The surety of any treasurer shall be held responsible for all acts of his principal and the assistant treasurer until a successor to the office of state treasurer is elected or appointed, commissioned and qualified; except, that if a new bond is given by the state treasurer in accordance with the provisions of this chapter, and the new bond is approved by the governor, as in this chapter provided, then the surety on the first bond shall only be held liable for all acts or omissions of his principal and the assistant treasurer occurring prior to the giving and approving of the new bond.