The plan of campaign determined upon by Grant was to concentrate all the national forces into a few distinct armies, which should advance on the same day against the opposing Confederate armies, and, by fighting incessantly, prevent any one of them from reinforcing the other. The armies of the enemy were themselves to be the objective points, and they were to be given no time for rest. Sherman was to advance from Atlanta against Johnston, who had an army larger in numbers than that of Lee; Banks' army, as soon as it could be withdrawn from the disastrous Red River expedition, was to act against Mobile; Sigel was to pass down the valley of Virginia and prevent the enemy from making annoying raids from that quarter; Butler was to ascend the James and threaten Richmond; and, finally, the Army of the Potomac, under the immediate command of Meade, was to protect Washington, and essay the most herculean task of all--the conquest of Lee and his army. Orders were issued by Grant for a general movement of all the national forces on the 4th of May. Since they were so numerous, and began nearly at the same time, it is necessary to give the particulars of each in turn, reserving that of the most important--Grant's own--for the last. BANKS' RED RIVER EXPEDITION. One of the most discreditable affairs of the war was what is known as Banks' Red River Expedition. That officer was in command at New Orleans, when it was decided to send a strong force up the Red River, in quest of the immense quantities of cotton stored in that region, though the ostensible object was the capture of Shreveport, Louisiana, 350 miles above New Orleans, and the capital of the State. The plan was for the army to advance in three columns, supported by Admiral Porter with a fleet, which was to force a passage up the Red River. General A.J. Smith was to march from Vicksburg, with the first division of the army, which numbered 10,000 men; Banks was to lead the second from New Orleans, and Steele the third from Little Rock. General Edmund Kirby Smith was the Confederate commander of the Trans-Mississippi Department. Although he had fewer men than the invaders, he prepared for a vigorous resistance. He sent Generals Price and Marmaduke to harass Steele, directed General Dick Taylor to obstruct the Red River as much as he could, while he made ready to make the best fight possible. Fifty miles above the mouth of the Red River stood Fort de Russy, which, although considerably strengthened, was carried by assault, March 13th. On the 15th, Porter's twelve gunboats and thirty transports joined Franklin at Alexandria. The Federal cavalry occupied Natchitoches, on the last day of the month, and in the van of the army; they arrived at Mansfield on the 8th of April, several days after Admiral Porter had reached Grand Echore on the Red River.