XXXI. Napoleon addresses a Second Letter to the King of England personally—Answered by the British Secretary of State to Talleyrand—Alliance formed betwixt Russia and England—Prussia keeps aloof, and the Emperor Alexander visits Berlin—Austria prepares for War, and marches an Army into Bavaria—Her impolicy in prematurely commencing Hostilities, and in her Conduct to Bavaria—Unsoldierlike Conduct of the Austrian General Mack—Buonaparte is joined by the Electors of Bavaria and Wirtemberg, and the Duke of Baden—Skilful Manœuvres of the French Generals, and successive losses of the Austrians—Napoleon violates the Neutrality of Prussia, by marching through Anspach and Bareuth—Further Losses of the Austrian Leaders, and consequent Disunion among them—Mack is cooped up in Ulm—Issues a formidable Declaration on the 16th October—and surrenders on the following day—Fatal Results of this Man's Poltroonery, want of Skill, and probable Treachery, 79 Chap. XXXII. Position of the French Armies—Napoleon advances towards {v}Vienna—The Emperor Francis leaves his Capital—French enter Vienna on 13th November—Review of the French Successes in Italy and the Tyrol—Schemes of Napoleon to force on a General Battle—Battle of Austerlitz is fought on the 2d December, and the combined Austro-Russian Armies completely Defeated—Interview betwixt the Emperor of Austria and Napoleon—The Emperor Alexander retreats towards Russia—Treaty of Presburgh signed on the 26th December—Its Conditions—Fate of the King of Sweden—and of the Two Sicilies, 95 Chap. XXXIII. Relative situations of France and England—Hostilities commenced with Spain, by the Stoppage, by Commodore Moore, of four Spanish Galleons, when three of their escort were taken, and one blew up—Napoleon's Plan of Invasion stated and discussed—John Clerk of Eldin's great System of Breaking the Line, explained—The French Admiral, Villeneuve, forms a junction with the Spanish Fleet under Gravina—Attacked and Defeated by Sir Robert Calder—Nelson appointed to the Command in the Mediterranean—Battle of Trafalgar, fought 21st October, 1805—Death of Nelson—Behaviour of Napoleon on learning the Intelligence of this signal Defeat—Villeneuve commits Suicide—Address of Buonaparte to the Legislative Body—Statement of M. de Champagny on the Internal Improvements of France—Elevation of Napoleon's Brothers, Louis and Joseph, to the Thrones of Holland and Naples—Principality of Lucca conferred on Eliza, the eldest Sister of Buonaparte, and that of Guastalla on Pauline, the youngest—Other Alliances made by his family—Napoleon appoints a new Hereditary Nobility—Converts from the old Noblesse anxiously sought for and liberally rewarded—Confederation of the Rhine established, and Napoleon appointed Protector—The Emperor of Austria lays aside the Imperial Crown of Germany, retaining only the Title of Emperor of Austria—Vacillating and Impolitic Conduct of Prussia, 111 Chap.