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Abstract. The paper is devoted to a confrontation of the apsidal-motion rates in close binaries due to the tidal perturbations of the stellar components that are predicted by Sterne's formula (1939) with the corresponding apsidal-motion rates that are determined in the framework of the theory of the dynamic tides. Sterne's formula is derived in the supposition that the orbital period and the star's rotational period are sufficiently long so that, in accordance with an earlier suggestion of Cowling (1938), the star is almost adjusted to the gravitational field of the companion. From the point of view of the theory of the dynamic tides, the second-degree tide is then approximated at each instant by an appropriate linear combination of three second-degree tides which are considered to be static. In this limiting case, the rate of secular apsidal motion predicted by Sterne's formula agrees, up to large orbital eccentricities, with the rate of secular apsidal motion determined in the framework of the theory of the dynamic tides and depends on the star's central mass condensation. For close binaries with shorter orbital periods, the use of Sterne's formula leads to deviations because of the increasing influence of the compressibility of the stellar fluid and resonances of dynamic tides with lower-order g + -modes. The relative deviations may to amount to a few tens of percents for models of zero-age main sequence stars of 5 M , 10 M , and 20 M .

The double cluster h and χ Persei has since long been known to be rich in Be stars (Trumpler, 1926). It belongs to an age group in which various types of variable stars occur (Mermilliod, 1981). Other clusters of this age group are NGC 3293, the cluster that is richest in β Cephei variables (Balona and Engelbrecht, 1983), IC 2581, NGC 4755, and NGC 6871. The comparison of the characteristics of variable stars in all these clusters and in clusters of other age groups could reveal to which extent the cluster stellar content is determined by age and by other parameters, such as galactic location, and so metallicity. Since h and χ Persei are very rich clusters that have not yet been studied intensively as far as stellar variability is concerned (Percy, 1972), we have undertaken a study of the photometric variability of the brightest stars in the double cluster. Our first interest was to detect β Cephei variables, but it rapidly turned out that the double cluster contains a considerable amount of highly variable Be stars.