We measured experimentally very weak interactions between microscopic particles by means of a torsion microbalance of sensitivity better than 10(-9) N. The model system consists of two thin glass cylinders of radii 50 mu m immersed vertically in a liquid at the liquid/air interface. The cylinders attract each other by a capillary immersion force due to deformation of the liquid surface around them. The magnitude of the measured force ranges between 4 x 10(-7) and 10(-9) N, depending on the separation distance and the surface tension. At a fixed interparticle distance the force for solution of sodium dodecyl sulfate is about twice as small as that for pure water due to the lower surface tension. The experimental data are well described by the theory of lateral capillary forces. The presented results can be applied to the explanation of the interaction between spherical particles forming two-dimensional arrays on substrate.