It shall be competent, in all charters, framed under the authority given by this section to provide, in addition to any other provisions allowable by this constitution, and the same shall provide, for the following matters: 1. For boards of supervisors and for the constitution, regulation and government thereof, for the times at which and the terms for which the members of said board shall be elected, for the number of members, not less than three, that shall constitute such boards, for their compensation and for their election, either by the electors of the counties at large or by districts; _provided_, that in any event said board shall consist of one member for each district, who must be a qualified elector thereof; and 2. For sheriffs, county clerks, treasurers, recorders, license collectors, tax collectors, public administrators, coroners, surveyors, district attorneys, auditors, assessors and superintendents of schools, for the election or appointment of said officers, or any of them, for the times at which and the terms for which, said officers shall be elected or appointed, and for their compensation, or for the fixing of such compensation by boards of supervisors, and, if appointed, for the manner of their appointment; and 3. For the number of justices of the peace and constables for each township, or for the number of such judges and other officers of such inferior courts as may be provided by the Constitution or general law, for the election or appointment of said officers, for the times at which and the terms for which said officers shall be elected or appointed, and for their compensations, or for the fixing of such compensation by boards of supervisors, and if appointed, for the manner of their appointment; and 4. For the powers and duties of boards of supervisors and all other county officers, for their removal and for the consolidation and segregation of county offices, and for the manner of filling all vacancies occurring therein; _provided_, that the provisions of such charters relating to the powers and duties of boards of supervisors and all other county officers shall be subject to and controlled by general laws; and [29]4½. For the assumption and discharge by county officers of certain of the municipal functions of the cities and towns within the county, whenever, in the case of cities and towns incorporated under general laws, the discharge by county officers of such municipal functions is authorized by general law, or whenever, in the case of cities and towns organized under section eight of this article, the discharge by county officers of such municipal functions is authorized by provisions of the charters, or by amendments thereto, of such cities or towns.