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Our Cairo Correspondence.

CAIRO, Feb. 5th, 1862.

COL. J. B. DANFORTH — Dear Sir: The expedition has gone up the Tennessee river, Gen. Grant in command of the land forces, and Commodore Foote of the gunboat flotilla. We are hourly expecting the report of the capture of Fort Henry and the advance of our troops south so as to pierce the centre of the line of the enemy between Richmond, Va., and Columbus, Ky. The troops embarked in good spirits but in the worst weather of the season. It has been cold, wet and muddy. The steamboats were too much crowded with troops, and while we hope for great success, we fear loss of life to many from inevitable exposure.

Gen. E. A. Paine is left in command at Cairo, and a large reserve of troops is accumulating here.

Yesterday a flag of truce came up from Columbus to make an exchange of prisoners. It was met by Gen. Paine and Cols. Buford and Murphy. The parole prisoners were exchanged.

Col. Buford recognized on the rebel steamboat Charm, several officers — one Capt. Williams, late aid-de-camp to Gen. Scott, and whose brother is not one of Gen. MeClellan's aids; and three distinguished Kentucky gentlemen of the south, whom he formerly knew in Kentucky, Mr. Tobias Gibson, who was accompanied by his three sons, all officers in the rebel army, M. C. Fellows, a prominent merchant of Louisville and New Orleans, and Mr. Norton, of New Orleans. They entered into free conversation with Col. Buford, which they commenced with bitterness, but happily he changed the tenor of it, and it became rational.

Colonel Buford's regiment was ordered to march, and was instantly ready, but before going on board the order was countermanded, as he commanded the fort, and had immense stores of munitions and artillery under his charge. He will go with the column down the river.

Nine of the great 13 inch mortars have arrived from Pittsburg, and are not being put on board the mortar boats. They weigh 17,000 pounds each, and require a charge of 26 lbs. of powder, and 7 pounds for a bursting charge of the shells. They will throw shells two miles.

We shall soon be ready.
G.

6 O'CLOCK P. M. — Dispatches are just received from up the Tennessee, ten miles below Fort Henry, Feb. 4th. The troops were landed, and the transports sent back to Paducah for Gen. Smith's command. Our force is 15,000, assisted by six gun boats. The attack was expected to be made to-day on the fort.