels, a caboose, some gun-barrels, cutlasses, grapplings, chains, 8ec. The Rose, and the other two tenders, remained at their moorings; but it was said that one of the tenders was deserted by her crew, for a time. Several of our galleys were said to have been inactive; otherwise, a very considerable advantage would have been reaped. The Americans sustained no loss or injury, saving one man, who, in communicating fire to one of the vessels, got considerably burnt in the face, hands, &c.