"ONE OF MR. LINCOLN'S JOKES.--The second verse of our campaign song published on this page was probably suggested by an incident which occurred on the battle-field of Antietam a few days after the fight. While the President was driving over the field in an ambulance, accompanied by Marshal Lamon, General McClellan, and another officer, heavy details of men were engaged in the task of burying the dead. The ambulance had just reached the neighborhood of the old stone bridge, where the dead were piled highest, when Mr. Lincoln, suddenly slapping Marshal Lamon on the knee, exclaimed: 'Come, Lamon, give us that song about Picayune Butler; McClellan has never heard it.' 'Not now, if you please,' said General McClellan, with a shudder; 'I would prefer to hear it some other place and time.'" This story has been repeated in the New York "World" almost daily for the last three months. Until now it would have been useless to demand its authority. By this article it limits the inquiry to three persons as its authority,--Marshal Lamon, another officer, and General McClellan. That it is a damaging story, if believed, cannot be disputed. That it is believed by some, or that they pretend to believe it, is evident by the accompanying verse from the doggerel, in which allusion is made to it:-- "Abe may crack his jolly jokes O'er bloody fields of stricken battle, While yet the ebbing life-tide smokes From men that die like butchered cattle; He, ere yet the guns grow cold, To pimps and pets may crack his stories," etc. I wish to ask you, sir, in behalf of others as well as myself, whether any such occurrence took place; or if it did not take place, please to state who that "other officer" was, if there was any such, in the ambulance in which the President "was driving over the field [of Antietam] whilst details of men were engaged in the task of burying the dead." You will confer a great favor by an immediate reply. Most respectfully your obedient servant, A. J. PERKINS.