Within thirty days after the issuance by the president of the United States of his proclamation announcing the result of said election so ascertained, all officers elected at such election, except members of the legislature, shall take the oath of office and give bond as required by this constitution or by the laws of the territory of New Mexico in case of like officers in the territory, county or district, and shall thereupon enter upon the duties of their respective offices; but the legislature may by law require such officers to give other or additional bonds as a condition of their continuance in office.