The Rhode Island Republican

Capt. Gray, who has arrived at Philadelphia from Cadiz, and who sailed August 1, informs that the Treaty with Algiers was signed by Com. Decatur and Wm. Shaler, Esq. No Tribute to be hereafter paid.

Capt. Smith, in the brig Edwin, was to receive $15,000 for his capture and detention by the Algerines. The Independence, 74, Com. Bainbridge, passed Gibraltar about the 30th of July.— Com. Decatur had proceeded to Tripoli with his squadron : there being an account to settle with the Bey, for suffering his neutrality to be violated to the prejudice of the United States ; several American prizes being retaken in port.

Treaty with Algiers.—Com. Decatur's despatches to the Secretary of the Navy, announcing the conclusion of a Treaty of Peace, with Algiers, we learn, are dated on the 5th of July.—The Commodore does not state on what day the Treaty was signed, but it was probably two or three days previous to the date of the Despatches. He states that 19 American prisoners at Algiers had been given up, and that he should send them home in the Epervier which was to sail with despatches. It is understood that as soon as the arrangements were finished with Algiers, Com. Decatur would visit the other Barbary powers. The terms of the Treaty were such as Com. Decatur chose to dictate. The release of the Algerine vessels captured by him was not stipulated in the Treaty, but he afterwards gave them up to the Dey as a present.—Reg.