Not apprized, till very late, that any boats were building on Cumberland, the effect of the proclamation had been trusted to for some time in the State of Tennessee; but on the 19th of December, similar communications and instructions with those of the neighboring States were despatched by express to the governor, and a general officer of the western division of the State, and on the 23d of December our confidential agent left Frankfort for Nashville, to put into activity the means of that State also. But by information received yesterday, I learn that on the 22d of December, Mr. Burr descended the Cumberland with two boats merely of accommodation, carrying with him from that State no quota toward his unlawful enterprise. Whether after the arrival of the proclamation, of the orders, or of our agent, any exertion which could be made by that State, or the orders of the governor of Kentucky for calling out the militia at the mouth of Cumberland, would be in time to arrest these boats, and those from the falls of the Ohio, is still doubtful. On the whole, the fugitives from Ohio, with their associates from Cumberland, or any other place in that quarter, cannot threaten serious danger to the city of New Orleans. By the same express of December nineteenth, orders were sent to the governors of New Orleans and Mississippi, supplementary to those which had been given on the twenty-fifth of November, to hold the militia of their territories in readiness to co-operate for their defence, with the regular troops and armed vessels then under command of General Wilkinson. Great alarm, indeed, was excited at New Orleans by the exaggerated accounts of Mr. Burr, disseminated through his emissaries, of the armies and navies he was to assemble there. General Wilkinson had arrived there himself on the 24th of November, and had immediately put into activity the resources of the place for the purpose of its defence; and on the tenth of December he was joined by his troops from the Sabine. Great zeal was shown by the inhabitants generally, the merchants of the place readily agreeing to the most laudable exertions and sacrifices for manning the armed vessels with their seamen, and the other citizens manifesting unequivocal fidelity to the Union, and a spirit of determined resistance to their expected assailants.