Since your last session Mexico has threatened to renew the war, and has either made or proposes to make formidable preparations for invading Texas. She has issued decrees and proclamations, preparatory to the commencement of hostilities, full of threats revolting to humanity, and which if carried into effect would arouse the attention of all Christendom. This new demonstration of feeling, there is too much reason to believe, has been produced in consequence of the negotiation of the late treaty of annexation with Texas. The Executive, therefore, could not be indifferent to such proceedings, and it felt it to be due as well to itself as to the honor of the country that a strong representation should be made to the Mexican Government upon the subject. This was accordingly done, as will be seen by the copy of the accompanying dispatch from the Secretary of State to the United States envoy at Mexico. Mexico has no right to jeopard the peace of the world by urging any longer a useless and fruitless contest. Such a condition of things would not be tolerated on the European continent. Why should it be on this? A war of desolation, such as is now threatened by Mexico, can not be waged without involving our peace and tranquillity. It is idle to believe that such a war could be looked upon with indifference by our own citizens inhabiting adjoining States; and our neutrality would be violated in despite of all efforts on the part of the Government to prevent it. The country is settled by emigrants from the United States under invitations held out to them by Spain and Mexico. Those emigrants have left behind them friends and relatives, who would not fail to sympathize with them in their difficulties, and who would be led by those sympathies to participate in their struggles, however energetic the action of the Government to prevent it. Nor would the numerous and formidable bands of Indians--the most warlike to be found in any land--which occupy the extensive regions contiguous to the States of Arkansas and Missouri, and who are in possession of large tracts of country within the limits of Texas, be likely to remain passive. The inclinations of those numerous tribes lead them invariably to war whenever pretexts exist. Mexico had no just ground of displeasure against this Government or people for negotiating the treaty. What interest of hers was affected by the treaty? She was despoiled of nothing, since Texas was forever lost to her. The independence of Texas was recognized by several of the leading powers of the earth. She was free to treat, free to adopt her own line of policy, free to take the course which she believed was best calculated to secure her happiness.