With the other powers of Europe our relations continue on the most amicable footing. Treaties now existing with them should be rigidly observed, and every opportunity compatible with the interests of the United States should be seized upon to enlarge the basis of commercial intercourse. Peace with all the world is the true foundation of our policy, which can only be rendered permanent by the practice of equal and impartial justice to all. Our great desire should be to enter only into that rivalry which looks to the general good in the cultivation of the sciences, the enlargement of the field for the exercise of the mechanical arts, and the spread of commerce--that great civilizer--to every land and sea. Carefully abstaining from interference in all questions exclusively referring themselves to the political interests of Europe, we may be permitted to hope an equal exemption from the interference of European Governments in what relates to the States of the American continent. On the 23d of April last the commissioners on the part of the United States under the convention with the Mexican Republic of the 11th of April, 1839, made to the proper Department a final report in relation to the proceedings of the commission. From this it appears that the total amount awarded to the claimants by the commissioners and the umpire appointed under that convention was $2,026,079.68. The arbiter having considered that his functions were required by the convention to terminate at the same time with those of the commissioners, returned to the board, undecided for want of time, claims which had been allowed by the American commissioners to the amount of $928,620.88. Other claims, in which the amount sought to be recovered was $3,336,837.05, were submitted to the board too late for its consideration. The minister of the United States at Mexico has been duly authorized to make demand for payment of the awards according to the terms of the convention and the provisions of the act of Congress of the 12th of June, 1840. He has also been instructed to communicate to that Government the expectations of the Government of the United States in relation to those claims which were not disposed of according to the provisions of the convention, and all others of citizens of the United States against the Mexican Government. He has also been furnished with other instructions, to be followed by him in case the Government of Mexico should not find itself in a condition to make present payment of the amount of the awards in specie or its equivalent. I am happy to be able to say that information which is esteemed favorable both to a just satisfaction of the awards and a reasonable provision for other claims has been recently received from Mr. Thompson, the minister of the United States, who has promptly and efficiently executed the instructions of his Government in regard to this important subject.