(Per Jura.)

New York, May 1st, Morning.
GENERAL HOOKER'S whole army is moving.  A portion of the army crossed the Rappahannock at KELLY'S FORD, above Fredericksburg, on Monday last, and captured the Confederate pickets.   GENERAL HOOKER sent out skirmishers, but found no enemy.  Since that time the remainder of the army has been crossing three other fords above and below Fredericksburg; and it is supposed that the whole army is now across the Rappahannock.
The Confederates are reported to have been everywhere surprised, and to have offered no serious resistance to the passage of the Rappahannock at any point.

 The Federals have captured from 300 to 400 prisoners.

Prisoners state that GENERAL STONEWALL JACKSON commands the right wing of the Confederate army.  The Richmond Enquirer of 20th says, there is some reason to believe that GENERAL HOOKER is changing his plan of operations from Fredericksburg to the Peninsula, and would not be surprised if the Federals were found ascending the Yazoo River.   Skirmishing along the upper Rappahannock will not alter this purpose, as this may be undertaken to ascertain the presence of the Confederate army, as well as the make GENERAL LEE believe that a real advance from Fredericksburg is intended.  The Enquirer thinks GENERAL HOOKER cherishes an idea that by leaving a strong corps well fortified at Fredericksburg, and moving his army to Whitehouse, he will compel GENERAL LEE to fall back on Richmond.  The Mobile Register says that Fort Pemberton is now the Key of the Mississippi valley, and should be held at all hazards there.  It is said to be a line of breastworks, composed of cotton bales and mud running across from the Yazoo to the Tallahatchie rivers.  The distance across, in a straight line, not exceeding 250 yards.

GENERAL DORING, a very skilful officer, commands at Fort Pemberton.
  The steamers Alice and Nita arrived from Mobile on the 19th of April, and several other small crafts have arrived from the South, all with cotton.  Four Confederate schooners left Havana for Matamoras on the 20th of April.

The barque Lysander which has arrived at Boston, reports that on the 10th, while standing in towards Colorado Reef, she saw a burning vessel which was supposed to be a privateer.  Upon the 12th, she was overhauled by a privateer schooner, and ordered to send a boat alongside, but the captain of the Lysander refused and ordered the crew to arm themselves.  The privateer seeing an armed crew, tacked the ship and left.  This was in long 83-45, lat. 23-18.

NEW YORK, May 1, Evening.

The federal army at Milliken's Bend, above Vicksburg, received orders on the 24th ult. to march with six days' rations.  Four Federal transports which attempted to pass Vicksburg on the 23rd, were sunk, and two others badly damaged.  Some Confederate rams were expected to come down the Yazoo to attack GENERAL GRANT'S position at Carthaes, above Vicksburg.

A man in Ohio has been sentenced to four months' hard labour for expressing publicly his sympathy with the Secessionists.

  The Richmond Despatch says there is a system of communication between the blockading fleet off Charleston and the blockade runners,  which bring in American goods, or carry out cotton.  This is certain from the fact that the only vessels captured are those freighted with stores for the Confederate government.

The City of Manchester has arrived out.

New York, May 2nd, Evening.

The New York Tribune says that on Thursday last, the 30th ult., three corps of GENERAL HOOKER'S  army were across the Rappahannock marching straight in the rear of Fredericksburg by way of Chancellorsville, 12 miles from Fredericksburg.  Three other corps were at Banks's Ford, and in communication with the advancing columns.  All the corps were in position to move directly upon the Confederate line of communication, and still another corps was threatening to cross below and assail the flank of the Confederates.

The Tribune says that GENERAL LEE has no other alternative but to march out of Fredericksburg, or fight with the certainty that if defeated, his whole army is destroyed or captured.

GENERAL STONEMAN'S Federal  cavalry is in the rear of any position to which LEE can have possibly have fallen back, and the Tribune expects to hear that both the Virginia Central and Richmond and Fredericksburg railways are severed; if so, LEE must fight with the forces he has, because no reinforcements could reach him before he was attacked by GENERAL HOOKER.

It is reported that the Federals have occupied the Grand Gulf between Vicksburg and Port Hudson.

Some official despatches say that GENERAL BANKS'S expedition has not only destroyed the army and navy of the enemy, but captured his material for reorganization, his ablest sea and land officers, and between 1,060 and 2,000 prisoners.  GENERAL BANKS lost in the two last battles between 600 and 700 in killed and wounded.

The Federal force from Corinth destroyed twenty miles of the Central Mississippi Railway, causing considerable excitement in that region.
The steamer Eagle, from Nassau, has arrived at the southern port.

NEW YORK, 2nd May, Afternoon.
There is a large Confederate force at Morgantown, Western Virginia, on the Pennsylvanian states line of railway.  They have repulsed COLONEL MULLIGAN at Fairmount, and destroyed the Baltimore and Ohio bridges at Fairmount cheak rivers.

GENERAL CARTER, with 5,000 men, crossed the Cumberland river below Somerset, Kentucky, and after a severe fight, drove the Confederates out of the town.

The Federals are making an active movement on the Mobile and Ohio Railroad to break up the southern railroad communication in Mississippi.

QUEENSTOWN, Wednesday, 3p.m.
The Edinburgh, from New York, was reported off harbour.
                              (Per Edinburgh.)
The NEW YORK press generally consider that the action of MR. ADAMS in giving a certificate to a vessel bound to Matamoras with arms for Mexico does not justify the severe comments of the British press upon the subject, and thinks it proves there is a hostile feeling in England ready to resent even the shadow of an affront.

Some journals consider MR. ADAMS'S action perfectly justifiable.