For the purpose of giving cities organized under the provisions of Article VI, Section 19, of the Constitution having less than three hundred thousand inhabitants representation on the county board of equalization when the board is sitting for the purpose of equalizing the assessment of property in such cities the cities shall have the same number of representatives thereon as such city was entitled to prior to the adoption of such constitutional charter. The representatives of the cities shall be appointed by the council, one of whom may be the director of finance. The city council may prescribe the compensation the city members of the board of equalization shall receive from the city treasury.