COLUMBUS, KY., December 2, 1861.

Major General L. POLK,

Commanding First Division, Western Department:

GENERAL: Having been requested by you to put in writing the opinion I gave you yesterday with reference to the proposition made by Brigadier-General Pillow of an attack upon Cairo and the gun-boats now receiving their armament, I have the honor of submitting the following: The movement under consideration can only be accomplished by an attack upon the boats of the enemy by our river navy, and at the same moment by a demonstration upon Paducah, Holt's fort [Fort Holt] and Bird's Point; in all, 11,000 men. The whole force under your command being 14,000 men are required for the false attack upon Paducah, 3,500 for that upon Holt's fort [Fort Holt] and the same number for that upon Bird's Point; in all, 11,000 men. The whole force under your command being 14,000 men it would only leave 3,000 men for the defense of Columbus. This force is insufficient to hold this place should an attack be made upon it during the expedition. Should the projected expeidtion fail and our troops be defeated, Columbus with its large supplies ordnance, &c., might probably fall into the hands of the enemy, leaving the valley of the Mississippi without protection, and the cities of Memphis, Vicksburg, Natchez, Baton Rouge, and New Orleans seriously threatened. I conceive that the Confederate States Government and the whole population of the valley look upon you as the guardian of the modern Thermopylae of the South. This post of honor must not be abandoned and the cause we defend jeapardized by any movement whose success is not perfectly sure. We cannot afford at the present time to be defeated. Should it prove successful, I fully understand the immense advantages of the proposed expedition- capture or destructionf of the enemy's gun-boats capture of the stronghold from which they may pounce upon our river cities and destroy them are immense results, for which I would be willing to sacrifice many valuable lives should it be demonstrated beforehand that such an expeidtion might offer chances of success. Far from it. I contend that it is impracticable with the forces at our disposal and the enemy's means of resitance. Cairo is a strongly fortified point, defended by numerous batteries and a force of 20,000 men; Holt's fort [Fort Holt] flanks the fire of the city's batteires, and three well-armed gun-b0ats ready at any moment, day and night, add much to the efficinecy of the defnese. The force at Holt's fort [Fort Holt] is estimated at 3,500 men; that at Paducah at 10,000; that at Bird's Point at 3,500. Therefore, with a force of 11,000 men and a few river boats liable to be disabled by a single shot, it is proposed that we should attack a strongly intrenched force of 34,500 men. The risks attending such an expedition are too great, and the lives of our volunteers too valuable to be recklessly sacrificed. I now admit, for the sake of argument, that we should capture the boats and occupy Cairo, Bird's Point, and Paducah. Now the military question becomes a political one; our defensive policy becoming an aggressive one, the war will put on another face. Hundreds of men will volunteer from the Western, Northern, and Eastern States to wrench from us the possession of their soil. It is not my mission to examine this question. I here merely allude to it to show its vital importance

Respectfully, your obedient servant,

J. TRUDEAU,

Brigadier-General.

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