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The Success on Red River.

The capture of Fort DeRussy on Red River, reported in our dispatches yesterday, is a brilliant beginning of an important expedition. Though the forces under Gen. Smith have done nobly, their success seems to be due in about equal proportions to Gen. Smith's consummate strategy and the rebel Gen. Taylor's blundering. A more brilliant and important success has probably not been achieved since the war began at so small a cost of life.

We are unable to state the exact location of Fort DeRusy, but it appears to be located on the south bank of Red River at some point between the mouth of the Washita and Alexandria — the latter place 150 miles from the mouth of Red River. Gen. Smith with his expedition left Vicksburg on the 10th, and landing his force at Semmesport, near the mouth of Atchafalaya Bayou, he marched up the south side of the river. The rebel forces in the vicinity fell back before him, and Gen. Taylor finding himself about to be attacked in the rear while he would be exposed to the fire of the gunboats from the river, marched out to attack General Smith before he should reach the fort. Attempting to cut Gen. Smith off from his communications with the river, he found himself cut off from the fort, for which Gen. Smith, disregarding the force in his rear, made as good time as possible. The result was that the fort was reached and captured with the small force in it, and its armament, ammunition, etc., by a splendid coup de main, several hours before the rebel forces came up. When Taylor came up he found the fort in the hands of his enemy, with his own guns turned against him, and himself "left out in the cold." As usual, Illinois troops bore an important part in this gallant affair — the 58th Illinois, Colonel Lynch, being the first to place their colors on the rebel works.

This is probably the strongest, if not the only important fortification below Shreveport, upon which the rebels depended for the protection of Red River. If so, the future advance of the expedition will be rapid, and it is not improbable that it has already reached Shreveport. It is stated that the fortifications at Fort DeRussy, which seems to have been constructed with great care and labor, were to be destroyed before the expedition advanced further.

The effect of this movement, co-operated with, as it undoubtedly is, by Gen. Banks along the Bayou Teche, and by General Steele from Little Rock, if prosecuted as prosperously as it has commenced, will be to relieve the whole of Southern Arkansas and Northern and Western Louisiana of the presence of an organized rebel force.