Section 134. Constitution of police and fire departments

The police and
  fire departments shall, as to  their  membership  and  component  parts,
  remain  as  now constituted until the same shall be changed by action of
  the common council. The  common  council  has  power  at  all  times  by
  ordinance  to  determine  the  number of officers and members of each of
  said departments and the classes and grades into  which  they  shall  be
  divided,  except that it shall not have the power to diminish the number
  of the members of either of said departments as now fixed. The number of
  officers or members of either of said departments shall not be increased
  without the approval of the board of  estimate  and  apportionment.  The
  common  council  may  pass  ordinances not inconsistent with law for the
  government of the police and fire departments, and regulating the powers
  and duties  of  their  officers  and  members.  The  commissioner  shall
  appoint, as vacancies in said department occur, all officers and members
  thereof,  and classify and apportion them into grades to conform to such
  ordinances.