The library board, herein provided to be appointed and their successors in office shall have power, and it shall be their duty to manage, supervise and control the free public library of the City of Austin, taking under their control all property which has now been set apart to the existing library board, and all improvements thereon, and all books, periodicals, manuscripts and other articles of whatsoever character belonging to and forming a part of such library, and all books, papers or portions of libraries which may be hereinafter acquired, either by purchase or donation; and to provide for the proper, convenient and suitable use of such books, manuscripts and periodicals as the library may contain from time to time, under such rules and regulations and subject to such conditions as the board may impose, and in all things, control and maintain said library. And it shall be the duty of said board through its proper offices to make an annual report to the city council of the City of Austin, reciting the number, and in general, the character of the books, manuscripts, periodicals, materials and resources in the library, also the amount of money expended during the then preceding year and the amount which will be required, in order to maintain said library and keep the building open for public use, which amount however, shall not exceed in any one year the limitations set forth by state law. Upon receipt of such report from the library board, and on or before the time provided for the making of the budget and tax levy under this Charter, the city council shall levy a tax upon the taxable property of the City of Austin; such sum that the city council shall determine to be levied, not to exceed in any one year the limitations set forth by state law; and such proposed tax shall be subject to the approval of the mayor in the same manner as in this Charter provides for the levying of other taxes. Such tax when so levied shall be certified by the finance director to the county auditor to be extended as a part of the general tax levy for said city, and when the amount has been collected, it shall be set apart and appropriated to the library fund, and the finance director shall keep a separate account thereof, and it shall be paid out of the treasury only upon the order of the library board signed by its president and secretary. The city council may appropriate to the library fund from the general fund such further sum or sums during any year as may be determined by the council, and when so appropriated such sum shall be credited to said fund to be drawn out only in the manner herein provided.