The costs of maintaining such joint city and county workhouse, over and above the proceeds arising from the sale of the products thereof, shall be borne by such city and county jointly, and such expenses shall be paid quarterly by such city and county out of the respective treasuries thereof, upon the certificate of such secretary of such joint city and county workhouse, on the approval of the council of such city and the commissioners of such county. And the county court of any county having such joint city and county workhouse is hereby authorized and required to levy upon all the real and personal property, outside of the corporate limits of such city, such sum as may be necessary, and the city council of such city is hereby authorized and required to levy upon all the real and personal property, inside of the corporate limits of such city, such sum as may be necessary for the maintenance aforesaid; and the board of such joint city and county workhouse directors, the city council of such city, and the county commissioners of such county, in ascertaining and determining at the end of each quarter the amount to be paid to such board to meet any deficiency in the products of such joint workhouse to maintain the same, shall take into account and be governed by the number of convicts furnished by such city and county, the number of days' labor performed by the convicts from each, the value of such labor, and the relative costs and expenses of taking care of, managing and disciplining the convicts of each, and give to such city and county each full credit for the value of the products of such workhouse produced by the labor, skill and diligence of the convicts from each, and charge to the account of each (city and county) the cost to such institution of working, managing, maintaining, taking care of, and disciplining its convicts, and make assessments upon such city and county for the maintenance of such institution accordingly.