than those following from the measurements of Ref. [23]. The advantage of the constraints of Ref. [57] is that they are obtained at a high confidence level, whereas the confidence level of the constraints obtained from the data of Ref. [23] cannot be determined on a solid basis. VII. CONCLUSIONS AND DISCUSSION In the foregoing we have considered constraints on the Yukawa-type corrections to New- tonian gravity in micrometer and submicrometer interaction ranges following from the mea- surements of the Casimir and Casimir-Polder forces. This field of research has already re- ceived wide recognition as an important adjunct to the gravitational experiments of E¨ otvos- and Cavendish-type. Novel constraints on the parameters of Yukawa-type interactions from the Casimir effect were obtained at a high confidence level and were used for constrain- ing masses of predicted light elementary particles and other parameters of the theory of fundamental interactions beyond the Standard Model [58]. In this paper we have analyzed several experiments on measuring the Casimir and Casimir-Polder force which were not used up to date for constraining corrections to Newto- nian gravity. The most striking result obtained above is that recent experiment on measuring the lateral Casimir force between corrugated surfaces of a sphere and a plate [38] leads to a great strengthening of the previously known high confidence constraints up to a factor of 2 . 4 × 10 $^{7}$. The constraints obtained from this experiment are shown to be the strongest in the interaction range from 1.6 to 14 nm. This raises a question on the role of corrugated surfaces in other experimental configurations used to obtain constraints on the parameters of Yukawa-type interactions. The influence of sinusoidal corrugations on the Yukawa force was calculated above by using the approximate method of geometrical averaging. This method is applicable under several conditions which are well satisfied for the experimental configurations considered in the paper. In fact, the geometrical averaging works better for the Yukawa force than for the Casimir force. The point is that the Yukawa force is static and is not influenced by the diffraction-type effects which are essential for the Casimir force (the better applicability of the geometrical averaging to the electrostatic than to the Casimir force was also noted in Ref. [38]). We have shown that the replacement of a plane plate with a sinusoidally corrugated plate in the experiment on measuring the normal Casimir force in a sphere-plate 19