When the returns from the election herein provided for shall show that a majority of the electors of the county voting thereon have approved the resolution of the board of supervisors aforesaid, the county clerk shall make a certificate to this effect and shall record the same with the official record of the proceedings of the board of supervisors and thereupon said resolution shall become and be effective and binding upon the county, its officers, agents, servants and electors, and the authority delegated to and the duties imposed upon officers, agents and servants shall attach to and become and be binding upon such officers, agents and servants of the county and all who deal with them as representatives of the county; and all things provided for in said resolution may be done for, on behalf of, and on account of said county.