On the 17th of June the Emperor of Austria issued a manifesto, in which he formally announced to his subjects the state of war existing between Austria and Prussia. Italy declared war against Austria three days later. We can now see the immense results following from the thorough military preparation of Prussia. Launching, as it were, a thunderbolt of military force upon her enemies at the first moment of war, less than two weeks sufficed for the complete conquest of Hanover, Hesse-Cassel and Saxony. Indeed, four days had sufficed for the seizure of the last two. The King of Hanover had been dethroned; the Elector of Hesse-Cassel was a prisoner, and the King of Saxony was a fugitive with his army in Bohemia. The military results were even greater than the political consequences. The severed portions of the Prussian kingdom were united. The Hanoverian army had been eliminated from the military problem, and there was no longer any menace to Prussia from the rear. Von Falckenstein was now free to turn his undivided attention to the Bavarians and the Federal Corps, and the occupation of Saxony prevented all possibility of a junction of the Bavarian and Saxon armies. But the strategical advantages gained in regard to operations in Bohemia were the grandest result of the occupation of Saxony. We have seen that on the 14th of June the Army of the Elbe was around Torgau, the First Army near Görlitz; and the Second Army in the vicinity of Neisse; being thus separated from each other by from 100 to 125 miles. The Second Army covered Breslau, the Army of the Elbe covered Berlin, and the First Army was in a position to support either of the others. Geographical circumstances thus compelled the separation of the Prussian armies, and only two of them were available for the invasion of Bohemia. The occupation of Saxony changed matters for the better. The distance between the Army of the Elbe and the First Army was reduced to the extent of actual junction, and these combined armies were only about 120 miles from Landshut, where the right of the Second Army now rested, and with which there was communication by means of the hill road of Schreiberschau. The entire force was now available for the invasion of Bohemia; the northern passes of the Bohemian frontier were secured; and if compelled to act upon the defensive, Frederick Charles could find in the mountains of Southern Saxony many advantageous positions for defensive battle.