The Minister Plenipotentiary of France has the honor of communicating to Mr Livingston a letter from the Marquis de Bouille, commanding officer of the Windward Islands, and a memorial presented to that General by the Council and Assembly of the Island of Dominica. One of the two cases mentioned in them, that of the Dutch vessel, the Resolution, has been decided by the Court of Appeals, and the sentence of the Court of Admiralty of Philadelphia, has been amended in almost every point. The case of the Eeirsten has been decided at Boston in the first instance, and recently by the Supreme Court of Appeals. As the annexed papers seem to contain means for the revision of the first case, and proofs which were not known to the Judges when the decision was made, the undersigned has the honor of communicating them to Mr Livingston, and requests him to be pleased, after reading them, to send them back to him. The agent of the merchants at Dominica designs to solicit the said revision, with a view to have all the cargo, without exception, acquitted. The undersigned Minister flatters himself, that Congress will be pleased to enable the said agent to avail himself of the new proofs, which he says that he has obtained. The letter of the Marquis de Bouille, and the request of the Council and Assembly of Dominica, may hereafter serve to determine the true meaning of the capitulations of the English Islands, taken by the forces of his Majesty; and it is for this reason also, that the undersigned requests that they may be laid before the Tribunal of Appeals. This letter and this request, leave no room to doubt, that the Ostend ship Eeirsten sailed under the faith of the capitulation, and that her owners ought to participate in the advantages secured by it to the capitulators. The undersigned Minister appeals to the justice of Congress, and of the American tribunals, in favor of those inhabitants or capitulators of the Island of Dominica, who are interested in the cargo of this ship, as subjects of the King, his master, and in favor of those people of Ostend who are interested, as subjects of his Imperial Majesty, who is allied to the King, his master, both by blood and by treaties. LUZERNE. * * * * * THE MARQUIS DE BOUILLE TO M. DE LA LUZERNE. Translation. Without date. Sir, I have the honor to transmit you a Memorial from the Council and Assembly of the Island of Dominica, who lay claim to the Dutch ship Resolution, Captain Waterburg, which has been retaken from an English privateer from Carolina, by the American privateer Ariel, belonging to Messrs Robert Morris, Samuel Inglis, and William Bingham, brought into Philadelphia, and condemned there as a legal prize.