Decrease in the Orbital Period of Hercules X-1

From a pulse-timing analysis of Ginga observations of the binary X-ray pulsar Her X-1 obtained during the interval 1989 April-June we have determined local orbital parameters for a Short High state. We have also determined an orbital epoch in the adjacent Main High state. By comparing these orbital solutions with previously published results, we have detected a decrease in the orbital period for Her X-1 at an average rate of dot-P/P = (- 1.32 +/- 0.16) x 10(exp -8) yr(exp -1) over the interval 1971-1989. This is substantially larger than the value predicted from current estimates of the mass transfer rate, and motivates consideration of other mechanisms of mass transfer and/or mass loss. A second result from these observations is a close agreement between orbital parameters determined separately in Main High and Short High states. This agreement places strong constraints on the obliquity of the stellar companion, HZ Her, if undergoing forced precession with a 35 day period. As a consequence further doubt is placed on the slaved-disk model as the underlying cause of the 35 day cycle in Her X-1.