There is a story afloat that Mr. John Morrissey made his appearance, one day during the past week, in Madison Square, in full evening dress, including white gloves and cravat, and bearing a French dictionary under his arm, and that, being questioned by his friends as to the object of this display, he replied that he was going to see Major Wickham and ask him for an office in the only costume in which such an application would have a chance of success. In other words, he was acting what over in Brooklyn would be called "an allegory," and which was intended to expose in a severe and telling way the Mayor's gross partiality, in the use of his patronage, for the well-dressed and well-educated members of society--a partiality which Mr. Morrissey and his party consider not only unfair but ridiculous. This demonstration, too, was one of the few indications which have as yet met the public eye of a very real division of the Democratic party in this city into two sets of politicians, known familiarly as "Short-Hairs" and "Swallow-Tails"--the former comprising the rank and file of the voters and the latter "the property-owners and substantial men," who are endeavoring to make Tammany an instrument of reform and to manage the city in the interest of the taxpayers. Mayor Wickham belongs, it is said, to the latter class, and has given, it seems, in the eyes of the former, some proofs of a desire to reserve responsible offices for persons of some pretensions to gentility, and exhibited some disfavor for the selections of the "workers" in the various wards.