Jacob Rehm resigned yesterday afternoon as police superintendent of the City of Chicago. After the customary farewells, Mr. Rehm went to the Grand Pacific Hotel to spend a pleasant hour as a private citizen, Mr. Hickey, assistant police superintendent, will take charge of Mr. Rehm's office for the time being, until the mayor can submit a successor to the City Council. Sergeant Charles Rehm, brother of Mr. Jacob Rehm, has a good chance of becoming assistant superintendent.