The republic of Texas had now applied for admission into the federal Union, as one of its States. Its minister at Washington, Memucan Hunt, Esq., had made the formal application to our executive government. That was one obstacle in the way of annexation removed. It was no longer an insult to her to propose to annex her; and she having consented, it referred the question to the decision of the United States. But there was still another objection, and which was insuperable: Texas was still at war with Mexico; and to annex her was to annex the war--a consequence which morality and policy equally rejected. MR. PRESTON, of South Carolina, brought in a resolution on the subject--not for annexation, but for a legislative expression in favor of the measure, as a basis for a tripartite treaty between the United States, Mexico and Texas; so as to effect the annexation by the consent of all parties, to avoid all cause of offence; and unite our own legislative with the executive authority in accomplishing the measure. In support of this motion, he delivered a speech which, as showing the state of the question at the time, and presenting sound views, and as constituting a link in the history of the Texas annexation, is here introduced--some extracts to exhibit its leading ideas. "The proposition which I now submit in regard to this prosperous and self-dependent State would be indecorous and presumptuous, had not the lead been given by Texas herself. It appears by the correspondence of the envoy extraordinary of that republic with our own government, that the question of annexation on certain terms and conditions has been submitted to the people of the republic, and decided in the affirmative by a very large majority; whereupon, and in pursuance of instructions from his government, he proposes to open a negotiation for the accomplishment of that object. The correspondence has been communicated upon a call from the House of Representatives, and thus the proposition becomes a fit subject for the deliberation of Congress. Nor is it proposed by my resolution, Mr. President, to do any thing which could be justly construed into cause of offence by Mexico. The terms of the resolution guard our relations with that republic; and the spirit in which it is conceived is entirely averse to any compromise of our national faith and honor, for any object, of whatever magnitude. More especially would I have our intercourse with Mexico characterized by fair dealing and moderation, on account of her unfortunate condition, resulting from a long-continued series of intestine dissensions, which all who have not been born to liberty must inevitably encounter in seeking for it. As long, therefore, as the pretensions of Mexico are attempted to be asserted by actual force, or as long as there is any reasonable