configuration [28] would strengthen the constraints obtained from the measurement data of Ref. [28] in Ref. [36] by a factor of 1 . 1 × 10 $^{12}$. 

Next, we have obtained constraints on the Yukawa-type interaction from the measure- ment data of the dynamic experiment using a micromechanical torsional oscillator [36] when the plane plate is replaced with the corrugated one. It was shown that up to an order of mag- nitude strengthening is achievable in this way in comparison with the previously obtained constraints. 

We have also obtained constraints from the measurement data of two dynamic experi- ments which were not used previously for constraining the Yukawa-type interaction. These are the measurement of the gradient of the Casimir pressure in the configuration of two par- allel plates [40] and of the gradient of the thermal Casimir-Polder force between an atom and a dielectric plate [39]. For the parallel plate experiment, the obtained constraints are weaker than those obtained from other experiments, but they can be significantly strengthened by replacing a Cr metal coating with a thicker Au coating. For the experiment dealing with the Casimir-Polder interaction, a frequency shift of the condensate oscillating due to the presence of Yukawa-type interaction was found. It was shown that the obtained constraints are weaker than those found in Ref. [24] from the torsion pendulum experiment [23]. It was also shown that the constraints following from the measurement of the Casimir-Polder interaction are of almost the same strength as the constraints obtained in recent experi- ment [57]. For both the experiment with two parallel plates and the measurement of the Casimir-Polder force, the replacement of a plane plate with a grating does not lead to a no- table improvement in the strength of constraints because of the relatively large separation distances between the test bodies in these experiments. 

Thus, we have shown that the use of the measurement data of recent experiment on the lateral Casimir force leads to more than seven orders of magnitude strengthening in the previously obtained constraints. We have demonstrated that even higher promise is expected from the measurement of the normal Casimir force by means of an AFM if the plane plate were replaced with a corrugated plate. These results and the analysis of some other experiments confirm prospective future trends for obtaining stronger constraints on non- Newtonian gravity from the measurement of both the Casimir and Casimir-Polder forces. 

