The civil and military authorities seem to me to be laboring under a great mistake in regard to the true key of the war in the South-west. It is not the Mississippi, but the Tennessee River. Now, all the military preparations made in the West indicate that the Mississippi River is the point to which the authorities are directing their attention. On that river many battles must be fought and heavy risks incurred, before any impression can be made on the enemy, all of which could be avoided by using the Tennessee River. This river is navigable for medium-class boats to the foot of Muscle Shoals in Alabama, and is open to navigation all the year, while the distance is but two hundred and fifty miles by the river from Paducah on the Ohio. The Tennessee offers many advantages over the Mississippi. We should avoid the almost impregnable batteries of the enemy, which can not be taken without great danger and great risk of life to our forces, from the fact that our forces, if crippled, would fall a prey to the enemy by being swept by the current to him, and away from the relief of our friends. But even should we succeed, still we have only begun the war, for we shall then have to fight the country from whence the enemy derives his supplies. Now an advance up the Tennessee River would avoid this danger; for, if our boats were crippled, they would drop back with the current and escape capture. But a still greater advantage would be its tendency to _cut the enemy's lines in two_, by reaching the Memphis and Charleston Railroad, threatening Memphis, which lies one hundred miles due west, and no defensible point between; also Nashville, only ninety miles north-east, and Florence and Tuscumbia in North Alabama, forty miles east. A movement in this direction would do more to relieve our friends in Kentucky, and inspire the loyal hearts in East Tennessee, than the possession of the whole of the Mississippi River. If well executed, it would cause the evacuation of all those formidable fortifications on which the rebels ground their hopes for success; and in the event of our fleet attacking Mobile, the presence of our troops in the northern part of Alabama, would be material aid to the fleet.