To enable the boards to perform the duties imposed upon them, they are hereby authorized and required to appoint, enroll and employ a permanent police force for the cities which they shall equip and arm as they may judge necessary. Except as provided below, the number of patrolmen to be appointed shall not be more than one thousand six hundred eighty-three of which number not more than two hundred fifty are to be probationary patrolmen. Any increase in the number of patrolmen authorized, in addition to that provided for above, shall be permitted upon recommendation by the board of police commissioners, with the approval of the municipal board of estimate and apportionment. The number of turnkeys to be appointed shall be sixty-five, except that for each patrolman hereafter promoted, demoted, removed, resigned or otherwise separated from the force, an additional turnkey may be appointed, but under no circumstances shall more than one hundred fifty turnkeys be appointed. As each additional turnkey is appointed, the maximum number of patrolmen to be appointed shall be reduced accordingly so that when one hundred fifty turnkeys have been appointed, the number of patrolmen to be appointed shall not be more than one thousand five hundred ninety-eight.