There is no intelligence of special interest from any of the South American States. From _Buenos Ayres_, our dates are to the 15th of May, when every thing was quiet, and political affairs were in a promising condition. The new Legislature met on the 1st, and resolutions had been introduced tendering public thanks to General Urquiza for having delivered the country from tyranny. He had been invested with complete control of the foreign relations, and the affairs of peace and war. Don Lopez was elected Governor of the province of Buenos Ayres on the 13th, receiving 33 of the 38 votes in the Legislative Chamber. The choice gives universal satisfaction to the friends of the new order of things. The Governors of all the provinces were to meet at Santa Fé on the 29th, to determine upon the form of a Central Government. General Urquiza was to meet them in Convention there, and it is stated that he was to be accompanied by Mr. Pendleton, the United States Chargé, whose aid had been asked, especially in explaining in Convention the nature and working of American institutions.----At _Rio Janeiro_ a dissolution of the Cabinet was anticipated. Great dissatisfaction was felt at certain treaties recently concluded with Montevideo, and at the correspondence of Mr. Hudson, the late English Minister, upon the Slave Trade, which had been lately published in London.----From _Ecuador_ there is nothing new. Flores still remained at Puna, below Guayaquil, with his forces.----In _Chili_ there was a slight attempt at insurrection in the garrison at Trospunta, but it was soon put down. Six persons implicated in previous revolts were executed at Copiapo on the 22d of May. GREAT BRITAIN.