John Brown was hung to-day at about half-past eleven A. M. He behaved with unflinching firmness. The arrangements were well made and well executed under the direction of Colonel Smith. The gibbet was erected in a large field, south-east of the town. Brown rode on the head of his coffin from his prison to the place of execution. The coffin was of black walnut, enclosed in a box of poplar of the same shape as the coffin. He was dressed in a black frock-coat, black pantaloons, black vest, black slouch hat, white socks, and slippers of predominating red. There was nothing around his neck but his shirt collar. The open wagon in which he rode was strongly guarded on all sides. Captain Williams (formerly assistant professor at the Institute) marched immediately in front of the wagon. The jailer, high sheriff, and several others rode in the same wagon with the prisoner. Brown had his arms tied behind him, and ascended the scaffold with apparent cheerfulness. After reaching the top of the platform, he shook hands with several who were standing around him. The sheriff placed the rope around his neck, then threw a white cap over his head, and asked him if he wished a signal when all should be ready. He replied that it made no difference, provided he was not kept waiting too long. In this condition he stood for about ten minutes on the trap-door, which was supported on one side by hinges and on the other (the south side) by a rope. Colonel Smith then announced to the sheriff `all ready' -- which apparently was not comprehended by him, and the colonel had to repeat the order, when the rope was cut by a single blow, and Brown fell through about five inches, his knees falling on a level with the position occupied by his feet before the rope was cut. With the fall his arms, below the elbows, flew up horizontally, his hands clinched; and his arms gradually fell, but by spasmodic motions. There was very little motion of his person for several moments, and soon the wind blew his lifeless body to and fro. His face, upon the scaffold, was turned a little east of south, and in front of him were the cadets, commanded by Major Gilman. My command was still in front of the cadets, all facing south. One howitzer I assigned to Mr. Trueheart on the left of the cadets, and with the other I remained on the right. Other troops occupied different positions around the scaffold, and altogether it was an imposing but very solemn scene. I was much impressed with the thought that before me stood a man in the full vigor of health, who must in a few moments enter eternity. I sent up the petition that he might be saved. Awful was the thought that he might in a few minutes receive the sentence, `Depart, ye wicked, into everlasting fire!' I hope that he was prepared to die, but I am doubtful. He refused to have a minister with him. His wife visited him last evening. His body was taken back to the jail, and at six o'clock P. M. was sent to his wife at Harper's Ferry. When it arrived, the coffin was opened, and his wife saw the remains, after which it was again opened at the depot before leaving for Baltimore, lest there should be an imposition. We leave for home via Richmond tomorrow.