When any incorporated city containing over three hundred thousand inhabitants shall have decided to establish and maintain a public library and reading room under this chapter, the mayor of such city shall, with the approval of the city council, proceed to appoint a board of nine directors for the same, chosen from the citizens at large, with reference to their fitness for such office; and no member of the municipal government shall be a member of said board; provided, that not more than five of such directors shall be members of the same political party.