The county board of any one of the counties of this state may require the county treasurer to give additional surety or sureties whenever in its opinion the existing security shall have become insufficient, and such board is hereby also empowered to demand and receive from such county treasurer an additional bond as required by law with good and sufficient surety or sureties in such sum as said board, or a majority thereof, may direct, whenever in its opinion more money shall have passed or is about to pass into the hands of such treasurer than is or would be recovered under the penalty in the previous bond. If any county treasurer shall fail or refuse to give such additional security or bond for and during the time of ten days from and after the day on which said board shall have required such treasurer so to do, his office shall be considered vacant, and another treasurer shall be appointed agreeable to the provisions of law.