No judge of the Supreme, Circuit or inferior courts of law or equity, Secretary of State, Attorney General for the State, Auditor or Treasurer, Recorder, clerk of any court of record, Sheriff, Coroner, member of Congress, nor any other person holding any lucrative office under the United States or this State (militia officers, justices of the peace, postmasters, officers of public schools and notaries excepted), shall be eligible to a seat in either house of the General Assembly.