An ink fountain for rotary offset printing presses with an ink dosing device which includes of a plurality of zone-width dosing elements located next to one another in close proximity. The dosing elements have support and dosing areas, and the support areas are in constant direct or indirect contact under spring pressure with an ink fountain roller. The dosing areas can be adjusted to different ink gap thicknesses by rotating the dosing elements. The hydrodynamic forces or the spring pressure on the dosing elements can therefore be reduced.