Unless otherwise provided by this amended Constitution or Schedule, all persons elected or appointed before this amended Constitution shall take effect, to State or county offices made elective by this amended Constitution, whose terms will expire before the first Tuesday in January in the year one thousand eight hundred and ninety-nine, shall hold their respective offices until the said last mentioned day; and all persons elected or appointed as aforesaid to such offices, whose terms will expire between the said first Tuesday in January in the year one thousand eight hundred and ninety-nine and the first Tuesday in January in the year one thousand nine hundred and one, shall hold their respective offices until the said last mentioned day; and all persons elected or appointed as aforesaid to such offices, whose terms will expire between the said first Tuesday in January in the year one thousand nine hundred and one and the first Tuesday in January in the year one thousand nine hundred and three, shall hold their respective offices until the said last mentioned day; and the successors of such persons shall be elected at the general election next before the expiration of the terms as hereby extended; provided, however, that the successors of the present Auditor of Accounts, State Treasurer and Insurance Commissioner shall be elected at the general election next preceding the expiration of their several terms of office, and the persons so elected shall enter upon the duties of their respective offices on the first Tuesday in January following their election. The officers whose terms of office are extended by this section shall renew their official obligations upon the expiration of their present terms.