In the much talked of case of Daniel Mulligan vs. the city of New Orleans, counsel for plaintiff, Messrs. Cotton & Levy, yesterday made a motion to set aside the appeal, and the city ordered to show cause, on the 25th inst., why it should not le set aside on the grounds, first : that the order granting the sus pensive appeal unprovidentially. issued at the instance and on the motion of J. R. Beckwith, the attorney of the Corporation, Corporation, as he was not authorized by the Common Council to take an appeal, although he had asked the authority from them ; second, that there is no bond or security furnished in this case, as re quired by the acts of 1868 - 69. In the same court, Sixth District, Judge Cooley, a petition has been filed asking for the canceling and annulling of tho appointment of John F. Irwine as a com missioner for liquidating the affairs of the Bank of Louisiana. This is asked by R. H. Bowles, of this parish, who represents that he is a large stockholder, of the bank, and a holder and owner of a large amount of the notes of the bank, and interested in the settle ment'of the affairs of the bank, and charges that Mr. Irwine fails and neg lects to attend to the duties incumbent upon him as Liquidating Commissioner. Mr. Irwine is called upon to show cause, on the 25th inst., why his commission should not be canceled.