Whenever any highways, roads, or bridges are maintained by either county in which a diking and drainage district may be established, as herein provided, and it shall appear that the construction and maintenance of such diking and drainage system will be beneficial to such highways, roads, and bridges, or which will be beneficial to such highways, roads and bridges as may thereafter be constructed or maintained by the county, in which any part of the system of dikes and drains is situated, then the board of county commissioners of such county may, and it shall be the duty of such board to appropriate to such diking and drainage district an amount of money sufficient to pay the proportionate share of such county in accordance with the benefits received or to be received; and whenever it may appear to the board of county commissioners of any county that any improvements made or to be made in any diking or drainage district under the provisions of this chapter, shall on account of the health of the people of the county be beneficial in respect thereto, the board of county commissioners may make an appropriation of money to such diking and drainage district in such an amount to such board as may seem proper.