The negotiation which had been long depending with the French Government on several important subjects, and particularly for a just indemnity for losses sustained in the late wars by the citizens of the United States under unjustifiable seizures and confiscations of their property, has not as yet had the desired effect. As this claim rests on the same principle with others which have been admitted by the French Government, it is not perceived on what just ground it can be rejected. A minister will be immediately appointed to proceed to France and resume the negotiation on this and other subjects which may arise between the two nations. At the proposal of the Russian Imperial Government, made through the minister of the Emperor residing here, a full power and instructions have been transmitted to the minister of the United States at St. Petersburg to arrange by amicable negotiation the respective rights and interests of the two nations on the North West coast of this continent. A similar proposal had been made by His Imperial Majesty to the Government of Great Britain, which has likewise been acceded to. The Government of the United States has been desirous by this friendly proceeding of manifesting the great value which they have invariably attached to the friendship of the Emperor and their solicitude to cultivate the best understanding with his Government. In the discussions to which this interest has given rise and in the arrangements by which they may terminate the occasion has been judged proper for asserting, as a principle in which the rights and interests of the United States are involved, that the American continents, by the free and independent condition which they have assumed and maintain, are henceforth not to be considered as subjects for future colonization by any European powers. Since the close of the last session of Congress the commissioners and arbitrators for ascertaining and determining the amount of indemnification which may be due to citizens of the United States under the decision of His Imperial Majesty the Emperor of Russia, in conformity to the convention concluded at St. Petersburg on July 12th, 1822, have assembled in this city, and organized themselves as a board for the performance of the duties assigned to them by that treaty. The commission constituted under the 11th article of the treaty of February 22nd, 1819, between the United States and Spain is also in session here, and as the term of three years limited by the treaty for the execution of the trust will expire before the period of the next regular meeting of Congress, the attention of the Legislature will be drawn to the measures which may be necessary to accomplish the objects for which the commission was instituted.