FORT TAYLOR, KEY WEST, FLA., January 26, 1861.

SIR: I have to report that no demonstration has been made upon this fort to this date. There is no apprehension from the population of moment from the mainland. If my company was filled up to a hundred men, and a sloop of war stationed in this harbor, there would be no danger of any successful attack, or even an attempt at present. The defenses are improving daily.

I am, sir, very respectfully, your obedient servant,

J. M. BRANNAN,

Captain, First Artillery, Commanding.

Colonel S. COOPER,

Adjutant-General U. S. Army, Washington, D. C.

P. S.-I have received no communication from the Department in answer to my letter of December 11, 1860.

FORT TAYLOR, KEY WEST, FLA., January 31, 1861.

SIR: I have the honor to acknowledge the receipt on the 26th instant of a communication [following] from the headquarters of the Army, dated the 4th instant, ordering my whole company to this fort. I had anticipated the order some time ago. This is the only dispatch I have received from the Department on this subject. There are about sixty men, mechanics and laborers, on the work, who are willing to take the fate of it, and assist in defending the same. I require at least fifty more muskets for these men. If my company was raised to a hundred and a sloop of war stationed here there would be no apprehension of an attack at present. The power is not the best, and the supply of ammunition is limited except for heavy guns. It is very necessary that the Ordnance Department should attend to it immediately. I have sent a requisition direct to Colonel Craig. The fort is being put in a very good state of defense by Captain Hunt, and will be in short time able to stand an attack very successfully. With a vessels of war in the harbor a landing could be easily prevented.

I transferred to Major Arnold six 8-inch columbiads, with seven hundred shells; two 6-pounder and two 12-pounder howitzers, with a small supply of ammunition for the latter; 10,000 pounds of powder. He has all of his guns mounted and in position, and is really stronger than I am, as he cannot be attacked by land. We have communication with each other every few days.

In about a week I shall have ten 8-inch guns on the gorge or land front, which will enable me to prevent the establishing of breaching batteries without considerable difficulty. The General-in-Chief may rest assured that this work will not be taken without a severe struggle.

The Macedonian passed Key West on the night of the 29th instant for Turtugas. The Brooklyn arrived in the harbor this morning and will sail to-morrow night. All well on board.

I would suggest that a paymaster be ordered here to pay the troops. Last payment to October 31.

I am, sir, very respectfully, your obedient servant,

J. M. BRANNAN,

Captain, First Artillery, Commanding.

Lieutenant Colonel L. THOMAS,

Asst. Adjt. General, Hdqrs. of the Army, Washington, City, D. C.

P. S.-I send this dy the U. S. steamer Mohawk.