SIR:—According to the request contained in your note, I have placed Mr. Gibson's letter of resignation in the hands of the President. He has read the letter, and says he accepts the resignation, as he will be glad to do with any other, which may be tendered, as this is, for the purpose of taking an attitude of hostility against him.

He says he was not aware that he was so much indebted to Mr. Gibson for having accepted the office at first, not remembering that he ever pressed him to do so, or that he gave it otherwise than as was usual, upon request made on behalf of Mr. Gibson.

He thanks Mr. Gibson for his acknowledgment that he has been treated with personal kindness and consideration, and says he knows of but two small drawbacks upon Mr. Gibson's right to still receive such treatment, one of which is that he never could learn of his giving much attention to the duties of his office, and the other is this studied attempt of Mr. Gibson's to stab him.

I am very truly,

Your obedient servant,

JOHN HAY. [ [!-- H2 anchor --] ]

TO COLONEL, FIRST N. Y. VETERAN CAVALRY.

EXECUTIVE MANSION, WASHINGTON, JULY 25, 1864.

Thomas Connor, a private in the First Veteran New York Cavalry, is now imprisoned at hard labor for desertion. If the Colonel of said Regiment will say in writing on this sheets that he is willing to receive him back to the Regiment, I will pardon, and send him.

A. LINCOLN. [ [!-- H2 anchor --] ]