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Vicksburg. The siege of Vicksburg is still going on — a fact which leads us to doubt the accuracy of our telegram from Jackson, stating the enemy's loss to have reached thirty thousand. That they have been severely punished, however, is evident, not only from all the information we have, but also from the withholding of late Northern papers at City Point. Gen. Pemberton's defiant reply to Grant's summons is doubtless the only foundation for the story so extensively circulated at the North, that Pemberton had proposed a conditional surrender of the place. The investment of Port Hudson by the forces under Banks is not likely to last very long, as he will very shortly be placed on the defensive, and probably be compelled to fall back to New Orleans.
Latest from Vicksburg. Grant Demands a surrender — Pemberton's defiant haply — the Federal Lessees. Jackson, June 1--General Grant demanded the surrender of Vicksburg on Thursday, giving three days to Gen'l Pemberton to consider the demand Gen'l Pemberton replied that he did not want fifteen minutes, and that his troops would die in the trenches before they would surrender. The Federal troops are demoralized, and refused to renew the attack on Saturday. The enemy's gunboats are firing hot shot at the city. The Federal loss is estimated at twenty-five to thirty thousand, including Generals Kerr, Lay, Bubridge, Bonan, and one other. Por. Hudson is investe