It shall be the duty of the governor, at least three times a year and oftener if he sees fit, at such times as he may deem proper, to go to the treasury without giving notice to the treasurer, to verify the cash balance as shown by the books, and to publish the fact that he has done so, stating whether the amount called for by the books be actually in the treasury and whether the treasurer had any notice whatever that the verification would be made. He shall verify the count of the funds in the treasury and certify to the statements of the treasurer, if true, showing the condition of the treasury in the months of January and July of each year, as required by section 137 of the constitution.