The arguments in the case were worthy of the best days of the criminal bar of New York. Mr. Ashmead distinguished himself highly in his appeal for the prisoner, and had the case gone to the jury before the cool and dispassionate reasoning of Mr. McKeon had partially weakened the effect of Mr. Ashmead’s eloquence, the result might have been different. The charge of the Recorder was decidedly against the prisoner, and his sentence, it will be seen, was severe in its terms to an excess that was not called for. The punishment imposed was the extent of the law, and was by no means disproportioned to the offence; but it was entirely gratuitous on the part of the Recorder to drag into his remarks matters extraneous to the issue, and not at all connected with the present trial. The Recorder’s announcement of the rod he has in pickle for certain other libellers who he intimates are shortly to be tried, will probably put those prospective culprits upon their guard, and they will at least have this advantage over Mr. Branch that they will not be taken unawares. We congratulate the distinguished citizens whose characters have been cleared again by this conviction of Mr. Branch; but can assure them that their fair fame by no means suffered so much from the attacks of the “ALLIGATOR” as they presumed that it did. We understand that Mr. Ashmead will to-day prepare a bill of exceptions, and move in the Supreme Court for a writ of certiorari and stay of proceedings. The bill will not be settled until late in the day, and the motion in the Supreme Court cannot be made until to-morrow. In case, therefore, that Mr. Branch should be sent to Penitentiary to-day, the motion will not avail him. It is hardly to be presumed that when a motion for arrest of judgment was denied without argument, the prisoner will be allowed time to benefit by an appeal to the Supreme Court. [_From the N. Y. Tribune._] STEPHEN H. BRANCH was yesterday convicted of a gross libel on Mayor Tiemann and others, and sentenced by the Recorder to the Penitentiary for one year, and to pay a fine of $250. Considering that the libel, however groundless essentially, appears to have had a real foundation in statements made to Branch by persons whom he undoubtedly believed, and whom his counsel had ready to produce (but their testimony was not allowed), we must consider this sentence a severe one. We believe it will excite for him a sympathy which it is unwise to provoke. Branch, we believe, has been trying pretty hard to libel _us_ in his abusive little sheet; but we have never considered his slanders worth any sort of notice. It may be well to stop his career, but not to make him a martyr. And we say most decidedly, that considering the libel for which he was indicted was really based on information furnished him by persons whom he had reason to believe, we deem his sentence a harsh one, and trust it may be mitigated by pardon.