the confidence level of constraints given by the long-dashed line cannot be determined. This is caused by some uncertain features of the experiment [23] discussed in Refs. [21, 22]. The short-dashed line in Fig. 5 presents the strongest constraints in this interaction range fol- lowing from gravitational experiments. These are high confidence constraints obtained in Ref. [17]. A new experimental technique suited for obtaining stronger constraints on the Yukawa-type interaction from the measurements of the Casimir-Polder force is discussed in Ref. [56]. Recently one more determination of the limits on the Yukawa-type interaction in the range of about 1 µ m from the measurement of the Casimir force using a torsion balance has been reported [57]. In this experiment a glass plate and a spherical lens of R = 20 . 7 cm radius were used as the test bodies, both coated with a 20 nm Cr layer and then with a 1 µ m layer of Au. This experiment is not an independent measurement of the Casimir force, like experiments in Refs. [26–28, 34–36], because the measurement data for the gradient of the force were fitted to the sum of two functions: the gradient of the expected electrostatic force and the gradient of the Casimir force taking into account the conductivity and roughness effects. To obtain the limits on α , the fit to the sum of three functions was performed with inclusion of the Yukawa-type force and λ as an additional fitting parameter. The Yukawa- type force was calculated using the results of Ref. [24]. The obtained limits determined at a 95% confidence level are shown as the grey line in Fig. 5. As can be seen in Fig. 5, these limits are a bit stronger than the limits obtained from the measurement of the Casimir-Polder force (the solid line), but much weaker than the limits shown by the long-dashed line which are obtained [24] from the measurement data of Ref. [23]. The authors of Ref. [57] note, however, that the accuracy of the experiment [23] was overestimated and compare their limits not with the results of Ref. [24], but with the results of Ref. [25] where much weaker constraints from the same measurement data [23] were found. From this they conclude that their limits are stronger than those obtained on the basis of Ref. [23]. It seems that this conclusion is not well justified. The point is that Ref. [24] had already taken into account that the accuracy of the experiment [23] was overestimated (this is discussed in [24] in detail). The difference between the constraints obtained in Refs. [24] and [25] using the same data of Ref. [23] is explained by the fact that in [24] the corrections due to the surface roughness, finite conductivity of the boundary metal and nonzero temperature were taken into account, whereas in [25] they were disregarded. Thus, in fact the constraints of Ref. [57] are weaker 18