I herewith communicate to the Senate the copy of a letter, under date of the 27th ultimo, from the Secretary of State of the United States to the minister of foreign relations of the Mexican Republic, again proposing to open negotiations and conclude a treaty of peace which shall adjust all the questions in dispute between the two Republics. Considering the relative power of the two countries, the glorious events which have already signalized our arms, and the distracted condition of Mexico, I did not conceive that any point of national honor could exist which ought to prevent me from making this overture. Equally anxious to terminate by a peace honorable for both parties as I was originally to avoid the existing war, I have deemed it my duty again to extend the olive branch to Mexico. Should the Government of that Republic accept the offer in the same friendly spirit by which it was dictated, negotiations will speedily commence for the conclusion of a treaty. The chief difficulty to be anticipated in the negotiation is the adjustment of the boundary between the parties by a line which shall at once be satisfactory to both, and such as neither will hereafter be inclined to disturb. This is the best mode of securing perpetual peace and good neighborhood between the two Republics. Should the Mexican Government, in order to accomplish these objects, be willing to cede any portion of their territory to the United States, we ought to pay them a fair equivalent--a just and honorable peace, and not conquest, being our purpose in the prosecution of the war. Under these circumstances, and considering the exhausted and distracted condition of the Mexican Republic, it might become necessary in order to restore peace that I should have it in my power to advance a portion of the consideration money for any cession of territory which may be made. The Mexican Government might not be willing to wait for the payment of the whole until the treaty could be ratified by the Senate and an appropriation to carry it into effect be made by Congress, and the necessity for such a delay might defeat the object altogether. I would therefore suggest whether it might not be wise for Congress to appropriate a sum such as they might consider adequate for this purpose, to be paid, if necessary, immediately upon the ratification of the treaty by Mexico. This disbursement would of course be accounted for at the Treasury, not as secret-service money, but like other expenditures.