Secretary of State Adams writes from Washington, D.C., to Sheldon he Paris that he received Sheldon's two dispatches; encloses copies of correspondence from Count de Menon; the president received with great satisfaction the testimonial of Viscount de Chateaubriand to the ability with which Mr. Gallatin has performed the duties of his office in France; discusses claims of U.S. citizens against France and France's claim to special privileges in the ports of Louisiana; a proposal to Great Britain of a convention for regulating neutral and belligerent rights in time war, but not for the consideration of Great Britain alone, but to other nations, including Russia and France, the proposal being that in the event of war, no privateering should be allowed , nor any hostilities against private persons or property upon the ocean; such an agreement has been concluded with Prussia, but other nations were not then prepred for its adoption, and the present is believed to be a more favorable moment for its success.