The habeas corpus case of Sergeant Webster, which has attracted considerable attention from the public, will be taken to the Superior Court of Appeals, notwithstanding that the Hustings Court adjourned for the term, on Monday, without having agreed with his counsel upon a bill of exceptions. It will be taken into that Court on an original writ, and the witnesses will be re-examined there, and the case decided upon its merits alone, as if no decision had been previously rendered.