Bainbridge took possession of the Moorish ship. The next day he recovered the brig, which was standing in for the bay of Almeria, to the westward of Cape de Gatte. On inquiry he discovered that Ibraham Lubarez was cruising for Americans under an order issued by the governor of Mogadore. Although Morocco was ostensibly at peace with the United States, Bainbridge did not hesitate, now, about taking his prize to Gibraltar. Here he left the Meshboha in charge of Mr. M’Donough, under the superintendence of the consul, and then went off Cape St. Vincent in pursuit of a Moorish frigate, which was understood to be in that neighborhood. Failing in his search, he returned within the Straits, and went aloft, in obedience to his original orders. At Gibraltar, the Philadelphia met the homeward bound vessels, under Com. Rodgers, which were waiting the arrival of Preble, in the Constitution. As this force was sufficient to watch the Moors, it left the Philadelphia the greater liberty to proceed on her cruise. While together, however, Lieut. Porter, the first of the New York 36, exchanged with Lieut. Cox, the latter gentleman wishing to return home, where he soon after resigned; while the former preferred active service. The Philadelphia found nothing but the Vixen before Tripoli. A Neapolitan had given information that a corsair had just sailed on a cruise, and this induced Capt. Bainbridge to despatch Lieut. Com. Smith in chase. In consequence of this unfortunate, but perfectly justifiable, decision the frigate was left alone off the town. A vigorous blockade having been determined on, the ship maintained her station as close in as her draught of water would allow until near the close of October, when, it coming on to blow fresh from the westward, she was driven some distance to leeward, as often occurred to vessels on that station. As soon as it moderated, sail was made to recover the lost ground, and, by the morning of the 31st, the wind had become fair, from the eastward. At 8, A. M., a sail was made ahead, standing like themselves to the westward. This vessel proved to be a small cruiser of the Bashaw’s, and was probably the very vessel of which the Vixen had gone in pursuit. The Philadelphia now crowded every thing that would draw, and was soon so near the chase as to induce the latter to hug the land. There is an extensive reef to the eastward of Tripoli, called Kaliusa, that was not laid down in the charts of the ship, and which runs nearly parallel to the coast for some miles. There is abundance of water inside of it, as was doubtless known to those on board the chase, and there is a wide opening through it, by which six and seven fathoms can be carried out to sea; but all these facts were then profound mysteries to the officers of the Philadelphia. Agreeably to the chart of Capt. Smyth, of the British navy, the latest and best in existence, the eastern division of this reef lies about a mile and a half from the coast, and its western about a mile.