ENGINEER BUREAU, Richmond, Va., December 2, 1862.

SIR: Indorsed on a letter of the 1st instant, from Brigadier-General Pillow to you, I have had the honor to receive your instructions, as follows:

On the allegations of General Pillow, as within, justice requires a supplemental report from Colonel Gilmer, and he will accordingly make it.

In the letter on which your instructions are indorsed General Pillow complains that in an order of your predeCEssor, reflecting on his conduct in the operations of the army at Fort Donelson, injustice was done him, and then states:

The knowledge of Colonel Gilmer, chief of engineers, is important for the information of the Government. His original report in regard to the result of the conference of general officers, on the night of February 14, at Dover, and his knowledge of the condition of the army when the field was won on the 15th, and his opinion of the practicability of a successful retreat from the battle-field on that day, is not as full as his knowledge of the facts will enable him to make.

As a preliminary to the supplemental report which I am directed to make, I have respectfully to state that my original report upon the defense of Fort Donelson was made the 17th of March last, to General Albert Sidney Johnston, then commanding the Western Department. That distinguished officer paid me the flattering compliment to say it gave him a clearer knowledge of the operations than he had received from other sources, which led me to suppose that my effort to report all that was "important for the information of the Government" had been successful. With this remark I have the honor to submit the following supplemental report:

On the evening of February 14, 1862, Generals Floyd, Pillow, and Buckner met in council at Dover, to decide upon a plan of action under the threatening state of affairs then existing. I was present by invitation. Although the gunboats had been repulsed that afternoon by the water batteries, it was evident from the movement of large bodies of troops towards the left of our lines that the enemy had resolved to complete the investment of the place by gaining the bank of the Cumberland River above, and then attack in overwhelming numbers, or force a capitulation by cutting off all supplies and re-enforcements. The necessity for prompt action was apparent, and, after mature deliberation and interchange of views, it was decided to attack the enemy at 5 o'clock next morning, on his extreme right and right center, with a view to drive him back and secure an opportunity to withdraw in safety our forces towards Charlotte and Nashville, Tenn. It was hoped even greater advantages might be gained by the attack, which, if well followed up on our part, might result in disaster to the besiegers. The brigade commanders were then sent for, the plan of operations explained and the positions for their respective commands in the order of attack assigned.

Brigadier-General Pillow was to direct the movement against the right of the enemy; Brigadier-General Buckner that against his right center, advancing along the Wynn's Ferry road. A few regiments were to remain to guard the lines. The details of preparations for carrying our the plan decided upon, such as the number of rations that should be prepared; whether blankets and knapsacks should be taken or not; what should be the other of march on retreat for the different commands; who should take the advance, and who should protect the rear,