In Kentucky a premature attempt to bring Burr to justice without sufficient evidence for his conviction had produced a popular impression in his favor and a general disbelief of his guilt.  This gave him an unfortunate opportunity of hastening his equipments.  The arrival of the proclamation and orders and the application and information of our confidential agent at length awakened the authorities of that State to the truth, and then produced the same promptitude and energy of which the neighboring State had set the example.  Under an act of their legislature of December 23 militia was instantly ordered to different important points, and measures taken for doing whatever could yet be done.  Some boats (accounts vary from five to double or treble that number) and persons (differently estimated from 100 to 300) had in the meantime passed the Falls of Ohio to rendezvous at the mouth of Cumberland with others expected down that river.

Not apprised 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 to the neighboring States were dispatched by express to the governor and a general officer of the western division ofthe 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 Ohio is still doubtful.

On the whole, the fugitives from the Ohio, with their associates from Cumberland or any other place in that quarter, can not threaten serious danger to the city of New Orleans.

By the same express of December 19 orders were sent to the governors of Orleans and Mississippi, supplementary to those which had been given onthe 25th of November, to hold the militia of their Territories in readiness to cooperate for their defense 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 defense, and on the 10th of December he was joined by his troops from the Sabine.  Great zeal was shewn 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.