Yesterday three of the enemy's gunboats came up to reconnoiter, bur finding two of ours lying below the camp they did not venture near enough to see our position or for our gunboats to gunboats to engage them effectually. They place d themselves across the stream at very long range, and by the time Captain Porter and Lieutenant Paulding, commanding the gunboats, weighed anchor and got under headway they were off. Captain Porter chased them under their guns at Columbus, one shot certainly, and he thinks two, taking effect upon one of their boats, disabling her to some extant, if not entirely, for present use. Captain Porter pulled up and brought with him one of their buoys, intended to mark the location of their torpedoes or the channel to navigate to avoid them. Re-enforcements starting from Saint Louis on Monday, as I am advised by your telegram, I will commence the move again on Tuesday. I have just learned through the Memphis Appeal, and also from a man who has just made his way from New Orleans and who spent Thursday and Friday at Columbus, that seven regiments have left Columbus recently for Bowling Green. I am now inclined to believe that the garrison of Columbus is now weaker than it has been for several months back. It is also probable that the best armed and best drilled troops have been taken.

I have placed Captain Hatch, assistant quartermaster, in arrest, and directed him to turn over all public property to Captain A. S. Baxter, assistant quartermaster. This was done on notice from Washington that charges would be preferred against the former, and, if not already in arrest, he should be so placed at once. Every day develops further evidences of corruption in the quartermaster's department, and that Mr. Dunton, chief clerk,if not chief conspirator, is at least on accomplice. I haver ordered his arrest and confinement.

I have telegraphed you requesting that no more vouchers given here by the quartermaster be audited for the present. This was intended to mean those given by Captain Hatch. As his conduct will probably be the subject of legal investigation, I forbear saying all that I fear is true. I address the commanding general in person, deeming this a matter which should only be known to such persons as he may desire should know it. I have directed the books and safe of Captain Hatch to be possession of and kept guarded until orders are received disposing of this matter.

U. S. GRANT,

Brigadier-General.

WASHINGTON, January 12, 1862.

Brigadier-General BUELL:

How are your transportation preparations progressing?

GEO. B. McCLELLAN.

LOUISVILLE, January 12, 1862.

General McCLELLAN:

I am sorry to say not as rapidly as the necessity for it . With the present condition of the roads it is by no means sufficient.

D. C. BUELL.