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Magnetic dips are generally assumed to be basic equilibrium configurations in quiescent solar prominences. Here we discuss two types of the magnetic dips which were considered in the literature: (1) dips resulting from a force-free magnetic equilibrium in the corona, and (2) magnetic dips which are formed in situations where the Lorentz force balances the weight of the prominence plasma. An important parameter which decides between these two cases is the plasma β. For β«1, the effect of the prominence material on the equilibrium structure is quite negligible and the case (1) holds. If, however, β is larger, say between 0.1 and 1 or even higher, magnetic dips of the second kind are formed and they can be characterized by the angle ψ1 between the vertical and the direction of the field lines at the surface of the prominence structure. A simple and illustratory formula is derived to relate this angle to the plasma β at the prominence center, namely βc≃cot2ψ1. βc = 1 thus corresponds to ψ1 = 45°. Finally, we discuss the range of values of both βc and ψ1 as deduced from various observations and conclude that the dips of the second kind are important for the prominence equilibria. We also suggest a new method for determination of the field-line inclination.