The library board shall have power to authorize any circulating library, reading matter, or work of art belonging to any private person, association or corporation, to be deposited in the public library rooms, to be drawn or used outside of the rooms only on payment of such fee or membership as the person, corporation or association owning the same may require. Deposits may be removed by the owner thereof at pleasure, but the books or other reading matter so deposited in the rooms of any such public library shall be separately and distinctly marked and kept upon shelves apart from the books of the public city or town library. Every such private or associate library or other property so deposited in any public library, while so placed or remaining, shall, without charge, be subject to use and reading within the library room by any person who is an inhabitant of such city or town and entitled to the use of the free library.