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New York, April 11.

— The World army Potomac correspondent giving details of the pursuit of Lee's army, dated near Rice's station, 7th, says that after another day of excitement and success we have a few miles more of the enemy's soil. The enemy were driven from his strong fortifications guarding approaches to the magnificent bridge crossing the Appomatox. The enemy had strong, well stocked forts, and though we anticipated a determined resistance, we captured them with little trouble, together with all that was in them, being 18 pieces of cannon of all fashions and calibers. The enemy then fell back, and took position near Farmsville. Here they held us the entire remainder of the day, notwithstanding strong efforts on part of two corps to dislodge them. The enemy tried several times to cut his way through our lines, but always with such fatal effects to himself that he finally abandoned the attempt. The second division was sent down the railroad to seize the village of Farmville, which they did without trouble. Previously they had a skirmish, in which Gen. Smith was, it is feared, mortally wounded.

Gen. Ewing, after his capture, said Gen. Lee long since wanted to take all his troops westward and there disband them, but Davis would not consent.

Another World's correspondent at Burksville, April 7th, says yesterday Sheridan discovered a force of the enemy and large wagon train pushing briskly toward their main army. He immediately pushed ahead his troops, found the enemy in a strong position from which they were driven, and after hard fighting, they fell back to another position, from which Sheridan could not with his cavalry alone budge them. The 2d and 6th corps came up, and were put in position, which they held through the night. Next morning Custar was sent forward to blockade the road the rebels would take in retreating. The formation in infantry being completed, the charge was sounded. The rebels held our troops at bay for some time, but our men finally rushed upon them, when they fled down the pike, where they were met by Custar and held in check. The enemy finding they could not get past Custar, turned again upon the infantry. They charged impetuously, and then our troops counter charged, when the enemy hoisted the white flag and surrendered. It was in this fight that Ewell and the other officers were captured. They were not only outfought, but handsomely outgeneraled.

The World's Washington special says it was reported last night that Johnston had surrendered on the same terms granted Lee.

The Tribune's special says Secretary Seward's injuries have assumed a serious character. If the erysipelas is passed, medical men fear that owing to his inability to take solid food, he cannot repair the waste of his vitality in time to meet the heat of the coming warm weather.

It is rumored that the President will call an extra session of congress.

The Herald's Washington special says prominent rebels, probably Judge Campbell and Mr. Hunter, are soon expected in Washington in connection with the business of restoration. Secretary Seward's condition is such as to make it necessary that conferences on the subject should be held there. The Herald's Washington special also says there is the best authority for the statement that Kirby Smith and the rebel trans-Mississippi army are ready to surrender. The State is also ready to come back.