On the 11th of May, the Hornet arrived from Derne, bringing accounts from Eaton of the capture of that place, and of all the occurrences since leaving Egypt, with a reply at length to Barron's letter of March 22d. He represented that the measures had been eminently successful; Hamet was in possession of the most valuable province of Tripoli, his enemies were retreating, and the supply of some funds with a few regular troops to give effect to operations requiring energy, would enable him without doubt soon to appear at the gates of the City. He had however been much discouraged by the Commodore's declaration, that all support to the Prince must cease, if the terms which the Pasha might offer, should be accepted; he was convinced that terms would be offered as soon as Yusuf entertained serious apprehensions for his safety, but he considered it incumbent on the United States, in case they were accepted, and it should be determined to withdraw all aid from Hamet, to place him in a situation at least as good as that from which he had been drawn, and out of the reach of his vindictive brother. He expressed his opinion that Derne should not be abandoned, nor peace made precipitately, as the navy might thus be crushed and the national honor receive a heavy blow. The result of all these communications, was a determination on the parts of the Commander of the forces, and the Consul General, to abandon the co-operation with Hamet and to enter into a negotiation with Yusuf. Barron considered the moment the most favorable for concluding peace, on advantageous terms, as the capture of Derne must doubtless have produced a powerful effect on the Pasha's mind; and although discarding the idea of yielding any point of national honor or advantage, to obtain the liberation of the prisoners, he yet contended that "the lives of so many valuable and estimable Americans should not be sacrificed to abstract points of honor." Mr. Lear in reply, conceived it his duty, "to open and bring to a happy issue, a negotiation for peace consistent with the tenor of their instructions, whenever the Commander of the American naval forces in the Mediterranean should judge the occasion proper and favorable;" he would therefore at once proceed to Tripoli for the purpose; he _could not however believe that any impression favorable to the United States had been made on Yusuf, by the measures in concert with his brother, unless the bravery and perseverance of the Americans at Derne, had given him a proof of what might be done against him without extraneous aid_.