The Paris correspondence of the London _Morning Chronicle_, furnishes the details of a diplomatic correspondence between the principal Continental Powers, which has decided interest and importance. It is stated that, on the 7th of February, Prince Schwarzenberg addressed a note to the representatives of Austria at St. Petersburg and Berlin, in which he urged that the object of the Northern Powers ought now to be to put down all that remained of constitutional government on the continent of Europe; and that for this purpose they ought to insist on the representative form of government being abolished in all the States where it was still tolerated, and more especially in Piedmont and in Greece. He further declared that Louis Napoleon, by his _coup d'état_ of the 2d of December, which, while it put an end to constitutional government, restored military government in France, had merited the applause of all the Northern Powers, and he suggested that they ought to concur in giving him their united and cordial support, even to the exclusion of both branches of the House of Bourbon, because none of the members of that illustrious House could reascend the throne without according representative government in some shape. The representatives of Austria at Berlin and St. Petersburg having been directed to communicate this dispatch to the governments to which they were accredited, did so, but the manner in which the communication was received by the two Powers was very different. The Prussian government at once declared that it strongly disapproved of the suggestion of the Austrian government, and that, as it looked upon a certain degree of constitutional freedom as necessary in the present state of Europe, it highly disapproved of the attempt of Louis Napoleon to establish a military despotism. The Russian Czar, who sets up as the arbiter of all that is done to Germany, gave a very characteristic answer to both Powers. He recommended to the Austrian government not to be so enthusiastic in its admiration of Louis Napoleon, and to the Prussian government, not to be so determined in its hostility to that personage; and thus, says the writer, the affair for the present rests.