When it becomes necessary, because of need for economy, lack of work or funds, or for other just causes, to reduce the number of subordinates, the emergency, special, temporary, part-time, or provisional subordinates, if any, shall be dismissed first, and thereafter subordinates shall be dismissed in order of shortest length of service in the Department, provided that, in cities where a record of service rating has been established prior to January 1, 1933, for the said subordinates, the emergency, special, temporary, and/or part-time provisional subordinates, if any, shall be dismissed first, and thereafter subordinates shall be dismissed in the order of the least efficient as shown by the said service rating.