Section 105. Such officers and employees as the city council, with the advice of the city manager, shall determine are necessary for the proper administration of the departments, commissions, boards and offices of the city for whose administration the city manager is responsible shall be appointed, and may be removed, by the city manager. The city manager shall report every appointment and removal made by him to the city council at the next meeting thereof following such appointment or removal. The city manager may authorize the head of a department, commission or board, or the holder of an office, for whose administration he is responsible, to appoint and remove subordinates in such department, commission, board or office. All appointments by, or under the authority of, the city manager, if subject to chapter thirty-one and the rules and regulations made under authority thereof, shall be made in accordance therewith, and all other appointments as aforesaid shall be on the basis of executive and administrative ability and training and experience in the work to be performed.