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Opening the Mississippi.

From the St. Louis Republican 21st.

If, as is probable, General Polk is preparing to evacuate Columbus; where months of labor and thousands of dollars have been expended to render the rebel fortifications impregnable, it is not likely he will attempt to make a stand above Randolph, Tenn., should he, indeed, stop short of Memphis. To get out of reach of the huge anaconda now winding its stupendous coils to strangle the rebellion in the Mississippi Valley, he will have to go at least that far for present safety. — Even this would not save him long, if the prophetic signs of events are verified. We assume, however, that efforts will still be made by the Confederate authorities to impede the navigation of the Mississippi river into the cotton-growing region, and as Randolph is the best available spot above Memphis not flanked by the union army on the Tennessee and Cumberland, it is not unreasonable to suppose that some resistance will be offered there, by concentration a force to obstruct the passage of our gun-boats to the commercial metropolis of Tennessee.

The keen prospective eye of Gen. Halleck is doubtless now upon Memphis, the key to the Gulf of Mexico. When Memphis falls, then good-bye to "New Orleans and intermediate landings," as the steamboat bills say. — That city, by far the most important between St. Louis and the mouth of the Mississippi, is the entrepot of four railroads traversing north, south, east and west. The shipments of cotton alone, in the year ending September 1st, 1860, amounted to 400,000 bales, and its general business, in ordinary times, is immense. With a population of 25,000 souls, we may well believe that if the inhabitants are sincerely and strenuously opposed to the union, (which they are not,) the approach of the union forces is a matter of profound concern. But though there are thousands of loyal people in Memphis, and though (as the papers of that city tell us) the recent successes of our generals were received by many there with undisguised satisfaction, it must be said that red-hot, howling secessionists are by no means scarce. The place has been strongly fortified, and the position of it will be very reluctantly given up. Nature has done much for it in the way of defenses. — The city is situated immediately below the mouth of Wolf river on the fourth Chickasaw bluff, from thirty to forty feet above high water mark. Extending in front is a beautiful terrace or esplanade, nearly a thousand feet wide, forming a glacis of sufficient compass to accommodate a large army facing the landing. Heavy cannon have been mounted upon the most eligible sites above the city, and the exposed portions greatly strengthened by skillful engineers. But the same military necessity which compelled the evacuation of Bowling Green, and which compels the evacuation of Columbus, will in due time make itself apparent at Memphis. — When everything is in readiness, it will fall into the hands of the federal troops, and most likely without any prolonged conflict.

Between Columbus and Memphis the rebels have erected no less than five somewhat formidable fortifications. A strong water battery, mounting twelve 32 and 42 pounders at Hickman, was erected to protect the Nashville and Northwestern railroad, connecting at Union City with the Mobile and Ohio, and at McKenzie, fifty-five miles southeast, with the Memphis and Ohio railroads, but as communication is not already cut off between Columbus and Nashville, the possession of Hickman is no longer of any use to either army. — The same remark holds good in relation to an extensive work near the state line separating Kentucky from Tennessee, upon which five hundred negroes under the superintendence of an able engineer officer are said to have been set to work in September. Fort Pillow, a short distance below a strong earthwork with bastions, walls and trenches, mounting thirty guns on barbette, and the redoubts and embankments raised by Jeff. Thompson at New Madrid, must likewise be abandoned as of no further service in the present position of Gen. Grant's force.

Having mentioned four defended points below Columbus, we next come to Fort Randolph, sixty miles above Memphis, and about three hundred and fifty miles from St. Louis. This is anything but a weak position. It is built upon the third Chickasaw bluffs, more than one hundred feet above the river, and immediately south of island No. 32, the lower part of which commands the three mouths of the Hatchie river, a stream, (navigable at good stages) that empties into the Mississippi just above the town of Randolph, at the upper edge of the bluffs. These bluffs form natural parapets for batteries, and command a view of the Mississippi river for six miles each way. By silencing whatever guns may be placed on the island, iron clad boats, in the present condition of the lower Mississippi, might enter the northern mouth of the Hatchie, out of the reach of Fort Randolph. The town of Randolph, near which the fort stands, consists of half a dozen or so dilapidated frame houses, and is approached in the rear by several good roads, but the country behind it being full of ravines and gorges is capable of being fortified to an almost indefinite extent. The position, however, is of no manner of use or benefit, except to dispute the navigation of the river. It has no railroad communications, and as any army stationed there would have to depend on the river exclusively for the transportation of supplies, it would not require long to starve it out. So Gen. Polk may take his choice. — If he concentrates at Randolph, the capture of Memphis will be so much the easier. If he falls back on Memphis, that much more territory is reclaimed to the federal authority.

The late trip of the gunboats up the Tennessee river demonstrated that the stream was unobstructed as far as the Muscle Shoals in Alabama. Am army could be landed near the southern boundary line of Tennessee, at a point nearest Corinth, where the Mobile and Ohio railroad crosses the Memphis and Charleston road, the seizure of which would be an immense advantage in bringing Memphis to terms. From Corinth to Memphis the distance by railroad is about ninety miles, and as reinforcements would be measurably cut off, the work of reducing the latter city could be prosecuted at leisure. That is to say, no attack would be required to be made until the result, by the concentration of men and arms, be rendered certain. The resources and vigor of Gen. Halleck give assurance that the country will not have long to wait, for the times and places of new conflicts and new victories have already been determined on. With the rebel blockade of the Mississippi raised, and commercial intercourse between the loyal people of the north and south resumed as of old, upon what can the rebellion maintain itself? The fertile valley, stretching from the great northwest to the Gulf of Mexico, once more in possession of the union, to which by every right it belongs, and ever shall belong, the insurrection must die for want of sustenance. To us of this section the navigation of the Mississippi, unobstructed by the secession cannon and unhampered by secession impost tributes, is natural necessity. The common treasure of the nation has been expended to secure its benefits, which are the property of a continent, and not until the noble stream is cleared to New Orleans will the people of the United States cease to prosecute a resolute and energetic war.