Sauntering out in search of an "item"--my custom always in the morning--I happened to be in the Galt House just as the altercation between General Nelson and General Jeff C. Davis was reaching its climax, and of which I telegraphed you within ten minutes after its occurrence. From what I learn, from parties who saw the commencement, it would seem that General Davis felt himself grossly insulted by Nelson's overbearing manner at their former meeting; and seeing him standing talking to Governor Morton, Davis advanced and demanded an explanation, upon which Nelson turned and cursed him, calling him an infamous puppy, and using other violent language unfit for publication. Upon pressing his demand for an explanation, Nelson, who was an immensely powerful and large man, took the back of his hand and deliberately slapped General Davis's face. Just at this juncture I entered the office. The people congregated there were giving Nelson a wide berth. Recognizing the General, I said "Good morning, General," (at this time I was not aware of what had passed). His reply to me was: "Did you hear that d----d insolent scoundrel insult me, sir? I suppose he don't know me, sir. I'll teach him a lesson, sir." During this time he was retiring slowly toward the door leading to the ladies' sitting-room. At this moment I heard General Davis ask for a weapon, first of a gentleman who was standing near him, and then meeting Captain Gibson, who was just about to enter the dining-room, he asked him if he had a pistol? Captain Gibson replied, "I always carry the article;" and handed one to him, remarking, as Davis walked toward Nelson, "It is a Tranter trigger." Nelson, by this time, reached the hall, and was evidently getting out of the way, to avoid further difficulty. Davis's face was livid, and such a look of mingled indignation, mortification, and determination I never before beheld. His hand was slowly raised; and, as Nelson advanced, Davis uttered the one word, "Halt!" and fired. Nelson, with the bullet in his breast, completed the journey up the entire stairs, and then fell. As he reached the top, John Allen Crittenden met him and said, "Are you hurt, General?" He replied, "Yes, I am, mortally." "Can I do any thing for you?" continued Crittenden. "Yes; send for a surgeon and a priest, quick." A rush was made by the crowd toward the place as soon as he was shot. No effort, as far as I can learn, has been made to arrest General Davis. A few minutes after the occurrence I was introduced to the Aid of Governor Morton, who told me he saw it all, from the very commencement, and that, had not Davis acted as he did, after the gross provocation he received, Davis would have deserved to have been shot himself.