On the 31st we saw the Flannen Islands, situated near the Lewis, on the N. W. coast of Scotland; and the next morning, off Cape Wrath, we gave chase to a ship to windward, at the same time two ships appearing in the N. W. quarter, which proved to be the Alliance and a prize ship which she had taken, bound, as I understood, from Liverpool to Jamaica. The ship which I chased brought to at noon; she proved to be the Union, letter of marque, bound from London for Quebec, with a cargo of naval stores on account of government, adapted for the service of British armed vessels on the lakes. The public despatches were lost, as the Alliance very imprudently hoisted American colours, though English colours were then flying on board the Bonhomme Richard. Captain Landais sent a small boat to ask whether I would man the ship, or he should, as in the latter case he would suffer no boat nor person from the Bonhomme Richard to go near the prize. Ridiculous as this appeared to me, I yielded to it for the sake of peace, and received the prisoners on board the Bonhomme Richard, while the prize was manned from the Alliance. In the afternoon another sail appeared, and I immediately made the signal for the Alliance to chase; but, instead of obeying, he wore and laid the ship's head the other way. The next morning I made a signal to speak with the Alliance, to which no attention was shown; I then made sail with the ships in company for the second rendezvous which was not far distant, and where I fully expected to be joined by the Pallas and Cerf. The 2d of September we saw a sail at daybreak, and gave chase; that ship proved to be the Pallas, and had met with no success while separated from the Bonhomme Richard. On the 3d the Vengeance brought to a small Irish brigantine, bound homeward from Norway. The same evening I sent the Vengeance in the N. E. quarter to bring up the two prize ships that appeared to me to be too near the islands of Shetland, while with the Alliance and Pallas I endeavoured to weather Fair Isle, and to get into my second rendezvous, where I directed the Vengeance to join me with the three prizes. The next morning, having weathered Fair Isle, and not seeing the Vengeance nor the prizes, I spoke the Alliance, and ordered her to steer to the northward and bring them up to the rendezvous.