The corrections to the Casimir forces for configurations used in experiments: The spherical lens above the plane and two crossed cylinders

A general calculation of the corrections to the Casimir force for configurations used in experiments is presented. These corrections are considered up to the second order with respect to the relative amplitudes of the deviations. It is shown that in the case of long scale deviations the leading correction is the first order one and may be both positive and negative. The relative corrections have estimated values of several tens of percent, so they must be taken into account in precision experiments on Casimir force measurements.