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Last Night's Dispatches.

NEW YORK, May 4 — 3:30 P. M. — Various rumors are afloat to-day,probably to influence stocks, that Hooker's right wing had suffered severely on Sunday. In the absence of anything official from Washington, or owing to the riged exclusion of all dispatches from that point by the censorship, considerable credence is gained for sensational stories, but no reports of disaster are credited. It is stated that the President has received dispatches from Hooker that he has severed rebel communication between Bowling Green and Hanover C. H.; that Slocum has captured 1,500 rebels after crossing above Falmouth; that our communication with Gen. Stoneman has been cut off by rebel gurrillas, but will be soon reinstated, and that he (Hooker,) hopes to capture all the rebels North of the Pamunkey river, and the news thus far is encouraging. The rumor is afloat here that 8,000 rebels have been captured, but not from a reliable source.

The Times prints the following, dated two miles below Fredericksburg, Sunday morning 4 o'clock.

Bartlett's brigade and Newton's division, consisting of the 16th and 121st New York 5th and 27th Maine, and 96th Penn., are charging upon the rebel battery in front of the Bunnell House, lead by the 96th Penn. It has fired with considerable precision, annoying us to considerable extent.

A schooner arrived from Port Royal reports that she was boarded off Morrell's Inlet by a boat from the Monticello, who reported that Lieut. Braine that day entered the Inlet to destroy two large warehouses filled with cotton; also two large schooners with cargoes of boots, shoes, &c., for the rebels.

Fredericksburg is occupied by the troops of Corcoran's old brigade, and the troops of Newton's division.

9 A. M. — After a temporary lull, musket firing has again commenced. Artillery on both sides is again opened, and is firing rapidly. Our troops are well protected behind the right side of the Richmond road.

9:20. — Our batteries on the left have changed position, and are doing better execution.

9:30. — A pontoon bridge has been thrown across the Rappahannock at Fredericksburg, and persons are passing to and fro. The rebels have removed their guns from the earthworks above Fredericksburg. Our signal guns on this side are throwing an occasional shell.