The board of supervisors of the county in which such city is located shall apportion the amounts to be raised as mentioned in the preceding section among the wards of the city, according to the equalized valuation of the property appearing upon the certificate of the several assessment rolls of the city for such year, as finally equalized by the board of supervisors, and the clerk of said board shall certify to the supervisor of each ward for assessment therein, the amount so apportioned to his ward; giving the amount apportioned for school, library and schoolhouse purposes in a separate sum, within 5 days after the board of supervisors of the county shall have completed the equalization of the valuation of the property in the county for the year. Said clerk of the board shall also certify to the city clerk the amounts apportioned to the several wards of the city, as aforesaid.