There was the Hon. THOS. JENKINS who refused to take it, because his wife had a prejudice against Bulls ever since she was scared by one that chased her five miles for no other reason than that she was what might be called a red woman--well-read in the exciting house-wife literature of the day. JENKINS positively declined. Then it was offered to Col. CANNONAYDE, who declined it because his mother-in-law declared that she would go along too, if he went, and he thought it would be better not to let her have a change of air, as she was in a fair way to wind up pretty soon by remaining near those swamps. CANNONAYDE wanted the place kept open till after the funeral, but this was not granted. The next offer was made to Gen. BRAYLEIGH; but _he_ refused it on the ground that he had made arrangements for going into the coal trade, and he could not be sure of holding the place more than a few weeks. Anyway, he thought it would not pay to give up the coalition he had entered into with another party. In fact, old BRAYLEIGH treated the whole matter very coldly. It was next tendered to the Hon. THEOPHILUS SKINNER, but peremptorily declined because SKINNER'S district had become Democratic since he was elected, and he knew that if he resigned an infamous cannibal copperhead would be sent to Congress in his stead. SKINNER consulted all the leaders of his party, and they unanimously agreed that it would be better to let every court in Europe be without an American representative than risk the loss of that district. Everybody knows why the Rev. Dr. BANGWELL, of Chicago, did not accept it. The Doctor expected his divorce case to come on in a few days, and could not neglect that; and besides, he had made all the arrangements for his other marriage, and sent out the invitations. If the President had just made some inquiries before appointing Dr. BANGWELL, he could have found out that the Doctor's engagements would not permit him to leave Chicago on any account. The offer that was made to Col. KAMPSTUHL was declined solely because the Colonel had an old score to settle with Gen. GRANT for something in the way of a court-martial that happened near Tricksburg. He swore that he would get square with the author of that business sometime, and when the mission was offered to him (by accident, for Gen GRANT had forgotten all about the court-martial), he got up a sepulchral voice, and said, "Ha, ha! R-e-e-e-vendge at last!" and then wrote a bitter letter to Washington on the subject.