Any county library which was established and existed on April 26, 1911, under the provisions of an act entitled “An act to provide county library systems,” approved April 12, 1909, is continued under the provisions of this chapter and shall be considered the same as if established under the provisions of this chapter. If a contract has been entered into between any county board of supervisors and any city pursuant to this article, the contract shall continue in force, and the provisions of Section 19112 shall be applicable thereto, until the establishment and equipment of a county free library under the provisions of this chapter, unless sooner terminated.