7 Conclusions

We derived updated light elements for four W UMa type eclipsing binaries by means of an O-C diagram analysis. It was shown that the periods of all four systems exhibit different kind of changes.

In the case of DK Cygni, the derived value of the period increase is in excellent agreement with the result of Awadalla (1994). Our observations confirm the steady transfer of mass. V401 Cyg shows a relatively large increase in orbital period for W UMa-type binaries. Our mass transfer value is in good agreement with the previously obtained value by Herczeg (1993). Concerning the orbital and physical parameters, the system of V401 Cyg seems us to be similar to the system DK Cyg. According to the widely accepted theory, W UMa systems undergo periodic thermal relaxation oscillations (TRO theory, Lucy 1976; Flannery 1976). Each of these oscillations comprise a contact phase, when the mass flows into the primary component, and semidetached configuration, when the mass transfer is opposite. This cyclic exchange of mass has a period of $\simeq 10^7$ years. The list of other short-period eclipsing binaries with a long-term continuous increase in orbital period, ordered according to the value of ${\rm d}P/{\rm d}E$, is given in Table 3.

The period of AD Phe seems to be constant in the observed time interval. Our new observations at SAAO do not support the continuous shortening of the period proposed by Cerruti (1986). Further monitoring of this seldom-observed southern system could reveal other possible period variations.

Y Sex, as noticed by Kaluzny (1985), has one of the shortest orbital periods for such a spectral type (F8). In this position in the period - colour diagram, one would expect an unevolved system with components with similar masses, but Y Sex seems to be evolved above ZAMS and its mass ratio is 5.5:1. The explanation of this paradox remains unknown. Period changes of Y Sex could be explained by a light-time effect caused by a third body on the eccentric orbit with a period of about 58 years. More high-accuracy timing of these systems are necessary in the future to enlarge the time span for a better analysis of period changes, especially for Y Sex, where the action of a third body in an eccentric orbit is predicted.

Acknowledgements

This study was supported by allocation of SAAO observing time, in part by the Grant Agency of the Czech Republic, grant No. 205/99/0255, and by the research plan J13/98: 113200004 Investigation of the Earth and the Universe. MW wishes to thank the staff at SAAO, Sutherland, for unfailing hospitality and help with the equipment and Dr. David Kilkenny for help with the photometric data reductions. We are also thankful to Mr. Franz Agerer, BAV, for timings of V401 Cyg from the Lichtenknecker's database. This research made use of the SIMBAD database, operated at CDS, Strasbourg, France.