A new experimental device is presented for measuring directly the attractive and repulsive specific forces between planar and spherically shaped bodies. Our method was applied for experimentally determining the interaction force-distance diagrams for two fused silica plates (one planar, one spherical) in aqueous potassium chloride solutions. The experimental results were interpreted by using the new numerical algorithm which allows one to calculate the electrostatic interaction forces between regularly shaped bodies bearing thin double-layers immersed in an arbitrary electrolyte. Our numerical procedure enabled the solution of the one-dimensional Poisson-Boltzmann equation in which corrections stemming from the excluded volume, the dielectric saturation and the specific interactions of ions with interfaces can be quantitatively taken into account. These one-dimensional solutions (parallel-plate system) were then integrated according to the modified Derjaguin summation method giving the electrostatic force between plane/spherical bodies in the vicinity of their contact area.