They arrived at Gibraltar on the 17th of May. Colonel Humphreys concluded that it was expedient for Mr. Donaldson to go first to Alicant, rather than Algiers, in order to be near at hand, to ascertain facts and profit of occasions. He gave him instructions accordingly; and having also instructed Mr. Simpson, our Consul at Gibraltar, to renew our peace with the Emperor of Morocco, Colonel Humphreys sailed from Gibraltar the 24th of May, and arrived at Havre de Grace on the 26th of June; from whence he set off immediately for Paris. The object of his mission was communicated by our Minister, Colonel Monroe, to the Committee of Public Safety. On the 1st of July he had received only a verbal answer, that the French Government was disposed to interest itself, and to do every thing in its power, to promote the accomplishment of our wishes on the subject in question. On the 28th, assurances were received that immediate measures should be taken for giving particular instructions to the agents of the Republic, to use its influence in co-operating with us. The multiplicity of affairs with which the officers of Government were occupied, and the getting from London a sum of money necessary to purchase the usual peace presents, prevented a conclusion of this arrangement at Paris until September. It had been judged expedient, by Colonel Humphreys and Colonel Monroe, that Joel Barlow should be employed in the negotiation with the Barbary States, and his consent had been obtained. By the 11th of September, all the writings on the part of Colonel Humphreys were prepared for Mr. Barlow, to proceed with the instructions and powers from the Government of the French Republic to its agents in Barbary, in favor of our negotiation. Colonel Humphreys left Paris the 12th of September, and reached Havre the 14th, where he found the master and mate of the United States brig Sophia, both sick with fevers. While waiting there impatiently for their recovery, he received intelligence from our Consul at Marseilles, that Mr. Donaldson had concluded a Treaty of Peace with the Dey of Algiers; nevertheless, Colonel Humphreys thought it expedient that Mr. Barlow should proceed with the presents prepared and preparing at Paris; for, if not needed at Algiers, they would be wanted in the negotiation with Tunis and Tripoli. About the 5th of October, Colonel Humphreys sailed from Havre, and after a stormy passage of more than forty days, arrived at Lisbon on the 17th of November. There he found Captain O'Brien, who had arrived about the 1st of October, with the Treaty with Algiers.